Developing the STELLA Model for a DSS for Mitigation Strategies for Transportation Infrastructure: Building the Model in STELLA Silvana V. Croope A working paper submitted to the University of Delaware University Transportation Center (UD‐UTC) January 5, 2010 1
DISCLAIMER: The contents of this working paper reflect the views of the authors, who are responsible for the facts and the accuracy of the information presented herein. This document is disseminated under the sponsorship of the Department of Transportation University Transportation Centers Program, in the interest of information exchange. The U.S. Government assumes no liability for the contents or use thereof. 2
Table of Contents Table of Contents ................................................................................................................ 3 List of Figures ...................................................................................................................... 4 List of Tables ....................................................................................................................... 7 Introduction ...................................................................................................................... 10 Background ................................................................................................................... 10 Objective of this Working Paper ................................................................................... 13 Overview of the Working Paper ................................................................................... 14 Building the Model ............................................................................................................ 14 Step_1 ........................................................................................................................... 14 Variables .................................................................................................................... 17 Predicting Changes in Performance .......................................................................... 19 Selecting Actions ....................................................................................................... 21 Network Definition and Data .................................................................................... 22 Using STELLA ............................................................................................................. 22 Step_2 ........................................................................................................................... 26 Including Data and Information from Other Software ............................................. 26 Phases in the Model from Pre to Post‐Disaster ........................................................ 27 Computing Variables ................................................................................................. 28 Condition and Performance Metrics – First Phase ................................................... 33 Step 3_4 – Second Phase .............................................................................................. 41 Disruption and Disruption Rate ................................................................................ 46 Calculation of Resilience ........................................................................................... 47 Post‐Disaster ‐ Third Phase ....................................................................................... 48 Calculating Degraded Condition and Performance .................................................. 51 Managing the Infrastructure ..................................................................................... 54 Completing the Second Phase .................................................................................. 58 Managing the Infrastructure – Fourth Phase ........................................................... 61 Estimating Costs under Normal Condition (Assuming No Disaster) ......................... 65 Step_5‐7 ........................................................................................................................ 69 Modeling Resilience for Mitigation........................................................................... 90 Cost Benefit Analysis ................................................................................................. 92 Step_8 ......................................................................................................................... 119 Acknowledgements ......................................................................................................... 135 References ...................................................................................................................... 135 3
List of Figures Figure 1 CIR‐DSS System Dynamics Diagram .................................................................... 10 Figure 2 Steps in CIR‐DSS Model Development in STELLA ................................................ 14 Figure 3 Decision Makers and Funds for Investing in CIS ................................................. 16 Figure 4 PCI Scale .............................................................................................................. 19 Figure 5 System Percent for Good‐Fair‐Poor Condition as Years Passes By .................... 20 Figure 6 STELLA Software Interface for Producing the Model and the Model’s Interface
........................................................................................................................................... 23 Figure 7 Initial Variables in the Model in STELLA .............................................................. 24 Figure 8 Initial Model Variables Connection and Put through Run Function ................... 25 Figure 9 Calculating Infrastructure Segments Cost .......................................................... 27 Figure 10 Initial Approach for Calculating Vulnerability and Impact with Data from the Disaster of June 2006 ........................................................................................................ 29 Figure 11 Assessing IS Vulnerability Flow Dialog Box ....................................................... 30 Figure 12 Assessing Vulnerability Flow Graph .................................................................. 30 Figure 13 Flood Warning Parameters Included ................................................................ 31 Figure 14 Model Run Including Initial Damage to Infrastructure System and Pre‐Disaster Warning ............................................................................................................................. 33 Figure 15 Initial Pre Disaster IS Performance and Condition Measures Framework ....... 34 Figure 16 Carrying Service Capacity Graphical Function .................................................. 35 Figure 17 Life‐Cycle Cost Analysis Primer ......................................................................... 36 Figure 18 Average IS Condition Graphical Function ......................................................... 37 Figure 19 Capturing Disaster Impact Details for Transportation ...................................... 43 Figure 20 Flooded IS Segments Graphical Function ......................................................... 46 Figure 21 Disruption Rate Model ...................................................................................... 47 Figure 22 Resilience for Normal Time or Pre‐Disaster ...................................................... 48 Figure 23 Capturing Variable Value “Available Average IS Segments Short Term” ......... 49 Figure 24 Defining “Loosing Usability” ............................................................................. 50 Figure 25 Error Message for Piece of Model for Increased Degraded Condition ............ 52 Figure 26 Building the Model to Capture Short‐Term Condition and Performance Measures ........................................................................................................................... 54 Figure 27 Complete Sector Frame for the Short‐Term Post‐Disaster Performance and Condition Measures .......................................................................................................... 55 Figure 28 Short_Term Carrying Service Capacity Graph ................................................... 57 Figure 29 Resilience of System Model for After Disaster Period ...................................... 58 Figure 30 Model for Capturing Infrastructure Condition and Performance During Disaster and the Resulting Variable "Available Average IS Segments Short Term” ....................... 59 Figure 31 During Disaster Onset Resilience of System Assessment ................................. 61 4
Figure 32 Concept for Starting to Address Solutions for Damaged Infrastructure System
........................................................................................................................................... 62 Figure 33 Model for Cost of IS Normal Operations .......................................................... 66 Figure 34 Financial Resources Responsibilities per Agency and Stakeholders to Maintain Infrastructure Condition and Performance ...................................................................... 69 Figure 35 Defining the Real Segments Damage Values .................................................... 72 Figure 36 Model Sector‐Frame for Recovery Cost Adding to Cost of Normal Operations74 Figure 37 Agencies Financial Composition to Carry‐On Recovery Projects ...................... 76 Figure 38 Closer View of the IS Recovered Condition and Performance Measures Sector‐
Frame ................................................................................................................................ 77 Figure 39 Getting the Total Value for Recovered Damaged Lanes ................................... 79 Figure 40 Restoring the Transportation Infrastructure to Its Original Elements Quantity Prior to Disaster ................................................................................................................ 80 Figure 41 Resilience of Recovered Infrastructure System ................................................ 80 Figure 42 Mitigation Sector‐Frame Model ....................................................................... 84 Figure 43 Modeling Expected Decrease on Vulnerability ................................................. 86 Figure 44 Model for Infrastructure Mitigation Condition and Performance Measures ... 87 Figure 45 LOS and Flow Rate for Mitigation ..................................................................... 89 Figure 46 Model of Resilience for Mitigated Infrastructure ............................................. 90 Figure 47 Expected Decreased Infrastructure Vulnerability Using Mitigation Measures 90 Figure 48 Comparison Between Recovery and Mitigation Strategies to Decrease System Vulnerability ...................................................................................................................... 91 Figure 49 Federal Disasters Damage Graph – Sussex ....................................................... 94 Figure 50 Model for Disasters Historical Frequency, Impacts and Savings ...................... 95 Figure 51 Difference between Original and Short Term Infrastructure Level of Service . 97 Figure 52 Calculation of Delay Time and Cost .................................................................. 98 Figure 53 Benefit‐Cost Analysis Savings Diagram Example ............................................ 102 Figure 54 Difference Between Recovery and Mitigation NPV per Frequency of Events 106 Figure 55 NPV for Recovery Project ................................................................................ 107 Figure 56 Graphical Function for Recovery Project NPV ................................................ 108 Figure 57 Mitigation Project NPV and Graphical Function ............................................. 108 Figure 58 Savings Resulting from Investment in Mitigation Rather than Recovery ....... 109 Figure 59 Benefits of Mitigation Project and Final BCR .................................................. 111 Figure 60 Graphical Function for Mitigation Loss of Function NPV ................................ 112 Figure 61 Benefits of Recovery Project and Final BCR .................................................... 113 Figure 62 Graphical Function for Recovery Loss of Function NPV ................................. 114 Figure 63 Adjusted Mitigation Project Cost .................................................................... 116 Figure 64 FEMA BCA‐LM for Riverine Flood Report Example ......................................... 118 Figure 65 Capturing Extent of Damage Considering Overall US‐13 Case Study Extension
......................................................................................................................................... 120 Figure 66 Recovery and Mitigation NPV for 1% Probability of 100‐year Event ............. 120 Figure 67 Graph for Changing Recovery NPV 2 .............................................................. 122 Figure 68 Recovery and Mitigation Benefit NPV for 1% Probability of 100‐year Event . 123 Figure 69 Recovery and Mitigation NPV for 8% Probability of 100‐year Event ............. 124 5
Figure 70 Recovery and Mitigation Benefit NPV for 8% Probability of 100‐year Event . 125 Figure 71 Recovery and Mitigation BCR for 1% Probability of 100‐year Storm Event ... 126 Figure 72 Recovery and Mitigation BCR for 8% Probability of 100‐year Storm Event ... 126 Figure 73 Savings from Investing in Mitigation Projects for 1% and 8% Probability of 100‐
year Storm Events ........................................................................................................... 126 Figure 74 Damaged Segments Participation in Relation to the Overall Infrastructure Extension ......................................................................................................................... 127 Figure 75 Extension of Infrastructure Not Included in Current Mitigation Projects ...... 128 Figure 76 US‐13 Post‐Disaster System Resilience ........................................................... 129 Figure 77 Capturing Resilience for Sequential 2nd, 3rd and 4th Disasters ........................ 129 Figure 78 Increasing Resilience of Systems Adopting Mitigation for Damaged Infrastructure in Future Sequential Events ..................................................................... 130 Figure 79 Calculating System Resilience Improvement Considering 4 Sequential Similar Disasters .......................................................................................................................... 131 Figure 80 Graph for Capturing Changes in Growing Infrastructure Resilience .............. 132 Figure 81 Model for Capturing Change of Resilience of System throughout the June 2006 Event ............................................................................................................................... 132 Figure 82 Graph for Resilience Change Through Time ................................................... 133 6
List of Tables Table 1 GIS Analysis Results for Seaford Transportation Infrastructure .......................... 11 Table 2 HAZUS‐MH MR3 Analysis Results for Seaford Transportation Infrastructure ..... 12 Table 3 HAZUS‐MH Highway Network Simplified Inventory for the Study Region .......... 17 Table 4 HAZUS‐MH US13 Simplified Inventory for the Study Region .............................. 18 Table 5 Infrastructure Data for Step 1 in STELLA .............................................................. 22 Table 6 Description of Initial Model Variables .................................................................. 23 Table 7 Change of Initial Flow Constant Values to Equations .......................................... 25 Table 8 Assessment Values for US13 Included in the Model in STELLA (000’s $) ............ 27 Table 9 Variables Values and Equations for Impact, Damage, and Pre‐Disaster Warning Mitigation .......................................................................................................................... 33 Table 10 Variables Values and Equations for Impact, Damage, and Pre‐Disaster Warning Mitigation .......................................................................................................................... 37 Table 11 LOS Criteria for Multilane Highways .................................................................. 40 Table 12 US 13 LOS Proposed Reading of LOS .................................................................. 40 Table 13 Variables Values and Equations for Assessing Infrastructure Availability and Disaster Duration .............................................................................................................. 44 Table 14 Attributing Rating Scale to Infrastructure Damage/Disruption (1) .................... 52 Table 15 Attributing Rating Scale to Infrastructure Damage/Disruption (2) .................... 53 Table 16 Assigning and Calculating Additional Infrastructure Deterioration Condition Post‐Disaster ..................................................................................................................... 53 Table 17 Short‐Term Post‐Disaster Performance and Condition Model Variables Description ........................................................................................................................ 56 Table 18 During Disaster Impacted Lanes and Condition Variables Description ............. 59 Table 19 Table for Interpreting Resilience Component Variables Input .......................... 61 Table 20 – Infrastructure Physical Condition Classification .............................................. 63 Table 21 MR&R for Agency and User Costs ...................................................................... 63 Table 22 Infrastructure Inventory with Adjusted Shape Length Units ............................. 64 Table 23 Case Study Segments and Adjusted Length ....................................................... 64 Table 24 MR&R Procedures Cost Estimation for US13 Study Area .................................. 65 Table 25 During Disaster Impacted Lanes and Condition Variables Description ............. 67 Table 26 Financial Sources for IS Recovery ....................................................................... 68 Table 27 Financial Sources for IS Normal Operations ...................................................... 68 Table 28 Agencies and Stakeholder Variables Responsible Financial Resources for Normal Operations ........................................................................................................... 69 Table 30 Description of Converters Values or Equation for Real Segments Damage Values ................................................................................................................................ 73 Table 31 Variable Values or Equations Matching Model Recovery Cost and Operations in Figure 36 ........................................................................................................................... 75 Table 32 Variables’ Description for Post‐Disaster Financial Composition ........................ 76 7
Table 33 Infrastructure Recovered Condition and Performance Variables Values e Equations .......................................................................................................................... 78 Table 34 Simplified Visualization of Damaged Infrastructure Type and Associated Deterioration ..................................................................................................................... 81 Table 35 Description of Mitigation Strategies and Costs per Project per Segment ......... 82 Table 36 Financial Sources for IS Mitigation ..................................................................... 85 Table 37 Mitigation Model Converters Values or Equations Descriptions ....................... 85 Table 38 Calculating Recovery Result on Reducing Infrastructure Vulnerability ............. 86 Table 39 Mitigation Sector‐Frame Condition and Performance Variables Description ‐ I 88 Table 40 Mitigation Sector‐Frame Condition and Performance Variables Description ‐ II
........................................................................................................................................... 89 Table 41 Description of Variables Used for Capturing Decreased Vulnerability Because of Mitigation .......................................................................................................................... 91 Table 42 Recovery and Mitigation Comparison Variables Description for Decrease on Vulnerability ...................................................................................................................... 91 Table 43 Categories of Avoided Damages ........................................................................ 92 Table 44 Mitigation Projects Categories of Benefits for Roads and Bridges .................... 93 Table 45 Historical Events Data for Current case Study Area ........................................... 94 Table 46 Disaster Historical Events Frequency, Impacts and Savings Model Variables Description ........................................................................................................................ 95 Table 47 Variables description for Delay/Detour Time in the Delay Caused by Disaster Sector‐Frame ..................................................................................................................... 99 Table 48 Summary of the 5 Steps to Define the Direct Economic Impacts of Road or Bridge Closures ............................................................................................................... 100 Table 49 Variables Values and Assumptions for Calculating the BCA of Mitigation Projects ........................................................................................................................... 101 Table 50 Benefit‐Cost Analysis Guide for Hazard Mitigation Projects for Roads and Bridges ............................................................................................................................ 102 Table 51 FEMA BCA Analysis ‐ Project Cost‐Effective Likelihood ................................... 103 Table 52 Elements Considered for the Calculation of Recovery and Mitigation Net Present Value .................................................................................................................. 104 Table 53 Recovery and Mitigation NPV Calculations in Excel ........................................ 105 Table 54 Equations Format for the NPV Difference between Recovery and Mitigation Projects ........................................................................................................................... 106 Table 55 Recovery Projects NPV ..................................................................................... 107 Table 56 Mitigation Project NPV Variables Description ................................................. 109 Table 57 Main Disasters Declared in Sussex County ...................................................... 110 Table 58 Summary of Benefits for Mitigation Projects .................................................. 111 Table 59 Mitigation Project Benefit and Benefit‐Cost Ratio Variables Description ....... 112 Table 60 Summary of Benefits for Recovery Projects .................................................... 113 Table 61 Recovery Project Benefit and Benefit‐Cost Ratio Variables Description ......... 114 Table 62 Benefit‐Cost Analysis Comparison Summary for Recovery and Mitigation Projects ........................................................................................................................... 115 8
Table 63 Summary of Recovery and Adjusted Mitigation Benefits, Effectiveness and BCR
......................................................................................................................................... 117 Table 64 Variables Description for Capturing Damage Impact in the Overall US‐13 ..... 120 Table 65 Recovery and Mitigation NPV for 1% Probability of 100‐year Event Variables Description ...................................................................................................................... 121 Table 66 Recovery and Mitigation Benefit NPV for 1% Probability of 100‐year Event Variables Description ...................................................................................................... 123 Table 67 Recovery and Mitigation NPV for 8% Probability of 100‐year Event Variables Description ...................................................................................................................... 124 Table 68 Recovery and Mitigation Benefit NPV for 8% Probability of 100‐year Event Variables Description ...................................................................................................... 125 Table 69 Variables Description for Transportation Infrastructure Extension not Under Mitigation ........................................................................................................................ 128 Table 70 Variables Equations for Resilience of Systems Improvement per Event ......... 129 Table 71 Resilience Values Increment with Successive Mitigation Projects Taking Place per Event ......................................................................................................................... 130 Table 72 Difference of Project Costs Considering Different Event Probabilities ............ 134 9
Introduction Background This working paper documents the model development for the PhD dissertation titled “Managing Critical Civil Infrastructure Systems for Disaster Resilience: A Challenge.” The overall objective of this research is to develop a Decision Support System to improve the resilience of critical infrastructure. This involves the exploration of the potential impacts of natural disasters on infrastructure operation and management. This includes understanding the nature of operations and management, the data and tools to support decision making and an analysis of the consequences of failure or degraded operations and performance. This also includes the use of existing computational systems to develop a geographical context, civil infrastructure systems analysis, asset management systems, and insights into mitigation strategies to the development of the system. The model, referred to as the Critical Infrastructure Resilience Decision Support System (CIR‐
DSS), uses the concept of resilience to support infrastructure decision making using Systems Dynamics. The framework is shown in Figure 1. Figure 1 CIR‐DSS System Dynamics Diagram 10
To implement this framework, inputs to the system dynamics model are generated using Geographical Information System (GIS) tools and HAZUS‐MH MR‐3 (Federal Emergency Management Agency 2007), a tool to assess the impact of hazards. These inputs are used to describe the overall resilience of an infrastructure system. The system is then analyzed using systems dynamics. Graphically oriented modeling software, STELLA (isee systems 2004, 1‐165), is used to develop the systems dynamics models. The concepts are illustrated using the June 25, 2006 flood event in Seaford, Delaware. This event also demonstrates how the complex system changes over time. The analysis developed in GIS (ESRI 2007) and HAZUS‐MH is not repeated in STELLA. GIS and HAZUS‐MH are used to generate maps for vulnerability assessment, and estimate exposure. The Level 1 analysis in HAZUS‐MH organizes and structures relevant data. The results from GIS are shown in Table 1. The maps originally developed are not readable in this table, but are included to demonstrate how to organize results. Table 1 GIS Analysis Results for Seaford Transportation Infrastructure System Results Description GIS (ArcInfo) From the left to the right: • Detours Set Up during the Flood of June 25, 2006 (DelDOT’s paper map), • Seaford Study Area, • Seaford Area Elevation Profile in 3D Image, • Rainfall recorded in Seaford area, • Flooded Area and Bridges impacted in Seaford area, • Seaford Road Network and Detours Analysis, • Location of Damaged Infrastructure in the Seaford Flooded Area. Event information supplied and maps developed can help direct relief supplies to areas of critical need and give out‐of‐state teams’ knowledge of local terrain and access to places. The results from HAZUS‐MH are shown in Table 2, including maps, tables and reports, helping organize all existing outputs. 11
Table 2 HAZUS‐MH MR3 Analysis Results for Seaford Transportation Infrastructure System HAZUS‐MH MR3 Results
Comments From the left to the right: • Base Map built in HAZUS‐MH for Seaford Area (include limited area around US13), • Seaford Area Annual Losses Map of Depth, • “What if” Levee Protection Scenario, • “What if” Flow Regulation Scenario, • Floodwater Velocity Estimation Scenario, • Damage related to US13 in Sussex County, • (There is an embedded mitigation measure for “warning” not reflected in the images). Organized information for helping interpret results (left to right) • Hazards Identification for Working with HAZUS‐MH, • Hazard Identification and Characterization, • Profile Hazard for Case Study, • Similar Federal Disasters and Damage between 1962 and 2006 in Sussex County, • Federal Disasters Damage Graph ‐ Sussex‐DE, Analyses Results
• Summarized Report for Transportation System Dollar Exposure, • Summarized Report of Estimation for Debris (require 112 truckloads), • Summarized Mitigation Measures based on HAZUS‐MH and History for Transportation Infrastructure – Roads, HAZUS‐MH gives no value for direct economic loss analysis for transportation. Transportation Inventory table is adjusted in excel for modeling. 12
Once GIS and HAZUS‐MH have been used to generate some results important to the overall analysis of the resilience of an infrastructure system, the resilience of the system is better analyzed using systems dynamics. This is what STELLA is being used for. In other words, using system dynamics modeling for the transportation infrastructure helps describe the state of the system before and after the June 25, 2006 flood event, and how the complex system changes over time. Once this model is developed, the results are organized for presentation to the target audience. Systems Thinking skills include trade‐offs of time, and management possibilities, and forecasting factors that are included in the model. The items in italics in Table 2 are important for the model in STELLA. These items in italics include data used in STELLA and mitigation options according to the FEMA STAPLEE criteria (Rock Island County 2008) for being a feasible mitigation measure. The mitigation options include enhancing the resilience of the system as opposed to a regular rebuilding or repair of the infrastructure system segments according to its original design. The Highway inventory in HAZUS‐MH is not in a proper format to be an input in STELLA. This data exported to EXCEL is used in the modeling and simulation process imported into STELLA. Each named column in EXCEL must match the elements in the model in STELLA. Also, to simplify the demonstration of the model, a sample was identified ‐‐ US13. The data related to US13 was obtained by comparing the Highway inventory from HAZUS‐MH, and the road data from DataMIL clipping it to fit the study region in HAZUS‐
MH and then highlighting the HAZUS‐MH segment links to identify their given identification code. This process used the Select Feature tool, because when opening the inventory table from ArcMap or HAZUS‐MH interface, the available tables did not present the information for “name” of US13 segments and the value for “cost” in a one same and only “attribute table”. Also, to highlight US13 in GIS for a qualitative network assessment, the creation of this new layer helps set up the boundary for the analysis later on. The model in STELLA cannot handle these geographical spatial analyses, therefore the need for integrating the results from these different systems. The working paper “Working with HAZUS‐MH” (Croope 2009) describes in more detail how the results were obtained. The working paper “Developing the STELLA Model for a DSS for Mitigation Strategies for Transportation Infrastructure: Introduction to STELLA” (Croope 2010) provides background on how complex systems are represented in STELLA. Objective of this Working Paper The purpose of this working paper is to document the model development in STELLA including alternative representations and errors. 13
Overview of the Working Paper The working paper is organized according to the steps identified in Figure 2. The following Section is organized in terms of each of the steps in model development: • Step 1 – getting local infrastructure information, initializing the system • Step 2 – getting system performance measures • Steps 3 and 4 – degrading system performance due to a disaster • Step 5 to 7 – improving system performance • Step 8 – assessing performance The working paper follows the development process including some of the changes in structure of the model and experience in dealing with the errors encountered in the development process. Observations and notes are also included to illustrate the model development process. Figure 2 Steps in CIR‐DSS Model Development in STELLA Building the Model Step_1 The first step in building the model in STELLA involves identifying all the variables not already used in the GIS or HAZUS‐MH analysis for resilience and functional and financial analysis. It includes the infrastructure system inventory, condition and performance measures, the decision makers and decisions. However, because the model integrates the current policy procedures for disaster declarations, its structure is scaled down to be consistent with these policies. For example, the impact assessment required by FEMA and calculated in HAZUS‐MH gives an aggregate result of several infrastructure system types, indirect and direct impacts such as population losses, economic and social factors. This impact/risk assessment is important to verify when an incident reaches the US$ 1 million threshold for a Federal Disaster Declaration. The impact assessment is, therefore, for the purpose of the model in STELLA, a variable that will be affected 14
depending on the overall performance of the infrastructure being analyzed, although this is just one element in the HAZUS‐MH risk assessment. The main assessments for the model in STELLA are, therefore, damage and vulnerability assessments, but damage assessment at first. This relates directly to the decision makers and to decisions regarding construction projects under the policy for recovery and mitigation, including enhancement of system resilience or not. Even though mitigation options are looking at the final mitigation options listed after consideration of the STAPLEE criteria (Croope 2009), just some of those options are included in the current model. The role of FEMA is integrated into the model as a decision maker and regulator. For example, FEMA determines when the damage assessment threshold of US$1 million measured in the beginning of the post‐event phase is met and a Federal Disaster declared. Once the threshold is reached, the process for granting funds needed to recover the related “local” damage takes place. This includes granting funds to other Federal organizations such as FHWA, and State level organizations. Because the transportation infrastructure is organized in a functional hierarchy, there are roads that are under the responsibility of FHWA and not the local DOT, which may be eligible to receive FEMA funds. FHWA has its own agenda for granting funds for transportation, but its main purpose is not directed to disaster related issues. For the specific case study being simulated, Delaware Department of Transportation (DelDOT), the State level decision maker is in charge of managing the transportation infrastructure network at the State level. DelDOT works with a budget and plan, which may have a special account for emergency events. The local elected representatives (who can also be identified as Stakeholders) are granted a small percentage of the State budget that can be used on transportation projects in response to the needs of their constituents. DelDOT is the main decision maker, but depends on and uses information and resources coming from other decision makers such as FEMA and FHWA. Figure 3 shows a diagram that trims down all possible variables to be included in the model and position the decision makers under the CIR‐DSS framework in a decision making and resource distribution perspective. The funding and resources determine the extent of investment in transportation repair, rebuild, replacement, rehabilitation and/or new development. These investments impact the options for increasing the system resilience. In this sense, the first decision making to look at the whole impacted area specific infrastructure is something already established, being directed to specific agencies responsible for each infrastructure or factor. This is not included in the model. For the particular case study for Seaford area – transportation system infrastructure, DelDOT is the agency that determines if the analysis will be looking at the overall impacted infrastructure, or some specific parts of it. This decision only impacts the input variables in the model such as number of segments, cost, and infrastructure condition and performance. This data must be updated for new analysis anyway. 15
Figure 3 Decision Makers and Funds for Investing in CIS The other decisions that take place in the process gradually involve other and more decision makers. This means, the subsequent steps in the model reflect other decisions and other or additional decision makers. Because this is a network system approach, the variables tend to be aggregates of large parts of the system or of the whole system. For example, total network cost is used instead of cost for each road segment. Because the most disaggregate values in HAZUS‐
MH are generated for the road inventory (e.g. cost for each segment), the existing data is used for getting general results at the project level and aggregate results for the management level analyses. Existing data does not focus on or make easy calculations for a detailed approach, although it is possible to have better accuracy in this model strategic level by including more project level variables and including more detailed analyses. This model’s purpose is principally to show the feasibility of the CIR‐DSS framework and register the know‐how to improve and expand this type of analysis. The stretch of US13 chosen as the partial highway network to be analyzed did not include the consideration of the intersecting roads to enable consideration of connectivity. This means the analysis of a partial highway network for a small geographic area may result in the identification of some mitigation measures that may already exist, such as the construction of an alternative route (involving building more roads). This helps to understand the relation of dependency, and also validates the model. Within the case study area, as defined previously in the HAZUS‐MH analyses, the geographic area can be redefined to better address the disaster impacted area, as a means to better accommodate the required analyses looking at specific infrastructure 16
physical condition and performance measures. A small geographic area may lack to include important features of a transportation network, which hierarchy and function exists through the many miles built. For example, to analyze accessibility and connectivity, the DataMIL road layer is an important inclusion to the highway layer given by HAZUS. Mobility, rather than accessibility, is a better performance measure for this type of analysis as mobility considers the highways’ function and existing inventory. Therefore only general result insights can be expected from the current analysis, once the DataMIL road layer is not completely included in the analyses. Variables In Step‐1 of building the model in STELLA, there are many variables required to establish the initial conditions for the analyses. Table 3 shows the highway network data for the study region from HAZUS‐MH simplified in terms of the number of variables. The other highway features in the HAZUS‐MH inventory tables – object ID, name, and traffic – are not used at present, but can be useful for further analysis. Also some additional variables, number of lanes and capacity, are included to highlight the segments that are part of US13 and required to complete the data needed for the analysis in STELLA. Table 3 HAZUS‐MH Highway Network Simplified Inventory for the Study Region Source: modified from HAZUS‐MH MR3 (FEMA 2007). The capacity is derived by assuming the maximum capacity per road lane is 1900 cars. Consider US13 has 4 lanes (2 in each direction). Total capacity considering all 4 lanes is 4 17
X 1900 = 7600 cars per lanes. The number of lanes per segment and the capacity per lane are variables with these values included in the model (Step_2). According to Meyer and Miller (2001), “the theoretical capacity of a freeway with ideal traffic and geometric conditions is 2,400 passenger cars per lane per hour”. The factors that affect road capacity, besides the number of lanes and its widths, include type of facility and surrounding land, shoulder widths and lateral clearance, design speed, traffic conditions, intersection controls, signal phasing, one‐way street routings, and others. The 1900 cars per lane (cpl) used in the analyses is the number suggested by the NCHRP Report 599 (2008), which identifies the default value of 1,900 passenger cars per lane per hour (pcplph), in the Highway Capacity Manual, as a more accurate value for base saturation flow rates for signalized intersections. The total cost to replace the 26 segments of the existing highway infrastructure for the study area is US$ 205.4. However, the replacement cost for the seven (7) segments of US13 is $71.1 m. Table 4 shows the same data Table 3, but only includes the seven (7) US 13 segments that are used for the analysis. Table 4 HAZUS‐MH US13 Simplified Inventory for the Study Region Source: modified from HAZUS‐MH MR3 (FEMA 2007). As noted the available inventory also includes some additional features. Not all these elements are included in the Step_1 of 8 in the CIR‐DSS framework description, nor it is included in the beginning of the model developed in STELLA. Each of the 4 lanes is identified because they can serve different purposes. For example, in the case of an evacuation, the 2 lanes going in the opposite direction could be used for contra‐flow. Also, if 2 lanes for a same direction are temporarily inaccessible, the other 2 lanes could, in theory, be put to work to compensate for such a problem. In this case, 1 lane of the only 2 available lanes would be used to one direction and the other 1 lane would be used to the opposite direction. These scenarios consider the need for continuing flow of goods and people. In these cases, all traffic rules may change to address what is the need at that specific time. The closer a road gets to its capacity; more likely one can expect to see problems with congestion, thus observe a decrease on the level‐of‐service measure. The road in operation/use is what matters. 18
The road capacity for US13 is considering 4 lanes multiplied per 1,900 passenger cars per lane per hour = 7,600. The carrying/service capacity classification here is defined as good (5,070 ‐ 7,600), fair (2,530 – 5,070), poor (1 – 2,530), or none (0). The assumption is that US13 has a good carrying/service capacity in the order of 7,600 passenger cars per hour. This assumption is modeled using standard constant values (e.g. passenger car per lane = 1900), and the calculation of 4 lanes (determined per segment) multiplied by the 1900 to get the total 7600 cpl for normal conditions/operations. These assumptions can be debated but this is beyond the scope of the current work. The pavement material type for US13 is assumed to be asphalt that is good condition prior to the disaster. A pavement condition index (PCI) value of 70 on a scale of zero to 100 would reflect this assumption using a conventional scale for PCI. The borrowed scale used by the Metropolitan Transportation Commission is shown in Figure 4. Figure 4 PCI Scale Source: Metropolitan Transportation Commission and Eres Consultants Inc. (1986). Predicting Changes in Performance Changes in the physical condition of the pavement over time can be represented as change in the percentage of pavement in a given condition over time, as described in NCHRP Report 551 (2006), and shown in Figure 5. Figure 5 serves to give an idea of the behavior of the pavement. However the threshold limit adopted here, considering Figure 4, is 40, just for rounding purpose. In this sense, the system can be considered good (80 ‐ 100), fair (60 ‐ 80), bad (40 ‐ 60), or destroyed (0 ‐ 40). The PCI (Pavement Condition Index) indicates the condition of a roadway between 0 (failed) and 100 (excellent) resulting from visual surveys of samples of the pavement. This value for physical condition is first included in the model and later calculated as part of the process for capturing the different stages the infrastructure goes through time when looking at the stress imposed by disasters. 19
Figure 5 System Percent for Good‐Fair‐Poor Condition as Years Passes By Source: modified NCHRP Report 551 (2006). Although a value such as 20 does not mean the system’s pavement is completely destroyed, the condition of it is so poor that the pavement is considered to present a significant risk to users. Options are maintenance or renewal, closure or abandonment. A low condition indicates there is the need for defining the type of interference/action to be taken including repair, rebuilding, replacing, rehabilitation, or permanent closure and demolition. This is why below 40 one must consider the system destroyed for general purposes. The degraded pavement condition through time can be seen as a deterioration process, which for the purpose of this research is considered the complement of the PCI converted to a scale of 0 (zero) to 1 (one). This means if the PCI for US13 is 0.7, the deterioration condition is 0.3. Deterioration variable is also included in the model, and is reflected in different ways (e.g. calculations including “degraded IS condition”). Influences on deterioration include load/usage, environment, material degradation, construction quality, interactions (i.e., material load, nature), and more. Deterioration manifests as surface defects, deformation, cracking/disintegration/breaks, failure aging/structural capacity, and occasionally, catastrophic failure due to disasters. In this model catastrophic failure due to fire, arson, terrorists, accidents, and floods are the primary cause of failure (Hudson et al 1997). Catastrophic failure is the result of a sudden increase in strain, stress, load pressure, displacement due to corrosion, shock waves, ground failure, and/or the combination of some of these factors. In the case of a catastrophic failure, the infrastructure normal life‐cycle is abruptly interrupted, causing decision makers to change the normal course of maintenance, repair, rehabilitation, or replacement. For each segment of interest, knowing the point at which the segment is in its lifecycle helps to understand the best option in terms of maintenance, repair or rehabilitation intervention. 20
Selecting Actions For each segment, appropriate actions can be identified and the “best” action selected on the basis of the least life cycle cost. The process steps in Life‐Cycle Cost Analysis (LCCA), according to the United States Department of Transportation, are listed below (USDOT and FHWA 2002). The steps are in sequential order where the analysis builds upon information gathered from the prior step. LCCA provides a comprehensive means to select among two or more alternatives to accomplish a project. “1. Establish design alternatives 2. Determine activity timing 3. Estimate costs (agency and user) 4. Compute life‐cycle costs 5. Analyze the results” The standard life for infrastructure projects getting some type of mitigation assistance, determined by FEMA, is 50 years ‐ activity timing, (FEMA 2007). This value is included in the model, as well as estimation of costs for current operations, recovery and mitigation projects. The analyses include an evaluation of benefits for different projects, highlighting users’ benefits as a consequence for the different type of project options. The process requires good estimates of the various agency costs associated with initial construction and periodic maintenance and rehabilitation activities. The construction costs include putting the transportation asset into initial service, where data is “obtained from historical records, current bids, and engineering judgment (particularly when new materials and techniques are employed)” (USDOT and FHWA 2002). For this model and simulation, a road segment replacement cost is given by HAZUS‐MH inventory. The aspects of new technology are not included in the model at this time; neither is the bidding processes or historical records. This estimate varies with different types of resources and services, and their values change through time. The estimate may easily be updated in the model when needed. Maintenance and rehabilitation activities costs included in a LCCA are identified in Step 3. This includes costs relating to maintaining the asset above the predetermined threshold for condition, performance, and safety levels. Examples of these activities are (USDOT and FHWA 2002) • preventive activities intended to extend the asset’s life, • day‐to‐day routine maintenance directed to address safety and operations, and • rehabilitation or restoration. These costs are the agency’s responsibility. Alternative projects for these activities must be considered because of the use of a certain financial resources and its cost at the end of the analysis period. There are also “terminal values” such as “salvage value” (recycling) or the “remaining service life” (RSL) value that can be included in the model if appropriate. In this model, we assume there is no salvage value.
21
User costs included in a LCCA include vehicle operating costs, travel time costs, crash costs, and more. These costs relate to the “timing, duration, scope, and number of construction and rehabilitation work zones (restriction of normal capacity of the facility and reduced traffic flow) characterizing each project alternative (USDOT and FHWA 2002). Typical user costs related to work zones are “speed changes, stops, delays, detours, and incidents”. User costs are important in the current analysis and model development because of the overall disruption and economic impacts. If user costs were just to be included to be used for comparison among maintenance or repair activities alternatives throughout an asset life‐cycle, these costs were more likely to be removed because they are often similar among projects. However, because the different project options focus in future less damage and loss, the need for regular maintenance is challenged, because the infrastructure must continue to be of use during and after being stricken by some hazardous event. User costs incorporated into a LCCA “enhances the validity of the results”. This part of the analyses is included towards the end of the model. In other words, the LCCA is included in the model to get a better idea of the existing amount of life (years) the infrastructure had until the occurrence of a disaster. The user benefits are one of the main factors when considering the benefit‐cost analysis (BCA) between options for recovery and for mitigation. These BCA are calculated close to the end of the model development also. These results are intended to illustrate and support decision‐making on activities and/or projects to be carried on. These results are presented and discussed later on during the presentation of the simulation of the case study which was used to help build the model. Network Definition and Data The case study to which the STELLA model is applied, could consider either the whole network or a part of it. For ease of computation a stretch of US13 was selected based on the study area defined in HAZUS‐MH. Table 5 shows the number of segments for the infrastructure and their aggregate replacement cost. The values brought into the model are the 7 segments related to US 13 and the cost of its infrastructure system network. infrastructure system network segments 26 Table 5 Infrastructure Data for Step 1 in STELLA infrastructure system infrastructure system network segments network cost (US$) sample (US13) 205,419,690
7
infrastructure system network cost sample (US$) 71,079,020
Using STELLA The basic functions used in STELLA are shown in Figure 6 (isee systems 2004). Basically to use any of the three initial icons (stock, flow, or converter) just click over it and drag it to the middle of the page and let go > click on top of the new diagram to name it. If it is 22
a “stock” the name must start with a capital letter, otherwise always use small caps. To open the diagram to include the value or equation, double click it. To start a “sentence”, always drop a stock first and then drop the flows and adjust it to link it properly to or from the stock. The other icons will be explained as they are used to building the model. Figure 6 STELLA Software Interface for Producing the Model and the Model’s Interface Source: Based of STELLA Software (isee systems 2004). In STELLA, the Step_1 in the model starts by including the infrastructure system segments, and the identification of one decision maker, as shown in Figure 7, and described in Table 6. First define stocks, flows, converters and assign constant values. After this is finished, from the final defined variable, include the connections, and thus define operations. This helps building the logic dynamic mechanism. Table 6 Description of Initial Model Variables Variable Value or Equation being used 7 Local Infrastructure System Segments 7 loosing usability 4 Deldot 1 Note: The original statewide damage to the transportation Infrastructure included 28*roads (segments) with high water, 6 road closures, 2 washed out bridges, 12 road failures, and 1 sink hole as shown in Table 4 in the HAZUS Working Paper (Croope 2009), which just for US13 included: ‐ high water in US13 – 2 places; ‐ road closed in US13 – 1 place; ‐ bridge washout in US13 – 1 place; ‐ road failure in US13 – 2 places; ‐ sink hole in US13 – 1 place. The case study area used in the model is a subset of the overall impacted statewide transportation infrastructure, reduced to 7 segments. Based on the DelDOT‐TMC report the types of impacts described in this report were replicated in the transportation infrastructure in the case study. * These road segments are from the DelDOT‐TMC Report, not the segments for the case study area defined later in HAZUS‐MH. The cloud is the starting point which leads to the flow “being used”, and the second cloud is the open end for the model continuation or end. This first step includes: 23
•
•
•
•
names for the stock, flows, and converters; constant values for the quantity of “Local Infrastructure System Segments”; constant values for the partial infrastructure system network segments – the converters (Table 4); constant value for the DelDOT decision‐maker (initially 0 – “zero”). Figure 7 Initial Variables in the Model in STELLA All the variables starting with “de” received the value according to their cost specified in Table 4 (e.g. de060 = 32206.29). The variables “being used” and “loosing usability” were defined as constants. Passing the computer mouse over the model elements shows the defined value without having to double click. If variables do not get an input for value or equation associating all connected converters, it shows a “?” inside, and it does not allow for any simulation. It generates an error that identifies the need for the inclusion of this value or equation. The variable which has no assigned value/operation, does not allow running the simulation. When a flow is assigned a value/operation, when passing the mouse over it, it will show a value “0”. This first part of the model including the two flows and one stock are in the format of the Main Chain infrastructure. One could choose to build a graph to check if the model is running according to the expected behavior, with a graph similar to the one following a certain type of template infrastructure, as shown earlier in this paper. A graph at this point may not be essential depending on the size and key elements of the model and one can choose either to build to see the model’s behavior and delete it, or to build it and use it to explain the model dynamics later on. Including the connectors to define the relationship, the initial flows defined as constants need to change to an equation including all converters that are now linked to the flow. This is shown in Figure 8. The symbols shown in Figure 8 have full color inside (e.g. full blue stock), or little gauges indicating the use of the flow and converters. The gauge indicates an operation is going on, either the constant value being used, or a variable gaining or loosing values. This helps verify all variables are working properly. To access this view one must run the model: menu RUN > RUN. In the case where some variable 24
was not assigned a value, the symbol still carries a “?” inside, the “Run” is not enabled; the symbols do not participate in the test for the model’s development. Figure 8 Initial Model Variables Connection and Put through Run Function Table 7describes the equations used in the model shown in Figure 8. Table 7 Change of Initial Flow Constant Values to Equations Variable Equation being used (de060/de060+de066/de066+de068/de068+de069/de069+de085/de08
5+de509/de509+de511/de511) deldot SUM(de060,de066,de068,de069,de085,de509,de511)/SUM(de060,de06
6,de068,de069,de085,de509,de511) Local 7 Infrastructure System Segments The model is developed to take in consideration events in the scale of disasters and/or catastrophes. In this sense, DelDOT is a key decision maker, but the model also later includes FEMA, FHWA, and the local Stakeholders as they participate in the decisions about the investment in recovery and/or mitigation projects in the post‐disaster phase. DelDOT is represented in the model by a value 1 linked from the individual road segments because the agency is responsible for each segment to the extent of their values, and the sum of the segments value is not the entity DelDOT. For the case study 25
area, the assumption is that FEMA resources are available for the damage that occurred on the specific US13 segments included in the partial system network. Step_2 Step_2 involves a diagnosis of the problem based on the infrastructure condition before the event and the potential hazard. This step includes doing a vulnerability assessment, an impact assessment, a damage assessment, and developing initial insights into strategies for recovery and mitigation. Step 2 starts with developing the model to get the infrastructure system performance measures for the infrastructure system in normal condition – before the disaster. Including Data and Information from Other Software The first challenge in the development of the model involves defining the types of data inputs generated by the other software (e.g. GIS and HAZUS‐MH). This involves building the links among actions and data that give the model structure. Also, from this point forward, it is important to recognize variables that were included in the previous step (in this case Step 1) and then add variables as needed, including repeating variables from Step 1 to understand why and when they are used. Whenever a variable in the model is being used again, its role can be identified as a feedback process, closing loops impacting the analysis. The feedback includes some action or information to complete the logic of such dynamics that is not shown in the System Dynamics Diagram for the CIR‐DSS framework. This actually emphasizes the differences between a framework, a model framework, and a model. The framework was developed as an approach to deal with the challenges for supporting decisions for improving infrastructure system resilience. The model framework consists of a conceptual diagram that provides insight and demonstrates how the model is organized, how the model will look like and the types of outcomes the model will generate. This particular model, built in the STELLA software, simulates the complex problem under different scenarios including changing the value of variables, different geographical spaces (case study areas), hazards, time periods/events, decision makers, and infrastructure. The values to be included in the model come from HAZUS‐MH and DelDOT, are adjusted based on FEMA models and data, and include assumptions shown in Table 8. 26
Table 8 Assessment Values for US13 Included in the Model in STELLA (000’s $) Highway Cost Vulnerability Asses. Impact Assessment Damage 205,420 205,420 3,000 Assessment 342 US‐13 Cost Vulnerability Asses. Impact Assessment Damage 71,079 71,079 1,038 Assessment 118 Assumed assessment values for the specific US13 sections were calculated as a percentage based the replacement costs for the study area defined in HAZUS‐MH for the overall highway infrastructure system segments cost (34.60%). The case study being modeled is 34.6% of the overall study area. In STELLA, building the piece in the model to get the cost for the Infrastructure segments is shown in Figure 9. Figure 9 Calculating Infrastructure Segments Cost The variable “cost of IS” is given by the equation cost of IS= SUM(de060,de066,de068,de069,de085,de509,de511) Phases in the Model from Pre to Post‐Disaster Because the model must capture the changes in the infrastructure system condition and performance through time, there are 4 distinct phases in the process. The first phase is the condition/performance before disaster, which is taken care in this Step‐2, and includes vulnerability assessment and impact assessment (estimate). The second phase 27
is the transition of condition/performance pre‐disaster to during the disaster, which includes the damage assessment being related directly to the impacted system segments identifying exclusive problems with the infrastructure. The third phase is the post‐disaster stage and the overall resulting damage, which is actually built while the second phase is still unfolding. The fourth phase is the investigation for infrastructure recovery including where appropriate mitigation strategies. The mitigation strategies may be prioritized based on increasing resilience of the system. In this Step‐2, the existing conditions, variables and values described but not used in Step‐1, are included. In other words, to understand how the infrastructure system behaved during the hazard strike it is important to capture the physical condition and system performance measures. After these metrics are captured, for starting to build a way for comparing past, present and future infrastructure system dynamic it is important to get these metrics from different points in time, including • capturing the metrics for “before event condition and performance measures”, • capturing the metrics for “during the event infrastructure behavior”, • capturing the metrics for “immediate after disaster hazard source stopped its activity”, finalizing with • capturing the metrics for “post disaster strategies for recovery or mitigation” condition and performance measures. Computing Variables Include the variables for calculating infrastructure segments vulnerability and impact to reflect the values shown in Table 8. Remember the relationship existing among key variables: if impact goes up (value = 1,038,000), probably vulnerability goes up. If adaptive capacity goes up, the vulnerability goes down. In the model include the direct application for the equation for vulnerability (Bhadwal Unknown): V= Vulnerability, I = Impacts and AC = Adaptive Capacity Figure 10 shows the addition to the model for vulnerability and impact calculations. Variables are defined as: “impact on IS = 1038000 (which includes not only infrastructure) adaptive capacity = impact_on_IS‐cost_of_IS (related to savings in US$) assessing vulnerability = impact_on_IS‐adaptive_capacity” 28
Figure 10 Initial Approach for Calculating Vulnerability and Impact with Data from the Disaster of June 2006 Figure 11 shows the built graph as a result to the flow’s “assessing IS vulnerability” function shown in Figure 12. The reasoning behind this graph is that if vulnerability goes up, the adaptive capacity is likely going down. The dialog box shown in Figure 12 and the “Become a Graphical Function” button to build the graph carries the name “To Graphical Function” circled in red because the graph was defined prior to capturing this image. This relationship between the converters “adaptive capacity” and “impact on IS” is a hypothetical relationship to illustrate the concept described earlier with the equation “V=fx(I‐AC)”. Again the model was tested using the “RUN” command. This process is necessary to help identify errors, such as a division by zero, or other types of errors. Fixing the model at each stage in the development process makes it easier to build the model. These checks reduce the risk of getting confused with the variables and connections existing in the model and ultimately saving time. 29
Figure 11 Assessing Vulnerability Flow Graph Figure 12 Assessing IS Vulnerability Flow Dialog Box 30
Because damage assessment defines the overall disaster impact, the model must include such assessment. However, adding the damage assessment to the model not only starts to make the model a bit more complex, but also requires some reasoning to get this piece right. When working with HAZUS‐MH, one of the mitigation strategies already included helping minimize impacts is the use of “warning systems”. In the real world weather monitoring is used and the time provided to prepare for the hazard event is beneficial in saving lives. The parameters associated with the first mitigation strategy, a “flood warning”, are shown in Figure 13. This integrates data from HAZUS‐MH into the model in STELLA. Figure 13 Flood Warning Parameters Included Source: based on HAZUS‐MH Software (FEMA 2007). The 10% reduction loss in the model in STELLA relates to the decrease in the real value for the road infrastructure damage. The parameters and percentages associated with the reduced loss or damage (value of savings), are based on the USACE Day Curve from the U.S. Corps of Engineers (USGS 2006). The value of savings from the “USACE Day Curve” for the maximum level of damage reduction by providing a flood warning is around 35% for structural, content, and business inventory losses; and this reduction is accounted for in the it calculated damage reduction. In HAZUS_MH Software dialog box for the flood warning parameters it is possible to choose and define any percentage of reduction between 0% and 35%. For the specific flood of June 2006 used in the case study the structure and inventory loss reduction input was defined as 10%. Again, only this warning is included in the 31
model as a pre‐disaster mitigation action. Flow regulation and levee construction, also mitigation measures in HAZUS‐MH, are not included in the current model. Disaster impacts measured by FEMA, through the HAZUS‐MH software, consider the amount of debris, damage to buildings, and loss of direct and indirect economic elements (i.e., jobs). It is a big picture approach to estimation that considers the flood level, as discussed and shown in the HAZUS‐MH Working Paper (Croope 2009). The variable “impact on IS” could include • amount of debris in tons from HAZUS‐MH – At this stage this information just underscores the need for functional transportation infrastructure, and is not included in the model; • cost to clean the road, personnel training, and volume of calls requesting road cleanup (service demand) – This data and information is not available at present for inclusion in the model; • impacts in terms of damage assessment to quantify the loss monetarily –This item is included in the model for roads. The 2006 flood impacts listed for Seaford area included road and bridge repair under the responsibility of the Delaware Department of Transportation, totaling $341,888 as shown in Table7 Profile Hazard for Case Study in Croope (2009). Also percent of affected properties that may be destroyed or suffer major damage is assumed to be 10% for the local road network, which matches the loss reduction due to warning mitigation. The variable “damaged IS” considers the estimate value of $118,293 as the 34.60% for the specific HAZUS‐MH study area calculated based on values shown in Table 8. One can assume the real damage was 10% more extensive if it wasn’t for the warning system mitigation measure. Total damage was, therefore, US$131,437 (x – 10%x = 118,293). Variable “other components” is the original value assigned to “impact on IS” “‐ “assessing IS damage”” = US$919,707. The replacement cost (in thousands of US dollars), which is also the value for exposure/vulnerability, as specified for each road segment previously defined and shown in Table 4 is useful to analyze damage. After including damage and pre‐disaster mitigation actions in the model, the model is run to verify if calculations and mechanism used in the model are correct and/or feasible. As the model runs the user can observe the symbols and see the colors and little gauges change. Figure 14 shows the results of running the model. No problems showed up in a popup dialog box. 32
Figure 14 Model Run Including Initial Damage to Infrastructure System and Pre‐
Disaster Warning The values and calculations defined for this part of the model are summarized in Table 9. Table 9 Variables Values and Equations for Impact, Damage, and Pre‐Disaster Warning Mitigation Variable Equation other components 919707 pre disaster mitigation 0.10 insight warning damaged IS 131437 assessing IS damage damaged_IS‐
(damaged_IS*pre_disaster_mitigation_insight_warning) Impact on IS assessing_IS_damage+other_components Condition and Performance Metrics – First Phase Now the damage from the flood disaster of June 2006 has been included in the model, the condition and performance values can be captured. The first phase is the condition/performance before the disaster, in other words, the current infrastructure condition and performance for normal operations. 33
A new resource is used in STELLA at this time: “ghost”, which is represented by the “ghost icon” in the top of the model’s interface screen. This resource is used to avoid the visual pollution one could get when building the model. It basically copies a variable and pastes it someplace in the screen when clicking. Just click the “ghost”, click on top of the variable one needs to have a copy, drag the variable to a desired location and unclick the computer mouse. In Figure 15 “ghost” was used for each segment now represented by a dashed‐line converter. It is important to understand that a lot of the analyses being developed bring the values from an operational level. These values are then summarized as an aggregated value. This value is used at the management level as information for making decisions. The following discussion of the condition and performance metrics chosen serves as background for understanding the calculations built into the model. This piece of the model starts on the left (copied dashed line variables), and moves to the right side (e.g. overall IS capacity) of Figure 15 including the values and concepts discussed earlier. Figure 15 Initial Pre Disaster IS Performance and Condition Measures Framework 34
After getting the “total IS number of lanes”, its time to define the carrying service capacity, which requires the inclusion of the variable “passenger cars per lane per hour”. This is done by building the graph for carrying service capacity and drawing the graph. The graph in STELLA is defined not only by the equation defined in the dialog box, but also by the line drawn. This model captures the relationships among the variables participating in the model. The capacity of the road is a function of the number of lanes in operation. For normal conditions, all 4 lanes (2 in each direction) contribute to the overall number of passengers cars per lane that can use the road. This is shown in Figure 16 with the full capacity being reached at a total of 4 lanes. Figure 16 Carrying Service Capacity Graphical Function The process continues as follows: After defining the carrying service capacity, is time to • Define the “current IS condition”, which requires adding the variables for the pavement condition index to the maximum value it can assume. • Add the degraded IS condition to reflect the current infrastructure physical condition. • Transform the result of the carrying service capacity into a percentage value by including a normalizing factor in the model. • Define the average IS condition using the standard time for IS lifecycle (that is 25 years and not the 50 years defined for mitigation projects by FEMA). Using this lifecycle time and the number of years the infrastructure exists, the number of the infrastructure lifecycles was defined. • Determine the age of the infrastructure (this serves not only to determine in which point of its life‐cycle it is, but also, based on this information, provides an 35
idea of when some type of maintenance will/is needed.) Figure 17 shows the life‐
cycle that infrastructure generally goes through, starting at the time the infrastructure was built and including several rehabilitation cycles to extend the service life through many cycles. Figure 17 Life‐Cycle Cost Analysis Primer Source: USDOT and FHWA (2002). In Table 10 the US 13 is described as being 59 years old, and the standard life‐cycle of 25 years includes a rehabilitation procedure. In this sense one could consider dividing the number of years the infrastructure has by the standard number of year for rehabilitation to get an idea of where in the Pavement Condition curve of the infrastructure is. In other words 59/25=2.36 (US13 had life‐cycle rehabilitation already 2 times). To reflect such design the converter “average IS condition” was assigned a graph (click on “become a graphical function” button), as shown in Figure 18. The graph can be read as the “0.36” of the life cycle being the edge of the graph touching the “Y‐axis”. There is some time to complete the cycle and then start the new cycle where the graph shows a “v” in the middle. When reaching the highest point, another rehabilitation procedure was completed and then the graph starts to decline again. 36
Figure 18 Average IS Condition Graphical Function Table 10 shows the values and equations included for the variables shown in the diagram in Figure 15. To start, the only value of interest for each “segment number of lanes” is the number of lanes existing for the “road specific segments”. This means that the initial cost values (dashed converters) have to be brought to the value=1 to fit the equation. Each segment equation was set up as this example: (de069/de069)*4. This is how one builds the connections among different information needed in the real world and links among existing variables. Table 10 Variables Values and Equations for Impact, Damage, and Pre‐Disaster Warning Mitigation Variable Equation de060 number of Example: lanes (and all other (de069/de069)*4 similar converters) total IS number of SUM(de060_number_of_lanes,de066_number_of_lanes,de068_
lanes number_of_lanes,de069_number_of_lanes,de085_number_of_l
anes,de509_number_of_lanes,de511_number_of_lanes)/7 passenger cars per 1900 lane per hour carrying service total_IS_number_of_lanes*passenger_cars_per_lane_per_hour capacity (AND click on “become a graphical function” – Figure 16) pavement condition 1 (equivalent to 100%) index degraded IS 0.3 (or 30%) condition current IS condition pavement_condition_index‐
degraded_IS_condition*(total_IS_number_of_lanes/total_IS_nu
mber_of_lanes) 37
normalizing factor overall IS capacity standard time for IS lifecycle years of existing IS average IS condition 1 (equivalent to 100%) (carrying_service_capacity*normalizing_factor)/7600 25 (years for life‐cycle) current flow rate 2009 – 1950= 59 (unit: years, AND explanation with Figure 17)a current_IS_condition*standard_time_for_IS_lifecycle/standard_t
ime_for_IS_lifecycle (SEE graph in Figure 18) 0.4 (or 40%) level of IS service passenger_cars_per_lane_per_hour*current_flow_rate a
US 13 construction date used in this research is 1950, considering the segments for the study area(Wikipedia contributors 2009). The other piece included is the infrastructure performance in terms of traffic flow. The metrics associated with traffic flow used in this model is the “Level of Service”. Another metric that would help understand traffic flow for the current infrastructure design is connectivity. Connectivity is understood as a very important measure which completes the evaluation of the resilience of a system. However, infrastructure connectivity analysis is not included in the model. Olufikayo and Okine (2009) provide more details on capturing (road and bridge) transportation connectivity. Continuing, “Level of Service” for the transportation infrastructure system is one way to measure performance. Some other measures are connectivity, carrying/service capacity, and network resilience network. Network resilience is actually defined here as one measure that aggregates the results of each of these earlier measures just described. The calculation of resilience of the system is presented later in this work. In other words, system performance relates to the level and quality of the service outputs being produced, which also include how this service affects society and the environment. Examples in transportation are number of vehicles miles traveled, level of congestion, average travel delay, number/severity of transportation accidents, and others. The “Level of Service” describes operational performance conditions of interest to the users (e.g., speed and travel time, freedom to maneuver, comfort, convenience), and are typically measured from the best (A) to the worst (F) condition for traffic flow. Travel flow predictions “use performance functions on each link of the network to influence the level of demand that will be assigned to that link, given link performance” (Meyer and Miller, 2001). Transportation system performance can also include impact on economic development, environmental quality, societal equity, sustainable community development, mobility, accessibility, and more. Level‐of‐service (LOS) depends on connection patterns, which implies different costs, and therefore leads the problem to evaluation of trade‐offs. Level‐of‐service variables can vary according to models. For example, common LOS for freight and travelers include price, and travel time. Specific LOS measures for freight include service liability, 38
probability of loss and damage; while for travelers LOS includes service frequency, and comfort (Sussman 2000). In fact, level‐of‐service in transportation is multidimensional, and it can also include safety or it can vary by time of day and/or over a longer period of time. The LOS related to the network performance is complicated because the operations within the context of the overall network allows for very modest or no control (Sussman 2000). Measuring the performance of systems that are impacted by stresses that are not controllable, such as disasters, is challenging. The overall customer perception of a system’s performance does not account for the specific components performance – what happens in the process for getting a service. Customers are interested in travel time, and service reliability. However, the management of the infrastructure system components impacts the overall system performance. Again, the level‐of‐service included in the model for evaluating the network refers to the amount of traffic using the road. The maximum value is the capacity of the road, at which one can expect to find congestion. This relates to the quality of service of the infrastructure, which also implies the infrastructure is maintained throughout its life cycle to sustain this LOS. The LOS rates highways in terms of interaction between cars and capacity (Trani 2006). It is used to justify improvements in congested roads. The rating system uses letters to identify the different LOS, “A” meaning excellent LOS, “E” meaning the LOS is near capacity, and “F” meaning “recurrent congestion ‐ unstable traffic flow” with stop and go traffic. The LOS for a multilane highway as defined in the Highway Capacity Manual is shown in Table 11 (Muench, 2006). 39
Table 11 LOS Criteria for Multilane Highways Source: Muench 2006. The US 13 speed limit is 55 mph, and the average LOS is known to be B. According to NCHRP Report 599 (2008), the recommended default values for freeway segments LOS are shown in Table 12. The level‐of‐service is related to the amount of traffic using the road. Based on Table 12, and the knowledge that the LOS for US‐13 is B, the flow is 760 pc/lane/h (passenger car per lane per hour). Table 12 US 13 LOS Proposed Reading of LOS Free‐Flow Criteria LOS Speed A B C D E F 55 mi/h Maximum Service Flow Rate 475 760 1,045 1,330 1,615 1900 (25%) (40%) (55%) (70%) (85%) (100%)
(pc/lane/h) The LOS included in the model makes use of the variable “passenger cars per lane per hour”, and registers the known US 13 “LOS B” (40%) under the variable “current flow rate”, which together gives the (number) value for US 13 LOS. To help organize the model, the pieces of the model that were developed to generate specific answers, such as this piece for capturing road condition and performance before a disaster, are grouped together. The icon to the right of the “?” icon is a little . This is called the “sector‐frame”. Click it once rectangle with some design inside, and take the mouse on top of the piece of diagram desired to be put in the sector‐
frame. Verify if all variables desired are in the sector frame by clicking on the selector 40
icon . Click the mouse once and it drops a box that can be resized by clicking at the edges and sliding the frame sides to the extent needed. Clicking twice on the top part of the sector‐frame opens the title for renaming it. When finished, one can click on the open lock icon and the sector frame is locked. The advantage for closing the lock is that it enables moving the whole diagram inside the box to any space in the model screen, cutting or pasting without losing its integrity. It also enables the sector frame to be later selected to run apart from the whole model under the “run” menu and “run‐
spec”. Each of the other little icons inside this “sector‐frame” box has a different function, but the most dangerous is the “dynamite” because it “explodes with everything” by cleaning up the space/values in the diagrams. At this stage the model includes: • current (pre‐disaster) physical condition (absolute and percentage), • current carrying service capacity (absolute and percentage), and • current level of service (absolute and with the current flow rate percentage value which translate the given qualitative measure “B”). Step 3_4 – Second Phase Steps 3 and 4 focus on the second phase in terms of the changes in the condition and performance. This second phase establishes the transition of condition/performance from the pre‐disaster status to the status during the disaster. This includes the damage assessment of the impacted system segments identifying problems exclusively associated with the infrastructure. Thinking about a disaster, it is important to understand the different impacts on the infrastructure in terms of a “time‐stamp”, because it helps understand the direct or indirect cost result related to it. In other words, a “disaster duration” variable should be included in the model. Where to position this variable in the model structure is important, one can have such a variable “loose” in the model page as a place‐holder for later integration within the other model functional variables. This is a good strategy to make sure key variables are included in the model. When a disaster strikes, transportation agencies must find functional transportation routes along which to move people and goods, and to get access for rescue and/or response activities. The variable “assessing IS availability” performs this function recognizing segments that are damaged and flow is disrupted. Several scenarios are possible: 1. The usual number of segments is available for traffic flow. 2. These segments may not be available anymore. 3. The loss of road segments does not happen all at once, but it depends on elevation, drainage, storm intensity, and many other factors (as occurred in the 41
case study flood). These specific time‐stamps are not included in the model although they could be. In this model, “disruption” is simply the interruption of traffic flow. It can be temporary (e.g. water on road), or long term/permanent (e.g. bridge washout – structure does not exist anymore). This recognizes that it is important to know not only the existing available segments before the disaster, but also during and after. This knowledge during disaster helps to identify traffic flow conditions and road bottlenecks for rescue/response and redirection of traffic (detours). This knowledge after the disaster helps to identify critical locations in need of mitigation projects against future disasters, and where there is continuous need for maintaining detours. A detour typically is a secondary access path from point A to point B, which implies more time and gas consumption. Figure 19 shows the model structure developed to capture disruption. Some variables in this model were built apart and then copied (ghost) to complete this model sequence shown in Figure 19. To make things easier, first this entire piece of the model is described in Table 13, and later the “ghost” variable specifically for “available IS segments short term” is described. This new piece of the model starts with the Infrastructure System Availability, “assessing IS availability”, than assessing IS availability during disaster, and Infrastructure System Temporarily Available. Assessing IS availability uses data inputs related to secondary roads, and Local Infrastructure System Segments. The secondary roads IS segments converter is the place where one could include a second road network with a different hierarchy classification and function to enrich the analysis. It is also the place for including the analysis of connectivity. This piece of the model development also enables the analyst to start looking at aspects of the network system resiliency based on the initial condition and performance measures. Assessing the infrastructure availability adds the current number of segment existing in the case study (7) and the secondary roads segments (0). Assessing infrastructure segments availability while disaster strikes here in the model, considers the peak or maximum impacted transportation infrastructure for the event. It means looking at the number of flooded segments, which got “that way” considering the duration of the disaster onset. Assessing infrastructure after the main hazard associated with the disaster is gone looks at the infrastructure that “survived the attack” or the extreme load of stress imposed on it – that is still in place. One could add the variable for evaluating remaining infrastructure segments to be considered safe and in condition to be put back in service; however this would just go back as another component part of the damage assessment, so it was not included in the model. 42
Figure 19 Capturing Disaster Impact Details for Transportation The model translates the value of damage into the number of lanes or part of lanes of segments damaged. This approach is explored further in the continuation of the model development. No complete segment of US13 was damaged, therefore the value for IS damaged segments does not apply exclusively to one or another segment. The results from HAZUS‐MH, and the way the segments were grouped does not allow for a perfect match of specific damaged location to the value of damage. As one can see, the map of the model in Figure 19 carries not only elements for during the disaster, but also for immediately after the disaster. This is where the model development really starts to run away from the perfect step‐by‐step development format initially thought and presented in Figure 1. This because Figure 1 was conceptualized looking at the CIR‐DSS Framework steps, and as mentioned before there are some differences between a framework, a model framework, and the model itself. The policy linkage in the model for allocating resources for recovery of the system after disaster is included at this point because after doing a damage assessment and reaching the US$1 million threshold, FEMA’s initial requirement is fulfilled. FEMA is included in the model just as a place holder at the moment, as the new decision‐maker responsible for “judging” policy compliance with the pledge submitted by the State of Delaware through DelDOT. Considering the disaster happened in June 25, 2006 and FEMA released the funds on August 4, 2006; the date FEMA released funds to start infrastructure recovery work it had past 40 days already (“fema fund released”). The “total time to repair or rebuild damage IS” is the period/time to repair/rebuild ignoring the temporary fix that in real world usually takes place because traffic flow needs to continue. 43
Also included is the overall duration of the disaster including the time for disaster onset, the repair/rebuilding time, and the overall time of the impact of disaster on the transportation infrastructure. The number of flooded segments cannot exceed the maximum number of the segments being used (at present they are 7). But because the disaster duration includes the time rain was falling, in a period of 24 hours, the number of segments flooded gradually increases. According to the United Nations Center for Regional Development (UNCRP and World Bank 1990) rehabilitation is typically ten times longer than the emergency response, and reconstruction lasts ten times longer than rehabilitation. Assuming designs and contracts are in order, hands‐on rebuilding of 1 lane for each of the 4 segments that suffered damage independent of the extent of segment/lane, damage is assumed to be repaired/rehabilitated in 20 days because damage was not too significant on US13. The time for response (including rescue and “containing” the disaster ‐ 1 day) is counted from the time the hazard strikes to the time it ends. Note that response took place over 2 days – 06/25/06 and the 06/26/06, therefore “ten times longer” for rehabilitation is 2 x 10= 20. Also knowing that there was more than one type of damaged infrastructure, and rehabilitation was not the only type of maintenance required, the reconstruction involved in the process for damaged infrastructure is 20 x 10= 200 days. The converter named “rebuilding time” is actually 200 days. While social and economic impacts are important, they are not the focus of this model, and specific variable are not included. Table 13 shows all new variables included in the model. The variables introduced in previous steps and repeated in the model, such as “being used”, and “total number of lanes”, are not included in the table. The new variable “available average IS segments short term”, shown as a ghost in Figure 19, and the model map that builds up to it in Figure 23 is shown after Table 13. Table 13 Variables Values and Equations for Assessing Infrastructure Availability and Disaster Duration Variable Value/Equation assessing IS availability Local_Infrastructure_System_Segments+secondary_roads_IS_s
egments secondary roads IS 0 (zero) segments Infrastructure System assessing_IS_availability Availability assessing IS availability Infrastructure_System_Availability‐flooded_IS_segments during disaster onset Infrastructure System assessing_IS_availability_during_disaster_onset Temporarily Available 44
Continue Table 13 flooded IS segments being_used*disaster_duration (number of problems in US13 excluding bridge washout are 6) graphical function (Figure 20) disruption disaster_duration/flooded_IS_segments disaster duration 24 (hours) disaster expanded (disaster_duration/24)+total_time_to__repair_or_rebuild_dam
time impact aged_IS total time to repair or fema_fund_released+rebuilding_time+(total_damaged_IS_seg
rebuild damaged IS ments_lanes*0) total damaged IS total_IS_number_of_lanes‐
segments lanes available_average_IS_segments_short_term available average IS SUM(available_de060_lanes,available_de066_lanes,available
segments short term _de068_lanes,available_de069_lanes,available_de085_lanes,
available_de509_lanes,available_de511_lanes)/7 rebuilding time time_for_rehabilitation*10 fema fund released 40 (days) fema fema_fund_released/fema_fund_released assessing IS availability after disaster Infrastructure System Short Time Available time for rescuing and containing disaster disaster response available_average_IS_segments_short_term assessing_IS__availability_after_disaster 1 (disaster_duration/24)+time_for_rescuing_and_containing_dis
aster time for rehabilitation disaster_response*10 The “flooded IS segments” captures the flow disruption process which could be used to get the disruption rate of onset ‐ the length of time from inception of the causal agent to the point of disruption threshold (variation: instantaneous like a blackout, to protracted like drought) (Rose Unknown). In fact, the graph in Figure 20 shows it is a protracted process. Also, even though not all the segments were flooded, because this infrastructure system is being analyzed isolated from other minor roads, the set up of detours is not a possibility, thus flow of people and goods (traffic) was disrupted. This underscores the importance of including other hierarchy roads in the analysis, and the assessment for connectivity. 45
Figure 20 Flooded IS Segments Graphical Function Disruption and Disruption Rate The disruption of traffic flow due to rain and resulting flooding, although related and is responsible for damage, is not the same approach and definitely not the same concept. In other words, just because a road was flooded, it does not mean it was damaged. In fact, with the exception of one location (shown in Table 2 – where small bridge that was washed out is pictured), no complete segment of US13 was damaged, therefore the value for IS damaged segments does not apply exclusively to one or another segment. Again, the results from HAZUS‐MH, and the way the segments were grouped does not allow for a perfect match of specific damaged location to the value of damage. In HAZUS‐MH it is possible to identify the US13 segments that were flooded and damaged. For the purpose of further analysis, these US13 flooded segments can be identified from the HAZUS‐MH inventory, with some accuracy as being DE000060, DE000069, DE000085, and DE000511. The other segments were not flooded. There were 3 locations where the infrastructure was damaged by flooded river flows, despite around 50% (visual assessment based on the map of the flooded area) of US 13 in the study area, was under water during the event. During the flood, detours were set up around US13, and after the floodwater went down some portions of road segments were found damaged. This infrastructure with degraded physical condition continued to disrupt traffic until it was temporarily fixed and later properly repaired/rehabilitated to its original design. This is the history behind the current development of the model. Therefore, disruption rate model includes disaster duration, segments being used, disruption, and a normalizing factor to make sure all variables are working under the 46
same unit and representation. Figure 21shows the diagram of the model for “disruption rate”. Figure 21 Disruption Rate Model The equation for disruption rate is “(disaster_duration/being_used)*normalizing_factor/disruption” The logic behind this model follows the reasoning described next. It starts by considering the variable of disruption shown in Figure 19. The “disaster duration” = 24 hours (length of time from inception of the causal agent). The threshold for disruption = 1 complete segment with any sort of problems for all 4 lanes such as 1 road segment closure, any high water, bridge washout, or even a sink whole). This way, if in 24 hours 7 segments had problems resulting in interrupted traffic flow, the disruption is 3.43. Continuing: if in 24 hours all 7 segments were flooded, the final coefficient is 1 ‐ the result of maximum values applied in the equation for disruption rate (e.g. (24/7)x1/3.43 = 3.43/3.43=1); which result 1 is equal to 100% or total disruption and failure to provide service. A disruption value 6 under the same condition is equal to a disruption rate of 57% (or 0. 57). This means that results smaller than 1 is more favorable to the infrastructure because it means there was less disruption in the system. Calculation of Resilience At this stage in the model’s development the three measures used to assess the system resilience for pre‐disaster condition and performance that are available are: • physical condition (absolute and percentage), • carrying service capacity (absolute and percentage), and • level of service (absolute and current flow rate as a percentage value of the flow for the qualitative LOS “B”). Pre‐disaster condition means normal condition and no expected disruption; this is why disruption is not a variable included in the specific before event condition and performance measures model development. Because each one of these measures is a relative value expressed in terms of “percentage”, it is possible to define resilience as the result of the combination of all these values. Ideally connectivity would also be 47
included in the IS resilience measure. For now, disruption rate is used to capture system resilience. Figure 15shows the basic metric variables needed to include in the calculation for resilience. Figure 22shows resilience of system for the pre‐disaster period. Figure 22 Resilience for Normal Time or Pre‐Disaster The converter “resilience for normal IS operations” equation is a simple average of the three measures: “((1‐current_flow_rate)+current_IS_condition+overall_IS_capacity)/3” The simulation calculated a value of “0.77”. Post‐Disaster ‐ Third Phase After the model development for disruption and disruption rate, it is easy to take the direction towards building the model for capturing during disaster infrastructure condition and performance measures. However, before proceeding, it is important to define the model to answer the “available average IS segments short term” – the “immediate after disaster strike stopped”. This is when the third phase happens. It accounts for the post‐disaster and the overall resulting damage. Figure 23 is the mechanism used for capturing the value for the converter named “available average IS segments short term”. 48
Figure 23 Capturing Variable Value “Available Average IS Segments Short Term” It starts with the ghosts copies of the segments “deXX number of lanes”. Include the variable per segment to get the information of “available deXX lanes”, which depends on the inclusion of the variables “deXX damage lanes” per segment. The “deXX damage lanes” were defined initially based on information shown in Table 4, and by looking at the flooded area and segments impacted by the flood (DE000060, DE000069, DE000085, and DE000511). For the specific DE000060 and DE000069 account for 2 lanes with damage each segment. For DE000085, and DE000511, consider damage to exist in 1 lane of each of these segments. For the other 2 segments consider no damage (or 0). Include the converters for all segments to capture the resulting number of lanes just after disaster onset – recovery phase (not response), example 49
“available de511 lanes= de511_number_of_lanes ‐ de511_damaged_lanes” Calculate the average number of available lanes from all segments. This is implemented by including the converter and equation “available average IS segment short term = SUM(available_de060_lanes,available_de066_lanes,available_de068_lanes,available_d
e069_lanes,available_de085_lanes,available_de509_lanes,available_de511_lanes)/7” This “available average IS segments short term” variable is used in the sequential model shown in Figure 19, and also links that piece of the model to the original starting point of the overall model, as shown in Figure 24. Defining “total damaged IS segment lanes” re‐dimensions the flow “loosing usability” earlier defined as a constant (value = 4). This initial value assumed loss of segments was larger considering the impact of disaster. However, the ultimate value for loosing usability is not as bad (0.86). Figure 14 showed the initial approach to “loosing usability”. Figure 24shows the improved approach to the same part in the model, using the following equation: “Local_Infrastructure_System_Segments ‐ total_damaged_IS_segments_lanes” This equation is actually doing the math (7 – 0.86 = 6.14). One can see a ghost copy was made of the “total damaged IS segments” calculated earlier (Table 13), and used to obtain the result that is integrated into the model to define “loosing usability”. Figure 24 Defining “Loosing Usability” 50
The result of the operation for “available average IS segment short term” is a number with decimals. This is because US13 did not lose a complete lane all the way along all segments. This completes the piece of the model for capturing disaster short‐term impact details for transportation. Calculating Degraded Condition and Performance Once the part of the short‐term post disaster measures is finished to complete the model’s sequence shown in Figure 24, one might as well continue developing the other pieces of the condition and performance measures, which is shown on the right part of the model in Figure 23. One of the elements needed to capture the new values for infrastructure physical condition measure is the additional deterioration of the built infrastructure due to the flooding. This means one must look at existing deterioration levels and apply the additional load to cause the results found and reported in the DelDOT damage assessment report. The existing deterioration condition is an average value defined in Table 10, shown in Figure 15, which value is 30% or 0.3 in the model. Because there were different types of damage found in the infrastructure, one can assume the stress imposed by flooding in different locations had different factors and water strength contributing to these scenarios. Therefore, the deterioration associated with different locations must observe a ranking process. In this research assumed rankings were assigned. According to the information on roads condition shown in Table 6, US13 road segments problems included high water, road closures, road failures, and sink holes. Assume each of these problems have a different scale for deterioration, and assign rating values to them according to the degree of damage. Use this assigned rating to “update” deterioration condition of roads after disaster. For the purpose of illustrating the types of insights/help one can get when building the model in STELLA, this part of the model includes: • how the original piece was built, • running the model, including the popup error message the system shows, and • correcting errors. Using a rating value of 4 (four, to match different road issues) for the most severe type of degradation, and assume that failure that is a “100%” deteriorated road, assume the other rates correspond to the quarters of the 100% and add to previous road deterioration rate. This methodology was based on USDHS and National Emergency Response and Rescue Training Center (2005). This rating system used in the model needs further investigation to include several different types of degradation, and reflect the severity of each type of degradation. This information is input into the model considering the damage locations for each segment. The location of each type of road degradation was randomly assigned, 51
although for better accuracy in the future, problems should be better matched with the reported locations. Table 14 shows initial rates and percentage values associated with each report problem for infrastructure. Table 14 Attributing Rating Scale to Infrastructure Damage/Disruption (1) Road Issue # Impacted Deterioration Associated Deterioration Rate (Original road deterioration rate: Locations Assigned Rate 30%) high water in US13 2 places 1 30% + 25% road closed in US13 1 place 2 30% + 50% road failure in US13 2 places 4 100% sink hole in US13 1 place 3 30% + 75% Running the model an error message pops‐up as shown by Figure 25: Figure 25 Error Message for Piece of Model for Increased Degraded Condition Source: generated by (isee systems 2004). This means the reasoning behind the value assigned to that variable is incorrect, and the logic behind this assumption needs to be changed. To find the problem, review values assigned remembering that the final value cannot be greater than 100%, and that there was an initial road deterioration rate that needs to be taken into account. This means the assigned rate 4 to reach 100% deterioration has only 70% to go. Therefore all the other values have to be adjusted having 70% as the maximum value possible. Therefore if rate 4 is 70%, then 3 is 52.25%, 2 is 35%, and 1 is 17.5%. Table 15 shows the corrected assumptions. 52
Table 15 Attributing Rating Scale to Infrastructure Damage/Disruption (2) Road Issue # Deterioration Associated Deterioration Rate* (Original road deterioration rate: 30%) Impacted Assigned Locations Rate high water in US13 2 places 1 30% + 17.5% road closed in US13 1 place 2 30% + 35% road failure in US13 2 places 4 30% + 70% sink hole in US13 1 place 3 30% + 52.3% Table 16 shows all variables and assigned values or equations translating the diagram shown in Figure 23. Table 16 Assigning and Calculating Additional Infrastructure Deterioration Condition Post‐Disaster Variable Value/Equation de511 deterioration 0.35 associated with rank de509 deterioration 0 associated with rank de085 deterioration 0.523 associated with rank de069 deterioration 0.175 associated with rank de068 deterioration 0 associated with rank de066 deterioration 0 associated with rank de060 deterioration 0.7 associated with rank de511 increased (de511_deterioration_associated_with_rank+degraded_IS_con
degraded condition dition)*(available_de511_lanes/available_de511_lanes) Note: all variables with similar names to “de511 increased degraded condition” in this model sector‐frame have the same equation structure. To capture IS resilience after disaster, one need to determine the infrastructure short term post‐disaster physical condition, the LOS, and the carrying/service capacity. Start by defining the process for capturing those measures, and adjusting the equations to generate the desired outputs as shown in model development stages in Figure 26. 53
Figure 26 Building the Model to Capture Short‐Term Condition and Performance Measures The variables are added one by one in the model, have their values, equation and units defined, a graph or table included to quantify the contribution to the model and demonstrate the process, and if appropriate, group in a sector‐frame. After those actions than move to the next issue involved in the challenge for managing infrastructure and the multitude of variables that take place in this complex system. Managing the Infrastructure As mentioned before, the inventory in HAZUS‐MH looks like the result of grouping segments, showing long lines for each identified road segment, making it difficult to identify perfect matches of specific road damaged location. This means matching road damage location to the value of damage carries the same problem. The final diagram format for the short‐term post‐disaster performance and condition measures is shown in Figure 27. 54
Figure 27 Complete Sector Frame for the Short‐Term Post‐Disaster Performance and Condition Measures Each variable and their defined values and/or equations are described in Table 17. The graph associated with the short‐term carrying service capacity is discussed in sequence. 55
Table 17 Short‐Term Post‐Disaster Performance and Condition Model Variables Description Variable Value/Equation average degraded IS (de060_increased_degraded_condition+de066_increased_degr
condition aded_condition+de068_increased_degraded_condition+de069
_increased_degraded_condition+de085_increased_degraded_c
ondition+de509_increased_degraded_condition+de511_increas
ed_degraded_condition)/7 shortterm IS condition pavement_condition_index‐
degraded_postdisaster_IS_condition*(available_average_IS_se
gments_short_term/available_average_IS_segments_short_ter
m) average IS shortterm shortterm_IS_condition*standard_time_for_IS_lifecycle/standa
condition rd_time_for_IS_lifecycle available_average_IS_segments_short_term*passenger_cars_
shortterm carrying per_lane_per_hour service capacity becoming a graphical function (Figure 28) shortterm overall IS (shortterm_carrying_service_capacity*normalizing_factor)/760
capacity 0 de511 level of IS (level_of_IS_service*4)/available_de511_lanes service Value = 1013 de509 level of IS (level_of_IS_service*4)/available_de509_lanes service Value = 760 de085 level of IS (level_of_IS_service*4)/available_de085_lanes service Value = 1013 de069 level of IS (level_of_IS_service*4)/available_de069_lanes service Value = 1520 de068 level of IS (level_of_IS_service*4)/available_de068_lanes service Value = 760 de066 level of IS (level_of_IS_service*4)/available_de066_lanes service Value = 760 de060 level of IS (level_of_IS_service*4)/available_de060_lanes service Value = 1520 shortterm post (de060_level_of_IS_service+de066_level_of_IS_service+de068_
disaster level of level_of_IS_service+de069_level_of_IS_service+de085_level_of
service _IS_service+de509_level_of_IS_service+de511_level_of_IS_serv
ice)/7 shortterm flow rate (shortterm_post_disaster_level_of_service*current_flow_rate)/
level_of_IS_service The graph for normal conditions and operations shown in Figure 16 is not the same when looking at a post‐disaster period. The new graph shows the degraded capacity to carrying traffic. The adjusted graph must express, in general, the loss of capacity under 56
the converter “shortterm carrying service capacity”. The resulting value running the model for “available average IS segments short term” is 3.1, which multiplied by lane capacity gives a total of 5,890 cars. In other words, this means one could assume 3 lanes can work like for normal time, but the fourth lane is limited. This limitation is a problem that asks for more investigation, unless one knows it is due to road failure, closure, sink holes and other problems described in the DelDOT‐TMC report mentioned earlier. The true impact of decreased road capacity requires further investigation. Figure 28 shows the decreased carrying service capacity. Figure 28 Short_Term Carrying Service Capacity Graph The calculation for the level‐of‐service for the short‐term post‐disaster must also consider the loss of normal physical infrastructure condition to carry traffic. That is why each segment although having the same approach for calculating the resulting LOS show different results. These results are included in Table 17 together the expression “Value =”. One can assume traffic flow accumulates on existing available lanes‐segments, making them busier. This can indicate the appearance of congestion, even if as a temporary condition. This is what helps understand change in the LOS and flow rate. To get the short‐term flow rate, which is the variable that matters to analyze resilience, the process is not the same as for infrastructure under normal operations. Normal operations flow rate that relates to the level of service, is a given‐information from, in this case, the road planning and operations sections from the Department of Transportation. To capture the overall change of the segments level‐of‐service due to the impact of disaster, it is important to account for the initial level‐of‐service and the initial flow rate. The overall result from running the model shows LOS moved from “B” to “C” (55.26% or 0.5526). Adding all elements to calculate resilience of system after disaster is shown in Figure 29. 57
Figure 29 Resilience of System Model for After Disaster Period The “resilience after disaster” (simulation value = 0.31) equation is similar to “resilience for normal IS operations” shown in Figure 22. “resilience after disaster= ((1‐shortterm_flow_rate) + shortterm_IS_condition+shortterm_overall_IS_capacity)/3” This ends the third phase, and lead efforts back to defining infrastructure condition and performance during the disaster onset – the model second phase. To get the correct physical condition and performance measures is important to realize that during the flood the process for degrading the physical condition was in action. Therefore it is important to address this issue in the model. Just a reminder: The model is built in a sequence where every new needed variable has to come in with its final value or equation to integrate the model. This is how the interrelation and interconnection throughout the infrastructure history is built. Now that there are no pending variables (to the sequence being built in the model) it is possible to continue the model development. Completing the Second Phase Figure 30 shows the model’s sector‐frame for “during disaster impacted lanes and condition”, including the definition of the LOS at that point in time. During a disaster the impacted road segments do not show clearly what is happening to them – they are “under water”. Therefore all segments impacted (does not matter at present the length of road compromised) are considered as temporary completely out of service. This matches with the disaster duration for 1 day and 4 segments compromised as described earlier. This means segments de060, de069, de085 and de511 for “stricken lanes” are all getting a value 4. 58
The model starts with the ghost of each segment “number of lanes”. It includes variables to “stricken lanes”, which are used to calculate the “impacted available deXX lanes”. Example applied to all similar named variables “impacted available de509 lanes = de509_number_of_lanes‐de509_striken_lanes” Figure 30 Model for Capturing Infrastructure Condition and Performance during Disaster and the Resulting Variable "Available Average IS Segments Short Term” Table 18 shows all new variables in Figure 30 and their values or equations: Table 18 During Disaster Impacted Lanes and Condition Variables Description Variable Value/Equation de060 striken lanes 4 de066 striken lanes 0 de068 striken lanes 0 de069 striken lanes 4 de085 striken lanes 4 de509 striken lanes 0 de511 striken lanes 4 impacted available de060_number_of_lanes‐de060_striken_lanes de060 lanes (Same for all segments) 59
Continue Table 18 average impacted IS segments de060 all lanes temporary condition overall impacted IS condition temporary capacity SUM(impacted_available_de060_lanes,impacted_available_de
066_lanes,impacted_available_de068_lanes,impacted_availabl
e_de069_lanes,impacted_available_de085_lanes,impacted_av
ailable_de509_lanes,impacted_available_de511_lanes)/7 impacted_available_de060_lanes*current_IS_condition (Same for all segments) (SUM(de060_all_lanes_temporary_condition,de066_all_lanes_
temporary_condition,de068_all_lanes_temporary_condition,d
e069_all_lanes_temporary_condition,de085_all_lanes_tempor
ary_condition,de509_all_lanes_temporary_condition,de511_al
l_lanes_temporary_condition)/4)/7 average_impacted_IS_segments*passenger_cars_per_lane_pe
r_hour (temporary_capacity*normalizing_factor)/7600 overall temporary capacity de060 temporary LOS level_of_IS_service*impacted_available_de060_lanes temporary impacted IS (SUM(de060_temporary_LOS,de066_temporary_LOS,de068_te
LOS mporary_LOS,de069_temporary_LOS,de085_temporary_LOS,d
e509_temporary_LOS,de511_temporary_LOS)/7)/4 impacted flow rate (temporary_impacted_IS_LOS*current_flow_rate)/level_of_IS_
service Finishing the calculation for during the event condition and performance measure, one now has condition to calculate resilience. The calculation for resilience of infrastructure during an event adds the element of disruption. This makes the understanding of the calculation for resilience a little different. Resilience combines all the performance and condition measures, represented as factors that account for the system capacity to withstand the impact of disaster. To get such resilience factor value it is important to understand how condition and performance measures must be interpreted. Some variables values must be inverted because of what they mean and ensure that the direction of any change in the variable is consistent with the direction of change in resiliency. For example, the closer the disruption rate is to 1, the closer the system is to complete failure/disruption. The value of interest is how much capacity for traffic movement is left in the system to withstand the disaster imposed stress on the system, thus an inverted value adding to the overall resilience. The correct interpretation for this operation in the model is shown in the Table 19 below: 60
Table 19 Table for Interpreting Resilience Component Variables Input Variable Interpretation Resilience
current flow rate low is good (e.g. Table 12) 1 current IS condition high is good (e.g. Figure 4 and 5) 1 overall IS capacity high is good (e.g. Table 4 and Figure 16) 1 disruption rate low is good (e.g. description pp. 44‐47) 1 The model for resilience was initially defined in a “Main Chain” type of template infrastructure, but was later changed to have its diagram only with converters, because it was more convenient to capture the different phases of system resilience through time and project resilience values according to the strategy used to recover/mitigate the infrastructure. Figure 31 shows the final model diagram for the resilience of the system during the event (while raining and flooding). It includes physical condition, carrying service capacity, level of service, and disruption rate. Figure 31 During Disaster Onset Resilience of System Assessment The equation included for the converter “resilience during disaster” is “((1‐impacted_flow_rate)+overall_impacted_IS_condition+overall_temporary_capacity‐
disruption_rate)/4” Its simulation value is 0.25. It is a bit lower than after disaster resilience (0.31), and a lot lower than the initial resilience value for normal operations (0.77). Managing the Infrastructure – Fourth Phase Up to this point a lot of the problem with the infrastructure was captured and now it is time to move forward with ways to fix the problem. Specifically, this involves asset management, which will deal with the infrastructure life‐cycle, projects for maintenance‐repair‐rehabilitation, or replacement. It will consider projects’ financial trade‐offs and incorporate the benefit‐cost analysis defined by FEMA to ensure that the users’ benefits are being considered. 61
This puts the model development in its fourth phase, which is the investigation for infrastructure recovery including or not mitigation strategies. The mitigation strategies may prioritize increasing resilience of system or not. It relates later on to steps 5 through 8 shown in Figure 2, although Step_8 basically summarizes results for decision‐
making, and is shown separately. All these steps are considered at phase four, altogether, because the improvement of system performance is built by recovering the damage system, which requires the consideration of project financial cost and the use of current disaster policy for recovery and mitigation. It requires the value for supporting normal infrastructure operations. In other words, the analyses for infrastructure fix/improvement alternatives start by getting the information about the cost for normal operations. This concept is shown in Figure 32. Figure 32 Concept for Starting to Address Solutions for Damaged Infrastructure System Reviewing the IS physical condition, and knowing that US13 had life‐cycle rehabilitation already 2 times (59/25=2.36), one can assume it is about time for some type of maintenance procedure to maintain the quality of road. A key variable is therefore deterioration of US13, which before disaster was 30%. There are many types of maintenance repair and rehabilitation (MR&R) activities used in practice including (Park 2004): 1. do nothing, 2. routine maintenance, 3. 1‐in overlay, 4. 2‐in overlay, 5. 4‐in overlay, 6. 6‐in overlay, and 7. reconstruction. Building on data used by Durango‐Cohen, and Tadepalli (2004) we use four M&R activities (do nothing, routine maintenance, 2” overlay and reconstruction) to illustrate 62
the decision that need to be made. Table 20 relates the PCI range to a modified roughness scale and condition states. Table 21 the agency and user cost associated with each of the activities for each condition state. Costs are expressed in 1994 dollars and in $/m2. Official units in the U.S. are miles, which are used in HAZUS‐MH, which continues to be the unit for segment length. Appropriate conversions are used. Table 20 – Infrastructure Physical Condition Classification Source: Durango‐Cohen, Pablo, and Tadepalli (2004). Table 21 MR&R for Agency and User Costs Source: Madanat and Ben‐Akiva (1994). The “do nothing” action means not to interfere with the deterioration process taking place on the facility, making it degrade its physical condition. The “Routine Maintenance” relates to actions to be taken to prevent the facility from continuous deterioration. The other two actions, 2” overlay and reconstruction, are improvements modifying the roughness scale (Madanat and Ben‐Akiva 1994). User cost, although shown in Table 21, is not the approach used by FEMA with the “Benefit Cost Analysis” tool, and is currently not used in this model. The total replacement cost for reconstruction considering the 7 segments is US$71,079,020 for the total segments length of 19.24 decimal degrees. Decimal degrees is not an easy measure to understand, therefore it is important to transform decimal 63
degrees into an easier metric to work with, for example feet. To do this, go to HAZUS‐
MH and project highway segments layer (using tool for projection in ArcInfo) to: NAD_1983_HARN_StatePlane_Delaware_FIPS_0700_Feet Linear Unit: Foot_US Table 22 shows the new values for the segments’ length in the HAZUS‐MH Inventory. Table 22 Infrastructure Inventory with Adjusted Shape Length Units Source: HAZUS‐MH Software (FEMA 2007). The specific case study segments and adjusted length units are shown in Table 23. Table 23 Case Study Segments and Adjusted Length Segment de060 de066 de068 de069 de085 de509 de511 Total Length in Decimal Degrees 10.83
0.88
2.54
0.33
3.62
0.77
0.27
19.24
Length in Feet 21,722.55 2,881.99 8,275.91 1,083.84 11,778.11 2,496.88 888.95 49,128.23 64
Estimating Costs under Normal Condition (Assuming No Disaster) The first objective now is to determine the cost to have the infrastructure be at service during normal operations (excluding disaster). The best way to do this is to estimate the “average IS cost per mile”, base on initial cost of segment and length of segment to work with the smallest single unit – cost per mile. Figure 33 shows the new sector‐frame for Cost of IS Normal Operation. Start by making ghosts for all “deXXX”, which variables carry the value for the replacement of segment. Include new variables for length (e.g., de060 length), and define the cost per foot. The cost per mile is given by using the segments cost for replacement divided by the length, both values coming from HAZUS‐MH. The variable “deXXX cost per mile” carries such equation (e.g. de060 cost per foot = de060/de060_length). Add all variables “deXXX cost per foot” and divide it per the 7 case study segments: average IS cost per foot = SUM(de060_cost_per_foot,de066_cost_per_foot,de068_cost_per_foot,de069_cost_per
_foot,de085_cost_per_foot,de509_cost_per_foot,de511_cost_per_foot)/7 This “average IS cost per foot” resulting value is used to build a table for costs for the different MR&R (maintenance, repair and rehabilitation) procedures. Note: The model was not initially working with feet, but working with decimal degrees. The correction of the length units helped bring more understanding and accuracy to the model. Therefore Table 24 shows the adjusted segment length units. The reconstruction value obtained when running the model is US$139.00. The values for the MR&R procedures were estimated in a percentage approximation to the relational value shown in Table 24. Although this is a rough way for getting this information, it helps approaching the problem in a convenient way. The cost of the various procedures change through time and can be found by working together offices that deals with purchasing/contracting construction projects. Table 24 MR&R Procedures Cost Estimation for US13 Study Area State Do‐nothing 0 0 1 0 2 0 Routine Maintenance 26.57% 36.93 7.70% 10.70 5.39% 7.50 2” Overlay
Reconstruction
User Costs 83.98%
165.52 47.40%
65.90 41.16%
57.21 139.00 385.06% 535.23 100.11% 139.15 84.71% 117.71 139.00 139.00 65
Continue Table 24 3 0 4 0 5 0 6 0 7 0 3.19% 4.43 2.50% 3.48 1.19% 1.65 0.58% 0.81 0.15% 0.21 34.89%
48.50 25.57%
35.54 15.82%
22.00 15.05%
20.92 14.67%
20.40 139.00 139.00 139.00 139.00 139.00 53.91% 74.93 30.80% 42.81 15.40% 21.41 7.70% 10.70 0 The initial US13 deterioration and point in the life‐cycle fits current MR&R procedures to be in state 5 in Table 20. Assumption is that it was time for 2” overlay because of the life‐cycle being almost at the middle of expected duration. Therefore “mr&r for normal IS operations” = 22.00 US$ average cost per foot as an agency costs. In the model shown in Figure 44, the “mr&r for normal IS operations” converter is included as a given data because of the other types of maintenance and cost variation per infrastructure condition. Figure 44 shows the overall model for the cost of infrastructure for normal operations. Figure 33 Model for Cost of IS Normal Operations 66
The description for all variables values or equations is shown in Table 25. One special explanation for one variable is needed before presenting the table. The converter “mr&r for normal IS operations” in the model maintain the defined value described earlier, however, because it must integrate the model building the necessary links, the other variables that were used to get its value are connected to it by a dashed connector. Again, the dashed connector works as an “input” to the converter. Also, the value 0 given to the stock ‐ “Infrastructure System Cost for Normal Operations” ‐ enables the model to run and assumes the new value (output value) after the run. Table 25 During Disaster Impacted Lanes and Condition Variables Description Variable Value/Equation de060 length 21722.55 de066 length 2881.99 de068 length 8275.91 de069 length 1083.84 de085 length 11778.11 de509 length 2496.88 de511 length 888.95 de060 cost per foot de060/de060_length (Same for all segments) average IS cost per SUM(de060_cost_per_foot,de066_cost_per_foot,de068_cost_
foot per_foot,de069_cost_per_foot,de085_cost_per_foot,de509_c
ost_per_foot,de511_cost_per_foot)/7 mr&r for normal IS 22*(average_IS_cost_per_mile/average_IS_cost_per_mile)*(cu
operations rrent_IS_condition/current_IS_condition) total IS length SUM(de060_length,de066_length,de068_length,de069_length,
de085_length,de509_length,de511_length) assessing IS resources total_IS_length*mr&r_for_normal_IS_operations cost for normal operations Infrastructure System 0 Cost for Normal Operations total deldot cost assessing_IS_resources_cost_for_normal_operations*deldot_fi
provision nancial_responsibility total fhwa cost assessing_IS_resources_cost_for_normal_operations*fhwa provision total de stakeholders assessing_IS_resources_cost_for_normal_operations*de_stake
cost provisions holders 67
These last three variables in the table were included in the model after looking at the business process for funding infrastructure MR&R activities. One thing is to find out how much it costs, the other is to identify the sources to keep the engine running”. According to Reddick (2007) and practices of the State of Delaware, there is a distribution on the funding participation across Decision Makers for the overall resources defined for projects resulting from disasters occurrence. An example of such distribution is shown in Table 26. Table 26 Financial Sources for IS Recovery Financial Sources Percent (%) FEMA (General fund/existing budget) 70.6 FHWA (Asset seizure funds) 22.2 DelDOT (Reallocate/cut spending) 6.2 DE Stakeholders (Legislative) 1.0 During normal times, the assumption is that FEMA does not participate as a financial source for MR&R activities. In this sense, the table for Financial Sources will have a different distribution, as shown in Table 27. This distribution is the one used for the sector frame model in Figure 34. Table 27 Financial Sources for IS Normal Operations Financial Sources Percent (%) FHWA (planned budget and special funds) 35.0 DelDOT (planned budget) 64.0 DE Stakeholders (Legislative) 1.0 TOTAL 100.0 Because the “DelDOT” variable already carries an equation definition, it is important to assign another “name” to reflect this specific role. The converter “deldot” is, therefore, linked as an input to “deldot financial responsibility”. For the first time the Federal Highway Administration (FHWA) is included in the model, as well as the State of Delaware Stakeholders (e.g. local legislators that can choose priorities to attend their specific communities). Figure 34 shows the “Normal Operations Financial Composition” of agencies and stakeholders that define the use of resources for the infrastructure. 68
Figure 34 Financial Resources Responsibilities per Agency and Stakeholders to Maintain Infrastructure Condition and Performance The variables included in the model in Figure 34 are just “deldot financial responsibility, fhwa, and de stakeholders. The other converter is just to reinforce the idea that the resulting added value reaches 100% of the funding. In the real world it is possible to see the need to adjust such financial responsibility depending on the amount of revenues the government collects, or change in policy, or the infrastructure aging or growing and the revenues not matching the amount of financial resources needed. Table 28 shows the converters values and equation. Table 28 Agencies and Stakeholder Variables Responsible Financial Resources for Normal Operations Variable Value/Equation deldot financial 0.64*deldot responsibility fhwa 0.35 de stakeholders 0.01 financial sources for IS fhwa+de_stakeholders+deldot_financial_responsibility maintenance for normal operations Step_5‐7 Figure 2 summarizes all required actions and calculations for Steps 5‐7 under the flow title “improving system performance”. In fact Steps 5, 6, and 7 can be identified in the CIR‐DSS framework as the relationship among elements of the “Result Presentation System”, “Financial Subsystem”, “Decisions Making Subsystem”, and the “Resilience Management Information System”, in Figure 1. A brief description of what is included in each of these 3 Steps that contributes to the overall activity of “improving system performance” includes • Step_5: consideration of the disaster impact and estimation of resources needed to recover/mitigate damaged infrastructure 69
•
•
Step_6: consideration of decision‐makers objectives and factors that impact or contribute to the infrastructure system recovery/mitigation to enhance the resilience of the system Step_7: revision of the complex‐system problem, constraints, and requirements to improve the resilience of the system. It includes the completion, revision, and/or the adjustment of data and analysis in the model to obtain more realistic results. This also includes identifying different scenarios, and the consideration of the mitigation insights that were initially developed. Therefore, now it is time to define the minimum resources needed for (post‐disaster) recovery to get back to normal operations. This includes restoring the infrastructure to end disruption by fixing damaged infrastructure. The cost for fixing damage infrastructure is in addition to the cost for normal operations. The cost for fixing infrastructure is different to the projects to repair, build, rehabilitate or replace infrastructure. The approach to project options can also vary, and in this research two different approaches are considered: recovery and mitigation focused in improving infrastructure system resilience. Start by considering the new variable needed for all segments – converters for recovery costs. The converters to build the model must be thought out carefully. First it is important to highlight that the following part of the model is not in the initial structure. This part of the model was added after the mitigation part was built. The value for the total disaster damage cost and, therefore, the values for recovery had to be adjusted. These two values were lacking the right connection because no approximation was initially made to capture the extent of the impacted segments (in terms of area), making it impossible to match the damage with the value of damage from the disaster. To assume the impact was over the whole extent of a segment lane increases the overall disaster impact, making current recovery and mitigation values not real and extraordinarily large. This is an easy problem to run into because the data in HAZUS‐MH looks like an aggregation of several real road segments in larger segments as discussed earlier. The details of this part of the model is not described, just the final structure. The adjusted approach to build the correct converters for the model for calculating the cost of recovery and the total value to have the infrastructure back in operation requires the consideration of • all damaged segments according to the assumption of damage lanes made earlier, • all segments values, • the disaster value for the study area, and • the definition and distribution of a disaster value. 70
These values are rearranged and details added based on data in Table 2. The implication is that if a segment was not damaged, it has no damage value, therefore it is 0 (zero). It relates the damage per segment to the overall value of damage shown in Table 8. Table 29 shows the basic organization for looking at the adjusted damage cost per segment. Table 29 Defining More Accurate Damage Cost Per Segment Segments de060 de066 de068 de069 de085 de509 de511 Total Damaged lanes Segment length (feet) Segment value (million) 2 0 0 2 1 0 1 ‐‐‐‐‐‐‐‐
21,722.55
2,881.99
8,275.91
1,083.84
11,778.11
2,496.88
888.95
49,129 32,206.20
2,628.59
7,543.82
987.21
21,534.23
4,555.43
1,623.54
71,079.02
Segment damaged value (million) 32,206.20
0
0
987.21
21,534.23
0
1,623.54
56,351.18
Associated % per damaged segment value 57.15
0
0
1.75
38.22
0
2.88
100
Related disaster value (millions) 67.61
0
0
2.07
45.21
0
3.41
118.29
The column “segment damaged value” was defined to separate damage segments from the ones that had no damage. Its total value was then used to record the relational percent of each segment on the total under the column “associated % per damage segment value”. Thus the column for “related disaster value (millions) was defined by multiplying the percentage damaged by the total damage value. The elements defined in Table 29 are used as new variables in the continuation of the model development. Figure 35 shows the sector‐frame built to define the segments corresponding damage value. It starts by including only the segments value that had damage caused by flooding – not the value for the damage. Then the percentage of total segment value is included to, together the value of “assessing IS damage”, define each segment damage value contribution to the total damage value reported (the total damage value for the case study = “assessing IS damage”). In other words, the mechanism here was to use the total final value, which was given, to find each segment damage value that added to the total. 71
Figure 35 Defining the Real Segments Damage Values The connections among the variables shown in Figure 35 (and in all other model diagrams) are how the model reads the relationship and enables the construction of equations. If a variable is not attached to a piece of the model by a connector, the variable cannot be in an equation. Other types of resources such as building tables or building graphs do not depend exclusively in such ties. Actually, the STELLA software helps to identify which variables are allowed to be used in these other relationships as will be shown later. Table 30 show all values or equations assigned for each converter in the model diagram shown in Figure 35Figure 36. 72
Table 30 Description of Converters Values or Equation for Real Segments Damage Values Variable Value/Equation de060 damaged 32206.20 segment value de066 damaged 0 segment value de068 damaged 0 segment value de069 damaged 987.21 segment value de085 damaged 21534.23 segment value de509 damaged 0 segment value de511 damaged 1623.54 segment value total IS damaged SUM(de060_damaged_segmant_value,de066_damaged_segm
segment value ent_value,de068_damaged_segment_value,de069_damaged_s
egment_value,de085_damaged_segment_value,de509_damag
ed_segment_value,de511_damaged_segment_value) de060 percentage of de060_damaged_segmant_value*100/total_IS_damage_segm
total IS damaged ent_value segment value (Same for all similar variables) de060 correspondent (assessing_IS_damage*de060_percentage_of_total_IS_damag
damage value ed_segment_value)/100 (Same for all similar variables) Now that a more accurate value of damage per segment has been defined, it is possible to move forward on getting the value for recovery and normal operations. The next thing to consider is that in reality, when starting to return infrastructure to the condition for operations, different construction material costs, additional services, inflation, time, and other related issues impose changes to costs. That is why one should consider working with a bigger threshold of funding. The assumption here is that there is an additional 10% increase in recovery project costs (cost adjustment = 0.1). It is important to understand that the value calculated for damage implies the cost of construction should be about the same. Before showing the model sector‐frame for recovery cost added to normal operations cost, it is important to mention that with this damage approach taken there was found no need to identify or calculate the length of damage per segment or per lane in the model. All recovery costs per segment are defined in the model as shown in Figure 36. 73
Figure 36 Model Sector‐Frame for Recovery Cost Adding to Cost of Normal Operations The model works first by placing ghosts of the segments corresponding damage value in a new spot in the models interface screen. Create one (1) converter for cost adjustment and make other copies to place near all other segments corresponding damage value converters. Create converters for all segment recovery cost, and add all the segments recovery costs to get the total. Add this total to the resources needed for normal operations to get the idea of the size of this one time investment needed to get back to normal operations. This helps understand why it is so important to have a “savings” to deal with unexpected extreme events, how difficult it is for some communities to recover (if they do), and gives insights for the recovery time. Table 31 shows the variables and its values or equations matching the model diagram in Figure 36. 74
Table 31 Variable Values or Equations Matching Model Recovery Cost and Operations in Figure 36 Variable Value/Equation de511 recovery cost (de511_correspondent_damage_value*cost_adjustment)+de5
11_correspondent_damage_value (Same for all variables) total lanes recovery de060_recovery_cost+de066_recovery_cost+de068_recovery_
cost cost+de069_recovery_cost+de085_recovery_cost+de509_reco
very_cost+de511_recovery_cost assessing IS recovery total_lanes_recovery_cost+assessing_IS_resources_cost_for_n
cost with operations ormal_operations Infrastructure System 0 Recovery Cost fema recovery cost total_lanes_recovery_cost*fema_recovery_funding estimate deldot recovery cost total_lanes_recovery_cost*deldot_recovery_funding estimate fhwa recovery cost total_lanes_recovery_cost*fhwa_recovery_funding estimate de stakeholder total_lanes_recovery_cost*de_stakeholder_recovery_funding recovery cost estimate It is important to note that “normal conditions” under the policy for recovery, which puts infrastructure back to its original configuration, does not consider increasing demand that such infrastructure may have had through time. This does not really imply “normal conditions” because original design looks at specific traffic volume demand, but conditions prior disaster, may be already in an under‐capacity situation with the presence of congestion. This means such effort may simply minimize the problem, but in a questionable way, in an insufficient and consequently costly way, because it will require new investments later on to improve capacity for better traffic flow conditions. The organizations/agencies converters in the model are a second sequential part that is how to bring resources together to take care of the job. This way, consider the cost for recovery, a post‐disaster condition; plus the need for operations to the level of the pre‐
disaster condition, and the financial responsibility for each financial “source”. The percentage distribution for recovery now has a different provision of cost (check Table 26). This adds to the normal operations cost that is usually in a yearly‐based plan. Figure 37shows the agencies and stakeholders financial participation in funding recovery projects. 75
Figure 37 Agencies Financial Composition to Carry‐On Recovery Projects This part of the model is fairly simple. Again financial sources for damaged IS recovery must try to reach 100% of total investment needed for projects. Table 32 shows the variables’ description and values. Table 32 Variables’ Description for Post‐Disaster Financial Composition Variable Value/Equation financial sources for dedot_recovery_funding+de_stakeholder_recovery_funding+f
damaged IS recovery ema_recovery_funding+fhwa_recovery_funding fema recovery funding fema*0.706 fhwa recovery funding 0.222 deldot recovery 0.062 funding de stakeholder 0.01 recovery funding If this direct, traditional recovery approach is adopted; there is little improvement to the transportation infrastructure system. To capture this improvement, consider the return to operations of the earlier damaged, but now recovered segments. This part of the model is composed by the converters located at the middle of the diagram in Figure 38, linked to the converter “restored IS segments”. This result should be equal the 4 lanes the infrastructure originally had. Note: this part of the model also required revision and adjustments. 76
Figure 38 Closer View of the IS Recovered Condition and Performance Measures Sector‐Frame Note that the connectors coming from a single converter enable the use of this converter in different equations. The first result being looked for is the restored/recovered infrastructure for which the cost was defined in Figure 38. It needs to consider the available lanes per segment, the recovery cost, and the damaged lanes. The recovery cost is used to “fix” the damage lanes, which results are shown in the 77
converter “deXX recovered damaged lanes”. Than the available lanes – the ones that were not damage, is added together the recovered lanes under the converter “deXX final number of lanes”. All segments final number of lanes are put together to get the network aggregate result, which is used to define recovered capacity. The converters for damage lanes and available lanes are also used to define infrastructure condition – at the middle to the left side of the diagram. The calculation for LOS – at the right side of the diagram, takes advantage of the segments final number of lanes. Table 33 describes all variables values and equations for infrastructure recovered condition and performance measures. Table 33 Infrastructure Recovered Condition and Performance Variables Values and Equations Variable Value/Equation de069 recovered de069_damaged_lanes+(de069_recovery_cost‐
damaged lanes de069_recovery_cost) (Same for all segments) de069 final number of available_de069_lanes+de069_recovered_damaged_lanes lanes (Same for all segments) restored IS segments SUM(de066_final_number_of_lanes,de068_final_number_of_l
anes,de069_final_number_of_lanes,de085_final_number_of_l
anes,de509_final_number_of_lanes,de511_final_number_of_l
anes,de60_final_number_of_lanes)/7 recovered carrying restored_IS_segments*passenger_cars_per_lane_per_hour service capacity recovered overall IS (recovered_carrying_service_capacity*normalizing_factor)/760
capacity 0 de069 lanes recovered de069_damaged_lanes*de069_increased_degraded_condition condition (Same for all segments) de069 average ((available_de069_lanes*current_IS_condition)+de069_lanes_r
condition post ecovered_condition)/4 recovery (Same for all segments) average IS recovered SUM(de060_average_condition_post_recovery,de066_average
condition _condition_post_recovery,de068_average_condition_post_rec
overy,de069_average_condition_post_recovery,de085_averag
e_condition_post_recovery,de509_average_condition_post_re
covery,de511_average_condition_post_recovery)/7 de069 recovered LOS (level_of_IS_service*4)/de066_final_number_of_lanes (Same foa all segments) 78
Continue Table 33 overall recovered IS LOS recovered IS flow rate SUM(de060_recovered_LOS,de066_recovered_LOS,de068_rec
overed_LOS,de069_recovered_LOS,de085_recovered_LOS,de5
09_recovered_LOS,de511_recovered_LOS)/7 (overall_recovered_IS_LOS*current_flow_rate)/level_of_IS_ser
vice Going back to the original flow sequence showing infrastructure segments being used and loosing usability, it is time to put back recovered segments into place. This requires knowing the “average IS recovered damaged lanes” shown in Figure 39. Figure 39 Getting the Total Value for Recovered Damaged Lanes The equation for “average IS recovered damaged lanes” is “SUM(de060_recovered_damaged_lanes,de066_recovered_damaged_lanes,de068_reco
vered_damaged_lanes,de069_recovered_damaged_lanes,de085_recovered_damaged_l
anes,de509_recovered_damaged_lanes,de511_recovered_damaged_lanes)/7” This variable connection to the initial flow is shown in Figure 40. The equation for “recovering usability” is “Degraded_Local_Infrastructure_System_Segments+average_IS_recovered_damaged_la
nes” 79
Figure 40 Restoring the Transportation Infrastructure to Its Original Elements Quantity Prior to Disaster This recovery activity in terms of cost, and condition and performance measures opens the opportunity to calculate resilience for the system also. Figure 41 shows the model diagram for capturing resilience for the recovered US‐13 infrastructure system. Figure 41 Resilience of Recovered Infrastructure System The equation for “resilience of recovered IS” is “((1‐recovered_IS_flow_rate) + recovered_overall_IS_capacity+average_IS_recovered_condition)/3” As one can see, disruption is not included in the equation, exactly because this is something not present at this phase of the infrastructure life‐cycle. While up to this point the model did analyses generating values for recovery, the goal is to analyze mitigation as means for better resilience of the infrastructure system when facing more disasters. This means that later on it is important to do a comparison to find out when recovery could be the “optimum solution” to an event given a certain location and the history of events, or when mitigation would be the best way for dealing with frequent events, and up to which frequency such option should be adopted. This type of 80
analysis privileges a financial investment approach instead of a social approach. The big difference is that while the financial approach with recovery looks at the best use of money, the more immediate decision to go with the mitigation approach independent of the event frequency per geographic area can privilege society in terms of really increasing chances to avoid losses such as deaths and injuries. The trade‐off between human lives, and sustainability of human way‐of‐life, which has a financial component that could likely be the result of limited resources invested in recovery or mitigation, where mitigation would create the impedance for other economic development projects is not being analyzed. This additional analysis could really help define if mitigation approach should be the option to be always given priority to recovery. Based on earlier determination of the types of problems occurred with the infrastructure and the degraded condition of specific segments, the problems per segment can be identified as shown in the simplified Table 34 below. Table 34 Simplified Visualization of Damaged Infrastructure Type and Associated Deterioration Segment Length Road Issue de060 de066 de068 de069 de085 de509 de511 10.83
0.88
2.54
0.33
3.62
0.77
0.27
Road failure None None High water Sink hole None Road closed # Impacted Locations/Lanes Associated Deterioration Rate 2
0
0
2
1
0
1
0.7
0
0
0.175
0.523
0
0.35
Recovery in the model took in consideration the impacted road lanes/segment, calculated the cost for each impacted road lanes/segment, and later defined the average cost value for all impacted segments. Mitigation in the model considers the policy for FEMA’s Hazard Mitigation Grant Program. This program provides funding to reduce risk of future damage based on the amount of damage resulting from a specific event in the order of 15% as federal grant assistance that can be used for planning projects for mitigation. Also, FEMA funds up to 75% of the cost of mitigation projects approved (USDHS and National Emergency Response and Rescue Training Center 2005). Recording specified values as discussed earlier, the specific event of June 2006, focusing in the Study‐Area for US‐13, had an impact of US$1,038,000 and (road) infrastructure damage of US$118,293 (which final value is the result including the use of warning system – a mitigation measure). The 15% of infrastructure damage = 17,744, which is approximately 17,750.00. There is no obligation for any Agency access this 15% FEMA 81
Grant. Therefore the use of this policy is not included in the development of the analysis for mitigation projects. The general assumptions used to develop the model for infrastructure mitigation projects are • DelDOT is just interested in the 75% fund for mitigation projects • Recovery cost is the starting value for infrastructure mitigation projects option working with resilience improvement for existing road segments • Stakeholders and FHWA share counterpart funding together DelDOT to match the 25% resource needed to implement mitigation projects • Mitigation strategies are possible to be implemented, considering the STAPLEE criteria defined as a requirement by FEMA (Croope 2009). The mitigation strategy and cost per segments are listed in Table 35. Table 35 Description of Mitigation Strategies and Costs per Project per Segment Segment Length Road Issue # Impacted Locations/ Lanes Associated Deterioration Rate de060 21,722.55
Road failure
2
0.7
de066 de068 de069 2,881.99
8,275.91
1,083.84
None None High water 0
0
2
0
0
0.175
de085 11,778.11
Sink hole 1
0.523
de509 de511 2,496.88
888.95
None Road closed
0
1
0
0.35
Mitigation Strategy Mitigation Cost (assumption)
Reinforce (+ resistance) None None Elevate Reinforce (+ resistance) None Build containing wall with drainage ducts Recovery cost + 20% None
None
Recovery cost + 50% Recovery cost + 20% None
Recovery cost + 30% The approach chosen for mitigation incorporates the recovery process. In other words, instead of just putting the infrastructure back in place according to its original design, this design is proposed with improvements towards improving the overall infrastructure system network resilience. In the model, the cost of a regular recovery project is maintained, and the additional needed investment is added. The important thing to consider is that recovery projects need to be repeated from times to times, but mitigation projects, according to FEMA, are practically permanent. In this sense, why not instead of doing, for example, 4 recovery projects in 25 years (say adds up to US$100,000), why not invest in 1 mitigation project that lasts 25 years (say it costs US$55,000 representing savings of US$45,000 for the same period)? The model developed now follows this logic. Starting by considering that the PCI for the segments can only have its index showing in the maximum a perfect good physical condition, for example, 100% good infrastructure and mitigation improvement that would be increasing good situation cannot be show as 82
130% good. Consider that the level of service also cannot be more than A. The expected result from adopting mitigation measures can be reflected in other condition and performance metrics such as having less disruption and less damage. It is important to observe that FEMA works with two separate grants/funds when it comes to strategies and projects for recovery and mitigation. The mitigation approach for which the model is being developed requires real‐world flexibility of the current FEMA policy’s to either: • give the option for using both grants/funds for improved projects addressing recovery needs and mitigation (principally when including resilience analyses), or • give the option for opting to use or the recovery fund or the mitigation grant. In this sense this approach is an invitation to the Federal Government and principally FEMA start thinking about different ways to do things which may result in more effective and efficient use of limited existing resources. Other mitigation strategies that could be further investigated include • expansion of infrastructure network capacity including an alternative route, adding 2 lanes to existing minor functional roads, similar to a detour route, but improved; • considering the path through Seaford City as not essential for the overall flow of goods and people (City would be evacuated before flooding), therefore this alternative route considering traffic origin and destination would add strong justification for investing in the construction of an alternative route; • calculation of mitigation project cost including “segment length”, “average cost per mile” for adding 2 lanes (make it a 4 lane road as US13), the 15% funding for planning evaluating the need for buying right‐of‐way, and adding another 10% in cost for adopting new technology such as better pavement resistance material and improved design; • considering total project cost (100%) with approved funding, and an unexpected 10% cut of total project funding by FEMA, where DelDOT has to absorb the difference, being forced to find new solutions and partnership . This new scenario represents a new challenge, which model and resulting numbers would be a good exercise and use of the CIR‐DSS framework developed. Focusing in the initial mitigation approach, the initial variables made available for this part of the model are the ghosts for the segment recovery cost. The second group of variables, to be included in the mitigation model, is the variables that add a percentage of costs to the recovery costs, as defined in Table 35. These two variables combined results in the mitigation cost per each segment that added all together gives the overall cost for the mitigation project. 83
It is important to mention that while the focus given in this model is for capturing network resilience, recognizing the role of resilience engineering when defining structural improvements for the infrastructure. Because this level of detail is not the objective of this research, the model does not include any modeling for specific infrastructure segment construction projects. Mitigation projects are funded by FEMA. Policy and funding mechanisms for mitigation are separate from recovery. All agencies and stakeholders involved in the recovery discussion are included in the discussion for mitigation. Figure 42 shows the model for mitigation. Figure 42 Mitigation Sector‐Frame Model Financial resources for mitigation are shown in Table 36. For example, there are FHWA resources that can be used for enhancing infrastructure conditions, as shown in the table as “asset seizure funds”. These funds illustrate the possibility of integration of different funding sources to enable working projects such as mitigation. 84
Table 36 Financial Sources for IS Mitigation Financial Sources Percent FEMA (General fund/existing budget) 75% FHWA (Asset seizure funds) 20% DelDOT (Reallocate/cut spending) 4% DE Stakeholders (Legislative) 1.0% Table 37 shows all converters values or equations for the piece of the model shown in Figure 42. Table 37 Mitigation Model Converters Values or Equations Descriptions Variable Value/Equation de511 added cost for 0.30 (value assigned in the Table 35 under mitigation cost) mitigation de509 added cost for 0 (value assigned in the Table 35 under mitigation cost) mitigation de085 added cost for 0.20 (value assigned in the Table 35under mitigation cost) mitigation de069 added cost for 0.50 (value assigned in the Table 35under mitigation cost) mitigation de068 added cost for 0 (value assigned in the Table 35under mitigation cost) mitigation de066 added cost for 0 (value assigned in the Table 35 under mitigation cost) mitigation de060 added cost for 0.20 (value assigned in the Table 35 under mitigation cost) mitigation de511 mitigation cost (de511_added_cost_for_mitigation*de511_recovery_cost)+de
511_recovery_cost (Same for all similar variables) total IS mitigation cost SUM(de060_mitigation_cost,de066_mitigation_cost,de068_mi
tigation_cost,de069_mitigation_cost,de085_mitigation_cost,d
e509_mitigation_cost,de511_mitigation_cost) fema mitigation grant 0.75 (value in Table 36) deldot mitigaton 0.04 (value in Table 36) match fhwa mitigation match 0.20 (value in Table 36) stakeholders 0.01 (value in Table 36) mitigation match fema mitigation cost fema_mitigation_grant*total_IS_mitigation_cost support deldot mitigation 1 deldot_mitigation_match*total_IS_mitigation_cost cost 85
Continue Table 37 fhwa mitigation 1 cost fhwa_mitigation_match*total_IS_mitigation_cost stakeholders stakeholders_mitigation_match*total_IS_mitigation_cost mitigation match mitigation required deldot_mitigation_match+fema_mitigation_grant+fhwa_mitig
resources ation_match+stakeholders_mitigation_match At this point there is a recovery value and a mitigation value. How to tell which is best to adopt requires a little bit more information. Start by looking at the recovery policy from FEMA and the real improvement is in terms of the infrastructure physical condition in part of its segments structure. One could say it does little or nothing for reducing the overall infrastructure vulnerability. Making a rough estimation for reducing vulnerability, start by considering original IS condition and the resulting condition after recovery, and then apply the percentage to decrease vulnerability. Figure 43shows the calculation for expected decrease on vulnerability. Figure 43 Modeling Expected Decrease on Vulnerability The two new variables defined to capture the decrease on vulnerability issue are shown in Table 38. Table 38 Calculating Recovery Result on Reducing Infrastructure Vulnerability Variable Value/Equation improved IS recovered (average_IS_recovered_condition‐current_IS_condition condition expected decreased Infrastructure_System_Vulnerability‐
vulnerability (Infrastructure_System_Vulnerability*improved_IS_recovered_
condition/100) The reduced infrastructure system vulnerability as a result of mitigation requires estimating the post‐mitigation infrastructure condition and performance. Start by 86
making available the converters for “available deXX lanes”, the “deXX damaged lanes”, and the “deXX mitigation cost”. Define the “deXX mitigated lanes”, and then define the “deXX final total lanes”. Add all segments values to get a result for the “mitigated IS segments”. Define capacity. This initial part of the model is shown in Figure 44in the top part of the diagram. Figure 44 Model for Infrastructure Mitigation Condition and Performance Measures To get the estimated improvement in the infrastructure physical condition, one must start by considering the initial IS condition prior to the disaster. Calculate expected values for “deXX improved condition”, calculate “deXX lanes mitigation condition”. Define the “deXX average condition post‐mitigation”, define the overall IS infrastructure mitigated condition. Table 39 describes all converters values or equations. 87
Table 39 Mitigation Sector‐Frame Condition and Performance Variables Description ‐ I Variable Value/Equation de511 final total lanes available_de511_lanes+de511_mitigated_lanes (Same for all similar variables) de511 mitigated lanes de511_damaged_lanes+(de511_mitigation_cost‐
de511_mitigation_cost) (Same for all similar variables) de511 lanes mitigated de511_damaged_lanes*de511_improved_condition condition (Same for all similar variables) de511 improved de511_added_cost_for_mitigation+de511_lanes_recovered_c
condition* ondition (Same for all similar variables) de511 average condition post (Same for all similar variables) mitigation mitigated IS segments SUM(de060_final_total_lanes,de066_final_total_lanes,de068_f
inal_total_lanes,de069_final_total_lanes,de085_final_total_lan
es,de509_final_total_lanes,de511_final_total_lanes)/7 average IS mitigated SUM(de060_average_condition_post_mitigation,de066_avera
condition ge_condition_post_mitigation,de068_average_condition_post
_mitigation,de069_average_condition_post_mitigation,de085_
average_condition_post_mitigation,de509_average_condition
_post_mitigation,de511_average_condition_post_mitigation)/
7 mitigated carrying mitigated_IS_segments*passenger_cars_per_lane_per_hour service capacity mitigated overall IS (mitigated_carrying_service_capacity*normalizing_factor)/760
capacity 0 * Assumption: the segment “added cost for mitigation” is the same value for the physical condition solution improvement. The calculation for LOS for the mitigation project is shown in Figure 45. Although this part of the model and the flow rate modeling are both included under the same mitigation sector‐frame, they are being shown as separate because the diagram got too big to be shown all at once. An interesting observation is that although infrastructure physical condition and performance modeling is needed for the different phases the infrastructure system goes through, the calculation differs reflecting the different strategies; although the models each have s similar structure. 88
Figure 45 LOS and Flow Rate for Mitigation The new variables used in Figure 45are described in Table 40. Table 40 Mitigation Sector‐Frame Condition and Performance Variables Description ‐ II Variable Value/Equation de511 mitigated LOS (level_of_IS_service*4)/de511_final_total_lanes (Same for all similar variables) overall mitigated IS SUM(de060_mitigated_LOS,de066_mitigated_LOS,de068_miti
LOS gated_LOS,de069_mitigated_LOS,de085_mitigated_LOS,de509
_mitigated_LOS,de511_mitigated_LOS)/7 mitigated IS flow rate (overall_mitigated_IS_LOS*recovered_IS_flow_rate)/level_of_I
S_service 89
Modeling Resilience for Mitigation Now use all the key variables to get resilience measure for mitigation. Figure 46shows the model for resilience for mitigated infrastructure. Figure 46 Model of Resilience for Mitigated Infrastructure The equation for “resilience of mitigated IS” is “((1‐mitigated_IS_flow_rate) + mitigated_overall_IS_capacity+average_IS_mitigated_condition)/3” A rough estimation for reducing vulnerability, in the same way it was done for recovery, is developed by considering the original IS condition and the post mitigation resulting condition, and then apply the percentage to decrease the infrastructure system vulnerability. The comparison between the original vulnerability value, to the recovery value, and the mitigation value, helps show which option benefits the most when the objective is to decrease the chances for major damage and disruption. The initial total value for the infrastructure vulnerability for US‐13 is $71,079,020. Figure 47 shows the decreased vulnerability when adopting mitigation measures for the infrastructure. Figure 47 Expected Decreased Infrastructure Vulnerability Using Mitigation Measures 90
Table 41 shows the description for the new variables in Figure 47. Table 41 Description of Variables Used for Capturing Decreased Vulnerability Because of Mitigation Variable Value/Equation improved IS mitigated (average_IS_recovered_condition*100/current_IS_condition)‐
condition 100 expected decreased Infrastructure_System_Vulnerability‐
vulnerability 2 (Infrastructure_System_Vulnerability*improved_IS_mitigated_
condition/100) A basic comparison between recovery and mitigation strategies in terms of the infrastructure system vulnerability is shown in Figure 48. Figure 48 Comparison Between Recovery and Mitigation Strategies to Decrease System Vulnerability The equations used to compare these options are described in Table 42. Table 42 Recovery and Mitigation Comparison Variables Description for Decrease on Vulnerability Variable Value/Equation difference 1 for Infrastructure_System_Vulnerability‐
improving system for expected_decreased_vulnerability less vulnerability (result of simulation = 5661) difference 2 for Infrastructure_System_Vulnerability‐
improving system for expected_decreased_vulnerability_2 less vulnerability (result of simulation = 128782) 91
Cost Benefit Analysis Finally one gets to move towards the cost‐benefit analysis for the recovery and mitigation approaches. According to FEMA, “benefits are simply avoided damages and losses”, such as benefits to the community and not just to FEMA or the federal government (FEMA 2007a). A summary of these possible avoided damages is shown in Table 43. Table 43 Categories of Avoided Damages Buildings, Contents, Landscaping, Site Avoided Physical Damages Contamination, Vehicles, Equipment, and Infrastructure Displacement costs for temporary quarters Loss of: rental income, business income, Avoided Loss‐of‐Function Costs wages Disruption time for residents Loss of public services Economic impact of loss of utility services Economic impact of road/bridge closures Avoided Casualties Deaths, Injuries, Illnesses Emergency operations center costs Evacuation or rescue costs Avoided Emergency Management Security costs Costs Temporary protective measure costs Debris removal and cleanup costs Other management costs Basically a benefit‐cost analysis looks at damages and losses twice: first, before mitigation (the as‐is situation) and second, after mitigation. It also considers • probabilities of various levels of natural hazard events and damages, • mitigation project useful lifetime, and • discount rate related to the time value of money The economic loss of function impacts to roads and bridges take into consideration their closures. Impacts of closures are: functional downtime, delay or detour time, daily traffic load, and economic value per person per hour. This leads to disruption, the cost of which may be significant and add significantly to the total benefits. Looking at reducing vulnerability through hazard mitigation projects for roads and bridges, means, to work with the possibility for “reducing physical damages in future disasters”, and to reduce the negative impacts that their closures may have on the affected communities. That is, the primarily purpose for mitigation projects for roads and bridges are to keep the roads and bridges open during disaster events. According to 92
FEMA – (FEMA 2007a), the Main Benefits Mitigation Projects for Roads and Bridges include the categories shown in Table 44 Table 44 Mitigation Projects Categories of Benefits for Roads and Bridges Categories of Damages/Benefits Notes for Mitigation Projects 1 Physical Damages Consider vulnerability according to flooding. 2a Loss‐of‐Function Impacts (e.g. Not applicable (road and bridge cannot be displacement costs) displaced to temporary other locations). 2b Loss‐of‐Function Impacts Other (e.g. Road/bridge closures ‐ generally the largest loss of service ‐ economic impact) category of benefits. 3 Casualties Generally not significant for flood 4 Emergency Management Costs “Generally not considered; road/bridge mitigation projects neglects impact on a communities overall emergency management costs.” Source: FEMA (2007a). FEMA only considers “acquisition/relocation” mitigation projects to be 100% effective in avoiding future damages and losses. Assumption For this case study, however, mitigation for roads is assumed to be 100% effective (FEMA 2006). This assumption is made just to simplify building the model, given that the intended purpose is to demonstrate the feasibility of the application of the CIR‐DSS Framework. The vulnerability of roads and bridges to flood damage varies depending on the specific materials and designs, their age, and their condition. In this sense, facility‐specific estimates consider historical damage data and professional judgment. The historical overall impact for similar events were earlier defined and shown in HAZUS‐MH Working Paper (Croope, 2009). The analysis is repeated here for completeness. The 2006 event is the one for which analyses are being done, included in Figure 49. 93
Figure 49 Federal Disasters Damage Graph – Sussex Source: Croope (2009). Considering the adjusted values for the case study area, and adjusting the other related values accordingly, this helps start building the model diagram for evaluating the cost‐benefit of mitigation and recovery projects. Figure 49 is better understood when looking at Table 45. Table 45 Historical Events Data for Current case Study Area Events 1 2 3 4 Event Number 126 1017 1205 1654 Year 1962 1994 1998 2006 Impact (US$ Million) ~21,391,000
~8,908,000
~3,721,000
~3,000,000
Adjusted Case Study Area Impact* ~7,402,000
~3,082,000
~1,287,000
~1,038,000
Adjusted Case Study Damage Assessment** ~ 845,000 ~ 351,000
~ 147,000 ~ 119,000 Source: based on Croope (2009). * Adjusted value was calculated as 34.60% as Table 10 in Croope (2009) ** Adjusted value for damage assessment assumed same proportion for previous years in the order of 11.40%. The model for capturing the financial result of continuous mitigation (including preparedness) strategies and infrastructure improvements is shown in the “Disaster Historical Frequency, Impacts and Savings” sector‐frame in Figure 50. It is important to understand that this simple piece of the model does not evaluate the effectiveness of any policy, neither has listed actions or improvement projects to infrastructure which could use to in the learning process of best practices and become insight for future mitigation strategies. 94
Figure 50 Model for Disasters Historical Frequency, Impacts and Savings Only disaster number 4 has an additional variable to account for the impact on infrastructure. This is because disaster number 4 is the event in which the analyses are being developed. This one variable also provides the link to the overall model developed so far. Table 46 describes variables values and equations. Table 46 Disaster Historical Events Frequency, Impacts and Savings Model Variables Description Variable Value/Equation disaster 1 year 1962*disaster_event_1 disaster event 1 1 disaster 1 impact 7401450*disaster_event_1 value disaster 2 year 1994*disaster_event_2 disaster event 2 1 disaster 2 impact 3082150*disaster_event_2 value disaster 3 year 1998*disaster_event_3 disaster event 3 1 disaster 3 impact 1287500*disaster_event_3 value disaster 4 year 2006*disaster_event_4 disaster event 4 1 95
Continue Table 46 disaster 4 impact impact_on_IS*disaster_event_4 value disaster 1 to 2 savings disaster_1_impact_value‐disaster_2_impact_value disaster 2 to 3 savings disaster_2_impact_value‐disaster_3_impact_value disaster 3 to 4 savings disaster_3_impact_value‐disaster_4_impact_value percentage saved 100‐((disaster_2_impact_value*100)/disaster_1_impact_value)
between disaster 1 (run result is = ~58%) and 2 percentage saved 100‐((disaster_3_impact_value*100)/disaster_2_impact_value)
between disaster 2 (run result is = ~58%) and 3 percentage saved 100‐((disaster_4_impact_value*100)/disaster_3_impact_value)
between disaster 3 (run result is = ~19%) and 4 The functional downtime for road and bridge closures, considers first an estimate for damaged road or bridge number of days for repair and reopening to normal traffic flow. Then it considers an estimate while bridge/road is closed for the average delay or detour time for motorists – the primary economic impact: loss of time. The functional downtime was actually calculated in the beginning of the development of the model. If one includes the disaster onset plus the recovery time, the “functional downtime” = “disaster expanded time impact” (a total of 241 days). The loss of time by using detour to damage roads is defined by FEMA in the direct road/bridge closure economic impact. The direct economic impacts of road or bridge closures can be estimated in five steps – originally identified as 4 steps by FEMA (2007c): 1. Estimate the functional downtime (repair time to restore normal traffic flow = 241 days) 2. Calculate average daily traffic count for the closed road/bridge. The average traffic count for the degraded infrastructure resulted in a LOS C, calculated previously in the model. In the case study, considering the original LOS, and thus the degraded LOS, this difference represents the delay. In the model, original LOS is defined by the variable “level of IS service”, which represents the traffic volume for a LOS B = 760. The flow rate associated with this is 40%. The “passenger car per lane per hour” is 1900. The degraded LOS is represented by the variable “shortterm post disaster level of service” = 1050, with associated “shortterm” flow rate = 55%. This “shortterm” LOS is categorized as LOS C. The difference between each LOS is shown in Figure 51. 96
Figure 51 Difference between Original and Short Term Infrastructure Level of Service The equation for average traffic count delay is “shortterm_post_disaster_level_of_service‐level_of_IS_service (simulation result = 290 passenger car per lane per hour)” 3. Estimate the average delay/detour time because of road/bridge closure. The total delay/detour time in the model is obtained as shown in Figure 52. It starts by considering 1 hour = 760 pc/l = 4 lanes = 55 mph, therefore 1 hour = 1050 pc/l = 3.1 lanes = ? 97
Figure 52 Calculation of Delay Time and Cost The model defines first the total capacity of roads under normal conditions, and the degraded capacity caused by the flood. It considers the speed of roads during normal condition, and the consequent decreased speed. The decreased speed is used to calculate impact on travel time. The second part of this sector‐frame calculates the cost of delay based on the time delay. Table 47 shows the variables values and equations. 98
Table 47 Variables description for Delay/Detour Time in the Delay Caused by Disaster Sector‐Frame Variable Value/Equation total capacity for road level_of_IS_service*total_IS_number_of_lanes normal condition total capacity for road available_average_IS_segments_short_term*shortterm_post_
degraded condition disaster_level_of_service road normal condition 55 (mph) speed decreased speed (total_capacity_for_road_normal_condition*road_normal_con
dition_speed)/total_capacity_for_road_degraded_condition hour in minutes 60 travel time because of (road_normal_condition_speed*hour_in_minutes)/decreased_
degraded road speed condition total delay travel_time_because_of_degraded_road_condition‐
hour_in_minutes one day hours 24 one day total delay total_delay*one_day_hours*average_traffic_count_delay*avai
lable_average_IS_segments_short_term total delay for the one_day_total_delay*disaster_expanded_time_impact disaster total disaster delay in (total_delay_for_the_disaster/one_day_hours)/hour_in_minut
days es average dollar per 32.23 vehicle hour delay (value given by FEMA)* total disaster delay average_dollar_per_vehicle_hour_delay*total_disaster_delay_
cost in_days * Source: based on FEMA (2007c). 4. Fit extra 290 cars (1050 pc/l – 760 pc/l) in degraded roads, the average delay time adds in 5.1 minutes more (65 minutes). To get the total time delay for the disaster, multiply the extra 5 minutes to the 241 days roads were not recovered. 5. Define a typical or average financial value per person/hour or per vehicle/hour of delay/detour. The benefit‐cost analysis of road/bridge closures is $32.23 per vehicle hour of delay. With these results, the FEMA suggested approach for “benefit‐cost analysis of hazard mitigation projects for roads and bridges” is implemented, although not using the whole Benefit‐Cost Analysis Tool (BCA) developed by FEMA (2007a). The suggested five steps require information for condition of the road/bridge, both before and after mitigation. 99
This is a function of the severity of disaster. Table 48 shows these values for easy identification, earlier developed in the model. Table 48 Summary of the 5 Steps to Define the Direct Economic Impacts of Road or Bridge Closures Order Steps Before Disaster $ After Disaster $ 1 Estimate physical damages to 0.00* ~118,200** road/bridges in dollar 2 Estimate repair time to restore 0* 241 days normal traffic flow 3 Estimate average delay/detour time 0* (total disaster delay in days) 18,647 days 4 Obtain average daily traffic count 760 1050 (290 c/l/h for road/bridge more) 5 Calculate economic impacts of loss (total disaster delay of function of road/bridge with the 0.00 cost) 601,006.00 above data and the value of lost travel time ($32.23). * Consider value zero (0) for regular maintenance needs and related time, and existing traffic flow condition. ** Value of damage (not impact). Using a benefit‐cost analysis, the cost‐effectiveness of projects can be determined. In other words, it shows if the financial investment in mitigation project today (cost) will result in future reduced damages (benefits), enough to justify spending the money. This means (FEMA 2007b) “benefit > cost = cost‐effective project” Also, cost‐effectiveness calculation compares the cost of a project to the value of after mitigation prevented damages. The benefits dollar‐value greater than the costs of funding the project means the project is cost‐effective (1.0 or greater value result). The equation “Benefits/Costs= benefit‐cost ratio (BCR)” is used to show if the project cost exceeds the project benefit and by how much. The total benefits are the sum of the Potential Future Avoided Damages and the additional benefits (specified in the FEMA BCA module), as “(Potential Future Avoided Damages + Additional benefits) / Total Project Cost = BCR”. The project “benefits” compared to the “costs” of a project is the benefit‐cost ratio. Demonstrating that the proposed mitigation measure protects up to the proposed level of protection is given. The flooding under analyses is that for which the mitigation project is being developed, and each solution shown already has percentages for improvement. The benefit‐cost analysis demonstrates if the current level of protection 100
associated with each type of improvement is worth. Table 49 shows a summary of data values or equations that can be used to doing the BCA. Table 49 Variables Values and Assumptions for Calculating the BCA of Mitigation Projects Segments Damaged lanes Road Issue Mitigation Strategy Mitigation Cost (assumption) de060 2 0 0 2 Reinforce (+ resistance) None
None
Elevate
Recovery cost + 20% de066 de068 de069 de085 1 Road failure None None High water Sink hole Reinforce (+ resistance) None
Build containing wall with drainage ducts ‐‐‐‐‐‐‐‐‐‐‐‐‐‐
Recovery cost + 20% de509 de511 0 1 None Road closed Total ‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐ Recovery Cost ($) Recovery cost + 50% ~3,400 ~59,700 0
Recovery cost + 30% ~4,900 ~157,200
total IS mitigation cost
Related disaster value (thousands) 57.15 ~67,600
0
0
~2,300
de069 recovery cost 0 0 1.75 0
0
~2,070
49,725
38.22 ~45,200
0
~3,700
de511 recovery cost 0 2.88 0
~3,400
~130,100
100 ~118,200 ~74,400
~89,200 de060 recovery cost 0
0
Associated % per damaged segment value de085 recovery cost
total lanes recovery cost
The Benefits of flood mitigation projects can be shown by elevation data, such as elevating the road to 0.5 foot above the elevation of a 100‐year flood. Other mitigation strategies are shown in Table 49. The Loss of Function (services value not being provided due to damage = $601,006.00) and the Functional Downtime (time of effect of loss of function = 241 days) require reasonable, defensible, and documented approach. The current case study presented started based on real documentation – pictures and a report produced by DelDOT‐TMC. The model also is a clear demonstration of the use of standard values defined by FEMA – a reasonable and defensible approach as well. The proposed level of flood protection for the current mitigation project being analyzed is for roads up to a 100‐year flood event on Seaford Area. To verify the effectiveness of the mitigation project, the value of the mitigation project is included in the project application, which takes advantage of the recovery initial fund. In the FEMA “Yellow Book” digital version Table 7.2 (FEMA 2007b), there is the indication of parameters and data sources for hazard mitigation projects for roads and bridges, based on flood depth or flood frequency. Table 50 shows the parameters and data sources for hazard mitigation projects for roads and bridges. 101
Table 50 Benefit‐Cost Analysis Guide for Hazard Mitigation Projects for Roads and Bridges Parameter 1. Physical damages to road or bridge 2. Repair time to restore normal traffic flow 3. Average delay/detour time 4. Average daily vehicle count 5. Economic impact of road or bridge closure Data Sources Historical data and knowledgeable individuals’ professional judgment about roads and bridges. For the case study, historical data is used. Historical data and professional judgment/estimates from local traffic officials. For the case study, historical data is used. Historical data or estimates from local traffic officials. For the case study, estimates are used. Historical data or estimates from local traffic officials. For the case study, estimates are used. $32.23 per vehicle hour of delay or detour. This value is included in the model being developed to analyze the 2006 Flooding in Seaford‐DE. Source: FEMA (2007b). In fact, all this data must be used in the benefit‐cost analysis to show the intended savings once a mitigation project is implemented as the example in Figure 53shows. Figure 53 Benefit‐Cost Analysis Savings Diagram Example Source: FEMA (2007b). The likelihood for damage and cost‐effective projects expectancy classification is shown in Table 51. 102
Table 51 FEMA BCA Analysis ‐ Project Cost‐Effective Likelihood Likelihood/ Very High High Moderate Low Attribute Frequency of Flood/Level of Damage Project Cost Project Benefits Criticality (impact or loss of function) 10‐year Flood Very high damage Low relative to damages 10‐25‐year Flood 25‐50‐year Flood
High damage Limited damage Moderately‐low relative to damages Close to cost of damages in frequent floods Very high High
Moderate
Very high, broad damages to community High damages to key facility; community Moderate loss of certain functions limited impact 50‐100‐year Flood Minor damage High relative to damages in frequent floods Low Little or no loss of functions; minor impact Source: FEMA (2007b). The use of benefit‐cost analysis for hazard mitigation projects by FEMA is to (FEMA 2007a) • Meet statutory and regulatory requirement eligibility requirement (Stafford Act and in 44 CFR for projects cost‐effectiveness), for FEMA funding under the HMGP or Flood Mitigation Assistance (FMA) program. • Determine if it is worth doing a mitigation project. • Provide a common basis used to compare and prioritize mitigation projects, helping ensure limited mitigation funds result in future greatest reduction possible of damages and losses. • Demonstrate that mitigation project works. The benefit‐cost analysis helps to sell the concept of mitigation and “convince individuals and communities that mitigation investments are in their own self interest”. It also helps demonstrate that the program and its actions are fiscally sound. A Mitigation project’s useful lifetime is an estimate of the time (in years) that a project will continue to be effective to prevent or reduce future disasters damages and losses. For the road infrastructure, the project lifetime determined by FEMA is to be 50‐years on average, producing benefits each year for 50 years. This project useful lifetime is translated as “the period over which the benefits are accumulated and then discounted to net present value” (FEMA 2007a). In other words, the net present value is the value of money today that is going to be received in the future, or the amount of money needed today in order to have a specified amount of money sometime in the future. Recognizing the time‐value of money requires setting a discount rate. For example, $10 today buys $10 worth of goods and services, but $10 that you have to wait 20 years to get it won’t buy the same amount of goods and services that time. This means that “if you have $13.14 today, after 30 years at 7% interest (OMB Circular A‐94), you will have 103
$100” (FEMA 2007a). The $100 net present value received in 30 years is only $13.14. Another way to understand this is if one considers the net present value of $1.00 per year for 30 years with a discount rate 0 would result in just $30.00. The calculation of the Net Present Value (NPV) considering these elements is shown in Table 52. Table 52 Elements Considered for the Calculation of Recovery and Mitigation Net Present Value Scenario 1
$
Scenario 2
$
Difference
$
total
lanes
recovery cost
road
infrastructure
project lifetime
standard time for
IS lifecycle
discount rate
maintenance
cost
rehabilitation
cost (= ½ of the
cost
of
infrastructure)
~130,100
50 years (2
times more
than standard
IS lifecycle)
25 years
7%
gradual
71,079,000 / 2
=
~35539500
total IS mitigation
cost (including
recovery)
road
infrastructure
project lifetime
~157,200
standard time for
IS lifecycle
discount rate
maintenance
cost
rehabilitation
cost
25 years
50 years
7%
gradual
71,079,020 / 2
=
~35539500
additional cost to
do mitigation from
recovery
road
infrastructure
project lifetime
157,206 –
130,123 =
~27,000
standard time for
IS lifecycle
discount rate
maintenance cost
25 years
rehabilitation
cost
50 years
7%
gradual
71,079,000 / 2
=
~35539500
Observation: Because maintenance will happen for the infrastructure and the benefits from mitigation is not investigated in terms of reducing speed for deterioration, this value is not included in the calculation for the project cost Net Present Value. Also, because FEMA defines 50 years for the infrastructure project lifetime, the standard time for IS lifecycle assumes the role for helping identify in which part of the cycle the road may be, and does not participate in the NPV calculation. Rehabilitation cost is assumed to be half of replacement cost given by FEMA dataset in HAZUS‐MH. The difference in value to do mitigation may not be a problem when considering the frequency of disaster and the overall result for NPV. Using this data in a excel spreadsheet as well as the probability that a 100‐year storm is a 1 event in 100 years. Adding events of same magnitude (increasing frequency) to the same span of 100 years, 1 event per year up to ten (10) 100‐year storm events, helps to identify the optimum time for choosing to adopt a recovery or a mitigation strategy. Table 53 shows a summary of the calculations in excel to get the NPV and the difference between financial values used for recovery and mitigation. 104
Table 53 Recovery and Mitigation NPV Calculations in Excel If the probability of a 100‐year storm was really just 1:100, mitigation project costs would not justify the use of the money. However, in the case of 2 or more events happening in the period of 100 years, mitigation already represents savings for the future. The basic equations used in this table for all columns are “B0”= total lanes recovery cost “B1” =B$3*C$1 “B2” =B$3*$C$1 “line below # 50, under Column B” =+B3+NPV(0.07,B4:B53) “line below # 50, under Column C” =+C3+NPV(0.07,C4:C53) The difference between recovery and mitigation NPV values is shown in Figure 54. One can see that as frequency of events grows, mitigation project grows also in savings (benefits). 105
Figure 54 Difference Between Recovery and Mitigation NPV per Frequency of Events The calculation for the first event is set up a little different than for the following events in Excel just to make the result is coming from the same equation logic. Table 54 shows the smooth change in the equations for the first and second event. Table 54 Equations Format for the NPV Difference between Recovery and Mitigation Projects Probability of Event Calculation of Difference in NPV 0.01 ‐C54+B54 0.02 D54‐E54 (and subsequent sequential probability of events) Looking at the historical data, it is able to see that between 2006 and 1962, a 44 year interval, there were 4 similar flooding events in Sussex County. Checking the table calculated in excel, this means savings could be as much as ~$45,000.00. This initial analysis using Excel helps to understand what and how to include this piece of analysis in the model in STELLA. It is interesting to see that this is a one part of the development of the model that really relied on parallel analysis to serve as a guide for developing the new piece of the model in STELLA. To include these calculations in the model, the net present value for the overall mitigation project for the road infrastructure in Seaford is calculated based upon the frequency of past events, including the current event, for a 100 year period. In this case, only the registered events described earlier are being considered (4 events), although there are more records of many other disasters that reached the threshold for being under a Federal Disaster Declaration caused by different hazard types. This disaster historical data in the model starts being shown in the framework “Recovery NPV” in Figure 55. 106
Figure 55 NPV for Recovery Project In other words, because there was record of 4 events, this data is being used to define the probability that is included in the model. Also, the calculations executed in Excel generated specific values used as inputs for building this part of the model, and building the graph shown in Figure 56. Table 55 shows variables values or equations for the recovery project NPV. Table 55 Recovery Projects NPV Variable Value/Equation probability of 100year (SUM(disaster_event_1,disaster_event_2,disaster_event_3,dis
storm events aster_event_4))/100 partial value of events total_lanes_recovery_cost*probability_of_100year_storm_eve
nts rate 0.07 changing recovery NPV(partial_value_of_events,rate) NPV (this is a built in financial function in STELLA) recovery NPV total_lanes_recovery_cost+changing_recovery_NPV The initial model for NPV only gets properly adjusted to give the expected result after adding the “to graphical function” for the converter “changing recovery NPV”. The NPV works as a “time element”. The graph plotted for capturing and properly adjusting the model is shown in Figure 56. The graph is manually drawn, therefore it is important to have the calculations in Excel – the graph adopts the “drawn” behavior. 107
Figure 56 Graphical Function for Recovery Project NPV The mitigation strategy, as explained before, assumes that problem is solved for future events with similar characteristics. This means there is no value associated with the probability of future damage occurrence of similar events. Figure 57shows the mitigation approach and the calculation of mitigation project NPV. Note that all the values from running the model match earlier calculations in the spreadsheet in Excel. Figure 57 Mitigation Project NPV and Graphical Function Table 56 shows the variables values or equations for the mitigation project NPV model. 108
Table 56 Mitigation Project NPV Variables Description Variable Value/Equation partial value of events total_IS_mitigation_cost*(probability_of_100year_storm_even
for mitigation ts/probability_of_100year_storm_events) changing mitigation NPV(partial_value_of_events_for_mitigation,rate) NPV mitigation NPV partial_value_of_events_for_mitigation+changing_mitigation_
NPV The savings resulting from investing in the mitigation project are shown in Figure 58. Figure 58 Savings Resulting from Investment in Mitigation Rather than Recovery The equation for “result from mitigation investment” is “recovery_NPV ‐ mitigation_NPV” One could examine the benefits yet in other ways, such as the Present Value Coefficient (PVC), which is identified as the “benefits in the benefit‐cost analysis” (FEMA 2007a). This PVC also included in the FEMA BCA methodology and the other calculation for damages for before and after mitigation, which helps to highlight the relevance for mitigation, was not thoroughly investigated in terms of the interface with HAZUS‐MH nor was any record found. Both approaches are currently accepted by FEMA. The objective of the development of this model is to integrate the results obtained from working with different software systems to demonstrate how one can approach and work with the proposed CIR‐DSS Framework. The only additional part to address the projects benefits at this point is to remember to observe the calculation for inflation adjustment, an element needed to bring accuracy to these investments evaluations. 109
For the present case study, values in the model were already adjusted according to the publication of the Public Entity Risk Institute (PERI) for the main disasters declared in Sussex County shown in Table 57(PERI Unknown). Therefore this calculation is not included in the current model. This inflation adjustment is a “must do” for an effective modeling for mitigation project evaluation. This item must be identified prior to running this model. Table 57 Main Disasters Declared in Sussex County Number County Date Type (FEMA)
Disaster Desc Statewide Cost Constant 2006 $ President 126 Sussex, Delaware 03/09/1962 F – flood Severe Storms, High Tides & Flooding 207 Sussex, Delaware 08/18/1965 D – drought Water Shortage 933 Sussex, Delaware 02/06/1992 F – flood Severe Coastal
Storm 4,676,664 GHWBush 976 Sussex, Delaware 01/15/1993 C – coastal storm Severe Coastal
Storm & Flooding 1,727,522 GHWBush 1017 Sussex, Delaware 03/16/1994 W – severe storm Severe Ice Storms
and Flooding 8,907,958 Clinton 1082 Sussex, Delaware 01/12/1996 S – snow Blizzard of 96 (Severe Snow Storm) 4,092,779 Clinton 1205 Sussex, Delaware W – severe 02/13/1998 storm Severe Winter
Storms, High Winds, Rain and Flooding 3,721,100 Clinton 1494 Sussex, Delaware 09/20/2003 H – hurricane Hurricane Isabel 21,391,487 Kennedy 0 Johnson 7,000,888 GWBush Source: modified from PERI. Search Result. All About Presidential Disaster Declarations (PERI Unknown). Table 58 summarizes the evaluation for investing in mitigation. For the current infrastructure case study maintenance following mitigation is assumed not to add significant costs to current operations costs, therefore it is not included in this analysis. The variables including infrastructure damage value and loss of function compose the benefits with mitigation. Note that the FEMA BCA methodology considers the value of maintenance in its analysis. 110
Table 58 Summary of Benefits for Mitigation Projects Net Present Value of Future Benefits • No damage to mitigated infrastructure (assuming small part of road segment mitigation is possible instead of the whole segment length) • No Loss of Function ‐ services value not being provided due to damage (total disaster delay cost) Total: Mitigation Project Costs Benefit‐Cost Ratio (Net Present Value of Future Benefits ÷ Project Costs) $118,293.25 $601,006.00 $719,299.25 $157,206 4.6 Source: based on FEMA (2007a). Building the mitigation project benefit calculation in STELLA, the new piece of the model is shown in Figure 59 (left) and the calculation for getting the final “Benefit Cost Ratio” discussed earlier is shown in Figure 59(right). Figure 59 Benefits of Mitigation Project and Final BCR Table 59 shows mitigation project benefits and benefit‐cost‐ratio. 111
Table 59 Mitigation Project Benefit and Benefit‐Cost Ratio Variables Description Variable Value/Equation partial value of LOF (total_disaster_delay_cost+assessing_IS_damage)*(probability
_of_100year_storm_events/probability_of_100year_storm_ev
ents) changing LOF NPV NPV(partial_value_of_LOF,rate) Loss of function NPV partial_value_of_LOF+changing_LOF_NPV mitigation benefitcost loss_of_function_NPV/total_IS_mitigation_cost ratio The graph for “changing LOF NPV” for the mitigation project follows the same pattern of no future losses. Figure 60shows the graph for the mitigation changing LOF NPV. Figure 60 Graphical Function for Mitigation Loss of Function NPV Table 60 summarizes the evaluation for investing in recovery, considering improved road condition. One can assume improved road condition has a beneficial impact in the same proportion of minimizing damages and disruptions due to disasters. 112
Table 60 Summary of Benefits for Recovery Projects Net Present Value of Future Benefits • Possible repetition of damage to mitigated infrastructure (no certainty of extent of damage possible to be bigger and/or smaller, despite physical conditions improvement) • Possible repetition of Loss of Function ‐ services value not being provided due to damage (total disaster delay cost) • Improved road condition ( 1% ‐ average IS recovered condition) Total: Recovery Project Costs (total lanes recovery cost) Benefit‐Cost Ratio (Net Present Value of Future Benefits ÷ Project Costs) ($118,293.25) ($601,006.00) 1% x(118,293.25 + 601,006.00) ($23,042.00) $130,123.00 ‐0.18 Note that this shows there is really no benefit, but investment is actually a loss of money. In STELLA, the recovery project benefit calculation, is shown in Figure 61(left) and the calculation for getting the final “Recovery BCR” discussed earlier is shown in Figure 61(right). Figure 61 Benefits of Recovery Project and Final BCR 113
Table 61 shows recovery project benefits and benefit‐cost‐ratio. Table 61 Recovery Project Benefit and Benefit‐Cost Ratio Variables Description Variable Value/Equation improved road average_IS_recovered_condition‐current_IS_condition condition partial recovery ((assessing_IS_damage+total_disaster_delay_cost)*improved_r
value of LOF oad_condition)‐
(assessing_IS_damage+total_disaster_delay_cost)*probability_
of_100year_storm_events changing recovery NPV(partial_recovery_value_of_LOF,rate) LOF NPV loss of function for partial_recovery_value_of_LOF+changing_recovery_LOF_NPV recovery NPV recovery benefitcost loss_of_function_for_recovery_NPV/total_lanes_recovery_cost ratio The graph for “changing recovery LOF NPV” for the recovery project shows an increasing loss of resources with the continuous need for new recovery projects as time goes by. Figure 62 shows the graph for the mitigation changing LOF NPV. Figure 62 Graphical Function for Recovery Loss of Function NPV 114
The benefit‐cost analysis looking at the benefits considering disasters and its current historical frequency (note recorded data used in the simulation does not add to 100‐
years events) is summarized in Table 62: Table 62 Benefit‐Cost Analysis Comparison Summary for Recovery and Mitigation Projects SUMMARY
Project
Benefits (avoided
Cost-Effective
BCR
(all NPV)
Cost
damages and
losses)
201954
-23042
NO (-23042 < 130123)
-0.18
Recovery
157206
719299
YES (719299 > 157206 )
4.6
Mitigation
What can be observed is that, in percentage, 78.15% of the total extended damages and losses arise from the economic impact of the road closure. Only 21.85% of the total damages and losses are due to repair costs. In the benefit‐cost analysis for mitigation projects for roads (and bridges), it is important to count the benefits of avoiding road closures to avoid grossly undercount the benefits. To understand how flexible the model is to include new situations, assume these initial results are not completely satisfactory to stakeholders. Stakeholders are making the case that adjustment in mitigation project cost did not consider the need to adjust road project at the beginning and end of project extension through adding a transitional length for the project that was adding elevation to the segment. Example: 100 feet, 50 each side of the road segment getting it 1 foot above flooding depth. Therefore, it is important to add another 30% in cost for the segment having addressed this elevation solution. Add this new parameter to the model in STELLA. Figure 63 shows the additional variable included in the model, and the result obtained after running the model. 115
Figure 63 Adjusted Mitigation Project Cost Check to see if increased values did not make mitigation project fail cost‐effectiveness parameters. If one had chosen to do such addition in a copy of the mitigation option sector‐frame, it would be simple as using the copy function (right click), and paste. STELLA automatically would call it “Mitigation Option 2”, and would rename all new variables adding the number “2” to them. As shown in Figure 63, the new variable for increasing cost for the projects for elevating road partial segments is adding cost to the project for the segment de069. Simple adjustments or corrections to variables are only straight forward if chosen variables are not participating in other calculations in other steps all the way to the benefit‐cost analysis in the model. Major changes that imply rebuilding connections may disrupt the logic of the model, therefore the STELLA software does not allow it. For example when making ghost copies of the variables that were the sums of variables. Such variables cannot be copied as a ghost and redo calculations. The connectors do not attach to the variable to redo the same original calculation. This unnecessary redundancy is avoided in STELLA. Overall results are summarized with this new addition in Table 63. As one can see, the overall different in mitigation projects cost did not impact results in a significant fashion. 116
Table 63 Summary of Recovery and Adjusted Mitigation Benefits, Effectiveness and BCR SUMMARY Project Cost Benefits (avoided
Cost-Effectiveness
BCR
damages and
(all NPV)
losses)
Recovery
201954
-23042
NO (-23042 < 130123)
-0.18
Mitigation
157206
719299
YES (719299 >
4.6
157206)
Net Present Value of Future Benefits • No damage to mitigated infrastructure (assuming small part of road segment mitigation is possible instead of the whole segment length) • No Loss of Function ‐ services value not being provided due to damage (total disaster delay cost) Total:
Mitigation
(adjusted)
157890
719299
$118,293 $601,006 $719,299
4.6
YES (719299 >
157890)
Net Present Value of Future Benefits • No damage to mitigated infrastructure (assuming small part of road segment mitigation is possible instead of the whole segment length) • No Loss of Function ‐ services value not being provided due to damage (total disaster delay cost) Total:
$118,293 $601,006 $719,299
A brief description of the FEMA BCA tool highlights the calculations and parameters that can be later incorporated into the model, in terms of integrating results and methodology to produce an even more in depth analysis. The FEMA BCA analyses for infrastructure are usually done in what is called Very Limited Data module. This is one of 3 types of BCA analysis alternatives accepted by FEMA (2007b). • Very Limited Data (VLD) • Limited Data, and • Full Data. The VLD uses a lower bound analysis, which is appropriate for flood, wind or earthquake hazard mitigation projects for non‐building facilities (e.g. culverts, roads, bridges, and utility systems). If the analyses focus in two or more events with similar frequencies, it is suggested to use an average damage amount per event and an average frequency to input data in the VLD module. This lower bound analysis is used for cases where available data are complete or not, using only one or two key pieces of data. The other 2 types of analysis according to the data treatment are (FEMA 2007b): • Upper bound – used only to confirm project is not cost‐effective, using in addition to the earlier calculations the “professional judgment to estimate about input data that give the highest reasonable benefits that can be expected from a mitigation project”, and 117
•
Best estimate – used when the data of a project are complete or almost complete – a more accurate approach. This method can be used to rank priority projects in a competitive environment. An example of a report generated using the FEMA BCA LM is shown in Figure 64(FEMA 2007b). Figure 64 FEMA BCA‐LM for Riverine Flood Report Example Source: FEMA (2007b). 118
The biggest advantage of this analysis report is the presentation of many fields accounting for different flood frequencies and the related number of floods, damages before and after mitigation, and the amount of savings all at once. Such report format can be imaged to show results from running the model in STELLA if desired. At this point, the model development starts focusing on alternative solutions to fix and improve damaged infrastructure, one can see the preparation of information for supporting decisions, starting by considering different 100‐year events probability, simulating more and less events and their impact on infrastructure, and the comparisons among recovery and mitigation alternatives are leveraged. Step_8 In Step_8, the evaluation of alternative project approaches looks at the most effective critical infrastructure system resilience considering both recovery and mitigation strategies. The evaluation and communication of results show the benefits, effectiveness, consequence, methodology, and complementary approaches to integration of different types of data. It includes the presentation of options, alternatives and defines actions to improve the resilience of critical infrastructure systems. While the CIR‐DSS Framework includes the “presentation of results of analyses” as a broad concept (implying the presentation of the overall system dynamics and analyses results), the model developed in STELLA offers 2model building phases for Step_8: 1. Final analyses generating the results Stakeholders would likely be looking for such as costs and benefits, trade‐off of projects in terms of long‐term investments, and more); and 2. The overall organization and presentation of the process for building the model, keys concepts and equations, and the disposition of a “presentation” toll able to run different scenarios. This includes a demonstration of the model’s robustness through a sensitivity analysis. The current working paper is focused on the first phase of Step_8. Continuing, thinking about the occurrence of hazard events, assume the 100‐year event happens repeatedly. Looking at projections for recovery and for mitigation is important to start by determining the extension of damage compared to the whole road including all segments for this case study. Also include the mitigation project useful time that has to be 50 years according to FEMA’s parameters (FEMA 2007c). Figure 65shows the model capturing this relationship. 119
Figure 65 Capturing Extent of Damage Considering Overall US‐13 Case Study Extension The equations for these 2 new converters are shown in Table 64. Table 64 Variables Description for Capturing Damage Impact in the Overall US‐13 Variable Value/Equation percentage IS ~1.7 damaged with a 100year event mitigation project standard_time_for_IS_lifecycle*2 useful time Back to the discussion of recovery and mitigation benefit‐cost analysis; assume the 100‐
year event happen a number of times. Define the new event probabilities as 1% and 8% for recovery and for mitigation, and thus calculate NPV for them. The calculation for projects considering event probability as 1% is shown in Figure 66. Figure 66 Recovery and Mitigation NPV for 1% Probability of 100‐year Event 120
Table 65 shows the variables values or equations included in the model for Recovery and Mitigation NPV considering 1% probability of 100‐year storm events. Table 65 Recovery and Mitigation NPV for 1% Probability of 100‐year Event Variables Description Variable Value/Equation probability of 100year 0.01 storm events 2 partial value of events total_lanes_recovery_cost*probability_of_100year_storm_eve
2 nts_2 (=1301) rate 2 0.07 changing recovery NPV(partial_value_of_events_2,rate_2) (=17958) NPV 2 recovery NPV 2 total_lanes_recovery_cost+changing_recovery_NPV_2 (=148081) partial value of events 157890 for mitigation 2 changing mitigation 0 NPV 2 mitigation NPV 2 157890 Note that the equations used for this new approach are the same as the first similar model shown in Table 55and Table 56. Basically what changes is the value for probability, impacting on the overall results. Therefore results are the only information attached to the variables shown from now on. Figure 67 shows the graph for the converter “changing recovery NPV 2” shown in Figure 66, which to be accurate depends on those earlier calculations in Excel. 121
Figure 67 Graph for Changing Recovery NPV 2 Now the calculation for projects benefit considering event probability as 1% is shown in Figure 68. 122
Figure 68 Recovery and Mitigation Benefit NPV for 1% Probability of 100‐year Event Table 66 shows the variables values or equations included in the model for Recovery and Mitigation Benefit NPV considering 1% probability of 100‐year storm events. Table 66 Recovery and Mitigation Benefit NPV for 1% Probability of 100‐year Event Variables Description Variable Value/Equation improved road 0.007964 condition 2 partial recovery value ‐1464 of LOF 2 changing recovery LOF 1 NPV 2 loss of function for ‐1463 recovery NPV 2 partial value of LOF 719299 changing LOF NPV 2 0 loss of function NPV 2 719299 Now the calculation for projects considering event probability as 8% is shown in Figure 69. 123
Figure 69 Recovery and Mitigation NPV for 8% Probability of 100‐year Event Table 67 shows the variables values or equations included in the model for Recovery and Mitigation NPV considering 8% probability of 100‐year storm events. Table 67 Recovery and Mitigation NPV for 8% Probability of 100‐year Event Variables Description Variable Value/Equation probability of 100year 0.08 storm events 3 partial value of events 10410 3 rate 3 0.07 changing recovery 143664 NPV 3 recovery NPV 3 273786 partial value of events 157890 for mitigation 3 changing mitigation 0 NPV 3 mitigation NPV 3 157890 The calculation for projects benefit considering event probability as 8% is shown in Figure 70. 124
Figure 70 Recovery and Mitigation Benefit NPV for 8% Probability of 100‐year Event Table 68 shows the variables values or equations included in the model for Recovery and Mitigation Benefit NPV considering 8% probability of 100‐year storm events. Table 68 Recovery and Mitigation Benefit NPV for 8% Probability of 100‐year Event Variables Description Variable Value/Equation improved road 0.007964 condition 3 partial recovery value ‐51815 of LOF 3 changing recovery LOF 1 NPV 3 loss of function for ‐51814 recovery NPV 3 partial value of LOF 3 719299 changing LOF NPV 3 0 loss of function NPV 3 719299 Calculate the BCR for Recovery and Mitigation projects for 1% and 8% probability of 100‐year storm events. Figure 71shows Recovery and Mitigation BCR for 1% probability of 100‐year storm event. Simulation results were ‐0.0112455 for “recovery benefitcost ratio 2”, and 4.6 for “mitigation benefitcost ratio 2”. 125
Figure 71 Recovery and Mitigation BCR for 1% Probability of 100‐year Storm Event Figure 72shows Recovery and Mitigation BCR for 8% probability of 100‐year storm event. Simulation results were ‐0.40 for “recovery benefitcost ratio 3”, and 4.6 for “mitigation benefitcost ratio 3”. Figure 72 Recovery and Mitigation BCR for 8% Probability of 100‐year Storm Event The savings resulting from investing in the mitigation projects for 1% and 8% probability of 100‐year storm events are shown in Figure 73. Simulation results were ‐9809 for “result from mitigation investment 2” and 115896 for “result from mitigation investment 3”. Figure 73 Savings from Investing in Mitigation Projects for 1% and 8% Probability of 100‐year Storm Events Moving towards calculating new resilience measures assuming the case of new disaster; start by considering the proportional size of this disaster impact on current case study 126
infrastructure. The US 13 total value of segments = ~7,107,900 = 100%; and IS damage value = ~118,293 = 1.7%, modeled as shown in Figure 74. Figure 74 Damaged Segments Participation in Relation to the Overall Infrastructure Extension The equation for the variable “percentage of IS damage considering all IS” is “(assessing_IS_damage*100/cost_of_IS)/100” The result obtained when running the model means this type of damage, considering the location, is very small compared to the overall US13 totals. Even though the damage result is small in this comparison, the financial implication of an increasing number of disasters analyzed under the methodology for benefit‐cost analysis reinforces the option for mitigation. This because in the long run it represents savings that, otherwise, if just working with recovery, it would mean to deal with an ongoing and thus large loss of resources, due to cumulative need for redoing construction that gets damaged with every new similar event. Benefits coming from recovery to the infrastructure physical condition do not reflect in any reasonable infrastructure improvement, also little affecting the overall resilience of system. Recovery is somewhat effective only for the present and only to put back in place “the minimum condition for traffic flow and to stop bleeding the economy”; and for the case of truly rare and not frequent events. Investigating a little further, there is yet to occur other 60 disasters in different locations with same cost impact to the whole infrastructure be completely mitigated including the resilience of system improvement factor to the 100‐year storm event. The adoption of mitigation for the total transportation infrastructure extent in the case study, even without doing any mathematical calculation, is very unlikely. This because unless the objective is to build transportation infrastructure with longer life‐cycles and better materials making the need for maintenance smaller, looking at vulnerability will define just certain special areas and transportation segments that need mitigation. This 127
definitely excludes transportation segments with low vulnerability from the list that needs improvement. The calculation of frequency of events to improve the whole case study transportation infrastructure extent is included in the model through the variable “number of times current disaster fits in US13 IS”; which equation is “cost_of_IS/assessing_IS_damage” Looking at a complementary process of how much of the infrastructure was not included in mitigation projects, this gives the percentage of infrastructure that will most likely be the focus of attention in the case of future events. Figure 75shows the model for obtaining the “percentage of IS not mitigated”. Figure 75 Extension of Infrastructure Not Included in Current Mitigation Projects Table 69 shows the equation for the variables in the assessment of transportation infrastructure not being mitigated. Table 69 Variables Description for Transportation Infrastructure Extension not Under Mitigation Variable Value/Equation infrastructure not cost_of_IS‐assessing_IS_damage mitigated percentage of IS not ((infrastructure_not_mitigated*percentage_of_IS_damage_co
mitigated nsidering_all_IS)/assessing_IS_damage) The overall result for US‐13 system resilience post‐disaster, therefore, needs to consider infrastructure improved condition by mitigation projects, and the original resilience value for the rest of the extent of US‐13. Running the model shown in Figure 76, the value resultant is 0.76841 (~0.77); and the equation for “system resilience for US13 IS” is 128
“((resilience_for_normal_IS_operations*percentage_of_IS_not_mitigated)+(resilience_o
f_mitigated_IS*percentage_of_IS_damage_considering_all_IS))” Figure 76 US‐13 Post‐Disaster System Resilience Examining the progress in system resilience for other similar impact events helps understand how the value of resilience of system changes per event. Figure 77shows the modeling for another 3 sequential events. Figure 77 Capturing Resilience for Sequential 2nd, 3rd and 4th Disasters Table 70 shows the equations for each event calculation for resilience of system improvement. Table 70 Variables Equations for Resilience of Systems Improvement per Event Variable Value/Equation resilience of system (resilience_for_normal_IS_operations*(percentage_of_IS_not_
improvement with 2nd mitigated‐
event percentage_of_IS_damage_considering_all_IS))+(resilience_of
_mitigated_IS*(2*percentage_of_IS_damage_considering_all_I
S)) [running model result = 0.76941; ~ 0.77] 129
Continue Table 70 resilience of system improvement with 3rd event resilience of system improvement with 4th event (resilience_for_normal_IS_operations*(percentage_of_IS_not_
mitigated‐
(2*percentage_of_IS_damage_considering_all_IS))+(resilience
_of_mitigated_IS*(3*percentage_of_IS_damage_considering_
all_IS))) [running model result = 0.77041 ~ 0.77] (resilience_for_normal_IS_operations*(percentage_of_IS_not_
mitigated‐
(3*percentage_of_IS_damage_considering_all_IS)))+(resilience
_of_mitigated_IS*(4*percentage_of_IS_damage_considering_
all_IS))) [running model result = 0.77141 ~ 0.77] The increment difference in resilience is shown in Figure 78 for the sequential events. Figure 78 Increasing Resilience of Systems Adopting Mitigation for Damaged Infrastructure in Future Sequential Events Table 71 shows the equations for each resilience value increment following new disasters, when adopting mitigation strategies. Table 71 Resilience Values Increment with Successive Mitigation Projects Taking Place per Event Variable Value/Equation improving resilience system_resilience_for_US13_IS/resilience_of_system_improve
rate per disaster ment_with_2nd_event [result running the model = 0.99870 ~ 1.00] improving resilience resilience_of_system_improvement_with_2nd_event/resilienc
rate between disaster e_of_system_improvement_with_3rd_event 2 and 3 [result running the model = 0.99870 ~ 1.00] improving resilience resilience_of_system_improvement_with_3rd_event/resilienc
rate between disaster e_of_system_improvement_with_4th_event 3 and 4 [result running the model = 0.99870 ~ 1.00] Considering US‐13 design in the case study, the best value one could expect to reach with current resilience improvement for the whole infrastructure is a maximum of 0.83 130
or 83%. This because the aspects of physical condition, connectivity, mobility, uncertainties, and other condition‐performance and safety measures make it difficult (probably more like “impossible”) to reach 100% resiliency. Considering mitigation focused in resilience is adopted for all 4 sequential disasters, the overall US‐13 infrastructure system resilience can be expected to be only ~ 0.77. This because 4 similar events do not get even close to half of the number of disasters (60 total events in different locations) that would slowly bring the wished resilience to the overall network. Figure 79shows how the overall model for capturing resilience was drawn. Figure 79 Calculating System Resilience Improvement Considering 4 Sequential Similar Disasters The equation for the “overall system growing resilience” is “system_resilience_for_US13_IS+(resilience_of_system_improvement_with_2nd_event‐
system_resilience_for_US13_IS)+(resilience_of_system_improvement_with_3rd_event‐
resilience_of_system_improvement_with_2nd_event)+(resilience_of_system_improvem
ent_with_4th_event‐resilience_of_system_improvement_with_3rd_event)” The graph that shows the pattern for system increasing resilience is shown in Figure 80. One can see that the maximum value for resilience is 0.83, and the total number of events goes from 1 to 4. Each value obtained for resilience for sequential events has a small increment that can be seen in the dialog box at the upper right side, just below “overall system growing resilience”. 131
Figure 80 Graph for Capturing Changes in Growing Infrastructure Resilience The question now is what would a graph for capturing different phases of resilience of system look like when looking close to all stages US‐13 went through, from normal conditions, to disrupted, damaged, recovered and mitigated? Figure 81 shows the model for capturing Resilience of System change during the event of June 2006. Figure 81 Model for Capturing Change of Resilience of System throughout the June 2006 Event It is important to observe that recovery and mitigation approaches are both included in this part of the model to help understand the difference that each approach brings to the network. In fact, the proposal here is to take advantage of recovery, but work principally with mitigation. In the case of the approach to work directly with mitigation being accepted, the recovery piece would be excluded of the present part of the model, 132
affecting the shape of the graph showing such change in resilience though time. The equation considering the model as shown in Figure 81, for the variable “resilience change through time” is “resilience_for_normal_IS_operations‐(resilience_for_normal_IS_operations‐
resilience_during_disaster)+(resilience_after_disaster‐
resilience_during_disaster)+(resilience_of_recovered_IS‐
resilience_after_disaster)+(resilience_of_mitigated_IS‐resilience_of_recovered_IS)” The graph shown in Figure 82 shows in more detail what happened to the infrastructure system during that event. Again, if recovery was removed from the model at this point, the final line would go from 3.00 (resilience for normal IS operations + resil…) to 5.00. This meaning the 0.770 (resilience change through time) would not be in the graph. Figure 82 Graph for Resilience Change Through Time The number of future (similar) disasters is unknown, although there is a certain historical trend that makes it expected from times to times. Assuming there is another disaster; one can factor it in as shown with this last part of the model considering sequential disasters, and assume resilience of system will grow with similar pattern. It is important to consider that this pattern will probably vary through time because infrastructure deteriorates through time, and disaster carries much uncertainty (e.g. type, scale, location, and more). Therefore, the overall results one would likely summarize for Stakeholders are • the different results when analyzing alternative projects considering different event probabilities as shown in Table 72, 133
•
the improved system resilience between recovery and mitigation project options as shown in Figure 81, and • the different costs of projects in terms of present value to help understand what can be expected in terms of reducing impact versus project choice (which is shown in the working paper Developing the Model’s Interface in STELLA.) Table 72 Difference of Project Costs Considering Different Event Probabilities 134
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