2016 International Conference on Mechanics Design, Manufacturing and Automation (MDM 2016)
ISBN: 978-1-60595-354-0
Simulation Management of Industrial Projects Based on the
Calculated Coupling: The Case for Anchorage Temperature Field
with Passenger Rope-bridge in Mengshan-Tianmeng
Shao-Hui PENG1,2,a,*, Kui WANG3,b, Nan-Qi HU4,c
1School
of Management and Economics, Beijing Institute of Technology, Beijing, 100081, PR
China
2Shandong
3Shandong
4School
Commercial Group Co., Ltd., Jinan, 250000, PR China
Institute of Commerce and Technology, Jinan, 250000, PR China
of Civil Engineering, Shandong University, Jinan, 250061, PR China
[email protected], [email protected], [email protected]
*Corresponding author
Keywords: Anchorage simulation, Numerical simulation, Temperature field, Stress field,
Crack.
Abstract. This paper carries out numerical simulation analysis on temperature field of
massive concrete anchorage; integrate the control of thermal analysis differential equations
and integrating heat-conduction differential equations of thermodynamics. According to
actual of Wanghailou anchorage and Yuhuangding anchorage, determine reasonably the
relevant parameters and construction conditions and launch the numerical simulation of the
subparagraph layering and pouring. According to variations in temperature and stress
distribution in Anchorage pouring process, develop a program of mass concrete pouring, and
simulation results are compared with the results of traditional norms. Research for large
volume of hydration heat and crack analysis is of great guiding significance.
Introduction
Simulation is one of the common methods of enterprise project management, Through
analysis of engineering materials, information or changes the system state using the
mathematical equation of expression conceptualization description, Through computer
simulation. In recent years, with the rapid development of computer technology, Simulation
accuracy and precision, Simulation of engineering is also more consistent with the actual
situation, such as Shin and Hak Chul studied thermal changes and contraction on
characteristics of concrete at early age, prepared considering the effect of these factors was a
more realistic simulation of engineering programs.
Wilson Professor at the University of California for the United States Army Corps of
engineers developed the DOT-DICE program(Stage construction of massive concrete
structure of two-dimensional temperature field finite element simulation program)and
successful applicate to Dvorchak dam temperature field calculation in the year 1968 [1,2];
1985 United States Army Corps of engineers Tatro and Schrader in the United States was
published in the journal of the society for the concrete results of one-dimension finite element
analysis of temperature field; 1988 Elgaaly study theory of beams and slabs of concrete
structure temperature gradient and test it, and influence the structure parameter calculation
formulas are derived [3,4]. 1994 Emborg and Bemander conducted a number of experiments
about the concrete temperature stress at the early-age and temperature cracks, and in
theoretical calculation model take into account conduction of early-age concrete temperature,
temperature exchange and factors such as the reinforcement of concrete[5]; During
1997-2001, European Union countries discussed early stage hardening, stress field
measurement method of distribution and field measurement for high performance concrete,
presented a set of suitable design and construction control of concrete crack in early expert
system[6,7,8,9].
Thus, domestic and foreign experts and scholars as well as engineers and technicians on
concrete structure temperature field and stress issues are of the greatest importance. But how
can be better simulate actual working conditions, in order to guide the practical engineering;
still is a hot research point in this area.
The paper develop project of scenic spot based on Mengshan-Tianmeng passenger
rope-bridge as an example, based on coupling algorithm to simulation and modeling the
industrial projects. Numerical simulation on temperature field simulation under different
working conditions, the paper analyze of thermal stress of mass concrete and their
geographical distribution, make staged placement programs based on results and finally
achieve the objective of effectively preventing cracks.
Temperature Stress Coupling Calculation Simulation Method
Temperature stress means that when the temperature field T has been obtained, the heat
stress inside the object of each part can obtain through stress-strain relationship of materials:
firstly, the initial strain can be calculated by the hot deformation, then, we deduce the thermal
equivalent node load on the unit from the initial, and the nodal displacement caused by the hot
deformation, finally, the heat stress can be solved. If the structure is also under other loads, we
can also set up simultaneous equations together with other loads, and solve the coupled stress
including the heat stress. For the three dimensional problems, the functional expression of
solving the heat stress is:
  0   D  
      
R

2

T
T
T
    D  0       f  d R      R d r

D
(1)
T
In this formula, a is the coefficient of thermal expansion of materials, 0 is the initial
 0  is
the temperature strain, T is the value of the elastic
 D is the elastic matrix related with the unit
body’s present temperature at any point,
material.
Aforementioned loads array contains the equivalent temperature load caused by the
temperature strain, therefore, it is different from the general finite element solving equations
which does not include the temperature strain, and we need to make the solve domain R finite
element discrete, finally, we get:
temperature of the structure,
P 0  =  P 0 
e
e
    B   D  0  dR
T
e
R
(2)
P 
 B is the element
In this formula,  0 is the load item caused by the temperature strain,
strain matrix.
From the above equation, in addition to increasing the temperature load item expressed in
the form of initial strain, structure thermal stress problem and stress problem without thermal
loading is exactly the same.
Assuming the one-dimensional equivalent conduction equation is:
T

T
 k  2  T0  TW 
 0
t
t
t
(3)
In this formula, k is the concrete one-way thermal conductivity, and its unit is KJ/(m*h* ),
 is the function which is related to thermal conductivity and time.
From the above equation, the manifestation of the temperature change caused by concrete
surface heat is the same as the temperature change caused by no surface insulation and
interior heat absorbing heat. Therefore, make the heat change into the category of the
adiabatic temperature rise, and the heat change caused by heat exchange between the concrete
surface and the outside world. So we change the above equation as follows:
T
   0   
 k  2T  T0  TW 

t
t
t
(4)
Three-dimensional temperature field calculation of concrete structures has more space
corresponding relation than one-dimensional temperature field, its equivalent conduction
equation is:
c
T   T    T    T 
  kx
q
   kz
   ky
  
t   x    y    z 
(5)
In this formula, kx、ky、kz are the heat transfer coefficients along the three directions
respectively, and their unit are KJ/(m*h* ), q is the heat built up (the amount of heat per
unit volume and per unit time of the object), and it can reflect concrete chemical reaction heat,
and its unit is kg/(m3*h).
In the homogeneous and isotropic material, the thermal conductivities in all directions are
equal, scilicet: kx=ky=kz. The comparison of the formula (4) and (5) shows that, simply
substituting thermal conductivity according to k   , and through editing the user subroutine,
and make the hydration heat generation rate as follows:

q  c

t
(6)
In practical applications, adopt a common ABAQUS program, and make a unity of thermal
analysis control differential equation and heat transfer differential equation in
thermodynamics. Then, give a certain boundary conditions, and use temperaturedisplacement coupling analysis method to calculate the temperature field of mass concrete.
Finally, apply the load of the corresponding moment based on the results, and calculate the
distribution of the stress field.
Simulation Model
Project Profile
Mengshan-tianmeng tourist area is located in the northeast of Fei county in Linyi city of
Shandong province, and its planning area is 240 square kilometers. In Mengshan-tianmeng
tourist area, two scenic spots called Wanghailou and Yuhuangding are separated by valleys,
and design as the twin towers and single span suspension bridge with a main span 420m. The
volume of concrete in the rope bridge is huge, particularly anchorage part. During
construction period, hydration heat caused by concrete pouring will have a huge impact on the
bridge quality, and topographic and geologic conditions of the mountain are complex. And
during construction period, key technologies, such as temperature field, thermal stress
simulation and crack control, are significant for ensuring construction quality of the
anchorage and safety control.
According to the characteristics of the project, model on the massive concrete anchorage
structure using solid element with ABAQUS program, and the unit type is eight-node
hexahedral elements thermal coupling (C3D8T). The anchorage model units of Yuhuangding
are 34468 in total, and that of Wanghailou are 39900.
Condition Design Simulation
The anchorage consists of the massive concrete, and it should be layered pouring. In order
to determine the reasonable value of the stratification, we select several different stratification
conditions, and set up finite element model respectively to analog the case of concrete layered
pouring and calculate its temperature field.
Yuhuangding Anchorage. The total height of Yuhuangding Anchorage is about 16m. We
layer evenly according to the thickness direction and take four different placement programs
to simulate. The case of layered pouring of each condition is shown in Table 1.
Table 1. The condition of Yuhuangding Anchorage.
Hierarchy
number
The thickness of each
layer of pouring (m)
The interval of each
layer of pouring (day)
Condition 1
6
2.67
4
Condition 2
12
1.33
4
Condition 3
18
0.89
4
Condition 4
24
0.67
4
The maximum stress value of each condition is shown in Table 2.
Table 2. The stress value of each condition.
Condition
Condition 1
Condition 2
Condition 3
Condition 4
The maximum stress in the
process of pouring (MPa)
14.12
3.98
1.65
1.00
Based on the temperature of casting concrete, the temperature rise of the concrete pouring
is not more than 50Ԩ. According to the results, the maximum temperature of the concrete
pouring in condition 3 is 66.96Ԩ, and that in condition 4 is 57.95Ԩ, and the initial
temperature of casting concrete is 20Ԩ, so the temperature rise can meet regulatory
requirements. But the maximum temperature stress in condition 3 is 1.65MPa, and it is too
large for the concrete during construction period. The maximum tensile stress value of stress
field in Condition 4 has dropped to 9.993×105Pa, and it can meet the requirements of the
tensile strength of the concrete. So we adopt the pouring scheme of 24 layers (Condition 4).
We take the average value of the temperature in each condition and summarize (Table 3),
and then we can obtain the maximum temperature varies with the changes of the layer
numbers.
Table 3. The stratified temperature value.
The layer
numbers
6
12
18
24
The average temperature (Ԩ)
102.22
65.70
53.69
47.69
Wanghailou Anchorage. Wanghailou anchorage is smaller, and its height is 12.5m. We
layer evenly according to the thickness direction and take five different placement programs
to simulate. We set up finite element model respectively and calculate its temperature field.
The maximum stress value of each condition is shown in Table 4.
Table 4. The stress value of each condition.
Condition
Condition 5
Condition 6
Condition 7
Condition 8
Condition 9
The maximum stress in the process of
pouring (MPa)
4.68
3.45
2.60
1.83
0.71
The maximum temperature of the concrete pouring in condition 7 is 60.30Ԩ, and the
maximum temperature of the concrete pouring in condition 8 is 56.26Ԩ, and the maximum
temperature of the concrete pouring in condition 9 is 51.36Ԩ, and the initial temperature of
casting concrete is 20Ԩ, so the temperature rise can meet regulatory requirements. But the
maximum temperature stress in condition 7 is 2.60MPa, and the maximum temperature stress
in condition 8 is 1.83MPa, it may produce the temperature cracking during construction
period. The maximum tensile stress value of stress field in Condition 9 is 0.71MPa, and it can
meet the requirements of the tensile strength of the concrete. So we think the construction in
this layered approach is safe.
We take the average value of the temperature in each condition and summarize (Table 5),
and then we can obtain the maximum temperature varies with the changes of the layer
numbers.
Table 5. The stratified temperature value.
The layer numbers
6
9
12
15
18
The average temperature(Ԩ)
87.97
64.36
56.05
50.85
46.70
Segmented pouring. To illustrate the influence degree of segmented pouring on
temperature field, taking Yuhuangding anchorage for example, each layer is divided into two
sections for casting on the basic of the working condition of every layer, and we set up a step
analysis, establish a model, and then analyze the temperature field for each casting section,
respectively. The different layered and segmented working conditions are shown in table 6.
Table 6. The working conditions of segmented pouring.
Condition 10
Condition 11
Condition 12
Condition 13
layered and segmented conditions
Six layers, each layer is divided into two sections for casting
Twelve layers, each layer is divided into two sections for casting
Eighteen layers, each layer is divided into two sections for casting
Twenty-four layers, each layer is divided into two sections for casting
Take the average temperature in each condition as a summary, and compare it with the
temperature value which is not segmented. The obtained data are shown in table 7, and the
stress contrasts are shown in table 8.
Table 7. The comparison of temperature when segmented or not segmented.
Layered number
6
12
18
24
The highest temperature in the process of casting (Ԩ)
Segmented
Not segmented
98.67
102.22
55.91
65.70
52.65
53.69
46.99
47.69
Table 8. The comparison of stess when segmented or not segmented.
Layered number
6
12
18
24
The maximum stress in the process of casting(MPa)
Segmented
Not segmented
8.02
14.12
1.89
3.98
0.92
1.65
0.62
1.00
After dividing the period of construction into two segments, the highest temperature
decline is not obvious when compared with that not segmented pouring. In the stress value
contrast, the maximum tensile stress value has an obvious drop after poured subsection, as the
biggest stress value change is more than 111%. Thus it can be seen that during the large
volume concrete pouring for the pedestrian bridge in Mengshan-Tianmeng scenic area,
layered casting can accelerate the concrete cooling, effectively reduce the internal temperature
of concrete. And segmented pouring can reduce the tensile stress of concrete in the same
hierarchical situation. Both are effective ways to prevent temperature cracks.
The Comparative Analysis between Numerical Simulation and the Result of Traditional
Calculation
The comparison between the results of FEM computation and traditional formula
calculation:
If there are no experimental data, adiabatic temperature rise of concrete should be
calculated according to the following formula:
T =
WQ
c
(7)
Where Tα is the ultimate adiabatic temperature rise of concrete (Ԩ); W is the amount of
concrete gelled material per cubic meter (kg/m3); Q is the total hydration heat of gelled
material (kJ/kg); ρ is the density of concrete (kg/m3), set as 2400 kg/m3; c is the specific heat
capacity of concrete (kJ/(kg*Ԩ)), set as 1.0 kJ/(kg*Ԩ).
The maximum inside temperature of concrete can be calculated according to the following
formula:
Tmax  Tp   T  Tco
(8)
Where Tmax represents the maximum inside temperature of concrete; Tp is
concrete placement temperature (Ԩ); ξ is temperature reduction coefficient; Tα is the ultimate
adiabatic temperature rise of concrete (); Tco is the cooling effect value of cooling water pipe
(Ԩ), generally set as 2-4Ԩ, which taken lager value when pipe spacing is small, whereas
smaller value. Specially, the value is set as 0 Ԩ when no water pipe.
According to the data related to temperature, we got Tα=45.65Ԩ by calculating. Therefore,
with the changing of concrete lift thickness, the calculation results of the maximum inside
temperature of concrete are shown in table 9:
Table 9. The Tmax of different concrete lift thickness.
Concrete lift thickness(m)
0.5
1
1.5
2
2.5
3
Coefficient ξ
0.28
0.46
0.55
0.62
0.68
0.74
Tmax
32.78082
40.99707
45.10519
48.3004
51.03914
53.77789
The results of the comparison are displayed, as shown in Figure 1.
Figure 1. The contrast curve figure of highest temperature and casting thickness.
According to Fig.1, the results by the way of traditional formula calculation are greatly
different from that by the way of finite element simulation. What’s more, the temperature is
much lower and more dangerous by the way of traditional formula calculation.
Meanwhile the formula just points out the relationship between temperature and concrete
lift thickness, not considering the influence of the section on temperature field. So the results
from numerical simulation are more accurate and more comprehensive.
Standard can only control the maximum temperature changes, and the traditional formula
can only calculate the temperature. Whereas numerical simulation can analyze the
temperature field and stress field at the same time, and from the analysis of calculation results
we can see that the control of thermal stress is more critical in the control of mass concrete
construction. Therefore, the numerical simulation can really guide the engineering design and
construction scheme and ensure the construction quality.
Conclusions
This paper takes the pedestrian bridge as an example which is one of the development
projects in Mengshan-Tianmeng scenic area, and discusses the simulation modeling about the
industrial projects based on the coupling algorithm. Specifically, the temperature field,
thermal stress was simulated during the pedestrian bridge construction, and some concrete
anti-cracking measures are put forward targetedly, the main conclusions are as follows:
Firstly, through the analysis of infinitesimal heat conduction, the concrete heat conduction
equations and the concrete transient temperature field equations was deduced based on the
principle of heat conservation, and the temperature field equivalent conduction equation is
extended to the three dimensional to meet the need of numerical simulation.
Secondly, the numerical model was established according to Wanghailou anchorage,
Yuhuangding anchorage and structure features, the related parameters and the construction
condition were determined reasonably, the numerical simulation of the layered and segmented
pouring was carried out, and the mass concrete casting plan was made according to change of
temperature and the stress distribution during the anchorage of pouring.
Thirdly, layered casting can accelerate the concrete cooling; effectively reduce the internal
temperature of concrete. And segmented pouring can reduce the tensile stress of concrete in
the same hierarchical situation. Both are effective ways to prevent temperature cracks.
Finally, according to the result of finite element calculation and in combination with mass
concrete construction experience, we targetedly put forward the concrete scheme to control
the temperature cracks.
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