OPTIMAL ALIGNMENT OF A CANAL ROUTE
by
SRIDEBI BASU
Department of Civil Engineering
Submitted in partial fulfillment of the requirements of the degree of
Doctor of Philosophy
to the
,
INDIAN INSTITUTE OF TECHNOLOGY DELHI
OCTOBER 2013
© Indian Institute of Technology Delhi (IITD), New Delhi, 2013
CERTIFICATE
This is to certify that the dissertation entitled, “Optimal Alignment of a Canal Route’’
is a bonafied record of project work carried out by Mrs. Sridebi Basu in partial
fulfillment of the requirement of the degree of Doctor of Philosophy. She has worked
under my supervision and guidance at Indian Institute of Technology Delhi, and has
fulfilled the requirements for the submission of her report.
The results presented in the report have not been submitted in part or in full to any other
University or Institute, for the award of any degree or diploma.
New Delhi
Professor B. R. Chahar
October 2013
Department of Civil Engineering
Indian Institute of Technology Delhi
Delhi-110 016, India
i
ACKNOWLEDGEMENTS
I feel great pleasure and privilege to express my deep sense of gratitude, indebtedness
and thankfulness towards my supervisor, Prof. B. R. Chahar for his invaluable
guidance, constant supervision, and continuous encouragement and support throughout
the project work. His recommendable suggestions and critical views have greatly helped
me in successful completion of this work.
I also acknowledge with sincerity, the help rendered by Mr. Rajveer Aggarwal and my
friend Mr. Raktim Haldar at various stages of this project.
I also want to convey my thanks to my family and office colleagues for their
encouragement, support and moral boosting to carry on my studies. I am also thankful to
all those who helped directly or indirectly in completion of this work. I want to take this
opportunity to thank Engineers India Limited management for giving me their consent
to carry out my studies.
New Delhi
(Sridebi Basu)
October 2013
ii
ABSTRACT
Water is the most valued natural resource for mankind’s sustainable
development. India is getting water stressed as water demand is increasing due to
modernization and as a result. The natural allocation of water resources over space and
time is irregular in Indian scenario which makes the situation more complicated. Due to
its geographical location, India is having both extreme dry climate as well as wettest
place of Earth. Seasonal rivers are having intermittent and flash flow whereas perennial
rivers continuously discharging huge volume of water to the sea. Thus allocation of
water resources is required to balance between the surplus and deficit areas of the
country. Interlinking of rivers is envisaged for interbasin transfer of water.
The channel must be capable of transporting water between the source and the
destination in a secure and cost effective manner. Canal design includes canal crosssections design. It also comprises horizontal and vertical layout design. In an ideal
condition the minimum cost of canal route alignment means the minimum cost of canal
section per unit length multiplied by the shortest distance between source and
destination but that may it not possible due to practical considerations. The layout
depends on the prevailing topography. The shortest distance may not be feasible or
optimal due to many reasons thus optimal route to be studied. The minimum cost canal
alignment is a complex function of cost of land acquisition, earthwork, lining, water loss
and canal structures. The canal along the natural ground slope may have least excavation
cost for canal section per unit length but due to maximum travelled path the total cost is
higher than other options. In contrary, the shortest route will increase earthwork cost per
unit length, cost of falls/drops and cross drainage works. The minimum cost of the
alignment can be accomplished by minimizing the total cost of canal route alignment
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considering all possible cost factors. Design of minimum cost canal alignment involves
minimization of sum of earthwork cost which varies with canal geometry and
topography of the area, cost of lining which varies with type of lining; cost of water loss
which varies with soil properties if unlined and meteorological properties of the
location; land cost which varies with land use pattern, resettlement and rehabilitation
cost, environmental cost and alignment of the canal; cost of canal falls/drops which
varies with type and height of fall; cost of cross drainage works, subject to uniform
flow, mass balance condition and other topographical and local restrictions. Such
minimum cost canal route alignment problem results in non-linear objective function
and non-linear equality constraint, making the problem hard to solve analytically.
Solution of such problem requires special optimization techniques. The complexity is
reflected in the design equations for minimum cost canal route alignment.
The canal route alignment problem is a variational control problem. The optimal
alignment of a canal route is a nonlinear optimization problem with non linear equality
and inequality constraints. In special cases it can be converted into fixed boundary or
moving boundary control problems. In general the problem can be solved by dynamic
programming, but the present formulated problem could not be solved easily using
conventional methods like GA, PSO, ACO, etc due to its complex nature. Hence, in this
study the same has been solved using hybrid approach of dynamic programming and
Dijkstra’s method for global solution and considering the flow along the restricted area.
The same is solved with the help of macros on MS Excel. The software solution will
reduce the computation time for selection of optimal alignment of a canal route and will
allow more options to explore. Due to speedy selection the desired route the project
duration will be abridged which is beneficial to end users.
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TABLE OF CONTENTS
Description
Page No.
Certificate
i
Acknowledgements
ii
Abstract
iii
List of Notation
xv
Chapter 1
1
Introduction
1
1.1
General
1
1.2
State of Art
3
1.3
Research Gap
5
1.4
Objective of the Study
5
1.5
Organization of the Thesis
6
Chapter 2
9
Literature Review
9
2.1
General
9
2.2
Necessity of Canal
10
2.3
Falls
12
2.4
Cross Drainage Works
13
2.5
Canal Section Design
15
2.6
Balancing Depth and Balancing Length
20
2.7
Canal Route Alignment
22
2.8
Optimization Methods
22
2.9
Concluding Remarks
24
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Chapter 3
27
Canal Section Cost and Special Cases
27
3.1
General
27
3.2
Canal Section Cost
28
3.2.1
Earthwork Cost
28
3.2.2
Lining Cost
30
3.2.3
Cost of Water (Lost as Seepage and Evaporation)
31
3.2.4
Land Acquisition Cost
32
3.2.5
Unit Length Canal Section Cost
32
3.3
Flow Requirement
33
3.3.1
Uniform flow
34
3.3.2
Carrying Capacity
34
3.3.3
Permissible Velocities
35
3.3.4
Freeboard
35
3.4
Geometric Properties of Combined Sections
37
3.5
Design of Optimal Canal Sections
40
3.5.1
Best Hydraulic Section
41
3.5.2
Optimal Section with Constraints on Canal Dimensions
42
3.5.3
Minimum Cost Canal Section
46
3.6
Optimal Design Procedure of Composite Trapezoidal Section
48
3.6.1
Triangular Section with Circular Bottom
48
3.6.2
Trapezoidal Section with Circular Corners
50
3.6.3
Rectangular Section with Circular Corners
52
3.7
Optimal Design Steps of Canal Cross Section
53
3.8
Balancing Depth
54
vi
3.9
Balancing Length
66
3.10
Balancing Length Cost Function Formulation
75
3.11
Concluding Remarks
79
Chapter 4
81
Canal Alignment: Problem Formulation
81
4.1
General
81
4.2
Data Requirement
81
4.3
Alignment of a Canal Route
82
4.4
Cost Function
87
4.5
Different Boundary Conditions
91
4.5.1
Problem Formulation for Case I
93
4.5.2
Problem Formulation for Case II
94
4.5.3
Problem Formulation for Case III
94
4.5.4
Problem Formulation for Case IV
95
4.6
Unconstrained Formulation
96
4.7
Concluding Remark
99
Chapter 5
101
Canal Alignment: Solution And Results
101
5.1
General
101
5.2
Solution Technique
101
5.3
Input
102
5.4
Solution for Different Boundary Conditions
104
5.4.1
Case I : Fixed Source and Fixed Destination
107
5.4.2
Case II : Fixed Source and Variable Destination
111
5.4.3
Case-III : Variable Source and Fixed Destination
113
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5.4.4
Case IV : Variable Source and Variable Destination
5.4.5
Case I : Fixed Source and Fixed Destination with Variable
Canal Bed Slope
5.5
117
122
Concluding Remark
126
Chapter 6
127
Summary and Conclusion
127
References
131
Appendix – A
143
Recommended Side Slopes
143
Appendix – B
145
Limiting Velocities for Channel Surfaces
Appendix – C
145
147
Radii of Curves for Canals
147
Appendix – D
149
Solved Problem
147
Bio Data
153
viii