APPLICATION OF GENETIC ALGORITHM TECHNIQUE FOR OPTIMIZING DESIGN OF REINFORCED CONCRETE RETAINING WALL

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1 International Journal of Civil Engineering and Technology (IJCIET) Volume 8, Issue 5, May 2017, pp , Article ID: IJCIET_08_05_107 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed APPLICATION OF GENETIC ALGORITHM TECHNIQUE FOR OPTIMIZING DESIGN OF REINFORCED CONCRETE RETAINING WALL Sasidhar T M.Tech Student, Structural Engineering, VIT University, Vellore, Tamilnadu, India Neeraja D Associate Professor, Department of Structural and Geotechnical Engineering, VIT University, Vellore, Tamilnadu, India V Samba Murthy Sudhindra Senior Engineer in Bridges, HBS Infra Engineers Pvt. Ltd, Hyderabad, Telangana, India ABSTRACT Retaining walls are generally used in geotechnical engineering applications such as bridge abutments supporting deep excavations, tied back retaining wall, etc. The design of retaining walls is majorly based on thumb rules and the experience of the designer in taking out initial dimensions and to make necessary checks for complying against design codes. Most procedures consider cross-section dimensions and material grades. On the trial and error basis, the conventional procedures lead to safe designs. But the cost of retaining wall depends on experience of the structural engineer. Here structural optimization techniques are clear alternative to design based on experience. Optimum design is a structural synthesis which collects all engineering aspects to develop structures not only safe but also economic. In the present study optimum design is performed for cantilever retaining wall of different heights for various cases using genetic algorithm technique provided with Mat Lab. Comparisons are made with results obtained from conventional method of retaining wall design. This justifies the effectiveness and efficiency of genetic algorithm technique in the optimum design of cantilever retaining wall. Key words: Retaining walls, Optimization, Genetic Algorithm, Mat lab. Cite this Article: Sasidhar T, Neeraja D and V Samba Murthy Sudhindra, Application of Genetic Algorithm Technique for Optimizing Design of Reinforced Concrete Retaining Wall. International Journal of Civil Engineering and Technology, 8(5), 2017, pp editor@iaeme.com

2 Sasidhar T, Neeraja D and V Samba Murthy Sudhindra 1. INTRODUCTION Retaining wall is a structural element which is intended to support back fill soils, e.g. support deep excavations, as abutments of bridge and as anchored retaining wall, etc. Retaining walls are known to be simplest structures but there design should satisfy some stability requirements. Those are internal and external stability conditions. First one talks about structural stability of different parts of retaining wall where as second one gives the wall-soil interaction after construction will be in equilibrium. While designing a structure, engineers need to adopt many technological and managerial decisions at different stages. At present the optimizing design in structural elements mainly follows rules which are formed according to experience of designer. Most of the designs will be done by assuming cross sectional dimensions and material grades and then lead to safety design by compiling them with design code requirements. In this type of designs optimization techniques are best alternative to designs which depends on experience. Optimum design is the process of structural synthesis which give designs not only safe but economical. In any design optimization is done on reliability base or cost minimization. The constraints are formed by using stability conditions. Mathematically it is defined as minimization task of constrained function. And it is solved by a method based on simple mathematical Program. In recent years new developments in numerical methods has given some optimization techniques which are conceptually different from traditional methods. These methods are termed as non traditional methods of optimization. These methods work depending on biological behavior, molecular swarm of insects and system of neutral biologics. Genetic algorithm belongs to methods of stochastic search that is formed by natural biological evolution processes. The primary reason behind use of genetic algorithm is optimization. This algorithm works on population which belongs to potential solutions by the application of survival of the fittest principal to produce best solution to a particular problem. The various stages in genetic algorithm technique are selection, recombination and mutation. This genetic algorithm Optimum tool of Mat Lab is used for optimizing design of retaining wall. The optimization mode is combination of design variables and objective function. Objective function is cost per structure. Results obtained from design of retaining wall using genetic algorithm are compared with that of obtained from conventional method. The efficiency and effectiveness of genetic algorithm in optimizing design is studied from the comparison of results obtained from two methods. 2. LITERATURE ON APPLICATION OF ALGORITHM TECHNIQUE IN OPTIMIZING DESIGN OF RETAINING WALL Algorithm techniques are used in optimizing design of many structural elements such as beams, culverts, girders retaining walls etc. Many studies have been carried out for comparison with conventional method of design. Some of them are: 2.1. Nabeel A.Jasim et al (2016): Optimum design of tied back retaining wall Presents an optimization algorithm for the design of tied back retaining wall. The aim of the study is to find the values of design variables which minimize the cost function subjected to constraints of the problem. The optimization of such structure is done by using genetic algorithm optimum tool of Mat lab program editor@iaeme.com

3 Application of Genetic Algorithm Technique for Optimizing Design of Reinforced Concrete Retaining Wall 2.2. Amir H.Gandomi et al (2015): Optimization of retaining wall design using recent swarm intelligence technique Considered two different bench mark cases. They are particle swarm intelligence algorithm and classical swarm intelligence algorithm. A code is developed to model retaining wall design based on ACI procedure. In this study continuous variables are used for wall geometry, discrete variables are used for steel reinforcement to optimize the structural design George papazafeiropoulos et al (2013): Optimum design of cantilever walls retaining linear elastic backfill by use of genetic algorithm Optimum design of retaining wall is performed for two heights using numerical two dimensional simulations and genetic algorithm. Numerical simulations are performed using the finite element code ABAQUS where as for optimization purposes, the genetic algorithm provided with MAT LAB is utilized. The results on the optimum solutions are presented and comparisons are made with corresponding results according to conventional methods. 3. OBJECTIVE OF PROJECT The objective of study is to study the maximum height of retaining wall with both horizontal and surcharge load considering optimization as the main factor. Application of genetic algorithm technique is studied for the optimizing design of reinforced concrete retaining wall. 4. METHODOLOGY The geometrical parameters like height, width and thickness etc., are considered as design variables in the analysis. Genetic algorithm technique is applied to solve the formed constraints (using MAT Lab) such as factor of safety against overturning and sliding, base soil pressures etc., within the defined number of trails. The effectiveness and efficiency of the applied optimization technique can be validated by comparing the results obtained from conventional design method. The maximum height and the properties of retaining wall to which genetic algorithm technique can be applied considering the optimization as the main function is justified Description of Structural Element In this project, Retaining wall considered is a cantilever type retaining wall. Different cases have been formed by varying parameters which are involved in the design such as angle of internal friction, surcharge load, depth of foundation, water table level etc. Each case is tried for different heights of retaining wall from 3 meters to 10 meters for every 1 meter interval. Parameter Table 1 Description of retaining wall Value / Properties Type of backfill Horizontal backfill with surcharge Density of soil 20 kn/m 3 Angle of repose 30 0 S.B.C of soil 160 kn/m 3 Surcharge load 40 kn/m 3 Coefficient friction editor@iaeme.com

4 Sasidhar T, Neeraja D and V Samba Murthy Sudhindra 4.2. Optimization Scheme Design Variables Figure 1 Design variables in design by using algorithm technique The above figure 1 shows 8 design variables included in this study. This variables includes 5 geometrical design variables and 3 reinforcement design variables. The 5 design variables are Length of base slab(x 1 ), thickness of base slab(x 2 ), top and bottom width of vertical wall (x 3 and x 4 ) and depth of foundation(x 5 ) Objective Function Cost function of cantilever retaining wall is considered as objective function. This cost function includes cost per one cubic meter of concrete and cost of reinforcement per one linear meter. Remaining things like labour, formwork, material losses etc. are neglected in order to simplify the analysis. Volume of concrete per m 3 x cost per cubic meter Fitness function = + Area of reinforcement per meter x unit weight x cost per kg Design Constraints The design of retaining wall should provide safety and stability against failure modes and satisfy the code requirements. These requirements are used to form the constraint equations in the design optimization procedure. Table 2 Failure modes of retaining wall Failure mode Equation Sliding failure 1 - (F r / (F s x Pa 1 )) < 0 Overturning failure 1 - (M r / M o x Pa 2 ) < 0 Bearing capacity 1 - (q u / (F b x q app ))<0 Eccentricity of resultant force 1 - (2 x B/ 3 x C) < 0, 1- (3 x C / B) < 0 Minimum area of reinforcement 1 - (A sreq /A smin )<0 In the above table 2, F r represents resisting force, F s represents sliding force, Mr represents resisting force, M o represents overturning moment, Pa 1 and Pa 2 represents factor of editor@iaeme.com

5 Application of Genetic Algorithm Technique for Optimizing Design of Reinforced Concrete Retaining Wall safety values for sliding and overturning respectively, q u represents safe bearing capacity of soil, q app is applied load on soil, B represents base slab length, C is distance of resultant force from toe Program for Algorithm The program for algorithm to solve the created fitness function involves linking of fitness function, defining number of variables has to be defined, stating lower and upper bound values, linking of Constraint function and final code for algorithm. The program code for algorithm is given below. [X, fval] = ga (objfcn, nvars, [ ], [ ], [ ], [ ], LB, UB, consfcn) Figure 2 Fitness function Figure 3 Constraint function Figure 4 Program for genetic algorithm editor@iaeme.com

6 Sasidhar T, Neeraja D and V Samba Murthy Sudhindra 5. RESULTS 5.1. Design of retaining wall by conventional method and optimization technique In this chapter comparisons of various parameters for the retaining wall by conventional method and optimization technique method have been done. The results have been shown both in tabular and graphical form. Case 1: Angle of Internal Friction Angle of internal friction Table 3 Angle of internal friction by conventional method 28 o ` o o o o Angle of internal friction Table 4 Angle of internal friction by optimization technique 28 o o o o o Tables 3 and 4 shows the quantity of concrete required for different angle of internal friction and for different heights of wall. From the results obtained from both methods, the variation in concrete quantity has been noticed. Case 2: Surcharge Load Surcharge load(kn/m 3 ) Table 5 Surcharge load by conventional method editor@iaeme.com

7 Application of Genetic Algorithm Technique for Optimizing Design of Reinforced Concrete Retaining Wall Surcharge load(kn/m 3 ) Table 6 Surcharge load by optimization technique Tables 5 and 6 shows the quantity of concrete required for different surcharge load conditions and for different heights of wall. From the results obtained from the both methods, the variation in concrete quantity has been noticed. Case 3: Water Table Level Water table level(m) Table 7 Water table level by optimization technique Quantity of concrete(m 3 /m) ¼ of h ½ of h ¾ of h h Water table level(m) Table 8 Water table level by optimization technique Quantity of concrete(m 3 /m) ¼ of h ½ of h ¾ of h h Tables 7 and 8 shows the quantity of concrete required for different levels of water table in backfill soil and for different heights of wall. From the results obtained from the both methods, the variation in concrete quantity has been noticed. And the variation has been noticed which is positive editor@iaeme.com

8 Sasidhar T, Neeraja D and V Samba Murthy Sudhindra Case 4: Depth of Foundation Depth of foundation Table 9 Depth of foundation by conventional method Varying Constant Depth of foundation Table 10 Depth of foundation by optimization technique Varying Constant Tables 9 and 10 shows the quantity of concrete required for variation of depth of foundation and for different heights of wall. From the results obtained from the both methods, the variation in concrete quantity has been noticed. And the variation has been noticed which is positive. Case 5: Grade of Concrete Grade of concrete Table 11 Grade of concrete by conventional method Quantity of steel (mm 2 /m) M M M Grade of concrete Table 12 Grade of concrete by optimization technique Quantity of steel (mm 2 /m) M M M Tables 11 and 12 shows the quantity of concrete required for different grades of concrete and for different heights of wall. From the results obtained from the method, the variation in concrete quantity has been noticed editor@iaeme.com

9 Application of Genetic Algorithm Technique for Optimizing Design of Reinforced Concrete Retaining Wall 6. CONCLUSION Use of genetic algorithm technique in the design of retaining wall has given considerable percentage of cost optimization in all the cases which are taken for the analysis. This genetic algorithm technique is found to be useful in the designs where number of trails have to be done for making it more economical. It requires lower and upper bound values of considered variables. The range of boundary conditions will alter the objective function value. Hence, the provision of genetic algorithm technique in the design of retaining wall is advantageous in optimization of cost. But it is time taking method as it requires new program for every change properties of retaining wall. There is more scope to work on this modern optimization technique in the design of structural elements. REFERENCES [1] Amir H.Gandomi, Ali R.Kashani, David A. Roke, Mehdi Mousavi (2015), Optimization of retaining wall design using recent swarm intelligence techniques. Engineering structures 103(2015): [2] C.M.Chan, L.M.Zang, Zenny TM (2016), Optimization of pile group using hybrid genetic algorithm. Geotechnical Engineering 135(4) : [3] Charles V.Camp, Alper Akin (2012), Design of retaining wall using big-bang big crunch optimization, Structural Engineering 2012,138(3): [4] Mathivanan Periasamy, Behavior of Tensile, Flexural and Interlaminar Shear Strength of Microfilled Aluminium-Glass Fiber Reinforced Plastic Sandwich Panels, International Journal of Mechanical Engineering and Technology, 7(6), 2016, pp [5] Nabeel A.Jasim, Ahmed M.Al-Yaqoobi (2016), Optimum design of tied back retaining wall. Engineering structures 7(2016) : [6] Yaoyao Pei, Yuanyou Xia (2012), Design of reinforced cantilever retaining wall using Heuristic optimization algorithms. Procedia earth and planetary science 5(2012): [7] Sayyad Khaseem Babu, P. Venkata Sarath and P. Polu Raju, Comparative Study on Compressive and Flexural Strength of Steel Fibre Reinforced Concrete (SFRC) Using Fly Ash. International Journal of Civil Engineering and Technology, 8(3), 2017, pp [8] D. Satyanarayana and M. Pramila Devi, Special Heuristics For Flowshop Scheduling Based on Hybrid Genetic Algorithm Under SDST Environment, International Journal of Civil Engineering and Technology, 8(4), 2017, pp