Optimization of Reinforced Concrete Cantilever Retaining Wall using Particle Swarm Optimization

Abstract

The design of structures depends on designer’s experience and generally, the designer proceeds with trial and error until he arrives at a design which satisfies prescribed limit states. This is especially true for reinforced concrete structures in which the structural configuration is decided first and then reinforcement requirements are determined, resulting in higher cost. Retaining walls involve a large number of variables and therefore have been far from optimization. However, since retaining walls comprise of 20-30 percent of the cost of highways in hilly regions, their optimization is critical to economy of the project. Particle Swarm Optimization (PSO) does not require the objective function to be linear or differentiable and hence is ideally suited for optimization of retaining walls. This study uses PSO as a tool for the optimizing a Cantilever RC Retaining Wall. The objective function consists of two parts - cost function and penalty term. A program and GUI was developed to implement PSO. A reduction in cost was achieved from 8% -17% depending on the height of retaining wall, while the optimization in weight varied from 9%-34%.

Design Optimization of Reinforced Concrete Cantilever Retaining Walls: A State‐of‐the‐Art Review

“…All these variables must be provided with their upper and lower bounds; otherwise an infeasible section may be obtained. A penalty function must be applied while using continuous variables without bounds to ensure the algorithm rejects the infeasible answer and moves on to a better solution as done by Sarıbas and Erbatur [19], Medhekar [20], Srivastava et al [32], Camp and Akin [42], Khajehzadeh and Eslami [43], Sheikholeslami et al [50], Kaveh and Laien [60], Kumar and Suribabu [63], Moayyeri et al [69], Kayabekir et al [75], and Temür [99].…”

“…Optimization can be applied through multiple programming software; however, due to their complexities civil engineers often choose simpler programming languages such as MATLAB (Schmied and Karlsson [24], Pei and Xia [28], Al Sebai et al [31], Srivastavaa et al [32], Babu and Basha [36], Khajehzadeh et al [38], Khajehzadeh and Eslami [43], Sable and Patil [44], Sable and Patil [45], Kaveh and Behnam [46], Kaveh et al [47], Khajehzadeh et al [49], Gandomi et al [52], Kaveh and Mahdavi [53], Gandomi et al [61], Öztürk and Türkeli [70], Uray et al [71], Kalemci et al [78], Kayabekir [79], Kashani et al [82], Mevada et al [88], Uray et al [92], Tutus ¸et al [95], Khajehzadeh et al [101], and Khajehzadeh et al [103]), Fortran (Villalba et al [27] and Ukritchon et al [65]), C#.NET (Linh et al [93]), Python (Dodigović et al [94]), and C++ (Dagdeviren and Kaymak [72]). Studies have also tried to combine analysis software such as ABAQUS, ANSYS, PLAXIS 2D, and GeoSlope (Rahbari [23], Papazafeiropoulos et al [29], Uray and Tan [30], Rahbari et al [64], and Ravichandran et al [84]) with optimization.…”

“…Although the design codes advise coarse aggregates as prescribed material for backfill, it may not be feasible to provide them in all cases. Some studies have researched this aspect and tried to optimize the design for backfill with different types of soil with different cohesion, unit weight, bearing, and internal angle of friction values (Al Sebai et al [31], Srivastavaa et al [32], Yepes et al [37], Kaveh and Abadi [40], Kaveh and Behnam [46], Kaveh and Laien [60], Konstandakopoulou et al [76], Uray et al [83], Uray and Çarbas ¸ [89], and Dodigović et al [94]). e backfill included coarse granular fill (gravel), granular soils with more than 12% of fines (GW, GS, SM, and SL), and fine soils with more than 25% of coarse grains (CL-ML).…”

“…e provision of shear key is also a topic of interest among multiple research studies. While some studies have simply modeled a retaining wall with a shear key [32,84,87,95], others have performed comparative analysis between retaining walls with and without shear keys (Naeem [22], Ceranic et al [34], Sable and Patil [45], Kaveh and Behnam [46] [98], and Temür [99]). e consensus on the findings is clear and it indicates that although the provision of key does increase the safety factors it also increases both cost and weight of a retaining wall.…”

“…However, the novel study was of Sarıbas ¸and Erbatur [19] which solidified the direction taken by researchers for problem formulation of RC cantilever retaining walls and is the most common reference study used by subsequent researchers. Since then multiple theses (Medhekar [20], Purohit [21], Naeem [22], Rahbari [23], and Schmied and Karlsson [24]), conference papers (Bhatti [25], Ahmadi-Nedushan and Varaee [26], Villalba et al [27], Pei and Xia [28], Papazafeiropoulos et al [29], Uray and Tan [30], Al Sebai et al [31], Srivastavaa et al [32], and Yücel et al [33]), and journal articles (Ceranic et al [34], Chau and Albermani [35], Babu and Basha [36], Yepes et al [37], Khajehzadeh et al [38], Ghazavi and Bonab [39], Kaveh and Abadi [40], Khajehzadeh et al [41], Camp and Akin [42], Khajehzadeh and Eslami [43], Sable and Patil [44], Sable and Patil [45], Kaveh and Behnam [46], Kaveh et al [47], Kaveh and Khayatazad [48], Khajehzadeh et al [49], Sheikholeslami et al [50], Talatahari and Sheikholeslami [51], Gandomi et al [52], Kaveh and Mahdavi [53], Singla and Gupta [54], Bekdas ¸et al [55], Kaveh and Farhoudi [56], Sheikholeslami et al [57], Temür and Bekdas…”