• Structural Engineering and Mechanics
• /
• 제57권4호
• /
• pp.763-783
• /
• 2016

A methodology based on Teaching Learning-Based Optimization (TLBO) algorithm is proposed for optimum design of reinforced concrete retaining walls. The objective function is to minimize total material cost including concrete and steel per unit length of the retaining walls. The requirements of the American Concrete Institute (ACI 318-05-Building code requirements for structural concrete) are considered for reinforced concrete (RC) design. During the optimization process, totally twenty-nine design constraints composed from stability, flexural moment capacity, shear strength capacity and RC design requirements such as minimum and maximum reinforcement ratio, development length of reinforcement are checked. Comparing to other nature-inspired algorithm, TLBO is a simple algorithm without parameters entered by users and self-adjusting ranges without intervention of users. In numerical examples, a retaining wall taken from the documented researches is optimized and the several effects (backfill slope angle, internal friction angle of retaining soil and surcharge load) on the optimum results are also investigated in the study. As a conclusion, TLBO based methods are feasible.

• Geomechanics and Engineering
• /
• 제20권6호
• /
• pp.527-536
• /
• 2020

The paper represents an optimization algorithm for reinforced concrete retaining wall design. The proposed method, called Rao-3 optimization algorithm, is a recently developed algorithm. The total weight of the steel and concrete, which are used for constructing the retaining wall, were chosen as the objective function. Building Code Requirements for Structural Concrete (ACI 318-05) and Rankine's theory for lateral earth pressure were considered for structural and geotechnical design, respectively. Number of the design variables are 12. Eight of those express the geometrical dimensions of the wall and four of those express the steel reinforcement of the wall. The safety against overturning, sliding and bearing capacity failure were regarded as the geotechnical constraints. The safety against bending and shear failure, minimum and maximum areas of reinforcement, development lengths of steel reinforcement were regarded as structural constraints. The performance of proposed algorithm was evaluated with two design examples.

• Structural Engineering and Mechanics
• /
• 제47권2호
• /
• pp.227-245
• /
• 2013

The term "constructability" in regard to cast-in-place concrete construction refers mainly to the ease of reinforcing steel placement. Bar congestion complicates steel placement, hinders concrete placement and as a result leads to improper consolidation of concrete around bars affecting the integrity of the structure. In this paper, a multi-objective approach, based on the non-dominated sorting genetic algorithm (NSGA-II) is developed for optimal design of reinforced concrete cantilever retaining walls, considering minimization of the economic cost and reinforcing bar congestion as the objective functions. The structural model to be optimized involves 35 design variables, which define the geometry, the type of concrete grades, and the reinforcement used. The seismic response of the retaining walls is investigated using the well-known Mononobe-Okabe analysis method to define the dynamic lateral earth pressure. The results obtained from numerical application of the proposed framework demonstrate its capabilities in solving the present multi-objective optimization problem.

• Geomechanics and Engineering
• /
• 제24권3호
• /
• pp.237-251
• /
• 2021

The main purpose of this study is to investigate the performance of the proposed hybrid teaching-learning based optimization algorithm on the optimum design of reinforced concrete (RC) cantilever retaining walls. For this purpose, three different design examples are optimized with 100 independent runs considering continuous and discrete variables. In order to determine the algorithm performance, the optimization results were compared with the outcomes of the nine powerful meta-heuristic algorithms applied to this problem, previously: the big bang-big crunch (BB-BC), the biogeography based optimization (BBO), the flower pollination (FPA), the grey wolf optimization (GWO), the harmony search (HS), the particle swarm optimization (PSO), the teaching-learning based optimization (TLBO), the jaya (JA), and Rao-3 algorithms. Moreover, Rao-1 and Rao-2 algorithms are applied to this design problem for the first time. The objective function is defined as minimizing the total material and labor costs including concrete, steel, and formwork per unit length of the cantilever retaining walls subjected to the requirements of the American Concrete Institute (ACI 318-05). Furthermore, the effects of peak ground acceleration value on minimum total cost is investigated using various stem height, surcharge loads, and backfill slope angle. Finally, the most robust results were obtained by HTLBO with 50 populations. Consequently the optimization results show that, depending on the increase in PGA value, the optimum cost of RC cantilever retaining walls increases smoothly with the stem height but increases rapidly with the surcharge loads and backfill slope angle.

• Earthquakes and Structures
• /
• 제7권6호
• /
• pp.909-935
• /
• 2014

The seismic characteristics of two semi-gravity reinforced concrete cantilever retaining walls are examined via an experimental program using an outdoor shake table (one with and the other without concrete masonry sound wall on top). Both walls are backfilled with compacted soil and supported on flexible foundation in a steel soil container. The primary damages during both tests are associated with significant lateral displacements of the wall caused by lateral earth pressure; however, no collapse occurs during the tests. The pressure distribution behind the walls has a nonlinear trend and conventional methods such as Mononobe-Okabe are insufficient for accurate pressure estimation.

• Geomechanics and Engineering
• /
• 제6권2호
• /
• pp.99-115
• /
• 2014

Uncertainties in design variables and design equations have a significant impact on the safety of geotechnical structures like retaining walls and slopes. This paper presents a possible framework for obtaining the partial safety factors based on reliability approach for different random variables affecting the stability of a reinforced concrete cantilever retaining wall and a slope under static loading conditions. Reliability analysis is carried out by Mean First Order Second Moment Method, Point Estimate Method, Monte Carlo Simulation and Response Surface Methodology. A target reliability index ${\beta}$ = 3 is set and partial safety factors for each random variable are calculated based on different coefficient of variations of the random variables. The study shows that although deterministic analysis reveals a safety factor greater than 1.5 which is considered to be safe in conventional approach, reliability analysis indicates quite high failure probability due to variation of soil properties. The results also reveal that a higher factor of safety is required for internal friction angle ${\varphi}$, while almost negligible values of safety factors are required for soil unit weight ${\gamma}$ in case of cantilever retaining wall and soil unit weight ${\gamma}$ and cohesion c in case of slope. Importance of partial safety factors is shown by analyzing two simple geotechnical structures. However, it can be applied for any complex system to achieve economization.

• Structural Engineering and Mechanics
• /
• 제86권3호
• /
• pp.337-348
• /
• 2023

The optimization of reinforced concrete (RC) cantilever retaining walls is a complex problem and requires the use of advanced techniques like metaheuristic algorithms. For this purpose, an optimization model must first be developed, which involves mathematical complications, multidisciplinary knowledge, and programming skills. This task has proven to be too arduous and has halted the mainstream acceptance of optimization. Therefore, it is necessary to unravel the complications of optimization into an easily applicable form. Currently, the most commonly used method for designing retaining walls is by following the proportioning limits provided by the ACI handbook. However, these limits, derived manually, are not verified by any optimization technique. There is a need to validate or modify these limits, using optimization algorithms to consider them as optimal limits. Therefore, this study aims to propose updated proportioning limits for the economical design of a RC cantilever retaining wall through a comprehensive parametric investigation using the genetic algorithm (GA). Multiple simulations are run to examine various design parameters, and trends are drawn to determine effective ranges. The optimal limits are derived for 5 geometric and 3 reinforcement variables and validated by comparison with their predecessor, ACI's preliminary proportioning limits. The results indicate close proximity between the optimized and code-provided ranges; however, the use of optimal limits can lead to additional cost optimization. Modifications to achieve further optimization are also discussed. Besides the geometric variables, other design parameters not covered by the ACI building code, like reinforcement ratios, bar diameters, and material strengths, and their effects on cost optimization, are also discussed. The findings of this investigation can be used by experienced engineers to refine their designs, without delving into the complexities of optimization.

• 한국지반신소재학회논문집
• /
• 제12권2호
• /
• pp.35-42
• /
• 2013

흙 구조물의 안정성은 물과 직접적인 관련이 있고, 강우나 침투수에 대한 충분한 대책을 세우지 않는다면 구조물에 큰 피해를 입을 수 있다. 최근 이상기후로 인한 집중호우의 횟수가 잦아짐에 따라 흙 구조물의 안정성에 대한 관심이 커지고 있으며, 구조물의 배수에 대한 여러 가지 방법이 제시되고 있다. 본 연구에서는 연직 배수공법에 사용되는 PBD(Plastic Board Drain)를 보강토 옹벽의 수평 배수재로 이용했을 시 적용성 여부에 대해 평가 하였다. 특히 전면벽을 콘크리트 블록이 아닌 토낭으로 하여 시공성과 경제성을 높이고, 토낭과 연결재, PBD를 일체화 시켜 안정성을 확보하였다. PBD를 활용한 배면수의 투수능 시험결과 보강토체 사이에 자갈층을 포설한 것과 유사한 효과를 나타내었으며, 실제 현장에서의 수평배수재로 활용이 가능한 것으로 판단된다.

• Structural Engineering and Mechanics
• /
• 제81권1호
• /
• pp.93-102
• /
• 2022

The optimum design of reinforced concrete cantilever retaining walls subjected to seismic loads is an extremely important challenge in structural and geotechnical engineering, especially in seismic zones. This study proposes an adaptive sperm swarm optimization algorithm (ASSO) for economic design of retaining structure under static and seismic loading. The proposed ASSO algorithm utilizes a time-varying velocity damping factor to provide a fine balance between the explorative and exploitative behavior of the original method. In addition, the new method considers a reasonable velocity limitation to avoid the divergence of the sperm movement. The proposed algorithm is benchmarked with a set of test functions and the results are compared with the standard sperm swarm optimization (SSO) and some other robust metaheuristic from the literature. For seismic optimization of retaining structures, Mononobe-Okabe method is employed for dynamic loading conditions and total construction cost of the structure is considered as the single objective function. The optimization constraints include both geotechnical and structural restrictions and the design variables are the geometrical dimensions of the wall and the amount of steel reinforcement. Finally, optimization of two benchmark retaining structures under static and seismic loads using the ASSO algorithm is presented. According to the numerical results, the ASSO may provide better optimal solutions, and the designs obtained by ASSO have a lower cost by up to 20% compared with some other methods from the literature.

• 대한토목학회논문집
• /
• 제3권3호
• /
• pp.71-86
• /
• 1983

현재(現在) WSD로 설계(設計)되고 있는 우리 나라 철근(鐵筋)콘크리트 옹벽구조물(擁壁構造物)에 있어서 가장 보편적으로 사용되고 있는 캔틸레버 옹벽(擁壁)의 안정해석(安定解析) 및 각부설계(各部設計)를 보다 합리적(合理的)이며 확률적(確率的)인 신뢰성(信賴性) 이론(理論)을 도입하여 신뢰성(信賴性) 모델에 따른 안정해석(安定解析) 및 각부설계(各部設計)에 대한 신뢰성(信賴性) 설계규준(設計規準)을 LRFD에 의거하여 제안(提案)하고, 또 안정해석(安定解析)의 공칭안전율(公稱安全率)에 대한 이론적(理論的)인 근거를 제시(提示)하는 것이 본(本) 연구(硏究)의 주요내용(主要內容)이다. 신뢰성(信賴性) 이론(理論)에 의해 안정해석(安定解析) 및 각부설계(各部設計)에 대한 한계상태방정식(限界狀態方程式)을 유도하고, Coulomb의 주동토압계수(主動土壓係數), Hansen의 지지력공식(支持力公式)을 사용하여 Cornell의 MFOSM에 의해 불확실량(不確實量) 산정(算定)의 알고리즘을 유도하였으며 그에 따른 불확실량수준(不確實量水準)은 우리 나라의 현실(現實)을 고려한 적절한 값으로 제안(提案)하였다. 현행(現行) R.C. 옹벽설계규준(擁壁設計規準)에 따라 Calibration 하므로서 목표신뢰성지수(目標信賴性指數)${\beta}_0$를 다음과 같이 선택하고(전도(轉倒): ${\beta}_0$=4.0, 골동(滑動): ${\beta}_0$=3.5, 지지력(支持力): ${\beta}_0$=3.0, 휨: ${\beta}_0$=3.0, 전단(剪斷): ${\beta}_0$=3.2), 이 ${\beta}_0$에 대응하는 하중(荷重) 및 저항계수(抵抗係數)를 산정(算定)하였으며, 안정해석(安定解析)에 대한 현행(現行) 철근(鐵筋)콘크리트 표준시방서(標準示方書)의 안전율(安全率)을 검토한 결과 다음과 같은 값이 적절하다는 것을 알았다(전도(轉倒): 1.8, 골동(滑動): 1.9, 지지력(支持力): 3.6). 또한 현행(現行) WSD R.C. 옹벽(擁壁)의 설계규준(設計規準)을 위해 신뢰성(信賴性)에 의한 공칭안전율(公稱安全率)과 허용응력(許容應力)을 제안(提案)하였다. 그리고 본(本) 연구(硏究)에서 제안(提案)하는 R.C. 옹벽(擁壁)의 LRFD 신뢰성(信賴性) 설계규준(設計規準)을 현행(現行) R.C. 표준시방서(標準示方書)의 설계규준(設計規準)에 대응(對應)하는 설계규준(設計規準)으로 도입함이 바람직하다는 사실을 확인할 수 있었다.