Studies have shown that compressible materials between a rigid Retaining Wall and backfill reduced static and dynamic forces on the Wall. Nowadays, panels with low density are used. Expanded polystyrene, which is one of the geo-synthetic products known as geofoam, is a compressible material. Geofoam is one of the geo-synthetic materials that are made of foam. Geofoam is very practical in geotechnical engineering due to its low bulk weight versus soil bulk weight and high compressibility, rapid and simple implementation, thermal insulation, and resistance against water absorption. It can be used in Retaining Walls, road construction projects as light fillers, and to reduce stress due to vertical loads in the base and sub base layers. Geofoam is one of the geosynthetic product which is made of lightweight expanded polystyrene (EPS) or extruded polystyrene (XPS). EPS geofoam is a block or planar rigid cellular foamed polymeric material that can be used in geotechnical applications. Studies have been shown that geofoam placed directly against a rigid Retaining Wall can reduce static loads on the Wall. This study employed a finite difference method program, FLAC (Itasca, Version 7. 00), with considering yielding and non-yielding states for Retaining Walls to evaluate the effectiveness of geofoam panels in improving the static behavior of Retaining Walls. To determine the effects of geofoam in soil displacement and earth force acting on the rigid Wall, parameters such as the height of Retaining Wall, density and thickness of geofoam, cross-sectional shape of geofoam panel behind the Wall, and also using of two geofoam panels with four panel spacing (50, 100, 150, 200 cm) have been studied via static analysis. In this numerical study three gravity – type Retaining Walls at heights of 3, 6 and 9 meters and geofoam panels with densities of 15, 20 and 25 (kg/m3) at three relative thicknesses of t/H=0. 05, 0. 2 and 0. 4, were modeled. According to the results using of EPS15 with density equal to 15(kg/m3) which has the lowest density among other geofoam panels has a significant role in reducing of lateral stresses. Although the performance of geofoam in non-yielding Retaining Walls is better than yielding Retaining Walls. The results of the present research are as follows: 1-According to results, increasing the geofoam thickness increases soil lateral displacement and reduces forces on gravity Retaining Walls. The same effect can be achieved by reduction of geofoam density with equal thickness. In other words, Forces on gravity Retaining Walls are reduced and soil lateral displacement is increased by a reduction of geofoam density with equal thickness. 2-Using two geofoam panels with distance of 50 cm, unlike 3-meter high Wall, is proper in the 6 and 9 meters yielding Retaining Walls. 3-Trapezoidal geofoam increases soil lateral displacement and reduces forces on Retaining Walls compared to a rectangular geofoam panel with the same cross-sectional area. 4-Effect of geofoam on the reduction of forces on non-yielding Retaining Walls is more than that on yielding Walls. 5-According to results, stiffness of geofoam panel (K=E/t) has significant role in reducing of lateral forces acting on Retaining Walls. In this study, it was observed that K ≤ 5 MN/m3 provide the most effective range for the design of these system to reduce static force.

A method is used to obtain the fundamental frequency of a Retaining Wall quite accurately and carry out a dynamic analysis of such Wall based on modal response technique. The present procedure establishes both the general and particular cases of dynamic response of Retaining Wall based on improved Rayleigh-Ritz method. The Wall will be assumed to be a flexural member. The fundamental frequency of the Retaining Wall with soil mass has been computed. The results based on proposed method are then used to back propagation neural network (BPN). In the present work, the fundamental frequency of a Retaining Wall is calculated by BPN. A significant benefit of BPN is its ability to learn relationships between variables with repeated exposure to those variables. Therefore, instead of deriving an analytical relationship from mathematical formulations, the BPN learns the relationship through an adaptive training process. Numerical example shows the merit of the BPN.

Results obtained from geotechnical studies show that the amount of shear wave velocity in various parts of soil is dependent on location of each particle. Therefore, changes of shear wave velocity in soil depth introduce soil as an inhomogeneous material. This research studies the seismic performance of Retaining Wall in inhomogeneous soil through presenting a proper model which considers mechanism of soil-Wall system. In this study, analytical studies have been done in plane strain with rigid Retaining Wall and linear viscoelastic soil. In order to understand seismic performance of Retaining Wall, lateral pressure of soil on Wall, shear force of Retaining structure and bending moment on the Wall are presented. Results of this research show that the amount of lateral earth pressure on the Wall is dependent on changes of soil shear wave velocity, seismic excitation frequency and geometric parameters of system and response of system is different from homogenous soil. Distribution of inhomogeneous soil lateral pressure expresses that by increasing shear wave velocity at soil surface to shear wave velocity at soil base, location of maximum horizontal stress change from 0. 55H to 1H (H: height of Retaining Wall). In addition, by increasing the damping coefficient of the soil, the lateral pressure exerted on the structure decreases. In the case where the damping coefficient is equal to zero, the amount of horizontal stress increases significantly. The vertical stress of soil is maximum in the Wall toe while the amount of horizontal stress is minimum at the same point. Critical vertical pressure distribution occurs in a specific excitation frequency and at the same frequency maximum amount of lateral pressure is applied on the Wall. Results also show that lateral earth pressure on Retaining Wall makes it similar to the behavior of cantilever beam. Thus, implementing the inhomogeneous properties of soil presents a more realistic image of Retaining structures and improves design of these types of structures.

In the present study static response of cantilever Retaining Walls have been investigated by consideration of various soil constitutive models by means of finite element method with using PLAXIS 2-D software. Simulations have been performed at heights of 3, 6, and 9 meters Retaining Walls with considering two types of soils (cohesive and cohesionless) as backfill material. In this study, analysis have been conducted for two kinds of cohesionless backfill (loose and dense sand in dry condition) and at both conditions, saturated and unsaturated, for cohesive backfill. Analysis have been carried out by using three constitutive behavioral methods: Mohr-Coulomb (MC), Hardening-Soil (HS) and Hardening soil model with Small-Strain stiffness (HSS) for cohesionless backfill and additional method, Soft Soil model (SS), for cohesive backfill. The results show that, for cohesionless and cohesive backfill materials the lateral forces acting on the Retaining Wall are underestimated by the MC and SS constitutive models, respectively.

In order to design Retaining Walls, first the initial dimensions of the Wall should be estimated. In order to choose these dimensions, the designer should use reasonable proportions that were achieved by previous experiences of the designing different Retaining Walls. These dimensions are introduced based on a ratio of the height of Walls. Current reseasrches showed that by changing the conditions such as properties of the backfill materials of the Retaining Wall, the local seismic conditions, the height of the Wall and limitation in choosing the arbitrarily dimensions etc, these estimated dimensions would not be appropriate for an economical design. In this paper, by means of genetic and bees algorithms, economical dimensions of the Wall for static, pseudo static and pseudo dynamic loading conditions will be calculated precisely in a such way that stability of the Retaining Wall against sliding, overturning and bearing capacity are provided. Also from structural consideration point of view, the designed Walls could resist appropriately against the applied forces.

In this article, the problem of determining pseudo dynamic pressure and its associated forces on a rigid vertical Retaining Wall is solved analytically using the horizontal slices method for both reinforced and unreinforced Walls. The use of this method in conjunction with the suggested equations and unknowns offers a pseudo-dynamic method that is then compared with the results of an available software. In the proposed method, different seismic accelerations have been modeled at different soil structure heights. Reinforced soil pressure on a Retaining Wall and the angle of the critical failure wedge are calculated using the new formulation. It is shown that as the horizontal seismic acceleration coefficient increases the angle of the critical failure wedge is reduced and that the maximum extension force can be increased for each layer by using stronger and longer reinforcements. The results of the pseudo-dynamic method show that both vertical and horizontal seismic accelerations are essential coefficients for calculation of the required length and extension force of the reinforcements and that their importance increases as the vertical and horizontal seismic accelerations increase. Also, the location of the application point of the resultant pressure rises as the horizontal seismic acceleration coefficient increases.

The design of the Retaining Wall requires a complete examination of the Wall in static and dynamic conditions. The movement and movement of the Wall can be very effective on the analysis and design of the Wall. In this paper, numerically and using the ABAQUS / CAE finite element software, seismic performance of the suspended Wall under harmonic loading and under resonant frequency conditions for various factors has been investigated. In this research, various variables including substrate profile, type of embankment, geometry and Wall dimensions, acceleration and vibration frequency have been investigated. The results of this study indicate that with increasing Wall height and denting density, vertical stress and mean of maximum absorbed acceleration decreases, which can be considered in the economic design of the Wall. The design of the Retaining Wall requires a complete examination of the Wall in static and dynamic conditions. The movement and movement of the Wall can be very effective on the analysis and design of the Wall. In this paper, numerically and using the ABAQUS finite element software, seismic performance of the suspended Wall under harmonic loading and under resonant frequency conditions for various factors has been investigated. In this research, various variables including substrate profile, type of embankment, geometry and Wall dimensions, acceleration and vibration frequency have been investigated. The results of this study indicate that with increasing Wall height and denting density, vertical stress and mean of maximum absorbed acceleration decreases, which can be considered in the economic design of the Wall.

Discrete Element Method can be used for numerical analysis of different geotechnical problems such as Retaining Wall earth pressure distribution. This paper is an effort to use the method in determining active and passive earth pressure distribution behind a Retaining Wall. Soil mass in the present method is treated as comprising of blocks, which are connected by elasto-plastic Winkler springs. The solution of this method satisfies all equilibrium and compatibility conditions. The method has the simplicity of the classic limit analysis and offers more ability in solving problems in complex geometry and loading conditions such as seismic impacts, pore water pressure, non-homogeneity of the soil reinforced backfill soils, etc. In this paper, the formulation of the method is briefly reviewed. Examples are shown to demonstrate the applicability of the method for analysis of earth pressure behind a Retaining Wall including dynamic lateral pressure of non-homogeneous soil. The results are compared with previous classic methods. Applicability of DEM for analysis of reinforced soil structure and advantages of this method over conventional methods are also discussed.

One-dimensional view of optimized design of engineering systems focusing on costs without considering other aspects such as risk and uncertainty in engineering design can increase risks during the operation of that engineering system. This paper indicates that if there are uncertainties in design parameters this cannot always cause poorly system operation, whereas may strengthen that system operation. For this purpose, a gravity Retaining Wall is optimized and the optimal dimensions of that Retaining Wall are calculated. Then the effect of uncertainties, which are in the design parameters of that optimal gravity Retaining Wall, on the stability factors is calculated. Finally, using the concept of reliability, the risk in the safety factors of the Retaining Wall is obtained. In this paper, it is shown that if there is 10% uncertainty in design parameters the uncertainty propagation on safety factors is about (-80, +345)%, but this uncertainty propagation can increase the reliability(positive aspect of uncertainty) and risk(negative aspect of uncertainty) with a probability of 98. 6039% and 1. 3961% respectively. Then using the reliability block diagram, the total amount of reliability and risk for the gravity Retaining Wall is calculated which are equal to 79. 3169 and 20. 6830%, respectively. The innovations of this paper can be listed as below: 1) using Self-Adaptive Genetic Algorithm and Many Objective Genetic Algorithm, which have been used to optimize the Retaining Wall and calculate the uncertainty propagation on safety factors respectively. 2) Calculating reliability and risk using fuzzy set theory. 3) using reliability block diagram (RBD) to calculate the overall reliability and risk.