In this paper, an algorithm for calculation of active lateral pressure on RETAINING WALLS at seismic condition is presented. In this algorithm, that its formulation is based on lower bound of limit analysis method, by considering a stress discontinuity and finding the acceptable stress fields on its two sides, active force is calculated. Soil cohesion and internal fraction angle, also the cohesion and friction between the soil and wall are considered. Results are compared with other researchers and the algorithm validation is confirmed.

The purpose of this study is to investigate the seismic design methods of the RETAINING WALLS. Seismic behavior of the RETAINING WALLS for dynamic loads, seismic design and stability of these structures during the earthquake were studied by studying RETAINING wall design methods. The overall lateral pressures during earthquake vibrations are the static pressures that occur before the earthquake and the dynamic pressures generated by the earthquake, and the wall response is affected by both pressures. The results of this study show that if there is a possibility of sliding, rotating, or deforming to a sufficient degree to be able to mobilize the active soil pressure, the dynamic wall pressures will be applied via static or semi-static Mononobe-Okabe methods. In case of impermeability of the RETAINING WALLS (fixed WALLS), elastic analysis is also performed, and the most common dynamic analysis methods include the Mononobe-Okabe semi-static method, the Steedman-Zeng method, the Wood method and the Westergaard method, which can be developed.

In the present paper, lessons are learnt from ant society so that humankind can optimize his engineering issues. As an example of such issues, a reinforced concrete RETAINING wall for which the application of optimization can reduce the costs involved is considered. Traditional design procedure for reinforced concrete RETAINING WALLS is unable to design an optimized wall unless a large trial effort is undertaken. This paper introduces a learning procedure from ants, which is a general search technique for the solution of difficult combinatorial problems with its theoretical roots based on the foraging behavior of ants. This methodology arrives at an optimal design for concrete RETAINING WALLS due to its capability to explore and exploit the solution space effectively. The basis of analysis in this paper is to determine the minimum weight and costs in the design of concrete RETAINING WALLS following a computation of lateral total thrust on the wall due to backfill pressures, bearing capacity consideration, settlement analysis, stability analysis, and application of design of reinforced concrete principles. The results clearly indicate that ant colony can educate engineers comprehensively to reach a minimum cost justified RETAINING wall through an optimization approach.

Gravity WALLS are commonly used as earth RETAINING systems supporting fill slopes adjacent to roads and residential areas, especially to protect the transportation facilities and/or nearby structures in regions prone to earthquakes. Analysis of RETAINING WALLS behavior against earthquake is an important task for geotechnical engineers for reasons such as soil complex seismic behavior and inefficiency of quasi-static analyses. Seismic analysis and design of earth RETAINING WALLS is a difficult task, which traditionally requires the determination of the dynamic soil pressures induced by the soil seismic motion on the wall.Understanding the performance of a RETAINING wall during an earthquake is very important for an economical design and reducing the damages caused by large earthquakes. Calculated displacement of RETAINING WALLS has a key role in the optimal performance design of these structures under seismic loadings.The efficiency of a wall after an earthquake depends on its seismic displacement. Excessive displacements may not only cause the wall to collapse, but also cause to damage the adjacent structures.There have been numerous examples of this type of failure in recent earthquakes. Though the quasi static method for rational design methods of RETAINING structures has been performed for several decades, deformations ranging from slight displacement to catastrophic failure have been observed in many earth RETAINING structures during the recent major earthquakes.Many researchers have developed design methods for RETAINING WALLS during earthquakes by using different approaches. In this paper, an algorithm for calculation of permanent displacements of RETAINING WALLS in seismic conditions is presented. Formulation of this algorithm is based on the upper bound limit analysis. Displacement of the wall is calculated by obtaining its yield acceleration by limit analysis, and then combination of the proposed method with Newmark method. Effect of various parameters on the displacement of the WALLS is studied.For the upper bound theorem to be valid, the velocity field in the failure mechanism must conform to the normality flow rule (associated with the yield condition). The term normality rule originates from the geometric property of the potential law where the deformation rate vector is perpendicular (normal) to the yield surface.When dense sand is subjected to shear, it simultaneously exhibits volumetric changes (dilatancy). These changes, when described by the flow rule associated with the Mohr–Coulomb yield condition, tend to overestimate the true dilatancy. There are two distinct issues that need to be addressed: (1) How does the departure from the normality rule affect the yield acceleration of the structure, and (2) what flow rule should be used to obtain a reasonable estimation of the true displacements of a structure subjected to seismic excitation.The first question was addressed earlier by recent researchers who indicated that the yield acceleration of a soil structure built of “nonstandard" soil (“nonstandard” soil is one with deformation governed by the non-associative flow rule) can be obtained with sufficient precision by the kinematic approach if internal friction angle and cohesion of the soil is modified. For the second issue, the deformation description is described by the true dilatancy angle to conform the true material behavior and for prediction of the true (finite) displacements, Effect of various parameters on yield acceleration and the displacement of the WALLS is studied. Internal friction and dilatancy angles of the soils have the most important influence on the results.

Dolphin Echolocation Optimization (DEO) is a newly developed meta-heuristic optimization method inspired from dolphin’s rules for searching their environment. In this paper, reinforced cantilever RETAINING WALLS are designed by DEO. Results show that DEO not only leads to better results in comparison to the previously utilized algorithms but also optimality curves achieved with this method provides the engineers better understanding of the design.

RETAINING WALLS constructed adjacent to underground water are the structures which may be influenced by liquefaction. The design of these structures under vibration involves determining their displacements and forces caused by earthquake and liquefaction phenomena. In this study, it is attempted to assess the effect of liquefaction on the behavior of RETAINING WALLS using finite element method (FEM). The OPENSEES software is used for this purpose, which can simulate the behavior of saturated porous media using the u-P correlation formulation. Moreover, the Dafalias-Manzari critical state two-surface plas-ticity behavioral model is applied to simulate the behavior of sand, which can model a variety of behaviors of saturated sand in various uniaxial and cyclic loadings under drained and undrained conditions for different relative densities. The results of this study suggest that the OPENSEES software and Dafalias-Manzar behavioral model possess essential capabilities for numerical modeling of behavior of RETAINING WALLS under liquefaction conditions. The presence of RETAINING WALLS also chang-es the pattern of development of excess pore water pressure, particularly at middle depths of the wall.

In this study, by using analytical methods, new formulas for calculating natural frequencies of RETAINING WALLS with variable cross section are proposed. Different methods for calculating natural frequency, such as analytical, numerical and experimental methods, are described. Then, using the exact solution of the problem, new formula for calculating the first mode of vibration in RETAINING WALLS with constant cross sections is proposed. The Rayleigh approximation method was used to obtain the natural frequency of RETAINING WALLS with varying cross sections and taking the effect of backfill soil into the consideration. The results obtained from the proposed formulas are compared with the result of numerical analysis using finite element software and good agreements have been found.

Distribution of static active earth pressure on an inclined RETAINING wall, with frictional or cohesive-frictional backfill, has been studied in the present research. Based on the limit equilibrium concept, and by implementing the horizontal slices method (HSM), two formulations have been proposed for determination of critical failure wedge. Results obtained from these formulas and results of the suggested equations by other researchers have been compared. Findings of current study show that horizontal slices method is capable of predicting the stress distribution and angle of failure wedge for inclined WALLS with high degree of accuracy. In addition, this method is applicable for various conditions of soil and wall and is able to consider the slope of backfill, friction between soil and wall, cohesion of soil and the effect of surcharge, simultaneously. Application of achieved formulation from horizontal slices method reveals that active earth pressure on inclined WALLS is nonlinear for both frictional and cohesive-frictional soils and the center of mass point of the resultant force would be located in an elevation less than one third of the height of wall.

Current design of Geo synthetic-reinforced soil (GRS) WALLS, shows that the horizontal deformations in the WALLS increases rapidly with height. To take advantage of both the aesthetics and the economics of GRS WALLS while considering high heights, multi-tiered WALLS are often used. In this context, 12 models of the WALLS were constructed and their performance was determined under static loading. This study presents a series of model tests on the GRS WALLS in a tiered configuration, to evaluate the effects of factors, including the offset distance between adjacent tiers and number of tiers, on the lateral displacements of the wall facing and ultimate bearing capacities of the strip footings on the multi-tiered GRS WALLS. The ultimate bearing capacity and wall deflection can be significantly improved by increasing the number of tiers wall and increase of tier-offset. Interaction between the upper and lower WALLS significantly influences the tier-offset, and the interaction between the WALLS, significantly increase in the horizontal deformation in the wall face for the upper wall. With an increase in the offset distance, the lateral displacement decreased significantly, particularly in the upper tier. The experimental results showed that, the Performance in Four layers of reinforcement, and two tier WALLS, the optimum offset distance obtained for D/H= 0. 35. When the offset becomes significantly large, each tier functions independently

The shape of slip surface of the wedge creating lateral thrust on rigid RETAINING WALLS plays an important role in the magnitude, distribution, and height of point of application of lateral thrust. Considering the shape of slip surface as linear, circular, logarithmic spiral, or a combination of them has been used in the literature. In the Coulomb lateral earth pressure method, a linear distribution of soil pressure on RETAINING WALLS is tentatively assumed and thus the point of application of total thrust is placed at one third of the wall height from the wall bottom. However, some experimental studies have revealed non-linear distribution of lateral earth pressures and that the point of application of resultant thrust is placed upper than one third of the wall height. In the present study, a plasticity equation is used to determine the reaction of the stable soil on cohesionless backfill supported by a RETAINING wall using an empirical equation derived from experiments performed in the field by others. A new analytical solution for determining the total resultant thrust on the wall is introduced and the distribution of pressures and the point of application of total thrust are computed. The results have been compared with some analytical methods, experimental data, and also with available data reported from field, demonstrating the accuracy and capability of the developed method. The results show that the distribution of the active lateral earth pressure is nonlinear and the point of application of total thrust is located about 0.42H from the wall bottom (H=wall height). In addition, the application point of total thrust is nonlinear function of soil-soil, wall-backfill soil friction angels and the height of the wall.