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Although some 3D slope stability algorithms have been proposed in recent three decades, still role of pore pressures in three dimensional slope stability analyses and considering the effects of pore water pressure in 3D slope stability studies needs to be investigated. In this paper, a limit analysis formulation for investigation of role of the pore water pressure in three dimensional slope stability problems is presented. A rigid-block translational collapse mechanism is used, with energy dissipation taking place along planar velocity discontinuities. Results are compared with those obtained by others. It was found that water pressure causes the three-dimensional effects to be more significant, especially in gentle slopes. This may be related to the larger volume of the failure mass in gentle slopes resulting in more end effects. Dimensionless stability factors for three dimensional slope stability analyses are presented - including the 3D effect of the pore water pressure – for different values of the slope angle in cohesive and noncohesive soils.

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Presented is a method of three-dimensional stability analysis of convex slopes in plan view based on the Lower-bound theorem of
the limit analysis approach. The method’s aim is to determine the factor of safety of such slopes using numerical linear finite
element and lower bound limit analysis method to produce some stability charts for three dimensional (3D) homogeneous convex
slopes. Although the conventional two and three dimension limit equilibrium method (LEM) is used more often in practice for
evaluating slope stability, the accuracy of the method is often questioned due to the underlying assumptions that it makes. The
rigorous limit analysis results in this paper together with results of other researchers were found to bracket the slope stability
number to within ±10% or better and therefore can be used to benchmark for solutions from other methods. It was found that using
a two dimensional (2D) analysis to analyze a 3D problem will leads to a significant difference in the factors of safety depending
on the slope geometries. Numerical 3D results of proposed algorithm are presented in the form of some dimensionless graphs which
can be a convenient tool to be used by practicing engineers to estimate the initial stability for excavated or man-made slopes

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Most of the proposed methods for obtaining the free vibration natural frequency of the retaining wall have been presented, assuming the behavior of the wall in two-dimensional domain, and they are not able to express the three-dimensional behavior of these structures in a satisfying manner. In this paper, the plate theory is employed to analyze the free vibration of wall-soil system in three-dimensional domain. So the retaining wall is modeled as a clamped-free plate and the stiffness of the soil existing behind the wall is modeled as a set of springs. Using the approximate Rayleigh method, new analytical expression for obtaining the free vibration natural frequencies for the three first modes of the wall is represented. The results of the proposed model are compared with both the results of the other researchers and the ones from finite element method (FEM). They are also compared with the results of a full-scale experiment and it shows a good agreement. The comparison shows that modeling the wall in two-dimensional form is not accurate enough to calculate all the natural frequencies of the wall. The results of this paper show that there is a considerable difference between two- and three-dimensional behavior of the walls. The proposed method also gives the free vibration natural frequencies of the wall extensional modes with an acceptable accuracy. Finally, the effect of tensile and compressive behavior of the soil on the fundamental frequency is studied. This research can be considered as a new field in three-dimensional calculation of the retaining walls.