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Geotechnical structures often have position-dependent soil strength parameters as a consequence of stress history, deposition process, mineralogical composition, and weathering effect. However, most available theoretical models for estimating active earth pressures focus only on homogeneous cases. By a point by point technique, this work develops a friction-angle-dependent discretized failure mechanism to evaluate the active earth pressure on backfills in the framework of the limit-equilibrium slice method. The generated failure mechanism is composed of a series of horizontal elements. Compared with previous theoretical models, the benefits of the proposed method are twofold: (1) the friction-angle-dependent failure mechanism agrees well with the actual failure surface for heterogeneous backfills; (2) not only the multilayer frictional backfill but also the backfill with a position-dependent friction angle can be accounted for. The total active earth pressure coefficient, the earth pressure distributions, and the failure mechanisms are obtained, all showing excellent agreement with the available experimental data and the existing analytical solutions. For practical use, applications to backfills with a weathered zone and spatially variable frictional angles are then conducted. Finally, the proposed model is degraded into a two-layer case in which the active earth pressure coefficients under various mechanical and geometrical parameters are tabulated. [ABSTRACT FROM AUTHOR]

This work presents a probabilistic analysis of three-dimensional (3D) seismic active earth pressures acting on rigid retaining walls that are designed to support cohesive-frictional soil masses. The analysis is implemented using sparse polynomial chaos expansions (SPCE) to represent the physical model responses. The deterministic evaluation of 3D seismic active earth pressures is conducted with the application of the kinematic approach of limit analysis combined with a pseudo-static method. All of the input parameters are deemed as random variables. After the SPCE metamodels are determined, the method of Monte Carle simulations is applied to perform the probabilistic analysis of 3D seismic active earth pressures. The effects of uncertainty levels and correlation relationships of input parameters are investigated. Several illustrative examples of the reliability-based design of retaining walls are shown. Results indicate that uncertainties in input parameters possess a notable effect on 3D seismic active earth pressures, suggesting the need to investigate the problem from a stochastic perspective. In most cases, the soil cohesion, internal friction angle, and seismic coefficient are found to be three of the parameters that affect the final response the most significantly. It is also indicated that considering 3D effects and soil cohesion has a favorable effect on increasing the stability of retained slopes. [ABSTRACT FROM AUTHOR]

The available theoretical models for evaluating seismic active earth pressures are limited to plane strain analyses and linear failure criterion. To fill this research gap, with a combination of the kinematical approach of limit analysis, the spatial discretization technique as well as the pseudo-static approach, this work develops a discretized three-dimensional failure mechanism of sloping backfills that is composed of an end cap and a central plane-strain insert to estimate the seismic active earth pressure coefficient under nonlinear failure criterion. Compared with the existing three-dimensional kinematically admissible failure mechanisms, the developed one has three significant merits: (1) the normality condition is strictly satisfied in the generation of the end cap; (2) the work rates can be computed by a summation of elementary work rates conveniently instead of tedious integral schemes; (3) the considerations of the nonlinear failure criterion and the sloping backfill. Comparisons with the existing upper bound solutions and experimental results in terms of active earth forces or active earth pressure coefficients are conducted to verify the proposed model. Parametric studies are performed to study the influences of model parameters, including the seismic coefficient, the sloping angle of backfills as well as the nonlinear parameters, on the active earth pressure coefficients. [ABSTRACT FROM AUTHOR]

The existing analytical models for predicting earth pressures based on the kinematical approach of limit analysis are limited to soil masses with homogeneous internal frictional angles. To overcome this drawback, this work proposes a discretised failure mechanism to calculate the location of earth forces and evaluate the active and passive earth pressures against inclined retaining walls with horizontal backfills for the first time. Comparisons with other existing analytical solutions, numerical simulations and experimental tests are made to verify the proposed method for the cases of single-layer and multi-layer backfills. Practical design tables are presented for a two-layer case. Application of the proposed model to three-layer backfills with a middle weak layer is presented. The influence of the position of the weak layer on the critical earth pressures and failure mechanisms is discussed. [ABSTRACT FROM AUTHOR]