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The kinematical approach of limit analysis has been historically employed to assess slope stability in the geotechnical community, for which most three-dimensional (3D) failure mechanisms are generally based on a composite of multiple common geometrical bodies. Although these failure mechanisms are straightforward, they may not perform well for slopes that involve multilayered soils with heterogeneous shear strength parameters. This paper aims at proposing a new 3D failure mechanism for steep slopes using a spatial discretization technique. The proposed failure mechanism is composed of a large number of elemental blocks that are generated point by point obeying the kinematically admissible velocity field and the normality condition. The discretization scheme makes it possible to simplify the calculations of internal energy dissipations and external work rates on the failure mechanism when both the soil properties and external loadings are spatially changing. The performance of the proposed method is illustrated to examine the stability of steep slopes in homogeneous soils, multilayer soils, and spatially variable soils, showing good agreements with previously published results and numerical modelings. [ABSTRACT FROM AUTHOR]

In this work, the stability of a reinforced tunnel face is examined by combining the homogenization method with the kinematic approach of limit analysis. A three-dimensional (3D) heterogeneous and anisotropic failure criterion for reinforced soils is first proposed according to the homogenization method, in which the possible tensile failure and pullout failure of reinforcing members are considered. The proposed homogenization method is then incorporated into the 3D rotational failure mechanism to assess the safety factor of a tunnel face by using the strength reduction technique. The applicability of the proposed method is illustrated by comparing with existing results and numerical simulations. The influences of model parameters on the calculated safety factors are finally discussed. [ABSTRACT FROM AUTHOR]

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]