A new design equation for drained stability of conical slopes in cohesive-frictional soils

New plasticity solutions to the drained stability of conical slopes in homogeneous cohesive-frictional soils were investigated by axisymmetric finite element limit analysis. Three parameters were studied, i.e. excavated height ratios, slope inclination angles, and soil friction angles. The influences of these parameters on the stability factor and predicted failure mechanism of conical slopes were discussed. A new design equation developed from a nonlinear regression of the lower bound solution was proposed for drained stability analyses of a conical slope in practice. Numerical examples were given to demonstrate a practical application of the proposed equation to stability evaluations of conical slopes with both associated and non-associated flow rules.     

Axisymmetric loading on nanoscale multilayered media

Multilayered nanoscale structures are used in several applications. Because the effect of surface energy becomes nontrivial at such a small scale, a modified continuum theory is required to accurately predict their mechanical behaviors. A Gurtin–Murdoch continuum model of surface elasticity is implemented to establish a computational scheme for investigating an elastic multilayered system under axisymmetric loads with the incorporation of surface/interface energy. Each layer stiffness matrix is derived based on the general solutions of stresses and displacements obtained in the form of the Hankel integral transform. Numerical solutions to the global equation, which are formulated based on the continuity conditions of tractions and displacements across interfaces between layers, yield the displacements at each layer interface and on the top surface of the multilayered medium. The numerical solutions indicate that the elastic responses of multilayered structures are affected significantly by the surface material properties of both the top surface and interfaces, and that they become size dependent. In addition, the indentation problem of a multilayered nanoscale elastic medium under a rigid frictionless cylindrical punch is investigated to demonstrate the application of the proposed solution scheme.