Analytical solutions for three-dimensional stability of limited slopes

A method of three-dimensional limited slope stability analysis is presented here based on the upper-bound theorem of the limit analysis approach. A rotating collapse mechanism is considered in which energy dissipation takes place along curve velocity discontinuities. In the frictional soils, the failure surface has the shape of logarithm helicoids, with track outline defined by log-spirals. In the cohesive soils, the shape of the failure surface is torus. Angle is considered at slope top, and the critical height is less than top with no inclination. Numerical results of the proposed algorithm are presented in the form of nondimensional graphs. Some examples illustrate the practical use of the results.     

Three-dimensional stability analysis of excavation using limit analysis

The theory of limit analysis is presented for a three-dimensional stability problem of excavation. In frictional soil, the failure surface has the shape of logarithm helicoid, with the outline profile defined by a logspiral curve. The internal dissipation rate of energy caused by soil cohesion and gravity power of the failure soil is obtained through theoretical derivation. By solving the energy balance equation, the stability factor for the excavation is obtained. Influence of the ratio of width to height, the slope angle, and the top angle on the stability is examined. Numerical results of the proposed algorithm are presented in the form of non dimensional graph. Examples illustrate the practical use of the results.