A 2D and 3D kinematically admissible rotational failure mechanism is presented for homogeneous slurry trenches in frictional/cohesive soils.Analytical approaches are derived to obtain the upper bounds on slurry trench stability in the strict framework of limit analysis.It is shown that the factor of safety from a 3D analysis will be greater than that from a 2D analysis.Compared with the limit equilibrium method,the limit analysis method yields an unconservative estimate on the safety factors.A set of examples are presented in a wide range of parameters for 2D and 3D homogeneous slurry trenches.The factor of safety increases with increasing slurry and soil bulk density ratio,cohesion,friction angle,and with decreasing slurry level depth and trench depth ratio,trench width and depth ratio.It is convenient to assess the safety for the homogeneous slurry trenches in practical applications.
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 log- spiral 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.
