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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.

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