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Evaluating the reliability of trenches against sliding failure is complicated by the fact that most alluvial deposits are heterogeneous and spatially variable. This means that instead of perfectly circular or linear failure surfaces, trench failure tends to be more complex, following the weakest path or zones through the material, thereby, a new method named Continuous Slip-Surface (CSS) is adopted for calculating the critical excavation depth.CSS runs an algorithm to seek for continuous slip surface. The Finite Difference Method (FDM) coupled with random field theory and CSS method is well suited to slope stability calculations since it allows the failure surface to seek out the weakest path through the soil. For an unsupported vertical cut, it was shown that the critical excavation depth acquired from CSSM is indeed an upper bound solution. It was further shown both numerically and analytically through an idealized variation model that increasing the undrained shear strength density fades the effect of shear strength variability. Correlation structure of the input variable was also shown to influence the results, although the behaviour was found different in low and high scales of fluctuation.

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