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Abstract
Abstract A new approach for stochastic upper bound kinematical analyses is described. The study proposes an iterative algorithm that uses the Vanmarcke spatial averaging and kinematical failure mechanisms. The iterative procedure ensures the consistency between failure geometry and covariance matrix, which influences the quality of the results. The proposed algorithm can be applied to bearing capacity evaluation or slope stability problems. The iterative algorithm is used in the study to analyse the three-dimensional undrained bearing capacity of shallow foundations and the bearing capacity of the foundation for two-layered soil, in both cases, the soil strength spatial variability is included. Moreover, the obtained results are compared with those provided by the algorithm, based on the constant covariance matrix. The study shows that both approaches provide similar results for a variety of foundation shapes and scale of fluctuation values. Therefore, the simplified algorithm can be used for purposes that require high computational efficiency and for practical applications. The achieved efficiency using a constant covariance matrix for one realisation of a three-dimensional bearing capacity problem that includes the soil strength spatial variability results in about 0.5 seconds for a standard notebook. The numerical example presented in the study indicates the importance of the iterative algorithm for further development of the failure mechanism application in probabilistic analyses. Moreover, because the iterative algorithm is based on the upper bound theorem, it could be utilised as a reference for other methods for spatially variable soil.
Highlights
Stochastic analyses are currently used extensively in a wide range of geotechnical applications
The greatest differences in bearing capacity are observed between the constant covariance matrix (k=0) and the first iteration in algorithm ‘A’ (k=1) and between the first and the second iterations in algorithm ‘A’ (k=1, k=2)
The use of the iterative algorithm ensures the consistency between the failure geometry and the covariance matrix, from which the average soil strength parameters are determined - the averaging procedure is following Vanmarcke’s spatial averaging (Vanmarcke, 1977a, 1977b, 1983)
Summary
Stochastic analyses are currently used extensively in a wide range of geotechnical applications. This is the reason of soil spatial variability caused by the geological processes that form the soil layer (e.g., Ferreira et al, 2015). The numerical efficiency of most existing probabilistic methods is not sufficient for practical applications where three-dimensional analyses are crucial. This is true especially for three-dimensional issues for which the three-dimensional nature of soil strength spatial variability suggests that there are
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