An interpolation and remesh based large deformation finite element method considering soil spatial variability

Numerical modelling of soil spatial variability is of significant interest in stochastic analyses of geotechnical problems. For large deformation problems, the incorporation of spatial variability is challenging, as commonly used numerical techniques such as remeshing and interpolation inevitably modify the original random field which, in turn, affects the probabilistic assessment of the geotechnical performance. To analyse the extent of such modifications, this paper investigates first the effect of interpolation in a small strain problem to assess the undrained bearing capacity of a strip footing. As expected, the effects of interpolation in the original random field for undrained shear strength s u are small, with differences (or errors) of approximately 5.1% in the coefficient of variation (COV) and 8.5% in scale of fluctuation (SOF). Smaller errors close to 2% are observed in the mean bearing capacity and corresponding COV. The investigation is then extended to study large deformation finite element (LDFE) problems, where more frequent remeshing and interpolations are required. The results from the simulation of a cone penetration test (CPT) confirm that the repeated use of these numerical strategies introduce errors which accumulate during the simulation. To mitigate this accumulation of errors, a new approach is developed, extending existing LDFE into LDRFE (large deformation random finite element), using a set of dummy material points (MPs) to store the random field with their positions updated after each increment. The random field values in the new mesh are remapped from the dummy MPs (rather than from the old mesh), minimising the modifications to the random field, and facilitating the effective simulation of material redistribution.