Bearing Capacity of Spatially Random Cohesive Soil Using Numerical Limit Analyses

Abstract

This paper describes a probabilistic study of the two dimensional bearing capacity of a vertically loaded strip footing on spatially random, cohesive soil using Numerical Limit Analyses (NLA-CD). The analyses uses a Cholesky Decomposition (CD) technique with mid-point discretization to represent the spatial variation in undrained shear strength within finite element meshes for both upper and lower bound analyses, and assumes an isotropic correlation length. Monte Carlo simulations are then used to interpret the bearing capacity for selected ranges of the coefficient of variation in undrained shear strength and the ratio of correlation length to footing width. The results are compared directly with data from a very similar study by Griffiths et al. in which bearing capacity realizations were computed using a method of Local Average Subdivision (LAS) in a conventional displacement-based Finite Element Method (FEM-LAS). These comparisons show the same qualitative features, but suggest that the published FEM calculations tend to overestimate the probability of failure at large correlation lengths. The NLA method offers a more convenient and computationally efficient approach for evaluating effects of variability in soil strength properties in geotechnical stability calculations.

Finite Element Analysis for Spatially Stochastic Soil—Anisotropic Studies

“…1b showed that the probability of failure gradually decreased with increase of correlation length for FOS=3.0. The results from Kasama and Whittle (2011) are much lower than other data points and decreasing nearly to zero. Therefore, it requires some justifications on these different FEM methods.…”

“…3. The effect of anisotropic conditions for FOS=2.0 and 3.0 were presented and compared with Kasama and Whittle's results (Kasama and Whittle, 2011) in Fig. 3a&b.…”

“…The wide ranges of values of COV c and Θ from previous literature, either isotropic (Griffiths andFenton, 2001, Kasama andWhittle, 2011) or anisotropic (Vessia, et al, 2009) cases, were compared in this study are listed in Table 2. In addition, it is noticeable that in the study of Vessia, et al (2009) the horizontal Θ is much higher than the vertical one as soil in nature deposits in layers.…”

“…The results in isotropic condition from this study are very close to those of Griffiths and Fenton (2001) as expected. NLA method (Kasama and Whittle, 2011) gave the results of upper and lower limit of μ Nc and presented as 'shaded' area in Fig. 1.…”

“…Nonetheless, the deterministic approach does not provide the insights of parameter variability within a soil layer. Thus, many researchers (Griffiths and Fenton, 2001, Griffiths, et al, 2002, Kasama and Whittle, 2011, Rahman and Nguyen, 2012, Rahman and Nguyen, 2013 have used numerical approaches to capture variability of c within soil layer. For instance, Griffiths and Fenton (2001) used a random finite element method (RFEM), while Kasama and Whittle (2011) performed numerical limit analysis (NLA).…”