Abstract
The paper examines three-dimensional (3D) analyses of the load bearing capacity of square and strip footings on a spatially variable cohesive–frictional (c–φ) soil. Embedded, rigid and smooth footings are considered. Cohesion and friction angle are modelled using random fields. The vertical scale of fluctuation (SOF) is based on earlier studies of natural soils. For the square footing problem, the horizontal SOF is the subject of a parametric study. For the strip footing, only one value of the horizontal SOF is assumed, and the parametric study concerns the modelled length of the foundation. To generate the fields of strength parameters, the Fourier series method is employed. For both problems analyzed, the influence of the parameters on the probabilistic characteristics of the bearing capacity of the soil is investigated. For the square footing problem, both the mean value of bearing capacity and its coefficient of variation increase with an increasing horizontal fluctuation scale, but they stabilize at higher values of SOF. For the strip footing problem, it appears that 2D modelling is a very conservative approach, and for the precise assessment of the probability of foundation failure, the footing should be modelled in 3D.
Highlights
The past 20 years have seen increasingly rapid advances in the field of random analysis of foundations based on modelling spatial variability in soil properties using random fields
As indicated by Cherubini [10], the value of the horizontal scale of fluctuation is usually greater than the vertical one. It was demonstrated in papers [30, 39] that, for a given vertical SOF, using the same value of SOF in both the vertical and horizontal directions may lead to smaller values of bearing capacity coefficient of variation compared to cases where the horizontal SOF was significantly greater than the vertical one
It is worth noting that the maximum value of coefficient of variation (CoV) obtained for high values of SOF as well as the general trend in the CoV function is in good agreement with the results obtained in the previous study of a strip foundation modelled in 2D on the same soil for high values of horizontal SOF [30]
Summary
The past 20 years have seen increasingly rapid advances in the field of random analysis of foundations based on modelling spatial variability in soil properties using random fields. Simoes et al [35] used an upper bound formulation of finite element limit analysis (FELA) in order to check the influence of modelling strip foundations on spatially variable 3D soil with regard to the probability characteristics of structure bearing capacity. For these simulations, the Latin hypercube sampling technique was used, which allowed the limiting of a satisfactory number of simulations compared to the crude Monte Carlo technique. The present work, which is an extension of earlier studies, aims to analyze the random bearing capacity of embedded square and strip footings resting on a natural spatially variable cohesive–frictional soil. The work is summarized by a section discussing the conclusions of the study
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