Reliability assessment of shallow foundations on undrained soils considering soil spatial variability

Abstract

Structural design using partial safety factors aims at achieving an homogeneous safety level in geotechnical design without the use of more complex reliability analysis. In this work, the different Design Approaches proposed by Eurocode 7 for shallow foundations resting on the surface of undrained soils are compared in terms of the resulting reliability indices. The influence of both centered and eccentric loads, as well as homogeneous and heterogeneous isotropic and anisotropic distributions for the variability of soil properties were investigated in the reliability analysis.A finite element implementation of the upper bound theorem of limit analysis is combined with Latin Hypercube sampling to compute the probabilistic response of shallow foundations. Considering realistic probabilistic distributions for both permanent and live loads, First Order Reliability Method is used to calculate the reliability index of such structures designed according to the different Design Approaches present in Eurocode 7.The results obtained show that the Eurocode 7 leads to satisfactory reliability indices, but that significant differences between Design Approaches exist.

A computational study on the uncertainty quantification of failure of clays with a modified Cam-Clay yield criterion

“…The selection of the samples of a random variable can be used by crude Monte Carlo simulation, using pseudorandom algorithms to take a large vector of random values, or variance reduction methods can be implemented such as the importance sampling [11] and the Latin Hypercube Sampling (LHS) [3,53]. The implementation of LHS method saves a substantial computational effort in order to estimate mean value and coefficient of variation.…”

“…An alternative approach is the implementation of random field series expansion such as the spectral representation or the Karhunen-Loeve expansion or the spatial average method for providing the material input variability [1,4,13,41]. In both approaches, the sampling can be pseudorandom and non-biased or importance sampling methods can be implemented such as the Latin Hypercube Sampling (LHS) [3,53]. Then, for both methods, the standard Monte Carlo simulation can be implemented.…”

Probabilistic Failure Estimation of an Oblique Loaded Footing Settlement on Cohesive Geomaterials with a Modified Cam Clay Material Yield Function

“…Subsequently, random field processes may be implemented, like the spectral representation or the Karhunen-Loeve series expansion or the spatial average method [18][19][20][21][22][23][24][25]. The sampling method can be either non-biased through pseudorandom relations or an importance sampling method could be adopted, such as Latin hypercube Sampling (LHS) [26,27]. Then, the standard Monte Carlo simulation can be performed.…”

Uncertainty quantification in Geotechnical Engineering

“…The selection of the samples of a random variable can be used by crude Monte Carlo simulation, using pseudorandom algorithms to take a large vector of random values, or variance reduction methods can be implemented such as the importance sampling Methods and Applications, 2004 and the Latin Hypercube Sampling (LHS) A. Olsson, Sandberg, and Dahlblom, 2003a;Simoes et al, 2020a. The implementation Chapter 2.…”

“…The random sampling can be with pseudorandom and non biased methods or with the implementation of importance sampling methods such as the Latin Hypercube Sampling (LHS) (A. Olsson, Sandberg, and Dahlblom, 2003b;Simoes et al, 2020b). In some cases there are studies that implement realizations of non Gaussian random fields to the input material variables (Popescu, Deodatis, and Prevost, 1998).…”