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Control Variate Approach for Efficient Stochastic Finite-Element Analysis of Geotechnical Problems

Lookup NU author(s): Dr Tom CharltonORCiD, Dr Mohamed Rouainia, Professor Richard DawsonORCiD



This is the authors' accepted manuscript of an article that has been published in its final definitive form by American Society of Civil Engineers (ASCE), 2018.

For re-use rights please refer to the publisher's terms and conditions.


© 2018 American Society of Civil Engineers. Monte Carlo simulation is the most versatile solution method for problems in stochastic computational mechanics but suffers from a slow convergence rate. The number of simulations required to produce an acceptable accuracy is often impractical for complex and time-consuming numerical models. In this paper, an element-based control variate approach is developed to improve the efficiency of Monte Carlo simulation in stochastic finite-element analysis, with particular reference to high-dimensional and nonlinear geotechnical problems. The method uses a low-order element to form an inexpensive approximation to the output of an expensive, high-order model. By keeping the mesh constant, a high correlation between low-order and high-order models is ensured, enabling a large variance reduction to be achieved. The approach is demonstrated by application to the bearing capacity of a strip footing on a spatially variable soil. The problem requires 300 input random variables to represent the spatial variability by random fields, and would be difficult to solve by methods other than Monte Carlo simulation. Using an element-based control variate reduces the standard deviation of the mean bearing capacity by approximately half. In addition, two methods for estimating the cumulative distribution function as a complement to the improved mean estimator are presented.

Publication metadata

Author(s): Charlton TS, Rouainia M, Dawson RJ

Publication type: Article

Publication status: Published

Journal: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering

Year: 2018

Volume: 4

Issue: 3

Online publication date: 13/07/2018

Acceptance date: 12/04/2018

Date deposited: 12/10/2018

ISSN (electronic): 2376-7642

Publisher: American Society of Civil Engineers (ASCE)


DOI: 10.1061/AJRUA6.0000983


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