Probabilistic-based analysis of a shallow square footing using Monte Carlo simulation

Abstract

In this research, the bearing capacity (BC) of square shallow foundations at a depth of 0.5 m has been computed with different width ranged from 1 m to 4 m utilizing direct approach based on cone tip resistance (qc). The qcs have been measured through performing the Cone Penetration Tests (CPTs) on soil at four locations in the site of water intake project in Nasiriyah, Iraq as part of a soil site investigation program. The suggested applied vertical loads were 50–550 kPa. The qcs below the foundation level were considered uncertain and were simulated as random variables. Different probability distributions (PDs) were used to simulate the qcs values: normal, logistic, lognormal, Gamma, Weibull, Inverse Gaussian and Rayleigh distributions. Choosing the appropriate distribution was based on a goodness of fit (GOF) test. Monte Carlo simulation (MCS) was used to model the limit state function (LSF) based on a direct solution. It was found that the bearing capacity is sensitive to both the coefficient of variation of qcs and applied vertical load. It also was found that different PDs for soil parameters may result in the different PD of BC. Varying the width of shallow foundations changes the values of qcs and their probability distributions. According to this change, the reliability index of BC is slightly affected by the width of the foundation. The reliability index shows a good value at stress 100 kN/m2 higher than the target reliability and the reliability equal to zero at 550 kN/m2. A nonlinear behavior was observed between the probability of bearing capacity failure and the coefficient of variation of the applied vertical load.