This paper presents a reliability analysis of the pseudo-static seismic bearing capacity of a strip foundation using the limit equilibrium theory. The first-order reliability method (FORM) is employed to calculate the reliability index. The response surface methodology (RSM) is used to assess the Hasofer eLind reliability index and then it is optimized using a genetic algorithm (GA). The random variables used are the soil shear strength parameters and the seismic coefficients (kh and kv). Two assumptions (normal and non-normal distribution) are used for the random variables. The assumption of uncorrelated variables was found to be conservative in comparison to that of negatively correlated soil shear strength parameters. The assumption of non-normal distribution for the random variables can induce a negative effect on the reliability index of the practical range of the seismic bearing capacity.

Introduction

Uncertainty is an important issue in engineering design as geotechnical engineers can basically introduce uncertainty in the design when using a global safety factor. Reliability methods have therefore become promising when assessing the effect of uncertainty on geotechnical structure design. The designs using reliability assessment were applied to many geotechnical engineering projects (e.g. Mollon et al., 2009a,b, 2011, 2013; Griffiths and Fenton, 2001; Griffiths et al., 2002; Kulhawy and Phoon, 2002). Many theories have also been used to study the seismic bearing capacity of a strip foundation (e.g. Budhu and AlKarni, 1993; Dormieux and Pecker, 1995; Soubra, 1997). Their results indicated that the value of the bearing capacity decreased with the increase of the seismic acceleration coefficient. Inertia forces in the soil mass decrease the bearing capacity of the soil and, as a result, the bearing capacity of the foundation decreases. In recent years, some researchers such as Zeng and Steedman (1998), Garnier and Pecker (1999), Askari and Farzaneh (2003), Gajan et al. (2005), Knappett et al. (2006), and Merlos and Romo (2006) have drawn the same conclusions by using the dynamic centrifuge tests. Using the characteristics method, Cascone and Casablanca (2016) evaluated the static and seismic bearing capacity factors for a shallow strip foundation by the pseudo-static approach. Other researchers such as Pane et al. (2016) numerically obtained the bearing capacity of soils under dynamic conditions. Shafiee and Jahanandish (2010) employed the finite element method to determine the seismic bearing capacity of strip foundations with various seismic coefficients and friction angles. They also presented curves relating the seismic bearing capacity factors to the seismic acceleration coefficient. In this context, the homogeneous soils and seismic properties are used to analyze the seismic bearing capacity of strip foundations. The bearing capacity is calculated using a single deterministic set of parameters. Reliability analysis is then used to assess the combined effects of uncertainties and provide a logical framework for selecting the bearing capacity that is appropriate for a degree of uncertainty and the failure consequences. Thus, the reliability assessment useful for providing better engineering decisions is performed as an alternative to the deterministic assessment.