Applications of Statistics and Probability in Civil Engineering – Faber, Köhler & Nishijima (eds) © 2011 Taylor & Francis Group, London, ISBN 978-0-415-66986-3 1673 Probabilistic characteristics of strip footing bearing capacity evaluated by random finite element method J. Pieczyńska & W. Puła Institute of Geotechnics and Hydrotechnics, Wroclaw University of Technology, Poland D.V. Griffiths Division of Engineering, Colorado School of Mines, Golden, CO, USA G.A. Fenton Dalhousie University, Halifax, Nova Scotia, Canada ABSTRACT: The Random Finite Element Method has been employed for calculating the random characteristics of bearing capacity of a strip foundation. The study has been carried out for two different soils; a grey-blue clay from Taranto in Italy, which is well defined from a stochastic point of view, and a cohesionless soil with assumed stochastic characteristics. The authors have focused on developing a formulation, which includes anisotropic random fields of cohesion as well as the angle of internal friction. The effect of self weight has been incorporated for the first time in studying the bearing capacity of spatially variable soil. Results clearly show that the introduction of anisotropy into random fields is more realistic, and makes RFEM predictions more effective for design purposes. where q f is the ultimate bearing stress, c is the cohesion, q is the overburden load due to founda- tion embedment, γ is the soil unit weight, B is the footing width, and N c , N q and N γ are the bearing capacity factors. In earlier work, numerical algorithms created for RFEM by Fenton and Griffiths (2003) simplified the analysis and focused on the random character of soil parameters. The ultimate bearing stress (neglecting the contributions of both the footing embedment and the soil weight) was given by: q f = cN c (2) where the N c expression is given below (e.g. Bowles 1996): N c e = +       − π φ π φ φ tan tan tan 2 4 2 1 (3) Fenton and Griffiths (2003) have analyzed iso- tropic subsoil assuming that the spatial correla- tion is the same in both the vertical and horizontal directions. They have pointed out the presence of the so called “worst case”, which means that in every single situation it is possible to assign the characteristic value of correlation length corre- sponding to the most conservative evaluation of the bearing capacity. 1 INTRODUCTION The design of shallow footings is often based on the evaluation of bearing capacity. The random character of the physical and mechanical soil properties heavily influences the randomness of the bearing capacity estimation, which is not usually taken into account into practice. However, some new building codes, such as Eurocodes, have suggested reliability-based design as a one of the possible design approaches. In this paper 2D numerical simulations are employed for the estimation of shallow footing bearing capacity in conjunction with the Random Finite Element Method (RFEM). The numerical methodology of RFEM was first introduced by Griffiths and Fenton (1993) for a seepage problem, and has since been employed in many applications (e.g. Griffiths and Fenton 2001, Fenton and Griffiths 2003, Griffiths et al. 2006, Fenton and Griffiths 2008). RFEM connects random field theory (Vanmarcke 1984) and deterministic finite element methods by taking into account the mean value, standard deviation, and correlation length of strength and other geotechnical parameters. Usually bearing capacity design of shallow foun- dation utilizes the formula proposed by Terzaghi (1943). q f cN c qN q BN = + + 1 2 γ γ , (1)