Implementation of Fuzzy Reliability Analysis for Elastic Settlement of Strip Footing on Sand Considering Spatial Variability

This paper deals with the reliability analysis for the elastic settlement of the surface strip footing resting on cohesionless soil using the concept of fuzzy set theory in conjunction with the finite-element method (FEM). Three types of soil profile (homogeneous, inhomogeneous, and layered) are considered for the analysis. The elastic modulus of soil, $E_s$, is considered as a fuzzy variable maintaining a certain membership function, i.e., triangular or trapezoidal. The Poisson’s ratio ($\upsilon$) is kept constant throughout the analysis. Spatial variability of the soil parameter is taken into consideration for both isotropic and anisotropic scale of fluctuations. Depending upon the soil type, variation of the probability of failure ($P_f$) for different coefficients of variation (COVs), different modular ratio, and different COV ratios of $E_s$ is examined. A parameter ($s_{\lim }^0$) indicating the required limiting settlement to obtain zero failure probability is proposed to account for various soil conditions, which is more significant for the design perspective. Results indicate that the failure probability ($P_f$), more precisely $s_{\lim }^0$, increases as the COV of $E_s$ increases. Moreover, the influence of the correlation length on the $s_{\lim }^0$ value is also highlighted, and it is observed that the $s_{\lim }^0$ values are more sensitive to the horizontal scale of fluctuation (${\delta }_h$) than the vertical scale of fluctuation (${\delta }_v$) for the anisotropic case.