Chapter 19 - Probabilistic response of strip footing on reinforced soil slope

Abstract

Safe design of shallow foundation systems for structures such as buildings, electrical transmission towers, and bridge abutments situated on the reinforced foothills or sloping grounds is a challenging task for the engineers. The reduction in bearing capacity coupled with increasing chances of slope instability makes these structures more vulnerable than the structures situated on level ground. Over the years, several design engineers have been following the traditional deterministic approach for the design of such foundation system on the slopes, where constant values of soil strength parameters are considered. However, due to the different mineralogical constituents, formational process, and past loading history, natural soil deposit is very much random and heterogeneous. This chapter investigates the role of uncertainty of soil parameters on the performance of shallow foundation on the reinforced soil slope. Lower bound values of the probabilistic bearing capacity factors are obtained by combining lower bound finite element limit analysis method with random field modeling and Monte Carlo simulation (MCS) technique. Friction and dilation angles of purely cohesionless soil are considered as log-normally distributed random variables. Soil heterogeneity is incorporated by assuming different values of correlation lengths in the horizontal and vertical conditions. For both the cases, mean values of the bearing capacity factors reduce with the increasing randomness of soil friction angle and undrained shear strength for particular values of correlation lengths in the horizontal and vertical directions. The mean values of bearing capacity factors are always lower than the deterministic solutions for smaller correlation lengths, whereas for higher values of correlation lengths, values of probabilistic bearing capacity factors become almost equal to that obtained for deterministic analysis. On the other hand, to find out the settlement characteristics of footing resting on the reinforced soil slope, explicit finite difference software Fast Lagrangian Analysis of Continua is used. Along with the consideration of soil shear strength and dilation angle as log-normally random variables, the influence of geocell mattress is also studied. A series of parametric analyses are also performed with the variation of (i) setback distance of footing from the slope edge and (ii) flexural rigidity of the geocell mattress. The mean load carrying capacity of the strip footing corresponding to a particular settlement value is found to be less than that obtained for soil slope with uniform soil friction angle. Cross-correlation between soil cohesion and friction angle has significant impact on the computed value of mean load-carrying capacity of the footing. The effect of uncertainties associated with soil friction angle and soil unit weight on the stability of both unreinforced and reinforced cohesionless soil slopes subjected to strip loading are also investigated. Probability of failure of the slope is computed by performing MCS. With the increasing values of coefficient of variation of soil friction angle and unit weight, failure probability of both unreinforced and reinforced slopes increases.