Reliability analysis of three-dimensional reinforced slope considering the spatial variability in soil parameters

Abstract In this paper, a procedure is proposed for calculating the reliability of three-dimensional reinforced slopes, taking into consideration the spatial variability of soil strength parameters. An ellipsoidal sliding surface is utilized as an approximate substitute for the actual sliding surface. The Karhunen–Loève (KL) expansion method is employed to generate random fields. The safety factor of the reinforced slope is determined using the Bishop method, and the reliability is evaluated through the Monte Carlo method. Based on the procedure, the effects of different reinforcement parameters and random parameters on the mean safety factor and failure probability of three-dimensional slopes are studied and compared with the results of two-dimensional slopes. It is observed that slope reliability is significantly improved by the implementation of the upper sparse and lower dense reinforcement scheme, leading to a notable 38.4% reduction in failure probability and a 2.4% increase in the safety factor. Additionally, an effective means of enhancing slope reliability is found to be the increase in the length and number of reinforcement layers. The reliability of 3D reinforced slopes is notably influenced by the spatial variability of soil strength parameters. The degree of influence of autocorrelation distance on the failure probability is ranked as lz > lx > ly. When lz increases from 1m to 5m, the failure probability is increased by 221.85%, from 5.4–17.38%. As the correlation coefficient r(c, φ) increases from − 0.7 to -0.3, the failure probability is increased by 26.7%. The comparison with 2D reinforced slopes reveals that 3D reinforced slopes demonstrate a higher safety factor and a lower failure probability. As a result, slope reliability is tended to be underestimated by the 2D slope analysis.