Stochastic seismic performance of slopes reinforced by a combination of piles and anchor cables using the probability density evolution method

A combination of piles and anchor cables effectively enhances the seismic stability of slopes. However, due to the uncertainty of earthquake and soil properties, the stochastic response of slopes reinforced with piles and anchor cables (SRPC) remains unclear. This study presents a framework for the stochastic analysis of the SRPC using the probability density evolution method. The soil deformation, natural frequency of the slope, and the load sharing ratios of piles and anchor cables were investigated. Additional analysis was also conducted to evaluate the effects of the time-history characteristics and randomness of earthquakes, and pile modulus on the stochastic response of the SRPC. The results indicate that combining piles and anchor cables significantly reduced the probability of large soil deformation and increased the natural frequency of slopes compared to that reinforced with either piles or cables. However, the soil displacement increased considerably as the dominant frequency of earthquakes approached the natural frequency of the SRPC. Therefore, the variability in frequency spectra should not be neglected when considering the randomness of earthquakes. Furthermore, the load sharing ratio of piles increased dynamically and was higher than that of cables. A higher pile modulus contributed to the enhanced effectiveness of piles in sustaining earthquake loads.