Probabilistic analysis of tunnel deformation and ground surface settlement induced by surcharge in spatially variable soil

Existing tunnels are inevitably influenced by surrounding environments, with ground surface surcharge being one of the most significant factors affecting tunnel deformations and ground surface settlement. At the same time, the spatial variability of soils also plays a crucial role in these outcomes. However, many studies rely on deterministic analyses that overlook the spatial variability of soils, which can lead to inaccurate predictions of tunnel behavior and surface settlement. Furthermore, there is limited research that simultaneously considers the effects of both surcharge and the spatial variability of soil on these responses in a three-dimensional space. In this study, the impact of surcharge and uncertain soil properties on surface settlement and tunnel deformations was investigated based on random fields combined with the finite element method. The influence of surcharge positions L, eccentricities e, heights h, as well as the coefficient of variation of Young's modulus (COV_E) and scales of fluctuation (SOF) of Young's modulus on surface settlement and tunnel deformations were investigated. As L increases, with the surcharge shifting from the center towards the boundaries, the maximum tunnel deformations and surface settlement, along with the corresponding probability of failure (P_f) intensify, due to the limited space for dissipation of the surcharge. As e increases, these effects decrease. In contrast, an increase in h amplifies them. The larger the COV_E, the greater the impact of the surcharge on tunnel deformations, surface settlement, and the corresponding P_f. This is because a larger COV_E increases the probability of extreme realizations. Similar to the effect of COV_E, a larger SOF increases the impact of soil spatial variability.