Ground settlement induced by piggyback shield tunnelling in spatially variable soils: 3D random finite-element modelling

The expansion of urban rail transit has intensified the demand for tunnelling near existing infrastructure, heightening concerns over ground stability and structural integrity. Traditional deterministic analyses, which assume uniform or layered soil properties, often underestimate tunnelling risks. This study performs a three-dimensional (3D) probabilistic analysis of ground response to piggyback tunnelling in spatially variable soils, focusing on a double-track shield tunnel project in Tianjin, China. A 3D random finite element model incorporating Monte Carlo simulations is developed to evaluate the impact of spatial variability on ground settlement and tunnel deformation. The results show that the deterministic analysis predicts a maximum settlement of 8.81 mm, which is lower than the field-monitored result of 9.47 mm, while the probabilistic results align more closely with field observations. This demonstrates that deterministic analyses may underestimate settlement and highlights the advantages of random modelling in enhancing settlement predictions. To reduce the risk of tunnelling to adjacent structures, a probabilistic framework is proposed to define settlement thresholds based on exceedance probabilities. The likelihood of settlement exceeding allowable thresholds is observed to increase with higher coefficient of variation ( COV ) and vertical scale of fluctuation ( SOF y ) of Young's modulus. To maintain an acceptable exceedance probability below 1%, the allowable settlement should be conservatively set at 9.5 mm, 10.6 mm, and 11.9 mm for COV = 0.1, 0.3, and 0.5, respectively; and at 9.7 mm, 10.6 mm, and 12.0 mm for SOF y = 0.5 m, 2 m, and 10 m, respectively. These values provide a practical reference for defining safe design limits that realistically reflect site-specific soil variability. Overall, this study demonstrates the benefits of probabilistic modelling for achieving safer and more reliable piggyback tunnel designs.