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When predicting ground surface settlement caused by constructing a new tunnel beneath existing structures, traditional stochastic medium theory inadequately accounts for the effects of abrupt changes in the cross-sectional areas of variable-section tunnels and the presence of existing structures, potentially leading to significant errors. In this paper, an enhanced ground surface settlement prediction model, based on stochastic medium theory, is proposed. The model equates the settlement of the existing structure's base slab to that of the overlying soil and divides the horseshoe-shaped tunnel cross-section into eight arc segments, which are calculated using a polar coordinate system. Furthermore, the model treats soil loss at the junctions of variable-section tunnels as a linear transition, introduces the concept of a linear transition segment for variable sections, and accounts for the superimposed effects of closely spaced twin-tunnel excavations. Based on this model, a general-purpose calculation program has been developed that enables the rapid prediction of ground surface deformation caused by a variable-section tunnel passing beneath existing structures, simply by inputting engineering parameters. Finally, the accuracy of the prediction model was validated through comparisons with field measurement data, finite element analysis results, and calculations based on traditional stochastic medium theory. The results indicate that the proposed prediction model demonstrates high consistency with field data and finite element analysis results, whereas traditional stochastic medium theory results exhibit significant errors. This model is scientifically valid and provides a reliable reference for predicting ground surface settlement in comparable variable-section metro tunnel construction projects. [ABSTRACT FROM AUTHOR]

• Strength and fatigue properties of argillaceous siltstone under different upper limit loads investigated. • Weakening and strengthening mechanism of argillaceous siltstone under different upper limit loads was revealed. • Increased uniformity of crack size and increased effective bearing surface contribute to rock strengthening. • Crack development tends to become localized and an increase in fracture scale leads to rock weakening. To examine the strength and fatigue characteristics of argillaceous siltstone under varying upper limit loads, cyclic-to-monotonic loads and fatigue failure tests were carried out with the upper limit load in different characteristic stress ranges. At upper limit loads between crack initiation stress and damage stress, the anti-deformation capacity and peak strength of argillaceous siltstone improved considerably after cyclic loading. Rock fatigue failure occurred when cyclic loads surpassed the stress causing damage, and the strain at the control point on the uniaxial compression (UC) curve served as a benchmark for identifying rock fatigue failure. The fatigue strength of the argillaceous siltstone was around 80–89% of the UC strength. The logarithm of fatigue life showed a negative linear correlation with upper limit load. In addition, deformation characteristics and modulus of elasticity also confirmed the weakening and strengthening phenomenon of argillaceous siltstone at various upper limit loads. On the basis of the macroscopic mechanical behaviour and microscopic fracture features of argillaceous quartz sandstone, the weakening and strengthening mechanism of argillaceous siltstone at a range of upper limit loads was revealed. The results indicate that increased uniformity of crack size, reduced degree of fragmentation and increased effective bearing surface contribute to rock strengthening, while crack development tends to become localized and an increase in fracture scale leads to rock weakening. [ABSTRACT FROM AUTHOR]