This study presents an analytical elastic solution using the complex variable approach to determine the soil disturbance surrounding a shallow rectangular tunnel, taking into account the effect of gravity and considering the influence of grouting pressure applied at the tunnel boundary. A theoretical calculation model is first established by applying stress boundary conditions along the tunnel boundary. To handle the geometric complexity of the rectangular cavity, a conformal mapping function suitable for non-circular opening is adopted. This function maps the original half-infinite region with a rectangular cavity onto an annulus in the transformed plane, thereby converting the irregular cavity problem into a more tractable configuration. The boundary conditions at the ground surface and the tunnel interface are then addressed using Fourier series expansion. By solving these series-expanded equations, all unknown coefficients of the analytical functions are determined, leading to an analytical elastic solution for soil disturbance. Numerical verification validates the accuracy of the proposed approach. Moreover, parametric studies are conducted to evaluate the effects of soil mechanical properties and tunnel geometry on the soil disturbance. The findings offer a valuable reference for future investigations into construction-related issues associated with rectangular tunnels.

Inherent defects in engineering rock masses inevitably lead to randomness in mechanical parameters and uncertainty in tunnel deformation and failure. To address these challenges, this study proposes a novel coupled analysis method that integrates complex function theory, physical model testing, and Monte Carlo simulation (MCS) for the deformation estimation and failure probability analysis of non-circular tunnels. Theoretically, this method provides a high-speed, high-accuracy analytical framework that overcomes the limitations of purely numerical approaches, particularly in handling continuous–discontinuous failure processes. Practically, it enables a more reliable and efficient stability assessment of tunnel systems under uncertain geological conditions. The proposed method is applied to a traffic tunnel at the Baihetan Hydropower Station. A series of uniaxial compression tests on 40 rock specimens are conducted to obtain statistical distributions of rock deformation parameters. An analytical solution for tunnel displacement is derived using plane elastic complex function theory, and the random displacement field is estimated via MCS. Physical model tests reveal that the elastic stage accounts for 83% of the overload failure process, based on which an elastic limit displacement function is established for tunnel arch settlement and surrounding rock convergence. The failure probability of the tunnel is then calculated, and the effects of the mean, coefficient of variation, and cross-correlation coefficient of rock deformation parameters on failure probability are discussed. The entire computational process is characterized by high speed and precision, offering a new and practical tool for tunnel stability evaluation and reliability-based design.

Rock pillars in deep underground mines are subjected to complex stress environments. The combined effects of in situ stress and cyclic disturbances from mining activities lead to a redistribution of the surrounding rock mass stress field, which readily triggers instability and failure, posing severe threats to mining engineering safety. To investigate the damage mechanism of cyclic loading on rock and its weakening effect on the bearing capacity of mine pillars, this study takes limestone as the research object. A series of uniaxial compression tests were conducted on limestone specimens subjected to triaxial cyclic pre-damage, complemented by numerical simulations to further characterize the energy and deformation evolution of the damaged limestone under cyclic loading conditions. The findings are as follows: (i) Triaxial cyclic tests on limestone show that both the input energy and dissipated energy follow similar trends, decreasing rapidly in the initial stage before stabilizing. The elastic strain energy remains largely constant, with most of the input energy being stored as elastic strain energy. Under constant stress levels and cycle numbers, increases in confining pressure and frequency reduce the rock’s input energy, elastic strain energy, and dissipated energy. (ii) The peak stress of damaged limestone exhibits a positive correlation with the pre-damage confining pressure and cyclic frequency, while it decreases with an increasing number of cycles. Higher confining pressure and frequency raise the input energy, elastic potential energy, and dissipated energy at the peak stress point. (iii) Deformation and failure in damaged limestone originate from the development and propagation of localized deformation zones. Increased lateral displacement within these zones promotes the formation of macroscopic fractures. Due to significant structural heterogeneity inside the localized areas, the evolution of deformation energy is influenced by regional characteristics. (iv) Simulation results indicate that the uniaxial compressive failure of limestone involves the accumulation and propagation of micro-scale tensile cracks, which ultimately coalesce into macro-scale shear fracture surfaces. During uniaxial loading of pre-damaged limestone, newly generated cracks predominantly initiate around pre-existing cracks, with only a limited number distributed randomly. Their peak intensity shows a positive correlation with the pre-damage confining pressure.