Temperature differences between the surrounding ground and the tunnel lining will cause a variation of the tunnel lining forces. The hyperstatic reaction method (HRM) could be efficiently and simply used to investigate the impact of thermal load on tunnel linings. First, the steady state numerical solution is derived for a shallow circular tunnel to estimate the internal forces and displacements of tunnel lining caused by thermal load. The effective strain coefficient β_Tl is deduced to calculate the thermal stresses in tunnel lining. Secondly, the influence of the temperature difference on the internal forces of tunnel lining is investigated using the HRM method considering different lining elastic modulus, lining thickness and ground coefficient of thermal expansion. Lastly, the impact of fires which will be able to modify the elastic modulus of tunnel lining is investigated, which makes it possible to predict the damage of tunnel lining caused by fires.

Although quasi-rectangular tunnels have been widely used in underground projects, there is no related research work that was carried out to design this kind of tunnel excavated in the rock masses that followed the Hoek–Brown (HB) criterion. By transforming the strength parameters of the rocks that obey the HB failure criterion into equivalent strength parameters of the Mohr–Coulomb (MC) criterion, the lining internal forces of a quasi-rectangular tunnel are investigated in this manuscript in light of bending moments and normal forces using the Hyperstatic Reaction Method (HRM). After comparing with the values of a model test and verifying the present method, the influence of different tunnel depths, H, different rock unconfined compressive strengths, ${\sigma }_{ci}$, and the geological strength parameter GSI on the lining internal forces of the quasi-rectangular tunnel is then investigated. The obtained results indicate that the parameters H, ${\sigma }_{ci}$, and GSI have a significant effect on the lining internal forces of the quasi-rectangular tunnel. The work presented in this paper provides a theoretical reference for designing the quasi-rectangular tunnel support structure built in the rock masses following the Hoek–Brown criterion.

The kinematic method of limit analysis theory was adopted in this paper to calculate the seismic bearing capacity of the shallow strip foundation on a rock mass obeying the non-linear modified Hoek-Brown failure criterion. The generalized Prandtl failure mechanism was chosen, which is different from the multi-wedge failure mechanism assumption commonly used in previous research. Three angle parameters were used to control the mechanism shapes, and the equivalent friction angle and equivalent cohesive were adopted to faithfully reflect the shape characteristics of the failure mechanism. The seismic action was considered using the pseudo-static method, which is simplified to the inertial force determined by the horizontal seismic coefficient. The validation of the present method was carried out by comparing with previous analytical results and the finite element model. Subsequently, the influences of the surface overload, the properties of the rock mass, and the seismic action on the shape and ultimate bearing capacity of the failure mechanism were investigated. For the convenience of practical engineering, this paper gives the ultimate bearing capacity of strip foundations on five representative rock foundations, and the variation trend of bearing capacity with the unit weight of rock mass, surface overload, and horizontal seismic coefficient.

The present study performs a stability analysis of a three-dimensional (3D) rock slope in disturbed rock masses following the Generalized Hoek–Brown (GHB) failure criterion. The factor of safety (FoS) of the slope is derived and the optimal solution is captured combining the limit analysis method and the strength reduction technique. It is indicated by the parametric analysis that the 3D geometric characteristics have a significant impact on slope stability such that FoS decreases sharply with the increase in the width-to-height ratio $B/H$ within $0<B/H\le 2.0$ and thereafter reaches a constant value asymptotically. The FoS decreases more than 60% linearly when the disturbance factor D increases from 0 to 1.0. Stability charts and slope angle weight factor f_{β_3D} for 3D slopes are proposed to provide a convenient and straightforward approach to obtain the FoS solutions of 3D slopes. A case study was carried out to apply the stability charts on practical engineering cases, which showed that slope stability under two-dimensional (2D) plane strain will lead to conservative results, and a 3D stability analysis of slope is more appropriate, especially for a slope with a limited width.

As big cities become more dense, there is a growing demand for infrastructures, i