A theoretical method of mechanical analysis for a circular tunnel reinforced by fully grouted rock bolts

Analysis of the mechanical behavior of rock mass reinforced by fully grouted rock bolts is introduced based on the interaction between the rock mass and the bolts. The model is based on the following premises: (1) the elastic behavior of the rock mass and rock bolts; (2) the plane strain condition; (3) a deeply buried circular tunnel; (4) complete contact between the bolts and the surrounding rock, that is, they are bonded together; (5) the loads on the surrounding rock from the fully grouted rock bolts are replaced by innumerable concentrated forces along the longitudinal direction of the bolts. For this, the analytical radial displacement solution for a deeply buried circular tunnel subjected to concentrated forces at arbitrary points in surrounding rock is derived. As long as this displacement solution is integrated along the length direction of the bolt, the effect of the bolt on the surrounding rock can be obtained. According to the complete contact condition at the anchoring interface and the force balance condition of the bolts, under the action of the in situ stress, linear equations made up of shear stresses on the bolts are established, from which the distribution of shear stresses and axial forces along the bolts can be solved. Model simulations confirm the previous findings that each installed bolt has a pick-up length, an anchor length and a neutral point. Besides, the influence of the parameters of the rock bolts and the surrounding rock are discussed. The conclusion is consistent with the results of a practical project without adopting any empirical equations. The results of this method can provide a theoretical basis for the design and layout of rock bolts in underground caverns.

Research on the Method and Model for Calculating Impact Load in the Rockburst Tunnel

Among several design methods of tunnel supporting structure, the load-structure method is widely used in different countries, but the determination of load is essential in this design method. The problem of rockburst is becoming more prominent as tunnel engineering enters the deep underground space. However, the research on the impact load on the supporting structure is insufficient in relevant fields. Therefore, from the perspective of energy, this paper deduces the method and model for calculating the impact load of the rockburst tunnel acting on the supporting structure by using the method of structural mechanics first, after the location effect of impact load is determined under different section types and different section sizes. The results indicated that: dynamic load factor K is related to the stiffness EI and supporting size coefficient K0 of the supporting structure, also the difference of impact load in different sections is proved. Tunnel rockburst-prone location is related to lateral pressure coefficient, thus when λ = 1, the probability of rockburst in the whole circular tunnel is the same, while side wall and vault are prone to rockburst in single-track horseshoe tunnel, and the side wall is prone to rockburst in double-track horseshoe tunnel; furthermore when λ > 1, the vault and the inverted arch are prone to rockburst; additionally, when λ < 1, the rockburst is most likely to occur in the arch waist of the circular tunnel and the side walls and the arch waist of the horseshoe tunnel. Finally, the rockburst tunnel’s local load-structure calculation model and the calculation process based on the model are provided.

Analytical Solution for Circular Tunnel under Obliquely Incident P Waves considering Different Contact Conditions

An analytical solution for the seismic-induced thrust and moment of the circular tunnel in half-space under obliquely incident P waves is developed in this study, which is the superposition of the solution for deep tunnels under incident and reflected P waves and the reflected SV waves. To consider tangential contact stiffness at the ground-tunnel interface, a spring-type stiffness coefficient is introduced into the force-displacement relationship. Moreover, the tunnel lining is treated as the thick-wall cylinder, providing more precise forecasts than beam or shell models used in previous analytical solution, especially for tunnels with thick lining. The reliability of the proposed analytical solution is assessed by comparing with the dynamic numerical results. Based on the proposed analytical solution, parametrical studies are conducted to investigate the effect of some critical factors on the tunnel’s seismic response, including the incident angles, the tangential contact stiffness at the ground-tunnel interface, and the relative stiffness between the ground and the tunnel. The results demonstrate that the proposed analytical solution performs well and can be adopted to predict the internal forces of circular tunnels under obliquely incident P waves in seismic design.

Deformation and stress theory of surrounding rock of shallow circular tunnel based on complex variable function method

After reviewing many literature foundations, the thesis combines the basic methods of elastic mechanics with mathematical knowledge, sets the bipotential stress potential complex function and analyses the relationship between stress component, strain component and stress potential function, and applies the complex variable function. The expression of the relevant stress component is derived, and the displacement boundary conditions of the surrounding rock of shallow circular tunnel are obtained. Furthermore, the paper applies the basic theory of complex variable function to solve the boundary condition complex variable function for common tunnel sections, and obtains the analytical expression of the surrounding rock stress of shallow circular tunnel. The simulation is carried out by finite element method. The establishment of complex variable function has a good application value in solving the stress of surrounding rock of shallow tunnel.

A Simplified Way to Evaluate the Effect of Temperature on a Circular Tunnel

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 βTl 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.