# Study on the Damage Process and Numerical Simulation of Tunnel Excavation in Water-Rich Soft Rock
## 2 Staged Softening Process of Water-Rich Soft Surrounding Rock Based on Tunneling
### Unloading Softening Phase during Tunnel Excavation  
Tunnel excavation generates massive unloading, the direction of which is mainly related to the shape of the cavern. Unidirectional unloading is for round chambers and vaults of straight-walled arched chambers. Bi-directional unloading is for the location of the sidewalls of straight-walled arches, etc. Most of the highway tunnel cross-sections are in the form of three-centered arches or five-centered arches with a supine arch, which can be considered as unloading in the radial direction only. Figure 1 shows a typical stress-strain relationship for different loading history conditions [12]. There is a clear difference in the mechanical properties of the rock mass during loading and unloading. When the rock mass is loaded or not unloaded, the joint surface of the rock mass is in a closed state. While during unloading, the joint surface slides or opens, resulting in the mechanical parameters of the rock mass being mostly worse than those during loading or not unloading. In general, more unloading leads to more obvious deterioration of the mechanical parameters of a rock mass. Therefore, in the tunnel excavation analysis, the mechanical parameters measured by the loading test will underestimate the softening effect of the unloading of surrounding rock. The stress-strain curve can be divided into four segments, as shown in Figure 2. The OA segment is the elastic stage, indicated by a straight line; the AB part is the unloading yield phase, from which the rock is plastically deformed due to the unloading. The stress-strain relation in this state is a curve, which is in line with the elastoplastic constitutive model, and gradually reaches the peak strength with the increase of the unloading amount; the BC section is the stress-decreasing stage after the peak, and the unloading damage of the rock sample is mainly brittle damage, which can be expressed by linear strain-softening; the CD section is the ideal plastic phase, where the rock reaches the residual strength and shows obvious plastic mobility. The deformation of rock samples in the direction of unloading is intense, and brittle damage is obvious during the unloading test [5]. When the confining pressure is large, the shear damage is dominant, and when the confining pressure becomes small, the shear damage gradually transits to tensile damage. During unidirectional unloading, the peak strength, deformation modulus \(E\) and residual cohesion \(c\) of the rock sample decrease, and the residual friction angle \(\varphi\) increases, and the deterioration of rock parameters under bidirectional unloading is greater than that in unidirectional unloading. The cohesive force \(c\) decreases because the gelation capacity between fractures is weakened due to the opening of the joint during the unloading process of the rock sample; and the friction angle \(\varphi\) increases relatively because of the higher roughness of the resulting tension-shear joint surface. In order to better express the degree of deterioration of mechanical parameters during softening of rock samples, the degree of damage of physical and mechanical parameters is defined as the degree of deterioration. The experimental data of limestone  
Figure 1: Stress-strain relationship under different loading conditions [12]. from actual field projects found that the peak strength of limestone rock samples in the unloaded state deteriorated about 13.9-25.6% and the residual strength deteriorated about 22.8-44.3% compared with the loaded state, and the former was taken as a small value and the latter as a large value when the initial confining pressure was small; the former was taken as a large value and the latter as a small value when the initial confining pressure was large. The deterioration of elastic modulus during unloading is about 7-17%. When the rock is damaged along the fracture surface of the joints, the larger the initial confining pressure is and the slower the unloading rate is, then the greater decrease in elastic modulus is, and vice versa.