Unloading Response Characteristics of Cross Fault Caverns: Effect of Fault Angles

The research of unloading response characteristics of caverns with weak structure has important engineering value for the development and construction of underground space. In this paper, firstly, the cross fault cavity model is established based on particle flow code (PFC) software, considering different fault dip angles. The parallel bond model (PBM) is used in the cavern model and the smooth joint model (SJM) is used in the fault model. Then, the mechanical, acoustic emission (AE), energy response characteristics and failure modes of the cavern model with different fault angles are explored. The research result show that the fault angle has a great influence on the stress distribution and failure modes of surrounding rock. The existence of faults does not change the overall law of AE evolution curve, that is, the number of AE hits increases first and then decreases. However, the existence of faults changes the maximum number of AE hits and the duration of AE. When the cavern is unloaded, the strain energy of the model first decreases and then increases.


Introduction
With the development of economy and the increase of population, the development scale and depth of underground tunnel engineering are increasing (Zhao et al 2021). At present, the deepest tunnel project in the world has reached 1500 m. Meanwhile, the construction of underground tunnel will inevitably encounter weak geological structures such as faults, which makes the unloading response characteristics of surrounding rock more complex and more likely to induce tunnel dynamic disasters, such as rock burst (Ortlepp and Stacey 1994;He et al 2010;Manouchehrian and Cai 2015). Therefore, it is of great engineering significance to study the unloading response characteristics of cross fault caverns for the safety control of underground space.
Many scholars have done a lot of research work and made great achievements in the mechanical properties of unloading rock mass. The unloading deformation behavior and failure characteristics of rock were studied by Huang et al (2001) by experiments. Their result show that rock bursts occur in the unloading process of tunnel excavation and their characteristics are closely related to the deformation and failure characteristics of the rock mass. Based on the field test and numerical simulation, Sharma et al (2001) analyzed the influence of Large Space Excavation on the deformation of adjacent tunnels. It was found that the stiffness of the tunnel lining has significant influence on the displacement and distortion of tunnels caused by an adjacent excavation. A stiffer lining undergoes less displacement and distortion but is likely to experience significantly greater bending moments. Kojima and Yashiro (2005) established a method to evaluate the deformation characteristics of tunnel under the action of embankment and surface excavation through surface loading and unloading model test. The results show that the nonlinear deformation behavior of M-type tunnel is obvious in loading test, and that of S-type tunnel is obvious in unloading test. The larger the B/H is, the more obvious the deformation behavior is. Based on the theory and numerical simulation, Li et al (2016) studied the dynamic response of unloading times, stress level and tunnel spacing configuration to the surrounding rock of the existing tunnel. The results show that under the condition of high initial stress and high unloading rate, the surrounding rock of existing tunnel will produce dynamic effect. The particle peak velocity (PPV) induced by unloading can reach the PPV value induced by blasting and damage the existing tunnel. Using the self-defined visco-elastoplastic Nishihara constitutive model based on Particle Flow Code in three dimensions (PFC3D), Jin et al (2019) analyzed rheological properties and failure behavior of a tunnel surrounded by jointed rock mass and found the bonds of the joint faces in the jointed rock mass model were primarily destroyed by shear failure. Yu et al. (2020) based on particle flow analyzed the macro-micro mechanical response and energy mechanism of surrounding rock of roadyway under excavation disturbance and reported that during the excavation disturbance, the cracks are mainly produced in the stage of stress increase, concentrated at the bottom corner of the roadway and the vault. Chen et al. (2020) studied the failure characteristics of deep circular tunnel in rock mass with multiple weak surfaces by using two-dimensional combined finite element method/discrete element method (FEM/DEM). Then, parametric analysis is carried out to study the effects of dip angle and length on crack propagation behavior, failure mode, energy evolution and displacement distribution. The results show that the inclination angle has a great influence on the stability of the tunnel, and the failure strength and range first increase and then decrease with the increase of the inclination angle. With the increase of the length of weak surface, the possibility of dynamic disaster increases. These studies are of great significance for the prevention and control of tunnel unloading disasters. However, these studies did not consider the influence of fault on the response characteristics of tunnel during excavation.
Besides, the damage of surrounding rock is often accompanied by acoustic emission (AE), which can be used to predict and control rock burst and other disasters (Přikryl et al 2003;Shkuratnik et al 2005;Wang et al 2018). in addition, the energy evolution characteristics of the surrounding rock can better reflect the essence of the instability failure of the cavern (Persson 1997;Chen et al 2021a). Therefore, this paper not only analyzes the unloading failure mechanics and instability characteristics of cross fault cavern, but also analyzes the acoustic emission and energy evolution characteristics of surrounding rock. The specific contents are as follows: firstly, based on PFC, the cross fault cavity models with different fault dip angles are established, and the parameters are checked; Secondly, the mechanics, acoustic emission, energy and instability behavior or characteristics of the cross fault cavern are analyzed. The research results are helpful to further understand the unloading response characteristics of cross fault caverns and disaster prevention and control.

Numerical Method and Parameters Calibration
The particle flow model uses disk and bond to represent rock mass, which is a mature software and very suitable for simulating rock and soil materials. In PFC model, there are two kinds of contact models: contact bond model and parallel bond model (as shown in Fig. 1a) (Itasca Consulting Group Inc. 2014). Some researches results (Castro-Filgueira et al 2017; Chen et al 2021a) show that the contact bond model is suitable for simulating soil materials, and the parallel bond model is suitable for simulating rock materials. Therefore, the parallel bond model of PFC is used in this study. In addition, PFC software also provides a smooth joint model (as shown in Fig. 1b) to simulate geological structures such as joints and fissures. The simulation of cross fault chamber in this paper is based on parallel bond model and smooth joint model of particle flow.
Since the macro-mechanical property of the rock model established by PFC is determined by the micromechanical property of the particles and bonds and these parameters cannot be directly derived directly from in-situ tests and indoor experiments. Usually, the micro-parameters of PFC rock models are calibrated by simulating the uniaxial compression experiments (Castro-Filgueira et al 2017; Chen et al 2021a). However, for tunnels or other huge models, the scale level is meter (m). If the parameters of the indoor small-scale model are used to establish the large-scale model, the number of particles of largescale model needs tens of millions, and the general computer can not load. For this reason, one must consider the scale effect of the model in the parameter verification (Chen et al 2021b). Through lab tests, Li et al. (2016) found that when the scale of the model is larger than 80 mm, the uniaxial compressive strength (UCS) of the shale decreases by more than 40%, that is, from 80 MPa to 48 Mpa. The elastic modulus is 4-8 GPa. Combined with this information, uniaxial compression experiments were carried out on rock samples with model size of 20 m 9 40 m by trial and error method, and the parameters were checked repeatedly to obtain the meso parameters of PFC that can reflect the mechanical properties of shale, as shown in Table 1. Under this parameters, the compressive strength of rock mass is about 46.9 MPa and the elastic modulus is about 4.2 GPa, as shown in Fig. 2. The failure mode, as shown in Fig. 3a, is mainly in the split at the end and middle of the sample, which is consistent with the failure model of the large-scale model of indoor experiment, Fig. 3b.
Because it is difficult to measure the mechanical properties of the fault, the value of the meso parameters of the fault in this paper is 5% of the surrounding rock parameters according to research of Chen et al (2021a), as shown in Table 2.

Numerical Models
According to the engineering practice, the scale of the model is 60 m 9 60 m, as shown in Fig. 4; The diameter of the cavern is 12 m; There is a fault with a length of 40 m passing through the center of the cavern. The angle between the fault and the X-axis is a, which is the fault angle. Because this paper mainly studies the influence of fault angle on the unloading response characteristics of surrounding rock, the fault angle is set to 0°, 30°, 60°, 90°, 120°and 150°, as shown in Fig. 5. The model considers the deep buried geological conditions, the buried depth is 1500 m, the vertical confining pressure of the cavern is 39 Mpa, and the side pressure coefficient is 0.5. The process of model establishment: firstly, the rectangular surrounding rock model is generated, and then the confining pressure is applied; secondly, the fault model is added and the cavern is removed for unloading. In the cross fault model, 32,392 balls are generated. Before the run of the model, four measuring circle with a diameter of 2 m was established at the top, bottom, left and right sides of the cavern model to record the stress evolution process of surrounding rock mass. At the same time, the acoustic emission characteristics and energy characteristics of the whole model are recorded by writing FISH Language. Figure 6 show the stress response characteristics of surrounding rock of cavern without fault. It can be seen from the figure that after unloading, the stress of points M1 and M2 in the Y direction suddenly decreases, which is due to the loss of supporting rock mass due to the excavation of the cavern.  Table 3 show the stress response characteristics and maximum stress of the cross fault cavern under unloading. The angle of fault changes the    fault angles of 0°, 60°and 90°lead to stress increase, while other angles lead to stress decrease. When the fault angle is 0°, the stress increases most. When the fault angle is 30°or 150°, the stress reduction is the largest. The maximum stress of point M3 without fault, with fault angle = 0°, 30°, 60°, 90°, 120°, and 150°are 9.1 MPa, 13.5 MPa,8.5 MPa,9.9 MPa,9.4 MPa,8.5 MPa and 9.8 MPa. At point M4, the fault angle is 0°, 90°will lead to stress increase, while other angles will lead to stress decrease. When the fault angle is 0°, the stress increases most. When the fault angle is 150°, the stress reduction is the largest. The maximum stress of point M4 without fault, with fault angle = 0°, 30°, 60°, 90°, 120°, and 150°are 16.6 MPa, 18.4 MPa, 12.7 MPa, 16.7 MPa, 17.7 MPa, 15.2 MPa and 11.7 MPa. It can be seen that the fault angle has great influence on the X direction of surrounding rock, especially when the fault angle is 0°and 90°. At the same time, the fault angles of 30°and 90°can reduce the stress concentration of surrounding rock in X direction.

Stress Response Characteristics of Surrounding Rock
In general, the fault angle has a great influence on the stress distribution of surrounding rock. Faults with angles of 0°and 90°will increase the stress concentration of surrounding rock (except for some points), while faults with other angles will reduce the stress concentration of surrounding rock.

AE Characteristics
The acoustic emission (AE) characteristics of rock mass is directly related to the generation of micro cracks in the rock mass. In the PFC model, a contact (parallel bond) fracture will produce a release of strain energy, that is, an acoustic emission occurs. Therefore, the acoustic emission event of rock sample can be simulated by counting the number of particle contact fractures through FISH language (Chen et al 2021a, b).   Figure 9 shows the evolution characteristics of acoustic emission during unloading of faultless caverns. It can be seen from the figure that in the process of sudden unloading, a large number of acoustic emission hits events occurred in the surrounding rock of the cavern. The maximum value of acoustic emission hit event is 6, and there are two peaks, which is due to two times of rapid crack propagation in surrounding rock. At the same time, it can also be seen that the number of acoustic emission hits increases first and then decreases, which indicates that the stress concentration of the cavern needs a process. After the stress concentration leads to the damage and failure of the rock mass, it returns to the stable state of the surrounding rock, which is consistent with the stress evolution curve in Fig. 6. Figure 10 shows the AE evolution curves of surrounding rock under different fault angles. Generally, the existence of faults does not change the overall law of AE evolution curve, that is, the number of AE hits increases first and then decreases. However, the existence of faults changes the maximum number of AE hits and the duration of AE. Compared with the AE characteristics of no fault cavern, the maximum hit value of AE increases when the fault dip angle is 30°a nd 120°. The difference is that when the fault angle is 30°, the duration of AE hit event is longer, while the duration of AE hit event of 120°fault cavern model is slightly shorter. The maximum hit value of AE of the

Strain Energy Characteristics
The law of thermodynamics shows that energy conversion is the intrinsic essence of the change process of physical characteristics of materials. When the sample is loaded, part of the work done by the loading plate is used for the internal damage, plastic deformation and crack propagation of rock, which is called dissipation energy. The other part is stored in the rock in the form of strain energy. From the energy point of view, the damage and fracture of the specimen is the result of energy accumulation and transformation process such as internal strain energy and dissipation energy. Many studies (Xie et al., 2004;Ma et al, 2020) show that the analysis of strain energy is helpful to understand the instability mechanism of rock mass and control the stability of rock mass. In the PFC model, the strain energy consists of two parts: the strain energy E K and the parallel bonding strain energy E K , i.e., where, F l n and F l s are the normal and tangential contact forces of particles; k n and j s are the normal and tangential contact stiffness of particles; F n and F s are the normal and tangential parallel bond forces; k n and j s are the normal and tangential parallel bond stiffness; M t and M b are the torque and bending moment of parallel bonding; A is the area of parallel bonding; J and I are the polar moment of inertia and moment of inertia of parallel bonded section.
Through the fish language built in PFC, the strain energy can be monitored in real time. Figure 11 shows the strain energy characteristics of caverns with and without faults. Due to the confining pressure, a large amount of strain energy, about 32e7J, is accumulated in the early stage before unloading. When the cavern is unloaded, the strain energy of the model first decreases and then increases, because the energy in the rock mass is dissipated due to the sudden release of excavation space. However, with the stress re-distribution of surrounding rock, the strain energy of the whole model increases. Compared with the nonfault cavern model, the strain energy attenuation of the cross fault cavern model (in the early unloading stage) is larger, and the strain energy increment in the later unloading stage is also larger. This is because of the existence of faults, the deformation space and amount of the whole model are increased. In general, the strain energy increment of the cavern model with 0°and 30°f ault angles are the largest, followed by 150°, 60°, 120°and 90°. Figure 12 show the failure modes of cavern with different fault angles. It can be seen from the figure that in the case of cavern without fault, the damage of the cavern is mainly in the arch waist of the cavern. This is because the lateral pressure coefficient of the model is 0.5. The failure degree of the left and right sides of the tunnel is different because the model is a discrete When the fault angle is 0°, the damage of the cavern is transferred to the left arch waist of the cavern, and the overall damage of the cavern is smaller than that of the non-fault cavern. When the fault angle is 30°, the damage degree of the cavern is more severe, and the damage location is still mainly in the right arch waist of the cavern. When the fault dip angle is 60°and 90°, the failure mode of the cavern is basically consistent with that of the non-fault cavern model. When the fault angle is 120°and 150°, the damage degree of the cavern is less than that of the non-fault cavern. In general, the failure degree of the cavern model decreases when the fault angle is 0°, 120°and 150°, while the failure degree increases when the fault angle is 30°.

Conclusions
Based on the PFC model, the mechanical, acoustic emission and energy response characteristics of the cross fault cavern are analyzed, and the influence of joint angle is considered. At the same time, the failure modes of each model are analyzed. The main conclusions of this paper are as follow: The fault angle has a great influence on the stress distribution of surrounding rock. Faults with angles of 0°and 90°will increase the stress concentration of surrounding rock, while faults with other angles will reduce the stress concentration of surrounding rock. The existence of faults does not change the overall law of AE evolution curve, that is, the number of AE hits increases first and then decreases. However, the existence of faults changes the maximum number of AE hits and the duration of AE. Compared with the AE characteristics of no fault cavern, the maximum hit value of AE increases when the fault dip angle is 30°a nd 120°. When the fault angle is 30°, the duration of AE hit event is longer, while the duration of AE hit event of 120°fault cavern model is slightly shorter. The maximum hit value of AE of the tunnel model with fault angle of 90°is the same as that of the tunnel model without fault, both are 6, but the duration of AE hit increases. The maximum value of AE hits is smaller and the duration of AE hits is shorter when the fault angle is 0°, 60°and 150°.
When the cavern is unloaded, the strain energy of the model first decreases and then increases. Compared with the non-fault cavern model, the strain energy attenuation of the cross fault cavern model (in the early unloading stage) is larger, and the strain energy increment in the later unloading stage is also larger. The strain energy increment of the cavern model with 0°and 30°fault angles are the largest, followed by 150°, 60°, 120°and 90°.
Compared with no fault cavern, the failure mode of cross fault cavern has changed greatly. The failure degree of the cavern model decreases when the fault angle is 0°, 120°and 150°, while the failure degree increases when the fault angle is 30°.