## 2 Cyclic Triaxial Loading and Unloading Experiments on Rock
### Design of Test Schemes  
The triaxial test in this paper was conducted using the MTS-815 electro-hydraulic servo rock mechanics (MTS Systems, Eden Prairie, MN, USA) test system (as shown in Figure 2). During the test, the confining pressure was applied using liquid, the radial pressure \(\sigma\)2 = \(\sigma\)3, and the radial strain was measured using a chain-type transverse (radial) strain gauge. The radial strain was equal, that is, \(\varepsilon\)2 = \(\varepsilon\)3. This system integrates a loading mechanism, testing apparatus, and control unit, equipped with devices to measure axial and radial (transverse) strains. It supports various modes of load control, including force, stress, displacement, and strain, thereby facilitating the execution of triaxial loading and unloading along diverse and complex paths. The investigation involved conventional triaxial compression tests and CLU trials on sandstone samples, subject to six distinct confining pressures spanning from 1 MPa to 25 MPa. The experimental procedure was divided into two main parts, with the methodologies outlined in Table 1. Detailed procedural steps for both experimental approaches are provided below:  
Figure 1: Red sandstone slice imaged using a polarizing microscope. 1. Standard triaxial compression: (i) a sandstone sample was initially sealed and positioned inside a triaxial testing chamber, the sensor baseline was adjusted, and an initial axial force of 1.5 kN was applied to secure the sample in place; (ii) the self-balancing feature was activated, and the confining pressure was then increased to the predetermined levels (1, 5, 10, 15, 20, and 25 MPa) at a consistent rate of 0.2 MPa/s, guaranteeing that the specimens experienced consistent hydrostatic stress conditions; (iii) keeping an unvarying confining pressure, the axial force was incrementally administered in a displacement-guided mode at a velocity of 0.002 mm/s, leading to the specimen's failure. 2. Cyclic triaxial testing for loading and unloading: engineering practice has shown that, during construction and excavation of deep underground engineering including roadways (caverns and tunnels), the stresses on the surrounding rocks of previously excavated roadways change constantly due to the influence of subsequent construction (face mining and surrounding rock support) distributions. The initial stress state of surrounding rocks before excavation (equivalent to initial loading state, in which energy is input and accumulated) gradually changes to a state of stress redistribution induced by rock excavation (equivalent to an unloading state, in which energy is dissipated and released), to a stress state of subsequent surrounding rock support or mining-induced stress (loading state), to a state of stress release due to deformation of the surrounding rocks (unloading state), and so on. To accurately replicate the fluctuating stress conditions surrounding excavated roadways, simulations were conducted using CLU stress paths, as depicted in Figure 3. Initially, confining pressures were set to predetermined levels (1, 5, 10, 15, 20, and 25 MPa) as per the first two steps of the standard triaxial compression protocol. Given the challenge of capturing post-peak stress-strain responses under uniaxial CLU, tests with low confining pressure (\(\sigma\)3 = 1.0 MPa) were specifically designed to evaluate the effect of confinement pressure on the energy of the rock development. Axial loading proceeded at a pace of 0.002 mm/s, controlled by axial displacement, with each cycle's load gradient set at 0.12 mm. Upon reaching the predetermined axial displacement, the system switched to stress-controlled mode to lower the axial stress at a decrement rate of 1.0 kN/s until the specimen reached its residual state, marking the end of the test. To mitigate any impact from the specimen detaching from the press head, a new cycle commenced  
Figure 2: MTS-815 mechanical testing setup. only after reducing the axial load back to 1.5 kN upon unloading completion.