## 4 Effect of Oil-Water Infiltration on Rock Mechanical Properties
### Energy Evolution Characteristics of Damaged Rock Samples with Different Liquid Contents  
Material fracture failure is essentially an instability process triggered by energy. The intrinsic mechanism of rock deformation and failure is the continuous dissipation of energy, which reflects the ongoing accumulation of internal microdamage and the gradual reduction in the material's load-bearing capacity. According to the basic laws of thermodynamics, under adiabatic conditions, the external energy input is mainly divided into two parts: one is the irreversible dissipative energy that drives plastic deformation and crack evolution, and the other is the recoverable elastic energy stored in the load-bearing structure. This energy distribution mechanism determines the development path of the rock from microscopic damage to macroscopic rupture [27; 28; 29; 30]. The previous section's analysis of AE is essentially a form of dissipative energy. To comprehensively explore the energy evolution characteristics of damaged rock samples with different soaking times, energy calculations were carried out based on the rock's stress-strain curve. As shown in Figure 15, four energy values are involved in the energy analysis of uniaxial compression: the work done by the servo testing machine (\(W\)), the elastic strain energy stored in the rock sample (\(U_{e}\)), the dissipative energy used for the plastic deformation of the sample and crack propagation (\(U_{d}\)), and the energy consumed per unit volume during deformation and failure after the peak point (\(U_{p}\)). Therefore, the entire stress-strain curve needs to be split into the pre-peak and post-peak stages, and the energy values for each section calculated. The formulas for each energy value are as follows:  
\[W=\int_{0}^{\varepsilon_{p}}\sigma_{i}d\varepsilon \tag{1}\]  
\[U_{e}=\frac{\sigma_{p}^{2}}{2E} \tag{2}\]  
\[U_{d}=W-U_{e}=\int_{0}^{\varepsilon_{p}}\sigma_{i}d\varepsilon-\frac{\sigma_{ p}^{2}}{2E} \tag{3}\]  
\[U_{p}=\int_{\varepsilon_{p}}^{\varepsilon_{r}}\sigma_{i}d\varepsilon \tag{4}\]  
In the formula, \(\sigma_{i}\) is the stress at any point between axial stress and axial strain, MPa; \(\sigma_{p}\) is the peak stress, MPa; \(\varepsilon_{p}\) is the peak strain, %; \(E\) is the elastic modulus of the sample, MPa; \(\varepsilon_{r}\) is the maximum strain of the axial stress-strain curve, %. Figure 15: Energy evolution diagram during uniaxial compression. Based on Formulas (1) to (4), the energy data for different soaking times during the uniaxial loading process of damaged rock samples were calculated, and the energy evolution trend graphs were plotted. As shown in Figure 16, the energy evolution characteristics of damaged rock samples with different soaking times also conform to the general energy mechanism of rock failure processes. Based on the energy variation laws and their correspondence with the stress-strain relationship curve, the rock failure process is divided into the four stages below. 1. Compaction stage: In this stage, the original cracks inside the rock sample are continuously compacted and closed under external load. The energy input from the servo testing machine is mainly stored as elastic energy within the rock, with a small amount of dissipative energy used to close the internal cracks and overcome the frictional sliding between structural planes. 2. Elastic stage: In this stage, the original cracks inside the rock are completely compacted, and the entire rock sample can be viewed as a dense elastic body. At this time, the energy input from the servo testing machine is stored entirely as elastic energy within the rock, and the dissipative energy curve is close to the horizontal line, with almost no energy dissipation. 3. Plastic stage: In this stage, new cracks begin to form inside the rock, though the number of cracks is small and the overall state remains stable.