## 6 Analysis of the Energy Characteristics Under Uniaxial Compression  
Throughout the procedure of stone distortion and breakdown under stress, four main categories of power conversion take place: power intake, power gathering, power dispersion, and power discharge [40]. It is presumed that there exists no thermal transfer with the outer surroundings throughout the experiment, thereby considering the setup as a sealed setup. The overall input deformation energy, U, produced by outer forces acting on the stone throughout the experiment, can be ascertained. According to the primary principle of thermodynamics [41; 42]  
\[U=U_{e}+U_{d}+U_{0}, \tag{1}\]  
where \(U_{e}\) represents the elastic strain energy, \(U_{d}\) denotes the dissipative energy, and \(U_{0}\) refers to the energy released through heat radiation and heat exchange. Since the energy released by heat radiation and heat exchange is considered negligible, the total input strain energy is given by the following:  
\[U=U_{e}+U_{d}, \tag{2}\]  
Figure 10 illustrates the relationship between projectile properties and the dissipated energy of rock. Figure 10: Relationship between projectile property and the dissipated energy of rock. Figure 9: The 5 mm sample was sliced by CT scan with different dry and wet cycles: (**a**) 0 wetting–drying cycles; (**b**) 10 wetting–drying cycles; (**c**) 20 wetting–drying cycles. The energy of a rock element in the principal stress space is given as follows:  
\[U=\int_{0}^{\epsilon_{1}}\sigma_{1}\mathrm{d}\epsilon_{1}+\int_{0}^{\epsilon_{2} }\sigma_{2}\mathrm{d}\epsilon_{2}+\int_{0}^{\epsilon_{3}}\sigma_{3}\mathrm{d} \epsilon_{3}, \tag{3}\]  
Based on [PERSON]'s theorem, Equation (3) is reformulated as follows:  
\[U_{e}=\frac{1}{2E}\left[\sigma_{1}^{2}+\sigma_{2}^{2}+\sigma_{3}^{2}-2\eta( \sigma_{1}\sigma_{2}+\sigma_{1}\sigma_{3}+\sigma_{2}\sigma_{3})\right], \tag{4}\]  
where \(E\) is the elastic modulus (in GPa) and \(\eta\) is [PERSON]'s ratio. For the uniaxial compression test, the formula for calculating elastic strain energy is simplified as follows:  
\[U_{e}=\frac{\sigma_{z}^{2}}{2E}, \tag{5}\]  
Based on the concept of definite integrals, the formula for calculating the total energy can be presented as follows:  
\[U=\sum_{i=1}^{n}\frac{1}{2}(\sigma^{i}+\sigma^{i+1})(\epsilon^{i+1}-\epsilon^ {i}), \tag{6}\]  
where \(\sigma^{i}\) and \(\epsilon^{i}\) denote the stress and strain values at each corresponding point along the stress-strain curve, respectively. Consequently, the dissipated energy \(U_{\mathrm{d}}\) within the rock can be expressed as follows:  
\[U_{d}=U-U_{e}. \tag{7}\]  
Table 1 presents the peak energy indices of the samples under uniaxial compression along with the total input energy at failure, providing insights into the impact of cycles on the energy evolution of porous rocks. As shown in the table, under 0 cycles, the complete input energy at failure for the three samples is 26.82 MJ/m\({}^{3}\), 25.12 MJ/m\({}^{3}\), and 13.59 MJ/m\({}^{3}\). After 10 wet-dry cycles, these values are reduced to 22.89 MJ/m\({}^{3}\), 22.17 MJ/m\({}^{3}\), and 11.47 MJ/m\({}^{3}\), representing decreases of 14.7%, 11.7%, and 15.6%, respectively. Following 20 wetting-drying cycles, the total input energy further declines to 22.27 MJ/m\({}^{3}\), 19.32 MJ/m\({}^{3}\), and 8.37 MJ/m\({}^{3}\), which is a reduction of 16.9%, 23.1%, and 38.4% compared to the 0-cycle state. This demonstrates that the total input energy of the samples decreases significantly as the number of wetting-drying cycles increases. Additionally, in a comparison of the total input energy at the point of failure of the three types of hole-fissured specimens under the state of 0 cycles, it was discovered that the total input energy at the failure of the 5 mm and 10 mm specimens declined by 6.3% and 49.3%, respectively, in comparison with that of the 0 mm specimen.