## 2 Materials and Methods
### Experimental Methods
\[U_{R}=U-L_{S}\frac{dI}{dt} \tag{2}\]  
\[E=\int U_{R}Idt \tag{3}\]  
\[P=U_{R}I \tag{4}\]  
\[\eta=\frac{E}{W} \tag{5}\]  
where \(L_{S}\) is the inductance of the load structure, and represents the duration of the electrical explosion process. Strain gauges (BQ120-30 AA-P100) were affixed to the surface of the concrete block in a 0\({}^{\circ}\)-45\({}^{\circ}\)-90\({}^{\circ}\) arrangement, as illustrated in Figure 4b. These were connected to a TQ320X data acquisition system to precisely measure strains in three directions induced by the shock wave in Figure 4a. The system synchronously recorded the test data. Principal strains were calculated using Equation (6), enabling a detailed assessment of shock wave propagation effects in different media. \[ \begin{array}{l}\varepsilon_{max}=\frac{1}{2}\left[\left(\varepsilon_{x}+ \varepsilon_{y}\right)+\sqrt{2\left[\left(\varepsilon_{x}-\varepsilon_{u} \right)^{2}+\left(\varepsilon_{u}-\varepsilon_{y}\right)^{2}\right]}\right]\\ \varepsilon_{min}=\frac{1}{2}\left[\left(\varepsilon_{x}+\varepsilon_{y} \right)-\sqrt{2\left[\left(\varepsilon_{x}-\varepsilon_{u}\right)^{2}+\left( \varepsilon_{u}-\varepsilon_{y}\right)^{2}\right]}\right]\end{array}  \tag{6}\]  
Figure 4: Schematic diagram of the experimental setup for metal wire electrical explosion rock fragmentation (**a**) and strain gauge arrangement (**b**). where \(\varepsilon_{x}\), \(\varepsilon_{y}\), \(\varepsilon_{u}\) correspond to the uniaxial strain in a single direction as shown in Figure 4b; \(\varepsilon_{max}\) is the maximum principal strain at the measured point, and \(\varepsilon_{min}\) is the minimum principal strain at the measured point. The electrical explosion of metal wires is a complex process involving extensive physical changes and chemical reactions. This complexity increases significantly when conducted in various dielectric media, making it challenging for conventional instruments to accurately measure the associated energy changes. To address this, this study introduces the shock wave energy equivalence method [30], aimed at precisely characterizing the energy release during the electrical explosion process in different dielectric media. This method utilizes a strain acquisition system to measure the stress experienced by the concrete block, enabling an integrated analysis of the shock wave energy generated by metal wire electrical explosions in various dielectric media. Compared to analyzing individual energy conversion stages, this approach effectively reduces the estimation errors of energy losses caused by different mechanisms. The energy calculation formula is given by Equation (7):  
\[E_{w}=\frac{4\pi D^{2}}{\rho C_{S}}\int_{0}^{t}{P_{sw}}^{2}(t)dt \tag{7}\]  
where \(D\) is the horizontal distance from the strain gauge to the discharge channel, \(\rho\) is the density of the solid medium, \(C_{S}\) is the propagation speed of the shockwave in the solid medium, and \(P_{sw}\) is the principal stress of the shockwave as measured by the strain gauge. The concrete block fracturing experiments employed a repeated discharge strategy until significant cracks appeared. By analyzing the changes in crack dimensions after each discharge, the impact of different dielectric media on rock-breaking efficiency was quantitatively evaluated. Concurrently, time-response curves of discharge voltage and current were obtained using the data acquisition system. Analysis of the variations in electrical signals under different dielectric media conditions allowed for an in-depth investigation of the mechanisms by which dielectric composition influences the discharge process. Furthermore, the strain-time curves of the concrete block under electrical explosion, recorded by the strain measurement system, were combined with the reaction characteristics of metal wire electrical energy in various dielectric media.