# Study on Explosive Fracturing Mechanism of Qianjiang Shale Oil
## 2 Computational Methods  
Modeling methods commonly employed for simulating the fracturing of brittle rock materials under dynamic loads encompass the finite element method [21], discrete element method [22], near-field method [23], phase-field method [24], and non-local method [25]. Among these approaches, the finite element method implemented via the nonlinear finite element software ANSYS LS-DYNA 19.0 is selected for the current simulation. This choice is driven by its versatility, widespread adoption, and the advanced constitutive models available within ANSYS LS-DYNA 19.0. The Holmquist-Johnson-Cook (HJC) constitutive model implemented in ANSYS LS-DYNA 19.0 [26] is capable of capturing the dynamic response of brittle materials under conditions of large strain, high strain rates, and high confining pressures. It also accounts for material damage and failure due to impact loading while maintaining simplicity and accuracy for large-scale computations. However, the HJC model is incapable of accurately describing the propagation of tensile cracks within -fracture zones. Therefore, it is necessary to couple the HJC model with an additional failure criterion by incorporating the keyword *MAT_ADD_EROSION. When the compressive strength in the model attains the predefined threshold, it is automatically removed [27].  
With the rapid advancement of computer technology, numerical simulation has emerged as a crucial tool for researchers investigating reservoir rock blasting. This approach holds significant importance for optimizing blasting parameters and elucidating the mechanisms of rock blasting [28; 29]. In ANSYS LS-DYNA 19.0, explosives are typically modeled as uniform continuous media, utilizing the MAT_HIGH_EXPLOSIVE_BURN model and the Jones-Wilkins-Lee (JWL) equation of state to characterize the relationship between the pressure generated by the blasting load and the volume of the explosive product [30]. The formula elucidates the constitutive relationship between detonation pressure and the expansion dynamics of detonation products.  
\[P=A\bigg{(}1-\frac{\omega}{R_{1}V}\bigg{)}e^{-R_{1}V}+B\bigg{(}1-\frac{\omega} {R_{2}V}\bigg{)}e^{-R_{2}V}+\frac{\omega E}{V} \tag{1}\]  
where \(P\) denotes the detonation pressure, \(V\) represents the relative volume, and \(A\), \(B\), \(R_{1}\), \(R_{2}\), and \(\omega\) are dimensionless constants, and \(E\) signifies the internal energy per unit of initial volume.  
In numerical simulations, air is modeled as a fluid. The ANSYS LS-DYNA 19.0 program characterizes air using two fundamental approaches: the equation of state and the constitutive equation. The equation of state expresses the relationship between pressure and volume, whereas the constitutive equation delineates the flow properties of materials by examining the interdependencies among stress, strain, and time [27].  
In this paper, the MAT_NULL model and the LINEAR_POLYNOMIAL equation of state (2) are employed for air materials. The pertinent parameters are detailed in Table 1.  
\[P=C_{0}+C_{1}\mu+C_{2}\mu^{2}+C_{3}\mu^{3}+\Big{(}C_{4}+C_{5}\mu+C_{6}\mu^{2} \Big{)}E \tag{2}\]  
In the formula, \(C_{0}\sim C_{6}\) represent constants; \(\mu=\frac{1}{V}-1\), where \(V\) denotes the relative volume; and \(E\) represents the internal energy per unit of initial volume.  
Using the Gaussian 16 (A.03) software package, the transition states (TSs) in the vicinity were identified in the gas phase at the B3 LYP/6-311+G(d,p) level of theory, and the geometries as well as the activation barriers of the reactants and products were computed. The reaction pathway was characterized using intrinsic reaction coordinate (IRC) analysis, which links the optimized structures of the reactants and products.