A length-scale insensitive degradation function is applied to extend the cracks during hydraulic fracturing under stress boundary conditions in this study. The phase field method is an effective modeling technique that has great potential for use in hydraulic fracturing. Nonetheless, current hydraulic fracturing research is still concentrated on small scales. The phase field model employs a degradation function that is insensitive to length scale, allowing for the decoupling of the phase field length scale from the physical length scale. This facilitates the simulation of hydraulic fracturing crack extensions in larger structures with a consistent mesh density. The correctness of the phase field method is verified firstly by comparing with the experimental results, and the accuracy and efficiency of the proposed method are further verified through a series of numerical calculations.

Shaped charge is widely used in petroleum drilling, yet the inherent parametric uncertainty of oil shale introduces significant uncertainties that affect perforation outcomes. The complex coupling of oil shale constitutive parameters under extreme strains poses challenges for uncertainty quantification. A coupled algorithm integrating an improved material point method (MPM) and polynomial chaos expansion (PCE) is presented, and polynomial chaos expansion (PCE) is used to systematically analyze the uncertainty and sensitivity of shaped charge jet penetration depth. Mechanical parameters from oil shale samples at Checun Coal Mine well No. 1 were tested to define key parameter ranges and establish a reliable uncertainty space. A benchmark simulation of a single isolated shaped charge jet validated the algorithm, and Sobol’ global sensitivity analysis identified internal friction angle, density, and Poisson’s ratio as strongly sensitive parameters, while tensile strength, Young’s modulus, and cohesion showed weak sensitivity, supporting surrogate model dimensionality reduction. Composite detonation models of three and five charges further revealed the effects of multi-projectile blast wave coupling on jet dynamics, providing new theoretical insights into cluster effects under high-energy, high-pressure, and extreme-strain conditions. Sensitivity and uncertainty analyses based on surrogate models emphasized the critical influence of internal friction angle alongside Poisson’s ratio and density. A reliable numerical framework is established for multi-physics coupled simulations of geomechanical responses under complex multi-source explosive loading.