A Physics-Informed Neural Network for Modeling Pressurized Cavities of Arbitrary Smooth Shape Embedded in Heterogeneous Rock

Pressurized cavity expansion underlies a wide range of rock engineering applications like tunneling, drilling, and in situ testing, but accurate field prediction is challenging in heterogeneous rock masses where discontinuities are pervasive and measurements are sparse. This work proposes a Physics-Informed Neural Network to solve forward problems of pressurized cavity expansion of arbitrary smooth shape embedded in heterogeneous elastic media. A single shared network is augmented with signed-distance and level-set embeddings, and domainconditioned activation functions allow representation of piecewise-smooth fields across discontinuities. The physics-informed loss enforces equilibrium, constitutive relationships, traction boundary conditions, interface continuity, and sparse observation data. Ground truth data are generated using Finite Element simulations. The model achieves displacement mean absolute errors of O(10 ⁻⁵ ) m in both homogeneous and heterogeneous rock masses. In homogeneous benchmarks, the mean absolute percentage errors for the non-shear stress components remain below 0.2% across ten randomized cases. In heterogeneous cases with intersecting discontinuities, the mean absolute percentage errors for σxx and σyy remain below 0.5%, with discrepancies localized near interfaces. Compared with XPINN, the proposed PINN framework delivers comparable stress accuracy with smaller displacement errors near discontinuities while keeping the number of parameters nearly constant across subdomains, yielding a 5 times training speedup. Furthermore, the number of training epochs for related heterogeneous cases can be reduced by half through transfer learning.