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 domain-conditioned 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 0.00001 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 horizontal and vertical stresses 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 five-times training speedup. Furthermore, the number of training epochs for related heterogeneous cases can be reduced by half through transfer learning. More in this preprint.

Active learning with physics-informed neural networks for optimal sensor placement in deep tunneling through transversely isotropic elastic rocks

We developed a deep learning strategy to simultaneously solve Partial Differential Equations (PDEs) and back-calculate their parameters in the context of deep tunnel excavation. A Physics-Informed Neural Network (PINN) model is trained with synthetic data that emulates in situ displacement measurements in the host rock and at the cavity wall, obtained from extensometers and convergence monitoring. As acquiring field observations can be costly, a sequential training approach based on active learning is implemented to determine the most informative locations for new sensors. In particular, Monte Carlo dropout is used to quantify epistemic uncertainty and query measurements in regions where the model is least confident. This approach reduces the amount of required field data and optimizes sensor placement. The PINN is tested to reconstruct the displacement field around a deep tunnel of circular section excavated in transversely isotropic elastic rock and to determine rock constitutive and stress-field parameters. Results demonstrate excellent performance on small, scattered, and noisy datasets, achieving high precision for the Young’s moduli, shear modulus, horizontal-to-vertical far-field stress ratio, and the orientation of the bedding planes. The proposed framework shall ultimately support decision-making for optimal subsurface monitoring and for adaptive tunnel design and control. More in this preprint.

Bio-inspired excavation mechanics

Ants are outstanding excavators, which led us to take inspiration of their burrowing and construction techniques for possible translation to the practice. We extracted 3-D renderings of Florida Harvester ant structures from a nest cast in situ and simulated the stress and displacement fields around that nest with the Finite Element Method (FEM). Stress invariants around the main shaft were compared to those around idealized geometric representations of that shaft, i.e. helixes with a fixed pitch angle and a uniform elliptical cross-section. We found that helical structures made of circular cross-sections and horizontally oriented elliptical cross-sections interact in a way that reduces the risk of tension failure and distributes the shear stress more evenly. One can show that in addition to the extra stability that they offer and the lower risk of tensile or shear failure that they exhibit, helical shafts have the advantage of requiring less power to excavate than straight sub-vertical shafts. We also investigated the role of ant chamber spatial distribution, orientation, and shape on soil behavior and chamber-to-chamber interactions, and showed that the chambers are strategically placed in the next to create 3D arching effects that increase the stability of the nest. Additionally, we numerically showed that emulating the staged excavation process of Harvester ants can reduce the force, torque, energy and power that are needed for microtunnelling compared to more traditional single-pass excavation processes, particularly for low apparent cohesion soils and deep cavities. The key to power and energy savings lies in the incremental formation of localized plastic zones around the tunnel face, which is accompanied by stress redistribution and arching. This lowers the lateral earth pressure that must be supported at the excavation front, the normal stress that controls the shear strength against the applied torque, and the radial stress normal to the sides of the excavating device which controls the frictional force that must be overcome to advance the tunnelling device. More in this preprint.