  Cavity expansion is a canonical problem in geotechnics, which can be
described by partial differential equations (PDEs) and ordinary differential
equations (ODEs). This study explores the potential of using a new solver, a
physics-informed neural network (PINN), to calculate the stress field in an
expanded cavity in the elastic and elasto-plastic regimes. Whilst PINNs have
emerged as an effective universal function approximator for deriving the
solutions of a wide range of governing PDEs/ODEs, their ability to solve
elasto-plastic problems remains uncertain. A novel parsimonious loss function
is first proposed to balance the simplicity and accuracy of PINN. The proposed
method is applied to diverse material behaviours in the cavity expansion
problem including isotropic, anisotropic elastic media, and elastic-perfectly
plastic media with Tresca and Mohr-Coulomb yield criteria. The results indicate
that the use of a parsimonious prior information-based loss function is highly
beneficial to deriving the approximate solutions of complex PDEs with high
accuracy. The present method allows for accurate derivation of solutions for
both elastic and plastic mechanical responses of an expanded cavity. It also
provides insights into how PINNs can be further advanced to solve more complex
problems in geotechnical practice.
