Inverse Physics-Informed Neural Network for CSFM Stress Field Reconstruction in Concrete D-Regions

Abstract

The Compatible Stress Field Method (CSFM) delivers the complete stress field of a structural-concrete discontinuity region (D-region) by combining a continuous stress field with kinematic compatibility and realistic, softening material laws. For an existing or monitored structure the internal stress state is the quantity of interest for assessment, but a finite-element analysis cannot supply it from measurements alone: it requires the loads and the full boundary data as input. This study formulates the recovery of the field as an inverse problem and solves it with a physics-informed neural network. Strain measured at a set of points is assimilated together with the CSFM physics, the cracked rotating compression field, kinematic compatibility and the traction boundary conditions, by a mixed formulation in which one network carries the strain field and a second the displacement field; the stress follows from a differentiable embedding of the cracked-membrane constitutive law. On a deep-beam D-region the internal stress field is reconstructed to within about 7% of an independent continuum CSFM solution from a dense, low-noise strain field, and on a cantilever-bracket corbel, a qualitatively distinct D-region with a single inclined strut and a top tie, to about 12%. Applied to the geometry of an experimentally tested wall pier from the validation suite of the CSFM, the reconstruction reaches 1.5%, though the simultaneously recovered axial and horizontal forces carry larger errors of 7.6% and 10.7% respectively. The error grows with measurement noise, to about 19% at 3% gauge noise on the deep beam, as the constitutive amplification quantified below predicts. This study identifies and quantifies the limiting mechanism: the cracked constitutive law amplifies strain error by a factor of about 3.4, because the crack direction is governed by the shear strain, so that measurement uncertainty propagates magnified into the stress. The applied load, never supplied to the network, is recovered to within 1.2% on the deep beam and 8.3% on the corbel by integrating the reconstructed vertical stress across an interior horizontal cut, where the gauge data densely constrains the field; the naive boundary integration on the load patch itself, where the field is least constrained, gives errors above 25% and is reported only as a diagnostic. A forward physics-only network is shown to be unsuitable, and the strong-form equilibrium residual is found to be detrimental as a training objective.