A Coupled Weibull–Numerical Stress-Field Probabilistic Model for Predicting Fracture and Post-Breakage Load Capacity of Laminated Structural Glass Panels

Structural glass is increasingly used as a primary load-bearing element in facades, roofs, and floor systems, yet its brittle fracture behaviour and surface-flaw-dependent strength remain difficult to capture using deterministic design approaches. Current provisions rely on empirically derived allowable stresses that do not explicitly represent either the statistical distribution of surface flaws or the residual load-transfer capacity of laminated assemblies after initial cracking. This study develops and independently tests a physically grounded framework for predicting first-crack probability and post-fracture residual capacity of laminated glass within a unified formulation.

A two-tier probabilistic-mechanical model couples a two-parameter Weibull surface-flaw distribution with a numerical plate-bending stress formulation incorporating a viscoelastic polyvinyl butyral (PVB) interlayer law. The Weibull failure-probability integral is evaluated over principal tensile stress fields obtained from a finite-difference solution of the governing plate equations. Post-breakage response is represented by a scalar damage variable degrading the effective shear coupling of the cracked laminate, combined with a traction–separation description of glass–PVB debonding. The relaxation spectrum, degradation exponent, and interfacial fracture energy were obtained from independent material-level characterisation rather than fitted to plate-level failure data. Four-point bending tests on 120 annealed laminated specimens (6–12 mm) at several loading rates were divided into calibration and independent validation subsets, stratified by thickness and loading rate. Weibull parameters were estimated using maximum likelihood from the calibration data only. Quasi-static loading and flaw independence are assumed.

Calibration yielded a Weibull modulus of 6.2 and a characteristic strength of 45.3 MPa. On the withheld validation subset, predicted failure loads achieved a mean absolute error of 8.3% and a coefficient of determination of R² = 0.94, while post-breakage capacity was predicted with a mean absolute error of 12.1%. Bootstrap resampling and Monte Carlo simulation showed that 91.5% of observations fell within the nominal 95% prediction interval, indicating slight under-coverage of the predicted scatter.

The framework provides a unified approach for reliability-based assessment of laminated glass. Broader validation across glass types, geometries, loading rates, temperatures, and comparison with EN 16612 and ASTM E1300 is required before application to design guidance.