Three-dimensional modeling of failure in quasi-brittle materials and structures

In most serviceability conditions, concrete structures present quasi-brittle behavior and failure due to the presence of a nonlinear fracture process zone ahead of the crack front. Predictive models and design methodologies have to be able to reliably calculate the load capacity, or structural strength, of structures while taking into account the nonlinearity of the material behavior and the consideration of realistic conditions such as geometry, size, boundary conditions, and loading configuration. The main objective of this study was to develop models and apply numerical tools to predict the cracking potential in three-dimensional concrete structures. A damage-based cohesive zone model was formulated and implemented to simulate mode I crack growth in quasi-brittle materials based on the thermodynamics of irreversible processes allowing for loading, unloading, and re-loading of a 3-D specimen geometry. The model is a improvement to existing cohesive zone formulations to consider three-dimensional geometries and also overcome numerical instability, lack of convergence, and oscillations in the traction profile commonly reported in cohesive models.;This study also explored the novel computational framework of the generalized finite element method (GFEM) to predict the potential for crack propagation in large-scale problems such as three-dimensional airfield concrete slabs. A multi-scale approach, using the global-local concept within the GFEM framework (GFEMg-1), is applied to multi-site damage problems (MSD), where several crack geometries are placed simultaneously at different positions in a slab and loaded by different aircraft gears. This approach efficiently simulated multiple cracks not discretized in the global mesh, but only modeled in the local problem domains. The GFEMg-1 enrichment functions allowed the kinematics to be represented in the global domain through enrichment function from the local problems rather than explicitly modeling each crack discretely in the global domain.;This research effort also proposed an integrated approach called nonlinear strength fracture model (NLSFM) to predict the structural strength or load capacity of three-dimensional concrete structures considering the structure geometry, loading configuration, and the nonlinearities ahead of the crack front. In this approach, the extraction of crack front quantities, such as stress intensity factors, were performed through finite element analysis (GFEM), and then an analytical approximation based on the equivalent elastic crack approach for quasi-brittle materials accounted for the FPZ effects on the nominal strength of the structure under mode I fracture. The NLSFM uses the size- and shape-independent fracture properties defined through the critical energy release rate, Gf, and size of fracture process zone, c (as provided by the size effect model and two-parameter fracture model for quasi-brittle materials). The NLSFM predicted a material independent strength curve for a given the structural geometry, boundary conditions, loading, and initial crack length. The model required defining geometric functions for the three-dimensional structure with partial-depth cracks, which were derived from 3D computational modeling of these structures using the GFEM. The model was validated with large-scale, notched slab tests supported by an elastic foundation and extended to load capacity predictions for airfield concrete slabs with various gear loadings. The NLSFM advances the state-of-the-art of computational modeling of failure in quasi-brittle materials, currently limited to 2-D structures or laboratory test specimens, to large scale 3-D problems with realistic boundary conditions and loading configurations.;The proposed numerical tools, GFEM with multi-site damage and the NLSFM, are used as a computational platform to analyze the cracking potential for airfield concrete slabs with existing surface- and bottom-initiated cracks. The results show that starter cracks can induce unstable crack propagations under specific loading configurations and material fracture properties. Given existing surface and bottom starter cracks of the same geometry in the concrete slabs, it was much easier to propagate surface cracks under triple dual tandem gear loading relative to the traditional design assumption that bottom-up fatigue cracks are the critical failure mode for airfield concrete slabs.