Numerical Investigation of Time-Dependent Deformation and Fracture Evolution in Flawed Sandstone

Mechanics of Materials and Structures

Numerical Simulation Study of the Permeability Evolution of Sandstone during the Loading and Failure Process Based on FDEM

Rock failure under hydromechanical coupling is a complex process that has attracted considerable attention in deep underground engineering. In this study, a hydraulic coupling analysis method for rock loading and failure is developed based on the finite–discrete-element method (FDEM) combined with the grain-based model, which integrates the dual-medium seepage–stress coupling theory to simultaneously capture pore and fracture seepage. Numerical simulations of sandstone under varying confining pressures were performed and validated against laboratory experiments, and the effects of confining pressure and weak joint content on the permeability evolution were systematically investigated. The results demonstrate that the permeability evolution during loading is governed by the competitive interplay between matrix seepage and fracture seepage, exhibiting a nonlinear pattern. Higher confining pressures prolong the stage of slow permeability growth, whereas an increase in the weak joint content reduces strength and stiffness, leading to an earlier occurrence of the permeability inflection point and an enhanced dominance of fracture flow in controlling macroscopic permeability. These findings provide new insights into the mechanisms of hydromechanical coupling in fractured porous rocks and offer theoretical support for predicting and controlling hydraulic hazards in deep rock engineering.

Numerical Simulation of Crack Propagation in Concrete with Prefabricated Array Fractures Based on the Discrete Element Method

Concrete readily develops cracks under service loads, which poses severe risks to the overall safety of engineering structures. In this work, the discrete element method (DEM) integrated with PFC2D 5.0 numerical software is adopted to construct a mesoscale concrete numerical model containing pre-existing internal fractures, and uniaxial compressive loading simulations are subsequently carried out. Unlike previous studies that predominantly examined isolated fracture parameters, this work systematically investigates the coupled effects of fracture inclination angle, length, and quantity on crack propagation mechanisms at the mesoscale, and for the first time establishes a quantitative relationship between microcrack spatial distribution patterns and macroscopic mechanical degradation. Parametric analyses are performed to quantify the influences of fracture geometric characteristics, including fracture inclination angle (30°, 45°, 60°), fracture length (short, long and extra-long), fracture quantity (4, 8 and 16), as well as the comparison between intact and fractured concrete specimens. The fracture quantities of 4, 8, and 16 are selected to represent low, medium, and high levels of initial defect density within the concrete matrix, corresponding to approximately 1%, 2%, and 4% of the total specimen area, respectively, thereby enabling a systematic investigation into the progressive deterioration of mechanical performance with increasing internal damage severity. The whole evolution process of crack initiation, crack propagation and ultimate failure patterns of concrete is systematically explored. Numerical results reveal that specimens with larger fracture angles exhibit higher compressive strength yet generate abundant newly formed microcracks, whereas low-angle prefabricated fractures are prone to triggering abrupt brittle failure. Specimens embedded with shorter fractures achieve superior mechanical strength and develop denser, more intensive microcrack distributions; in contrast, long pre-existing fractures drastically degrade compressive strength while limiting the generation of secondary cracks. Reducing the number of internal defects simultaneously improves compressive strength and expands the coverage range of the induced fracture network. Specimens with 16 prefabricated fractures deliver the weakest mechanical performance, owing to the excessively high initial defect density inside the matrix. In comparison with fractured samples, intact concrete without pre-set fractures achieves better comprehensive performance in terms of compressive strength, deformation compatibility and uniform microcrack development. A core conclusion drawn from this study is that the total quantity of microcracks cannot serve as a direct indicator to evaluate the damage degradation degree of concrete; instead, the spatial distribution pattern of microcracks dominates the deterioration level. Evenly scattered microcrack populations maintain relatively high residual strength, whereas the concentrated coalescence of microcracks into continuous penetrating macrocracks leads to an abrupt decline in structural load-carrying capacity. The findings of this research can provide theoretical references for stability evaluation and safety diagnosis of defective concrete structures in practical engineering.

On phase-field regularization in dynamic fracture with brittle and cohesive formulations

Phase-field models of fracture are widely used for simulating crack nucleation and propagation, yet the role of the phase-field regularization in the dynamic regime is not fully understood and depends critically on how the damage variable is coupled to the displacement field. In this paper, we analyze three alternative formulations: the brittle model with stiffness degradation, its variant with stiffness+density degradation, and our recently proposed phase-field regularization of cohesive fracture, which we extend to elastodynamics. By studying the interaction of a tensile and a compressive elastic wave with a phase-field crack in a one-dimensional bar, we determine for which models and under which conditions the phase-field regularization preserves the features of the wave-crack interaction expected for a sharp crack, and we theoretically explain which variables control the behavior. For the new cohesive model extended to dynamics, we further derive an analytical dynamic cohesive opening law. Finally, we study the dynamic behavior including branching of a two-dimensional notched plate at two loading intensities.

Modeling Time-Dependent Rock Behavior: Simultaneous Validation of Creep and Stress Relaxation Using a Combined Viscoplastic Approach

This study investigates the time-dependent mechanical behavior of rocks and granular materials, challenging the conventional view of their response as time-independent. We present a rheological model that effectively simulates active loading, creep, and stress relaxation in geomaterials, validated through laboratory experiments on a wet limestone sample. Traditional elastic and plastic models often fail to capture the complexities of rock behavior under prolonged stress, necessitating the use of viscoplastic models that integrate rate-dependent plasticity. Building on existing research, we developed a combined elasto-viscoplastic model featuring two groups of Shvedova–Bingham–Norton viscoplastic elements. The first pair accounts for elastoplastic deformation during active loading, while the second pair activates beyond a critical stress level, known as the D-point, at which significant microstructural changes occur. The model accurately captures the essential time-dependent behaviors of creep and stress relaxation, demonstrating excellent correlation with experimental data across all loading stages. Parametric studies reveal the model's unique behavior and its sensitivity to parameter variations, highlighting its robustness. This research contributes to the understanding of rock mechanics and provides a simplified yet physically interpretable framework for modeling complex deformation processes, facilitating practical applications in geotechnical, mining, and petroleum engineering contexts.

Investigating Fracture Behavior of Lattice Structures Using the XFEM and Equivalent Solid Material Model Techniques

This study aims to numerically investigate the mode I, II, and III fracture behaviors of additively manufactured degradable, bioplastic polylactic acid (PLA) lattice specimens. Numerical simulations were performed using the eXtended Finite Element Method (XFEM) based on the extracted PLA's mechanical and fracture material properties. The maximum principal stress and fracture energy power‐law criteria were utilized to simulate damage initiation and evolution in three‐dimensional (3D) numerical analyses. To consider the effects of build orientation, the transversely isotropic elasticity model (TIEM) was implemented. To facilitate the XFEM analyses, the equivalent solid material model (ESMM) technique was also utilized. The experimental load‐displacement responses of single‐edge notched bending specimens under the symmetric and asymmetric four‐point bending and mode III transverse shear cracked plate tests were conducted for comparison with the XFEM analyses in mode I, II, and III fracture, respectively. A common calibration factor, as well as the simultaneous utilization of the TIEM model, as well as the XFEM and ESMM techniques, reflected numerical results of acceptable accuracy compared to the experimental results; 5.3% (3.4%), 4.4% (5.8%), and 9.6% (5.4%) differences for the stiffness (peak load) of mode I, II, and III specimens, respectively.