Research on the Stability of Arc-Fractured Rock–Concrete Composites: Mechanical Response and Energy Evolution

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.

AE responses, energy evolution, and damage constitutive model of jointed rock-like material subjected to unilaterally confined compression.

Faults, joints, and other weak structural surfaces are commonly present in the surrounding rocks of tunnels and goafs. To investigate the effect of different joint angles on the instability and failure of surrounding rock, joints of varying angles are fabricated using 3D printing technology. Unilateral confined compression tests are conducted using a custom L-shaped mold to systematically examine the mechanical response, acoustic emission (AE) characteristics, macroscopic failure modes, energy evolution, and damage constitutive behavior of the jointed specimens. The results show that the joint angle significantly influences the mechanical properties and macroscopic failure characteristics of the specimens. Compressive strength reaches its maximum at a joint angle of 90°, whereas the highest degree of specimen failure occurs at a joint angle of 30°. Stress reduction is accompanied by increased AE activity and a decline in dynamic b-values. Additionally, the elastic energy of the jointed specimen rises with increasing joint angle, resulting in a higher energy storage capacity. The compaction coefficient K is incorporated to develop a damage constitutive model for jointed rock masses under unilateral confined compression, and the theoretical predictions closely match the experimental results.

Investigation of Compressive–Shear Fracture in Rock Considering Flaw Distribution and Interaction via an Improved Energy-Stress-Based Peridynamics Model

Predicting compressive–shear fracture in rock masses containing complex flaw distributions remains a major challenge in rock engineering. We propose an improved non-ordinary state-based peridynamics (NOSB-PD) model to simulate rock fracture behavior in this work. A stabilized NOSB-PD formulation is developed by incorporating a bond-level deformation gradient strategy to effectively suppress the zero-energy mode inherent in conventional NOSB-PD formulations, thereby ensuring deformation compatibility and numerical robustness. More importantly, the triple-shear energy criterion is introduced into the PD framework for the first time, enabling a more accurate characterization of shear fracture in rocks under complex stress states. The proposed NOSB-PD model is validated using two examples, demonstrating its excellent capability in suppressing the zero-energy mode and capturing fracture behavior in rock under compressive–shear conditions. Subsequently, the proposed model is used to systematically investigate the influence of flaw distribution on crack propagation and failure modes in rocks. The results indicate that variations in flaw distribution alter the local stress field, leading to a change in the rock fracture mode. Consequently, the rock bridge failure mode transitions from shear-dominated direct coalescence to mixed tensile-shear failure, and finally to tension-dominated indirect failure. The overall rock specimen is more prone to tensile–shear-mixed failure under conditions of shorter rock bridges with larger inclinations, or longer rock bridges with smaller inclinations. These findings provide new insights into the role of flaw distribution on rock fracture behavior.

Modeling Dynamic Crack Propagation in Heterogeneous Variable Stiffness Composites Using the Phase-Field Method

Composites are widely used in the building sector for high-rise building load-bearing components, bridge decks, prefabricated structural panels, and seismic-resistant members, where excellent mechanical performance and structural durability are critical. As specialized advanced composites, variable stiffness composites (VSCs) have gained increasing engineering applications due to their excellent overall performance. Nevertheless, exploring the fracture characteristics of composite materials, especially VSCs, remains a significant challenge. In particular, cracks in composite components can adversely affect structural integrity and durability. In this study, a dynamic fracture phase-field model for VSCs is developed within the framework of elastic dynamics to investigate crack propagation behavior of VSCs under dynamic loads. The proposed model is first validated by experimental results of fracture behavior of single-edge cracked FRC laminae. Then, the proposed model is employed to systematically study the effects of three fiber orientation design variables and internal defects on the fracture behavior of VSCs. Additionally, fiber trajectories are optimized for different pore distribution configurations. The results demonstrate that the model effectively captures the fracture behavior of VSCs and that optimizing these three design parameters enables the fabrication of high-performance VSCs with enhanced crack propagation resistance. This work provides fundamental insights for the design of curvilinearly fiber-reinforced composites and lays a solid theoretical foundation for the practical application of VSCs in building engineering.

Mechanical response and failure mechanisms of sandstone under water–rock interaction: a multi-scale study and constitutive modeling

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.