Stress Intensity Research Articles

New in assessing the fire resistance of reconstructed reinforced concrete ribbed building panel

The article describes the innovative application of a methodology for assessing the design fire resistance of a reconstructed reinforced concrete ribbed floor panel based on the criterion of the occurrence of a limit state based on loss of load-bearing capacity. In this case, the fire resistance limit of a bending element is established without thermal force destruction based on a set of single quality indicators of structural concrete and reinforcing steel, which simplifies engineering calculations and reduces the cost of expensive experiments. The results of a study of the influence of the geometric dimensions of a reconstructed reinforced concrete ribbed panel, the heating scheme of the design section in fire conditions, the placement of the main and additional reinforcement in the design section, the depth of the cores of the main and additional reinforcement and the degree of its fire protection, the thermal diffusion coefficient of structural concrete, the magnitude of the test load on the panel are presented. and the intensity of stress in the rods of longitudinal working reinforcement to the design fire resistance indicator, which is established based on the loss of load-bearing capacity. The use of the new proposed technical solution makes it possible to determine the design fire resistance of a reconstructed reinforced concrete ribbed panel without natural thermal force effects, simplifies engineering calculations, increases the reliability of statistical quality control of reinforced concrete materials and non-destructive tests, and reduces experimental costs.

The interaction between a piezoelectric screw dislocation and collinear rigid lines in one-dimensional hexagonal quasicrystals

The interaction between a piezoelectric screw dislocation and collinear rigid lines in one-dimensional (1D) hexagonal quasicrystals (QCs) under anti-plane mechanical and in-plane electrical loading is analysed. Two idealized electrical assumptions, namely electrically conductive and dielectric, are considered. By using Muskhelishvilid’s complex transformation method, the explicit expressions for the field variables, the singularity of the field variables at the line tip and the force on the dislocation are obtained for a single rigid line. Based on the generalized Peach–Koehler formula, the generalized stress intensity factors and image force on dislocations in piezoelectric quasicrystal (PQC) are obtained. It is evident that the existence of phason field has an effect on image force.

Influence of Specimen Width on Crack Propagation Process in Lightly Reinforced Concrete Beams

Models used to study the fracture process of concrete are often considered 2D, ignoring the influence of specimen width. However, during the fracture process in pre-cracked concrete beams, the crack length varies along the thickness direction, especially in reinforced concrete. To study the influence of specimen width on reinforced concrete fracture behavior, a 3D numerical method was used to simulate the crack propagation processes of lightly reinforced concrete beams based on Fracture Mechanics. Nonlinear spring elements with different stress-displacement constitutive laws were employed to characterize the softening behavior of concrete and the bond-slip behavior between the steel bars and concrete, respectively. It is assumed that the crack begins to propagate when the maximum stress intensity factor at the crack tip along the beam width reaches the initial fracture toughness of concrete. To verify the validity of the proposed method, the completed crack propagation processes of lightly reinforced concrete three-point bending notched beams were simulated, and the calculated load-crack mouth opening displacement curves showed a reasonable agreement with the experimental data. Moreover, the impact of the 2D reinforced concrete beam model on the crack propagation process was analyzed. The results indicate that at the initial loading stage, the external load P obtained from the 2D model is significantly larger than the result from the presented 3D model.

Stronger Westerly Wind Bursts in a Warming Climate: The Effects of the Pacific Warming Pattern, the Madden–Julian Oscillation, and Tropical Cyclones

Abstract Westerly wind bursts (WWBs) in the western–central equatorial Pacific are critical in El Niño–Southern Oscillation (ENSO) dynamics. Understanding how they may change with global warming has important implications for future projections of El Niño. In this study, we investigate how the enhanced eastern equatorial Pacific warming pattern, emerging in future climate projections, can influence WWB characteristics in an atmospheric general circulation model, CAM6. Changes in three main factors affecting WWBs—El Niño-conditions mean westerly wind stress anomalies, the Madden–Julian oscillation (MJO), and tropical cyclones (TCs)—are analyzed. We find that during El Niño onset (December–April), the WWB wind stress intensity remains largely unchanged but WWBs shift westward by about 20° of longitude. In contrast, during El Niño development (May–November), the WWB intensity increases by 41% or 79% in two warming scenarios considered [shared socioeconomic pathways (SSP5-8.5) and SSP2-4.5, respectively], which is mainly caused by a higher frequency of TC occurrence in the central tropical Pacific within 15°N/S. Further, we find that westerly wind speed anomalies associated with El Niño and the MJO also increase during El Niño development. However, as trade winds weaken in the central-eastern equatorial Pacific, the mean strength of the resulting westerly wind stress anomalies does not change much, and no significant eastward shift of WWBs is observed. Thus, our atmospheric model simulations suggest a strong TC-driven increase in WWB wind stress anomalies during El Niño development and hence a more important role of TCs in WWB generation, which in a coupled system could lead to stronger ENSO events, enhanced TC–ENSO coupling, and even greater intensification of WWBs.

Stress-strain state of implant-supported restorations in tooth replacement

Background: Dental implant therapy may be associated with breakage and deformation of implant-supported restorations, necessitating an assessment of their stress-strain state when applying a load. Aim: To compare the stress-strain state of implants with their respective fixed restorations in tooth replacement. Materials and Methods: A 3D mathematical model of the posterior mandible with three missing teeth was used to assess the stress-strain state for the following dental restoration options: three implant-supported crowns; a two-implant-supported bridge; or a bridge supported by tooth and implant. A 150 N load was applied to the central part of a restoration in both vertical and oblique directions to compare maximum stress values and their distribution. Results: Oblique load was found to have a negative impact on stress intensity and distribution (471.7 MPa vs 90.7 MPa with vertical load for three implants). The most heavily loaded parts of restorations were identified: the border of the crown and the implant connection zone. A homogeneous stress distribution from a bridge to the two supporting implants was observed, along with a decrease in stress when using a bridge rather than three implant-supported crowns (160.0 MPa vs 16.1 MPa). In contrast, the load on the supporting implant increased when a bridge supported by tooth and implant was used (1,053.5 MPa with oblique load). Conclusion: Compared to three implants replacing three missing teeth, a two-implant-supported bridge decreases stress on the implants and their respective restoration. Replacing one supporting implant with a tooth increases stress on the implant to the ultimate strength of titanium alloy in the abutment.

Mixed FEM implementation of three-point bending of the beam with an edge crack within strain gradient elasticity theory

AbstractThis paper considers the problem of symmetrical three-point bending of a prismatic beam with an edge crack. The solution is obtained by the mixed finite element method within the simplified Toupin–Mindlin strain gradient elasticity theory. A mixed variational formulation of the boundary value problem for displacements–strains–stresses and their gradients is applied, simplifying the choice of approximating functions. The concept of energy balance is adopted to calculate the energy release rate with a virtual increase in crack length. The increment of the potential energy of an elastic body is determined by accounting for the strain and stress gradient contribution. Numerical calculations were performed using a quasi-uniform triangular mesh of the cross-type. The mesh refinement was applied in the vicinity of the crack tip, at the concentrated support, and the point of application of the transverse force, and uniform mesh partitioning was utilized in the rest of the beam. The fine-mesh analysis was carried out on the successively condensed meshes in the stress concentration domain for different values of the length scale parameter. The crack opening displacements and the distribution of strains and Cauchy stresses for various values of the length scale parameter are presented. An increase in this parameter increases the stiffness of the crack, which leads to a decrease in the crack opening displacements and a smooth closure of its faces at the crack tip. In addition, accounting for the scale parameter reduces the calculated values of strains and stresses near the crack tip. Based on the energy balance criterion, local fracture parameters such as the release rate of elastic energy at the crack tip and the stress intensity factor are determined for different values of the mesh step. The numerical calculations indicate the convergence of the obtained approximations. The main feature of solutions, which includes the strain gradient contribution, is the decrease in the values of the calculated parameters associated with the fracture energy compared to the classical elasticity theory.

Operational control of concrete frost resistance

The analysis of some methods for determining the frost resistance of concrete, including computational and experimental and accelerated ones, has been performed.It is noted that direct methods for determining the frost resistance of concrete are characterized by considerable labor intensity, as well as a long test time, which for concretes of high grades in frost resistance can be several months. Indirect methods do not always make it possible to determine the grade of concrete by frost resistance with a high degree of reliability. The paper proposes an accelerated method for determining the frost resistance of concrete, based on the principles of fracture mechanics, namely the relationship between the frost resistance of concrete and changes in the stress intensity coefficient after a single freeze to a temperature of -50оC. The proposed method allows for operational control of concrete produced monolithic and prefabricated structures. It is shown that the provisions of fracture mechanics describing the process of fatigue failure can be used to describe and analyze the mechanism of frost failure.This will make it possible to develop ways to control the process of frost destruction, slow it down and increase the frost resistance of concrete.

Research on the Propagation Law of Temperature-Induced Reflective Cracks in Semi-Rigid Base Asphalt Pavement

In order to solve the problem of reflection cracks in semi-rigid base asphalt pavement, a study of temperature-type reflection crack expansion is carried out according to the typical climatic characteristics of Guilin, Guangxi Province. According to the theory of fatigue fracture mechanics, the stress intensity factor analysis at the crack tip is carried out, the reflection crack propagation life under single-factor and multi-factor changes is calculated using the Paris fatigue growth formula, and the prediction model of the propagation life of reflected crack under the action of a temperature gradient is established. The results show that the propagation life of temperature-type reflective cracks increases with an increase in the thickness of the middle course and bottom course, and decreases with an increase in the surface course modulus, base course modulus, base course thickness, and temperature decrease. The prediction model includes the factors that have a great influence on the reflection crack extension and provides a theoretical supplement and reference for the design and calculation of asphalt pavement structure in areas with large temperature differences.

Modeling Hydraulic Fracture Entering Stress Barrier: Theory and Practical Recommendations

Numerical modeling of hydraulic fracturing is complicated when a fracture reaches a stress barrier. For high barriers, it may require changing the computational scheme. In view of the strong influence of stress barriers on the final footprint and opening of a hydraulic fracture, for decades, their modeling has been the subject of special investigations. Actually, classical models of propagation within a pay layer with impenetrable boundaries referred to the case of extremely high-stress contrast in neighbor layers. Further improvements tended to account for the fracture growth in these layers by including stress contrasts as input parameters of a model. This tendency resulted in the suggestion and successive enhancements of pseudo-three-dimensional models. All of them have used stress intensity factors (SIFs) to characterize the combined resistance caused by stress contrasts, material strength, and fluid viscosity. Specifically, the SIFs served to formulate the conditions that control the front penetration into a neighbor layer. This key concept presents the background of our research. Despite examples of modeling propagation through barriers, there is no general theory clarifying when and why conventional schemes may become inefficient and how to overcome computational difficulties. This paper presents the theory and practical recommendations following it. We start with the definition of the barrier intensity, which exposes that the barrier strength may change from zero for contrast-free propagation to infinity for channelized propagation. The analysis reveals two types of computational difficulties caused by spatial discretization as follows: (i) general, arising for fine grids and aggravated by a barrier, and (ii) specific, caused entirely by a strong barrier. The asymptotic approach, which avoids spatial discretization, is suggested. It is illustrated by solving benchmark problems for barriers of arbitrary intensity. The analysis distinguishes three typical stages of the fracture penetration into a barrier and provides theoretical values of the Nolte–Smith slope parameter and arrest time as functions of the barrier intensity. Special analysis establishes the accuracy and bounds of the asymptotic approach. It appears that the approach provides physically significant and accurate results for fracture penetration into high, intermediate, and even weak stress barriers. On this basis, simple practical recommendations are given for modeling hydraulic fractures in rocks with stress barriers. The recommendations may be promptly implemented in any program using spatial discretization to model fracture propagation.

Stress state and strength of welded joints with V-shaped elements

It has been established that in the vicinity of V-shaped elements with a sharp apex, the stress field has a singularity of type σ→∞, which requires the use of the concept of “stress intensity factor” in strength calculations. This need arose due to different dimensions of the SIF and fracture toughness. Special criteria for the destruction of structures with V-shaped stress concentrators have been developed, which include, as special cases, the criteria of classical mechanics and the criteria of fracture mechanics. An experimental test of the proposed criteria and calculation methods was carried out. The information obtained is useful for analyzing welded joints on main pipelines and other equipment.

A numerical simulation study on the characteristics of wrap shell lightweight aggregate concrete based on random aggregate model

It is a way to reuse solid waste by using dredged silt as raw material to prepare unburned wrap shell lightweight aggregates and replacing crushed stone aggregate to prepare unburned wrap shell lightweight aggregates concrete specimen. In order to understand the characteristics of wrap shell lightweight aggregates concrete, this paper adopts the method of combining laboratory test and numerical simulation to design the mix ratio test scheme of concrete specimens with different substitution rates of wrap shell aggregate (0 %, 25 %, 50 %, 75 %, 100 %), and conducts indoor mechanical properties test and numerical simulation simulation test on them, so as to obtain and analyze the mechanical properties and failure characteristics.The results show that:(1) The peak stress intensity of concrete specimens decreases linearly with the increase of the substitution rate of wrap shell aggregate.(2) The peak stress of concrete under different wrap shell round aggregate substitution rates is normally distributed, and the dispersion of peak strength decreases with the increase of wrap shell aggregate substitution rate. When the substitution rate is 0 %, the dispersion of peak strength is the largest.(3) Under the uniaxial compression simulation test, the failure mode of concrete specimens changes with the addition of the substitution rate of wrap shell aggregate. When the crack failure occurs, natural coarse aggregate with high strength is chosen to bypass, while when it comes to wrap shell aggregate with low strength, it is chosen to penetrate. With the continuous addition of round aggregate, the stress concentration phenomenon inside concrete can be effectively improved and the number of micro-cracks can be reduced.But at the same time, the penetration cracks gradually increase and gradually tend to be straight.The fractal dimension is negatively correlated with the compressive strength and positively correlated with the substitution rate of wrap shell aggregate.The above research can provide theoretical basis for the popularization of recycled concrete with wrap shell aggregate.

Improvements for the solution of crack evolution using extended finite element method

It is demonstrated that the eXtended Finite Element Method (XFEM) is of remarkable efficiency in simulating crack evolution by eliminating the need for remeshing and refinement. In this paper, it is shown how to enhance the solution efficiency through a comprehensive mathematical investigation of the solution process using XFEM. A typical example is presented to illustrate the disparities in nodal displacements along the two symmetric faces of the crack resulting from the approximation of XFEM. By analysing the structure and components of the global stiffness matrix, the underlying causes of these discrepancies are identified. Building upon these findings, two improvements of the solution are proposed to gain an acceptable accuracy in computing the nodal displacements. The first improvement consists of the subdivision of the enriched elements depending on the characteristic of the distribution of Gauss points. The second improvement is set by determining the optimal number of Gauss points in each sub-element near the crack tip. To calculate the stress intensity factor of the crack under surface pressure, such improvements are applied in conjunction with the interaction integral method, which significantly reduces computational time and eliminates the influence of surface tractions. The numerical solution is validated by comparing it with the analytical solution and the standard XFEM solution. The proposed improvements can enhance both the accuracy of the solution and the computational efficiency of XFEM.

An accelerated corrosion-fatigue testing method for marine high-strength steel based on equivalence principle of fatigue crack growth

The corrosion-fatigue test is widely used to assess marine equipment. However, due to the low-frequency and high-cycle loading of marine equipment in service, conventional test methods require long cycle times and high costs. This makes it challenging to meet the rapid evaluation demands associated with equipment development effectively. In this study, an accelerated corrosion test method was proposed for steel by adjusting the composition, temperature, pH and H2O2 concentration of environment. Fatigue crack growth tests were conducted under various corrosion environments and load frequencies. The matching relationships between corrosion fatigue acceleration multiplier, corrosion environment parameters and load parameters were established. Additionally, a corrosion fatigue acceleration test method was proposed based on the equivalent principle of fatigue crack growth. The results show that effective coupling between corrosion and fatigue can be achieved by gradually reducing the load frequency as the stress intensity factor amplitude increases throughout the crack growth process. It is consistent with the trend of fatigue crack growth rate in the seawater environment. The 4.85% fatigue life deviation and the 15.68 times corrosion fatigue acceleration can be achieved by our method. This work improves the accuracy and reliability of fatigue performance evaluation for offshore equipment.

An Analytical Approach for the Near‐Tip Field Around V‐Notch in Orthotropic Materials

ABSTRACTThis study introduces a novel theoretical framework for determining the notch stress intensity factors (NSIFs) in composite materials. The approach involves utilizing Irwin's complex stress functions for Mode I and Mode II loading conditions. By investigating displacement and singular stress components around V‐notch tips, the research aims to provide a comprehensive understanding of NSIFs in composite materials. Three different composite materials were considered in the study to explore the relationship between stress and material properties. The stress singularity order, denoted as , is determined through eigenequations. Moreover, explicit solutions for displacement and singular stress fields are derived for a more thorough understanding of the behavior around notches in composite materials. To validate the proposed theoretical framework, a rigorous numerical study is conducted using FEM on finite‐size notches. The results obtained from the numerical simulations are compared with theoretical predictions to assess the accuracy and reliability of the developed approach.

An innovative approach to study the influence of microstructure on thermal shock resistance of porous ceramics

AbstractPorosity is a critical microstructural factor in ceramic materials, influencing their mechanical and thermal properties. However, the detailed mechanisms through which porosity, grain size, and grain boundary fracture energy affect the thermal shock resistance of porous ceramics are still not fully understood. This study introduces a dual‐scale model that integrates these microstructural parameters to predict fracture toughness and thermal shock resistance. Using the single‐edge V‐notch fracture toughness testing principle, we calculate the thermal stress intensity factor and establish its relationship with temperature differentials. The critical temperature differential, which marks the onset of thermal shock damage, is determined when the thermal stress intensity factor reaches the fracture toughness threshold. The model reveals a significant interplay between porosity, grain size, and grain boundary fracture energy, with fine‐grained ceramics (grain size < 10 µm) showing a sharp decrease in fracture toughness as porosity increases, while coarser‐grained ceramics are less affected by porosity. These findings provide a deeper understanding of the microstructural optimization needed to enhance the thermal shock resistance of high‐performance porous ceramics.

Construction of Freezing Injury Grade Index for Nanfeng Tangerine Plants Based on Physiological and Biochemical Parameters.

Low-temperature freezing stress constitutes the most significant meteorological disaster during the overwintering period in the Nanfeng Tangerine (NT) production area, severely impacting the normal growth and development of the plants. Currently, the accuracy of meteorological disaster warnings and forecasts for NT orchards remains suboptimal, primarily due to the absence of quantitative meteorological indicators for low-temperature freezing stress. Therefore, this study employed NT plants as experimental subjects and conducted controlled treatment experiments under varying intensities of low-temperature freezing stress (0 °C, -2 °C, -5 °C, -7 °C, and -9 °C) and durations (1 h, 4 h, and 7 h). Subsequently, physiological and biochemical parameters were measured, including photosynthetic parameters, chlorophyll fluorescence parameters, reactive oxygen species, osmoregulatory substances, and antioxidant enzyme activities in NT plants. The results demonstrated that low-temperature freezing stress adversely affected the photosynthetic system of NT plants, disrupted the dynamic equilibrium of the antioxidant system, and compromised cellular stability. The severity of freezing damage increased with decreasing temperature and prolonged exposure. Chlorophyll (a/b) ratio (Chl (a/b)), maximum quantum yield of photosystem II (Fv/Fm), soluble sugar, and malondialdehyde (MDA) were identified as key indicators for assessing physiological and biochemical changes in NT plants. Utilizing these four parameters, a comprehensive score (CS) model of freezing damage was developed to quantitatively evaluate the growth status of NT plants across varying low-temperature freezing damage gradients and durations. Subsequently, the freezing damage grade index for NT plants during the overwintering period was established. Specifically, Level 1 for CS ≤ -0.50, Level 2 for -0.5 < CS ≤ 0, Level 3 for 0 < CS ≤ 0.5, and Level 4 for 0.5 < CS. The research results provide valuable data for agricultural meteorological departments to carry out disaster monitoring, early warning, and prevention and control.

Mixed mode stress intensity factor analysis on edge cracked FGM plate with different material distribution models by XFEM

Mixed mode stress intensity factor analysis on edge cracked FGM plate with different material distribution models by XFEM

Relation Between Striations Spacing and Fatigue Crack Growth Rates for Additive Manufactured Inconel 625

ABSTRACTThe principles of the mechanisms for fatigue crack propagation in metals have been established several decades ago. By definition, fatigue might be summarized as a damage process imparted to a material under the action of cyclic loads. The relation between fatigue crack growth rates (FCGRs) and formation of striation marks has been a controversial topic. Some authors stated that, in certain fatigue regimes, several fatigue cycles are required to form a single striation. The disagreement found was the motivation for the present work. This study's main goal is to provide a comparison between the striation spacing and the respective FCGR. These analyses will be performed in a Nickel superalloy, Inconel 625, obtained via directed energy deposition. Investigation of the striations spacing are compared with data obtained from FCGR tests. A good agreement between striation spacing and FCGRs was found to intermediate and large values of stress intensity factor.

Agronomic adaptations to heat stress: Sowing summer crops earlier

CONTEXTSummer crops are exposed to heat and drought stresses at critical stages during and after flowering, and their intensity and frequency are likely to increase with climate change. Agronomic stress avoidance offers the opportunity to temporally separate critical crop stages from heat and drought events. However, it might require sowing cold-sensitive summer crops earlier into colder than recommended soil temperatures. There is a need to understand how cold is too cold to sow summer crops early in late winter as well as what are the yield benefits and risks. OBJECTIVEHere, we quantify the likely benefits and trade-offs of sowing sorghum, a summer cereal, earlier to adapt to the increased frequency and intensity of heat and water stresses during flowering and grain filling. METHODSTwo years of multi-environment (n=32) genotype by management trials were conducted across the main sorghum growing regions of Australia. Environments (E) consisted of the combination of years, sites, three times of sowing (early, spring, and summer), and the use of supplementary irrigation. At each E a factorial combination of four plant populations (M) and eight commercial sorghum hybrids (G) were sown with three replications. Crop growth and yield components were measured, and the APSIM model was used to simulate all trials and treatments to quantify risks and derive insights into functional relationships between simulated and measured environmental covariates, and measured crop traits. RESULTSThe tested hybrids showed small differences in cold tolerance during crop establishment. Across the tested environments, the G×M combinations produced up to 60% variation in treatment yields across environment yields, which varied between <0.5 to about 10t ha-1; this translated into a ~5.5-fold variation in water use efficiency. Significant G×E and M×E interactions were observed for grain yield components. No G×M or G×E×M interactions were observed on yield or yield components. Early sowing was associated with a reduced risk of heat stress and water use transfer from vegetative to reproductive stages. Early sowing in late winter or early spring resulted in no significant yield gain or loss when all sites and years were included in the analysis. However, early sowing yielded between 1-2 t ha-1 more when the hottest sites and years were considered separately. This resulted from both the avoidance of heat stresses and milder or no terminal drought stresses. CONCLUSIONSEarly sowing of sorghum can reduce the likelihood of heat stresses around flowering as well as the likelihood of terminal drought stresses. Advantages include reduced yield losses in the hottest years and a transfer of water use to grain filling stages, resulting in increased grain yield and improved grain quality parameters. IMPLICATIONSEarly sowing, an agronomic adaptation, offers the opportunity to quickly adapt to the increase in the frequency and intensity of extreme hot events during critical crop stages. However, for the practice to be de-risked, there is a need to increase cold and chilling tolerance in sorghum and/or identify interventions that enhance seed germination and seedling vigour when the crop is sown early into cold soils.

Infrared temperature distribution characteristics and state assessment method of sandstone under tension and compression stress

Abnormalities in infrared radiation temperature (IRT) often accompany the loading In this investigation, stress experiments and splitting tests were conducted on sandstone to investigate the IRT characteristics of sandstone under various loading conditions. The results shows that the Maximum Infrared Radiation Temperature (MAXIRT) increases by up to 5 °C, while in splitting tests, the minimum infrared radiation temperature (MINIRT) decreases by approximately 1.5 °C. Compared to the average infrared radiation temperature (AIRT), MAXIRT is more sensitive to compressive stress, whereas (MINIRT) is more responsive to tensile stress. The correlation between IRT indicators and stress were further analyzed. The findings reveal a positive correlation between IRT and compressive stress. At low stress levels, the correlation coefficient fluctuates between −0.4 and 0.6, generally showing low correlation. As stress increases, the correlation coefficient rises, reaching above 0.8, indicating a high correlation. Tensile stress exhibits a negative correlation, with a consistent trend. Additionally, a statistical analysis of the frequency distribution of IRT under different stress conditions was conducted, followed by hypothesis testing. The results demonstrate that the probability distribution of IRT during loading follows a skewed normal distribution. The changes in skewness can be divided into three stages: initial fluctuation, stable variation, and abrupt failure. Under compressive stress, a right-skewed distribution is observed, with skewness exceeding 3.5 before fracture and reaching above 10 near fracture. Under tensile stress, a left-skewed distribution is noted, with skewness reaching −4.5 near fracture. These findings contribute to the assessment of rock stress states and provide early warning information for predicting rock failure.