Intermediate Principal Stress Research Articles

Strength characteristics and energy evolution of cement stone under true-triaxial loading conditions

Oil well cement is a commonly used cementing material in oil and gas extraction engineering. Due to the change of stress conditions, it is prone to microcracks or micro annular gaps, leading safety concerns. To study the strength characteristics and energy evolution of oil well cement stone under three-dimensional stress states, a series of true-triaxial compression tests were carried out. Based on the experimental results, the mechanical properties and energy evolution mechanisms during the true-triaxial compression process of cement stone under different stress states were explored. The research results indicate that there is an intermediate principal stress effect on the true-triaxial compressive strength of cement stone specimens. When the minimum principal stress remains constant, the strength of cement stone first increases and then decreases with the increase of intermediate principal stress. When the minimum principal stress is 5MPa, the specimen exhibits brittle failure, with ε1 at peak stress approximately 0.015. As the minimum principal stress increases to 20MPa, the specimen gradually transits to plastic failure, with ε1 at failure exceeding 0.04. The type of failure is determined by the energy ratio at the time of failure; when there is more elastic energy, it results in brittle failure, otherwise it leads to ductile failure. Due to the high porosity of cement stone samples, most of the input energy is converted into dissipated energy. At minimum principal stresses of 5MPa, 10MPa and 20MPa, the ratio of peak dissipated energy to total input energy fluctuates around 0.55, 0.73 and 0.85, respectively. There is a strong linear relationship between the peak elastic energy, peak dissipated energy, and total input energy, with fitting correlation coefficients of 0.847 and 0.996, indicating that the cement stone sample also follows the linear energy storage law. A strength criterion for cement stone was established based on the modified Lade criterion, which is more suitable for describing the strength of high porosity materials compared to traditional strength criteria. Finally, based on the interaction mechanism between energy accumulation and energy dissipation, a nonlinear model of energy evolution in cement stone was established. The results of the theoretical model are in good agreement with the experimental data.

Effect of Mineral Composition and Particle Size on the Failure Characteristics and Mechanisms of Marble in the China Jinping Underground Laboratory.

In deep underground engineering, the deformation, failure characteristics, and mechanism of surrounding rock under the influence of grain sizes and mineral compositions are not clear. Based on CJPL-II variously colored marbles, the differences in grain size and mineral composition of the marble were analyzed by thin-section analysis and XRD tests, and the effect of intermediate principal stress on the mechanical properties of marble was investigated. Both SEM and microfracture analysis were coupled to reveal the failure mechanisms. The results highlight that the crack initiation strength, damage strength, peak strength, and elasticity modulus of Jinping marble exhibit an increasing trend with an increase in intermediate principal stress, while the peak strain initially increases and subsequently decreases. Moreover, this study established negative correlations between marble strength, brittleness characteristics, and fracture angle with grain size, whereas positive correlations were identified with the content of quartz, sodium feldspar, and the magnitude of the intermediate principal stress. The microcrack density in marble was found to increase with larger grain sizes and decrease with elevated quartz and sodium feldspar content, as well as with increasing intermediate principal stress. Notably, as the intermediate principal stress intensifies and grain size diminishes, the transgranular tensile failure of marble becomes more conspicuous. These research findings contribute to the effective implementation of disaster prevention and control strategies.

Performance of multi-ribbed composite wall incorporating reactive powder concrete-filled steel tubular columns under axial compression

In this study, axial compression researches of an innovative composite shear wall, named multi-ribbed composite wall incorporating reactive powder concrete-filled steel tubular columns, were conducted using theoretical analyses as well as experimental and numerical investigations. This precast hybrid system embedded reactive powder concrete-filled steel tubular columns as boundary elements of multi-ribbed composite wall. A novel approach, namely the unified strength theory, was adopted in consideration of various materials diversity. The outcomes of unified strength theory were utilized to predict the ultimate compressive capacity of multi-ribbed composite wall equipped with reactive powder concrete-filled steel tubular columns. The proposed theoretical formulas were validated against the experimental results reported in this paper. Despite the fact that the calculated formula with b= 0 was obtained to predict the closest capacity value of the test specimen infilling ordinary concrete. The calculations with different values of b clearly indicated that the intermediate principal stress effect should be rationally considered. Experimental observations suggested that the frame column significantly contributed to improving the compressive performance throughout the entire process and maintained the wall integrity. Meanwhile, finite element models were developed using the ABAQUS program, followed by the elaboration of its numerical implementation. The numerical predictions of ten shear wall specimens infilling reactive powder concrete were found to be reasonably in agreement with the calculated results corresponding to b= 0.5. These findings revealed the characteristics of multiple defensive lines of "block-ribbed column-frame column" under axial compression. Following the successful validation of finite element models, parametric studies were carried out to evaluate the influences of the filled block compressive strength, steel tube wall thickness and height-width ratio. The results show that the axial compression capacity of multi-ribbed composite wall incorporating reactive powder concrete-filled steel tubular columns can be noticeably improved with an increase in block strength and tube thickness. The proposed composite wall demonstrates favorable cooperative working performance and desirable displacement ductility. Subsequently, the primary objective of this pilot study aimed at developing a reliable theoretical calculation formula and conducting numerical simulation verification of the innovative composite wall. The aforementioned conclusions are intended to provide insights for the guidance and optimization of engineering structures.

Anisotropic characteristics and creep model for thin-layered rock under true triaxial compression

The failure phenomenon of thin-layered rock tunnels not only exhibits asymmetric spatial characteristics, but also significant time-dependent characteristics under high in-situ stress, which is attributed to the time-dependent fracture of thin-layered rocks. This paper conducted a series of true triaxial creep compression tests on typical thin-layered rock siliceous slate with acoustic emission technique to reveal its anisotropic time-dependent fracture characteristics. The anisotropic long-term strength, creep fracturing process, and fracture orientation characteristics of thin-layered rocks under different loading angles (β, ω) and intermediate principal stress were summarized. A three-dimensional (3D) non-linear visco-plastic creep model for thin-layered rock was developed to simulate its anisotropic creep behavior. The time-dependent fracturing of rocks during true triaxial creep loading is reflected through the change of equivalent strain based on an improved Euler iteration method. By constructing the plastic potential function and overstress index related to loading angles and stress state, the anisotropic time-dependent fracturing process and propagation of thin-layered rocks under different loading angles and intermediate principal stress are expounded. The model was validated experimentally to show it can reflect the long-term strength and creep deformation characteristics of thin-layered rocks under true triaxial compression.

A three-dimensional elastoplastic constitutive model incorporating Lode angle dependence

A comprehensive three-dimensional elastoplastic constitutive model is presented to characterize the stress-strain behavior of cement stone under the true triaxial stress state. This constitutive model incorporates a three-dimensional yield function and a three-dimensional potential function. The three-dimensional yield function is designed to accurately represent the true triaxial stress state during hardening. The three-dimensional potential function is devised to depict the plastic flow direction under true triaxial stress state. The yield and potential functions include parameters that control the shape of the deviatoric and meridian planes, and these parameters vary with the plastic internal variable. Consequently, the yield function can accurately describe the stress state, and the potential function can precisely capture the variations in plastic flow direction. Additionally, a detailed procedure for determining the parameters of the yield function and potential function is proposed based on the full deformation process. The constitutive model is presented in the form of analytical solution. The comparison of experimental data with the constitutive model confirms its accuracy and validity. A sensitivity analysis of the deviatoric and meridian parameters in the potential function is performed, shedding light on their impact on the model behavior. Furthermore, the significance of incorporating Lode angle dependence into the potential function is discussed, emphasizing its essential role in accurately capturing strain in the direction of the intermediate principal stress.

Damage characteristics of rock induced by unloading in hole under true triaxial boundary stresses: Experimental study

In order to study the effect of unloading of underground rock excavation on the stability of surrounding rock, the true triaxial compression (TTC) and coupled true triaxial compression and in-hole loading-unloading tests (TTC-HU) were conducted on hollow cubic rock (100mm × 100mm × 100mm). The experimental results indicate that the compressive strengths of the specimens increase as confining pressure increases in the equal biaxial stressand increase with increasing intermediate principal stresses in the unequal biaxial stress. At low confining pressure (σ < 30 MPa), the internal stress at unloading damage in the hole of hollow cubic specimen increases with the increase of the three-directional boundary stresses. At high confining pressure (σ ⩾ 30 MPa), the specimen will not be damaged during the entire unloading process in the hole. The damage mode of the specimen is dominated by tensile damage. The shape of the holes in the specimens did not significant change, and hole wall of specimen have layered destruction along the circumference in low confining pressure. In high confining pressure, the hole area of the specimen undergoes significant deformation damage, forming a V-groove along the direction of the minimum principal stress, and the wall of the hole is completely peeled off. This study can reasonably predict the actual engineering damage patterns and guide the optimization of surrounding rock support.

A discrete approach for modelling the permeability evolution of granite under triaxial and true-triaxial stress conditions

In deep underground engineering, modelling the seepage characteristics of rock masses under complex stress conditions is crucial for the safe construction and stable operation of a project. The permeability of the rock mass is not only controlled by its internal pore structure but is also closely related to the deformation and fracturing of the rock. Although discrete methods offer advantages in describing the formation and development of fractures, these methods still face challenges due to the difficulties in establishing microscopic seepage models. This paper introduces a new hydro-mechanical coupled numerical model. In this model, a simple method is proposed to couple the Rigid-Body-Spring Method (RBSM) for rock deformation and fracturing simulation and the Equivalent Matrix-Fracture Network (EMFN) for seepage simulation. Subsequently, the model is employed to simulate the permeability of granite under three-dimensional stress conditions. The simulation results show that under hydrostatic stress conditions, the model accurately captures the decrease in permeability due to pore compression and collapse. Additionally, under deviatoric stress conditions, it reveals the stage-wise increase in permeability caused by granite fracturing. Finally, the model is applied to study the permeability evolution behaviour of rocks under true triaxial stress conditions. The results unveiled the significant impact of the intermediate principal stress on permeability evolution and revealing the microscopic mechanisms underpinning these effects. This paper paves a way for enhancing the application of discrete methods in forecasting the permeability evolution behaviour of intricate rock masses.

Study on the Damage Mechanism of Coal under Hydraulic Load

Hydraulic fracturing is extensively utilized for the prevention and control of gas outbursts and rockbursts in the deep sections of coal mines. The determination of fracturing construction parameters based on the coal seam conditions and stress environments merits further investigation. This paper constructs a damage analysis model for coal under hydraulic loads, factoring in the influence of the intermediate principal stress, grounded in the unified strength theory analysis approach. It deduces the theoretical analytical equation for the damage distribution of a coal medium subjected to small-flow-rate hydraulic fracturing in underground coal mines. Laboratory experiments yielded the mechanical parameters of coal in the study area and facilitated the fitting of the intermediate principal stress coefficient. Leveraging these datasets, the study probes into the interaction between hydraulic loads and damage radius under assorted influence ranges, porosity, far-field crustal stresses, and brittle damage coefficients. The findings underscore that hydraulic load escalates exponentially with the damage radius. Within the variable range of geological conditions in the test area, the effects of varying influence range, porosity level, far-field stress, and brittle damage coefficient on the outcomes intensify one by one; a larger hydraulic load diminishes the impact of far-field stress variations on the damage radius, inversely to the influence range, porosity, and brittle damage. The damage radius derived through the gas pressure reduction method in field applications corroborates the theoretical calculations, affirming the precision of the theoretical model. These findings render pivotal guidance for the design and efficacy assessment of small-scale hydraulic fracturing in underground coal mines.

Elastic–plastic criterion solution of deep roadway surrounding rock based on intermediate principal stress and Drucker–Prager criterion

AbstractExcavation‐induced rock failure and deformation near an underground opening boundary is closely associated with the intermediate principal stress, strain softening and rock mass dilation. By combining theoretical analysis and numerical simulation to explore the mechanical evolution of the roadway surrounding rock during excavation. The elastic–plastic criterion solutions for surrounding rock stress, displacement, and the plastic zone of a circular roadway were deduced by including the intermediate principal stress, strain softening and rock mass dilation, based on the Drucker–Prager criterion and the nonassociated flow rule. Furthermore, ABAQUS finite element software was utilized for numerical simulations to scrutinize the influence of mechanical parameters on stress redistribution, surface displacement, and plastic range. The results of the numerical simulations verify the reliability of the theoretical analysis and affirm the high consistency of the results with the theoretical solution. The research findings indicate that the strength of surrounding rock is significantly influenced by the intermediate principal stress, and the deformation and failure of rock mass are primarily impacted by rock mass dilation, while strain softening mainly affects the thickness of the fractured zone. Moreover, the study reveals that enhancing the residual strength of the surrounding rock can improve its resistance to deformation and failure. Furthermore, the excavation of the roadway is observed to increase the original rock stress in the surrounding rock, but increasing the ground support strength effectively controls the deformation and failure of surrounding rock. Ultimately, the research outcomes offer valuable references for engineering calculations and ground support design of surrounding rock in deep roadways.

Experimental Study on Energy Release Mechanism and Crack Propagation Evolution of Sandstone under True Triaxial Loading

The instability of hard and brittle rock often leads to disastrous consequences in underground engineering. Under various surrounding rock pressure conditions, in situ stress induces corresponding deformation and damage to the floor post-mining. Therefore, it is crucial to examine the effects of mining under different confining pressures on rock disturbance, damage characteristics, and their distribution. Consequently, triaxial loading experiments under varying intermediate principal stress conditions were conducted on red sandstone specimens, using an acoustic emission monitoring system to track energy changes during rock damage and failure. This approach aids in studying crack generation, propagation, and fracture damage evolution. The results indicate that rock deformation results in axial compression and dilatancy, aligned with the direction of minimum and intermediate principal stresses. Ductility in rock failure becomes more pronounced with increased stress, primarily manifesting as shear failure. Internal cracks in the specimen lead to stress concentration and marked plastic deformation under compression, yet do not result in macroscopic surface cracks. The fracture angle θ of specimens post-failure generally exceeds 45° and varies with stress changes; at consistent burial depths, the angle of the sandstone failure surface increases with intermediate principal stress. This paper preliminarily establishes the informational linkage between rock failure and energy release, analyzing the rock samples over time and space. This research offers insights for analyzing and mitigating sudden rock instability.

Investigation of the dense granular soil behaviour inside and outside the shear band: a three-dimensional DEM-FDM study

The present paper aims to compare the behaviour of dense granular soils inside and outside the Shear Band (SB) during the Plane Strain Compression (PSC) test using the Discrete Element Method (DEM). The flexible membrane in the PSC test was modelled by adopting a discrete element–finite difference (DEM-FDM) hybrid approach. In contrast with previous 2D studies, the present study employed 3D simulations to consider the effects of out-of-plane characteristics such as the intermediate principal stress. According to the findings, the minimum and intermediate principal stresses outside the SB were twice as high as those inside at the residual state. It was also found that mechanical coordination numbers and redundancy indexes both inside and outside the SB decreased up to the onset of the residual phase, with a higher reduction rate inside the SB. As far as fabric anisotropy is concerned, the degree of anisotropy increased both in and out the SB until the peak state, with a somewhat higher rate inside the SB. A further finding was that the distribution of normal contact forces outside the SB remained symmetrical around the vertical axis after shear banding, however, it became asymmetrical inside the SB.

Three-dimensional numerical simulation on failure mechanical characteristics of fissured sandstone specimens under true triaxial conditions

Understanding intermediate principal stress influences on deformation characteristics and failure mechanism of fractured rock from deep engineering often necessitates long term on-site detection and complex experimental research, although very limited efficacy can be obtained. With presently available experimental data on conventional triaxial cuboid noncoplanar fissured sandstones, this study further investigated the effects of differential stress (σ2 − σ3) and rock bridge inclination angle (β30°, β60°, β90°, β120°, and β150°) on their damage evolution processes and failure modes based on 3D discrete element methods (PFC3D). Numerical simulation results indicated that the peak strength of the fissured sandstone under the same state of horizontal principal stress shows an overall increasing pattern with the increase of the inclination angle of the rock bridge, while its peak strain displays a decreasing and then increasing trend. Besides, in this work, five failure modes, nine crack types and two kinds of stress–strain curves are summarized which are significantly affected by the horizontal principal stress, rock bridge inclinations or cooperative interaction. Differential stress value of 15 MPa is an important threshold for determining the residual strength of the stress–strain curve from present to absent. The cracking and force chain evolution processes of five failure modes were analyzed in order to discover the corresponding failure mechanisms. Finally, differential stress and flaw inclination influences on rock mechanical parameters and failure behavior have significant implications for strategies of the design, operation, and maintenance of rock engineering under severe conditions in the underground.

A quantitative tunnel support design method considering the safety factor of the surrounding rock

The quantitative support design plays a vital role in tunnel design, while the conventional quantitative framework of tunnel support design through convergence-confinement method (CCM) generally focuses on the safety of the support structure element. Herein, a quantitative tunnel support design method considering the safety factor of the surrounding rock is proposed. First, the solution for the safety factor of surrounding rock element is derived under the CCM framework considering influences of the intermediate principal stress (IPS) and the dilatancy on rock-mass yielding. Second, the allowable safety factor of surrounding rock element is obtained based on the critical support line in the widely used rock quality (Q) system. Then, the framework and procedure of the quantitative tunnel support design method are outlined. Verification of the proposed method is conducted through comparisons with the analytical solution, laboratory model experiment and field monitoring data. Furthermore, a case study is employed to illustrate the proposed method, results indicate that the failure of the whole underground system is caused by the insufficient safety reserve of surrounding rock element. In general, the proposed method provides theoretical guidance for quantitative stability analysis and design optimization of tunnels.

Influence of advance direction on surrounding rock stability of main ramp under deep high ground stress

Due to the widespread use of trackless equipment in metal mines, the main ramp has become a major development roadway in large mines. Under deep high ground stress condition, the stability of the surrounding rock of the main ramp is subject to significant variability due to the change in the advance direction, leading to structural failure in different areas of the roadway. Because the support design scheme of surrounding rock of main ramp will not pay attention to the advance direction of roadway, leading to the key support area of the surrounding rock is not clear, resulting failure of the local supporting form occur frequently. Therefore, this paper adopts the combination of on-site investigation and numerical simulation to carry out the stability analysis of the surrounding rock under different advance directions of the roadway. Through on-site investigation, various failure modes of surrounding rock induced by the change of the advance direction of the roadway are summarized, and the key supporting area of surrounding rock of main ramp is determined according to the angle change between the roadway advance direction and the intermediate principal stress. The extent of the risk zone of the roadway surrounding rock is defined based on the Drucker-Prager criterion, which can be used as the new basis for the design of roadway support parameters. The results show that: As the angle between the advance direction and the intermediate principal stress increases, the degree of deformation of the surrounding rock decreases linearly, and the volume of the plastic and risk zones of the surrounding rock decreases nonlinearly. Based on the distribution of the strain energy density of the roadway surrounding rock, when the angle between the advance direction and the intermediate principal stress is small, the roadway surrounding rock is more prone to the floor heave phenomenon. When the angle between the advance direction and the intermediate principal stress is larger, the roadway surrounding rock is prone to the full-section failure phenomenon. Based on the block theory, when the advance direction is changed, the location and production of key blocks have significant variability, leading to the need for reasonable adjustment of the support parameters for the surrounding rock. The research results of this paper are of guiding significance for the optimization of the surrounding rock support scheme of the main ramp.

Influence of orientation of the intermediate principal stress on fracture reactivation in granite

Fracture (fault) reactivation can lead to dynamic geological hazards including earthquakes, rock collapses, landslides, and rock bursts. True triaxial compression tests were conducted to analyze the fracture reactivation process under two different orientations of σ2, i.e. σ2 parallel to the fracture plane (Scheme 2) and σ2 cutting through the fracture plane (Scheme 3), under varying σ3 from 10 MPa to 40 MPa. The peak or fracture reactivation strength, deformation, failure mode, and post-peak mechanical behavior of intact (Scheme 1) and pre-fractured (Schemes 2 and 3) specimens were also compared. Results show that for intact specimens, the stress remains nearly constant in the residual sliding stage with no stick-slip, and the newly formed fracture surface only propagates along the σ2 direction when σ3 ranges from 10 MPa to 30 MPa, while it extends along both σ2 and σ3 directions when σ3 increases to 40 MPa; for the pre-fractured specimens, the fractures are usually reactivated under all the σ3 levels in Scheme 2, but fracture reactivation only occurs when σ3 is greater than 25 MPa in Scheme 3, below which new faulting traversing the original macro fracture occurs. In all the test schemes, both ε2 and ε3 experience an accumulative process of elongation, after which an abrupt change occurs at the point of the final failure; the degree of this change is dependent on the orientation of the new faulting or the slip direction of the original fracture, and it is generally more than 10 times larger in the slip direction of the original fracture than in the non-slip direction. Besides, the differential stress (peak stress) required for reactivation and the post-peak stress drop increase with increasing σ3. Post-peak stress drop and residual strength in Scheme 3 are generally greater than those in Scheme 2 at the same σ3 value. Our study clearly shows that intermediate principal stress orientation not only affects the fracture reactivation strength but also influences the slip deformation and failure modes. These new findings facilitate the mitigation of dynamic geological hazards associated with fracture and fault slip.

Analysis of strength characteristics of loess before and after freezing using a hollow cylinder torsional shear apparatus

This paper aims to comprehensively analyze the influence of the principal stress angle rotation and intermediate principal stress on loess's strength and deformation characteristics. A hollow cylinder torsional shear apparatus was utilized to conduct tests on remolded samples under both normal and frozen conditions to investigate the mechanical properties and deformation behavior of loess under complex stress conditions. The results indicate significant differences in the internal changes of soil particles, unfrozen water, and relative positions in soil samples under normal and frozen conditions, leading to noticeable variations in strength and strain development. In frozen state, loess experiences primarily compressive failure with a slow growth of cracks, while at normal temperature, it predominantly exhibits shear failure. With the increase in the principal stress angle, the deformation patterns of the soil samples under different conditions become essentially consistent, gradually transitioning from compression to extension, accompanied by a reduction in axial strength. The gradual increase in the principal stress axis angle (α) reduces the strength of the generalized shear stress and shear strain curves. Under an increasing α, frozen soil exhibits strain-hardening characteristics, with the maximum shear strength occurring at α = 45°. The intermediate principal stress coefficient (b) also significantly impacts the strength of frozen soil, with an increasing b resulting in a gradual decrease in generalized shear stress strength. This study provides a reference for comprehensively exploring the mechanical properties of soil under traffic load and a reliable theoretical basis for the design and maintenance of roadbeds.

Effects of pressure relief holes on coal burst: Insights from true-triaxial unloading tests

Drilling pressure relief is one of the methods to reduce the risk of coal bursts in deep mines. However, the effect of the drill hole orientations has not been studied well enough to understand their impact on the burst failure mechanism. In this study, we investigated two designs of drill hole orientations. The first design includes drill holes located on the upper free face of the rectangular samples and labelled as upper hole (UH) and centre hole (CH) – the long axes of the drill holes are aligned with minor principal stress, σ3, direction. The second design includes drill holes at the top (TH) and the side (SH) of the rectangular samples in which the long axes of the drill holes are aligned with the maximum, σ1, and intermediate principal stress, σ2, directions, respectively. The coal samples with the proposed drill hole orientations were subjected to the true-triaxial unloading coal burst tests. The results show that the drill holes reduce the risk of coal bursts. However, we found that the intensity of coal burst was significantly reduced with the SH-type, followed by the CH-types. We also observed that the coal burst intensity is reduced better for the CH, UH, TH, and SH-type drilling patterns. However, it was found that the orientations of drill holes have little influence on the failure mode (splitting). The acoustic emission (AE) activities for coal with drill holes noticeably decreased, especially for the UH and CH layouts. The drill holes reduced the upper limit of the AE entropy (chaos of microcracks generation). However, regarding reducing the coal burst risk, the TH and SH are less effective than UH and CH.

Micromechanical modeling of hollow cylinder torsional shear test on sand using discrete element method

Previous studies on the hollow cylinder torsional shear test (HCTST) have mainly focused on the macroscopic behavior, while the micromechanical responses in soil specimens with shaped particles have rarely been investigated. This paper develops a numerical model of the HCTST using the discrete element method (DEM). The method of bonded spheres in a hexagonal arrangement is proposed to generate flexible boundaries that can achieve real-time adjustment of the internal and external cell pressures and capture the inhomogeneous deformation in the radial direction during shearing. Representative angular particles are selected from Toyoura sand and reproduced in this model to approximate real sand particles. The model is then validated by comparing numerical and experimental results of HCTSTs on Toyoura sand with different major principal stress directions. Next, a series of HCTSTs with different combinations of major principal stress direction (α) and intermediate principal stress ratio (b) is simulated to quantitatively characterize the sand behavior under different shear conditions. The results show that the shaped particles are horizontally distributed before shearing, and the initial anisotropic packing structure further results in different stress–strain curves in cases with different α and b values. The distribution of force chains is affected by both α and b during the shear process, together with the formation of the shear bands in different patterns. The contact normal anisotropy and contact force anisotropy show different evolution patterns when either α or b varies, resulting in the differences in the non-coaxiality and other macroscopic responses. This study improves the understanding of the macroscopic response of sand from a microscopic perspective and provides valuable insights for the constitutive modeling of sand.

Glass Beads Test with True Triaxial Stress Path Achieved by Conventional Triaxial Apparatus

The impact of fabric anisotropy, fractal dimension, and breakage on the strength and deformation of granular materials were diminished by uniform-size spherical glass beads. Triaxial drained and undrained tests were performed on glass beads based on a novel method to substitute true triaxial stress paths with conventional triaxial apparatus equivalents with varying intermediate principal stress coefficients (b-values). The result indicates that all specimens manifested a noticeable strain-softening phenomenon. The peak strength decreased with increasing b-value, and the specimens showed more pronounced dilatancy. This pattern is similar to the results of the true triaxial test in current research. Compared to the undrained test, the peak friction angle in the drained test displayed a greater variation with varying b-values, which indicated that the mechanical response of glass beads is sensitive to water. This difference provides experimental evidence for comprehending effective stress in granular materials with constant friction coefficients. The experiments reflect the effect of b-value changes on the p-q stress path, as well as on the peak stress ratio, the state transition stress ratio, and the critical state stress ratio. The specimens exhibited a distinct shear band at different b-values ranging from 0.2 to 0.6, which is different from observations in conventional triaxial tests for granular materials.

Failure behaviors and acoustic emission characteristics of flawed granite of different grain sizes: Insights from true triaxial experiments with a free face

In this study, a group of experiments using true triaxial stress conditions with free face loading are performed on granite specimens with non-penetrating double flaws. The crack development and failure characteristics of these specimens are explored by integrating video of the free face and acoustic emission technology, with the combination of the four different intermediate principal stresses and three different grain sizes of the granite chosen as variables. First, surface flaws with a depth of 50 mm are found to have limited influence on the specimen’s failure mode. The intermediate principal stress has a greater effect as it inhibits the development of surface cracks; however, surface cracks develop much more readily in coarse-grained specimens than in other specimens. Second, when the intermediate principal stress exceeds 10 MPa, the rock burst failure phenomenon occurs in the specimen. Third, irrespective of changes in the intermediate principal stress and granite specimen grain size, the specimens primarily fail by tensile-shear failure and shear failure. Extending inward from the free face in the σ3 direction, according to the failure types, the failure types can be classified into tensile failure, shear failure, and tensile-shear failure. Finally, using the stress state synthesis method, the specimen’s stress state and crack distribution mechanism on the σ2 loading plane are analyzed.