Macroscopic Failure Research Articles

Strength characteristics of different stress spaces of red sandstone under loading and unloading tests

Red sandstone tests were conducted on the rock mechanics test system to clarify the strength and failure characteristics of red sandstone under triaxial loading and different unloading confining pressure rates. Strength change rules of the red sandstone in various stress spaces were analyzed. Results show that a large initial confining pressure indicates a long yield section and large axial strain. A small unloading confining pressure rate indicates a long yield section and large axial strain at failure under the identical initial confining pressure. The confining pressure reduction increases with the unloading confining pressure rate increasing when the red sandstone fails. The stress path of unloading confining pressure weakens the red sandstone cohesion and strengthens its internal friction angle. The general octahedral shear stress formula for judging whether the red sandstone fails under loading and different unloading rates was acquired on the basis of the octahedral shear stress characteristics of the red sandstone. In addition, a 3D empirical criterion for evaluating the red sandstone strength was constructed through the deviator plane function of Eekelen and the strength envelope curve on the meridian plane. A great initial confining pressure indicates serious internal damage of the red sandstone at failure under the identical unloading rate of confining pressure. A low unloading rate of confining pressure indicates internal serious damage of the red sandstone at failure when the initial confining pressure is the same. The analysis of macroscopic failure characteristics revealed that the stress path significantly influences the failure mechanism of the red sandstone. The results are instructive for determining the stability of underground engineering of the red sandstone.

Study on dynamic mechanical properties and microscopic damage mechanisms of granite after dynamic triaxial compression and thermal treatment

As underground mining operations gradually extend deeper, the conditions for orebody occurrence become increasingly complex, and various geological disasters occur frequently. Rock masses are prone to different degrees and types of damage, making it impractical to continue using intact rock as a reference. To study the dynamic mechanical properties of damaged rock under actual conditions, this study subjected granite samples to impact and high-temperature damage. Detailed observations were made of the samples' surface morphology and microstructure before and after damage, and the patterns of damage changes were investigated. Subsequently, uniaxial compression tests at different loading rates were conducted on the damaged samples. By calculating the loading rate effect sensitivity, it was found that as the damage increased, the rate effect gradually diminished. In addition, this study also summarized the influence of damage and loading rate on the macroscopic failure characteristics of the samples. The novelty of this study lies in focusing on damaged rock, which more closely resembles the actual rock conditions encountered in most underground mining operations today. This research can provide a reference for stability assessment and safe construction in deep mining rock engineering and offers important insights into the feasibility of non-explosive extraction of damaged rock.

Parametric study to implement a water-weakening process in UDEC

Despite the prevalence and validity of the universal distinct element code (UDEC) in simulations in geotechnics domain, water-weakening process of rock models remains elusive. Prior research has made positive contributions to a presupposed link between modelling parameters and saturation degree, Sr. Nevertheless, this effort presents inaccurate results and limited implications owing to the misleading interpretation, that is, devoid of the basic logic in UDEC that modelling parameters should be calibrated by tested macroscopic properties in contrast to a presupposed relation with Sr. To fill this gap, a new methodology is proposed by coupling a computationally efficient parametric study with the simulation of water-weakening mechanisms. More specifically, tested macroscopic properties with different Sr values are input into parametric relations to acquire initial modelling parameters that are sequentially calibrated and modulated until simulations are in line with geomechanical tests. Illustrative example reveals that numerical water-weakening effects on macroscopic properties, mechanical behaviours, and failure configurations are highly consistent with tested ones with noticeable computational expediency, implying the feasibility and simplicity of this methodology. Furthermore, with compatibility across various numerical models, the proposed methodology substantially extends the applicability of UDEC in simulating water-weakening geotechnical problems.

Characterizing large deformation of soft rock tunnel using microseismic monitoring and numerical simulation

Surrounding rock deterioration and large deformation have always been a significant difficulty in designing and constructing tunnels in soft rock. The key lies in real-time perception and quantitative assessment of the damaged area around the tunnel. An in situ microseismic (MS) monitoring system is established in the plateau soft tock tunnel. This technique facilitates spatiotemporal monitoring of the rock mass's fracturing expansion and squeezing deformation, which agree well with field convergence deformation results. The formation mechanisms of progressive failure evolution of soft rock tunnels were discussed and analyzed with MS data and numerical results. The results demonstrate that: (1) Localized stress concentration and layered rock result in significant asymmetry in micro-fractures propagation in the tunnel radial section. As excavation continues, the fracture extension area extends into the deep surrounding rockmass on the east side affected by the weak bedding; (2) Tunnel excavation and long-term deformation can induce tensile shear action on the rock mass, vertical tension fractures (account for 45%) exist in deep rockmass, which play a crucial role in controlling the macroscopic failure of surrounding rock; and (3) Based on the radiated MS energy, a three-dimensional model was created to visualize the damage zone of the tunnel surrounding rock. The model depicted varying degrees of damage, and three high damage zones were identified. Generally, the depth of high damage zone ranged from 4 m to 12 m. This study may be a valuable reference for the warning and controlling of large deformations in similar projects.

The progressive failure features of shield tunnel lining with large section

Investigating the failure process of segmental lining is of great significance to the design and maintenance of shield tunnel. Indoor scaled model tests are carried out to study the inner force, structural displacement, acoustic emission signals and damage pattern of lining. Meanwhile, a new numerical approach is put forward based on particle element method to study the influence of geo-stress field and the position of void or key block to the failure features of lining. The results showed that the failure of lining is progressive and can be divided into four stages, that is, the initial elastic stage, meso-damage stage, macroscopic failure stage and overall instability stage. For the key block is located at the crown, there are two concentrated intervals for the generation of micro-cracks. For the key block is located on the spandrel, micro-cracks are uniformly produced throughout the loading process after the initial elastic stage. For the key block is located on the haunch, micro-cracks distributed in a large concentrated range. The influence of the position of void on the damage of lining can be divided into three kinds, namely, no effect; affecting the emerging order of cracks while not final fracture pattern; affecting the emerging order of cracks and the final fracture pattern.

Microscopic simulation of mechanical tests on red-bed soft rock based on the evolutionary law of mineral composition under dry-wet cycles

The macroscopic mechanical behavior of red-bed soft rock under different drying-wetting cycles was analyzed by uniaxial/triaxial compression tests, and the evolution of mineral components was analyzed by x-ray diffraction. Considering the characteristics of porosity and mineral composition, PFC2D was used to establish the meso-particle calculation model for mechanical tests. The macro-meso cracking characteristics and mechanism of rock treated by dry-wet cycle were discussed. The results show that the content of quartz and clay minerals in rock increases under dry-wet cycle treatment. Cementation degradation between mineral particles and dissolution leads to micro-cracks between and within particles. Under compressive load, the essence of the change of the macroscopic failure mode is the change of the dominant type of the micro-crack.

Study on the influence of temperature on the damage evolution of hot dry rock in the development of geothermal resources

In order to more accurately understand the rock mechanics properties of hot dry rock (HDR) reservoirs under high-temperature conditions and further guide the drilling and construction of HDR wells, conducting research on rock damage evolution under high-temperature conditions plays a guiding role in the efficient development of geothermal resources. To reveal the evolution law of fracture damage of HDR under temperature influence, taking marble as an example, the thermo-mechanical damage and failure mechanism under the conditions of 30 °C, 60 °C, 90 °C, 120 °C and 150 °C were studied using a rock high-temperature rheometer and an acoustic emission (AE) testing system. The numerical simulation results were compared with the indoor experimental results by combining the particulate flow program Particle Flow Code 3D (PFC3D) to verify the effectiveness of the simulation analysis model of thermo-coupled particulate flow at the micro scale. The results show that under high temperature, the marble three-axis compression failure passes through the compaction and elastic deformation stage, plastic deformation stage, ductile failure stage and instability failure stage, and the peak strength and elastic modulus of the marble decrease with the increase of temperature, and the acoustic emission b-value of the sample can judge the damage evolution process of the marble. At the micro scale, high temperature accelerates the force chain transmission between particles, the contact force between marble particles gradually decreases during the heating process, and the number of particle bonding failures increases steadily; the bearing capacity and elastic modulus attenuation of the rock are the result of microcrack evolution, and the force chain void zone and particle displacement field inside the sample are consistent with its macroscopic failure form. The development of microcracks in marble under different test loading conditions is different, and with the increase of test temperature, the total number of cracks inside the sample increases, but the proportion of shear cracks decreases, the activity of particle displacement increases, and the “plastic extension” characteristic of marble becomes more significant. The thermal damage evolution of marble was quantitatively analyzed based on the elastic modulus method and the peak stress method, and the damage evolution law of marble under different temperatures was obtained.

Effect of the level of anisotropy on the macroscopic failure of notched thin-ply laminates

This work presents a detailed experimental study conducted for a range of different lay-ups using thin-ply carbon fiber reinforced polymer (CFRP) laminates. The selection of the laminates was performed relying on their level of anisotropy. The laminates vary from a quasi-isotropic (QI) laminate, which is weakly anisotropic, to a cross-ply (CP) laminate, which is strongly anisotropic. The laminates were tested in on-axis and off-axis open hole tension (OHT). The main objective was to observe the effect of the level of anisotropy of the laminate on the macroscopic failure and observed failure patterns. It is shown that, contrary to most existing observations so far, depending on the lay-up and consequently its level of anisotropy, open-hole, quasi-homogeneous thin-ply laminates do not necessarily exhibit a fiber dominated failure mode, but could develop sub-critical damage mechanisms in a large extent prior to ultimate failure, reminiscent of what is observed for standard-ply CFRP laminates.

Compression characteristics and fractography of in‐situ polymerisable thermoplastic and bio‐epoxy based non‐crimp carbon and glass fiber composites

AbstractThis experimental work involves characterization and fractography of a bio‐based epoxy and an in‐situ polymerisable thermoplastic polymer matrix based non‐crimp glass and carbon fiber composites under compressive loading. The laminates are characterized under compression loading using a combined loading compression (CLC) fixture. Laminates made using the thermoplastic matrix exhibit higher compressive strength (approx. 20% along fiber direction) compared to the bio‐epoxy based laminates. Further, both composites exhibit comparable compressive modulus characteristics. The tested composites are subjected to fractography analysis using Scanning Electron Microscopy (SEM) and Computed tomography (CT). SEM results indicate a difference in fiber‐matrix interface characteristics between the thermoplastic matrix and the bio‐epoxy matrix. Additionally, the CT scans reveal a difference in failure modes due to fiber orientations. A difference between failure mode of the exterior and interior plies of the specimens was also noticed. However, no specific influence of matrix type was observed on the overall macroscopic failure behavior.Highlights Bio‐epoxy and thermoplastic based laminates were characterized in compression. Post‐test fractography was performed using SEM and x‐ray CT scans. Use of thermoplastic matrix exhibits better fiber‐matrix adhesion compared to bio‐epoxy. Both laminates performed well in compression under laboratory test conditions.

Investigation on uniaxial compression and fracture damage mode of prefabricated parallel double-jointed red sandstone.

As a special type of joint fracture, the fracture evolution characteristics of parallel double joints have important engineering significance for the stability analysis of fractured rock mass. In this work, a new method for calculating stress intensity factor of parallel double-jointed fractures was importantly proposed. Physical uniaxial compression tests were carried out on parallel double jointed red sandstone filled with cement mortar under different geometric parameters, and the macroscopic mechanical properties and failure characteristics of red sandstone are deeply analyzed. The results show that the larger the connectivity rate is, the smaller the peak stress and strain are. The increase of connectivity rate will affect the change rate of transverse strain in the center of rock bridge. The closer the dip angle of the joint is, the lower the peak stress is and the shorter the failure time is. The damage mode of joint tip encroachment affects the lateral displacement of the rock bridge center, and the displacement is always close to the first damage section. The closer the joint tip is to the load, the easier the end-face penetrating cracks occur. The research content can provide basic support for guaranteeing the stability of underground engineering rock mass.

Deterioration mechanisms of tuff with surface fractures under freeze–thaw cycles

In practical engineering, the development of surface cracks is one of the most important reasons for the destruction of the rock mass, and the development of complex morphology fractures on the rock mass surface significantly influences rock mass mechanics. This paper addresses the freeze–thaw damage issue in rock mass containing surface fractures in cold regions. Tuffs and a control group are selected as research samples, with the control group being prefabricated surface jointed specimens with an inclination angle of 70° and a fracture depth ratio d (crack depth) /t (sample width) of 0.26. The study analyzes the mass, wave velocity loss, macro-microcosmic fracture damage morphology, and mechanical properties of the two specimen groups through laboratory freeze–thaw cycle tests, uniaxial compression tests, and scanning electron microscopy examinations. The results show an overall decrease in mass, wave velocity, and uniaxial compressive strength as the cycle number increases, with the prefabricated jointed group samples showing more significant changes. However, the two specimen groups exhibit different macroscopic failure fracture states. In addition, scanning electron microscopy images illustrate that after freeze–thaw cycles, the large rock mass particles break into smaller fragments, resulting in looser particle arrangements and a transition from initial surface cementation to point contact., which weakens the compressive strength of the rock mass. The paper also explains the mechanism of the diminishing impact of freeze–thaw cycles on the strength of the rock mass after a certain number of cycles. The research outcomes hold significant reference value for engineering construction in cold regions.

Static mechanical properties and damage evolution characteristics of selected rocks in diversion tunnel under uniaxial loading

An in-depth understanding of the mechanical properties and damage and fracture mechanism of selected rocks in a diversion tunnel plays an important role in promoting the efficient construction and safety of rock blasting excavation in a diversion tunnel. To study the mechanical properties and damage evolution characteristics of selected rocks in diversion tunnels under uniaxial loading, the uniaxial compression and uniaxial splitting tests of granite and tuff were carried out. In terms of mechanical properties, the evolution characteristics of complete stress-strain curves, instantaneous modulus-strain curves, and input energy density-strain curves were analyzed. In the aspect of damage characteristics, the macroscopic and mesoscopic failure modes were analyzed and the damage fracture mechanism was revealed. Compression-shear failure mainly occurred in granite and tuff under uniaxial compression, showing the characteristics of elastic-brittle fracture failure. Both granite and tuff showed a failure mode of coexistence of “compression-shear failure zone at the loading ends” and “tension-shear failure zone in the middle” under uniaxial splitting. The compression-shear fracture of granite was relatively smooth, and the matrix and mineral particles produced fine particles due to friction in the process of shear slip. The compression-shear fracture of tuff was relatively rough and the characteristics of shear slip were not prominent enough. The fracture failure of granite and tuff was mainly caused by the common fracture of rock matrix and mineral particles. Based on the Lemaitre equivalent strain principle, the pre-peak-post-peak two-stage damage constitutive model established by Weibull statistical distribution theory can accurately describe the static stress-strain relationships of granite and tuff under uniaxial compression.

A Brittle Constitutive Law for Long‐Term Tectonic Modeling Based on Sub‐Critical Crack Growth

AbstractAdequate representations of brittle deformation (fracturing and faulting) are essential ingredients of long‐term tectonic simulations. Such models commonly rely on Mohr‐Coulomb plasticity coupled with prescribed softening of cohesion and/or friction with accumulated plastic strain. This approach captures fundamental properties of brittle failure, but is overly sensitive to empirical softening parameters that cannot be determined experimentally. Here we design a brittle constitutive law that captures key processes of brittle deformation, and can be straightforwardly implemented in standard geodynamic models. In our Sub‐Critically‐Altered Maxwell (SCAM) flow law, brittle failure begins with the accumulation of distributed brittle damage, which represents the sub‐critical lengthening of tensile micro‐cracks prompted by slip on pre‐existing shear defects. Damage progressively and permanently weakens the rock's elastic moduli, until cracks catastrophically interact and coalesce up to macroscopic failure. The model's micromechanical parameters can be fully calibrated against rock deformation experiments, alleviating the need for ad‐hoc softening parameters. Upon implementing the SCAM flow law in 2‐D plane strain simulations of rock deformation experiments, we find that it can produce Coulomb‐oriented shear bands which originate as damage bands. SCAM models can also be used to extrapolate rock strength from laboratory to tectonic strain rates, and nuance the use of Byerlee's law as an upper bound on lithosphere stresses. We further show that SCAM models can be upscaled to simulate tectonic deformation of a 10‐km thick brittle plate over millions of years. These features make the SCAM rheology a promising tool to further investigate the complexity of brittle behavior across scales.

Probing nanoscale structural response of collagen fibril in human Achilles tendon during loading using in situ SAXS

The specific viscoelastic mechanical properties of the human Achilles tendon are strongly dependent on the structural characteristics of collagen. Although research on the deformation mechanisms of the Achilles tendon in various animals is extensive, understanding of these mechanisms in the human Achilles tendon remains largely empirical and macroscopic. In this work, the evolution of D-space, orientation, and average length of voids between fibers are investigated during the stretching using SAXS techniques. Initially, the void length increases marginally, while the misorientation breadth decreased rapidly as the D-space steadily increased. In the second region, D-space and the void length increase sharply under rising stress, even though misorientation width decreased. During the third region, the increases in void length and D-space decelerate, but the misorientation width widens, suggesting the onset of irreversible microscopic fibril failure in the Achilles tendon. In the final region, the fibers undergo macroscopic failure, with D-space and void length returning to their initial states. The macroscopic alterations are elucidated by the nanoscale structural responses, providing a fundamental understanding of the mechanisms driving the complex biomechanics, tissue structural organization, and Achilles tendon regeneration.

Failure of adhesive bonding unveiled by in-situ strain testing by high-resolution scanning transmission electron microscopy

The nano-scale failure behaviors of adhesive interfaces were investigated through in-situ straining testing to observe real-time crack propagations under a scanning transmission electron microscope (STEM). Two different loading modes were applied to thin sections of adhesive interfaces: crack-opening mode applied to pre-cracks made at the interface and shear mode. The failure of aluminum alloy (Al6061) and a second-generation acrylic adhesive (SGA) was examined, enabling observation of the growth of crazing in the adhesive layer, which has a phase-separated structure, preceding the macroscopic failure of the interfaces. Furthermore, the failure of a direct joint of thermoplastic and Al was investigated, with a comparison made to that observed in the adhesive interface. The generation and propagation of cracks near the interface, attributed to the adhesive's phase separation, contribute to the toughness of the adhesive interface. Both the direction of stress acting on the interface and the interface's strength influence the initiation and growth of cracks throughout the adhesive layer.

Experimental study and numerical simulation verification of the macro- and micromechanical properties of the sandstone–concrete interface under freeze–thaw cycles

In cold-region tunnel engineering, the bonding surface between concrete and surrounding rock is highly susceptible to engineering disasters such as the cracking of support structures under the influence of freeze-thaw cycles, which severely affects the stability of tunnel engineering. This study investigates the macroscopic and microscopic mechanical properties of the sandstone–concrete interface under freeze–thaw cycles and reveals the microdamage and fracture evolutionary laws during the freeze–thaw loading process via the coupled expansion of water–ice particle phase changes via particle flow numerical simulation methods, aiming to provide theoretical support for the design and construction of rock–soil and tunnel engineering in high-altitude frozen soil areas. The results indicate that the interface strength characteristics of the sandstone–concrete specimens exhibit a stable decreasing trend with an increase in the number of freeze-thaw cycles and a decrease in roughness. Taking the most unfavorable condition as an example, the exacerbation of freeze-thaw deterioration resulted in shear strength reductions of 16.53%, 27.01%, and 37.17% for specimens (JRC=3.727), while an increase in roughness led to shear strength increases of 11.00% and 15.14% for specimens (NT=60 cycles). The acoustic emission characteristics during the loading process of the sandstone–concrete interface specimens reflect the microcracking evolutionary activity of the specimens quite well, and setting 1.0 as the recommended value for the precursor determination of the b-value and CV(k) index is most reasonable. Under freeze-thaw cycles, cracks first initiate partial microcracks at the interface and on the outer side of the specimen, primarily dominated by tensile cracks and evolving with a "slow–fast" trend toward both sides of the interface. Under shear stress, particles at the interface first undergo slip dislocation due to their lower bonding strength, generating cracks, subsequently inducing significant displacement of particles on both sides of the interface, resulting in crack propagation toward both sides of the interface, ultimately penetrating and forming shear bands leading to macroscopic failure.

Study on Permeability Evolution Law of Rock Mass under Mining Stress

In order to study the stress–strain–permeability coefficient relationship of overlying strata in a fractured zone after coal mining, taking the Changcun coal mine in the Changzhi basin as an example, the permeability evolution law of coarse sandstone, fine sandstone, siltstone and mudstone during a stress–strain process was analyzed through a triaxial compression permeability test. The generalized model of the rock mass permeability evolution process under mining stress was summarized, and then a coupling model of the stress–water pressure–permeability coefficient of fractured rock was established based on the continuum model of rock mass. The results showed that the maximum permeability coefficient of different coal overburden types was quite different, and the peak strength of the rock mass preceded the maximum permeability coefficient during the rock mass failure process; the permeability coefficient first decreased and then increased, reaching its maximum value after the peak stress, which occurred during the strain-softening stage; the generalized model of rock mass permeability included the compaction stage, elasticity stage, stable fracture stage, unstable fracture stage, macroscopic failure stage and residual strength stage.

Impact characterization of coral aggregate reinforced concrete beam: A 3D numerical study

Coral aggregate concrete (CAC), an innovative construction material, utilizes abundant marine resources, including coral aggregates and seawater. In the realm of reef engineering, CAC is widely used in structural elements such as reinforced beams and columns. This paper presents a three-dimensional (3D) mesoscale model to assess the impact behavior of coral aggregate reinforced concrete beams (CARCB), incorporating the heterogeneity characteristics of CAC and the explicit simulation of reinforcement components. The 3D mesoscale modelling approach developed in this paper was validated by previous experimental data of CARCB, and used for extensive parametric studies evaluating effects such as concrete strength grade, reinforcement ratio, and impact velocity on the static and dynamic bending behaviors of CARCB. Finally, based on the mesoscopic cracking process and damage patterns of CARCB under static and dynamic loads, this study illustrates the corresponding macroscopic mechanical behaviors and failure mechanisms. Results indicate that the predominant forms of flexural failure in CARCBs are tensile cracking in the mid-span region and diagonal shear cracking. Results demonstrate that the predominant forms of flexural failure in CARCBs are tensile cracking in the mid-span region and diagonal shear cracking. Specifically, local bending failures and symmetrical diagonal shear cracks were evident in the CARCBs subjected to dynamic loads, closely resembling those in ordinary concrete beams. With increasing concrete strength grades (C30 to C60) and reinforcement ratios (0.9 %–1.7 %), a significant reduction in the mid-span ultimate deflection of CARCB is observed, indicating enhanced impact resistance. Additionally, as the impact velocity increases from 1 m/s to 50 m/s, the mid-span ultimate deflection of CARCB is magnified by a factor of approximately 200, indicating intensified dynamic damage to CARCB with increasing impact velocities.

The macroscopic and microscopic fatigue failure mechanisms of high-temperature thermally-damaged granite under cyclic impact loading

The rock surrounding wells for developing geothermal energy are in an extreme environment with high temperature and long-term dynamic disturbance. To study the influences of different temperatures and dynamic disturbances on the damage, mechanical properties, and fatigue failure mechanism of rocks, a series of microscopic thermal damage analysis and dynamic cyclic impact tests were conducted on granite specimens treated at 25 ∼ 900 °C. Results show that after being thermally treated to different extents, granite specimens are weakened in terms of the dynamic strength and deformation resistance under cyclic impact loading. As the temperature rises, the number of impacts bearable by specimens before failure decreases accordingly. Under the joint action of temperature and strain rate, 450 °C is found to be the threshold temperature for the significant reduction of dynamic strength of the rock. Under action of temperature and strain rate, the proportion of dissipated energy gradually reduces with rising temperature. Moreover, the dynamic failure mode of rock specimens at high temperatures gradually changes from splitting failure to crushing failure, the fractal dimension gradually increases, and the cumulative dissipated energy density decreases. Finally, the deterioration degree of elastic modulus was adopted to describe the progressive damage evolution of thermally-treated granite under cyclic impact loading. Furthermore, the fracture morphologies of rock specimens after failure were analyzed from the microscopic perspective to reveal the macroscopic and microscopic fatigue failure mechanisms of the rock under the coupling of temperature and strain rate.

Propagation and complex morphology of hydraulic fractures in lamellar shales based on finite-discrete element modeling

We explore the controls of stress magnitude and orientation relative to bedding on the resulting morphology/topology of hydraulic fractures using a combined finite-discrete element method (FDEM). Behavior is shown conditioned by the ratio of principal stresses λ=σ3/σ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda ={\\sigma }_{3}/{\\sigma }_{1}$$\\end{document} and relative inclination of the bedding. When the lateral pressure coefficient (λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}) is less than 0.67, hydraulic fractures predominantly initiate as tensile fractures along the wellbore, aligning with the maximum principal stress direction. Conversely, for λ≥0.67\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda \\ge 0.67$$\\end{document}, shear cracks are favored to initiate for the minor stress difference, leading to a less predictable initiation and extension direction. Simultaneously, diminished stress differences correspond to elevated reservoir breakdown pressures, displaying a linear correlation with lateral pressure coefficients and little influenced by equivalent bedding orientation. Bedding plane orientation significantly impacts the mode and morphology of hydraulic fracture propagation. Bedding parallel to the direction of the minimum principal stress (σ3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\sigma }_{3}$$\\end{document}) favors layer-penetrating and bifurcated fractures, whereas inclined bedding facilitates the emergence of numerous steering-type and capture-type fractures. Especially at steeper inclinations (β=60∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta =60^\\circ$$\\end{document}), hydraulic fractures readily extend along the bedding surface, inducing macroscopic shear slip failure. Under high-stress disparities, the breakdown pressure exhibits greater sensitivity to bedding inclination, and its influence pattern aligns with the variations in tensile strength, typically reaching maximum and minimum values at bedding inclination angles of 0° and 60°, respectively.