Aiming at the problem of large deformation of arch shoulder in deep high stress roadway of Hudi Coal Mine, through field sampling, experimental test and numerical simulation, the deformation mechanism of arch shoulder under the coupling action of high stress, soft and hard rock strata of roof, weakening of surrounding rock and disturbance of space staggered roadway was revealed. Through the research results, the high stress increases the range of the plastic zone, and the soft and hard rock strata lead to the change of the expansion form of the plastic zone. With the decrease of the vertical distance of the space staggered roadway, the insufficient bearing capacity of the supporting material and other factors lead to the increase of the deformation of the shoulder angle and the side, forming the deformation characteristics of the arch shoulder. Based on this, the active and passive collaborative control technology is proposed, and the targeted support concept of “unloading control + strong support + collaborative” is adopted. The optimization scheme controls the deformation of roadway within 8

Conglomerate reservoirs are frequently subjected to coupled stress and seepage fields, and their mechanical response is strongly governed by the heterogeneous distribution of gravels, matrix, cementing materials, pores, and weak interfaces. In this study, X-ray diffraction, polarizing microscopy, nanoindentation, uniaxial compression, and seepage–stress coupling tests were combined to investigate the multiscale failure behaviour of conglomerate. The results show that gravel size and content affect the peak strength and deformation thresholds by modifying mesostructural heterogeneity and local stress redistribution. Under seepage–stress coupling, increasing seepage pressure promoted the development and coalescence of intergranular, transgranular, and intragranular cracks. Relative to the saturated state, increasing seepage pressure to 12 MPa reduced the peak strength and Young’s modulus by 25.2 %–33.5 % and 19.2 %–22.3 %, respectively, depending on the confining pressure. The quasi-steady-state permeability initially decreased because of pore and crack closure and subsequently increased as cracks progressively connected to form preferential seepage channels. Nanoindentation results further indicated that the matrix and cementing materials experienced more pronounced local mechanical degradation than the gravel phase. An effective-stress-corrected Weibull damage factor was incorporated into Mori–Tanaka and Dilute homogenization analyses to estimate the macroscopic modulus from phase-level mechanical properties. Under 20 MPa confining pressure, the damage-corrected Dilute method produced modulus deviations of 29.5 %, 16.0 %, and 3.4 % at seepage pressures of 6, 9, and 12 MPa, respectively, compared with 43.9 %, 27.2 %, and 15.5 % for the Mori–Tanaka method. These findings provide a multiscale experimental and analytical basis for interpreting how phase weakening, crack connectivity, and mesostructural heterogeneity jointly control the hydraulic–mechanical degradation and shear failure of conglomerate reservoirs.

This study combines T-shaped flange steel beams and circular concrete-filled steel tubular (CFST) beams to develop a novel structural form of concrete-filled steel tubular (CFST) beams incorporating a T-shaped flange (abbreviated as CFST beams with T-shaped flange). The flexural load-bearing performance of CFST beams with T-shaped flange and conventional CFST beams was comparatively analyzed through four-point bending tests. Building upon this foundation and validated against experimental results, a reasonable numerical model for CFST beams with T-shaped flange was established, followed by parametric sensitivity analysis. Finally, a calculation method for the normal cross-sectional bearing capacity of CFST beams with T-shaped flange was proposed and validated by experimental and numerical results. The findings demonstrate that, compared with conventional CFST beams, the yield load and the flexural bearing capacity of CFST beams with T-shaped flange have been increased by up to 88.76 % and 71.49 %, respectively; The T-shaped flange exerts a dual strengthening effect on the flexural load-bearing performance of CFST beams: the T-shaped flange itself enhances the structural bending performance while simultaneously inducing an inferior shift of the sectional neutral axis, thereby effectively activating its flexural potential; At identical steel consumption, T-shaped flange dimensions most significantly govern the flexural load-bearing performance of CFST beams with T-shaped flange. Parametric sensitivity increases sequentially as follows: web thickness, flange width, flange thickness, and web height.

Fluid flow through rough-walled rock fractures is governed by surface roughness, shear deformation, and scale, yet a unified description of permeability evolution remains elusive. Self-affine fracture surfaces with varying roughness levels (JRC = 2-18) were generated using a modified successive random addition algorithm, and progressive shear displacement (3-18 mm) was numerically simulated to resolve aperture field evolution. Fluid flow was subsequently modeled using the Reynolds equation to evaluate equivalent permeability and directional transport behavior across scales (20-200 mm). Three principal physical mechanisms are revealed: (i) a competitive interplay between shear-driven enhancement and roughness-induced resistance governs permeability evolution; (ii) shear deformation fundamentally reorganizes flow topology through channelization aligned with the shear direction and contact-structure anisotropy that restricts transverse transport; and (iii) scale dependence arises from statistical averaging of local geometric heterogeneity, with flow stabilizing as observation windows expand. These mechanisms are synthetically captured in a coupled empirical correlation unifying roughness attenuation, shear-induced enhancement, and scale effects. Validation against numerical simulations demonstrates reliable first-order permeability prediction across the investigated parameter space.

Moisture-rich underground environments demand cementitious lining and grouting materials that are both durable and mechanically reliable. Acrylic redispersible polymer (AP) can render cementitious matrices hydrophobic, but its coupled evolution with load-induced damage development remains poorly understood. Therefore, this study develops a hydrophobic-mechanical synergy framework and establishes cross-scale evidence linking AP dosage to hydrophobic transition, mechanical response and damage evolution, interpreted alongside pore structure and hydration signatures. Water contact angle (WCA) measurements, uniaxial compression with acoustic emission (AE) monitoring, mercury intrusion porosimetry (MIP) and thermogravimetric analysis (TG-DTG) were performed. A clear hydrophobic transition is identified at similar to 1.71-1.96% AP, corresponding to an apparent polymer coverage threshold of similar to 82.6% at the outer surface. Gaussian fits show that stiffness maximises at similar to 0.84-1% AP, compressive strength peaks at 2% AP (38.88 MPa; +12.73%), and deformability maximises near 3% AP (peak strain 1.14%; +29.5%). AE-based damage metrics reveal a crack-minimisation window at similar to 1-2% AP with delayed shear engagement, whereas dosages >= 3% shift damage toward more tensile-dominated, distributed cracking. By combining these results, a robust hydrophobic-mechanical dosage window centred at similar to 1.8-3.6% AP is delineated. Within this window, MIP and TG-DTG results indicate suppressed capillary pores (10 & sup2;-10 & sup3; nm) and a dense, well-hydrated skeleton, in contrast to macro-defects and weakened hydration at excessive dosages. The identified synergy window offers a mechanistic and quantitative basis for designing hydrophobic and mechanically robust cementitious systems for underground lining and grouting.

Understanding the coupled influence of material brittleness and fracture geometry on the mechanical degradation and failure behavior of fractured rock is critical for assessing instability in deep underground engineering. In this study, sandstone specimens with two distinct levels of brittleness were prepared with prefabricated fractures characterized by varying inclination angles and rock-bridge angles. A multiscale experimental framework integrating AE-DIC monitoring was employed to systematically investigate damage evolution and fracture mechanisms. To quantitatively characterize mechanical weakening, strength-degradation and elastic-modulus-degradation indices were proposed. The results show that prefabricated fractures significantly reduce the peak strength of sandstone. Increasing the fracture inclination angle leads to higher peak strength, whereas increasing the rock-bridge angle results in a non-monotonic decrease-increase trend. High-brittleness sandstone exhibits larger fluctuations in strength and stiffness under geometric disturbance, indicating stronger sensitivity to fracture-induced heterogeneity. AE-DIC results demonstrate that fracture inclination primarily controls the orientation and intensity of strain localization, while the rock-bridge angle governs the complexity of crack coalescence. High-brittleness specimens develop more concentrated and rapidly evolving strain localization bands, ultimately leading to abrupt mixed tensile-shear failure. Higher brittleness accelerates damage accumulation and promotes shear-dominated microcrack activity, particularly under high fracture inclination and large rock-bridge angles. In contrast, low-brittleness sandstone is characterized by a higher proportion of tensile microcracks and smoother b-value evolution, reflecting more progressive damage development. The degradation indices further reveal that strength deterioration is more pronounced in high-brittleness sandstone, whereas elastic modulus degradation shows greater sensitivity to brittleness reduction in low-brittleness sandstone. Overall, the findings highlight a coupled degradation mechanism in which fracture geometry controls the spatial evolution of damage, while material brittleness governs the rate and severity of mechanical degradation.

The cement industry is one of the major contributors to global CO2 emissions, and incorporating porous carbon materials into cementitious systems provides a promising pathway for carbon sequestration. Although coal-based carbon materials have been widely used in construction applications, their relatively limited porosity has constrained their broader utilization. Therefore, this study employs coal-derived carbon that has undergone activation treatment to significantly enhance its pore structure, and systematically investigates its mechanical behavior and microstructural evolution under high replacement ratios. A multiscale mechanical analysis framework is established to elucidate the micro-mechanisms underlying the observed macroscopic performance. The results show that the highly porous structure of activated carbon can adsorb cement hydration ions and CO2, thereby promoting carbonation reactions that form CaCO3 to fill the pore space and significantly improve its load-bearing capacity. After carbonation, the local elastic modulus and hardness of the activated carbon phase increased by approximately fourfold compared with the initial state, while achieving effective CO2 sequestration. Incorporating an optimal dose of activated carbon (5%) reduced pores larger than 1000 nm by 4.9%, improved hydration, densified the interfacial transition zone (ITZ), increased high-strength Calcium silicate hydrate(CSH) and improved compressive strength by approximately 4%. However, at higher replacement ratios (10% and 20%), compressive strength decreased to 78% and 77% of the reference group, and flexural strength decreased to 79% and 84%, respectively. At a 20% replacement ratio, although total porosity increased by 12.9% and harmful pores increased by 1.6%, the crystallinity of hydration products improved, leading to a partial recovery in mechanical performance compared with the 10% mixture. Overall, this study provides important insights into the high-replacement behavior and micro-mechanisms of activated porous coal-derived carbon in cement-based materials, offering valuable reference for its application in carbon-sequestering cement composites.

Fractured rock masses reinforced by cement filling are commonly encountered in underground and geotechnical engineering, yet their failure evolution and reinforcement mechanisms remain insufficiently understood, particularly under the coupled influence of fracture geometry and interfacial conditions. In this study, sandstone specimens containing a single pre-existing fracture were prepared with varying fracture dip angles and rock bridge angles under both unfilled and cement-filled conditions. An integrated acoustic emission (AE) and digital image correlation (DIC) multi-field monitoring system was employed to investigate the mechanical response, deformation localization, microcrack evolution, and failure characteristics during uniaxial compression. The results indicate that fracture dip angle and rock bridge angle play dominant roles in governing strength, deformation behavior, and failure modes, while cement filling markedly enhances mechanical performance and stabilizes the failure process. Compared with unfilled specimens, cement-filled specimens exhibit delayed crack initiation, suppressed strain localization, and a systematic reduction in tensile-dominated microcracking, accompanied by a transition from abrupt unstable failure to more progressive and stable damage evolution. AE-RA-AF analysis further reveals that the proportions of tensile and shear microcracks vary systematically with fracture geometry, and that cement filling effectively moderates microcrack activity and alters crack propagation paths. To quantitatively characterize fracture-induced degradation and cement-induced reinforcement, an interface weakening coefficient and a strength recovery coefficient are introduced, providing a unified framework for evaluating the mechanical effects of fracture geometry and interfacial filling. The findings offer new insights into the multi-field failure mechanisms of cement-filled fractured rocks and provide practical guidance for reinforcement design and stability control in fractured rock engineering.

Understanding the destabilization mechanisms of composite rocks is vital for mining engineering, especially in evaluating coal mine strata stability. This study investigates the fracturing mechanisms of rock composites, focusing on the effects of lithology and stress path at both micro- and macro-scales, using acoustic emission (AE), digital image correlation (DIC), and high-speed camera technologies. The accumulation of elastic energy is identified as the key factor influencing failure modes, with rock strength positively correlating with energy accumulation. In low-strength fine-grained sandstone and medium-grained sandstone composites, local spalling occurs due to minimal energy accumulation, with microscopic intergranular spalling observed. For medium-strength fine-grained sandstone and siltstone composites, local spalling progresses into blasting jet failure as elastic energy accumulates during staged loading. In high-strength sandy mudstone and fine-grained sandstone composites, the failure mode transitions from local to overall blasting jet failure, with scaly splitting cracks at the microscopic level. Local spalling involves slow fragment ejection, while blasting jet failure results in rapid, severe fragment ejection, with the local mode primarily causing upper ejection and the overall mode involving both upper and lower ejection. The failure process involves three stages: initial compaction, stable crack propagation, and unstable failure. The different failure modes vary significantly, the blasting jet mode is characterized by a block-like strain concentration and dominant upper AE activity. The local spalling mode displays strip-like strain concentration and uniform AE distribution. Therefore, monitoring the accumulation of elastic energy in rock strata can provide early warnings for the occurrence of dynamic hazard risks.

Equivalent drainage boundaries are computationally convenient, but they combine distinct internal processes into a single effective condition and cannot identify which process controls the hydraulic response: primary-lining recharge, circumferential geotextile conveyance, discrete drainage-point inflow, collector-pipe conveyance, outlet control, or inward leakage. This study develops a unified semi-analytical model for steady-state seepage transfer under a prescribed hydraulic head at the outer surface of the primary lining. Closed-form solutions are obtained for representative circumferential cells with ideal or finite drainage-point inlet capacity, and a transfer-matrix formulation is established for full-circumference systems with spatially non-uniform inlet capacities. The circumferential formulation is coupled with a one-dimensional collector-pipe model to resolve longitudinal head variation and outlet control. Numerical benchmarks agree closely, with a maximum absolute relative error of 3.2%, while independent physical-model data support the predicted pressure–discharge behavior and deterioration-induced hydraulic responses. Geotextile conveyance reduces circumferential head non-uniformity but provides limited system-wide pressure relief when drainage-point inlet capacity is severely degraded. Under representative severe-degradation conditions, increasing geotextile in-plane hydraulic conductivity by a factor of 50 lowers the mean geotextile head by only about 0.2%, whereas restoring drainage-point inlet capacities to their reference levels reduces the mean head by 42.5–59.4%. Increasing inlet capacity enhances collector-pipe inflow but may induce upstream backwater when longitudinal pipe conveyance is limited. A higher outlet head suppresses pipe discharge, whereas waterproof-board hydraulic conductivity primarily controls inward leakage. By resolving the internal controls hidden by equivalent boundaries, the model enables diagnosis of hydraulic bottlenecks and targeted maintenance assessment.

Accurate identification of crack types in rock masses is critical for understanding damage mechanisms and ensuring the structural safety of rock engineering. This study presents a novel unsupervised classification framework based on Gaussian mixture modeling (GMM) for distinguishing acoustic emission (AE) signatures associated with different fracture modes in sandstone samples that contain prefabricated fissures at varying inclination angles. The frequency-domain characteristics of the AE signals were extracted using fast Fourier transform (FFT), while the RA–AF (rise time/amplitude versus average frequency) parameter space was employed to characterize the crack mechanisms. To increase classification accuracy and model robustness, the Bayesian information criterion (BIC) was introduced to determine the optimal number of Gaussian components. Experimental results from uniaxial compression tests reveal that fissure inclination significantly affects crack evolution behavior: low-angle fissures favor shear and hybrid cracks, whereas high-angle fissures cause tensile failure. The proposed GMM-based method effectively identifies tensile, shear, and hybrid cracks with increased objectivity and accuracy, outperforming traditional empirical RA–AF thresholding techniques. This research provides a reliable and generalizable approach for AE signal classification, which presents theoretical insights and practical support for real-time monitoring, early warning, and structural health assessment in fractured rock masses.

The bedding structure of shale significantly influences its mechanical anisotropy. However, the meso-scale anisotropic control mechanism of bedding on shale damage evolution remains insufficiently understood. This study employs in-situ uniaxial compression CT scanning experiments, combined with grayscale thresholding and deep learning-based image segmentation, to achieve high-precision 3D reconstructions of shale pore-fracture networks. Additionally, by integrating Digital Volume Correlation (DVC) with image analysis, a cross-scale quantitative characterization and synergistic evaluation are conducted, bridging the evolution of microstructural damage with macroscopic full-field deformation in bedded shale. The results reveal that: (1) The dominant geometric factors influencing the complexity of the shale pore-fracture network during loading vary with bedding orientation: number and spatial distribution dominate for 0° shale, volume and area for 30°/60° shale, and coupled geometric parameters for 90° shale. (2) Displacement and strain fields exhibit distinct characteristics related to the bedding angle: 0° shale shows quasi-uniform deformation dominated by axial compaction; 30° and 60° shales form significant strain concentration bands along bedding planes due to shear slip effects; 90° shale is driven by radial tension, leading to tensile strain localization parallel to the bedding direction. (3) The strain accommodation mechanism in shale transitions with the bedding angle: it shifts from being dominated by matrix compaction and diffuse micro-damage at low angles to being primarily controlled by fracture propagation along bedding planes at high angles. In high-angle bedded shale, pre-existing pores and fractures tend to preferentially act as nucleation sites for damage initiation and strain localization.

Ensuring rock mass stability is a fundamental prerequisite for the long-term safety, reliability, and sustainability of underground engineering structures. In this study, sandstone specimens containing parallel pre-existing fractures were selected as research objects. By integrating acoustic emission (AE) and digital image correlation (DIC) techniques, the mechanical response and strain localization evolution of prefabricated sandstone under uniaxial loading were systematically investigated. To quantitatively evaluate the stability characteristics, a comprehensive stability index (SI) was established based on three key parameters: the strength reduction parameter (IC), brittleness parameter (I sigma), and energy storage parameter (IU). The Analytic Hierarchy Process (AHP) was applied to determine the relative weights of these parameters, enabling quantitative comparison of sandstone stability under varying fracture geometries. The results demonstrate that the presence of multiple prefabricated fractures markedly degrades the mechanical integrity of sandstone, leading to a reduction in peak strength ranging from approximately 30% to 60%. As the flaw dip angle increases, the peak AE amplitude rises correspondingly, and the failure mode transitions from axial mixed tensile failure to oblique tensile-shear failure. With an increase in the rock bridge angle, AE activity becomes more intense, and the dominant failure mechanism shifts from shear to tensile cracking around the rock bridge zone. Specimens classified within the stable zone generally exhibited larger dip angles (approximately 75 degrees) and rock bridge angles (greater than 90 degrees), whereas those within the hazardous zone were characterized by lower dip angles (approximately 15 degrees) and smaller rock bridge angles (less than or equal to 60 degrees). For specimens with rock bridge angles greater than 90 degrees, approximately 55.6% exhibited pronounced brittle behavior, suggesting a heightened potential for rockburst occurrence.

Mechanical behavior degradation of sandstone due to long-term water immersion is critical when assessing the stability of rock masses in geothermal recovery systems from abandoned/closed mines. In this study, a macro/meso-scale experimental framework was employed to investigate the influence of water immersion on sandstone. The sandstone samples were subjected to uniaxial compression after being immersed in water for various days (0–150 days). X-ray computed tomography (CT) was employed to reveal structural evolution and mechanical degradation under water – rock interaction. The results show that the peak strength and elastic modulus decreased by 64

Quantifying two-phase fluid flow in fractured rocks is essential for resource reutilization in abandoned mines, subsurface energy recovery and underground waste isolation. This study develops a mathematical framework for predicting the permeability of rough fracture networks by integrating fractal geometry with single-phase and two-phase seepage theory. A permeability model for rough fracture networks is first established, and its sensitivity to key geometric parameters is analyzed. A second model is then formulated to relate water-phase saturation to measurable variables, enabling the estimation of two-phase permeability from Reynolds number and aperture. Model predictions show deviations of less than 10% from numerical simulations for both single-phase and two-phase flow, demonstrating the accuracy and robustness of the proposed approach. The results highlight the dominant roles of fracture number, tortuosity and aperture in controlling permeability, as well as the influence of flow regimes on relative permeability. The proposed framework provides a practical and physically based method for analyzing multiphase seepage in fractured rock and offers a foundation for further applications to field-scale fractured systems.

Mechanical response,damage evolution,and surrounding-rock stability of coal-bearing sandstone under long-term low-temperature thermal cycling are investigated for closed-mine geothermal utilization.A combined experimental scheme of single low-temperature heat treatment and low-temperature thermal cycling is adopted.Uniaxial compression,acoustic emission(AE),three-dimensional digital image correlation(3D-DIC),and scanning electron microscopy(SEM)tests are performed.For single low-temperature heat treatment,seven temperature levels are set at 20,40,60,80,100,140,and 180℃.For low-temperature thermal cycling,four cycling intervals,namely 20-40℃,20-60℃,20-80℃,and 20-100℃,are designed,with cycle numbers of 10,30,60,and 100.Effects of temperature level and cycle number on the macroscopic mechanical properties,deformation localization,and microstructural evolution of coal-bearing sandstone are analyzed.The results show that,under single low-temperature heat treatment,the response of coal-bearing sandstone is dominated by water escape,closure of primary microcracks,and improvement of particle contacts.At 180℃,the mass loss rate is only 0.412%,the wave velocity loss rate remains generally negative,and the compressive strength increases with increasing temperature,indicating densification strengthening and a negative damage effect at the initial stage of low-temperature thermal disturbance.Under thermal cycling,the strength evolution of coal-bearing sandstone exhibits clear stage-dependent characteristics.At low cycle numbers,a strengthening effect is still maintained,and the compressive strength after 10 cycles ranges from 71.53 to 84.87 MPa.As the cycle number increases,thermal fatigue damage gradu-ally becomes dominant.After 100 cycles,the compressive strength decreases to 60.30-65.93 MPa,and deterioration be-comes more pronounced under cycling with a larger temperature difference.The loss rates of wave velocity,elastic modu-lus,and compressive strength indicate that temperature controls the intensity of thermal damage development,whereas cycle number determines the degree of damage accumulation.Their coupled effect drives the transition of coal-bearing sandstone from initial strengthening to continuous deterioration.AE results show that,with increasing thermal cycling in-tensity,concentrated bursts of high-amplitude signals are weakened,sustained activity of low-amplitude signals becomes more evident,and the dominant-frequency distribution shifts from high-frequency dominance to an increased proportion of low-frequency signals.The 3D-DIC and AE location results indicate that strain concentration zones appear earlier and ex-pand from a single localized region to multiple dispersed regions,while crack propagation changes from a simple through-going pattern to the coordinated development of multiple cracks.SEM observations show that the microstructure of coal-bearing sandstone successively undergoes densification,interfacial debonding,localized crack propagation,and enhanced crack connectivity.The microscopic damage is mainly controlled by thermal expansion mismatch among mineral particles and cyclic relaxation deterioration of cemented interfaces.Based on the macroscopic mechanical response,AE activity,deformation field,and microstructural characteristics,the damage evolution of coal-bearing sandstone under low-temperat-ure thermal cycling is divided into four stages:negative damage,damage initiation,damage localization,and damage in-stability.According to the stage-dependent deterioration characteristics,the long-term stability state of surrounding rock in closed-mine geothermal systems is classified into a stability-maintenance zone,cumulative-deterioration zone,failure-sensitive zone,and instability-failure zone.Engineering operation should follow the principles of prioritizing low temper-ature difference,controlling cycling intensity,implementing zoning-based monitoring,and applying dynamic regulation.For water-bearing closed-mine environments,additional strength reduction caused by water-rock interaction and hydro-thermal coupling should also be considered.

Steel plates are extensively employed for tunnel lining reinforcement, encompassing both flat and corrugated configurations, where corrugated variants have recently emerged as the primary research focus. To evaluate enhanced mechanical properties, comparative four-point bending tests were firstly conducted on concrete arches reinforced with 2-mm and 3-mm-thick flat steel plates versus corrugated counterparts. Then, a finite element model was developed and experimentally validated, accompanied by detailed parametric analysis. Experimental results indicate flat steel plate reinforcement increases ultimate load-bearing capacity by 241-318 % compared to the unreinforced arch, while corrugated reinforcement achieves 378-388 % improvement. Under equal consumption of the steel plate, concrete arches strengthened with corrugated steel plates exhibit approximately 25-35 % higher load-bearing capacity than those reinforced with flat plates. However, corrugated steelreinforced specimens show heightened vulnerability to localized buckling and interfacial debonding, potentially reducing ductility or limiting bending performance gains. Within the scope of this study, an increase in the wave height, plate thickness, and material strength of the corrugated steel plate leads to an enhancement in the load-bearing capacity of the composite arch. For optimal corrugated system design, wave height requires prioritized consideration, followed sequentially by plate thickness, and wave width to optimize structural performance while ensuring steel utilization efficiency.

Accurate description of cavity geometric structure and quantitative estimation of the permeability of porous media are crucial for understanding fluid flow and mass transport in various geosciences and geological engineering. A permeability fractal model was constructed by combining fractal theory, Poiseuille's law of flow, and Darcy's law, taking into account the characteristic parameters of three-dimensional (3D) pore and fracture network structure. The mechanical response of tortuous capillaries was analyzed theoretically to elucidate the dynamic evolution of geometry and permeability in porous media. In addition, the geometric parameter sensitivity of the stresses is analyzed in relation to the geologic reservoir. Results indicate that: (i) an incremental rise in stress results in increases in fractal dimension, porosity, and pore quantity of the porous medium while concurrently inducing a decline in the average pore radius; (ii) the permeability obtained based on the mathematical model this study proposed and the digital core reconstruction shows a good agreement; this validates the fractal permeability. Mathematical model of stress can be used to describe the relationship between stress and the microstructure of porous media; and (iii) during the uniaxial strain process of porous media, the effective surface porosity uniformly influences permeability across all directions, adhering to the same principle. As effective surface porosity diminishes, the sensitivity of permeability to strain intensifies. Conversely, the sensitivity of permeability to strain perpendicular to the compression direction diminishes with increasing tortuosity, while the sensitivity of permeability to strain parallel to the compression direction escalates with rising tortuosity.

A prediction model for estimating the permeability of fractal rough surface fractures is proposed, in which the mechanical aperture and contact ratio are incorporated into mathematical equations. Fracture surfaces of different roughness were generated via an improved successive random addition algorithm. A series of fracture model that considers normal stress, shear displacement and surface roughness were constructed to investigate the evolution behaviors of the geometry and permeability. The results indicate that the joint roughness coefficient of the fracture profile and the aperture distribution during shear follow Gaussian functions. The aperture–frequency curve changes from sharp to flat as the shear displacement increases, indicating that the more anisotropic aperture and mechanical aperture increase. Both the mechanical aperture and the standard deviation of the aperture distribution increase with increasing fracture surface roughness during shear. The fracture aperture decreases with increasing normal stress, whereas the standard deviation of the aperture distribution increases with increasing normal stress. The effects of normal stress, shear displacement, and roughness on the evolution of the mechanical aperture and were investigated to further clarify their effects on fracture permeability. We found that the mechanical aperture and contact can be correlated with permeability via a power law, and multiple regression algorithms were applied to construct a mathematical model for estimating the permeability of rough surface fractures. The reasonableness of the prediction model proposed in this study was verified by comparing its results with laboratory seepage tests.