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  • Rock and Soil Mechanics
    Supervised by: Chinese Academy of Sciences
    Publisher: Science China Press
    Period:Monthly Publication
    Editor-in-Chief:KONG LingWei
    Sponsored by :Institute of Rock and Soil Mechanics, Chinese Academy of Sciences
    Journal Tags: EI
    Language: Chinese
    Release Date: 1979
    ISSN 1000-7598 CN 42-1199/O3
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Table of Content
10 October 2026, Volume 47 Issue 10
Fundamental Theory and Experimental Research
Bearing characteristics and calculation method for bearing strength of annular geotubes
ZOU Wei-lie, GAO Gao, HAN Zhong, LAI Zhi-qiang, FAN Ke-wei
Rock and Soil Mechanics. 2026, 47 (10):  3301-3311.  DOI: 10.16285/j.rsm.2025.1211
Abstract ( 84 )  
In response to issues such as the low stability of traditional linear geotube embankments for dredged sludge containment, reliance on natural or artificial gullies/depressions, and low land utilization efficiency, this study proposes a novel impoundment structure composed of sand-filled annular geotubes. The pivotal scientific considerations in the design and stability analysis of this structure pertain to the pressure-bearing characteristics and strength of the annular geotubes. Utilizing a self-developed large-scale pressure test apparatus, pressure-bearing tests were conducted on a multi-layered annular geotube embankment model. The tests revealed the distribution of localized fabric tension under the combined effects of sand-fabric interface friction and inter-layer friction between the geotubes. Key findings are outlined as follows: (1) The geotextile in the pressure-bearing zone of the geotube is constrained by inter-layer friction, thereby restricting the development of its tension. Conversely, in the free zone, the geotextile tension is unevenly distributed, with the local maximum tension occurring at the interface between the pressure-bearing and free zones. (2) The modulus of the geotextile exerts minimal influence on its average tension; however, its ultimate tensile strength demonstrates a positive correlation with the pressure-bearing strength of the geotube. (3) The degree of sand fulfillment affects the development trend of geotextile tension by altering the morphological characteristics of the geotube. Based on these insights, a calculation method for determining the pressure-bearing strength of annular geotubes was developed, using the local maximum tension as the failure criterion and considering the effects of interface friction. The rationality of this method was validated through discrete element modeling.
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Influence of stress and temperature on compliance characteristics of granite anelastic strain recovery method
MA Chun-de, GONG Qiang, TAN Guan-shuang, LI Chen-yang, ZHOU Hong-bo, ZHAO Jun-kang
Rock and Soil Mechanics. 2026, 47 (10):  3312-3322.  DOI: 10.16285/j.rsm.2025.1160
Abstract ( 55 )  
In order to explore the influence of stress and temperature on the compliance characteristics of anelastic strain recovery (ASR) method, this study used granite specimens to carry out creep and post-creep unloading experiments. The results show that, under a stress level ranging from 40% to 50% of the uniaxial compressive strength (UCS), the rock predominantly undergoes viscoelastic deformation, with a notable recovery of anelastic strain. At stress levels between 60% and 70% UCS, the deformation of the rock is primarily characterized by a combination of viscoelastic and plastic deformation, resulting in a relatively diminished recovery of anelastic strain. As the stress level escalates, the compliance ratio gradually increases, while both types of compliance initially rise and subsequently decline. Furthermore, an elevation in temperature leads to an increase in both the recovery strain and compliance of the rock. Within the moderate to low temperature range of 25–200 °C, the compliance ratio increases with rising temperature, whereas it decreases within the high temperature range of 300–500 °C. This phenomenon arises because varying temperatures exert distinct effects on the shear. The findings of this study offer an experimental foundation for the judicious selection of the compliance in ASR method.
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Effective biomineralization depth of granite residual soil treated with a urease-based low-pH biotreatment solution
LAI Han-jiang, CHEN Jia-le, CUI Ming-juan, ZHANG Zhi-chao
Rock and Soil Mechanics. 2026, 47 (10):  3323-3332.  DOI: 10.16285/j.rsm.2025.1140
Abstract ( 35 )  
Granite residual soil is rich in hydrophilic minerals and exhibits strong water sensitivity; it tends to soften and disintegrate upon wetting. It is a soil type commonly associated with geohazards such as landslides. Urease-based biomineralization is an environmentally friendly soil-improvement approach that enhances resistance to disintegration of granite residual soil. However, granite residual soil generally has small pore size and low permeability, and its effective biomineralization depth is shallow using conventional spraying biotreatment solution in-situ. This study proposes using a urease-based, low-pH biotreatment solution for the biomineralization of granite residual soil. The effective biomineralization depth was evaluated, and the underlying mechanisms were elucidated using calcium carbonate content measurements, disintegration tests, and scanning electron microscope (SEM) analysis. The test results show that the urease-based low-pH biotreatment solution can significantly improve the effective biomineralization depth of granite residual soil. The biotreatment solution prepared with pH = 3.00 cementation solution and soybean urease solution at a 1:1 volume ratio has the best biomineralization. For granite residual soil with an initial water content of 24%, the effective biomineralization depth reaches 40 mm.
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Seismic ground motion of saturated frozen soil layered site under SV wave incidence
SHI Tian-yu, MA Qiang, ZHOU Feng-xi, CAO Ya-peng, JIAO Hao
Rock and Soil Mechanics. 2026, 47 (10):  3333-3351.  DOI: 10.16285/j.rsm.2025.1138
Abstract ( 33 )  
Based on the Biot’s three-phase medium theory, a two-dimensional layered site model of saturated frozen soil overlying bedrock is constructed to analyze the characteristics of seismic ground motion under plane SV wave incidence. The governing equations are decoupled via Helmholtz vector decomposition, and an analytical solution is derived by enforcing interlayer boundary conditions and employing the transfer-matrix method. The reliability of the solution procedure is validated through comparison with published results. On this basis, a systematic parametric study is conducted to investigate how incident frequency and angle, porosity, medium temperature, cementation and contact parameters, as well as the thickness of the surface saturated frozen layer influence the amplification of surface displacement. The results show that the amplification of seismic motion in layered saturated frozen sites is overall stronger than in homogeneous sites, with particularly pronounced amplification near the critical incident angle. Increases in porosity and temperature typically enhance horizontal displacement amplification, whereas the vertical displacement demonstrates notable structure-dependent and nonlinear behavior across various layering configurations. The cementation and contact parameters substantially modulate the stiffness of the soil skeleton, thereby altering both the magnitude and spatial distribution characteristics of surface displacement amplification; variations in the thickness of the surface frozen layer induce clear periodic fluctuations in the amplification factor. This study elucidates the mechanism of seismic ground-motion amplification in cold-region layered saturated frozen sites under SV wave incidence and provides theoretical support for site-effect assessment and earthquake-resistant design of relevant engineering in cold regions.
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Identification and characterization of rockburst precursor signals using acoustic emission spectral analysis
CUI Yi-bo, YAO Xu-long, ZHANG Yan-bo, SUN Lin, ZHAO Jian, GUO Bin, TAO Zhi-gang
Rock and Soil Mechanics. 2026, 47 (10):  3352-3364.  DOI: 10.16285/j.rsm.2025.1126
Abstract ( 31 )  
Rockbursts represent a formidable geological disaster in deep underground engineering endeavors, and their precise prediction is of paramount importance for safeguarding the security of deep mining activities. To overcome the constraints inherent in conventional acoustic emission (AE) monitoring, which assumes that a solitary AE signal corresponds to an individual fracture incident—a premise that often results in inaccuracies in parameter calculation, misidentification of fracture mode, and concealment of pivotal precursor characteristics of rock fracture—this study introduces an innovative methodology for discerning multiple fracture events grounded in AE spectral analysis. Rockburst simulation experiments were conducted on granite specimens to amass AE signal data. A spectral analysis model was subsequently formulated, employing short-time Fourier transform (STFT) alongside valley ray demarcation (VRD) techniques to identify multiple fracture events and execute parameter computations. The findings reveal that this approach effectively distinguishes multiple fracture events within a singular AE signal and precisely captures the precursor features of rockbursts. During the transitional periods of the rockburst precursor phase, low-frequency, high-energy events with relatively elevated absolute energy magnitudes were discerned; concurrently, critical features marked by sporadic mid-frequency signals and low-frequency, low-energy signals were observed preceding rock failure, thereby offering novel perspectives for rockburst prediction.
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Complex variable solution for strata deformation induced by tunnel excavation under arbitrary convergence patterns
ZHAO Jia-le, LIU Yang
Rock and Soil Mechanics. 2026, 47 (10):  3365-3380.  DOI: 10.16285/j.rsm.2025.1154
Abstract ( 42 )  
Tunnel convergence patterns, which serve as the key boundary condition for analyzing strata deformation induced by tunnel excavation, are strongly influenced by complex geological conditions and construction processes. However, existing analytical theories for strata deformation are based on idealized convergence assumptions, such as uniform or elliptical convergence, which limit their applicability in complex engineering conditions. To overcome this limitation, a unified equation for tunnel convergence patterns is first established based on Fourier series and coordinate transformations, enabling an accurate description of the tunnel contour trajectory. Subsequently, the deformation of tunnel contour under arbitrary convergence patterns is derived, and the analytical relationship between the parameters of the unified convergence-mode equation and the tunnel contour deformation is obtained. Further, based on complex variable theory, a conformal mapping of tunnel contour deformation under arbitrary convergence patterns is achieved. Finally, a complex variable solution for strata deformation under arbitrary convergence patterns is developed. The results from model degeneration analysis and engineering applications demonstrate that the proposed method generalizes traditional complex variable solutions and more accurately characterizes strata deformation induced by tunnel excavation. Actual engineering conditions are complex and variable, and under complex convergence patterns, the deformation characteristics of the surrounding strata during tunnel excavation differ significantly from traditional predictions. The proposed method enables refined analysis of strata deformation induced by tunnel excavation and supports inverse analysis of complex tunnel convergence patterns.
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Experimental investigation on heat transfer during injection-extraction processes in large-scale artificial rock specimens containing prefabricated fractures
LI Zong-ze, WEI Chun-lei, YANG Zi-rui, ZHU Hai-yan, YU bo, WANG Dao-bing , WANG Yue-she
Rock and Soil Mechanics. 2026, 47 (10):  3381-3388.  DOI: 10.16285/j.rsm.2025.1137
Abstract ( 27 )  
Hot dry rock (HDR) is a major carrier of deep geothermal energy, characterized by its vast reserves, extensive geographical distribution, and low-carbon clean attributes. It represents a key direction for renewable energy development under the framework of the dual carbon goals. To investigate the impact of complex fracture structures and injection-extraction schemes on the heat extraction efficiency of HDR reservoirs, this study developed a large-scale artificial rock sample with prefabricated fractures and established a thermo-hydro-mechanical (THM) coupled injection-extraction heat exchange experimental system. Fracture frameworks were constructed using paper and proppant particles, and artificial rock samples measuring 400 mm×400 mm×400 mm were fabricated through a mold casting technique. A series of heat exchange experiments was systematically executed under varying combinations of fracture geometries (long straight fracture, deflected fracture, branched fracture) and injection-extraction schemes (single injection-single extraction, single injection-dual extraction). The experimental outcomes indicate that fracture geometry exerts a limited effect on the temperature field, whereas seepage flow plays a predominant role. The injection-extraction scheme significantly affects heat exchange performance; when the injection rate escalates from 11 mL/min to 50 mL/min, the cooling rate of the produced fluid rises from 0.6  °C/10  min to 10.2  °C/10  min. This study reveals the critical roles of flow distribution and the stability of seepage pathways in short-term heat extraction capacity, providing experimental evidence and theoretical support for fracture design and optimization of injection-extraction parameters in enhanced geothermal system (EGS).
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Effects of alkali-activator types on the properties of silty clay solidified with phosphogypsum-slag cementitious materials
WANG Chong, LIU Jin-bao, TAN Yun-zhi, TIAN Miao-miao, LUO Jiang-tao
Rock and Soil Mechanics. 2026, 47 (10):  3389-3398.  DOI: 10.16285/j.rsm.2025.1105
Abstract ( 28 )  
The type of alkali activator is crucial for the strength development of phosphogypsum-based cementitious materials (PPSC), yet its role in soil solidification remains unclear due to the soil interference. Through unconfined compressive strength (UCS) tests, pH measurements, mercury intrusion porosimetry (MIP), and scanning electron microscopy (SEM), this study analyzed the effects of activator type (cement, quicklime, NaOH, NaOH+sodium silicate) and PPSC content on the mechanical properties and microstructure of solidified soil, revealing the regulatory mechanism of the alkaline environment on the performance of PPSC-solidified soil. The results indicate that the alkaline environment generated by the activator significantly influences the early-age strength development of the solidified soil. Notably, the alkaline environment induced by the cement activator exhibits the least potency, failing to effectively activate the reactivity of PPSC within the soil during the early hydration stage, resulting in the lowest early-age (7 d) UCS (0.46 MPa), which is substantially inferior to those observed in the quicklime-treated group (1.11 MPa), the NaOH+sodium silicate-treated group (0.84 MPa), and NaOH-treated group (0.98 MPa). However, with the continued hydration of the cement activator, the alkalinity in the solidified soil intensifies, thereby diminishing its impact on the later strength development. After 28 d of curing, the strength rankings of the solidified soil are as follows: cement-treated group (1.61 MPa)<quicklime-treated group (1.74 MPa)<NaOH+sodium silicate-treated group (1.95 MPa)<NaOH-treated group (2.08 MPa). Furthermore, the alkalinity of the solidified soil demonstrates a discernible pH threshold effect. When pH<10.08, the PPSC in the soil cannot fully hydrate, and the strength of the solidified soil is not significantly affected by the PPSC content. When pH≥10.08, the strength increases markedly with the increase of PPSC content. This study holds significant implications for the efficient resource utilization of phosphogypsum and soil solidification.
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Crack evolution mechanism of sandstone under influence of immersion depth and a new criterion for rockburst tendency
CHEN Guang-bo, ZHENG Shao-huang, TANG Wei, LI Tan, WANG Chuang-ye, WANG Er-yu, LIU Ye-jiao, ZHANG Guo-hua, ZHANG Jun-wen, LIU Gang, JIA Yan-yue
Rock and Soil Mechanics. 2026, 47 (10):  3399-3423.  DOI: 10.16285/j.rsm.2025.1159
Abstract ( 31 )  
Underground deep engineering projects, particularly in large water-rich mines or under water-rich mining conditions, are significantly affected by groundwater infiltration, which compromises the stability of engineering rock masses. To reveal the crack evolution characteristics and rockburst tendency of sandstone under different immersion depths, uniaxial compression tests, acoustic emission (AE) monitoring, and scanning electron microscope analysis were conducted on sandstone samples subjected to six immersion depths: 0, 20, 40, 60, 80, and 100 mm. The results indicate the following trends: 1) With increasing immersion depth, both the elastic modulus and compressive strength of the samples deteriorate to varying degrees, with the most significant reduction occurring in the 0–20 mm immersion depth range. 2) With increasing immersion depth, high-frequency AE signals gradually increase, accompanied by a rise in small-scale fractures. The cumulative energy of low-frequency AE decreases significantly, from 747 980.30 to 31 084.71 mV·ms, indicating a gradual reduction in fracture scale. The AE r value at the critical failure point decreases from 1.84 to 1.14, reflecting a lower energy concentration and a transition toward static failure modes. 3) With increasing immersion depth, the number of cracks in failed samples increases, whereas the energy associated with AE localization points decreases. At 100 mm immersion depth, the energy concentrates primarily in the range of 16.4–32.8 mV·ms, with large-scale fractures diminishing and small-scale fractures becoming more prevalent. 4) By integrating elastic strain energy, energy dissipation during failure, and failure duration, a new criterion for rockburst tendency—the residual energy release rate index ( WT )—is proposed. Using both the index WT  and the elastic-impact comprehensive energy index ( XE ), the rockburst tendency of sandstone samples under different immersion depths is classified as weak rockburst, with the index values gradually decreasing as immersion depth increases. The weak rockburst category is further subdivided into three subclasses: weak rockburst-high tendency, weak rockburst-medium tendency and weak rockburst-low tendency. 5) Under different immersion depths, the failure cracks are characterized as tensile-shear composite cracks, and the failure mode transitions from shear failure to tensile-shear composite failure. A multi-scale instability model for immersed sandstone is established, revealing the micro-meso-macro instability mechanism of sandstone under hydraulic coupling: water-rock interactions lead to the dissolution of mineral particles and clay minerals, as well as the generation of microcracks. Under loading, these microcracks propagate, connect, and fracture, ultimately forming macroscopic cracks that result in sample instability and failure. These findings provide insights for evaluating the stability of engineering rock masses affected by immersion depth and for predicting rockburst occurrences.
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Failure mechanism of sandstone under nonuniform cyclic stress
LIU Gang, ZHANG Qi-qi, ZENG Hong, WANG Miao, YANG Xing-zhou,
Rock and Soil Mechanics. 2026, 47 (10):  3424-3438.  DOI: 10.16285/j.rsm.2025.1147
Abstract ( 33 )  
Geological conditions and mining disturbance factors induce nonuniform stress fields in rock masses, with localized zones exhibiting large stress contrasts and cyclic loading–unloading patterns during mining. To investigate the mechanical properties and acoustic emission (AE) characteristics of sandstone under nonuniform cyclic stress, cyclic loading and unloading tests were conducted on sandstone subjected to different nonuniform stresses. The relationship between mechanical parameters and AE characteristic parameters under nonuniform cyclic stress was analyzed to explore crack evolution characteristics and energy evolution patterns during cyclic loading and unloading process of sandstone under nonuniform stress. The results show that under nonuniform stress, low-stress regions in sandstone exhibit elastic rebound prior to failure, leading to stress reduction. Nonuniform cyclic stress paths deteriorate sandstone mechanical properties and failure modes, with deterioration ordered as: D-G-Z > G-D-Z > D-Z-G (D, Z, and G represent low-stress, medium-stress, and high-stress zones, respectively). The modulus of sandstone decreases significantly at failure under nonuniform cyclic stress. AE energy evolves in a stepwise manner, and AE counts show a “dense-sparse-dense” pattern. Abnormal changes in the b-value can serve as precursors to rock failure under nonuniform stress. The nonuniform stress state strongly influences crack propagation paths in sandstone: under D-Z-G, shear cracks predominate; under G-D-Z, tensile cracks predominate; under D-G-Z, composite cracks predominate. The energy curve exhibits a U-shaped trend, with high-stress regions dominating the final failure and medium-stress regions providing a supplementary role. This study provides a theoretical basis for analyzing the stability of surrounding rock in deep mining.
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Model test study on soil damage and shallow failure of hydro-fluctuation belt induced by combined action of wetting-drying cycles and reciprocal seepage
CHEN Yong, YANG Xiao-dong, HE Yuan-yuan, WANG Li,
Rock and Soil Mechanics. 2026, 47 (10):  3439-3251.  DOI: 10.16285/j.rsm.2025.1128
Abstract ( 32 )  
Under the long-term influence of periodic water level fluctuations in the reservoir, bank collapse and frontal deformation of soil slopes are common geological disasters. By interpreting the hydraulic forcing as the coupled action of repeated wetting-drying cycles and periodic reciprocating seepage, this study employs a self-developed model testing device to construct a gravel slope using discontinuously graded soil. The individual and combined effects of multiple wetting-drying cycles and reciprocating seepage are simulated separately. The loss patterns of fine particles and the evolutionary process of surface cracks on the slope are systematically analyzed. Continuous monitoring of pore water pressure, volumetric water content, and displacement field evolution elucidates the synergistic damage mechanism of cracking and erosion within the hydro-fluctuation zone, as well as their influence on slope deformation and failure. Results indicate that repeated wetting-drying cycles promote the progressive development and pseudo-healing of surface crack networks, whereas reciprocating seepage induces substantial loss of fine particles. Under the alternating combined action of both processes, desiccation cracks compromise soil integrity and create preferential seepage pathways, thereby accelerating fine particle loss. Conversely, seepage erosion exposes coarse skeletal particles, diminishes the capacity for crack healing, and enhances soil permeability. It can be inferred that desiccation crack and erosion interact mutually and exert a synergistic aggravating effect on soil structural degradation, thus promoting the earlier slope failure. This behavior is primarily attributed to the combined driving forces arising from severe soil structure deterioration and seepage pressure. The findings offer a theoretical foundation and technical support for understanding the intrinsic relationship between periodic water level fluctuations and progressive slope deformation, enabling more accurate analysis and prediction of slope stability.
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Dynamic characteristics and constitutive models of deep sandstone under thermal-hydro-mechanical coupling effects
ZHANG Bo-bo, PING Qi, XI Zhang-peng
Rock and Soil Mechanics. 2026, 47 (10):  3452-3466.  DOI: 10.16285/j.rsm.2025.1124
Abstract ( 28 )  
The exploitation of deep coal resources constitutes a pivotal component of national energy strategic requirements. Notably, the deformation behavior of coal and rock masses in deep engineering settings is significantly influenced by complex environmental conditions, including elevated ground temperatures, high water pressures, intense stress levels, and strong disturbance loads. To investigate the dynamic strength characteristics and energy dissipation variations of deep sandstone under real-time thermo-hydro-mechanical (THM) coupling, dynamic impact tests were performed utilizing an enhanced THM multi-field coupled split Hopkinson pressure bar apparatus. Furthermore, a dynamic damage constitutive model for deep sandstone was formulated, integrating the viscoelastic-plastic Zhu-Wang-Tang (ZWT) model with the Drucker-Prager strength criterion. The test results reveal the following trends: Under varying water pressures, the plastic yield phase in the dynamic stress-strain curve is markedly prolonged, while the dynamic compressive strength and dynamic elastic modulus demonstrate a progressive increase with rising water pressure. As temperature escalates, these parameters initially rise before declining, with a discernible interval observed between 50 and 75 °C. The time-history curves of dynamic stress rate and dynamic strain rate generally adhere to evolutionary patterns characterized by “increase-decrease-decrease-decrease” and “increase-decrease-level-decrease”, respectively. At a constant water pressure, both incident and reflected energy exhibit a decrease followed by an increase with rising temperature. Conversely, at a constant temperature, transmitted energy displays a gradual increase, whereas dissipated energy initially increases before decreasing with increasing water pressure. The relationship between dissipated energy density and average strain rate transitions from a negative linear correlation to a positive linear correlation. A comparative analysis between the dynamic stress-strain test curves and theoretical curves demonstrates that the established dynamic constitutive model effectively captures the dynamic compressive strength and deformation characteristics of deep sandstone under THM coupling conditions.
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Solution method and application for stress state of slip surface in subgrade slopes based on Mindlin solution
CHEN Huai-lin, YANG Tao, ZHANG Zhe, WU Hong-gang, RAO Yun-kang, TENG Han-qing, LI Xi-yang
Rock and Soil Mechanics. 2026, 47 (10):  3467-3478.  DOI: 10.16285/j.rsm.2025.1174
Abstract ( 34 )  
Solving the stress state of the slip surface constitutes the core issue in the stability analysis of subgrade slopes. To facilitate the engineering application of analytical methods for slip surface stress, this study introduces a methodology for determining slip surface stress in subgrade slopes, grounded in the stress superposition principle within an elastic semi-infinite space. This approach treats the slope surface as the boundary of an elastic semi-infinite space and computes the stress state at any point within the slope body by the hypothetical resistive force acting on the slope surface (derived from the Mindlin solution). Based on this framework, the slip surface stress can be determined accordingly. Furthermore, this study introduces a model test method for measuring slip surface stress. Building upon this, two example slopes with potential slip surfaces were designed. The slip surface stresses obtained from the analytical method and the model test method were comparatively analyzed to verify the rationality of the analytical method. Concurrently, a calculation method for the stability coefficient based on the analytical solution of slip surface stress was proposed, and its engineering application value was explored. The research findings are as follows: Example calculations show that the proposed analytical method aligns fundamentally with model test results. Statistical analysis indicates that the correlation coefficients for normal stress and shear stress between both methods exceed 0.5, with the p-values of the correlation coefficient tests greater than 0.05, demonstrating a strong correlation and insignificant differences. The proposed stability coefficient method enables the simultaneous determination of local stability coefficients and global stability coefficients, reflecting both the overall landslide stability and the failure mechanism of potential landslides. Based on the explicit principle of stress superposition and facilitated by straightforward programming implementation, the proposed theoretical calculation method not only extends the existing analytical framework for stress calculation in homogeneous subgrade slopes, but also provides a clear pathway for its extension to more complex conditions. It offers a novel analytical tool for both stability evaluation and failure mechanism analysis of subgrade slopes.
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Extension of a dynamic constitutive model to rock: validation with granite
YANG Kai-hua, LIU Yi-jun, WANG Zi-hao, ZHOU Ao, LI Qing-wei
Rock and Soil Mechanics. 2026, 47 (10):  3479-3492.  DOI: 10.16285/j.rsm.2025.00398
Abstract ( 28 )  
The dynamic response and fracture of rock materials under high-rate and impact loading conditions are long-standing and critical issues in geotechnical engineering, impact dynamics, and protective engineering. Accurate constitutive modeling of rocks remains challenging due to the complex coupling among pressure dependence, strain-rate effects, damage evolution. In this study, a dynamic constitutive model integrated with an equation of state, originally developed for concrete-like materials, is extended to rock materials and validated using granite as a representative example. Triaxial compression tests were conducted using the RMT-301 rock mechanics testing system to systematically investigate the mechanical behavior of granite under varying confining pressures. The model parameters were determined based on a comprehensive experimental dataset, encompassing static triaxial compression tests, split Hopkinson pressure bar (SHPB) tests, split Hopkinson tension bar (SHTB) tests, and planar impact experiments. A user-defined material subroutine (VUMAT) was developed and implemented in the ABAQUS/Explicit finite element framework to simulate the mechanical response of granite under static triaxial loading, planar impact, and projectile penetration conditions. The results demonstrate that the proposed model accurately captures the stress-strain behavior of granite under different confining pressures, the particle velocity-time history, wave-structure evolution and Hugoniot elastic limit (HEL) under plate impact, and effectively predicts the penetration depth and failure morphology observed in projectile penetration tests. These results verify the reliability and robustness of the proposed model in capturing the dynamic response characteristics of granite over a broad range of impact conditions.
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Modeling of water retention behavior of compacted loess to account for soil texture variability
WANG Song-he, ZHAO Xu-wei, NIU Shuai, WANG Jia-ding
Rock and Soil Mechanics. 2026, 47 (10):  3493-3508.  DOI: 10.16285/j.rsm.2025.00386
Abstract ( 29 )  
This study aims to establish a generalized water-retention model by correlating model parameters with fundamental physical indexes of loess. Water retention test data from 35 sources of loess soils in Northwest China were optimally fitted to yield parameters for the generalized water retention model (the Zhou-Lu model). These loess soils, classified as lean clay, encompass a broad range of particle size distribution (8.60%–37.85% in clay content), plasticity index (7.20–17.00), and dry density (1.23–1.83 g/cm³). Spearman correlation analysis between model parameters and both single and synthetic physical indexes indicates significant correlations of maximum adsorbed water content wamax with fines content Pfine, air-entry value 1/α with wIPe (the product of weighted plasticity index wIP and void ratio e ), and capillary pore size distribution n with plasticity index IP, which were respectively described as simple empirical functions. The other three parameters (maximum matric suction ψmax, adsorption strength parameter m , mean cavitation suction ψc) are highly indeterminate and lack experimental evidence; therefore, the means were taken from their statistical distributions. The above parameters were incorporated into the Zhou-Lu model. Deviations of model predictions from the dataset mostly fall within ±30%. Further verification, based on water retention test data of compacted loess from three sampling sites (Baishui, Jingyang, and Hengshan), confirmed the rationale of the model. This preliminarily indicates the robustness of the Zhou-Lu model for loess soils with diverse textures, and allows for further refinement given improved datasets.
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True triaxial experimental study on the failure mechanism of coal-rock combination samples containing prefabricated rectangular opening
YAN Liang-huan, CHANG Ju-cai, QIAO Long-quan, SHI Wen-bao, WANG Tuo, QI Chao, FAN Lei, WANG Hong-da
Rock and Soil Mechanics. 2026, 47 (10):  3509-3524.  DOI: 10.16285/j.rsm.2025.1156
Abstract ( 27 )  
The instability mechanism of surrounding rock in deep roadways crossing coal seams differs fundamentally from that in homogeneous rock strata. To clarify this failure mechanism, true triaxial tests were conducted on coal‑rock combination samples containing prefabricated rectangular opening, using a true triaxial seepage coupling system equipped with a visual window. The failure characteristics and acoustic emission (AE) response under various coal‑rock configurations were synchronously captured by a miniature camera and AE monitoring. The results demonstrate that the failure process of the rectangular opening exhibits a four-stage evolutionary pattern, consisting of initial quiescence, particle detachment, block spalling, and complete collapse, ultimately leading to the formation of a through-going V-shaped pit and fracture zone. The fractal evolution characteristics of fragmentation in coal-rock combination samples are positively correlated with the degree of structural confinement. The fractal dimensions of coal-rock, rock-coal, and rock-coal-rock combination samples increase progressively, and the crack propagation patterns are governed by the synergistic effects of stress transfer mechanisms across the coal-rock interface and the plastic deformation characteristics of coal. The AE response exhibits distinct stage-dependent evolution characteristics, with low ring-down counts and energy levels during the initial quiescence stage, gradual enhancement of AE activity and a slow increase in the cumulative ring-down count curve during the particle detachment stage, multi-peak fluctuations of AE signals accompanied by high ring-down counts and energy release during the block spalling stage, and a sharp increase in AE activity with rapidly increasing ring-down counts and energy reaching their peak values during the complete collapse stage. The failure mode is jointly controlled by coal strength and interfacial confinement. Under single‑layer weak confinement, coal‑rock and rock‑coal combination samples initially experience tensile failure that gradually transitions to tensile‑shear mixed failure. Under bidirectional strong confinement, tensile crack propagation in rock‑coal‑rock combination samples is suppressed, and the failure mode progressively shifts from tensile failure, through tensile-shear failure, and ultimately to shear failure.
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Experimental study on static fracturing of coal and rock mass using directional energy-concentrating structure
CHENG Hong-ming, LAN Yong-qing, QIAO Yuan-dong, YANG Xiao-bin, ZHAO Zhen-bao, HAO Yong-xu, ZHOU Min-jia, YANG Ze-yuan
Rock and Soil Mechanics. 2026, 47 (10):  3525-3536.  DOI: 10.16285/j.rsm.2025.1143
Abstract ( 24 )  
To address the technical challenges of random crack direction, low energy utilization efficiency, and frequent blowouts in conventional perfusion static fracturing of coal and rock masses, a static fracturing method based on a directional energy-concentrating structure is proposed. Comparative experiments were conducted using three charging forms—conventional perfusion, directional structure, and directional energy-concentrating structure—on a self-built static fracturing test platform for coal and rock. The experiments utilized artificial rock-like materials to prepare cubic specimens with different borehole diameters, simulating the hard roof sandstone in the northern region of Shanxi province. The dynamic propagation of cracks was monitored in real time using digital image correlation technology. Three quantitative indicators—average crack initiation time, average fracture aperture, and crack propagation rate—were introduced to comprehensively evaluate the static fracturing effects under different charging structures. The results demonstrate that the directional energy-concentrating structure effectively guides the concentrated release of expansion stress from the static cracking agent along a predetermined direction, significantly suppressing energy dissipation and enabling directional crack initiation and propagation. Macroscopically, specimens tested with the directional energy-concentrating structure exhibited flatter and more integrated fracture surfaces, showing a clear three-stage evolution characteristic: “directional force application–linear cracking–planar coalescence.” Mesoscopic strain field analysis revealed that the displacement gradient and strain concentration were significantly higher than those in conventional perfusion and directional structure tests, with a maximum apparent displacement vector of 2.98 mm. For instance, in specimens with a 50 mm borehole diameter, the crack initiation time was 23.8 min, the average fracture aperture was 2.89 mm, and the crack propagation rate reached 1.46 m/s. These values represent improvements of 36.2%, 56.8%, and 99.3%, respectively, compared to conventional perfusion tests, and 14.7%, 51.7%, and 92.8% compared to directional structure tests. The findings validate the mechanical superiority and technical feasibility of the directional energy-concentrating structure in static fracturing, providing a theoretical and experimental basis for applying static fracturing technology to weaken and relieve pressure in deep high-stress hard rock masses.
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Dynamic fractal evolution of spherical single-particle fragmentation under cyclic impact
PAN Qian-tong, LIU Xing-yan, TIAN Jian-qiu
Rock and Soil Mechanics. 2026, 47 (10):  3537-3550.  DOI: 10.16285/j.rsm.2025.0953
Abstract ( 24 )  

By controlling impact energy (E=6.27, 9.41, 12.54 J), number of impacts (n =1−15), and particle size (d =20, 30, 40 mm), this study systematically investigates the dynamic evolution of the fractal dimension D during the crushing of spherical particles. The experimental results demonstrate that D increases with n in a nonlinear, multi-stage manner. During the initial impact stage (n =1−5), brittle fracture is induced. For example, with d=30 mm and E=12.54J, ΔD/Δn reaches 0.062 per impact. In the subsequent stage (n>5), the growth rate decreases to 0.015 per impact due to energy dissipation. A coupling mechanism exists among impact energy, particle size, and impact number. E dominates the initial crushing efficiency; increasing E from 6.27 J to 12.54 J enhances the final D by 13.5% for 40 mm particles. Smaller particles (20 mm) exhibit higher initial D due to stress concentration. The reinforcing effect of n on D decays as impacts accumulate. The basic model effectively characterizes the size effect, with errors <5% under most conditions. An extended model incorporating the fractal chaotic coefficient χ significantly improves prediction accuracy for fine particles. Both models capture the E-n-d coupling mechanism and provide an effective tool for quantitatively predicting particle crushing.

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Strength damage and mesoscopic mechanism of stabilized organic soil subjected to freeze-thaw cycles
ZHAO Ji-ling, YANG Ping, PAN Wei-dong, GUO Wen-bing, RUI Da-hu, ZHANG Jun
Rock and Soil Mechanics. 2026, 47 (10):  3551-3563.  DOI: 10.16285/j.rsm.2025.1139
Abstract ( 27 )  
Organic soils are widely distributed in cold regions, where their engineering properties are significantly influenced by F-T (freeze-thaw) cycles, which directly influence the long-term stability of subgrade in cold areas. While existing research has predominantly focused on conventional soils, the macro-meso response mechanisms of cement-and-fly ash stabilized organic soils under F-T cycles remain unclear. This study investigates the macro-mesoscopic damage evolution of stabilized organic soils subjected to F-T cycles through triaxial shear tests and computed tomography (CT) scanning. The results indicate that a mix proportion of 20% cement and 5% fly ash yields the optimal strength enhancement. When the organic content reaches or exceeds 15%, the failure mode of stabilized organic soils transitions from brittle to ductile. The strength deteriorates in a power-law function with increasing F-T cycles, while porosity increases logarithmically, accompanied by a tendency for pore morphology to become more elongated and narrow. A constitutive model incorporating both the number of F-T cycles and a mesoscopic damage factor modified by fractal dimension is developed. This model quantitatively correlates macro- and mesoscopic damage, elucidating the underlying damage mechanisms induced by F-T actions. The findings provide critical parameters and a theoretical basis for the design and durability assessment of stabilized organic soil subgrade in cold regions.
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Geotechnical Engineering
Field experiment and numerical study on rapid consolidation of dredged slurry as fill material using prefabricated horizontal drain vacuum preloading
SONG Ding-bao, WU Pei-chen, CHEN Wen-bo, YIN Jian-hua
Rock and Soil Mechanics. 2026, 47 (10):  3564-3574.  DOI: 10.16285/j.rsm.2025.1097
Abstract ( 31 )  
Existing laboratory model tests evidence that the prefabricated horizontal drain (PHD) vacuum preloading method exhibits significant potential for consolidating dredged slurry with high water content. However, systematic research on the practical engineering effectiveness of this method remains limited, with few related reports. To address this, a field experiment was conducted to rapidly consolidate marine dredged sediments used as fill material, employing the PHD vacuum preloading method. The experiment systematically evaluated the method’s treatment efficiency and effectiveness. Additionally, numerical modeling analysis was performed to validate the applicability and accuracy of the numerical model. Based on parameter sensitivity analysis, recommended ranges for key design parameters, including the horizontal spacing of drains and vertical layer spacing, were proposed for slurry with varying properties. Furthermore, a comparative analysis of multiple methods for treating dredged slurry was conducted, demonstrating that the PHD vacuum preloading method significantly enhances drainage consolidation efficiency. Early implementation of the vacuum preloading process was found to substantially improve consolidation effectiveness. For the treatment of high-compressibility soil slurry with a high initial void ratio, it is recommended that the horizontal spacing parameter of the drains (defined as the ratio of the horizontal spacing to the width of the drain) be set in the range of 5–8, and that the interlayer spacing parameter (defined as the ratio of the interlayer spacing to the total initial thickness of the slurry) be set within 0.1–0.3.
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Data-physics fusion-driven deformation prediction of geotechnical structures based on multi-fidelity networks: a case study of the Taihu Tunnel deep excavation
WANG Bin, FU Chen-yu, TAN Xu-yan, LI Yang, SHA Ru-chen
Rock and Soil Mechanics. 2026, 47 (10):  3575-3588.  DOI: 10.16285/j.rsm.2025.1155
Abstract ( 34 )  
Deformation serves as a pivotal indicator for the stability assessment of geotechnical structures, as exemplified by the deflection of deep excavation retaining systems and the convergence of shield tunnel segments. Addressing the limitation that conventional deformation prediction methodologies are predominantly data-driven—heavily contingent upon the quantity and fidelity of available data—we propose a physics-data dual-driven prediction framework anchored in multi-fidelity networks. The framework comprises two distinct modules. Initially, a low-fidelity sub-network is constructed utilizing the deep operator network (DeepONet) architecture, designed to mine fundamental deformation characteristics inherent in numerical simulation results and extract the physical modes of structural deformation. Subsequently, a residual-based high-fidelity sub-network is established, wherein high- and low-fidelity data are explicitly correlated at the input and output interfaces. Employing a long short-term memory (LSTM) architecture, this module realizes a physics-guided data-driven approach, whereby the low-fidelity solution provides guidance and correction to the high-fidelity prediction. By embedding physical paradigms, the framework effectively constrains the training of the data model, thereby mitigating the reliance on purely empirical data and surmounting the limitations imposed by data quality. Finally, the proposed framework is applied to the Taihu Tunnel deep excavation project. The results demonstrate that the predictive accuracy of the physics-embedded dual-driven methodology is significantly superior to that of a singular data-driven approach. For the two prediction tasks, the mean scores are 0.93 and 0.96, representing improvements of 0.37 and 0.035, respectively, relative to the single data-driven method; the mean MAEs are recorded at 0.265 and 0.21, corresponding to reductions of 28% and 27%; and the mean MSEs are 0.125 and 0.083, indicating substantial reductions of 84% and 47%.
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Buckling failure process and stress-structure control mechanism of thinly layered surrounding rock in deep roadways
KONG Rui, ZHU Jia-cheng, JIANG Quan, WANG Xiao-nan, DING Yong, WANG Xin
Rock and Soil Mechanics. 2026, 47 (10):  3589-3601.  DOI: 10.16285/j.rsm.2025.1098
Abstract ( 23 )  
To address the buckling failure observed in the thinly layered surrounding rock of deep roadways at the Sishanling iron mine, a comprehensive approach encompassing field investigation, in situ monitoring, and theoretical analysis was adopted. This study summarized the characteristics of buckling failure, elucidated the control effects and mechanisms of stress and structural factors on such failure, and proposed corresponding prevention and control strategies. The results indicate that the buckling failure evolution process can be summarized into four stages, including crack initiation, slab formation through splitting, rock slab buckling, and ultimate fracturing accompanied by collapse. During excavation, an increased stress differential in the surrounding rock facilitates crack propagation and eventual coalescence within the rock mass, thereby forming multilayer rock slabs. These slabs subsequently undergo bending and fracturing toward the free face under multidirectional loading. Buckling failure is a stress-structure controlled failure mode, wherein both lateral stress and normal stress contribute to the bending and fracturing of rock slabs. Due to stress gradient distribution, rock slab fracturing preferentially occurs in the high-stress concentration areas within the surrounding rock. Moreover, a smaller included angle between the bedding plane strike and roadway axis promotes crack propagation along bedding planes. It is recommended to adopt the cracking suppression concept to control the buckling failure through two measures: strengthening the support and optimizing the stope layout direction. This study contributes to ensuring safe and efficient mining at Sishanling iron mine and provides a reference for failure analysis and the prevention of similar layered rock mass engineering.
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Near-wellbore stress field evolution and sand production prediction in sandstone gas reservoir storage: a case study of the X23 storage
YUAN Wu-tao, JIA Shan-po, WEN Cao-xuan, LIU Tuan-hui, CHEN Zhi-xin, WANG Wei, ZHAI Yu-jia
Rock and Soil Mechanics. 2026, 47 (10):  3602-3614.  DOI: 10.16285/j.rsm.2025.1120
Abstract ( 26 )  
Sandstone reservoirs are the principal type of underground hydrocarbon storage reservoirs. Cyclic injection and production in underground gas-storage facilities increase rock damage and sand production. Understanding the critical drawdown pressure for reservoir sand production supports safe and stable operation. The distribution and evolution of stress fields in reservoirs under cyclic injection-production form the foundation for studying sand production. Based on elastic mechanics, the evolution patterns of stress fields in both distant- and near-wellbore reservoirs were derived. Utilizing cyclic damage theory, a critical drawdown pressure model was developed. The study specifically analyzed the influence of parameters such as stress field mechanism, distance from the wellbore center, and annular angle on the evolution of stress fields in near-wellbore reservoirs. Taking the X23 gas storage reservoir project as an example, stepwise cyclic mechanical tests were designed and conducted, leveraging stress concentration in the near-wellbore region and gas-water interface characteristics. The trend of critical drawdown pressure with injection-production cycle frequency was analyzed, and a critical drawdown pressure chart was developed based on actual production curves. Results indicate that reservoirs with lower water saturation and finer grain size exhibit greater resistance to cyclic damage. Damage accumulates with increasing cycle count. The critical drawdown pressure at the upper operating pressure limit decreased monotonically from 22.4 MPa to 10.5 MPa, while at the lower operating pressure limit it decreased monotonically from 15.8 MPa to 3.9 MPa. This study provides a novel approach for designing cyclic damage experiments in gas storage reservoirs, refines the critical drawdown pressure formula for sand production, and guides drawdown pressure control during injection and production operations in gas storage facilities.
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Time-dependent evolution and failure mechanism of surrounding rock stress in multiple disturbance dynamic pressure roadways
XU Dong, WANG Xin-xu, GAO Ming-shi, CUI Jiang-yi
Rock and Soil Mechanics. 2026, 47 (10):  3615-3632.  DOI: 10.16285/j.rsm.2026.0202
Abstract ( 33 )  
To tackle the challenges posed by significant large deformation and intense dynamic pressure in roadway surrounding rock subjected to multiple disturbances, this study delves into an analysis of the deformation and failure characteristics along with their influencing factors. A disturbance response instability model of the roadway surrounding rock is developed, revealing the deformation and failure mechanism under multiple disturbances and dynamic pressure. The time-dependent evolution characteristics of stress within the surrounding rock are clarified. Furthermore, a collaborative “unloading-supporting” prevention and control technology is proposed. Research findings indicates that the deformation and failure of surrounding rock in roadways subjected to multiple disturbances and dynamic pressure are governed by a combination of force source, structural, and physical property factors. The degree of damage to the surrounding rock is directly proportional to the deviatoric stress and the shock source energy, and inversely proportional to the critical failure stress of the roadway and the stress wave propagation distance. Under the influence of multiple disturbances, the deviatoric stress within the surrounding rock undergoes both clockwise and counterclockwise rotations, leading to stress transfer and intensification, with a weak failure zone forming at the stress concentration areas near the shoulder and bottom corners of the roadway. Dynamic loading exacerbates the differential failure of the surrounding rock, which evolves over time under static load conditions. The maximum acceleration of the surrounding rock increases exponentially with rising shock source energy. Moreover, multiple disturbances lower the critical impact failure energy of the roadway, enabling lower impact energies to induce dynamic load failure. The axial force of bolts and cables in the surrounding rock increases exponentially with both the disturbance coefficient and the shock source energy. When the shock source energy surpasses the critical impact energy and the disturbance coefficient rises, the stress response of the bolts and cables escalates accordingly. Three-dimensional pressure relief technology applied to roadway surrounding rock can fracture the far-field shock source layer, alter the near-field stress transfer path, and achieve active regulation of the stress distribution characteristics of the surrounding rock. The full-section targeted control support technology enhances the synergistic support and deformation synchronization of surrounding rock across different layers and key areas. Following the implementation of the “unloading-supporting” collaborative prevention and control measures in the field, the deformation of roadway surrounding rock under multiple disturbances was reduced by 36.1%-76.0%, and the stress level decreased by 12.3%-31.4%. The plastic zone was significantly reduced, and roadway stability was markedly improved.
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Numerical Analysis
Numerical investigation of water/supercritical CO₂ fracturing mechanisms in hot dry rock with pre-existing fractures
YU Hai-tao, ZHANG Gai, YAN Xiao, JIANG Wen-he, WANG Hai-bo, LI Shuan
Rock and Soil Mechanics. 2026, 47 (10):  3633-3650.  DOI: 10.16285/j.rsm.2025.1171
Abstract ( 30 )  

Water-enhanced geothermal system (EGS) and CO2-EGS are currently the primary technologies for geothermal resource extraction in hot dry rock (HDR) reservoirs. The presence of natural fractures in high-temperature HDR reservoirs significantly affects the fracture propagation path, and the interactions between fracturing fractures and natural fractures are closely related to the fracturing fluid. However, compared to conventional hydraulic fracturing, the interaction patterns and mechanisms between fractures during supercritical CO2 (ScCO2) fracturing in HDR reservoirs remain unclear in existing studies. Moreover, there is a lack of comparative analysis on the fracture interaction patterns and mechanisms between hydraulic fracturing and ScCO2 fracturing in the presence of natural fractures. A thermo-hydro-mechanical-damage coupled model is developed to simulate the interaction between fractures during water/ScCO2 fracturing in a HDR reservoir, which is validated by experimental results. Numerical simulations are then conducted under different in-situ conditions (horizontal stress difference, natural fracture inclination angle, cementation strength) and operational parameters (injection temperature and injection rate). The results show that the interaction patterns can be categorized into three types: turning along natural fractures, offsetting and crossing, and penetration through natural fractures. Compared to low-temperature water injection, the thermal stress induced by low-temperature ScCO2 reduces the initiation pressure and extension pressure by 17.86% and 0.9%, respectively, for every 10 °C decrease in injection temperature. Under high-temperature environments, ScCO2 has significantly higher permeability than water, allowing it to more effectively diffuse into micro-pores and connect natural fractures. This leads to intersecting fractures under varying reservoir horizontal stress differences, natural fracture inclination angles and injection rate conditions during ScCO2 fracturing. Additionally, the study further reveals that ScCO2 fracturing is suitable for deep, high-temperature, naturally fractured geothermal reservoirs with moderate to low cementation strength, facilitating the development of complex fracture networks. In contrast, hydraulic fracturing is more appropriate for intervals characterized by high cementation strength or elevated stress differences, where strict control over fracture propagation paths is required. These findings provide theoretical guidance for the rational selection of fracturing fluids and optimization of fracture network morphology in geothermal reservoir stimulation.

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A comparison of numerical and theoretical results for critical stresses of the roadway surrounding rock for different type-Ⅱ fracture energies and internal frictional angles
WANG Zhi-han, LI Hai-bin, WANG Xue-bin, PAN Yi-shan, LIU Dong, ZHENG Yi-fang
Rock and Soil Mechanics. 2026, 47 (10):  3651-3661.  DOI: 10.16285/j.rsm.2025.1108
Abstract ( 36 )  
The transition from qualitative to quantitative analysis of rockbursts has been achieved, but assuming a completely failed medium within the ring-shaped softening zone is inconsistent with typical localized failure. We combined the StrataKing-3D parallel computing system for strata movement with the disturbance response instability theory of rockbursts, demonstrating broad applicability. However, only a simplified formula for the critical stress is adopted. For the common square tunnel in coal mines, effects of the type-Ⅱ fracture energy and internal frictional angle were investigated numerically, and the numerical critical stress was compared with the theoretical critical stress based on the complete formula. The ratio of numerical critical stress to theoretical critical stress was defined as a modification coefficient. For different type-Ⅱ fracture energies, the occupied region by the modification coefficient versus uniaxial compressive strength curves likes a trumpet, narrow on the left and wide on the right, indicating that a lower uniaxial compressive strength (or internal frictional angle) leads to the fact that the numerical result is closer to the theoretical result. The maximum numerical critical stress is less than 2.24 times the theoretical result. When the type-Ⅱ fracture energy is 200 N/m, the numerical result is closer to the theoretical result. For lower type-Ⅱ fracture energies (100–200 N/m), burst energy index ranges from 0.381 to 8.107, which largely falls within the survey data from 131 rockburst coal mines in China. Rockburst mines with burst energy index of 0–8 are the most prevalent. This suggests that the adopted type-Ⅱ fracture energy is appropriate. Under this condition, the numerical result is usually higher than the theoretical result. This can be explained through the viewpoint that the localized surrounding rock can possess a higher load-carrying capacity than the surrounding rock subjected to uniform failure. The difference between numerical and theoretical results is deepened in this study, laying a foundation for more accurate roadway safety assessment.
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Time domain boundary element method for solving transient fluid-structure coupling problems in porous elastic media
ZHAO Feng, LUO Jun-cheng, ZENG Qi-hua, LEI Wei-dong, LI Hong-jun, LIN Jian
Rock and Soil Mechanics. 2026, 47 (10):  3662-3670.  DOI: 10.16285/j.rsm.2025.1068
Abstract ( 32 )  
In this paper, the time-domain boundary element method is employed to investigate transient fluid-structure interaction problems in porous elastic media. The proposed method automatically satisfies the far-field boundary condition at infinity, thus only necessitating boundary discretization, which renders it particularly well-suited for addressing problems characterized by infinite boundaries. Initially, the boundary integral equation for the transient fluid-structure interaction problem is derived from the governing partial differential equations that describe porous elastic media. Subsequently, numerical discretization is applied to the boundary integral equation, with a particular focus on accurately computing the Hadamard principal value of the element influence coefficients that exhibit strong singularities. This strategy effectively circumvents error accumulation in indirect numerical schemes and improves computational precision. Following this, second-order shape functions are adopted to determine the influence coefficients of semi-infinite elements, and the algebraic system corresponding to the boundary integral equation is constructed through assembly. Two representative numerical examples are used for validation purposes, wherein the numerical results generated by the proposed method are compared with analytical solutions. The results substantiate that the developed time-domain boundary element method is both applicable and reliable for solving transient fluid-structure interaction problems in porous elastic media.
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