A review of mechanical deformation and seepage mechanism of rock with filled joints

Abstract

	•In this study, the aim is to comprehensively understand the mechanical and seepage characteristics of filled rock joints.
	•We accurately evaluate the safety and stability of rock engineering.
	•We focus on the latest research on defective rock deformation and destruction mechanism.
	•A brief description of the seepage characteristics of fracture-filled rocks, revealing the role of stress–seepage coupling, is presented.
	•Future development trends of rock with filled fissures regarding rock damage, fracture mechanics, and fracture water emergence are envisioned.

Keywords

destruction mechanism / filled joints / hydraulic coupling / numerical simulations / seepage

References

[1] Ai-Yaarubi AH, Pain CC, Grattoni CA, Zimmerman RW. Navier-stokes simulations of fluid flow through a rock fracture. Dyn Flu Fra Rock. 2004;122:201.

[2] Baghbanan A, Jing L. Stress effects on permeability in a fractured rock mass with correlated fracture length and aperture. Int J Rock Mech Min Sci. 2008;45(8):1320-1334.

[3] Bai M, Elsworth D. Coupled Processes in Subsurface Deformation, Flow, and Transport. ASCE; 2000.

[4] Bai Y, Shan R, Ju Y, et al. Experimental study on the strength, deformation and crack evolution behavior of red sandstone samples containing two ice-filled fissures under triaxial compression. Cold Reg Sci. 2020;174:103061.

[5] Barton N. Review of a new shear-strength criterion for rock joints. Eng Geol. 1973;7(4):287-332.

[6] Brackbill TP, Kandlikar SG. Application of lubrication theory and study of roughness pitch during laminar, transition, and low Reynolds number turbulent flow at microscale. Heat Transfer Eng. 2010;31(8):635-645.

[7] Cai W, Wang Y, He F, Zhang P, Sun S. The seepage-destruction mechanism of water inrush channel of sandstone fault filling using the EDEM-fluent method. Adv Civ Eng. 2022;2022(1):3313013.

[8] Cen DF, Huang D. Mesoscopic displacement modes of crack propagation of rock mass under uniaxial compression with high strain rate. Coal J. 2014;39(3):436-444.

[9] Chai S, Wang H, Yu L, Shi J, Abi E. Experimental study on static and dynamic compression mechanical properties of filled rock joints. Lat Am J Solids Struct. 2020;17:e2600.

[10] Chang X, Dang F, Peng J. Failure behaviors of rock specimens containing a filled fissure under cyclic compression. Pure Appl Geophys. 2022;179(12):4541-4554.

[11] Chen JG, Zhang JF. Influence of mechanical responses of fillings on fracture seepage. Rock Soil Mech. 2006;27(4):577-580.

[12] Chen JG, Zhang L, Fan JW. Seepage-stress characteristics of brittle-plastic filled fracture. J Min Saf Eng. 2016;33(6):1103-1109.

[13] Chen JG, Zheng ZS, Zhang L. Seepage characteristics of fractures in coal rock filled with pulverized coal under confining pressure. Safety in Coal Mines. 2019;50(12):14-17.

[14] Chen JG, Zheng ZS, Zhang L, Wang JQ. The differential seepage-stress model of brittle-plastic filled fracture. Sci Tech Eng. 2019;19(13):228-234.

[15] Chen JT, Wu Q, Yin LM, Zhang WQ, Tan WF. Law of crack evolution in floor rock mass above high confined water. Coal Sci Tech. 2018;46(7):54-60.

[16] Chen LX, Guo WY, Zhang DX, Zhao TB. Experimental study on the influence of prefabricated fissure size on the directional propagation law of rock type-I crack. Int J Chin Univ Min Tech. 2022;160:105274.

[17] Chen Y, Wang CQ, Chen JG. Numerical simulation of expansion effect of full-filling medium in the fractured rock based on ANSYS. Saf Env Eng. 2012;19:115-118.

[18] Cheng J, Zhang H, Wan Z. Numerical simulation of shear behavior and permeability evolution of rock joints with variable roughness and infilling thickness. Geofluids. 2018;2018(1):1869458.

[19] Cotecchia F, Vitone C, Santaloia F, Pedone G, Bottiglieri O. Slope instability processes in intensely fissured clays: case histories in the Southern Apennines. Landslides. 2015;12:877-893.

[20] Cui J, Feng G, Li Z, et al. Failure analysis of sandstone with filled and unfilled cross-flaws under uniaxial compression. Arab J Sci Eng. 2022;47(10):13435-13449.

[21] Cui J, Feng G, Li Z, Han Y, Song C. Failure analysis of rock with filled and unfilled flaws under excavation stress path. J Central South Univ. 2023;30:175-188.

[22] Davies MCR, Hamza O, Lumsden BW, Harris C. Laboratory measurement of the shear strength of ice-filled rock joints. Ann Glaciol. 2000;31:463-467.

[23] Detwiler RL, Morris JP. Transmissivity anisotropy in rough-walled fractures: the combined influence of shear offset and normal deformation. In 48th US Rock Mech/GM Sym. ARMA; 2014.

[24] Dong JB. LBM Simulations and Experimental Validations of Fluid Flow through Single Fractures in Rock Media. Doctoral Dissertation. China University of Mining and Technology; 2020.

[25] Du Y, Li T, Wang B, et al. Experimental study on mechanical characteristics and permeability evolution during the coupled hydromechanical failure of sandstone containing a filled fissure. Acta Geotech. 2023;18(8):4055-4075.

[26] Esaki T, Du S, Mitani Y, Ikusada K, Jing L. Development of a shear-flow test apparatus and determination of coupled properties for a single rock joint. Int J Rock Mech Min Sci. 1999;36(5):641-650.

[27] Fan H, Xie YT, Zhou H, Lu JJ, Wang C. Seepage characteristics in shear fracture of marble. J Shenyang Ind Univ. 2020;42(4):464-469.

[28] Fan X, Chen R, Lin H, Lai H, Zhang C, Zhao Q. Cracking and failure in rock specimen containing combined flaw and hole under uniaxial compression. Adv Civ Eng. 2018;2018(1):1-15.

[29] Fereshtenejad S, Song JJ. Fundamental study on applicability of powder-based 3D printer for physical modeling in rock mechanics. Rock Mech Rock Eng. 2016;49:2065-2074.

[30] Fu JW, Liu SL, Zhu WS, Zhou H, Sun Z. Experiments on failure process of new rock-like specimens with two internal cracks under biaxial loading and the 3-D simulation. Acta Geotech. 2018;13:853-867.

[31] Gan L, Jin HJ, Shen ZZ, Ma HY, Xu LQ. Experimental investigation on seepage characteristics of limestone fractures with different roughness and filling gap width. Chin J Rock Mech Eng. 2023;42(Supp 2):3415-3424.

[32] Gao G, Yao W, Xia K, Li Z. Investigation of the rate dependence of fracture propagation in rocks using digital image correlation (DIC) method. Eng Fract Mech. 2015;138:146-155.

[33] Ghirian A, Fall M. Coupled thermo-hydro-mechanical–chemical behaviour of cemented paste backfill in column experiments. Part I: physical, hydraulic and thermal processes and characteristics. Eng Geol. 2013;164:195-207.

[34] Ghirian A, Fall M. Coupled thermo-hydro-mechanical–chemical behaviour of cemented paste backfill in column experiments. Eng Geol. 2014;170:11-23.

[35] Gong CG, Wang W, Shao JF, Wang RB, Feng XW. Effect of water chemical corrosion on mechanical properties and failure modes of pre-fissured sandstone under uniaxial compression. Acta Geotech. 2021;16:1083-1099.

[36] Grasselli G. Manuel Rocha medal recipient shear strength of rock joints based on quantified surface description. Rock Mech Rock Eng. 2006;39(4):295-314.

[37] Guo BH, Cheng T, Chen Y, Jiao F. Seepage characteristics of marble fissures and the influence of sand-filled soils. J Water Resour. 2019;50(4):63-474.

[38] Haeri H, Shahriar K, Marji MF, Moarefvand P. Cracks coalescence mechanism and cracks propagation paths in rock-like specimens containing pre-existing random cracks under compression. J Central South Univ. 2014;21:2404-2414.

[39] Indraratna B, Jayanathan M, Brown ET. Shear strength model for overconsolidated clay-infilled idealised rock joints. Géotechnique. 2008;58(1):55-65.

[40] Indraratna B, Welideniya HS, Brown ET. A shear strength model for idealised infilled joints under constant normal stiffness. Géotechnique. 2005;55(3):215-226.

[41] Jiang Q, Feng X, Gong Y, Song L, Ran S, Cui J. Reverse modelling of natural rock joints using 3D scanning and 3D printing. Comput Geotech. 2016;73:210-220.

[42] Jiang YJ, Wang G, Li B, Zhao XD. Experimental study and analysis of shear-flow coupling behaviors of rock joints. Chin J Rock Mech Eng. 2007;26(11):2253-2259.

[43] Jiao F, Guo BH, Zhai ML. Empirical formula for shear strength of marble joints infilled with sands. Rock Soil Mech. 2018;39(11):4102-4108.

[44] Jiao F, Guo BH, Zhai ML, Cheng T, Dong HY. Experimental study on shear strength of marble joint filled with sand. Chin J Ug Space Eng. 2019;15(2):352-357.

[45] Jiao F, Xu J, Guo BH, Peng SJ, Yan FZ, Chen YA. A shear test study on the influence of filled thickness on the shear strength of rock joints. J Min Saf Eng. 2022;39(2):405-412.

[46] Kacimov AR, Yakimov ND. 2-D Darcian flow in vicinity of permeable fracture perturbing unidirectional flow in homogeneous formation. J Eng Math. 2019;118(1):15-28.

[47] Kang SL, Yang JS, Yang F. Macro-and-meso analysis of failure behavior of rock-like samples with flaws using a numerical method. J Yz Riv Sci Res Ins. 2016;33(4):71-77.

[48] Kang ZQ, Zhang XY, Zhao JM, Zhang SQ. Effects of “S” type fractured rock anchoring and the distribution rule of stress field. Metal Mine. 2014;1(1):46-49.

[49] Kelsall PC, Case JB, Chabannes CR. Evaluation of excavation-induced changes in rock permeability. Int J Rock Mech Min GM Abs. 1984;21(3):123-135.

[50] Koyama T, Li B, Jiang Y, Jing L. Coupled shear-flow tests for rock fractures with visualization of the fluid flow and their numerical simulations. Int J Geotech Eng. 2008;2(3):215-227.

[51] Larmagnat S, Des Roches M, Daigle LF, et al. Continuous porosity characterization: metric-scale intervals in heterogeneous sedimentary rocks using medical CT-scanner. Mar Petrol Geol. 2019;109:361-380.

[52] Lee H, Jeon S. An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial com-pression. Int J Solids Struct. 2011;48(6):979-999.

[53] Li B, Wang JF, Liu YC, Wu FQ. Deformation, failure and nonlinear flow characteristics of a fracture subject to normal stress and shear displacement. Adv Eng Sci. 2021;6:103-112.

[54] Li KS, Luan YQ, Zhang JP, Liu CX. Experimental study on mechanical behavior, AE response and energy evolution of fissure-filled sandstone from mine roadway under conventional triaxial compression. Theor Appl Fract Mec. 2024;130:104334.

[55] Li LP, Li SC, Shi SS, Xu ZH. Water inrush mechanism study of fault activation induced by coupling effect of stress-seepage-damage. Chin J Rock Mech Eng. 2011;30(Supp 1):3295-3304.

[56] Li LP, Liu S, Li SC, et al. Development of testing system for coupled seepage and triaxial stress measurements and its application to permeability characteristic test on filling medium. Rock Soil Mech. 2017;38(10):3053-3061.

[57] Li S, Xiong ZM, Liu YM, Li ZH. Mechanical property and damage constitution of different thickness of backfill-surrounding rock combination. Sci Tech Eng. 2022;33:14841-14851.

[58] Li SJ, Wang LG, Lu YL, Zhang B. Slurry diffusion within cracked wall rock during the bolt grouting process. J Chin Univ Min Tech. 2011;40(6):874-880.

[59] Li T, Du Y, Zhu Q, Ran J, Zhang H, Xing X. Experimental study on strength properties, fracture patterns, and permeability behaviors of sandstone containing two filled fissures under triaxial compression. Bull Eng Geol Environ. 2021;80(7):5921-5938.

[60] Li XL, Zhang FY, Ding PP, Zhang L, Zhou JW, Lu GD. Coupled the rmo-hydro-mechanical-chemical model for overpressure evolution in accreting mine fills. J Eng Geol. 2020;5:1132-1139.

[61] Li Z. Study on Seepage and Diffusion of Rough Rock Fracture Based on Fractural Theory. Master Dissertation. Tianjin University; 2019.

[62] Lin ZB, Yang DF, Li YH. Influence on deformation and fracture of tunnel surrounding rock under different distribution forms of single fracture. J Henan Poly Univ (Nat Sci). 2017;36(1):114-121.

[63] Liu C. DEM-SPH Based Method for Modelling Water Inrush Disaster Due to Seepage-Erosion-Stress Coupling Instability of Filling Structure in Tunnels. Doctoral Dissertation. Shandong University; 2021.

[64] Liu CH, Chen CX, Fu SL. Experimental study of seepage patterns under shear displacement in sand-filled fissures. Chin J Rock Mech Eng. 2002;21(10):1457-1461.

[65] Liu CH, Chen CX, Fu SL. Study on seepage characteristics of a single rock fracture under shear stresses. Chin J Rock Mech Eng. 2003;22(10):1651-1655.

[66] Liu FN. Study on the Multi-Crack Initiation, Extension, and Connection Mechanism in Soft and Hard Rocks Based on Digital Image Technology. Master Dissertation. Chongqing University; 2016.

[67] Liu J, Elsworth D, Brady BH, Muhlhaus HB. Strain-dependent fluid flow defined through rock mass classification schemes. Rock Mech Rock Eng. 2000;33:75-92.

[68] Liu J, Li JL, Wang RH, Zhu T, Qu JJ, Zhao ZY. Experimental study of seepage in YICHANG fractured sandstone with tight original rock fillings. Chin J Rock Mech Eng. 2010;29(2):366-374.

[69] Liu XY, Liu AH, Li XB. Experimental study of columnar jointed sandstone-like material with preset filling. Chin J Rock Mech Eng. 2014;33(4):772-777.

[70] Liu XY, Tian Y, Zhu ZD. Seepage damage statistical model of filled fractured rock considering structural surface and failure characteristic. Adv Civ Eng. 2021;2021:1-9.

[71] Liu XY, Zhu ZD, Liu AH. Permeability characteristic and failure behavior of filled cracked rock in the triaxial seepage experiment. Adv Civ Eng. 2019;2019(1):3591629.

[72] Lu YL. Hydro-Mechanical Modeling of Fracturing Evolution in Rocks and Mechanism of Water-Inrush from Coal Seam Floor. Doctoral Dissertation. Xuzhou: China University of Mining and Technology; 2013.

[73] Luo X, Cao P, Lin Q, Li S. Mechanical behaviour of fracture-filled rock-like specimens under compression-shear loads: an experimental and numerical study. Theor Appl Fract Mech. 2021;113:102935.

[74] Miao S, Pan PZ, Wu Z, Li S, Zhao S. Fracture analysis of sandstone with a single filled flaw under uniaxial compression. Eng Fract Mech. 2018;204:319-343.

[75] Miao S, Pan PZ, Zhao S, Han J, Konicek P. A new DIC-based method to identify the crack mechanism and applications in fracture analysis of red sandstone containing a single flaw. Rock Mech Rock Eng. 2021;54:3847-3871.

[76] Miao XX, Liu WQ, Chen ZQ. Seepage Theory of Mining Rock Mass. Science Press; 2004.

[77] Mohanty S, Das RR. Influence of polymeric resin-infilling on onset and fracture growth along wing trajectory in open-flawed sandstone specimen. Theor Appl Fract Mech. 2023;125:103836.

[78] Morgan SP, Einstein HH. Cracking processes affected by bedding planes in Opalinus shale with flaw pairs. Eng Fract Mech. 2017;176:213-234.

[79] Morgan SP, Johnson CA, Einstein HH. Cracking processes in barre granite: fracture process zones and crack coales-cence. Int J Fract. 2013;180(2):177-204.

[80] Olsson R, Barton N. An improved model for hydromechanical coupling during shearing of rock joints. Int J Rock Mech Min Sci. 2001;38(3):317-329.

[81] Pan DD, Li SC, Xu ZH, et al. Seepage calculation model and numerical analysis of rock fracture considering effect of contact area and clastic rock. J Cent South Univ (Nat Sci Edit). 2019;50(7):1677-1685.

[82] Park CH, Bobet A. Crack initiation, propagation and coalescence from frictional flaws in uniaxial compression. Eng Fract Mech. 2010;77(14):2727-2748.

[83] Qian J, Chen Z, Zhan H, Guan H. Experimental study of the effect of roughness and Reynolds number on fluid flow in rough-walled single fractures: a check of local cubic law. Hydrol Process. 2011;25(4):614-622.

[84] Rutqvist J, Stephansson O. The role of hydromechanical coupling in fractured rock engineering. Hydro J. 2003;11:7-40.

[85] Sagong M, Bobet A. Coalescence of multiple flaws in a rock-model material in uniaxial compression. Int J Rock Mech Min Sci. 2002;39(2):229-241.

[86] Shan R, Bai Y, Ju Y, Han T, Dou H, Li Z. Study on the triaxial unloading creep mechanical properties and damage constitutive model of red sandstone containing a single ice-filled flaw. Rock Mech Rock Eng. 2021;54:833-855.

[87] Shao J, Zhang Q, Wu X, Lei Y, Wu X, Wang Z. Investigation on the water flow evolution in a filled fracture under seepage-induced erosion. Water. 2020;12(11):3188.

[88] Sheng JC, Gao P, Wang K, Gao HC, Tian XD. Experiments of seepage erosion influence on shear characteristics of rock fracture. Adv Sci Tech Water Res. 2021;41(2):42-48.

[89] Si JM, He JW. Experimental study on the damage of rocks containing filled fissures based on VIC-3D. Min Res Dev. 2019;39(1):68-71.

[90] Su BY, Zhan ML, Zhang ZT. Experimental research of seepage characteristic for filled fracture. Rock Soil Mech. 1994;15(4):46-52.

[91] Sun GZ. Mechanics of Rock Structures. Science Press; 1988.

[92] Sun GZ, Sun Y. Principle of Rock Mass Mechanics. Science Press; 2011.

[93] Sun TF, She CX, Wang LT. A peak shear strength model for cement filled rock joints. Chin J Rock Mech Eng. 2014;33(12):2481-2489.

[94] Sun W, Wang S, Dong F, Xue Y. Study of single fracture seepage characteristics of fault-filled materials based on CT technology. Water-SUI. 2022;14(22):3679.

[95] Tan WH, Wang PF. Experimental study on seepage properties of jointed rock-like samples based on 3D printing techniques. Adv Civ Eng. 2020;2020(1):9403968.

[96] Tang Z, Liu Q, Huang J. New criterion for rock joints based on three-dimensional roughness parameters. J Central South Univ. 2014;21(12):4653-4659.

[97] Tang ZC, Xia CC, Song YL, Liu T. Discussion about Grasselli’s peak shear strength criterion for rock joints. Chin J Rock Mech Eng. 2012;31(2):356-364.

[98] Tao TK. Characterization of water flow in filled fissures. Sci R Wtr Res Wtr Trans. 1995;1995(1):23-32.

[99] Tian KM, Chen MY, Wang HL. Fissure Water Bias Flow. Xueyuan Press; 1989.

[100] Tian WL, Yang SQ. Experimental and numerical study on the fracture coalescence behavior of rock-like materials containing two non-coplanar filled fissures under uniaxial compression. Geomech Eng. 2017;12(3):541-560.

[101] Tian Y, Liu Q, Ma H, Liu Q, Deng P. New peak shear strength model for cement filled rock joints. Eng Geol. 2018;233:269-280.

[102] Tzelepis V, Moutsopoulos KN, Papaspyros JNE, Tsihrintzis VA. Experimental investigation of flow behavior in smooth and rough artificial fractures. J Hydrol. 2015;521:108-118.

[103] Vaclav H, Jan S. Ground Water Hydraulics. Amsterdam; 1979.

[104] Wang C, Li Y, Dai F, et al. Experimental investigation on mechanical properties and failure mechanism of rock-like specimens containing an arc-shaped ice-filled flaw under uniaxial compression. Theor Appl Fract Mech. 2022;119:103368.

[105] Wang G, Huang N, Jiang YJ, Li B, Wu XZ, Zhang XP. Seepage calculation model for rough joint surface considering fractal characteristics. Chin J Rock Mech Eng. 2004;33(Supp 2):3397-3405.

[106] Wang GL, Liu WQ, Tao Y. Experimental study of permeability in fractured sandstone with sediment particles. Mech P. 2010;32(5):14-17.

[107] Wang J, Fu JX, Song WD, Zhang YF, Wang Y. Particle flow simulation of mechanical properties and micro-crack evolution characteristics of rock-backfill combined model. J Chin Univ Min Technol. 2020;3:453-462.

[108] Wang JX, Hu LS, Zhang J, Tang YQ, Yang P. Research on seepage-stress coupling mode in tunnel with high water pressure. Rock Soil Mech. 2008;29(Supp 1):237-240.

[109] Wang P, Liu Q, Zhang Y, Huang Z. Identifying rock fracture precursor by multivariate analysis based on the digital image correlation technique. Theor Appl Fract Mech. 2023;126:103987.

[110] Wang PT, Liu Y, Zhang L, Huang ZJ, Cai MF. Preliminary experimental study on uniaxial compressive properties of 3D printed fractured rock models. Chin J Rock Mech Eng. 2018;37(2):364-373.

[111] Wang S, Zhang J, Li C, Li Z, Yu Y. Seepage characteristics of fractured rock mass with non-equal width filling under cyclic loading. Ain Shams Eng J. 2022;13(6):101794.

[112] Wang Y, Fu JX, Yang ZL. Study on fine-scale parameters of rock-fill coupling contact surfaces and their mechanical properties. Min R Devt. 2020;3:113-118.

[113] Wang Y, Zhang H, Lin H, Zhao Y, Li X, Liu Y. Mechanical behavior and failure analysis of fracture-filled gneissic granite. Theor Appl Fract Mech. 2020;108:102674.

[114] Wei D, Jinqiang L, Wei Z, Zenggui K, Tong Z, Yulin H. Typical characteristics of fracture-filling hydrate-charged reservoirs caused by heterogeneous fluid flow in the Qiongdongnan Basin, northern south China sea. Mar Petrol Geol. 2021;124:104810.

[115] White WB. Geomorphology and Hydrology of Karst Terrain. Oxford University Press; 1988.

[116] Wong LNY, Einstein HH. Systematic evaluation of cracking behavior in specimens containing single flaws under uniaxial compression. Int J Rock Mech Min Sci. 2009;46(2):239-249.

[117] Wong RHC, Chau KT. Crack coalescence in a rock-like material containing two cracks. Int J Rock Mech Min Sci. 1998;35(2):147-164.

[118] Wong RHC, Chau KT, Tang CA, Lin P. Analysis of crack coalescence in rock-like materials containing three flaws-part I: experimental approach. Int J Rock Mech Min Sci. 2001;38(7):909-924.

[119] Wu DY, Yu LY, Su HJ, Wu JY, Liu RC, Zhou J. Experimental study and PFC^3D simulation on crack propagation of fractured rock-like specimens with bolts under uniaxial compression. Rock Soil Mech. 2021;42(6):1681-1692.

[120] Wu WL, Liu GS, Guo LJ, Fan C, Zhang ZH, Zhang XM. Experimental investigation on interface mechanical properties between cemented paste backfill and rock based on direct shear tests. Chin Min Ind. 2019;28(12):116-122.

[121] Wu X, Wang F, Xi X, Guo QF, Sun JL, Wang XL. Experimental investigation on the strength characteristics and fracture mechanism of rock with orthogonally crossed cracks. J Chin C Soc. 2020;45(7):2681-2690.

[122] Wu X, Zheng H, Wang G, Zhou Y, Guan Z. Effect of joint roughness and infill thickness on shear characteristics of rock mass. Adv Civ Eng. 2022;2022(1):1991188.

[123] Wu Y, Dong Q, He J, Chen Q. Performance of rock-like materials containing filled kinked fissures under uniaxial tension at failure. KSCE J Civil Eng. 2023;27(3):1205-1223.

[124] Wu YQ, Zhang ZY. Introduction to Rock Hydraulics. Southwest Jiaotong University Press; 1995.

[125] Wu Z, Wang S, Chen J, et al. Fracture propagation modes of lower Cambrian shale filled with different quartz contents under seepage-stress coupling. Geofluids. 2022;2022(1):1051284.

[126] Xia CC. Mechanics of Engineering Rock Joints. Tongji University; 2002.

[127] Xia CC, Tang ZC, Xiao WM, Song YL. New peak shear strength criterion of rock joints based on quantified surface description. Rock Mech Rock Eng. 2014;47(2):387-400.

[128] Xiao WM, Yu H, Zhu ZY, Li R, Liu WC. Experimental study on shear dilatancy characteristics of thinly-infilled rock joints. Chin J Geotech Eng. 2020;42(8):1499-1508.

[129] Xiong XB, Li B, Jiang YJ, Zhang CH. Flow mechanism test on single rock fracture and its three-dimensional numerical simulation. Chin J Rock Mech Eng. 2010;29(11):2230-2238.

[130] Xu J, Lei J, Liu YX, Wu JY. Experimental study on the shear behavior of joints filled with different materials. Rock Soil Mech. 2019;40(11):4219-4137.

[131] Xu J, Wu JY, Liu YX, Lei J. Experimental study of shear-seepage coupling properties of rock mass under different filling degrees. Rock Soil Mech. 2019;9:3416-3424+3434.

[132] Xu LH, Xie N. Test and theoretical research on permeability characteristics of shear fracture in rock mass. Chin J Rock Mech Eng. 2009;28(11):2249-2257.

[133] Xu Q, Yu YQ. Corrected cubic law for rock fracture seepage and its application. J Wuhan Univ. 2022;2022:1-9.

[134] Xu WY, Yang SQ. Experiment and modeling investigation on shear rheological property of joint rock. Chin J Rock Mech Eng. 2005;24(Supp 2):5536-5542.

[135] Xu WZ, Lin H, Cao RH. Simulation and macro-mesoscopic parameter analysis for direct shear of filled rough joints. J SW Jiaotong Univ. 2018;53(3):548-557.

[136] Xue LL, Chen SH. Coupling analysis of seepage and stress-strain of rock fracture during shear process. Chin J Rock Mech Eng. 2007;26(Supp 2):3912-3919.

[137] Yang J, Rong G, Cheng L, Hou D, Wang XJ. Experimental study of peak shear strength of rock joints. Chin J Rock Mech Eng. 2015;34(5):884-894.

[138] Yang J, Rong G, Hou D, Peng J, Zhou C. Experimental study on peak shear strength criterion for rock joints. Rock Mech Rock Eng. 2016;49:821-835.

[139] Yang Q, Wang YL, Ma YY. Distribution rule and influencing factors of geological disasters from 2001 to 2019 in China. Geol Haz Env Prot. 2020;4:43-48.

[140] Yang RS, Wang MY, Yang Y, Wang JG. Simulation material experiment on the dynamic mechanical properties of jointed rock affected by joint-filling material. Vib Shk. 2016;35(12):125-131.

[141] Yang SQ, Huang YH, Tian WL, Zhu JB. An experimental investigation on strength, deformation and crack evolution behavior of sandstone containing two oval flaws under uniaxial compression. Eng Geol. 2017;217:35-48.

[142] Yang TH, Liu J, Zhu WC, Elsworth D, Tham LG, Tang CA. A coupled flow-stress-damage model for groundwater outbursts from an underlying aquifer into mining excavations. Int J Rock Mech Min Sci. 2007;44(1):87-97.

[143] Ye F, Duan JC, Fu WX, Yuan XY. Permeability properties of jointed rock with periodic partially filled fractures. Geofl. 2019;2019(1):4039024.

[144] Ye Z, Liu X, Dong Q, Wang E, Sun H. Hydro-damage properties of red-bed mudstone failures induced by nonlinear seepage and diffusion effect. Water. 2022;14(3):351.

[145] Yin F, Li Y, Li K, et al. Mechanical behaviors and failure mechanism of flawed sandstone containing infillings under freeze-thaw cycles and uniaxial compression. Theor Appl Fract Mech. 2023;126:103979.

[146] Yin P, Wong RHC, Chau KT. Coalescence of two parallel pre-existing surface cracks in granite. Int J Rock Mech Min Sci. 2014;68:66-84.

[147] Yin Q. Experimental Study on Hydraulic Properties of Fractured Rock Mass in Complex Stress State. Doctoral Dissertation, China University of Mining and Technology; 2017.

[148] Yin Q, Jing H, Zhu T, Wu L, Su H, Yu L. Spatiotemporal evolution characteristics of fluid flow through large-scale 3d rock mass containing filling joints: an experimental and numerical study. Geofl. 2021;2021:1-23.

[149] Yin Q, Jing HW, Su HJ, Zhang K, Zhu TT. Strength characteristics and crack coalescence evolution of granite specimens containing orthogonal filling fissures under uniaxial compression. J Chin Univ Min Tech. 2016;45(2):225-232.

[150] Yin WT. Experimental research on the fracture distribution characteristics of fractured subsequently-filled granite. Chin J Rock Mech Eng. 2023;42(9):2203-2211.

[151] Yin WT, Zhao YS, Feng ZJ. Experimental research on permeability of fractured-subsequently-filled granite under high temperature and triaxial stresses. Chin J Rock Mech Eng. 2020;39(11):2234-2243.

[152] Yu L, Tao TK. Laws governing the movement of water flowing through rock fissures. Sci Res Wtr Res Wtr Transp. 1997;3:208-218.

[153] Yu X, Tan YY, Song WD, Wang J. Strength and failure mechanism of the rock-encased by backfills structure. J Chin Univ Min Tech. 2023;52(1):30-42.

[154] Yuan Y. Study on Uniaxial Compressive Rupture Process of Hard Rock with Filled Fissures. Master Dissertation, Hubei University of Technology; 2017.

[155] Yuan Y, Pan PZ, Zhao SK, Wang B, Song GH. The failure process of marble with filled crack under uniaxial compression based on digital image correlation. Chin J Rock Mech Eng. 2018;37(2):339-351.

[156] Zafar S, Hedayat A, Moradian O. Micromechanics of fracture propagation during multistage stress relaxation and creep in brittle rocks. Rock Mech Rock Eng. 2022;55(12):7611-7627.

[157] Zhang J, Xi X, Guo QF, Wu XH. Meso multi-phase particle flow simulation of granite failure with preexisting crack. J Huazhong Univ Sci Tech. 2021;4:79-85.

[158] Zhang JF, Chen JG, Zhang SX. Numerical simulation of hydraulic effect of fracture fillings on deformation of surrounding rocks. J Min Safe Eng. 2008;3:318-321.

[159] Zhang K, Zhang K, Liu WL, Xie JB. A novel DIC-based methodology for crack identification in a jointed rock mass. Mater Design. 2023;230:111944.

[160] Zhang L, Chen JG, Han JJ. Effect of microstructure on seepage-stress characteristics of half-filled fracture. Safe Env Eng. 2015;4:160-163.

[161] Zhang S. Mechanisms of Ordered Multi-Crack Initiation, Expansion and Connectivity in Rock-like Materials Based on Digital Imaging Techniques. Master Dissertation. Chongqing University; 2016.

[162] Zhang XP, Wong LNY. Cracking processes in rock-like material containing a single flaw under uniaxial compression: a numerical study based on parallel bonded-particle model approach. Rock Mech Rock Eng. 2012;45:711-737.

[163] Zhang YT. Rock Hydraulics and Engineering. China Water Conservancy and Hydropower Press; 2005.

[164] Zhang Z, Song Z, Lai J, Qiu J, Cheng Y, Zhang J. Critical slowing down precursor information for the acoustic emission response characteristics of defective tuffs. Theor Appl Fract Mech. 2024;129:104220.

[165] Zhang ZY, Chen X, Zhang SS. Study on seepage characteristics of brittle-plastic incomplete filling fissures. Shandong Coal Sci Tech. 2021;9:174-175.

[166] Zhao N, Wang Y, Meng B, Luo N. Numerical simulation on the seepage properties of soil-rock mixture. Adv Mater Sci Eng. 2018;2018:1-10.

[167] Zhao ZH. Study on water-rock interaction mechanisms and mechanical behaviors of single rock fractures. Chin J Rock Mech Eng. 2021;40(Supp 2):3063-3073.

[168] Zheng S, Zhang B, Fu WX. Permeability characteristics of fractured rock mass with filling medium. Chin Rur Wtr Res Hydro. 2020;2020(11):161-165.

[169] Zhong Z, Deng R, Zhang J, Hu X. Fracture properties of jointed rock infilled with mortar under uniaxial compression. Eng Fract Mech. 2020;228:106822.

[170] Zhou H, Hu DW, Zhang K. Mechanism and Theory of Fluid-Solid Coupling of Pore and Fissured Rocks Under High Osmotic Pressure. Science Press; 2014.

[171] Zhou JQ, Wang M, Wang L, Chen YF, Zhou CB. Emergence of nonlinear laminar flow in fractures during shear. Rock Mech Rock Eng. 2018;51(11):3635-3643.

[172] Zhou X, Niu Y, Cheng H, Berto F. Cracking behaviors and chaotic characteristics of sandstone with unfilled and filled dentate flaw. Theor Appl Fract Mech. 2021;112:102876.

[173] Zhu Z, Niu Z, Que X, Liu C, He Y, Xie X. Study on permeability characteristics of rocks with filling fractures under coupled stress and seepage fields. Water. 2020;12(10):2782.

[174] Zhu ZD, Guo HQ. Hydraulic Foundation of Fractured Rock Mass. Science Press; 2007.

[175] Zhuang X, Chun J, Zhu H. A comparative study on unfilled and filled crack propagation for rock-like brittle material. Theor Appl Fract Mech. 2014;72:110-120.

[176] Zhuang X, Zhou S. An experimental and numerical study on the influence of filling materials on double-crack propagation. Rock Mech Rock Eng. 2020;53(12):5571-5591.

[177] МИНЦ Д М, ШУБЕРТ СА. Hydraulics of Granular Materials. Water Resources Press; 1957.

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