Influence of roughness on the mechanical response of rock-like specimens with nonpersistent joints under uniaxial compression based on joint deformation analysis

Abstract

Joint deformation is a key factor controlling the mechanical behavior of discontinuous rock strata under changing stress conditions, including dominating the elastic deformation in near-surface excavations and serving as a major component of settlement under higher stress. This study, focusing on joint deformation behavior, investigates the effect of joint roughness on the peak stress and failure modes of specimens under uniaxial compression. Rock-like specimens with two layers of parallel, nonpersistent joints, one rough, were fabricated using 3D printing technology. Digital image correlation was used to capture real-time surface displacement fields, and a joint deformation analysis method was developed. The results show that joints exhibit staged, non-uniform closure and slip behavior, influenced by joint roughness, distribution of primary and secondary joints, and layered arrangement. Rough joints accelerate closure but hinder slip coordination, resulting in a three-stage loading process. In stage I, primary closure and layer-coordinated slip occur, accompanied by crack initiation, joint coalescence, and steady stress growth. Stage II involves secondary closure and overall coordinated slip, leading to localized failure and stress stabilization. Stage III is characterized by complete closure, uncoordinated slip, intensified crack propagation, and specimen failure, accompanied by stress hardening. The study reveals that joint deformation serves as a bridge linking roughness and peak strength. The average joint closure level and slip coordination are linearly negatively correlated with roughness but nonlinearly positively correlated with peak strength. Roughness restricts slip coordination, limiting crack propagation and delaying failure, which slows stress growth. Redistribution of joint aperture during slip reduces joint closure, weakens wall contact, and diminishes stress hardening.

Keywords

Jointed rock / Joint deformation / Crack propagation / Uniaxial compression

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

CRediT authorship contribution statement

Hong Yin: Writing - review & editing, Writing - original draft, Investigation, Formal analysis, Data curation, Conceptualization. Zehui Gao: Writing - review & editing, Writing - original draft. Yulong Shao: Investigation, Formal analysis, Conceptualization. Shuhong Wang: Supervision, Funding acquisition. Jae-Joon Song: Validation, Supervision. Ye Wang: Writing - review & editing. Jineon Kim: Conceptualization. Shan Guo: Investigation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This work was supported by the Natural Science Foundation of China (Grant Nos. 52408417 and 52374157), the Chinese Government Joint Education Project (D20240080), and the Key Science and Technology Projects of Liaoning Province, China (2024021200-JH2/1021)

References

[1] Afolagboye, L. O., He, J., & Wang, S. (2016). Experimental study on cracking behaviour of moulded gypsum containing two non-parallel overlapping flaws under uniaxial compression. Acta Mechanica Sinica, 33 (2), 394-405.

[2] Alcott, J. M., Kaiser, P. K., & Simser, B. P. (1998). Use of microseismic source parameters for rockburst hazard assessment. Pure and Applied Geophysics, 153 (1), 41-65.

[3] Amann, F., Ündül, O., & Kaiser, P. K. (2014). Crack initiation and crack propagation in heterogeneous sulfate-rich clay rocks. Rock Mechanics and Rock Engineering, 47 (5), 1849-1865.

[4] Asadizadeh, M., Hossaini, M. F., Moosavi, M., Masoumi, H., & Ranjith, P. G. (2019). Mechanical characterisation of jointed rock-like material with non-persistent rough joints subjected to uniaxial compression. Engineering Geology, 260, 105224.

[5] Asadizadeh, M., Moosavi, M., Hossaini, M. F., Hedayat, A., Sherizadeh, T., & Masoumi, H. (2023). Numerical modeling of rock blocks with nonpersistent rough joints subjected to uniaxial compressive and shear loadings. International Journal of Geomechanics, 23 (7), 04023103.

[6] Bandis, S. C., Lumsden, A. C., & Barton, N. R. (1983). Fundamentals of rock joint deformation. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 20 (6), 249-268.

[7] Barton, N., & Choubey, V. (1977). The shear strength of rock joints in theory and practice. Rock mechanics, 10 (1), 1-54.

[8] Bieniawski, Z. T. (1967). Mechanism of brittle fracture of rock: Part I—theory of the fracture process. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 4 (4), 395-406.

[9] Brady, B. H. G., & Brown, E. T. (2006). Rock mechanics: For underground mining. Springer.

[10] Cao, R., Yao, R., Meng, J., Lin, Q., & Li, S. (2020). Failure mechanism of non-persistent jointed rock-like specimens under uniaxial loading: Laboratory testing. International Journal of Rock Mechanics and Mining Sciences, 132, 104341.

[11] Chen, L., Wang, C. P., Liu, J. F., Liu, J., Wang, J., Jia, Y., & Shao, J. F. (2015). Damage and plastic deformation modeling of beishan granite under compressive stress conditions. Rock Mechanics and Rock Engineering, 48 (4), 1623-1633.

[12] Chen, X., Liao, Z.-H., & Peng, X. (2013). Cracking process of rock mass models under uniaxial compression. Journal of Central South University, 20 (6), 1661-1678.

[13] Chen, X., Liao, Z., & Peng, X. (2012). Deformability characteristics of jointed rock masses under uniaxial compression. International Journal of Mining Science and Technology, 22 (2), 213-221.

[14] Chen, Y., & Guo, B. (2020). Crack closure effect and energy dissipation model for rocks under uniaxial compression. Geotechnical and Geological Engineering, 38 (1), 621-629.

[15] Cook, N. G. W. (1992). Natural joints in rock: Mechanical, hydraulic, and seismic behavior and properties under normal stress. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 29 (3), 198-223.

[16] Cui, P., Ge, Y., Li, S., Li, Z., Xu, X., Zhou, G. G. D., Chen, H., Wang, H., Lei, Y., Zhou, L., Yi, S., Wu, C., Guo, J., Wang, Q., Lan, H., Ding, M., Ren, J., Zeng, L., Jiang, Y., & Wang, Y. (2022). Scientific challenges in disaster risk reduction for the Sichuan-Tibet Railway. Engineering Geology, 309, 106837.

[17] Eberhardt, E., Stimpson, B., & Stead, D. (1999). Effects of grain size on the initiation and propagation thresholds of stress-induced brittle fractures. Rock Mechanics and Rock Engineering, 32 (2), 81-99.

[18] Erdogan, F., & Sih, G. C. (1963). On the crack extension in plates under plane loading and transverse shear. Journal of Fluids Engineering, Transactions of the ASME, 85 (4), 519-525.

[19] Esterhuizen, G. S., Dolinar, D. R., & Ellenberger, J. L. (2011). Pillar strength in underground stone mines in the United States. International Journal of Rock Mechanics and Mining Sciences, 48 (1), 42-50.

[20] Fakoor, M., & Shahsavar, S. (2021). The effect of T-stress on mixed mode I/II fracture of composite materials: Reinforcement isotropic solid model in combination with maximum shear stress theory. International Journal of Solids and Structures, 229, 111145.

[21] Fereshtenejad, S., & Song, J. J. (2021). Applicability of powder-based 3D printing technology in shear behavior analysis of rock mass containing non-persistent joints. Journal of Structural Geology, 143, 104251.

[22] Gao, Y. T., Wu, T. H., & Zhou, Y. (2021). Application and prospective of 3D printing in rock mechanics: A review. International Journal of Minerals, Metallurgy and Materials, 28 (1), 1-17.

[23] Goodman, R. E. (1974). The mechanical properties of joints. In Proceedings of the third international congress international society of rock mechanic (pp.127-140). Denver: ISRM.

[24] Griffith, A. A. (1921). The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society A, 221, 163-198.

[25] Haeri, H., Sarfarazi, V., & Marji, M. F. (2021). Experimental and numerical investigation of uniaxial compression failure in rock-like specimens with l-shaped nonpersistent cracks. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 45 (4), 2555-2575.

[26] Hoek, E., & Bieniawski, Z. T. (1965). Brittle fracture propagation in rock under compression. International Journal of Fracture Mechanics, 1 (3), 137-155.

[27] Hopkins, D. L. (2000). The implications of joint deformation in analyzing the properties and behavior of fractured rock masses, underground excavations, and faults. International Journal of Rock Mechanics and Mining Sciences, 37 (1/2), 175-202.

[28] Hu, G., Li, Y., & Ma, G. (2021). Research on the size effect of roughness on rock uniaxial compressive strength and characteristic strength. Science and Engineering of Composite Materials, 28 (1), 613-627.

[29] Huang, C., Yang, W., Duan, K., Fang, L., Wang, L., & Bo, C. (2019). Mechanical behaviors of the brittle rock-like specimens with multi-non-persistent joints under uniaxial compression. Construction and Building Materials, 220, 426-443.

[30] Huang, D., Tang, W., & Li, X. Q. (2023). Numerical modeling and damage evolution research on the effect of joint geometrical parameters in nonpersistent jointed rock masses. Bulletin of Engineering Geology and the Environment, 82 (4), 137.

[31] Jiao, Y., Zuo, Y., Wen, Z., Chen, Q., Zheng, L., Lin, J.,... Du, S. et al. (2024). Crack-tip propagation laws and energy evolution of fractured sandstone. Engineering Failure Analysis, 166, 108832.

[32] Johansson, F., & Stille, H. (2014). A conceptual model for the peak shear strength of fresh and unweathered rock joints. International Journal of Rock Mechanics and Mining Sciences, 69, 31-38.

[33] Kumar, S., Tiwari, G., Parameswaran, V., & Das, A. (2022). Rate-dependent mechanical behavior of jointed rock with an impersistent joint under different infill conditions. Journal of Rock Mechanics and Geotechnical Engineering, 14 (5), 1380-1393.

[34] Li, H., Lai, Y., Zhang, M., Chen, Y., Ma, Q., Liang, T., & Gao, X. (2024). Elastoplastic damage behavior of quasi-brittle rocks considering crack closure evolution. Computers and Geotechnics, 166, 106031.

[35] Li, Y., & Zhang, Y. (2015). Quantitative estimation of joint roughness coefficient using statistical parameters. International Journal of Rock Mechanics and Mining Sciences, 77, 27-35.

[36] Liu, Z., Zhang, C., Zhang, C., Gao, Y., Zhou, H., & Chang, Z. (2019). Deformation and failure characteristics and fracture evolution of cryptocrystalline basalt. Journal of Rock Mechanics and Geotechnical Engineering, 11 (5), 990-1003.

[37] Lu, Y. L., Elsworth, D., & Wang, L. G. (2013). Microcrack-based coupled damage and flow modeling of fracturing evolution in permeable brittle rocks. Computers and Geotechnics, 49, 226-244.

[38] Luo, P. F., Chao, Y. J., Sutton, M. A., & Peters, W. H. III, ( 1993). Accurate measurement of three-dimensional deformations in deformable and rigid bodies using computer vision. Experimental Mechanics, 33 (2), 123-132.

[39] Ma, G., Hu, T., & Li, Z. (2024). Binder jetting 3D printing rock analogs using magnesium phosphate cement. Construction and Building Materials, 420, 135620.

[40] Martin, C. D. (1997). Seventeenth Canadian geotechnical colloquium: The effect of cohesion loss and stress path on brittle rock strength. Canadian Geotechnical Journal, 34 (5), 698-725.

[41] Park, C. H., & Bobet, A. (2009). Crack coalescence in specimens with open and closed flaws: A comparison. International Journal of Rock Mechanics and Mining Sciences, 46 (5), 819-829.

[42] Pradhan, S. P., & Siddique, T. (2020). Stability assessment of landslide-prone road cut rock slopes in Himalayan terrain: A finite element method based approach. Journal of Rock Mechanics and Geotechnical Engineering, 12 (1), 59-73.

[43] Ren, L., Zhao, L. Y., & Niu, F. J. (2022). A physically-based elastoplastic damage model for quasi-brittle geomaterials under freeze-thaw cycles and loading. Applied Mathematical Modelling, 106, 276-298.

[44] Ren, L., Zhao, L. Y., Niu, F. J., Lai, Y. M., & Shao, J. F. (2023). A nonlinear constitutive model for whole stress-strain behaviors of compressed rocks incorporating crack closure effect. International Journal for Numerical and Analytical Methods in Geomechanics, 47 (11), 2003-2026.

[45] Shan, R., Liu, N., Sun, P., Zhao, Z., Dong, R., Dou, H., Meng, H., & Bai, Y. (2025). Experimental and numerical simulation study of rough jointed rock samples under triaxial compression conditions. Engineering Fracture Mechanics, 314, 110707.

[46] Shao, Y., Kim, J., He, C., Yin, H., Mehrishal, S., Yao, C., & Song, J. J. (2024a). Experimental investigation of the coupled effects of bedding planes and flaws on fracture evolution of soft bedded rocks based on 3D printing and DIC technologies. Theoretical and Applied Fracture Mechanics, 133 (Part A).

[47] Shao, Y., Kim, J., Yang, J., Song, J. J., & Moon, J. (2024b). Experimental study on strength enhancement and porosity variation of 3D-printed gypsum rocks: insights on vacuum infiltration post-processing. Rock Mechanics and Rock Engineering, 57 (9), 6763-6786.

[48] Shao, Y., Yang, J., Kim, J., He, C., Song, J. J., Yin, H., & Leem, J. (2025). Strain localization-controlled rock failure using digital volume correlation technology: In situ compression tests on 3D-printed rock-like samples with a single initial flaw. Journal of Rock Mechanics and Geotechnical Engineering, 17 (7), 4329-4348.

[49] Shao, Y., Yang, J., Kim, J., Mehrishal, S., & Song, J. J. (2024c). Quantitative analysis and 3D visualization of crack behavior in 3D-printed rock-like specimens with single flaw using in-situ micro-CT imaging. Rock Mechanics and Rock Engineering, 57 (9), 7271-7291.

[50] Sih, G. C. (1974). Strain-energy-density factor applied to mixed mode crack problems. International Journal of Fracture, 10, 305-321.

[51] Tang, Y., Okubo, S., Xu, J., & Peng, S. (2019). Progressive failure behaviors and crack evolution of rocks under triaxial compression by 3D digital image correlation. Engineering Geology, 249, 172-185.

[52] Tse, R., & Cruden, D. M. (1979). Estimating joint roughness coefficients. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 16 (5), 303-307.

[53] Walton, G., Hedayat, A., Kim, E., & Labrie, D. (2017). Post-yield strength and dilatancy evolution across the brittle-ductile transition in Indiana limestone. Rock Mechanics and Rock Engineering, 50 (7), 1691-1710.

[54] Wang, B., Gerolymatou, E., & Jin, A. (2023a). Study on mechanical and fracture characteristics of rock-like specimens with rough non-persistent joints by YADE DEM simulation. Computers and Geotechnics, 158, 105382.

[55] Wang, D., He, S., & Tannant, D. D. (2019). A strain based method for determining the crack closure and initiation stress in compression tests. KSCE Journal of Civil Engineering, 23 (4), 1819-1828.

[56] Wang, M., Lu, Z., Zhao, Y., & Wan, W. (2025). Numerical study on the strength and fracture of rock materials with multiple rough preexisting fissures under uniaxial compression using particle flow code. Computational Particle Mechanics, 12 (1), 453-477.

[57] Wang, Y., Lu, H., & Wu, J. (2021). Experimental investigation on strength and failure characteristics of cemented paste backfill-rock composite under uniaxial compression. Construction and Building Materials, 304, 124629.

[58] Wang, Y., Yang, X., Li, W., & Qiao, W. (2023b). Experimental study on the effect of anchored bolts on failure and strength behavior of nonpersistent jointed rock model. Bulletin of Engineering Geology and the Environment, 82 (3), 95.

[59] Wu, X., Jiang, L., Tao, M., Mitri, H. S., & Xiang, G. (2024). Dynamic behaviors and bolt-strengthening effect of sand-powder 3D printing rock analog under static and dynamic coupled loading. Construction and Building Materials, 411, 134723.

[60] Xie, S., Han, Z., & Lin, H. (2022). A quantitative model considering crack closure effect of rock materials. International Journal of Solids and Structures, 251, 111758.

[61] Yang, S. Q., Chen, M., Huang, Y. H., Jing, H. W., & Ranjith, P. G. (2020). An experimental study on fracture evolution mechanism of a non-persistent jointed rock mass with various anchorage effects by DSCM, AE and X-ray CT observations. International Journal of Rock Mechanics and Mining Sciences, 134, 104469.

[62] Ye, Y., Ma, J., Wu, Z., & Zeng, Y. (2021). A novel 3D-FDEM method using finite-thickness cohesive elements to simulate the nonlinear mechanical behaviors of rocks. Computers and Geotechnics, 140, 10447.

[63] Yin, H., Wang, S., Song, J. J., Gao, Z., Kim, J., & Shao, Y. (2024). Mechanical behavior of rock-like specimens with 3D nonpenetrating and nonpersistent rough joints under uniaxial compression: Experimental study. Bulletin of Engineering Geology and the Environment, 83 (6), 239.

[64] Yuan, P., Li, A., Chen, C., & Lu, X. (2023). Experimental study of uniaxial compressive mechanical properties of rough jointed rock masses based on 3D printing. Applied Rheology, 33 (1), 20230114.

[65] Zhang, S., Chen, W., & Liu, H. (2023). Dynamic response of tunnels surrounded by thawing permafrost with anisotropic frost heave in cold regions: considering the movement of the frozen interface. Journal of Engineering Mechanics, 149 (2), 04022112.

[66] Zhang, Z., Wang, S., Yang, T., Dong, F., Gao, Z., & Wang, D. (2024). Influence of contact characteristics on nonlinear flow and eddy development in three-dimensional fractures under normal stress. Bulletin of Engineering Geology and the Environment, 83 (4), 129.

[67] Zhou, X. P., Cheng, H., & Feng, Y. F. (2013). An experimental study of crack coalescence behaviour in rock-like materials containing multiple flaws under uniaxial compression. Rock Mechanics and Rock Engineering, 47 (6), 1961-1986.