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Investigating the effect of initial cracks on the mudstone mechanical behavior under uniaxial compression using FDEM

初始裂纹对泥岩单轴压缩力学性质影响的FDEM研究

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Abstract

For investigating the effect of the initial cracks on the mechanical characteristics of mudstone specimens under uniaxial compression, firstly, uniaxial compression tests on mudstone specimens treated by different temperatures (20 °C, 30 °C, 60 °C and 80 °C, respectively) were carried out. Then, some uniaxial compression numerical models containing the certain number of initial elliptical cracks were built using finite-discrete element method (FDEM) to simulate laboratory tests. Lastly, a piecewise damage model was established to reveal the damage evolution process. It is found that the modelling results present a well agreement with laboratory tests in the aspect of stress-strain response. The test and simulation results reveal that initial crack density has a significant influence on the uniaxial compression mechanical characteristics. Specifically, with the increasing initial crack density, the initial nonlinearity is more obvious, but the elastic modulus and uniaxial compression strength are in decrease. And the cracking event counts are in decrease as increasing the initial crack density while the open fracturing mode is more dominant. Furthermore, the piecewise damage model can reproduce the stress-strain curves finely. If the initial nonlinearity is obvious, it is feasible to divide the damage evolution process into initial damage, damage decrease, and damage increase stages.

要为研究初始裂纹对泥岩试件单轴压缩力学性质的影响, 首先, 对经过不同温度处理后的泥岩试件开展单轴压缩力学实验. 然后, 运用有限元-离散元耦合方法(FDEM)建立含有不同数量初始椭圆裂纹的单轴压缩数值模型来模拟室内实验. 最后, 建立一个分段损伤 模型揭示单轴压缩损伤演化过程. 通过研究发现模拟的应力-应变曲线与实验结果存在较好一致性, 实验和数值结果表明初始裂纹密度 对单轴压缩力学特性存在重要影响, 尤其是随着初始裂纹密度的增加, 初始非线性特征越明显, 而弹性模量和单轴抗压强度有所下降. 同时初始裂纹密度越大, 扩展的裂纹数量越少, 张拉破坏模式则越明显. 此外, 分段损伤本构模型能够很好地对应模拟和实验中的应力- 应变曲线. 对于初始非线性比较明显的岩石材料, 应该将岩石的损伤演化过程划分为初始损伤、损伤减少和损伤增加三个阶段.

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References

  1. F. Birch, The velocity of compressional waves in rocks to 10 kilobars: 2., J. Geophys. Res. 66, 2199 (1961).

    Article  Google Scholar 

  2. W. F. Brace, B. W. PauldingJr., and C. Scholz, Dilatancy in the fracture of crystalline rocks, J. Geophys. Res. 71, 3939 (1966).

    Article  Google Scholar 

  3. Z. T. Bieniawski, Mechanism of brittle fracture of rock, Int. J. Rock Mech. Min. Sci. Geomech. Abstracts 4, 395 (1967).

    Article  Google Scholar 

  4. M. Cai, P. K. Kaiser, Y. Tasaka, T. Maejima, H. Morioka, and M. Minami, Generalized crack initiation and crack damage stress thresholds of brittle rock masses near underground excavations, Int. J. Rock Mech. Min. Sci. 41, 833 (2004).

    Article  Google Scholar 

  5. M. S. Diederichs, P. K. Kaiser, and E. Eberhardt, Damage initiation and propagation in hard rock during tunnelling and the influence of near-face stress rotation, Int. J. Rock Mech. Min. Sci. 41, 785 (2004).

    Article  Google Scholar 

  6. Q. H. Qian, and X. P. Zhou, Effects of incompatible deformation on failure mode and stress field of surrounding rock mass, Chin. J. Rock Mech. Eng. 4, 649 (2013).

    Google Scholar 

  7. H. Shen, X. Li, Q. Li, and H. Wang, A method to model the effect of pre-existing cracks on P-wave velocity in rocks, J. Rock Mech. Geotech. Eng. 12, 493 (2020).

    Article  Google Scholar 

  8. L. Li, G. Shi, Y. Zhang, and X. Liu, Relationship between the heterogeneity of low-permeability reservoirs and the dynamic evolution of fractures under uniaxial compression conditions by CT scanning: A case study in the jiyang depression of Bohai Bay Basin, China, Front. Earth Sci. 10, 1018561 (2023).

    Article  Google Scholar 

  9. M. F. Ashby, and S. D. Hallam (Née Cooksley), The failure of brittle solids containing small cracks under compressive stress states, Acta Metall. 34, 497.

  10. L. X. Xiong, H. J. Chen, and D. X. Geng, Uniaxial compression study on mechanical properties ofartificial rock specimens with cross-flaws, Geotech. Geol. Eng. 39, 1667 (2021).

    Article  Google Scholar 

  11. R. Kong, E. Tuncay, R. Ulusay, X. Zhang, and X. T. Feng, An experimental investigation on stress-induced cracking mechanisms of a volcanic rock, Eng. Geol. 280, 105934 (2021).

    Article  Google Scholar 

  12. C. Ding, R. Yang, and L. Yang, Experimental results of blast-induced cracking fractal characteristics and propagation behavior in deep rock mass, Int. J. Rock Mech. Min. Sci. 142, 104772 (2021).

    Article  Google Scholar 

  13. H. Wang, Y. Wang, Z. Yu, and J. Li, Experimental study on the effects of stress-induced damage on the microstructure and mechanical properties of soft rock, Adv. Civ. Eng. 2021, 1 (2021).

    Google Scholar 

  14. M. S. Boussaid, C. Mallet, K. Beck, and J. Clara, Multi-geophysical approach for the characterization of thermally-induced cracks in granite: Discussion of reproducibility and persistence, Pure Appl. Geophys. 177, 3301 (2020).

    Article  Google Scholar 

  15. Y. Shen, J. Hao, X. Hou, J. Yuan, and Z. Bai, Crack propagation in high-temperature granite after cooling shock: Experiment and numerical simulation, Bull. Eng. Geol. Environ. 80, 5831 (2021).

    Article  Google Scholar 

  16. A. Daoud, J. Browning, P. G. Meredith, and T. M. Mitchell, Microstructural controls on thermal crack damage and the presence of a temperature-memory effect during cyclic thermal stressing of rocks, Geophys. Res. Lett. 47, 1 (2020).

    Article  Google Scholar 

  17. Y. Zheng, Z. Ma, X. Zhao, and L. He, Experimental investigation on the thermal, mechanical and cracking behaviours of three igneous rocks under microwave treatment, Rock Mech. Rock Eng. 53, 3657 (2020).

    Article  Google Scholar 

  18. C. A. Tang, P. Lin, R. H. C. Wong, and K. T. Chau, Analysis of crack coalescence in rock-like materials containing three flaws—Part II: numerical approach, Int. J. Rock Mech. Min. Sci. 38, 925 (2001).

    Article  Google Scholar 

  19. P. Hamdi, D. Stead, and D. Elmo, Characterizing the influence of stress-induced microcracks on the laboratory strength and fracture development in brittle rocks using a finite-discrete element method-micro discrete fracture network FDEM-μDFN approach, J. Rock Mech. Geotech. Eng. 7, 609 (2015).

    Article  Google Scholar 

  20. T. Yin, S. Zhang, X. Li, and L. Bai, A numerical estimate method of dynamic fracture initiation toughness of rock under high temperature, Eng. Fract. Mech. 204, 87 (2018).

    Article  Google Scholar 

  21. J. Peng, L. N. Y. Wong, G. Liu, and C. I. Teh, Influence of initial micro-crack damage on strength and micro-cracking behavior of an intrusive crystalline rock, Bull. Eng. Geol. Environ. 78, 2957 (2019).

    Article  Google Scholar 

  22. K. Feng, and X. P. Zhou, Peridynamic simulation of the mechanical responses and fracturing behaviors of granite subjected to uniaxial compression based on CT heterogeneous data, Eng. Comput. 39, 307 (2023).

    Article  Google Scholar 

  23. S. Murakami, and K. Kamiya, Constitutive and damage evolution equations of elastic-brittle materials based on irreversible thermodynamics, Int. J. Mech. Sci. 39, 473 (1997).

    Article  MATH  Google Scholar 

  24. E. Eberhardt, D. Stead, and B. Stimpson, Effects of sample disturbance on the stress-induced microfracturing characteristics of brittle rock, Can. Geotech. J. 36, 239 (1999).

    Article  Google Scholar 

  25. W. H. Zhang, and Y. Q. Cai, Continuum Damage Mechanics and Numerical Applications (Zhejiang University Press, Hangzhou, 2010).

    Book  Google Scholar 

  26. B. Paliwal, and K. T. Ramesh, An interacting micro-crack damage model for failure of brittle materials under compression, J. Mech. Phys. Solids 56, 896 (2008).

    Article  MATH  Google Scholar 

  27. J. W. Zhou, W. Y. Xu, and X. G. Yang, A microcrack damage model for brittle rocks under uniaxial compression, Mech. Res. Commun. 37, 399 (2010).

    Article  MATH  Google Scholar 

  28. N. Xie, Q. Z. Zhu, L. H. Xu, and J. F. Shao, A micromechanics-based elastoplastic damage model for quasi-brittle rocks, Comput. Geotech. 38, 970 (2011).

    Article  Google Scholar 

  29. C. A. Tang, and X. Xu, Statistical damage analysis of the rock complete stress-strain process, J. Northeastern Univ. (Nat. Sci.) 2, 191 (1987).

    Google Scholar 

  30. W. G. Cao, M. H. Zhao, and X. J. Tang, Study on the model and its modifying method for rock softening and damage based on Weibull random distribution, Chin. J. Rock Mech. Eng. 6, 628 (1998).

    Google Scholar 

  31. S. Q. Yang, W. Y. Xu, L. D. Wei, and C. D. Su, Statistical constitutive model for rock damage under uniaxial compression and its experimental study, J. Hehai Univ. (Nat. Sci.) 2, 200 (2004).

    Google Scholar 

  32. J. B. Walsh, The effect of cracks on the compressibility of rock, J. Geophys. Res. 70, 381 (1965).

    Article  MATH  Google Scholar 

  33. J. B. Walsh, The effect of cracks on the uniaxial elastic compression of rocks, J. Geophys. Res. 70, 399 (1965).

    Article  MATH  Google Scholar 

  34. E. C. David, N. Brantut, A. Schubnel, and R. W. Zimmerman, Sliding crack model for nonlinearity and hysteresis in the uniaxial stress-strain curve of rock, Int. J. Rock Mech. Min. Sci. 52, 9 (2012).

    Article  Google Scholar 

  35. A. Munjiza, The Combined Finite-Discrete Element Method (John Wiley & Sons, Chichester, 2004).

    Book  MATH  Google Scholar 

  36. O. K. Mahabadi, Investigating the Influence of Micro-Scale Heterogeneity and Microstructure on the Failure and Mechanical Behaviour of Geomaterials, Dissertation for Doctoral Degree (University of Toronto, Toronto, 2012).

    Google Scholar 

  37. A. Munjiza, D. R. J. Owen, and N. Bicanic, A combined finite-discrete element method in transient dynamics of fracturing solids, Eng. Comput. 12, 145 (1995).

    Article  MATH  Google Scholar 

  38. A. Lisjak, and G. Grasselli, A review of discrete modeling techniques for fracturing processes in discontinuous rock masses, J. Rock Mech. Geotech. Eng. 6, 301 (2014).

    Article  Google Scholar 

  39. A. Hillerborg, M. Modéer, and P. E. Petersson, Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement Concrete Res. 6, 773 (1976).

    Article  Google Scholar 

  40. Q. Zhao, Investigating Brittle Rock Failure and Associated Seismicity Using Laboratory Experiments and Numerical Simulations, Dissertation for Doctoral Degree (University of Toronto, Toronto, 2017).

    Google Scholar 

  41. Y. Ida, Cohesive force across the tip of a longitudinal-shear crack and Griffith’s specific surface energy, J. Geophys. Res. 77, 3796 (1972).

    Article  Google Scholar 

  42. O. K. Mahabadi, A. Lisjak, A. Munjiza, and G. Grasselli, Y-Geo: New combined finite-discrete element numerical code for geomechanical applications, Int. J. Geomech. 12, 676 (2012).

    Article  Google Scholar 

  43. A. Lisjak, Q. Liu, Q. Zhao, O. K. Mahabadi, and G. Grasselli, Numerical simulation of acoustic emission in brittle rocks by two-dimensional finite-discrete element analysis, Geophys. J. Int. 195, 423 (2013).

    Article  Google Scholar 

  44. Z. Lei, E. Rougier, E. E. Knight, M. Zang, and A. Munjiza, Impact fracture and fragmentation of glass via the 3D combined finite-discrete element method, Appl. Sci. 11, 2484 (2021).

    Article  Google Scholar 

  45. J. Peng, M. Cai, and G. Rong, Stresses for Crack Closure and its Application to assessing stress-induced Microcrack Damage, Chin. J. Rock Mech. Eng. 6, 10 (2015).

    Google Scholar 

  46. A. Munjiza, and N. W. M. John, Mesh size sensitivity of the combined FEM/DEM fracture and fragmentation algorithms, Eng. Fract. Mech. 69, 281 (2002).

    Article  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 41572334), Fundamental Research Funds for the Central Universities (Grant No. 2022YJSSB05), and a grant from State Key Laboratory for GeoMechanics and Deep Underground Engineering.

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Contributions

Dejian Li designed the research methodology and provided the financial support for this study. Hao Qi conducted the present research and investigation process and wrote the submitted manuscripts. Chunxiao Li provided experimental data and implemented the computer code and supporting algorithms. Changqi Li applied computational techniques to analyze study data.

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Correspondence to Hao Qi  (祁浩).

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On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Li, D., Qi, H., Li, C. et al. Investigating the effect of initial cracks on the mudstone mechanical behavior under uniaxial compression using FDEM. Acta Mech. Sin. 39, 422421 (2023). https://doi.org/10.1007/s10409-023-22421-x

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