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Fracture Evolution and Energy Characteristics During Marble Failure Under Triaxial Fatigue Cyclic and Confining Pressure Unloading (FC-CPU) Conditions

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Abstract

This work aims at investigating the fracture evolution and energy characteristics of marble subjected to fatigue cyclic loading and confining pressure unloading (FC-CPU) conditions. Although rocks under separated fatigue cyclic loading and triaxial unloading conditions have been well studied, little is known about the dependence of the fatigue damage accumulation on the subsequent confining pressure unloading condition that influences the rock fracture behaviors. In this work, the servo-controlled GCTS 2000 rock mechanical system combined with the post-test X-ray computed tomography (CT) scanning technique were used to reveal the fracture behaviors of the marble samples. The samples were tested at three stages: the static loading stage, the fatigue cyclic loading stage, and the confining pressure unloading stage. Results show that the damage index-cycle number curve shows a different pattern—the damage increasing rate is different for the samples experiencing different fatigue damage. The damage accumulation at the fatigue cyclic stage influences the final failure mode and energy conversion. In addition, post-test CT scanning further reveals the effects of fatigue cycles on the crack pattern, as well as the stimulated crack scale and density after FC-CPU testing depending on the fatigue cycle. Furthermore, the stored elastic energy decreases and the dissipated energy increases with increasing fatigue cycle at the fatigue loading stage, and the energy conversion is consistent with the crack pattern analysis. By investigating the failure mechanism of marble under FC-CPU conditions, a theoretical basis for rock dynamic disaster prediction can be created.

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Abbreviations

FC-CPU:

Fatigue cyclic-confining pressure unloading

FCL:

Fatigue cyclic loading

U :

Total strain energy

U 0 :

Absorbed strain energy

U 1 :

Axial strain energy

U e :

Elastic strain energy

U d :

Dissipated energy

U 3 :

Circumferential strain energy

XRD:

X-ray powder diffraction

CT:

Computed tomography

σ 1 :

Axial stress

σ 3 :

Confining pressure

σ d :

Stress amplitude

ε 1 :

Axial strain

ε 3 :

Lateral strain

ε v :

Volumetric strain

ε 0 :

Axial strain at the end of first loading stage

ε d :

Axial strain at the end of the second loading stage

SEM:

Scanning electron microscope

CP:

Confining pressure

References

  • Bagde MN, Petroš V (2005) Fatigue properties of intact sandstone samples subjected to dynamic uniaxial cyclical loading. Int J Rock Mech Min Sci 42:237–250

    Article  Google Scholar 

  • Bertuzzi R, Douglas K, Mostyn G (2016) Comparison of intact rock strength criteria for pragmatic design. Int J Geotech Geoenviron Eng 143(4):06016029

    Article  Google Scholar 

  • Cerfontaine B, Collin F (2018) Cyclic and fatigue behaviour of rock materials: review, interpretation and research perspectives. Rock Mech Rock Eng 51(2):391–414

    Article  Google Scholar 

  • Cnudde V, Boone MN (2013) High-resolution X-ray computed tomography in geosciences: a review of the current technology and applications. Earth Sci Rev 123:1–17

    Article  Google Scholar 

  • Dai L, Pan Y, Wang A (2018) Study of the energy absorption performance of an axial splitting component for anchor bolts under static loading. Tunn and Undergr Sp Tech 81:176–186

    Article  Google Scholar 

  • Einstein HH (1996) Risk and risk analysis in rock engineering. Tunn Undergr Sp Tech 11(2):141–155

    Article  Google Scholar 

  • Fan J, Jiang D, Liu W, Wu F, Chen J, Daemen J (2019) Discontinuous fatigue of salt rock with low-stress intervals. Int J Rock Mech Min Sci 115:77–86

    Article  Google Scholar 

  • Fuenkajorn K, Phueakphum D (2010) Effects of cyclic loading on mechanical properties of Maha Sarakham salt. Eng Geol 112(1–4):43–52

    Article  Google Scholar 

  • Ge X (1987) Study of deformation and strength behaviour of the large-sized triaxial rock samples under cyclic loading. Rock Soil Mech 8(2):11–18 (in Chinese)

    Google Scholar 

  • Ge XR, Jiang Y, Lu YD, Ren JX (2003) Testing study on fatigue deformation law of rock under cyclic loading. Chin J Rock Mech Eng 22(10):1581–1585

    Google Scholar 

  • Guo YT, Yang CH, Fu JJ (2012) Experimental research on mechanical characteristics of salt rock under tri-axial unloading test. Rock Soil Mech 33(3):725–732 (in Chinese)

    Google Scholar 

  • He MC, Li N, Zhu C, Chen Y, Wu H (2019) Experimental investigation and damage modeling of salt rock subjected to fatigue loading. Int J Rock Mech Min Sci 114:17–23

    Article  Google Scholar 

  • He MC, Sousa LRE, Miranda T, Zhu GL (2015) Rockburst laboratory tests database—application of data mining techniques. Eng Geol 185:116–130

    Article  Google Scholar 

  • Higo Y, Oka F, Sato T, Matsushima Y, Kimoto S (2013) Investigation of localized deformation in partially saturated sand under triaxial compression using microfocus X-ray CT with digital image correlation. Soils Found 53(2):181–198

    Article  Google Scholar 

  • Huang D, Li Y (2014) Conversion of strain energy in triaxial unloading tests on marble. Int J Rock Mech Min Sci 66:160–168

    Article  Google Scholar 

  • Li N, Chen W, Zhang P, Swoboda G (2001) The mechanical properties and a fatigue damage model for jointed rock masses subjected to dynamic cyclical loading. Int J Rock Mech Min Sci 38:1071–1079

    Article  Google Scholar 

  • Li D, Sun Z, Xie T, Li X, Ranjith PG (2017) Energy evolution characteristics of hard rock during triaxial failure with different loading and unloading paths. Eng Geol 228:270–281

    Article  Google Scholar 

  • Liu E, He S (2012) Effects of cyclic dynamic loading on the mechanical properties of intact rock samples under confining pressure conditions. Eng Geol 125:81–91

    Article  Google Scholar 

  • Mao H, Mahadevan S (2002) Fatigue damage modeling of composite materials. Compos Struct 58:405–410

    Article  Google Scholar 

  • Martin C, Maybee W (2000) The strength of hard-rock pillars. Int J Rock Mech Min Sci 37(8):1239–1246

    Article  Google Scholar 

  • Moradian Z, Einstein HH, Ballivy G (2016) Detection of cracking levels in brittle rocks by parametric analysis of the acoustic emission signals. Rock Mech Rock Eng 49(3):785–800

    Article  Google Scholar 

  • Peng K, Zhou J, Zou Q, Zhang J, Wu F (2019) Effects of stress lower limit during cyclic loading and unloading on deformation characteristics of sandstones. Constr Build Mater 217:202–215

    Article  Google Scholar 

  • Ray SK, Sarkar M, Singh TN (1999) Effect of cyclic loading and strain rate on the mechanical behaviour of sandstone. Int J Rock Mech Min Sci 36:543–549

    Article  Google Scholar 

  • Ren S, Bai YM, Zhang JP, Jiang DY, Yang CH (2013) Experimental investigation of the fatigue properties of salt rock. Int J Rock Mech Min Sci 64:68–72

    Article  Google Scholar 

  • Sun B, Zhu Z, Shi C, Luo Z (2017) Dynamic mechanical behavior and fatigue damage evolution of sandstone under cyclic loading. Int J Rock Mech Min Sci 100(94):82–89

    Article  Google Scholar 

  • Taheri A, Squires J, Meng Z, Zhang Z (2017) Mechanical properties of brown coal under different loading conditions. Int J Geomech 17(11):06017020

    Article  Google Scholar 

  • Takeda M, Manaka M (2018) Effects of confining stress on the semipermeability of siliceous mudstones: implications for identifying geologic membrane behaviors of argillaceous formations. Geophys Res Lett 45(11):5427–5435

    Article  Google Scholar 

  • Tien YM, Lee DH, Juang CH (1990) Strain pore pressure and fatigue characteristics of sandstone under various load conditions. Int J Rock Mech Min Sci Geomech 27:283–289

    Article  Google Scholar 

  • Voznesenskii AS, Krasilov MN, Kutkin YO, Tavostin MN, Osipov YV (2017) Features of interrelations between acoustic quality factor and strength of rock salt during fatigue cyclic loadings. Int J Fatigue 97:70–78

    Article  Google Scholar 

  • Wang Z, Li S, Qiao L, Zhao J (2013) Fatigue behavior of granite subjected to cyclic loading under triaxial compression condition. Rock Mech Rock Eng 46(6):1603–1615

    Article  Google Scholar 

  • Wang Y, Li X, Zhang B, Wu YF (2014) Meso-damage cracking characteristics analysis for rock and soil aggregate with CT test. Sci China Technol Sci 57(7):1361–1371

    Article  Google Scholar 

  • Wang Y, Li CH, Hu YZ (2018a) Use of X-ray computed tomography to investigate the effect of rock blocks on meso-structural changes in soil-rock mixture under triaxial deformation. Constr Build Mater 164:386–399

    Article  Google Scholar 

  • Wang Y, Que JM, Wang C, Li CH (2018b) Three-dimensional observations of meso-structural changes in bimsoil using X-ray computed tomography (CT) under triaxial compression. Constr Build Mater 190:773–786

    Article  Google Scholar 

  • Wang Y, Feng WK, Li CH (2020a) On anisotropic fracture and energy evolution of marble subjected to triaxial fatigue cyclic-confining pressure unloading conditions. Int J Fatigue 134:105524

    Article  Google Scholar 

  • Wang Y, Gao SH, Liu D, Li C (2020b) Anisotropic fatigue behaviour of interbeded marble subjected to uniaxial cyclic compressive loads. Fatigue Fract Eng Mater Struct 43(6):1170–1183

    Article  Google Scholar 

  • Wang Y, Gao SH, Li CH, Han JQ (2020c) Investigation on fracture behaviors and damage evolution modeling of freeze-thawed marble subjected to increasing-amplitude cyclic loads. Theoret Appl Fract Mech. https://doi.org/10.1016/j.tafmec.2020.102679

    Article  Google Scholar 

  • Xie HP, Li L, Peng R, Ju Y (2009) Energy analysis and criteria for structural failure of rocks. J Rock Mech Geotech Eng 1(1):11–20

    Article  Google Scholar 

  • Xie HP, Li LY, Ju Y, Peng RD, Yang YM (2011) Energy analysis for damage and catastrophic failure of rocks. Sci China Technol Sci 54:199–209

    Article  Google Scholar 

  • Xu J, Jiang J, Xu N, Liu Q, Gao Y (2017) A new energy index for evaluating the tendency of rockburst and its engineering application. Eng Geol 230:46–54

    Article  Google Scholar 

  • Zhao XD, Wang J, Cai M, Cheng C, Ma LK, Su R, Zhao F, Li DJ (2014) Influence of unloading rate on the strain burst characteristics of Beishan granite under true triaxial unloading conditions. Rock Mech Rock Eng 47(2):467–483

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the editors and the anonymous reviewers for their helpful and constructive comments. Many thanks to Dr. X. M. Wei for his providing of the stope structure of Lilou iron mine. This study was supported by the Beijing Natural Science Foundation of China (8202033), the National Key Technologies Research and Development Program (2018YFC0808402), the Key Laboratory of Geo-hazards Prevention and Geo-environment Protection (Chengdu University of Technology) (SKLGP2019K017), and the Fundamental Research Funds for the Central Universities (FRF-TP-20-004A2).

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Authors and Affiliations

  1. Beijing Key Laboratory of Urban Underground Space Engineering, Department of Civil Engineering, School of Civil and Resource Engineering, University of Science and Technology Beijing, 30 Xueyuan Road, Haidian District, Beijing, 100083, China

    Y. Wang & C. H. Li

  2. State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu, 610059, Sichuan, China

    Y. Wang & W. K. Feng

  3. Key Laboratory of Shale Gas and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China

    R. L. Hu

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  1. Y. Wang
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  2. W. K. Feng
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  4. C. H. Li
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Correspondence to Y. Wang.

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Wang, Y., Feng, W.K., Hu, R.L. et al. Fracture Evolution and Energy Characteristics During Marble Failure Under Triaxial Fatigue Cyclic and Confining Pressure Unloading (FC-CPU) Conditions. Rock Mech Rock Eng 54, 799–818 (2021). https://doi.org/10.1007/s00603-020-02299-6

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