Abstract
A compressed-fracture slumping mode of the tower-column unstable rock mass is unusual, and the damage-catastrophe mechanism is a critical scientific issue in the mountainous disaster. Taking Zengziyan W12# unstable rock mass collapse in Jinfo mountain, Nanchuan District of Chongqing Municipality in China as an example, a multi-factor coupled damage-catastrophe geomechanical model consisted of freezing–thawing, dissolution, load, and the water-weakening effect was built. A damage constitutive model and a total damage evolution analytical formula were attained based on the equivalent strain principal, and the improved water-weakening function was easier to access in the indoor test. We generalize the geomechanical model into an equivalent spring model, and the energy balance theory acquires the damage fold-catastrophe model and gains the failure criterion of the compressed-fracture slumping mode and an eigenvalue expression of the critical mutation displacement. The theoretical catastrophic displacement value fits the real displacement inflection point value basically and the damage-catastrophe model is reasonable. The research can predict the damage evolution process and the critical catastrophic displacement eigenvalue of the compressed-fracture slumping mode of a tower-column unstable rock mass and provide theoretical support for the geo-disaster prevention in the mountainous zone.
Similar content being viewed by others
Availability of data and material
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
References
Atkinson BK (1984) Subcritical crack growth in geological materials. J Geophys Res-Solid Earth 89(B6):4077–4114. https://doi.org/10.1029/JB089iB06p04077
Bayram F (2012) Predicting mechanical strength loss of natural stones after freeze–thaw in cold regions. Cold Reg Sci Tech 83–84:98–102. https://doi.org/10.1016/j.coldregions.2012.07.003
Brantut N, Heap MJ, Baud P, Meredith PG (2014) Mechanisms of time-dependent deformation in porous limestone. J Geophys Res-Solid Earth 119(7):5444–5463. https://doi.org/10.1002/2014JB011186
Carine DP, Marc W, Denis J, Didier H, Bernard C, Michel S (2003) Investigation of a fractured limestone cliff (Chartreuse Massif, France) using seismic tomography and ground-penetrating radar. Near Surf Geophys 4:161–170. https://doi.org/10.3997/1873-0604.2003007
Chang Y, Chang L, Ren F (2020) Energy catastrophe of jointed rock slope considering spatiotemporal variability of strength. Geotech Geol Eng. https://doi.org/10.1007/s10706-020-01645-3
Chen HK, Qin X (2018) Status que and trend of unstable rock stability analysis. J Chongqing Jiaotong Univ 37(10):49–60. https://doi.org/10.3969/j.issn.1674-0696.2018.10.09
Chen HK, Wang SJ (2018) Study on failure model of Wangxia perilous rock and its mechanical interpretation. J Chongqing Normal Univ (nat Sci) 35(1):48–55. https://doi.org/10.11721/cqnuj20180106
Chen X, Eichhubl P, Olson JE (2017) Effect of water on critical and subcritical fracture properties of Woodford Shale. J Geophys Res-Solid Earth 122(4):2736–2750. https://doi.org/10.1002/2016JB013708
Chongqing Three Gorges Hydropower Construction Survey and Design Institute (2009) Geological survey report of Jinfoshan water conservancy project in Nanchuan, Chongqing
Cook NGW (1965) The failure of rock. Int J Rock Mech Min 2(3):389–403. https://doi.org/10.1016/0148-9062(65)90004-5
Ding WX, Xu T, Wang HY, Chen JP (2015) Experimental study of mechanical property of limestone under coupled chemical solution and freezing-thawing process. Chin J Rock Mech Eng 34(5):979–985. https://doi.org/10.13722/j.cnki.jrme.2014.0349
Dong P (2016) Experiment research on strike disintegration for perilous rock with quasi-masonry in limestone area. Chongqing Jiaotong University, Chongqing
Dong JH, Zhang L, Xu YF, Chen JY, Liu YK (2017) Application of catastrophe theory to determine the instability criterion for geo-mechanical model test. Adv Eng Sci 49(4):18–25. https://doi.org/10.15961/j.jsuese.201601327
Fang YQ, Liu XY, Li BX, Li YZ, Meng J (2019) Comparative study on the dissolution rate of limestones with different structures in acidic solution. Nat Sci J Harbin Normal Univ 35(6):93–101
Feng XT, Ding WX, Zhang DX (2009) Multi-crack interaction in limestone subject to stress and flow of chemical solutions. Int J Rock Mech Min 46(1):159–171. https://doi.org/10.1016/j.ijrmms.2008.08.001
Feng Z, Li B, Yin YP, He K (2014) Rockslides on limestone cliffs with sub-horizontal bedding in the southwestern calcareous area, China. Nat Hazards Earth Syst Sci 14(9):2627–2635. https://doi.org/10.5194/nhess-14-2627-2014
Feng Z, Chen YX, Li B, He K, Gao Y, Zhu SN (2016) Failure mechanism on the Zengziyanyan collapse in Nanchuan of Chongqing. Hydrogeol Eng Geol 43(1):50–56. https://doi.org/10.16030/j.cnki.issn.1000-3665.2016.01.08
Frayssines M, Hantz D (2006) Failure mechanisms and triggering factors in calcareous cliffs of the subalpine ranges (French alps). Eng Geol 86(4):256–270. https://doi.org/10.1016/j.enggeo.2006.05.009
Frayssines M, Hantz D (2009) Modelling and back-analysing failures in steep limestone cliffs. Int J Rock Mech Min 46:1115–1123. https://doi.org/10.1016/j.ijrmms.2009.06.003
Haghgouei H, Kargar AR, Amini M, Esmaeili K (2020) An analytical solution for analysis of toppling-slumping failure in rock slopes. Eng Geol 265:105396. https://doi.org/10.1016/j.enggeo.2019.105396
He X, Chen HK, Tang HM, Li Q (2014) Research on the mechanism of the development of unstable rocks in the limestone area in the Three Gorges and stability analysis for the rocks. J Southwest Univ (nat Sci Ed) 36(6):155–160. https://doi.org/10.13718/j.cnki.xdzk.2014.06.026
He K, Chen CL, Peng Z, Li B, Pan LB (2016) A review on the collapse hazards of tower-shaped rock. J Geomech 22(3):714–724. https://doi.org/10.3969/j.issn.1006-6616.2016.03.025
Ji SC (1989) Water weakening effect: an important tectonic geological effect-taking quartz as an example. Foreign Geol (beijing) 2:8–14
Jiang MJ, Niu MY, Liao ZW (2016) DEM analysis on direct shear test of rock with coplanar non-penetrating joints considering water softening. J China Inst Water Resour Hydropower Res 14(5):321–327. https://doi.org/10.13244/j.cnki.jiwhr.2016.05.001
Ko TY, John K (2011) Subcritical crack growth in rocks under shear loading. J Geophys Res-Solid Earth 116(B1):1–25. https://doi.org/10.1029/2010JB000846
Ko TY, Lee SS (2020) Experimental study on stress corrosion index governing time-dependent degradation of rock strength. Appl Sci 10(6):2175–2190. https://doi.org/10.3390/app10062175
Lemaitre J (1985a) Coupled elasto-plasticity and damage constitutive equations. Comput Meth Appl Mech Eng 51(1):31–49. https://doi.org/10.1016/0045-7825(85)90026-X
Lemaitre J (1985b) A continuous damage mechanics model for ductile fracture. J Eng Mater-Technol ASME 107:83–89. https://doi.org/10.1115/1.3225775
Ling SX, Wu XY, Sun CW, Liao X, Ren Y, Li XL (2016) Experimental study of chemical damage and mechanical deterioration of black shale due to water–rock chemical action. J Exp Mech 31(4):511–524. https://doi.org/10.7520/1001-4888-15-241
Liu Q, Lu YR, Zhang FE, Qi JX, Zhang S (2010) Qualitative analysis of microcorrosion of limestone induced by temperature and hydrodynamic pressure. Rock Soil Mech 31(S2):149–154. https://doi.org/10.16285/j.rsm.2010.s2.007
Liu C, Yu QY, Wang CB, Song ZY, Du BY (2019) Deterioration law of limestone freeze–thaw cycles. Explor Eng (Rock Soil Drill Tunn) 46(12):80–85. https://doi.org/10.12143/jtkgc.2019.12.015
Oztekin B, Topal T, Kolat C (2006) Assessment of degradation and stability of a cut slope in limestone, Ankara-Turkey. Eng Geol 84(1):12–30. https://doi.org/10.1016/j.enggeo.2005.11.012
Pan Y, Li AW (2008) Discussion of potencial function and equilibrium equation about problem of rock sample monaxial compress failure. J Qingdao Technol Univ 100(1):1–6. https://doi.org/10.3969/j.issn.1673-4602.2008.01.001
Park N, Olson JE, Holder J (2010) Stress-corrosion cracking as an alternative time-dependent shale-stability model. SPE Drill Complet 25(2):168–176. https://doi.org/10.3969/j.issn.1674-0696.2018.10.09
Poisel R, Angerer H, Pöllinger M, Kalcher T, Kittl H (2009) Mechanics and velocity of the Lärchberg–Galgenwald landslide (Austria). Eng Geol 109(1):57–66. https://doi.org/10.1016/j.enggeo.2009.01.002
Powell JW (1875) Exploration of the Colorado river of the west and its tributaries. Government Printing Office, Washington
Ren YR, Chen P, Zhang J, Xie Q (2005) Early-warning analysis on the rockfall for Zenziyan W12# dangerous rock mass in Nanchuan city of Chongqing. Chin J Geol Hazard Control 16(2):28–31. https://doi.org/10.3969/j.issn.1003-8035.2005.02.006
Shuang TZ, Wang ZM, Jiang WJ, Zhu XW (2021) Study on key elements and chemical dissolution index of limestone karstification of Maokou formation in western Guizhou. J Henan Polytech Univ (Nat Sci):1–12
Sichuan Geology Bureau’s 107 Geology Team (1995) Geology report on bauxite deposit in Loujiashan, Sichuan. 107 Geology Team, Chongqing
Song ZP, Cheng Y, Yang TT, Huo RK, Wang JB, Liu XR (2019) Experimental study of the influence of osmotic pressure on pore structure evolution in limestone. Rock Soil Mech 40(12):4607–4619. https://doi.org/10.16285/j.rsm.2018.1831
Song YQ, Liu JC, Shao ZX, Li XL, Zhen JJ (2020) Experimental study on physical and mechanical properties of limestone under freeze–thaw cycles. Sci Technol Eng 20(2):741–746
Sun Y, Zhai C, Xu JZ, Cong YZ, Qin L, Zhao C (2020) Characterisation and evolution of the full size range of pores and fractures in rocks under freeze–thaw conditions using nuclear magnetic resonance and three-dimensional X-ray microscopy. Eng Geol 271:105616. https://doi.org/10.1016/j.enggeo.2020.105616
Tang HM, Zhang XC, Wang LF, Shen JG (2018) Study on the landforms evolution of high cliff in limestone area: taking Zengziyan cliff of Jinfo mountain in Chongqing city as an example. J Chongqing Normal Univ (nat Sci) 35(5):54–62. https://doi.org/10.11721/cqnuj20180507
Tang HM, Shu QJ, Wang LF (2020) Reliability analysis of perilous toppling rock considering seismic force direction. Appl Math Mech 41(3):319–328. https://doi.org/10.21656/1000-0887.400057
Terzaghi K (1950) Mechanism of landslides. The Geological Society of America, Engineering Geology, Berkey
Vutukuri VS (1974) The effect of liquids on the tensile strength of limestone. Int J Rock Mech Min Sci Geomech Abstr 11(6):115. https://doi.org/10.1016/0148-9062(74)90158-2
Wang ZQ, Wu MY, Pan Y (2009) Fold catastrophe model of slope destabilization and its starting velocity. J China Univ Min Technol 38(2):175–181. https://doi.org/10.3321/j.issn:1000-1964.2009.02.006
Wang YL, Liu ZL, Lin SC, Zhuang Z (2016) Finite element analysis of seepage in rock based on continuum damage evolution. Eng Mech 33(11):29–37. https://doi.org/10.6052/j.issn.1000-4750.2015.03.0229
Wang J, Li Y, Song WD, Xu WB (2019) Analysis of damage evolution characteristic of jointed rock mass with different joint dip angles. J Harbin Inst Technol 51(8):143–150. https://doi.org/10.11918/j.issn.0367-6234.201805091
Wen L, Li XB, Su W (2015) Study of physico-mechanical characteristic of slope hard rocks of metal mine influenced by freeze–thaw cycles. J Min Saf Eng 32(4):689–696. https://doi.org/10.13545/j.cnki.jmse.2015.04.027
Wu KY, Jiang ZC, Ye H (2007a) Influence of different plant communities on erosion rates of limestone rock blocks. J Jilin Univ (earth Sci Ed) 5:967–971. https://doi.org/10.3969/j.issn.1671-5888.2007.05.020
Wu XD, Feng XT, Cheng BR (2007b) Study on the mechanical property and the evolutionary neural network constitutive model for limestone under chemical corrosive environments. Key Eng Mater 631:169–1174. https://doi.org/10.4028/www.scientific.net/KEM.340-341.1169
Xia KZ, Liu XM, Chen CX, Song YF, Ou Z, Long Y (2015) Analysis of mechanism of bedding rock slope instability with catastrophe theory. Rock Soil Mech 36(2):477–486. https://doi.org/10.16285/j.rsm.2015.02.025
Xiong SZ, Shi WB, Wang XM (2020) Damage and failure of characteristics of karst fractured rock mass under uniaxial compression. J Eng Geol. https://doi.org/10.13544/j.cnki.jeg.2020-158
Xu T, Ren SY, Fan C, Xu T (2018) The rheological model of rocks with water weakening effect based on variable parameters. China Sci Paper 13(1):70–77. https://doi.org/10.3969/j.issn.2095-2783.2018.01.015
Yin YQ, Du J (1994) The swallowtail catastrophe model of seismic process. Acta Seismol Sin 4:416–422
Yuan XQ, Liu HY, Liu JP (2015) A damage model of jointed rock under coupled action of freezing and thawing. Chin J Rock Mech Eng 34(8):1602–1611. https://doi.org/10.13722/j.cnki.jrme.2014.1342
Zhang HM, Yang GS (2011) Damage mechanical characteristics of rock under freeze–thaw and load coupling. Eng Mech 28(5):161–165
Zhang QS, Yang GS, Ren JX (2003) New study of damage variable and constitutive equation of rock. Chin J Rock Mech Eng 1:30–34. https://doi.org/10.3321/j.issn:1000-6915.2003.01.005
Zhang JX, Shu JQ, Zhang HB, Ren XH, Qi J (2015) Study on rock mass stability criterion based on catastrophe theory. Math Probl Eng. https://doi.org/10.1155/2015/850604
Zhang HM, Peng C, Yang GS, Ye WJ, Shen YJ, Liu H (2017) Study of damage statistical strength criterion of rock considering the effect of freezing and thawing. J China Univ Min Technol 46(5):1066–1072. https://doi.org/10.13247/j.cnki.jcumt.000740
Zhang HM, Meng XZ, Peng C, Yang GS, Ye WJ, Shen YJ, Liu H (2019) Rock damage constitutive model based on residual intensity characteristics under freeze–thaw and load. J China Coal Soc 44(11):3404–3411. https://doi.org/10.13225/j.cnki.jccs.2018.1681
Zhou YL, Wang JM (2019) The research on instability mechanism of rock slope with trailing edge cracks induced by rainfall. J Saf Sci Technol 15(4):103–108. https://doi.org/10.11731/j.issn.1673-193x.2019.04.016
Zhou ZH, Chen ZH, Shi SY, Chen S, Li YW, Zhang W (2020) Dynamic monitoring of the excavation stability of Xijing slope in Dagushan open-pit mine based on energy principle. Met Mine 523(1):130–140. https://doi.org/10.19614/j.cnki.jsks.202001017
Funding
This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 51378521, 51678097).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflicts of 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.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Zhou, F., Tang, H., Chen, S. et al. Research on the Damage-Catastrophe Mechanism of a Tower-Column Unstable Rock Mass with Compressed-Fracture Slumping Mode Under Multi-factor Couplings. Geotech Geol Eng 41, 135–151 (2023). https://doi.org/10.1007/s10706-022-02268-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10706-022-02268-6