Micro-tilting deformation behavior of tension-fractured hazardous rock mass preceding collapse under gravity
HE Zheng1, XIE Mowen2*, ZHAO Chen2
(1. National Institute of Natural Hazards, Ministry of Emergency Management of China, Beijing 100085, China; 2. School of Resources and Safety Engineering, University of Science and Technology Beijing, Beijing 100083, China)
Abstract：To elucidate the precursory tilt deformation patterns of tension-fractured hazardous rock masses under gravitational loading, this study conceptualizes the collapse process as subcritical propagation under stress corrosion, utilizing a bending Mode-I fracture model. A time-dependent evolution equation for tilt deformation is derived, and the theoretical characteristics of tilting behavior are examined. Based on the principles of micro-electro-mechanical system (MEMS) gravity accelerometry, a method for monitoring the cumulative tilt angle along the primary tilting direction is established using spatial vector angles. A physical model test simulating the collapse of such rock masses under predominantly gravitational loading is designed and conducted, with the resulting tilt deformation behavior analyzed. Additionally, high-low temperature tests are performed to calibrate MEMS tilt sensor drift, and automated field monitoring is implemented to capture time-series variation patterns of tilt angles during collapse events. Comprehensive analysis indicates that precursory tilt deformation transitions from a constant-rate phase to an accelerating phase. However, due to subcritical crack propagation within a heterogeneous medium, localized step-like fluctuations occur during the constant-rate stage, while trend alterations manifest during acceleration. A power-law relationship is identified between the tilt rate and its acceleration prior to collapse. Based on this relationship, a collapse time prediction equation utilizing the inverse of the tilt rate is proposed, and the predictive efficacy of both linear and nonlinear formulations is evaluated. These findings support the application of tilt-sensing technology in monitoring and early warning systems for rock collapse.
[1] 胡厚田. 崩塌分类的初步探讨[J]. 铁道学报，1985，7(2)：90–100.(HU Houtian. Preliminary investigation on the classification of landfalls[J]. Journal of the China Railway Society，1985，7(2)：90–100.(in Chinese))
[2] 陈洪凯，唐红梅. 拉剪型危岩发育过程的模型试验[J]. 重庆大学学报：自然科学版，2006，29(6)：115–119.(CHEN Hongkai，TANG Hongmei. Testing research on development of perilous rock in tension-shear fracture[J]. Journal of Chongqing University：Natural Science Edition，2006，29(6)：115–119.(in Chinese))
[3] 贺 铮，谢谟文，吴志祥，等. 应用微芯桩传感器的拉裂型边坡危岩体临崩倾斜变形特征现场实测研究[J]. 岩土力学，2024，45(11)：3 399–3 415.(HE Zheng，XIE Mowen，WU Zhixiang，et al. Field measurement study on the pre-collapse inclination deformation characteristics of tension-cracking slope rock mass using micro-core-pile sensor[J]. Rock and Soil Mechanics，2024，45(11)：3 399–3 415.(in Chinese))
[4] 王根龙，伍法权，祁生文. 悬臂–拉裂式崩塌破坏机制研究[J]. 岩土力学，2012，33(增2)：269–274.(WANG Genlong，WU Faquan，QI Shengwen. Research on failure mechanisms for cantilever and tension crack-type collapse[J]. Rock and Soil Mechanics，2012，33(Supp.2)：269–274.(in Chinese))
[5] 周德培. 岩石单向拉伸的蠕变特性[J]. 西南交通大学学报，1988，69(3)：21–29.(ZHOU Depei. Creep behaviour of rocks under uniaxial tension[J]. Journal of Southwest Jiaotong University，1988，69(3)：21–29.(in Chinese))
[6] 陈有亮，孙 钧. 岩石的流变断裂特性[J]. 岩石力学与工程学报，1996，15(4)：323–327.(CHEN Youliang，SUN Jun. Creep fracture of rock[J]. Chinese Journal of Rock Mechanics and Engineering，1996，15(4)：323–327.(in Chinese))
[7] WONG R H C，CHAU K T. Effect of cyclic heating on subcritical crack growth of rock beams under four-point bending test[J]. International Journal of Rock Mechanics and Mining Sciences，2021，138：1–23.
[8] ABELLÁN A，CALVET J，VILAPLANA J，et al. Detection and spatial prediction of rockfalls by means of terrestrial laser scanner monitoring[J]. Geomorphology，2010，119：162–171.
[9] ROYÁN M J，ABELLÁN A，JABOYEDOFF M，et al. Spatio- temporal analysis of rockfall pre-failure deformation using Terrestrial LiDAR[J]. Landslides，2014，11(4)：697–709.
[10] ROWE E，HUTCHINSON D J，KROMER R A，et al. An analysis of failure mechanism constraints on pre-failure rock block deformation using TLS and roto-translation methods[J]. Landslides，2018，15(3)：409–421.
[11] LI H B，QI S C，YANG X G，et al. Geological survey and unstable rock block movement monitoring of a post?earthquake high rock slope using terrestrial laser scanning[J]. Rock Mechanics and Rock Engineering，2020，53：4 523–4 537.
[12] UCHIMURA T，TOWHATA I，ANH T T L，et al. Simple monitoring method for precaution of landslides watching tilting and water contents on slopes surface[J]. Landslides，2010，7：351–357.
[13] 谢济仁，乔世范，余鹏鲲，等. 土质滑坡坡表倾斜变形的室内外试验研究[J]. 岩土力学，2021，42(3)：681–690.(XIE Jiren，QIAO Shifan，YU Pengkun，et al. Surface tilt deformation of soil landslides based on laboratory and field tests[J]. Rock and Soil Mechanics，2021，42(3)：681–690.(in Chinese))
[14] 李 程，宋胜武，孙进忠. MEMS 惯性传感器在水库岸坡变形监测中的应用及仿真研究[J]. 岩石力学与工程学报，2023，42(5)： 1 248–1 257.(LI Cheng，SONG Shengwu，SUN Jinzhong. Application and simulation research of MEMS inertial sensor in reservoir bank slope deformation monitoring[J]. Chinese Journal of Rock Mechanics and Engineering，2023，42(5)：1 248–1 257.(in Chinese))
[15] 贺 铮. 拉裂型边坡危岩体崩塌预测模型研究[博士学位论文][D]. 北京：北京科技大学，2023.(HE Zheng. Study on instability prediction model of tension-splitting rock mass on slopes[Ph. D. Thesis][D]. Beijing：University of Science and Technology Beijing，2023.(in Chinese))
[16] 陈洪凯，鲜学福，唐红梅. 危岩稳定性断裂力学计算方法[J]. 重庆大学学报，2009，32(4)：434–437.(CHEN Hongkai，XIAN Xuefu，TANG Hongmei. Stability analysis method for perilous rock by fracture mechanics[J]. Journal of Chongqing University，2009，32(4)：434–437.(in Chinese))
[17] 何思明，吴 永，李新坡. 地震诱发岩体崩塌的力学机制[J]. 岩石力学与工程学报，2010，29(增1)：3 359–3 363.(HE Siming，WU Yong，LI Xinpo. Collapse mechanism of danger rock triggered by earthquake[J]. Chinese Journal of Rock Mechanics and Engineering，2010，29(Supp.1)：3 359–3 363.(in Chinese))
[18] ATKINSON B. Subcritical crack growth in geological materials[J]. Journal of Geophysical Research，1984，89(B6)：4 077–4 114.
[19] 肖洪天，杨若琼，周维垣. 三峡船闸花岗岩亚临界裂纹扩展试验研究[J]. 岩石力学与工程学报，1999，18(4)：447–450.(XIAO Hongtian，YANG Ruoqiong，ZHOU Weiheng. Testing study of subcritical crack growth of granite at the three gorges shiplock[J]. Chinese Journal of Rock Mechanics and Engineering，1999，18(4)：447–450.(in Chinese))
[20] 李江腾，曹 平，袁海平. 岩石亚临界裂纹扩展试验及门槛值研究[J]. 岩土工程学报，2006，28(3)：415–418.(LI Jiangteng，CAO Ping，YUAN Haiping. Study on subcritical crack growth and thresholds of rocks[J]. Chinese Journal of Geotechnical Engineering，2006，28(3)：415–418.(in Chinese))
[21] 蒋青青，李江腾，胡毅夫，等. 水对亚临界裂纹扩展的影响[J]. 岩土力学，2008，29(9)：2 527–2 530.(JIANG Qingqing，LI Jiangteng，HU Yifu，et al. Effects of water on subcritical crack growth[J]. Rock and Soil Mechanics，2008，29(9)：2 527–2 530.(in Chinese))
[22] 万琳辉，曹 平，黄永恒，等. 水对岩石亚临界裂纹扩展及门槛值的影响研究[J]. 岩土力学，2010，31(9)：2 737–2 742.(WAN Linhui，CAO Ping，HUANG Yongheng，et al. Study of subcritical crack growth of rocks and threshold values in different environments[J]. Rock and Soil Mechanics，2010，31(9)：2 737–2 742.(in Chinese))
[23] WILLIAMS D，EVANS A. A simple method for studying slow crack growth[J]. Journal of Testing and Evaluation，1973，1(2)：264–270.
[24] TADA H，PARIS P，IRWIN G. The stress analysis of cracks handbook[M]. Hellertown：Del Research Corp，1973：1–252.
[25] 张 磊，巨能攀，何朝阳，等. 滑坡裂缝计时序数据实时异常检测分析[J]. 岩石力学与工程学报，2024，43(1)：206–215.(ZHANG Lei，JU Nengpan，HE Chaoyang，et al. Real-time anomaly detection and analysis of time series data for crack gauge in landslides[J]. Chinese Journal of Rock Mechanics and Engineering，2024，43(1)：206–215.(in Chinese))
[26] 唐红梅，陈洪凯，王 智，等. 危岩破坏激振效应试验研究[J]. 岩土工程学报，2013，25(11)：2 117–2 122.(TANG Hongmei，CHEN Hongkai，WANG Zhi，et al. Experimental study on excitation effect for unstable rock[J]. Chinese Journal of Geotechnical Engineering，2013，25(11)：2 117–2 122.(in Chinese))
[27] 傅宇方，梁正召，唐春安. 岩石介质细观非均匀性对宏观破裂过程的影响[J]. 岩土工程学报，2000，22(6)：486–492.(FU Yufang，LIANG Zhengzhao，TANG Chun?an. Numerical simulation on influence of mesoscopic heterogeneity on macroscopic behavior of rock failure[J]. Chinese Journal of Geotechnical Engineering，2000，22(6)：486–492.(in Chinese))
[28] 秦四清，王媛媛，马 平. 崩滑灾害临界位移演化的指数律[J]. 岩石力学与工程学报，2010，29(5)：873–880.(QIN Siqing，WANG Yuanyuan，MA Ping. Exponential laws of critical displacement evolution for landslides and avalanches[J]. Chinese Journal of Rock Mechanics and Engineering，2010，29(5)：873–880.(in Chinese))
[29] VOIGHT B. A method for prediction of volcanic eruption[J]. Nature，1988，332：125–130.
[30] SAITO M. Forecasting time of occurrence of a slope failure[C]// Proceedings of the 6th International Conference on Soil Mechanics and Foundation Engineering. Toronto：University of Toronto Press，1965：537–541.
[31] FUKUZONO T. A new method for predicting the failure time of a slope[C]// Proceedings of IV International Conference and Field Workshop on Landslides. Tokyo：Tokyo University Press，1985：145–150.
[32] PETLEY D N，BULMER M H，MURPHY W. Patterns of movement in rotational and translational landslides[J]. Geology，2002，30：719–722.
[33] ROSE N D，HUNGR O. Forecasting potential rock slope failure in open pit mines using the inverse-velocity method[J]. International Journal of Rock Mechanics and Mining Sciences，2007，44(2)：308–320.
[34] DICK G J，EBERHARDT E，CABREJO-LIEVANO A G，et al. Development of an early-warning time-of-failure analysis methodology for open-pit mine slopes utilizing ground-based slope stability radar monitoring data[J]. Canadian Geotechnical Journal，2015，52： 515–529.
[35] CARLÀ T，INTRIERI E，TRAGLIA F D，et al. Guidelines on the use of inverse velocity method as a tool for setting alarm thresholds and forecasting landslides and structure collapses[J]. Landslides，2017，14(2)：517–534.
[36] 贺 铮，谢谟文，赵 晨，等. 基于共振频率时变特征的拉裂型危岩体崩塌预测方程及试验研究[J]. 工程力学，DOI：10.6052/j.issn. 1000–4750.2024.10.0799(HE Zheng，XIE Mowen，ZHAO Chen，et al. Construction and experimental verification of collapse time prediction model for tension-splitting rock mass on slopes based on natural frequency[J]. Engineering Mechanics，DOI：10.6052/j.issn. 1000–4750.2024.10.0799.(in Chinese))
[37] 张晓勇，谢谟文，张 磊，等. 基于固有频率的坠落危岩体稳定系数计算模型研究[J]. 岩石力学与工程学报，2023，42(3)：585–593.(ZHANG Xiaoyong，XIE Mowen，ZHANG Lei，et al. Study on calculation model of stability coefficient of falling dangerous rock mass based on natural frequency[J]. Chinese Journal of Rock Mechanics and Engineering，2023，42(3)：585–593.(in Chinese))
[38] 杜 岩，张洪达，谢谟文，等. 大型危岩体崩塌灾害早期监测预警技术研究综述[J]. 工程科学与技术，2024，56(5)：10–23.(DU Yan，ZHANG Hongda，XIE Mowen，et al. Review on the monitoring and early warning technology of large-scale unstable rock collapse[J]. Advanced Engineering Sciences，2024，56(5)：10–23.(in Chinese))
2026, Vol. 45 
