Please wait a minute...
Journal of ZheJiang University (Engineering Science)  2022, Vol. 56 Issue (9): 1714-1723    DOI: 10.3785/j.issn.1008-973X.2022.09.004
    
Stability deterioration model of toppling unstable rock mass under freeze-thaw cycle
Jia-jun SHU1,2(),Zheng-ding DENG1,2,*(),Bing-ni WU3,Hua-dong GUAN1,2,Mao-sen CAO1,2
1. Jiangxi Province Key Laboratory of Environmental Geotechnical Engineering and Hazards Control, Jiangxi University of Science and Technology, Ganzhou 341000, China
2. School of Civil and Surveying and Mapping Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, China
3. School of Civil Engineering and Architecture, East China Jiaotong University, Nanchang 330013, China
Download: HTML     PDF(1376KB) HTML
Export: BibTeX | EndNote (RIS)      

Abstract  

The action mechanism and long-term deterioration law of freezing and thawing on the stability of toppling unstable rock mass were explored. Firstly, based on the limit equilibrium theory, considering the influence of the frost heave force of the structural plane and the tensile strength, freezing depth of the non-through section on the moment of the overturning point, the analysis method of stability deterioration of toppling unstable rock mass was put forward. Secondly, based on the frost heave theory of rock, considering the influence of rock debris loss, different dip angles and temperature of microfissures on pore radius’ mechanical properties, the deterioration model of rock tensile strength was constructed. Thirdly, Based on the uneven distribution of cracks, the empirical formula of Stephan freezing depth was modified, and the calculation method of rock freezing depth under freeze-thaw cycle was obtained. Finally, combined with an engineering example, the influence of different sensitive parameters on toppling unstable rock mass stability was discussed. Results showed that the lower the initial tensile strength and the higher the porosity, the more obvious the deterioration effect of the stability of unstable rock mass. When the ambient temperature was higher than 263.15 K (?10 ℃), the stability of unstable rock mass was more sensitive to the change of temperature, and the effect of thermal insulation measures for unstable rock mass in this temperature range was more significant. When the debris loss ratio was more than 0.8, the deterioration rate of unstable rock mass caused by freeze-thaw cycle was obviously accelerated, and the control of debris loss caused by frost heave failure was more conducive to the long-term stability of unstable rock mass in cold regions.



Key wordsfreeze-thaw cycle      toppling unstable rock mass      frost heave force      tensile strength      freezing depth      rock debris loss     
Received: 24 October 2021      Published: 28 September 2022
CLC:  TU 457  
Fund:  江西省自然科学基金资助项目(20202BAB214025);江西省教育厅科研技术项目(GJJ190499);江西省研究生创新专项资金资助项目(XY2021-S025)
Corresponding Authors: Zheng-ding DENG     E-mail: 1317019667@qq.com;dengzhengding@126.com
Cite this article:

Jia-jun SHU,Zheng-ding DENG,Bing-ni WU,Hua-dong GUAN,Mao-sen CAO. Stability deterioration model of toppling unstable rock mass under freeze-thaw cycle. Journal of ZheJiang University (Engineering Science), 2022, 56(9): 1714-1723.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2022.09.004     OR     https://www.zjujournals.com/eng/Y2022/V56/I9/1714


冻融循环作用下倾倒式危岩体稳定性劣化模型

为了探究冻融作用对倾倒式危岩体稳定的作用机理及长期劣化规律, 基于极限平衡理论,考虑结构面冻胀力、未贯通段抗拉强度劣化及冻结深度演化对倾覆点力矩的影响,构建倾倒式危岩体稳定性分析方法. 基于岩石冻胀理论,考虑岩石碎屑流失、微裂隙倾角、温度等参数对孔隙半径冻胀破坏的影响,建立岩石抗拉强度劣化模型并验证其合理性. 利用裂隙分布不均性修正Stephan冻结深度经验公式,得到冻融循环作用下岩石冻结深度计算方法. 结合工程算例,讨论不同敏感参数对倾倒式危岩体稳定性的影响. 结果表明:初始抗拉强度越低、孔隙率越大,危岩体稳定性劣化效果越显著;当环境温度高于263.15 K (?10 ℃)时,危岩体稳定性对温度的变化敏感,危岩体保温措施的效果显著;当碎屑流失比超过0.8时,冻融循环作用对危岩体的劣化速率明显加快,倾倒式危岩体的长期冻融劣化效应明显,控制冻胀破坏产生的碎屑流失有利于寒区危岩体保持长期稳定.


关键词: 冻融循环,  倾倒式危岩体,  冻胀力,  抗拉强度,  冻结深度,  碎屑流失 
Fig.1 Calculation model of toppling unstable rock mass
Fig.2 Schematic diagram of frost heave expansion of microfissures
Fig.3 Fitting curve of rock debris loss ratio
参数 数值 参数 数值
Er / GPa 67.3 fk0 / MPa 8.42
v 0.25 m 18
a0 / μm 50 b0 / μm 2
ω0 / % 1.13 T / K 253
q 0.793 ρ /( g·cm?3) 2.59
Tab.1 Calculation parameters of rock tensile strength deterioration
Fig.4 Comparison between experimental and theoretical results of tensile strength weakening of rock
Fig.5 Actual photo of toppling unstable rock mass
Fig.6 Schematic diagram of engineering example of unstable rock mass
参数 数值 参数 数值
Er / GPa 18.9 fk / MPa 0.78
v 0.24 m 18
ω0 / % 15.9 κw / % 12.4
ρd /( g·cm?3) 2.31 ρr / (g·cm?3) 2.42
T / K 263.4 ξ 0.337 5
S 86 400 K / (W·mK?1) 1.86
q 0.807 η / % 2.3
α / (°) 0 e / m 0
Tab.2 Calculation parameters of unstable rock mass engineering
Fig.7 Variation curve of stability coefficient of unstable rock mass with number of freeze-thaw cycles
Fig.8 Effect of initial porosity on stability coefficient of unstable rock mass
Fig.9 Effect of temperature on stability coefficient of unstable rock mass
Fig.10 Effect of rock debris loss on stability coefficient of unstable rock mass
[1]   奥兰多·B·安德斯兰德, 布兰科·洛达尼. 冻土工程(原著第二版)[M]. 杨让宏, 李勇, 译. 北京: 中国建筑工业出版社, 2011.
[2]   徐斅祖 中国冻胀研究进展[J]. 地球科学进展, 1994, 9 (5): 13- 19
XUE Xiao-zu Progress of frost heave research in China[J]. Advances in Earth Science, 1994, 9 (5): 13- 19
[3]   蒲春林, 邓丽华, 王凯, 等 寒区危岩主控裂隙扩展演化机制研究[J]. 重庆师范大学学报:自然科学版, 2016, 33 (5): 158- 164
PU Chun-lin, DENG Li-hua, WANG Kai, et al The evolutionary mechanism of control fracture propagation of dangerous rock in cold region[J]. Journal of Chongqing Normal University: Natural Science, 2016, 33 (5): 158- 164
[4]   刘慧, 蔺江昊, 杨更社, 等 冻融循环作用下砂岩受拉损伤特性的声发射试验[J]. 采矿与安全工程学报, 2021, 38 (4): 830- 839
LIU Hui, LIN Jiang-hao, YANG Geng-she, et al Acoustic emission test on tensile damage characteristics of sandstone under freeze-thaw cycle[J]. Journal of Mining and Safety Engineering, 2021, 38 (4): 830- 839
[5]   周元辅, 张丹锋, 李明勇, 等 季节性冻土区黏土冻结深度预测[J]. 科学技术与工程, 2021, 21 (13): 5460- 5466
ZHOU Yuan-fu, ZHANG Dan-feng, LI Ming-yong, et al Predicted frost depth of clay in seasonally frozen ground region[J]. Science Technology and Engineering, 2021, 21 (13): 5460- 5466
doi: 10.3969/j.issn.1671-1815.2021.13.040
[6]   CHEN G Q, WANG Y, LI Y, et al Time-dependent damage mechanism of rock deterioration under freeze-thaw cycles linked to alpine hazards[J]. Natural Hazards, 2021, 108 (1): 635- 660
doi: 10.1007/s11069-021-04699-5
[7]   CHEN Y L, WU P, YU Q, et al Effects of freezing and thawing cycle on mechanical properties and stability of soft rock slope[J]. Advances in Materials Science and Engineering, 2017, 2017: 3173659
[8]   陈洪凯, 唐红梅, 王蓉 三峡库区危岩稳定性计算方法及应用[J]. 岩石力学与工程学报, 2004, 23 (4): 614- 619
CHEN Hong-kai, TANG Hong-mei, WANG Rong Calculation method of stability for unstable rock and application to the Three Gorges Reservoir[J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 23 (4): 614- 619
doi: 10.3321/j.issn:1000-6915.2004.04.016
[9]   CHEN H K, TANG H M Method to calculate fatigue fracture life of control fissure in perilous rock[J]. Applied Mathematics and Mechanics, 2007, 28 (5): 643- 649
[10]   陈洪凯, 鲜学福, 唐红梅, 等 危岩稳定性分析方法[J]. 应用力学学报, 2009, 26 (2): 278- 282
CHEN Hong-kai, XIAN Xue-fu, TANG Hong-mei, et al Stability analysis method for perilous rock[J]. Chinese Journal of Applied Mechanics, 2009, 26 (2): 278- 282
[11]   丁王飞, 周云涛 基于主控结构面锁固段模型的危岩稳定性计算[J]. 人民长江, 2015, 46 (24): 72- 77
DING Wang-fei, ZHOU Yun-tao Analysis for unstable rock stability based on locking portion model of dominant fissure[J]. Yangtze River, 2015, 46 (24): 72- 77
[12]   申艳军, 杨更社, 王婷, 等 岩石内孔隙/裂隙冻胀力模型及其适用性评价[J]. 冰川冻土, 2019, 41 (1): 117- 128
SHEN Yan-jun, YANG Geng-she, WANG Ting, et al Evaluation of frost heave force models of pore/fissure in rock and their applicability[J]. Journal of Glaciology and Geocryology, 2019, 41 (1): 117- 128
[13]   LV Z T, XIA C C, LI Q, et al Empirical frost heave model for saturated rock under uniform and unidirectional freezing conditions[J]. Rock Mechanics and Rock Engineering, 2019, 52 (3): 955- 963
doi: 10.1007/s00603-018-1666-z
[14]   VLAHOU I, WORSTER M G Ice growth in a spherical cavity of a porous medium[J]. Journal of Glaciology, 2010, 56 (196): 271- 277
doi: 10.3189/002214310791968494
[15]   ZHOU J Z, WEI C F Ice lens induced interfacial hydraulic resistance in frost heave[J]. Cold Regions Science and Technology, 2020, 171: 102964
doi: 10.1016/j.coldregions.2019.102964
[16]   DERJAGUIN B V, CHURAEV N V Flow of nonfreezing water interlayers and frost heaving[J]. Cold Regions Science and Technology, 1986, 12 (1): 57- 66
doi: 10.1016/0165-232X(86)90020-0
[17]   REMPEL A W, WETTLAUFER J S, WORSTER M G Interfacial premelting and the thermomolecular force: thermodynamic buoyancy[J]. Physical Review Letters, 2001, 87 (8): 088501
doi: 10.1103/PhysRevLett.87.088501
[18]   DÖPPENSCHMIDT A, BUTT H J Measuring the thickness of the liquid-like layer on ice surfaces with atomic force microscopy[J]. Langmuir, 2000, 16 (16): 6709- 6714
doi: 10.1021/la990799w
[19]   刘红岩, 赵雨霞 冻融循环下隧道围岩冻胀力理论计算[J]. 中南大学学报:自然科学版, 2020, 51 (4): 1049- 1058
LIU Hong-yan, ZHAO Yu-xia Theoretical calculation of frost heaving pressure in tunnel surrounding rock during freeze-thaw cycles[J]. Journal of Central South University: Science and Technology, 2020, 51 (4): 1049- 1058
[20]   阎锡东, 刘红岩, 刑闯锋, 等 基于微裂隙变形与扩展的岩石冻融损伤本构模型研究[J]. 岩土力学, 2015, 36 (12): 3489- 3499
YAN Xi-dong, LIU Hong-yan, XING Chuang-feng, et al Constitutive model research on freezing-thawing damage of rock based on deformation and propagation of microcracks[J]. Rock and Soil Mechanics, 2015, 36 (12): 3489- 3499
[21]   WALDER J, HALLET B A theoretical model of the fracture of rock during freezing[J]. Geological Society of America Bulletin, 1985, 96: 336- 346
doi: 10.1130/0016-7606(1985)96<336:ATMOTF>2.0.CO;2
[22]   MUSKHELISHVILI N I. Some basic problems of the mathematical theory of elasticity [M]. 2nd ed. Leyden: Noordhoff International Publishing, 1977.
[23]   闻磊, 沈建琳, 梅松华, 等 冻融损伤岩体质量评价方法研究[J]. 矿业研究与开发, 2020, 40 (12): 57- 63
WEN Lei, SHEN Jian-lin, MEI Song-hua, et al Study on quality evaluation method of freeze-thaw damaged rock mass[J]. Mining Research and Development, 2020, 40 (12): 57- 63
[24]   张向东, 王浩, 敬鹏飞 基于岩石“等效损伤”探究宏观断裂规律[J]. 中国地质灾害与防治学报, 2020, 31 (3): 117- 125
ZHANG Xiang-dong, WANG Hao, JING Peng-fei Studying the macroscopic fracture rule based on rock “equivalent damage”[J]. The Chinese Journal of Geological Hazard and Control, 2020, 31 (3): 117- 125
[25]   胡亚元, 王超 多节理岩体的非线性耦合损伤本构模型[J]. 煤炭学报, 2019, 44 (增1): 52- 60
HU Ya-yuan, WANG Chao Nonlinear coupling damage constitutive model for multi-jointed rock mass[J]. Journal of China Coal Society, 2019, 44 (增1): 52- 60
[26]   高青鹏, 曹平, 王飞, 等 压剪作用下多节理类岩试样力学性质及破坏判据[J]. 岩土力学, 2019, 40 (3): 1013- 1022
GAO Qing-peng, CAO Ping, WANG Fei, et al Mechanical properties and failure criteria of multi-joint rock-like specimens under compression-shear[J]. Rock and Soil Mechanics, 2019, 40 (3): 1013- 1022
[27]   CARTA J A, BUENO C, RAMÍREZ P Statistical modelling of directional wind speeds using mixtures of von Mises distributions: case study[J]. Energy Conversion and Management, 2008, 49 (5): 897- 907
doi: 10.1016/j.enconman.2007.10.017
[28]   ERDEM E, SHI J Comparison of bivariate distribution construction approaches for analysing wind speed and direction data[J]. Wind Energy, 2011, 14: 27- 41
doi: 10.1002/we.400
[29]   闻磊, 李夕兵, 苏伟 冻融循环影响下金属矿山边坡坚硬岩石物理力学性质研究[J]. 采矿与安全工程学报, 2015, 32 (4): 689- 696
WEN-Lei, LI Xi-bing, SU Wei Study of physico-mechanical characteristics of slope hard rocks of metal mine influenced by freeze-thaw cycles[J]. Journal of Mining and Safety Engineering, 2015, 32 (4): 689- 696
[30]   JUMIKIS A R. Thermal Geotechnics [M]. New Brunswick: Rutgers University Press, 1977.
[31]   王仲锦, 叶阳升, 闫宏业, 等 寒区铁路路基防冻胀设计中冻深计算方法的探讨[J]. 铁道建筑, 2013, (2): 57- 59
WANG Zhong-jin, YE Yang-sheng, YAN Hong-ye, et al Discussion on calculation method of frost depth in anti-frost heave design of railway subgrade in cold regions[J]. Railway Engineering, 2013, (2): 57- 59
[32]   NELSON F E, OUTCALT S I A computational method for prediction and regionalization of permafrost[J]. Arctic and Alpine Research, 1987, 19: 279- 288
doi: 10.2307/1551363
[33]   裴万胜. 冻土水−热−力相互作用过程及数值模拟研究[D]. 北京: 中国科学院大学, 2015: 40-52.
LIU Wan-sheng. Study of the hydro-thermal-mechanical interaction process of frozen soil and its numerical simulation [D]. Beijing: University of Chinese Academy of Sciences, 2015: 40-52.
[34]   王超, 王川婴, 王益腾, 等 基于孔壁光学图像的岩石孔隙结构识别与分析方法研究[J]. 岩石力学与工程学报, 2021, 40 (9): 1894- 1901
WANG Chao, WANG Chuan-ying, WANG Yi-teng, et al Research on identification and analysis method of rock pore structure based on optical images of borehole walls[J]. Chinese Journal of Rock Mechanics and Engineering, 2021, 40 (9): 1894- 1901
[35]   孙利辉, 纪洪广, 杨本生 西部典型矿区弱胶结地层岩石的物理力学性能特征[J]. 煤炭学报, 2019, 44 (3): 866- 874
SUN Li-hui, JI Hong-guang, YANG Ben-sheng Physical and mechanical characteristic of rocks with weakly cemented strata in Western representative mining area[J]. Journal of China Coal Society, 2019, 44 (3): 866- 874
[36]   杜锋, PENG Syd S 神东矿区岩石物理力学性质变化规律研究[J]. 采矿与安全工程学报, 2019, 36 (5): 1009- 1015
DU Feng, PENG Syd S Change rule of physical and mechanical property of rock mass in Shendong mine[J]. Journal of Mining and Safety Engineering, 2019, 36 (5): 1009- 1015
[1] Kang-qiao HUANG,Cheng ZHAO,Wei ZHOU,Xing-hong LIU,Gang MA. Three-dimensional mesoscopic study on freeze-thaw of concrete based on multi-field coupled model[J]. Journal of ZheJiang University (Engineering Science), 2021, 55(1): 62-70.
[2] OU Zu-min, SUN Lu. Flexural fatigue-life reliability of frost-damaged concrete[J]. Journal of ZheJiang University (Engineering Science), 2017, 51(6): 1074-1081.
[3] WU Hai-rong, JIN Wei-liang, YAN Yong-dong, XIA Jin. Environmental zonation and life prediction of concrete in
frost environments
[J]. Journal of ZheJiang University (Engineering Science), 2012, 46(4): 650-657.
[4] WANG Hai-long, GUO Chun-ling, SUN Xiao-yan, JIN Wei-liang. Degradation mesomechanism of concrete deteriorated by soft water[J]. Journal of ZheJiang University (Engineering Science), 2012, 46(10): 1887-1892.