THMC多場耦合作用下巖石物理力學性能與本構模型研究綜述

顏丙乾; 任奮華; 蔡美峰; 郭奇峰; 喬趁

doi:10.13374/j.issn2095-9389.2019.07.29.003

THMC多場耦合作用下巖石物理力學性能與本構模型研究綜述

doi: 10.13374/j.issn2095-9389.2019.07.29.003

顏丙乾^{1, 2},
任奮華^{1, 2, ,},
蔡美峰^{1, 2},
郭奇峰^{1, 2},
喬趁^{1, 2}

1.
北京科技大學土木與資源工程學院，北京 100083
2.
北京科技大學城市與地下空間工程北京市重點實驗室，北京 100083

基金項目: 國家自然科學基金面上資助項目（51774022）；國家重點研發計劃資助項目（2017YFC0804101）

詳細信息

通訊作者:
E-mail：renfenhua @126.com

中圖分類號: TG741.7
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出版歷程
- 收稿日期: 2019-07-29
- 刊出日期: 2020-11-25

A review of the research on physical and mechanical properties and constitutive model of rock under THMC multi-field coupling

YAN Bing-qian^{1, 2},
REN Fen-hua^{1, 2
, ,},
CAI Mei-feng^{1, 2},
GUO Qi-feng^{1, 2},
QIAO Chen^{1, 2}

1.
School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China
2.
Beijing Key Laboratory of Urban Underground Space Engineering, University of Science and Technology Beijing, Beijing 100083, China

More Information

Corresponding author: E-mail: renfenhua @126.com

摘要

摘要: 巖石多場耦合作用的研究已經開展了數十年，包括巖石在單一物理場、兩場耦合或三場耦合作用效應的研究。然而深部礦產資源開采和地下空間開發中巖體的賦存環境非常復雜，巖體在高溫、高滲透壓、高應力及復雜水化學環境中將發生溫度–水流–應力–化學（THMC）多場耦合作用。綜合分析巖石多場耦合作用下的裂隙演化、變形力學機制、力學本構和耦合模型構建等方面的研究，在分析巖石強度理論的基礎上得出巖石多場耦合本構模型以及巖石蠕變本構模型。不同行業對巖石多場耦合作用的研究重點存在一定的差異，巖石多場耦合作用不僅涉及到礦產資源開發、油氣田開采、地熱資源開發等資源能源領域，其在水利水電工程、高寒工程、地下工程、地下核廢料處置及深埋能源儲庫等領域也是研究的重點。巖石在高應力、水流、高溫和化學作用下，不僅會發生耦合作用，而且會對巖石本身的物理力學性能產生影響。分析研究多場耦合作用下巖石的力學性能對于預防事故發生和保障工程安全開展具有重要的現實意義。最后探討分析了巖石多場耦合研究的重點、難點和今后研究的方向，為工程實踐和相關問題的解決提供參考。
- 裂隙巖體 /
- 多場耦合 /
- 損傷演化 /
- 巖石蠕變 /
- 本構模型
Abstract: The study of multi-field coupling of rocks has been carried out for decades, including the effects of single physical field, two-field coupling, and three-field coupling of rocks. However, the occurrence environment of rock mass in deep mining of mineral resources and underground space development is very complex. Thermal–hydrological–mechanical–chemical (THMC) multi-field coupling effect will occur in rock mass under high temperature, high osmotic pressure, high stress, and complex hydrochemical environment. The multi-field coupling of rocks is not the simple superposition of multiple physical fields, but the mutual influence and action of each physical field. The research on fracture evolution, deformation mechanics mechanism, mechanical constitutive and coupling model construction was comprehensively analyzed. Based on the analysis of rock strength theory, the development of a rock multi-field coupling constitutive model and a rock creep constitutive model were obtained. There are some differences in the research focus of multi-field coupling of rocks for different industries. The multi-field coupling of rocks not only involves the development of mineral resources, oil and gas fields, geothermal resources and other resources and energy fields, but also water conservancy and hydropower engineering, alpine engineering, underground engineering, underground nuclear waste disposal, and deep buried energy storage. Under the action of high stress, seepage, high temperature and chemical action, not only will the coupling effect occur, but the physical and mechanical properties of rock itself will be affected. It is of great practical significance to analyze and study the mechanical properties of rocks under the action of multi-field coupling for preventing accidents and ensuring engineering safety. Finally, the key and difficult points of rock multi field coupling research and the direction of future research were discussed, which provides a reference for engineering practice and related problems.
- fractured rock /
- multi-field coupling /
- damage evolution /
- rock creep /
- constitutive model

HTML全文

圖 1 油頁巖應力、化學損傷表征單元^[8]

Figure 1. Characterization unit of stress and chemical damage in oil shale^[8]

下載: 全尺寸圖片幻燈片

圖 2 THMD耦合作用模式

Figure 2. THMD coupling mechanism

下載: 全尺寸圖片幻燈片

圖 3 高地溫隧洞受力示意圖

Figure 3. Diagram of stress on tunnel with high geothermal temperature

下載: 全尺寸圖片幻燈片

圖 4 填埋場災變過程的多物理場耦合特征示意圖

Figure 4. Schematic diagram of the characteristics of multi-physics coupling for landfill catastrophe

下載: 全尺寸圖片幻燈片

圖 5 裂隙巖體變形的總體描述^[15]

Figure 5. General description of fractured rock masses deformation^[15]

下載: 全尺寸圖片幻燈片

圖 6 多場耦合巖體常見的場及耦合關系^[16]

Figure 6. Common fields and coupling relationships of multi-field coupled rock mass^[16]

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圖 7 THM耦合示意圖^[33]

Figure 7. Diagram of coupled THM^[33]

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圖 8 熱液力過程之間的相互關系

Figure 8. Interdependence of thermal-fluid-mechanical process

下載: 全尺寸圖片幻燈片

表 1 巖石強度理論^[24]

Table 1. Rock strength theory^[24]

Strength theory of rock mass
Theoretical strength criterion	Theoretical strength criterion of rock mass	Classical strength criterion	Maximum normal stress theory
			Maximum positive strain theory
			Maximum shear stress theory
			Octahedral shear stress theory
		Mohr–Coulomb strength theory
		Griffith strength theory
		Double shear strength theory
	Strength criterion of structural plane	Strength theory based on Mohr–Coulomb
Empirical strength criterion		Hoek–Brown strength criterion

下載: 導出CSV

久色视频

參考文獻(64)

[1]	Zhou C B, Chen Y F, Jiang Q H, et al. A generalized multi-field coupling approach and its application to stability and deformation control of a high slope. J Rock Mech Geotech Eng, 2011, 3(3): 193 doi: 10.3724/SP.J.1235.2011.00193
[2]	Su B Y, Zhang W J, Sheng J C, et al. Study of permeability in single fracture under effects of coupled fluid flow and chemical dissolution. Rock Soil Mech, 2010, 31(11): 3361 doi: 10.3969/j.issn.1000-7598.2010.11.001 速寶玉, 張文捷, 盛金昌, 等. 滲流–化學溶解耦合作用下巖石單裂隙滲透特性研究. 巖土力學, 2010, 31(11):3361 doi: 10.3969/j.issn.1000-7598.2010.11.001
[3]	Qin Z H. Study of Load-Bearing Characteristics of Surrounding Rock of Hydraulic Tunnels under High Geotemperature and Hydraulic Pressure Conditions Using Coupled THMD Numerical Model[Dissertation]. Nanning: Guangxi University, 2016 秦子華. 基于熱–水–損傷耦合模型的高地溫水工高壓隧洞圍巖承載特性數值模擬研究[學位論文]. 南寧: 廣西大學, 2016
[4]	Yang Y L, Zheng K Y, Li Z W, et al. Experimental study on pore–fracture evolution law in the thermal damage process of coal. Int J Rock Mech Min Sci, 2019, 116: 13 doi: 10.1016/j.ijrmms.2019.03.004
[5]	Hudson J A, Jing L. Demonstration of coupled models and their validation against experiment: the current phase DECOVALEX 2015//Rock Characterisation, Modelling and Engineering Design Methods—Proceedings of the 3rd ISRM SINOROCK, Symposium. Shanghai, 2013: 391
[6]	Zhou H, Feng X T. Research progress in rock stress–hydraulic–chemical coupling process. Chin J Rock MechEng, 2006, 25(4): 855 doi: 10.3321/j.issn:1000-6915.2006.04.021 周輝, 馮夏庭. 巖石應力–水力–化學耦合過程研究進展. 巖石力學與工程學報, 2006, 25(4):855 doi: 10.3321/j.issn:1000-6915.2006.04.021
[7]	Pan P Z, Feng X T, Huang X H, et al. Coupled THM processes in EDZ of crystalline rocks using an elasto-plastic cellular automaton. Environ Geol, 2009, 57(6): 1299 doi: 10.1007/s00254-008-1463-1
[8]	Li K. Hydrothermal Coupling Model and Hydraulic Fracturing Law of Oil Shale in Situ Mining[Dissertation]. Fuxing: Liaoning University of Engineering and Technology, 2011 李凱. 油頁巖原位開采水熱力耦合模型與水力壓裂規律研究[學位論文]. 阜新: 遼寧工程技術大學, 2011
[9]	Tan X J, Chen W Z, Wu G J, et al. Study of thermo–hydro–mechanical–damage (THMD) coupled model in the condition of freeze-thaw cycles and its application to cold region tunnels. Chin J Rock Mech Eng, 2013, 32(2): 239 doi: 10.3969/j.issn.1000-6915.2013.02.004 譚賢君, 陳衛忠, 伍國軍, 等. 低溫凍融條件下巖體溫度–滲流–應力–損傷(THMD)耦合模型研究及其在寒區隧道中的應用. 巖石力學與工程學報, 2013, 32(2):239 doi: 10.3969/j.issn.1000-6915.2013.02.004
[10]	Yang J H, Zhang G, Qiao T, et al. Establishment and verification of rock damage mechanics model under the coupled thermo–hydro–mechanical effect. J Saf Sci Technol, 2017, 13(4): 87 楊金輝, 章光, 喬彤, 等. 熱–水–力耦合作用下巖石損傷力學模型與驗證. 中國安全生產科學技術, 2017, 13(4):87
[11]	Hsieh P A, Neuman S P, Stiles G K, et al. Field determination of the three-dimensional hydraulic conductivity tensor of anisotropic media: 2. Methodology and application to fractured rocks. Water Resour Res, 1985, 21(11): 1667 doi: 10.1029/WR021i011p01667
[12]	Yang J B, Feng X T Pan P Z. Experimental study of permeability characteristics of single rock fracture considering stress history. Rock Soil Mech, 2013, 34(6): 1629 楊金保, 馮夏庭, 潘鵬志. 考慮應力歷史的巖石單裂隙滲流特性試驗研究. 巖土力學, 2013, 34(6):1629
[13]	He H J, Lan J W, Chen Y M, et al. Monitoring and analysis of slope slip process at a landfill in Northwest China. Chin J Geotech Eng, 2015, 37(9): 1721 doi: 10.11779/CJGE201509022 何海杰, 蘭吉武, 陳云敏, 等. 西北地區某填埋場堆體滑移過程監測與分析. 巖土工程學報, 2015, 37(9):1721 doi: 10.11779/CJGE201509022
[14]	Zhao Y, Yang D, Feng Z, et al. Multi-field coupling theory of porous media and its applications to resources and energy engineering. Chin J Rock Mech Eng, 2008, 27(7): 1321 doi: 10.3321/j.issn:1000-6915.2008.07.004 趙陽升, 楊棟, 馮增朝, 等. 多孔介質多場耦合作用理論及其在資源與能源工程中的應用. 巖石力學與工程學報, 2008, 27(7):1321 doi: 10.3321/j.issn:1000-6915.2008.07.004
[15]	Müller C, Frühwirt T, Haase D, Et al. Modeling deformation and damage of rock salt using the discrete element method. Int J Rock Mech Min Sci, 2018, 103: 230 doi: 10.1016/j.ijrmms.2018.01.022
[16]	Shi B. On fields and their coupling in engineering geology. J Eng Geol, 2013, 21(5): 673 doi: 10.3969/j.issn.1004-9665.2013.05.001 施斌. 論工程地質中的場及其多場耦合. 工程地質學報, 2013, 21(5):673 doi: 10.3969/j.issn.1004-9665.2013.05.001
[17]	Zhou C B, Chen Y F, Jiang Q H, et al. On generalized multi-field coupling for fractured rock masses and its applications to rock engineering. Chin J Rock Mech Eng, 2008, 27(7): 1329 doi: 10.3321/j.issn:1000-6915.2008.07.005 周創兵, 陳益峰, 姜清輝, 等. 論巖體多場廣義耦合及其工程應用. 巖石力學與工程學報, 2008, 27(7):1329 doi: 10.3321/j.issn:1000-6915.2008.07.005
[18]	Zhou C Y, Peng Z Y, Shang W, et al. On the key problem of the water-rock interaction in geoengineering: mechanical variabilityof special weak rocks and some development trends. Rock Soil Mech, 2002, 23(1): 124 doi: 10.3969/j.issn.1000-7598.2002.01.028 周翠英, 彭澤英, 尚偉, 等. 論巖土工程中水–巖相互作用研究的焦點問題— —特殊軟巖的力學變異性. 巖土力學, 2002, 23(1):124 doi: 10.3969/j.issn.1000-7598.2002.01.028
[19]	Griggs D. Creep of rocks. J Geol, 1939, 47(3): 225 doi: 10.1086/624775
[20]	Malan D F. Manuel Rocha medal recipient simulating the time-dependent behaviour of excavations in hard rock. Rock Mech Rock Eng, 2002, 35(4): 225 doi: 10.1007/s00603-002-0026-0
[21]	Xu W Y, Yang S Q, Xie S Y, et al. Investigation on triaxial rheological mechanical properties of greenschist specimen (II): model analysis. Rock Soil Mech, 2005, 26(5): 693 doi: 10.3969/j.issn.1000-7598.2005.05.004 徐衛亞, 楊圣奇, 謝守益, 等. 綠片巖三軸流變力學特性的研究(II): 模型分析. 巖土力學, 2005, 26(5):693 doi: 10.3969/j.issn.1000-7598.2005.05.004
[22]	Zhang X D, Yin X W, Fu Q. Study of triaxial creep properties of purple mudstone under stepwise loading. J Exp Mech, 2011, 26(1): 61 張向東, 尹曉文, 傅強. 分級加載條件下紫色泥巖三軸蠕變特性研究. 實驗力學, 2011, 26(1):61
[23]	Espada M, Lamas L. Back analysis procedure for identification of anisotropic elastic parameters of overcored rock specimens. Rock Mech Rock Eng, 2017, 50(3): 513 doi: 10.1007/s00603-016-1129-3
[24]	Wang Y M. Analysis of Temperature on the Mechanical Properties of Granite Experimental Study on Effect and the Hole Wall Stability[Dissertation]. Beijing: China University of Geosciences (Beijing), 2012 王艷梅. 溫度對花崗巖力學性能影響實驗研究及井壁穩定性的分析[學位論文]. 北京: 中國地質大學(北京), 2012
[25]	Rukhaiyar S, Samadhiya N K. Strength behaviour of sandstone subjected to polyaxial state of stress. Int J Min Sci Technol, 2017, 27(6): 889 doi: 10.1016/j.ijmst.2017.06.022
[26]	Huang D, Gu D M, Yang C, et al. Investigation on mechanical behaviors of sandstone with two preexisting flaws under triaxial compression. Rock Mech Rock Eng, 2016, 49(2): 375 doi: 10.1007/s00603-015-0757-3
[27]	Ewalds H L, Waanhill R J. Fracture Mechanics. London: Edwald Arnold, 1984
[28]	Zhou J W, Xu W Y, Shi C. Investigation on compression-shear fracture criterion of rock based on failure criteria. Chin J Rock Mech Eng, 2007, 26(6): 1194 doi: 10.3321/j.issn:1000-6915.2007.06.014 周家文, 徐衛亞, 石崇. 基于破壞準則的巖石壓剪斷裂判據研究. 巖石力學與工程學報, 2007, 26(6):1194 doi: 10.3321/j.issn:1000-6915.2007.06.014
[29]	Tang C A, Lin P, Wong R H C, et al. Analysis of crack coalescence in rock-like materials containing three flaws—part II: numerical approach. Int J Rock Mech Min Sci, 2001, 38(7): 925 doi: 10.1016/S1365-1609(01)00065-X
[30]	Liu G. Pore-Scale Modeling on Hydro–Mechanical Coupling Effects of Geotechnical Materials[Dissertation]. Wuhan: Wuhan University, 2016 劉廣. 巖土孔隙尺度水力耦合特性細觀模擬研究[學位論文]. 武漢: 武漢大學, 2016
[31]	Yan B, Ren F, Cai M, et al. Bayesian model based on Markov chain Monte Carlo for identifying mine water sources in submarine gold mining. J Clean Prod, 2020, 253: 120008 doi: 10.1016/j.jclepro.2020.120008
[32]	Zeng C L. Study on Mechanical Behavior of Soft Rock in Coupled Effect of High Temperature, High Pressure and Seepage[Dissertation]. Qingdao: Qingdao University of Science and Technology, 2007 曾春雷. 高溫、高壓和滲流耦合作用下軟巖力學行為的研究[學位論文]. 青島: 青島科技大學, 2007
[33]	Wang Z J. Damage Evolution Characteristics and the Accumulation Damage Model of Sandstone under Dry-Wet Cycle[Dissertation]. Chongqing: Chongqing University, 2016 王子娟. 干濕循環作用下砂巖的宏細觀損傷演化及本構模型研究[學位論文]. 重慶: 重慶大學, 2016
[34]	Bekele Y W, Kyokawa H, Kvarving A M, et al. Isogeometric analysis of THM coupled processes in ground freezing. Comput Geotech, 2017, 88: 129 doi: 10.1016/j.compgeo.2017.02.020
[35]	Dreybrodt W, Buhmann D. A mass transfer model for dissolution and precipitation of calcite from solutions in turbulent motion. Chem Geol, 1991, 90(1-2): 107 doi: 10.1016/0009-2541(91)90037-R
[36]	Taron J, Elsworth D, Min K B. Numerical simulation of thermal–hydrologic–mechanical–chemical processes in deformable, fractured porous media. Int J Rock Mech Min Sci, 2009, 46(5): 842 doi: 10.1016/j.ijrmms.2009.01.008
[37]	Yasuhara H, Elsworth D, Polak A. Evolution of permeability in a natural fracture: significant role of pressure solution. J Geophys Res Solid Earth, 2004, 109(B3): B03204
[38]	Yeh G T, Tripathi V S. A model for simulating transport of reactive multispecies components: model development and demonstration. Water Resour Res, 1991, 27(12): 3075 doi: 10.1029/91WR02028
[39]	Sheng J C, Xu X C, Yao D S, et al. Advances in permeability evolution in fractured rocks during hydro–mechanical–chemical processes. Chin J Geotech Eng, 2011, 33(7): 996 盛金昌, 許孝臣, 姚德生, 等. 流固化學耦合作用下裂隙巖體滲透特性研究進展. 巖土工程學報, 2011, 33(7):996
[40]	Wang B F, Sun K M, Liang B, et al. Experimental research on the mechanical character of deep mining rocks in THM coupling condition. Energy Sources, Part A, 2019. https://doi.org/10.1080/15567036.2019.1571125
[41]	Liu H L, Yang T H, Zhu W C, et al. Investigation on failure and water inrush from roof of 5th Coal Seam in Fangezhuang Coal Mine. J Min Saf Eng, 2009, 26(3): 332 doi: 10.3969/j.issn.1673-3363.2009.03.016 劉洪磊, 楊天鴻, 朱萬成, 等. 范各莊礦5煤頂板破壞及突水模擬研究. 采礦與安全工程學報, 2009, 26(3):332 doi: 10.3969/j.issn.1673-3363.2009.03.016
[42]	Xu X C, Sheng J C. Permeability of single fracture under coupled hydrological–mechanical–chemical action. J Liaoning Tech Univ Nat Sci, 2009, 28(Suppl): 270 許孝臣, 盛金昌. 滲流–應力–化學耦合作用下單裂隙滲透特性. 遼寧工程技術大學學報: 自然科學版, 2009, 28(增刊): 270
[43]	Liang W G. Study on multi-field coupling theory and its application of hydraulic fracturing and solution mining for salt deposits. Chin J Rock Mech Eng, 2005, 24(6): 1090 doi: 10.3321/j.issn:1000-6915.2005.06.035 梁衛國. 鹽類礦床水壓致裂水溶開采的多場耦合理論及應用研究. 巖石力學與工程學報, 2005, 24(6):1090 doi: 10.3321/j.issn:1000-6915.2005.06.035
[44]	Chen Q. Systemic Study on Engineering Geology of Long Tunnel in Karst and Gas-Storaging Area[Dissertation]. Chengdu: Southwest Jiaotong University, 2005 陳強. 巖溶儲氣長隧道工程地質系統研究[學位論文]. 成都: 西南交通大學, 2005
[45]	Zhou H, Shao J F, Feng X T, et al. Research on statistical penetration meso-model of rock— —Part II: case analysis. Rock Soil Mech, 2006, 27(1): 123 doi: 10.3969/j.issn.1000-7598.2006.01.024 周輝, 邵建富, 馮夏庭, 等. 巖石細觀統計滲流模型研究(II): 實例分析. 巖土力學, 2006, 27(1):123 doi: 10.3969/j.issn.1000-7598.2006.01.024
[46]	Liu Z J, Li X K, Wu W H. A constitutive model and numerical simulation for coupled chemo–thermo–hydro–mechanical process in porous media. Chin J Geotech Eng, 2004, 26(6): 797 doi: 10.3321/j.issn:1000-4548.2004.06.014 劉澤佳, 李錫夔, 武文華. 多孔介質中化學–熱–水力–力學耦合過程本構模型和數值模擬. 巖土工程學報, 2004, 26(6):797 doi: 10.3321/j.issn:1000-4548.2004.06.014
[47]	Wang B Y, Yu B H, Zhang Y Q. The influence of temperature on borehole stability. Inner Mongolia Petrochem Ind, 2008(8): 129 doi: 10.3969/j.issn.1006-7981.2008.08.055 王炳印, 蔚寶華, 張躍群. 泥頁巖地層井壁失穩的一種新機理. 內蒙古石油化工, 2008(8):129 doi: 10.3969/j.issn.1006-7981.2008.08.055
[48]	Ma L J, Wang M Y, Zhang N, et al. A variable-parameter creep damage model incorporating the effects of loading frequency for rock salt and its application in a bedded storage cavern. Rock Mech Rock Eng, 2017, 50(9): 2495 doi: 10.1007/s00603-017-1236-9
[49]	Yan B, Guo Q, Ren F, et al. Modified Nishihara model and experimental verification of deep rock mass under the water-rock interaction. Int J Rock Mech Min Sci, 2020, 128: 104250 doi: 10.1016/j.ijrmms.2020.104250
[50]	Andargoli M B E, Shahriar K, Ramezanzadeh A, et al. The analysis of dates obtained from long-term creep tests to determine creep coefficients of rock salt. Bull Eng Geol Environ, 2019, 78(3): 1617 doi: 10.1007/s10064-018-1243-4
[51]	Liu X W, Liu Q S, Lu C B, et al. A numerical manifold method for fracture propagation of rock mass considering thermo–mechanical coupling. Chin J Rock Mech Eng, 2014, 33(7): 1432 劉學偉, 劉泉聲, 盧超波, 等. 溫度–應力耦合作用下巖體裂隙擴展的數值流形方法研究. 巖石力學與工程學報, 2014, 33(7):1432
[52]	Xu W Y, Yang S Q. Experiment and modeling investigation on shear rheological property of joint rock. Chin J Rock Mech Eng, 2005, 24(Suppl 2): 5536 徐衛亞, 楊圣奇. 節理巖石剪切流變特性試驗與模型研究. 巖石力學與工程學報, 2005, 24(增刊2): 5536
[53]	Zhang Y, Xiong L X. Rock rheological mechanics: present state of research and its direction of development. J Geomech, 2008, 14(3): 274 doi: 10.3969/j.issn.1006-6616.2008.03.009 張堯, 熊良宵. 巖石流變力學的研究現狀及其發展方向. 地質力學學報, 2008, 14(3):274 doi: 10.3969/j.issn.1006-6616.2008.03.009
[54]	Liu Q S, Luo C Y, Chen Z Y, et al. Development of triaxial rheological testing equipment for in-situ rock mass. Rock Soil Mech, 2018, 39(Suppl 2): 473 劉泉聲, 羅慈友, 陳自由, 等. 現場巖體三軸流變試驗設備研制. 巖土力學, 2018, 39(增刊2): 473
[55]	Zhang C L. Multi-Field Coupling Analysis of Deep Rock Mass and Unloading Study on Underground Excavation[Dissertation]. Wuhan: Wuhan University of Technology, 2007 張成良. 深部巖體多場耦合分析及地下空間開挖卸荷研究[學位論文]. 武漢: 武漢理工大學, 2007
[56]	Liu L, Xu W Y, Wang H L, et al. Permeability evolution of granite gneiss during triaxial creep tests. Rock Mech Rock Eng, 2016, 49(9): 3455 doi: 10.1007/s00603-016-0999-8
[57]	Li F X. Experimental Study on Nonlinear Three-Dimensional Rheological Constitutive Model of Q₃ Remolded-Loess and Its Implementation in FLAC3D[Dissertation]. Xi'an: Chang’an University, 2016 李飛霞. Q₃重塑黃土三維非線性流變本構模型試驗研究及其在FLAC3D中的實現[學位論文]. 西安: 長安大學, 2016
[58]	Zhang Z L, Xu W Y, Wang W. Study of triaxial creep tests and its nonlinear visco-elastoplastic creep model of rock from compressive zone of dam foundation in Xiangjiaba Hydropower Station. Chin J Rock Mech Eng, 2011, 30(1): 132 張治亮, 徐衛亞, 王偉. 向家壩水電站壩基擠壓帶巖石三軸蠕變試驗及非線性黏彈塑性蠕變模型研究. 巖石力學與工程學報, 2011, 30(1):132
[59]	Bertram A, Glüge R. Solid Mechanics. Switzerland: Springer International Publishing, 2015
[60]	Zhao Y L, Wang Y X, Wang W J, et al. Modeling of non-linear rheological behavior of hard rock using triaxial rheological experiment. Int J Rock Mech Min Sci, 2017, 93: 66 doi: 10.1016/j.ijrmms.2017.01.004
[61]	Liu X R, Yang X, Wang J B. A nonlinear creep model of rock salt and its numerical implement in FLAC^3D. Adv Mater Sci Eng, 2015: 285158
[62]	Zhao Y L, Zhang L Y, Wang W J, et al. Creep behavior of intact and cracked limestone under multi-level loading and unloading cycles. Rock Mech Rock Eng, 2017, 50(6): 1409 doi: 10.1007/s00603-017-1187-1
[63]	Xu H B, Zhu W S, Bai S W. A visco–elastic–plastic–damage constitutive model of rock masses and its finite element analysis. Rock Soil Mech, 1992, 13(1): 11 徐海濱, 朱維申, 白世偉. 巖體粘彈塑性–損傷本構模型及其有限元分析. 巖土力學, 1992, 13(1):11
[64]	Zhu W S, Zheng W H, Wang W T. Numerical simulation of a new damage rheology model for jointed rock mass. Chin J Geotech Eng, 2010, 32(7): 1011 朱維申, 鄭文華, 王文濤. 新型節理巖體損傷流變模型數值模擬研究. 巖土工程學報, 2010, 32(7):1011