岩石有效应力系数测试方法与表征模型研究进展

doi:10.3724/1000-6915.jrme.2024.0958

摘要
图/表
参考文献
相关文章 (15)

全文: PDF (1744 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要有效应力原理是研究岩石流固耦合行为的重要方法，有效应力系数作为分析有效应力的关键参数，准确获取其量值，对于分析岩石的变形及破坏具有重要意义。从岩石有效应力系数测试方法、表征模型以及影响因素等方面，对国内外研究进行归纳总结。本文系统综述各向同性测法、各向异性测法、裂隙岩石测法以及致密岩石测试方法的特点和适用范围。不同测试方法适用范围不同，排水法精度高，适用所有孔隙度范围的岩石，可用于验证其他方法的有效性，刚度矩阵法可获取各向异性的有效应力系数，含裂隙和低渗岩石推荐采用等效有效应力系数法和Cross-plotting法。有效应力系数表征模型包括临界孔隙度模型、有效介质模型、BISQ模型等，通过已有数据开展模型评估，发现BISQ模型和等框架模型精度高，可应用于精密计算，但所需参数较多，计算相对繁琐；临界孔隙度模型仅需2个参数且精度较高，工程计算中推荐采用。有效应力系数的影响因素包括孔隙结构、矿物组分、孔隙流体等内部因素，以及温度、应力等外部因素，内部因素是本质原因，外部因素诱发岩石内部结构改变，影响有效应力系数。复杂应力扰动下的实时有效应力系数的测试方法、超高温高压条件下有效应力系数演变机制以及工程岩体有效应力系数的确定方法等是未来研究趋势。

	服务

	把本文推荐给朋友
	加入我的书架
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	胡大伟1
	2
	马涛1
	2
	祖凯3
	王倩3
	杨福见1
	2
	周辉1
	2

关键词 ：岩石力学, 有效应力系数, 测试方法, 表征模型, 影响因素

Abstract：The effective stress principle is a fundamental methodology for investigating fluid-solid coupling behavior in rocks. Accurately determining the effective stress coefficient (b) is a key parameter in effective stress analysis and is crucial for understanding rock deformation and failure mechanisms. This paper systematically reviews both domestic and international research progress regarding testing methods, characterization models, and influencing factors of the effective stress coefficient. A comprehensive comparison of isotropic testing methods, anisotropic testing methods, fractured rock testing methods, and tight rock testing methods is presented, highlighting their distinct applicability: (1) the drainage method exhibits high accuracy across all porosity ranges and can validate other methods; (2) the stiffness matrix method effectively captures the anisotropic effective stress coefficient; (3) for fractured and low-permeability rocks, the equivalent effective stress coefficient method and the cross-plotting method are recommended. Existing characterization models, including the critical porosity model, effective medium theory, and the BISQ model, are evaluated using experimental data. Results indicate that the Biot-squirt (BISQ) model and the isoframe model achieve high precision suitable for accurate calculations; however, their parameter requirements and computational complexity limit practical applications. The critical porosity model, which requires only two parameters while maintaining satisfactory accuracy, is recommended for engineering applications. Key influencing factors include intrinsic factors (such as pore structure, mineral composition, and pore fluids) and external conditions (such as temperature and stress). Intrinsic factors dominate fundamental behavior, while external factors induce microstructural changes that affect the effective stress coefficient. Future research directions should focus on: (1) real-time measurement of the effective stress coefficient under dynamic disturbances; (2) mechanisms of effective stress coefficient evolution under ultra-high temperature and pressure conditions; and (3) testing methods for engineering-scale rock.

Key words： rock mechanics effective stress coefficient testing methods characterisation models influencing factor

引用本文:

胡大伟1，2，马涛1，2，祖凯3，王倩3，杨福见1，2，周辉1，2. 岩石有效应力系数测试方法与表征模型研究进展[J]. 岩石力学与工程学报, 2025, 44(8): 1959-1987.
HU Dawei1, 2, MA Tao1, 2, ZU Kai3, WANG Qian3, YANG Fujian1, 2, ZHOU Hui1, 2. Research progress of testing method and characterization model of effective stress coefficient of rock. , 2025, 44(8): 1959-1987.

链接本文:

https://rockmech.whrsm.ac.cn/CN/10.3724/1000-6915.jrme.2024.0958 或 https://rockmech.whrsm.ac.cn/CN/Y2025/V44/I8/1959

[1]	FAN X，LI G，SHAH S N，et al. Analysis of a fully coupled gas flow and deformation process in fractured shale gas reservoirs[J]. Journal of Natural Gas Science and Engineering，2015，27(part_P2)：901-913.
[2]	ZAMANI M A M，KNEZ D. Experimental investigation on the relationship between Biot?s coefficient and hydrostatic stress for enhanced oil recovery projects[J]. Energies，2023，16(13)：4 999.
[3]	SELVADURAI A P S，ZHANG D，KANG Y. Permeability evolution in natural fractures and their potential influence on loss of productivity in ultra-deep gas reservoirs of the Tarim Basin，China[J]. Journal of Natural Gas Science and Engineering，2018，58(Supp.1)：162-177.
[4]	VILARRASA V，OLIVELLA S，CARRERA J. Geomechanical stability of the caprock during CO2 sequestration in deep saline aquifers[J]. Energy Procedia，2011，4(22)：5 306-5 313.
[5]	SALEMI H，IGLAUER S，REZAGHOLILOU A，et al. Laboratory measurement of Biot?s coefficient and pore pressure influence on poroelastic rock behaviour[J]. The APPEA Journal，2018，58(1)：182.
[6]	LI S ，LI X ，ZHANG D. A fully coupled thermo-hydro-mechanical，three-dimensional model for hydraulic stimulation treatments[J]. Journal of Natural Gas Science and Engineering，2016，34(2016)：64-84.
[7]	ROSHAN H，RAHMAN S S. Analysis of pore pressure and stress distribution around a wellbore drilled in chemically active elastoplastic formations[J]. Rock Mechanics and Rock Engineering，2011，44(5)：541-552.
[8]	LUO X，WERE P，LIU J，et al. Estimation of Biot?s effective stress coefficient from well logs[J]. Environmental Earth Sciences，2015，73(11)：7 019-7 028.
[9]	LI X，FENG Y，E L MOHTAR C S，et al. Transient modeling of borehole breakouts：a coupled thermo-hydro-mechanical approach[J]. Journal of Petroleum Science and Engineering，2019，172(000)： 1 014-1 024.
[10]	WESSLING S，JUNKER R，RUTQVIST J，et al. Pressure analysis of the hydromechanical fracture behaviour in stimulated tight sedimentary geothermal reservoirs[J]. Geothermics，2009，38(2)：211-226.
[11]	GUO R，XU H，PLÚA C，et al. Prediction of the thermal-hydraulic- mechanical response of a geological repository at large scale and sensitivity analyses[J]. International Journal of Rock Mechanics and Mining Sciences，2020，136(3/4)：104484.
[12]	胡大伟，周辉，谢守益，等. 大理岩破坏阶段Biot系数研究[J]. 岩土力学，2009，30(12)：3 727-3 732.(HU Dawei，ZHOU Hui，XIE Shouyi，et al. Study of Biot?s coefficients of marble during plastic deformation phase[J]. Rock and Soil Mechanics，2009，30(12)： 3 727-3 732.(in Chinese))
[13]	ASADOLLAHPOUR E，EZAZI M，MOSTAFAVI I，et al. Biot?s coefficient determination of carbonate reservoir rocks by using static and dynamic experimental tests at ambient and reservoir temperatures—A case study from Iran carbonate field[J]. Journal of Petroleum Science and Engineering，2021，196(2021)：108061.
[14]	KASANI H A，SELVADURAI A P S. A review of techniques for measuring the Biot coefficient and other effective stress parameters for fluid-saturated rocks[J]. Applied Mechanics Reviews，2023，75(2)：020801.
[15]	BIOT M A. General theory of three-dimensional consolidation[J]. Journal of Applied Physics，1941，12(2)：155-164.
[16]	SAURABH S，HARPALANI S. The effective stress law for stress-sensitive transversely isotropic rocks[J]. International Journal of Rock Mechanics and Mining Sciences，2018，101(2018)：69-77.
[17]	YU B，ZHANG D，LI S，et al. Biot?s coefficient and permeability evolution of damaged anisotropic coal subjected to true triaxial stress[J]. Rock Mechanics and Rock Engineering，2023，56(1)：237-260.
[18]	GEERTSMA J. The effect of fluid pressure decline on volumetric changes of porous rocks[J]. Transactions of the AIME，1957，210(1)：331-340.
[19]	TODD T，SIMMONS G. Effect of pore pressure on the velocity of compressional waves in low-porosity rocks[J]. Journal of Geophysical Research，1972，77(20)：3 731-3 743.
[20]	WALSH J B. Effect of pore pressure and confining pressure on fracture permeability[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1981，18(5)：429-435.
[21]	徐欣，王伟，胡明毅，等. 中孔中渗砂岩储层Biot系数测试方法对比研究[J]. 石油钻探技术，2018，46(2)：109-114.(XU Xin，WANG Wei，HU Mingyi，et al. Comparison and study over the Biot coefficients test methods in medium porosity and medium permeability sandstone reservoirs[J]. Petroleum Drilling Techniques，2018，46(2)：109-114.(in Chinese))
[22]	程远方，程林林，黎慧，等. 不同渗透性储层Biot系数测试方法研究及其影响因素分析[J]. 岩石力学与工程学报，2015，34(增2)：3 998-4 004.(CHENG Yuanfang，CHENG Linlin，LI Hui，et al. Research on testing methods of Biot coefficient in reservoir with different permeability and its influencing factors[J]. Chinese Journal of Rock Mechanics and Engineering，2015，34(Supp.2)：3 998-4 004.(in Chinese))
[23]	HE J，RUI Z，LING K. A new method to determine Biot?s coefficients of Bakken samples[J]. Journal of Natural Gas Science and Engineering, 2016，35：259-264.
[24]	SELVADURAI P，SELVADURAI P A，NEJATI M. A multi-phasic approach for estimating the Biot coefficient for Grimsel granite[J]. Solid Earth，2019，10(6)：2 001-2 014.
[25]	CHENG Z Y，CHEN Z，DONG W，et al. Effects of fracture filling ratio and confining stress on the equivalent effective stress coefficient of rocks containing a single fracture[J]. International Journal of Rock Mechanics and Mining Sciences，2022，160(2022)：105239.
[26]	ZHOU X J，GHASSEMI A. Poroelastic properties of sierra white granite[J]. Rock Mechanics and Rock Engineering，2024，57(10)： 7 777-7 793.
[27]	ASEM P，DETOURNAY E，HUANG H，et al. Saturating a tight rock and measuring its hydromechanical response[J]. Rock Mechanics and Rock Engineering，2024，57(12)：10 385-10 398.
[28]	贾利春. 横观各向同性页岩动、静态有效应力系数试验研究[J]. 岩石力学与工程学报，2023，42(增2)：4 130-4 139.(JIA Lichun. Experimental investigation on dynamic and static Biot coefficients of transversely isotropic shale[J]. Chinese Journal of Rock Mechanics and Engineering，2023，42(Supp.2)：4 130-4 139.(in Chinese))
[29]	KRIEF M，GARAT J，STELLINGWERFF J，et al. A petrophysical interpretation using the velocities of P and S waves(full-waveform sonic)[J]. Log Analyst，1990，31(6)：355-369.
[30]	LEE M W. Biot-Gassmann theory for velocities of gas hydrate‐bearing sediments[J]. Geophysics，2002，67(6)：1 711-1 719.
[31]	NUR A，MAVKO G，DVORKIN J，et al. Critical porosity：A key to relating physical properties to porosity in rocks[J]. The Leading Edge，1998，17(3)：357-362.
[32]	TAN X，KONIETZKY H. Numerical study of variation in Biot?s coefficient with respect to microstructure of rocks[J]. Tectonophysics，2014，610(6)：159-171.
[33]	OLSEN C，HEDEGAARD K，FABRICIUS I L，et al. Prediction of Biot?s coefficient from rock-physical modeling of North Sea chalk[J]. Geophysics，2008，73(2)：E89-E96.
[34]	FANG Y Y，SHI Y，SHENG Y，et al. Modeling of Biot?s coefficient for a clay-bearing sandstone reservoir[J]. Arabian Journal of Geosciences，2018，11(12)：302.
[35]	TERZAGHI K. Die berechnung der durchlassigkeitzifer des tones aus dem verlauf der hydrodynamischen spannungserscheinungen[J]. Mathematish-naturwissenschaftliche，1923，(132)：125-138.
[36]	BIOT M A. Le problème de la consolidation des matières argileuses sous une charge[J]. Annales de la Société Scientifique de Bruxelles，1935，(B55)：110-113.
[37]	BIOT M A. Mechanics of deformation and acoustic propagation in porous media[J]. Journal of Applied Physics，1962，33(4)：1 482- 1 498.
[38]	RICE J R，CLEARY M P. Some basic stress diffusion solutions for fluid‐saturated elastic porous media with compressible constituents[J]. Reviews of Geophysics，1976，14(2)：227-241.
[39]	CHENG A H D. Material coefficients of anisotropic poroelasticity[J]. International Journal of Rock Mechanics and Mining Sciences，1997，34(2)：199-205.
[40]	COUSSY O. Mechanics of porous continua[M]. Chichester：Wiley，1995：80-96.
[41]	DETOURNAY E，CHENG A H D. Fundamentals of poroelasticity[M]. Oxford，US：Pergamon Press，1993：113-171.
[42]	CROCHET M J，NAGHDI P M. On constitutive equations for flow of fluid through an elastic solid[J]. International Journal of Engineering Science，1966，4(4)：383-401.
[43]	MORLAND L W. A simple constitutive theory for a fluid-saturated porous solid[J]. Journal of Geophysical Research，1972，77(5)：890-900.
[44]	ATKIN R J，CRAINE R E. Continuum theories of mixtures：basic theory and historical development[J]. The Quarterly Journal of Mechanics and Applied Mathematics，1976，29(2)：209-244.
[45]	BOWEN R M. Compressible porous media models by use of the theory of mixtures[J]. International Journal of Engineering Science，1982，20(6)：697-735.
[46]	KATSUBE N，CARROLL M M. The modified mixture theory for fluid-filled porous materials：theory[J]. Journal of Applied Mechanics，1987，54(1)：35-40.
[47]	COUSSY O，DORMIEUX L，DETOURNAY E. From mixture theory to biot?s approach for porous media[J]. International Journal of Solids and Structures，1998，35(34/35)：4 619-4 635.
[48]	BLÖCHER G，REINSCH T，HASSANZADEGAN A，et al. Direct and indirect laboratory measurements of poroelastic properties of two consolidated sandstones[J]. International Journal of Rock Mechanics and Mining Sciences，2014，67(67)：191-201.
[49]	LING K，HE J，PEI P，et al. Comparisons of Biot?s Coefficients of Bakken Core Samples Measured by Three Methods[C]// 50th U.S. Rock Mechanics/Geomechanics Symposium. [S. l.]：[s. n.]，2016：ARMA-2016-030.
[50]	夏宏泉，彭梦，宋二超. 岩石各向异性Biot系数的获取方法及应用[J]. 测井技术，2019，43(5)：478-483.(XIA Hongquan，PENG Meng，SONG Erchao. Calculating method and application of rock anisotropic Biot coefficient[J]. Well Logging Technology，2019，43(5)：478-483.(in Chinese))
[51]	MA X，ZOBACK M D. Laboratory experiments simulating poroelastic stress changes associated with depletion and injection in low‐porosity sedimentary rocks[J]. Journal of Geophysical Research：Solid Earth，2017，122(4)：2 478-2 503.
[52]	RAMOS DA SILVA M，SCHROEDER C，VERBRUGGE J C. Poroelastic behaviour of a water-saturated limestone[J]. International Journal of Rock Mechanics and Mining Sciences，2010，47(5)：797-807.
[53]	AHMED S，MÜLLER TM，MADADI M，et al. Drained pore modulus and Biot coefficient from pore-scale digital rock simulations[J]. International Journal of Rock Mechanics and Mining Sciences，2019，114：62-70.
[54]	卢应发，周盛沛，田斌，等. 岩石与水相互作用的能量原理和Biot系数[J]. 岩土力学，2005，26(增2)：69-72.(LU Yingfa，ZHOU Shengpei，TIAN Bin，et al. Energy principle of rock and water interaction and Biot coefficient[J]. Rock and Soil Mechanics，2005，26(Supp.2)：69-72.(in Chinese))
[55]	SHAO J F. Poroelastic behaviour of brittle rock materials with anisotropic damage[J]. Mechanics of Materials，1998，30(1)：41-53.
[56]	HU DW，ZHOU H，ZHANG F，et al. Evolution of poroelastic properties and permeability in damaged sandstone[J]. International Journal of Rock Mechanics and Mining Sciences，2010，47(6)：962-973.
[57]	董丙响，程远方，刘钰川，等. 页岩气储层岩石物理性质[J]. 西安石油大学学报：自然科学版，2013，28(1)：25-28.(DONG Bingxiang，CHENG Yuanfang，LIU Yuchuan，et al. Shale gas reservoir petrophysical properties[J]. Xi?an Shiyou University：Natural Science，2013，28(1)：25-28.(in Chinese))
[58]	GASSMANN F. Elastic waves through a packing of spheres[J]. Geophysics，1951，16(4)：673-685.
[59]	李卉，魏臣兴，俞宏伟，等. 基于声波测试法对鹰滩页岩各向异性分析[J]. 地质与勘探，2022，58(6)：1 291-1 299.(LI Fen，WEI Chenxing，YU Hongwei，et al. Anisotropic properties of the Eagle Ford shale by ultrasonic velocity measurements[J]. Geology and Exploration，2022，58(6)：1 291-1 299.(in Chinese))
[60]	KNEZ D，ZAMANI M A M. Empirical formula for dynamic biot coefficient of sandstone samples from South-West of Poland[J]. Energies，2021，14(17)：5 514.
[61]	TSANG Y W，WITHERSPOON P A. Hydromechanical behavior of a deformable rock fracture subject to normal stress[J]. Journal of Geophysical Research：Solid Earth，1981，86(B10)：9 287-9 298.
[62]	陈跃都，梁卫国，杨健锋，等. 含水压粗糙岩石裂隙有效应力规律研究[J]. 岩石力学与工程学报，2018，37(增2)：3 850-3 860.(CHEN Yuedu，LIANG Weiguo，YANG Jianfeng，et al. Study on the effective stress characteristic of rough rock fractures with water pressure[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(Supp.2)：3 850-3 860.(in Chinese))
[63]	谢妮，徐礼华，邵建富，等. 法向应力和水压力作用下岩石单裂隙水力耦合模型[J]. 岩石力学与工程学报，2011，30(增2)：3 796-3 803.(XIE Ni，XU Lihua，SHAO Jianfu，et al. Coupled hydro mechanical modeling of rock fractures subject to both normal stress and fluid pressure[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(Supp.2)：3 796-3 803.(in Chinese))
[64]	赵志宏. 岩石裂隙水-岩作用机制与力学行为研究[J]. 岩石力学与工程学报，2021，40(增2)：3 063-3 073.(ZHAO Zhihong. Study on water-rock interaction and mechanical behaviors of single rock fractures[J]. Chinese Journal of Rock Mechanics and Engineering，2021，40(Supp.2)：3 063-3 073.(in Chinese))
[65]	温宏平，李炜光，王旭昊，等. 动态循环加载下花岗岩孔渗参数演化规律[J]. 工程科学与技术，2022，54(5)：119-128.(WEN Hongping，LI Weiguang，WANG Xuhao，et al. Evolution law of granite porosity-permeability parameters under dynamic cyclic loading[J]. Advanced Engineering Sciences，2022，54(5)：119-128.(in Chinese))
[66]	李尧，王伟，王如宾，等. 考虑渗压的二长花岗岩流变损伤本构模型研究[J]. 河北工程大学学报：自然科学版，2020，37(1)：30-34.(LI Yao，WANG Wei，WANG Rubin，et al. Study on rheological damage model of monzogranites with permeation pressure considered[J]. Journal of Hebei University of Engineering：Natural Science，2020，37(1)：30-34.(in Chinese))
[67]	乔丽苹，王者超，李术才. 基于Tight gas致密砂岩储层渗透率的有效应力特性研究[J]. 岩石力学与工程学报，2011，30(7)：1 422- 1 427.(QIAO Liping，WANG Zhechao，LI Shucai. Effective stress law for permeability of tight gas reservoir sandstone[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(7)：1 422-1 427.(in Chinese))
[68]	朱维耀，马东旭. 页岩储层有效应力特征及其对产能的影响[J]. 天然气地球科学，2018，29(6)：845-852.(ZHU Weiyao，MA Dongxu. Effective stress characteristics in shale and its effect on productivity[J]. Natural Gas Geoscience，2018，29(6)：845-852.(in Chinese))
[69]	李闽，肖文联. 低渗砂岩储层渗透率有效应力定律试验研究[J].岩石力学与工程学报，2008，27(增2)：3 535-3 540.(LI Min，XIAO Wenlian. Experimental study on permeability-effective-stress law in flow- permeability sandstone reservoir[J]. Chinese Journal of Rock Mechanics and Engineering，2008，27(Supp.2)：3 535-3 540.(in Chinese))
[70]	FREENY A. Empirical model building and response surfaces[J]. Technometrics，1988，30(2)：229-231.
[71]	BERNABE Y. Comparison of the effective pressure law for permeability and resistivity formation factor in Chelmsford granite[J]. Pure and Applied Geophysics，1988，127(4)：607-625.
[72]	郑玲丽，李闽，钟水清，等. 变围压循环下低渗透致密砂岩有效应力方程研究[J]. 石油学报，2009，30(4)：588-592.(ZHENG Lingli，LI Min，ZHONG Shuiqing，et al. Research on calculation of effective stress in low-permeability sandstone rock under cyclic loading and unloading[J]. Acta Petrolei Sinica，2009，30(4)：588-592.(in Chinese))
[73]	丁艳艳，李闽，肖文联. 围压对低渗砂岩渗透率有效应力系数的影响[J]. 地球物理学进展，2012，27(2)：696-701.(DING Yanyan，LI Min，XIAO Wenlian. The effect of confining pressure on effective pressure coefficient for permeability in low-permeability sandstones[J]. Progress in Geophysical，2012，27(2)：696-701.(in Chinese))
[74]	刘忠群，陈猛，李闽. 低渗砂岩地层因素的应力敏感研究[J]. 西南石油大学学报：自然科学版，2019，41(1)：91-101.(LIU Zhongqun，CHEN Meng，LI Min. Study on stress sensitivity of the formation factors of low-permeability sandstones[J]. Journal of Southwest Petroleum University：Science and Technology，2019，41(1)：91-101.(in Chinese))
[75]	REUSS A. Berechnung der fließgrenze von mischkristallen auf grund der plastizitätsbedingung für einkristalle[J]. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik，1929，9(1)：49-58.
[76]	HILL R. The elastic behaviour of a crystalline aggregate[J]. Proceedings of the Physical Society. Section A，1952，65(5)：349-354.
[77]	SELVADURAI A P S. The Biot coefficient for a low permeability heterogeneous limestone[J]. Continuum Mechanics and Thermodynamics，2019，31(4)：939-953.
[78]	AMIRI M，LASHKARIPOUR G R，GHABEZLOO S，et al. 3D spatial model of Biot’s effective stress coefficient using well logs，laboratory experiments，and geostatistical method in the Gachsaran oil field，southwest of Iran[J]. Bulletin of Engineering Geology and the Environment，2019，78(6)：4 633-4 646.
[79]	BERRYMAN J G. Effective stress for transport properties of inhomogeneous porous rock[J]. Journal of Geophysical Research：Solid Earth，1992，97(B12)：17 409-17 424.
[80]	SELVADURAI A P S，NGUYEN T S. Computational modelling of isothermal consolidation of fractured porous media[J]. Computers and Geotechnics，1995，17(1)：39-73.
[81]	COSENZA P，GHOREYCHI M，DE MARSILY G，et al. Theoretical prediction of poroelastic properties of argillaceous rocks from in situ specific storage coefficient[J]. Water Resources Research，2002，38(10)：25-1-25-12.
[82]	LAU J S O，CHANDLER N A. Innovative laboratory testing[J]. International Journal of Rock Mechanics and Mining Sciences，2004，41(8)：1 427-1 445.
[83]	DUAN Z B，SKOCZYLAS F. Experimental study of the permeability and poromechanical properties of thermally damaged granite[J]. European Journal of Environmental and Civil Engineering，2021，25(5)：955-965.
[84]	SELVADURAI A P S. On the poroelastic Biot coefficient for a granitic rock[J]. Geosciences，2021，11(5)：219.
[85]	STADTMULLER M，LIS-?LEDZIONA A，S?OTA-VALIM M. Petrophysical and geomechanical analysis of the Lower Paleozoic shale formation，North Poland[J]. Interpretation，2018，6(3)：SH91-SH106.
[86]	FERRARI A，FAVERO V，LALOUI L. One-dimensional compression and consolidation of shales[J]. International Journal of Rock Mechanics and Mining Sciences，2016，88(000)：286-300.
[87]	NOWAKOWSKI A. The influence of rate of change in confining and pore pressure on values of the modulus of compressibility of the rock skeleton and Biot?s coefficient[J]. Energies，2021，14(11)：3 056.
[88]	MAKHNENKO R Y，LABUZ J F. Elastic and inelastic deformation of fluid-saturated rock[J]. Philosophical Transactions of the Royal Society A：Mathematical，Physical and Engineering Sciences，2016，374(2078)：20150422.
[89]	HART D J，WANG H F. Laboratory measurements of a complete set of poroelastic moduli for Berea sandstone and Indiana limestone[J]. Journal of Geophysical Research：Solid Earth，1995，100(B9)： 17 741-17 751.
[90]	DU S. Anisotropic rock poroelasticity evolution in ultra-low permeability sandstones under pore pressure，confining pressure，and temperature：experiments with Biot?s coefficient[J]. Acta Geologica Sinica-English Edition，2021，95(3)：937-945.
[91]	马中高. Biot系数和岩石弹性模量的实验研究[J]. 石油与天然气地质，2008，29(1)：135-140.(MA Zhonggao. Experimental investigation into Biot?s coefficient and rock elastic moduli[J]. Oil and Gas Geology，2008，29(1)：135-140.(in Chinese))
[92]	WANG Y，JEANNIN L，AGOSTINI F，et al. Experimental study and micromechanical interpretation of the poroelastic behaviour and permeability of a tight sandstone[J]. International Journal of Rock Mechanics and Mining Sciences，2018，103(2018)：89-95.
[93]	王斌，赵建国，李伟，等. 异常高压对砂砾岩弹性性质影响的实验机制研究与压力预测新模型——以准噶尔盆地玛湖凹陷北斜坡三叠系为例[J]. 地球物理学报，2022，65(8)：3 157-3 171. (WANG Bin，ZHAO Jianguo，LI Wei，et al. Experimental study on the effect of abnormal high pressure on the elastic properties of glutenite and a novel pressure prediction model：a case study from Triassic Formation in north slope of Mahu Sag，Junggar Basin[J]. Chinese Journal of Geophysics，2022，65(8)：3 157-3 171.(in Chinese))
[94]	AHMADINEJAD A，KIVI I R. An experimental investigation on the poroelastic response of a water-saturated limestone to hydrostatic compression[J]. Bulletin of Engineering Geology and the Environment，2021，80(5)：3 817-3 832.
[95]	RAZIPERCHIKOLAEE S，SINGH V，KELLEY M. The effect of Biot coefficient and elastic moduli stress-pore pressure dependency on poroelastic response to fluid injection：laboratory experiments and geomechanical modeling[J]. Greenhouse Gases：Science and Technology，2020，10(5)：980-998.
[96]	ARTAMONOVA N B，SHESHENIN S V，FROLOVA Y U V，et al. Calculating components of the effective tensors of elastic moduli and Biot?s parameter of porous geocomposites[J]. Mechanics of Composite Materials，2020，55(6)：715-726.
[97]	GRAM T B，DITLEVSEN F P，MOSEGAARD K，et al. Water‐flooding and consolidation of reservoir chalk-effect on porosity and Biot?s coefficient[J]. Geophysical Prospecting，2021，69(3)：495- 513.
[98]	ALAM M M，BORRE M K，FABRICIUS I L，et al. Biot?s coefficient as an indicator of strength and porosity reduction：calcareous sediments from Kerguelen Plateau[J]. Journal of Petroleum Science and Engineering，2010，70(3/4)：282-297.
[99]	ZIMMERMAN R W，SOMERTON W H，KING M S. Compressibility of porous rocks[J]. Journal of Geophysical Research：Solid Earth，1986，91(B12)：12 765-12 777.
[100]	尹光志，李文璞，李铭辉，等. 加卸载条件下原煤渗透率与有效应力的规律[J]. 煤炭学报，2014，39(8)：1 497-1 503.(YIN Guangzhi，LI Wenpu，LI Minghui，et al. Permeability properties and effective stress of raw coal under loading-unloading conditions[J]. Journal of China Coal Society，2014，39(8)：1 497-1 503.(in Chinese))
[101]	TAN X，KONIETZKY H，FRÜHWIRT T. Experimental and numerical study on evolution of Biot?s coefficient during failure process for brittle rocks[J]. Rock Mechanics and Rock Engineering，2015，48(3)：1 289-1 296.
[102]	LI Q，AGUILERA R，LEY H C. A correlation for estimating Biot coefficient[J]. SPE-Society of Petroleum Engineer，2019，(19WRM)：14.
[103]	SELVADURAI A P S，SUVOROV A P. The influence of the pore shape on the bulk modulus and the Biot coefficient of fluid-saturated porous rocks[J]. Scientific Reports，2020，10(1)：18 959.
[104]	李闽，肖文联，郭肖，等. 塔巴庙低渗致密砂岩渗透率有效应力定律实验研究[J]. 地球物理学报，2009，52(12)：3 166-3 174.(LI Min，XIAO Wenlian，GUO Xiao，et al. laboratory study of the effective pressure law for permeability in Ta-Ba-Miao low-permeability sandstones[J]. Chinese Journal of Geophysics，2009，52(12)：3 166-3 174.(in Chinese))
[105]	HASSANZADEGAN A，BLÖCHER G，ZIMMERMANN G，et al. Thermoporoelastic properties of Flechtinger sandstone[J]. International Journal of Rock Mechanics and Mining Sciences，2012，49：94-104.
[106]	YANG F，WANG G，HU D，et al. Calibrations of thermo-hydro-mechanical coupling parameters for heating and water-cooling treated granite[J]. Renewable Energy，2021，168：544-558.