热–水–力作用下红砂岩力学性质及有限变形本构方程研究
|
摘要
温度、地下水及地应力是深部开采过程中影响岩体变形破坏的重要因素。从试验出发,基于正交试验原理,设计并开展温度–饱水时间–围压作用下的红砂岩变形破坏试验。分析并讨论温度、饱水时间和围压对红砂岩力学性质的影响。温度、饱水时间、围压均对岩样弹性模量和峰值应力具有显著影响,且显著性水平均在90%以上,其中围压的影响最大,温度的影响最小;利用线性模型描述了温度、饱水时间以及围压作用下岩样的弹性模量、峰值应力以及泊松比的变化规律。之后,针对深部开采中的大变形问题,基于有限变形理论,计算红砂岩变形破坏过程中平均整旋角并研究其演化规律,进而借助平均整旋角建立温度–水–力作用下的红砂岩大变形本构方程,通过和试验数据的对比表明,提出的本构方程可以较好地描述红砂岩变形破坏的过程。
Temperature,underground water and in situ stress are crucial environmental factors affecting rock strength and deformability during deep mining. In this study,temperature water immersion time-confining pressure coupled compression experiments of red sandstone is designed and conducted based on the orthogonal experimental principles. The effects of each influencing factor on red sandstone strength and deformability are statistically analyzed and discussed. The results indicate that the temperature,water immersion time and confining pressure have great influence on the elastic modulus,Poisson?s ratio and peak strength(significance level≥90%).The confining pressure has the most significant effects while the temperature has the least effects on these three parameters. The evolution of elastic modulus,Poisson?s ratio and peak strength under the influence of the three environmental factors is also studied. The linear correlations of those parameters with the three factors are obtained. Furthermore,based on the finite deformation theory,the mean rotation angle are employed to analyze the nonlinear deformation behavior of the test rock. The evolution of the mean rotation angle are studied and discussed. A constitutive model based on the mean rotation angle and finite deformation theory is also proposed.The comparison of model results and experimental data shows that the model proposed in this study can well describe the deformation and failure process of the red sandstone.
Temperature,underground water and in situ stress are crucial environmental factors affecting rock strength and deformability during deep mining. In this study,temperature water immersion time-confining pressure coupled compression experiments of red sandstone is designed and conducted based on the orthogonal experimental principles. The effects of each influencing factor on red sandstone strength and deformability are statistically analyzed and discussed. The results indicate that the temperature,water immersion time and confining pressure have great influence on the elastic modulus,Poisson?s ratio and peak strength(significance level≥90%).The confining pressure has the most significant effects while the temperature has the least effects on these three parameters. The evolution of elastic modulus,Poisson?s ratio and peak strength under the influence of the three environmental factors is also studied. The linear correlations of those parameters with the three factors are obtained. Furthermore,based on the finite deformation theory,the mean rotation angle are employed to analyze the nonlinear deformation behavior of the test rock. The evolution of the mean rotation angle are studied and discussed. A constitutive model based on the mean rotation angle and finite deformation theory is also proposed.The comparison of model results and experimental data shows that the model proposed in this study can well describe the deformation and failure process of the red sandstone.
引文
[1]谢和平,彭苏萍,何满朝.深部开采基础理论与工程实践[M].北京:科学出版社,2006:1-10.(XIE Heping,PENG Suping,HEMan-chao.Preliminary theory and engineering practice of deep mining[M].Beijing:Science Press,2006:1-10.(in Chinese))
[2]何满潮,吕晓俭,景海河.深部工程围岩特性及非线性动态力学设计理念[J].岩石力学与工程学报,2002,21(8):1 215-1 224.(HEManchao,LU Xiaojian,JING Haihe.Design of surrounding rock characteristics and nonlinear dynamic mechanics design of deep engineering[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(8):1 215-1 224.(in Chinese))
[3]范雁秋.膨胀岩与工程[M].北京:科学出版社,2008:5-12.(FANYanqiu.Expansive rock and engineering[M].Beijing:Science Press,2008:5-12.(in Chinese))
[4]董平川,徐小荷,何顺利.变形与渗流耦合问题的研究进展[J].地质力学学报,1999,5(1):17-26.(DONG Pingchuan,XU Xiaohe,HE Shunli.Study on coupling of deformation and seepage[J].Journal of Geomechanics,1999,5(1):17-26.(in Chinese))
[5]刘建军,冯夏庭.我国油藏渗流-温度-应力耦合的研究进展[J].岩土力学,2003,24(增):645-650.(LIU Jianjun,FENG Xiating.Study on seepage-temperature-stress coupling in reservoirs in China[J].Rock and Soil Mechanics,2003,24(Supp.):645-650.(in Chinese))
[6]夏小和,王颖秩,黄春醒,等.高温作用对大理岩强度及变形特性影响的实验研究[J].上海交通大学学报,2004,38(6):996-998.(XIA Xiaohe,WANG Yingzhi,HUANG Chunxing,et al.Experimental study on the effect of high temperature on the strength and deformation characteristics of marble[J].Journal of Shanghai Jiaotong University,2004,38(6):996-998.(in Chinese))
[7]RANJITH P G,VIETE D R,BAI J C,et al.Transformation plasticity and the effect of temperature on the mechanical behaviour of Hawkesbury sandstone at atmospheric pressure[J].Engineering Geology,2012,151:120-127.
[8]MOHAJERANI M,DELAGE P,SULEM J,et al.A laboratory investigation of thermally induced pore pressures in the CallovoOxfordian claystone[J].International Journal of Rock Mechanics and Mining Science,2012,52(3):112-121.
[9]ERGULER Z A,ULUSAY R.Water-induced variations in mechanical properties of clay-bearing rocks[J].International Journal of Rock Mechanics and Mining Sciences,2009,46(2):355-370.
[10]VáSáRHELYI B,VáN P.Influence of water content on the strength of rock[J].Engineering Geology,2006,80(1):70-74.
[11]LABUZ J F,ZANG A.Mohr-Coulomb failure criterion[J].Rock Mechanics and Rock Engineering,2012,45(6):975-979.
[12]CHANG C,HAIMSON B.True triaxial strength and deformability of the German Continental Deep Drilling Program(KTB)deep hole amphibolite[J].Journal of Geophysical Research,2000,105(B8):18 999-19 013.
[13]HASSANZADEGAN A,BL?CHER G,MILSCH H,et al.The effects of temperature and pressure on the porosity evolution of Flechtinger sandstone[J].Rock Mechanics and Rock Engineering,2014,47(2):421-434.
[14]严荣林,侯贤文.矿井空调技术[M].北京:煤炭工业出版社,1994:1-10.(YAN Ronglin,HOU Xianwen.Mine air conditioning technology[M].Beijing:Coal Industry Press,1994:1-10.(in Chinese))
[15]尹光志,王登科,张东明,等.两种含瓦斯煤样变形特性与抗压强度的实验分析[J].岩石力学与工程学报,2009,28(2):410-417.(YIN Guangzhi,WANG Dengke,ZHANG Dongming,et al.Experimental analysis of deformation characteristics and compressive strength of gas-bearing coal samples[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(2):410-417.(in Chinese))
[16]乔丽苹.砂岩的弹塑性及蠕变特性的水物理化学作用效应试验与本构研究[R].武汉:中国科学院武汉岩土力学研究所,2008.(QIAOLiping.Experimental and constitutive study of water physical and chemical effects of elastoplastic and creep properties of sandstone[R].Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2008.(in Chinese))
[17]吴群英.应用数理统计[M].天津:天津大学出版社,2004:131-163.(WU Qunying.Application of mathematical statistics[M].Tianjin:Tianjin University Press,2004:131-163.(in Chinese))
[18]王兴仁,张录达,王华方.正交试验设置重复的必要性和统计分析方法[J].土壤学报,2000,31(3):135-139.(WANG Xingren,ZHANG Luda,WANG Huafang.Numerical necessity and statistical analysis method of orthogonal test setup[J].Acta Agronomica Sinica,2000,31(3):135-139.(in Chinese))
[19]蒋长宝,许江,彭守建,等.含瓦斯煤热流固耦合的渗流试验研究[J].煤炭学报,2011,36(9):1 545-1 550.(JIANG Changbao,XU Jiang,PENG Shoujian,et al.Study on seepage test of heat and fluid coupling of gas-bearing coal[J].Journal of Coal Science,2011,36(9):1 545-1 550.(in Chinese))
[20]徐小丽.温度载荷作用下花岗岩的力学性质演化及微观机制研究[博士学位论文][D].徐州:中国矿业大学出版社,2008.(XU Xiaoli.Study on mechanical properties and microscopic mechanism of granite under temperature load[Ph.D.Thesis][D].Xuzhou:China University of Mining and Technology Press,2008.(in Chinese))
[21]陈建文.岩盐的温度效应及习惯机理研究[R].武汉:中国科学院武汉岩土力学研究所,2008.(CHEN Jianwen.Study on temperature effect and habit mechanism of rock salt[R].Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2008.(in Chinese))
[22]周青春.温度、空隙水和应力作用下砂岩的力学特性研究[R].武汉:中国科学院武汉岩土力学研究所,2006.(ZHOU Qingchun.Study on the mechanical properties of sandstone under temperature,void water and stress[R].Wuhan:Wuhan Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2006.(in Chinese))
[23]许江,杨红伟,彭守建,等.孔隙水压力-围压作用下砂岩力学特性的试验研究[J].岩石力学与工程学报,2010,29(8):1 618-1 623.(XU Jiang,YANG Hongwei,PENG Shoujian,et al.Experimental study on mechanical properties of sandstone under pore water pressure and confining pressure[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(8):1 618-1 623.(in Chinese))
[24]许江,鲜学福,杜云贵,等.含瓦斯煤的力学特性试验研究[J].重庆大学学报,1993,16(5):42-47.(XU Jiang,XIAO Xuefu,DU Yungui,et al.Experimental study on mechanical properties of gas-bearing coal[J].Journal of Chongqing University,1993,16(5):42-47.(in Chinese))
[25]张凯.脆性岩石力学模型与流固耦合机理研究[博士学位论文][D].武汉:中国科学院武汉岩土力学研究所,2010.(ZHANG Kai.Study on mechanics model and fluid-structure coupling mechanism of brittle rocks[Ph.D.Thesis][D].Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2010.(in Chinese))
[26]徐礼华,刘素梅,李彦强.丹江口水库区岩石软化性能试验研究[J].岩土力学,2008,29(5):1 430-1 434.(XU Lihua,LIU Sumei,LIYanqiang.Experimental study on rock softening performance of Danjiangkou reservoir area[J].Rock and Soil Mechanics,2008,29(5):1 430-1 434.(in Chinese))
[27]季明.湿度场下灰质泥岩的力学性质演化与蠕变特征研究[M].徐州:中国矿业大学出版社,2009:38-43.(JI Ming.Study on the evolution of mechanical properties and creep characteristics of gray mudstone in humidity field[M].Xuzhou:China University of Mining and Technology Press,2009:38-43.(in Chinese))
[28]龚选平.泥质粉砂岩含水率对其蠕变特性影响的研究[博士学位论文][D].西安:西安科技大学,2006.(GONG Xuanping.Study on the effect of moisture content on the creep characteristics of shale siltstone[Ph.D.Thesis][D].Xi?an:Xi?an University of Science and Technology,2006.(in Chinese))
[29]冒海军.板岩水力特性试验研究与理论分析[博士学位论文][D].武汉:中国科学院武汉岩土力学研究所,2006.(MAO Haijun.Experimental and theoretical analysis of hydraulic characteristics of slate[Ph.D.Thesis][D].Wuhan:Wuhan Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2006.(in Chinese))
[30]陈至达.有限变形力学基础[M].徐州:中国矿业大学出版社,2001:48-63.(CHEN Zhida.Finite deformation mechanics foundation[M].Xuzhou:China University of Mining and Technology Press,2001:48-63.(in Chinese))
[31]ADACHI T.,OKA K F,GIFU A Y.A finite element analysis of strain localization for soft rock using a constitutive equation with strain softening[J].Archive of Applied Mechanics,1991,61(3):183-191.
[32]王学滨.材料缺陷对岩样变形局部化影响的数值模拟[J].岩土力学,2006,27(8):1 241-1 247.(WANG Xuebin.Numerical simulation of the effect of material defects on the deformation of rock samples[J].Rock and Soil Mechanics,2006,27(8):1 241-1 247.(in Chinese))
[33]LIN Q X.Stength degradation and damage micromechanism of granite under long-term loading[R].Hong Kong:The University of Hong Kong,2006.
[34]赵洪宝.含瓦斯煤失稳破坏及声发射特性的理论与实验研究[博士学位论文][D].重庆:重庆大学,2009.(ZHAO Hongbao.Theoretical and experimental study on destabilization and acoustic emission characteristics of gas-bearing coal[Ph.D.Thesis][D].Chongqing:Chongqing University,2009.(in Chinese))
[35]陈至达.理性力学[M].重庆:重庆出版社,2000:68-73.(CHENZhida.Rational mechanics[M].Chongqing:Chongqing Publishing House,2000:68-73.(in Chinese))
[36]XIAO J H.Foundation of deformation stress fields and constitutive equations in rational mechanics[R].[S.l.]:[s.n.],2010.
[37]XIAO J H.Chen Rational Mechanics XII:calculating material constants for complicated stress-strain experimental curves[R].Science Paper Online,2007.
[38]左建平,周宏伟,谢和平.不同温度影响下砂岩的断裂特性研究[J].工程力学,2008,25(5):124-130.(ZUO Jianping,ZHOU Hongwei,XIE Heping.Study on fracture characteristics of sandstone under different temperature[J].Engineering Mechanics,2008,25(5):124-130.(in Chinese))
[39]左建平,谢和平,周宏伟,等.温度-拉应力共同作用下砂岩破坏的断口形貌[J].岩石力学与工程学报,2007,26(12):2 444-2 455.(ZUO Jianping,XIE Heping,ZHOU Hongwei,et al.Fractal morphology of sandstone failure under the combined action of temperature and tension[J].Journal of Rock Mechanics and Engineering,2007,26(12):2 444-2 455.(in Chinese))
[40]左建平,谢和平,周宏伟,等.温度影响下砂岩的细观破坏及变形场的DSCM表征[J].力学学报,2008,40(6):786-794.(ZUOJianping,XIE Heping,ZHOU Hongwei,et al.Microscopic failure of the sandstone and DSCM characterization of deformation field under the influence of temperature[J].Acta Mechanica Sinica,2008,40(6):786-794.(in Chinese))
[41]靖洪文,李元海,赵保太,等.软岩工程支护理论与技术[M].徐州:中国矿业大学出版社,2008:1-66.(JIN Hongwen,LI Yuanhai,ZHAO Baotai,et al.soft rock engineering support theory and technology[M]Xuzhou:China Mining University Press,2008:1-66.(in Chinese))
[42]张志镇,高峰,徐小丽.花岗岩力学特性的温度效应试验研究[J].岩土力学,2011,38(2):2 343-2 349.(ZHANG Zhizhen,GAO Feng,XU Xiaoli.Study on temperature effect of mechanical properties of granite[J].Rock and Soil Mechanics,2011,38(2):2 343-2 349.(in Chinese))
[43]蔡武,窦林名,韩荣军,等.基于损伤统计本构模型的煤层冲击倾向性研究[J].煤炭学报,2011,36(增2):1 394-1 402.(CAI Wu,DOU Linming,HAN Rongjun,et al.Study on impact tendency of coal seam based on damage statistical constitutive model[J].Journal of Coal Science,2011,36(Supp.2):1 394-1 402.(in Chinese))
[44]HUDSON J A,HARRISON J P.Engineering rock mechanics I[M].Oxford:Pergamon Press,2000:96-102.
[2]何满潮,吕晓俭,景海河.深部工程围岩特性及非线性动态力学设计理念[J].岩石力学与工程学报,2002,21(8):1 215-1 224.(HEManchao,LU Xiaojian,JING Haihe.Design of surrounding rock characteristics and nonlinear dynamic mechanics design of deep engineering[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(8):1 215-1 224.(in Chinese))
[3]范雁秋.膨胀岩与工程[M].北京:科学出版社,2008:5-12.(FANYanqiu.Expansive rock and engineering[M].Beijing:Science Press,2008:5-12.(in Chinese))
[4]董平川,徐小荷,何顺利.变形与渗流耦合问题的研究进展[J].地质力学学报,1999,5(1):17-26.(DONG Pingchuan,XU Xiaohe,HE Shunli.Study on coupling of deformation and seepage[J].Journal of Geomechanics,1999,5(1):17-26.(in Chinese))
[5]刘建军,冯夏庭.我国油藏渗流-温度-应力耦合的研究进展[J].岩土力学,2003,24(增):645-650.(LIU Jianjun,FENG Xiating.Study on seepage-temperature-stress coupling in reservoirs in China[J].Rock and Soil Mechanics,2003,24(Supp.):645-650.(in Chinese))
[6]夏小和,王颖秩,黄春醒,等.高温作用对大理岩强度及变形特性影响的实验研究[J].上海交通大学学报,2004,38(6):996-998.(XIA Xiaohe,WANG Yingzhi,HUANG Chunxing,et al.Experimental study on the effect of high temperature on the strength and deformation characteristics of marble[J].Journal of Shanghai Jiaotong University,2004,38(6):996-998.(in Chinese))
[7]RANJITH P G,VIETE D R,BAI J C,et al.Transformation plasticity and the effect of temperature on the mechanical behaviour of Hawkesbury sandstone at atmospheric pressure[J].Engineering Geology,2012,151:120-127.
[8]MOHAJERANI M,DELAGE P,SULEM J,et al.A laboratory investigation of thermally induced pore pressures in the CallovoOxfordian claystone[J].International Journal of Rock Mechanics and Mining Science,2012,52(3):112-121.
[9]ERGULER Z A,ULUSAY R.Water-induced variations in mechanical properties of clay-bearing rocks[J].International Journal of Rock Mechanics and Mining Sciences,2009,46(2):355-370.
[10]VáSáRHELYI B,VáN P.Influence of water content on the strength of rock[J].Engineering Geology,2006,80(1):70-74.
[11]LABUZ J F,ZANG A.Mohr-Coulomb failure criterion[J].Rock Mechanics and Rock Engineering,2012,45(6):975-979.
[12]CHANG C,HAIMSON B.True triaxial strength and deformability of the German Continental Deep Drilling Program(KTB)deep hole amphibolite[J].Journal of Geophysical Research,2000,105(B8):18 999-19 013.
[13]HASSANZADEGAN A,BL?CHER G,MILSCH H,et al.The effects of temperature and pressure on the porosity evolution of Flechtinger sandstone[J].Rock Mechanics and Rock Engineering,2014,47(2):421-434.
[14]严荣林,侯贤文.矿井空调技术[M].北京:煤炭工业出版社,1994:1-10.(YAN Ronglin,HOU Xianwen.Mine air conditioning technology[M].Beijing:Coal Industry Press,1994:1-10.(in Chinese))
[15]尹光志,王登科,张东明,等.两种含瓦斯煤样变形特性与抗压强度的实验分析[J].岩石力学与工程学报,2009,28(2):410-417.(YIN Guangzhi,WANG Dengke,ZHANG Dongming,et al.Experimental analysis of deformation characteristics and compressive strength of gas-bearing coal samples[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(2):410-417.(in Chinese))
[16]乔丽苹.砂岩的弹塑性及蠕变特性的水物理化学作用效应试验与本构研究[R].武汉:中国科学院武汉岩土力学研究所,2008.(QIAOLiping.Experimental and constitutive study of water physical and chemical effects of elastoplastic and creep properties of sandstone[R].Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2008.(in Chinese))
[17]吴群英.应用数理统计[M].天津:天津大学出版社,2004:131-163.(WU Qunying.Application of mathematical statistics[M].Tianjin:Tianjin University Press,2004:131-163.(in Chinese))
[18]王兴仁,张录达,王华方.正交试验设置重复的必要性和统计分析方法[J].土壤学报,2000,31(3):135-139.(WANG Xingren,ZHANG Luda,WANG Huafang.Numerical necessity and statistical analysis method of orthogonal test setup[J].Acta Agronomica Sinica,2000,31(3):135-139.(in Chinese))
[19]蒋长宝,许江,彭守建,等.含瓦斯煤热流固耦合的渗流试验研究[J].煤炭学报,2011,36(9):1 545-1 550.(JIANG Changbao,XU Jiang,PENG Shoujian,et al.Study on seepage test of heat and fluid coupling of gas-bearing coal[J].Journal of Coal Science,2011,36(9):1 545-1 550.(in Chinese))
[20]徐小丽.温度载荷作用下花岗岩的力学性质演化及微观机制研究[博士学位论文][D].徐州:中国矿业大学出版社,2008.(XU Xiaoli.Study on mechanical properties and microscopic mechanism of granite under temperature load[Ph.D.Thesis][D].Xuzhou:China University of Mining and Technology Press,2008.(in Chinese))
[21]陈建文.岩盐的温度效应及习惯机理研究[R].武汉:中国科学院武汉岩土力学研究所,2008.(CHEN Jianwen.Study on temperature effect and habit mechanism of rock salt[R].Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2008.(in Chinese))
[22]周青春.温度、空隙水和应力作用下砂岩的力学特性研究[R].武汉:中国科学院武汉岩土力学研究所,2006.(ZHOU Qingchun.Study on the mechanical properties of sandstone under temperature,void water and stress[R].Wuhan:Wuhan Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2006.(in Chinese))
[23]许江,杨红伟,彭守建,等.孔隙水压力-围压作用下砂岩力学特性的试验研究[J].岩石力学与工程学报,2010,29(8):1 618-1 623.(XU Jiang,YANG Hongwei,PENG Shoujian,et al.Experimental study on mechanical properties of sandstone under pore water pressure and confining pressure[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(8):1 618-1 623.(in Chinese))
[24]许江,鲜学福,杜云贵,等.含瓦斯煤的力学特性试验研究[J].重庆大学学报,1993,16(5):42-47.(XU Jiang,XIAO Xuefu,DU Yungui,et al.Experimental study on mechanical properties of gas-bearing coal[J].Journal of Chongqing University,1993,16(5):42-47.(in Chinese))
[25]张凯.脆性岩石力学模型与流固耦合机理研究[博士学位论文][D].武汉:中国科学院武汉岩土力学研究所,2010.(ZHANG Kai.Study on mechanics model and fluid-structure coupling mechanism of brittle rocks[Ph.D.Thesis][D].Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2010.(in Chinese))
[26]徐礼华,刘素梅,李彦强.丹江口水库区岩石软化性能试验研究[J].岩土力学,2008,29(5):1 430-1 434.(XU Lihua,LIU Sumei,LIYanqiang.Experimental study on rock softening performance of Danjiangkou reservoir area[J].Rock and Soil Mechanics,2008,29(5):1 430-1 434.(in Chinese))
[27]季明.湿度场下灰质泥岩的力学性质演化与蠕变特征研究[M].徐州:中国矿业大学出版社,2009:38-43.(JI Ming.Study on the evolution of mechanical properties and creep characteristics of gray mudstone in humidity field[M].Xuzhou:China University of Mining and Technology Press,2009:38-43.(in Chinese))
[28]龚选平.泥质粉砂岩含水率对其蠕变特性影响的研究[博士学位论文][D].西安:西安科技大学,2006.(GONG Xuanping.Study on the effect of moisture content on the creep characteristics of shale siltstone[Ph.D.Thesis][D].Xi?an:Xi?an University of Science and Technology,2006.(in Chinese))
[29]冒海军.板岩水力特性试验研究与理论分析[博士学位论文][D].武汉:中国科学院武汉岩土力学研究所,2006.(MAO Haijun.Experimental and theoretical analysis of hydraulic characteristics of slate[Ph.D.Thesis][D].Wuhan:Wuhan Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2006.(in Chinese))
[30]陈至达.有限变形力学基础[M].徐州:中国矿业大学出版社,2001:48-63.(CHEN Zhida.Finite deformation mechanics foundation[M].Xuzhou:China University of Mining and Technology Press,2001:48-63.(in Chinese))
[31]ADACHI T.,OKA K F,GIFU A Y.A finite element analysis of strain localization for soft rock using a constitutive equation with strain softening[J].Archive of Applied Mechanics,1991,61(3):183-191.
[32]王学滨.材料缺陷对岩样变形局部化影响的数值模拟[J].岩土力学,2006,27(8):1 241-1 247.(WANG Xuebin.Numerical simulation of the effect of material defects on the deformation of rock samples[J].Rock and Soil Mechanics,2006,27(8):1 241-1 247.(in Chinese))
[33]LIN Q X.Stength degradation and damage micromechanism of granite under long-term loading[R].Hong Kong:The University of Hong Kong,2006.
[34]赵洪宝.含瓦斯煤失稳破坏及声发射特性的理论与实验研究[博士学位论文][D].重庆:重庆大学,2009.(ZHAO Hongbao.Theoretical and experimental study on destabilization and acoustic emission characteristics of gas-bearing coal[Ph.D.Thesis][D].Chongqing:Chongqing University,2009.(in Chinese))
[35]陈至达.理性力学[M].重庆:重庆出版社,2000:68-73.(CHENZhida.Rational mechanics[M].Chongqing:Chongqing Publishing House,2000:68-73.(in Chinese))
[36]XIAO J H.Foundation of deformation stress fields and constitutive equations in rational mechanics[R].[S.l.]:[s.n.],2010.
[37]XIAO J H.Chen Rational Mechanics XII:calculating material constants for complicated stress-strain experimental curves[R].Science Paper Online,2007.
[38]左建平,周宏伟,谢和平.不同温度影响下砂岩的断裂特性研究[J].工程力学,2008,25(5):124-130.(ZUO Jianping,ZHOU Hongwei,XIE Heping.Study on fracture characteristics of sandstone under different temperature[J].Engineering Mechanics,2008,25(5):124-130.(in Chinese))
[39]左建平,谢和平,周宏伟,等.温度-拉应力共同作用下砂岩破坏的断口形貌[J].岩石力学与工程学报,2007,26(12):2 444-2 455.(ZUO Jianping,XIE Heping,ZHOU Hongwei,et al.Fractal morphology of sandstone failure under the combined action of temperature and tension[J].Journal of Rock Mechanics and Engineering,2007,26(12):2 444-2 455.(in Chinese))
[40]左建平,谢和平,周宏伟,等.温度影响下砂岩的细观破坏及变形场的DSCM表征[J].力学学报,2008,40(6):786-794.(ZUOJianping,XIE Heping,ZHOU Hongwei,et al.Microscopic failure of the sandstone and DSCM characterization of deformation field under the influence of temperature[J].Acta Mechanica Sinica,2008,40(6):786-794.(in Chinese))
[41]靖洪文,李元海,赵保太,等.软岩工程支护理论与技术[M].徐州:中国矿业大学出版社,2008:1-66.(JIN Hongwen,LI Yuanhai,ZHAO Baotai,et al.soft rock engineering support theory and technology[M]Xuzhou:China Mining University Press,2008:1-66.(in Chinese))
[42]张志镇,高峰,徐小丽.花岗岩力学特性的温度效应试验研究[J].岩土力学,2011,38(2):2 343-2 349.(ZHANG Zhizhen,GAO Feng,XU Xiaoli.Study on temperature effect of mechanical properties of granite[J].Rock and Soil Mechanics,2011,38(2):2 343-2 349.(in Chinese))
[43]蔡武,窦林名,韩荣军,等.基于损伤统计本构模型的煤层冲击倾向性研究[J].煤炭学报,2011,36(增2):1 394-1 402.(CAI Wu,DOU Linming,HAN Rongjun,et al.Study on impact tendency of coal seam based on damage statistical constitutive model[J].Journal of Coal Science,2011,36(Supp.2):1 394-1 402.(in Chinese))
[44]HUDSON J A,HARRISON J P.Engineering rock mechanics I[M].Oxford:Pergamon Press,2000:96-102.