基于应变非线性软化的圆形硐室围岩弹塑性分析
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摘要
依据塑性力学全量理论,将岩体单轴压缩的非线性软化本构关系推广,得到复杂应力状态下圆形硐室围岩塑性区的等效应力与等效应变关系;籍以求得应变非线性软化的圆形硐室围岩塑性区半径、弹塑性区应力、应变和位移;进而求得相应情况下的硐室围岩平衡方程、地应力与硐室周边位移关系以及围岩压力方程。首次给出围岩弹性区承载力、塑性区承载力的表达式。
According to the entire theory of plastic mechanics,the relationship between equivalent stress and equivalent strain of circular chamber plastic zone in the complex stress state is deduced from nonlinear softening constitutive relation of rock under uniaxial compression. On this basis,the stress,strain,and displacements of elastic and plastic zone in surrounding rocks of chamber,are derived. Then the equilibrium equation of surrounding rocks,relationship between geostress and chamber displacement,and pressure equation of surrounding rocks,are obtained under corresponding conditions. The concrete formulation of carrying power of elastic zone and carrying power of plastic zone are first proposed. Because the assumed constitutive relationship agrees well with practical condition of rocks,the obtained results maybe more closely approach to corresponding actual values in surrounding rocks of chamber,compared with Fenna′s solution that is based on ideal elasto-plastic relationship.
According to the entire theory of plastic mechanics,the relationship between equivalent stress and equivalent strain of circular chamber plastic zone in the complex stress state is deduced from nonlinear softening constitutive relation of rock under uniaxial compression. On this basis,the stress,strain,and displacements of elastic and plastic zone in surrounding rocks of chamber,are derived. Then the equilibrium equation of surrounding rocks,relationship between geostress and chamber displacement,and pressure equation of surrounding rocks,are obtained under corresponding conditions. The concrete formulation of carrying power of elastic zone and carrying power of plastic zone are first proposed. Because the assumed constitutive relationship agrees well with practical condition of rocks,the obtained results maybe more closely approach to corresponding actual values in surrounding rocks of chamber,compared with Fenna′s solution that is based on ideal elasto-plastic relationship.
引文
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[3]凌贤长,蔡得所.岩体力学[M].哈尔滨:哈尔滨工业大学出版社,2002.(LingXianchang,CaiDesuo.RockMechanics[M].Harbin:HarbinInstitute ofTechnologyPress,2002.(inChinese))
[4]沈明荣.岩体力学[M].上海:同济大学出版社,2002.(ShenMingrong.RockMechanics[M].Shanghai:TongjiUniversityPress,2002.(inChinese))
[5]孙广忠.岩体结构力学[M].北京:科学出版社,1988.(SunGuangzhong.RockStructuralMechanics[M].Beijing:SciencePress,1988.(inChinese))
[6]李晓.岩石峰后力学特性及其损伤软化的模型研究与应用[博士学位论文][D].徐州:中国矿业大学,1995.(LiXiao.Study and application on the mechanics characteristic and the damage softening model after pick of rock[Ph.D.Thesis][D].Xuzhou:ChinaUniversity ofMiningandTechnology,1995.(inChinese))
[7]金丰年.考虑时间效应的围岩特性曲线[J].岩石力学与工程学报,1997,16(4):344–353.(JinFengnian.Characteristic curves of surrounding rocks based time effect[J].ChineseJournal ofRockMechanics andEngineering,1997,16(4):344–353.(inChinese))
[8]KachanovL M.塑性理论基础[M].周承侗译.北京:人民教育出版社,1982.(KachanovL M.Fundamentals ofPlasticTheory[M].Translated byZhouChengtong.Beijing:People′sEducationPress,1982.(inChinese))
[9]过镇海,张秀琴.单调荷载作用下混凝土应力–应变全曲线的实验研究[A].见:科学报告集[C].北京:清华大学出版社,1987.1–6.(GuoZhenhai,ZhangXiuqin.Experimental study on full stress-strain curve of concrete under monotonic load[A].In:ScienceReportCorpus[C].Beijing:TsinghuaUniversityPress,1987.1–6.(inChinese))
[10]刑秋顺.约束混凝土应力–应变全曲线的研究[A].见:科学报告集[C].北京:清华大学出版社,1987.81–86.(XingQiushun.Study on full stress-strain curve of restricted concrete[A].In:ScienceReportCorpus[C].Beijing:TsinghuaUniversityPress,1987.81–86.(inChinese))
[11]郑颖人.岩土塑性力学原理[M].重庆:中国人民解放军后勤工程学院出版社,1998.(ZhengYingren.Theory ofRock-soilPlasticMechanics[M].Chongqing:LogisticalEngineeringUniversity ofPLAPress,1998.(inChinese))
[12]《数学手册》编写组.数学手册[M].北京:人民教育出版社,1979.(CompilationGroup ofMathematicalManual.MathematicalManual[M].Beijing:People′sEducationPress,1979.(inChinese))
[13]潘一山,章梦涛,王来贵.地下硐室岩爆的相似材料模拟实验研究[J].岩土工程学报,1997,19(4):49–56.(PanYishan,ZhangMengtao,WangLaigui.Study on rock burst by equivalent material simulation tests[J].ChineseJournal ofGeotechnicalEngineering,1997,19(4):49–56.(inChinese))
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