非线性硬化与软化的巷道围岩应力分布与工况研究
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摘要
采用摄动法得到接近岩体实际的弹性、应变非线性硬化和软化3段光滑连接的本构模型,求得静水压力下圆形巷(隧)道围岩塑性硬化区和软化区的应力分布规律。给出围岩平衡方程、地应力–硐室位移关系和围岩特征方程。分析中可自然导出围岩自承地应力上限概念。根据围岩平衡方程写出围岩弹性区、硬化区和软化区分担地应力的表达式。计算表明,围岩硬化区承载力ph大于弹性区承载力pe,软化区也有相当的承载能力。特别是所求得的切向应力σθ/p0-r/a曲线光滑连接,没有尖峰向上的应力集中,此结果与其他学者在巷(隧)道模拟试验中测得的σθ-r曲线形状一致,从理论上证明基于理想弹塑性本构模型的Kastener解在围岩软化区半径处的σθ-r曲线有尖峰向上的应力集中与实际不符。
A constitutive model,which can almost describe the characteristics of rock mass truly,is obtained by perturbation method.The curve of the constitutive model is linked glossily by elastic,strain nonlinear hardening and nonlinear softening segments.The stress distribution laws in plastic hardening and softening zones of surrounding rock under hydrostatic pressure are achieved.Based on the analyses,equilibrium equation of surrounding rock,relationship between geostress and tunnel displacement and characteristic equation of surrounding rock are presented;and the expressions of geostress shared by elastic zone,hardening zone and softening zone of surrounding rocks are given.Calculation shows that the bearing capacity of the hardening zone of surrounding rock is more large than that of elastic zone.Especially,the curve of σθ /po-r/a has no up-pinnacled stress concentration;and the result accords well with the experiment one of other scholar.It is pointed out that there are obvious limitations in Kastener formula which is based on ideal elastoplastic constitutive model;and the up-pinnacled stress concentration of σθ-r curve does not correspond with the practical one.
A constitutive model,which can almost describe the characteristics of rock mass truly,is obtained by perturbation method.The curve of the constitutive model is linked glossily by elastic,strain nonlinear hardening and nonlinear softening segments.The stress distribution laws in plastic hardening and softening zones of surrounding rock under hydrostatic pressure are achieved.Based on the analyses,equilibrium equation of surrounding rock,relationship between geostress and tunnel displacement and characteristic equation of surrounding rock are presented;and the expressions of geostress shared by elastic zone,hardening zone and softening zone of surrounding rocks are given.Calculation shows that the bearing capacity of the hardening zone of surrounding rock is more large than that of elastic zone.Especially,the curve of σθ /po-r/a has no up-pinnacled stress concentration;and the result accords well with the experiment one of other scholar.It is pointed out that there are obvious limitations in Kastener formula which is based on ideal elastoplastic constitutive model;and the up-pinnacled stress concentration of σθ-r curve does not correspond with the practical one.
引文
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[2]Pan Y,Dong J J.Time dependent tunnel convergence—II.advance rate and tunnel-support interaction[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1991,28(6):477–488.
[3]梁发云,陈龙珠.应变软化Tresca材料中扩化问题解答及应用[J].岩土力学,2004,25(2):261–265.(Liang Fayun,Chen Longzhu.Analytical solution to cavity expansion in strain-softening soils with Tresca yield criterion and its applications[J].Rock and Soil Mechanics,2004,25(2):262–265.(in Chinese))
[4]何满潮,景海河,孙晓明.软岩工程力学[M].北京:科学出版社,2002.(He Manchao,Jing Haihe,Sun Xiaoming.Engineering Mechanics of Soft Rock[M].Beijing:Science Press,2002.(in Chinese))
[5]潘岳,王志强.基于应变非线性软化的圆形硐室围岩弹塑性分析[J].岩石力学与工程学报,2005,24(6):915–920.(Pan Yue,Wang Zhiqiang.Elasto-plastic analysis of surrounding rock of circular chamber based on strain nonlinear softening[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(6):915–920.(in Chinese))
[6]贾乃文.黏塑性力学及工程应用[M].北京:地震出版社,2000.51–53.(Jia Naiwen.Viscoplasticity Mechanics and Its Engineering Application[M].Beijing:Earthquake Press,2000.51–53.(in Chinese))
[7]卡恰诺夫L M.塑性理论基础[M].周承侗译.北京:人民教育出版社,1982.147–148.(Kachanov L M.Fundamentals of Plastic Theory[M].Translated by Zhou Chengtong.Beijing:People′s Education Press,1982.147–148.(in Chinese))
[8]久武胜保.软岩隧洞非线性力学特性的理论分析[A].见:土木学会论文集[C].[s.l.]:[s.n.],1988.39–43.(Hisashi T.Theoretical analysis of nonlinear mechanical characteristic of soft rock tunnel[A].In:Dissertation Corpus of Civil Experimental Society[C].[s.l.]:[s.n.],1988.39–43.(in Chinese))
[9]Maranini E,Brignoli M.Creep behavior of a weak rock:experimental characterization[J].International Journal of Rock Mechanics and Mining Sciences,1999,36(1):127–138.
[10]Sato T,Kikuchi T,Sugihara K.In-situ experiments on an excavation disturbed zone induced by mechanical excavation in Neogene sedimentary rock at Tono Mine,central Japan[J].Engineering Geology,2000,56(1):97–108.
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