岩质隧道施工过程变形时空问题的位移释放系数法
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摘要
岩质隧道施工过程变形具有显著的成洞时间效应与开挖面空间效应。由于应力释放率与施工过程参数、围岩力学性态等的关系难以量化,应力释放系数法在解析岩质隧道施工过程变形问题时存在局限性。为描述岩质隧道与时间、空间相关的复杂的施工力学过程,假设围岩为Burgers体和Drucker–Prager组合模型。利用弹性–黏弹性对应原理与非关联流动法则建立无支护隧道变形解,采用位移释放系数法描述隧道施工过程变形的时空效应。获得的2维平面应变无支护隧道最大径向位移的数学函数形式与Manh解一致;当不考虑时间因素时,本文解可退化为Park解。通过与既有数值解和解析解对比,验证了本文解的正确有效性。进而分析隧道时空变形曲线,包括隧道蠕变特征曲线、围岩变形径向分布曲线和隧道纵剖面变形曲线,得到关于黏聚力、内摩擦角、扩容角与延迟时间等参数的敏感性规律。结果表明:随着时间推移或纵向距离的增大,隧道变形非线性递增;随着围岩深度的增加,隧道变形递减,隧道变形和塑性区半径均为黏聚力与内摩擦角的非线性递减函数;围岩扩容加剧了隧道变形;延迟时间控制了隧道变形的时程规律;隧道时空变形对介入参数的敏感性与其物理意义一致。位移释放系数法成功描述了岩质隧道施工过程变形的时空效应,可为施工过程提供理论指导。
The spatiotemporal effects of deformations of rocky tunnels are significant during the construction. Stress release coefficient method is not applicable to study the deformations of rocky tunnels because of the limited advance knowledge of the quantitative connection between the stress release rate and the parameters associated with the construction process and the surrounding rock properties. In order to investigate spatiotemporal deformations of rocky tunnels during construction, the combination model of Burgers body and Drucker–Prager criterion is applied to characterize the mechanical properties of surrounding rock. The closed-form solutions of tunnel's deformation are derived by using the correspondence principle of elasticity–viscoelasticity and the non-associated flow rule. The displacement release coefficient method is introduced to describe spatiotemporal deformations of the surrounding rock during the construction of rocky tunnels. The maximum short term radial displacement corresponding to plane strain analysis of a tunnel cross section has the similar function formations as the Manh solutions. Moreover, the present solutions reduce to the Park solutions when the time effect is neglected. The correctness and effectiveness of the present solutions are verified by comparing the previous numerical/analytical solutions and the present solutions. Finally, spatiotemporal deformations curves of rocky tunnels, which includes creep characteristic curve of tunnel, radial distribution curve of tunnel's deformation and longitudinal deformation profile of tunnel, are analyzed with considering the effects of different parameters, such as cohesive, internal friction angle, dilation angle and retardation time. The results show that the deformation of tunnel nonlinearly increases with the increase of time and longitudinal distance, but decreases as the depth of surrounding rock increases. The deformation of tunnel is the nonlinear decreasing function of cohesive and internal friction angle as well as the radius of plastic zone. The dilation of rock increases the deformation of tunnel. Besides, the retardation time determines the time history of tunnel's deformation. Effects of incorporated parameters on spatiotemporal deformations of rocky tunnels are consistent with their physical meanings. Displacement release coefficient method successfully describes the spatiotemporal deformations of rocky tunnels, which provides the theoretical guidance for the construction of rocky tunnels.
The spatiotemporal effects of deformations of rocky tunnels are significant during the construction. Stress release coefficient method is not applicable to study the deformations of rocky tunnels because of the limited advance knowledge of the quantitative connection between the stress release rate and the parameters associated with the construction process and the surrounding rock properties. In order to investigate spatiotemporal deformations of rocky tunnels during construction, the combination model of Burgers body and Drucker–Prager criterion is applied to characterize the mechanical properties of surrounding rock. The closed-form solutions of tunnel's deformation are derived by using the correspondence principle of elasticity–viscoelasticity and the non-associated flow rule. The displacement release coefficient method is introduced to describe spatiotemporal deformations of the surrounding rock during the construction of rocky tunnels. The maximum short term radial displacement corresponding to plane strain analysis of a tunnel cross section has the similar function formations as the Manh solutions. Moreover, the present solutions reduce to the Park solutions when the time effect is neglected. The correctness and effectiveness of the present solutions are verified by comparing the previous numerical/analytical solutions and the present solutions. Finally, spatiotemporal deformations curves of rocky tunnels, which includes creep characteristic curve of tunnel, radial distribution curve of tunnel's deformation and longitudinal deformation profile of tunnel, are analyzed with considering the effects of different parameters, such as cohesive, internal friction angle, dilation angle and retardation time. The results show that the deformation of tunnel nonlinearly increases with the increase of time and longitudinal distance, but decreases as the depth of surrounding rock increases. The deformation of tunnel is the nonlinear decreasing function of cohesive and internal friction angle as well as the radius of plastic zone. The dilation of rock increases the deformation of tunnel. Besides, the retardation time determines the time history of tunnel's deformation. Effects of incorporated parameters on spatiotemporal deformations of rocky tunnels are consistent with their physical meanings. Displacement release coefficient method successfully describes the spatiotemporal deformations of rocky tunnels, which provides the theoretical guidance for the construction of rocky tunnels.
引文
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[14]Zhang Changguang,Zeng Kaihua.Comparisons and applications of displacement release coefficients for a circular rock tunnel subjected to isotropic geostresses[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(3):498-510.[张常光,曾开华.等值地应力下岩质圆形隧道位移释放系数比较及应用[J].岩石力学与工程学报,2015,34(3):498-510.]
[15]Ramoni M,Anagnostou G.The interaction between shield,ground and tunnel support in TBM tunnelling through squeezing ground[J].Rock Mechanics and Rock Engineering,2011,44(1):37-61.
[16]Gao X,Zhang T,Zhou J,et al.On stress-state dependent plasticity modeling:Significance of the hydrostatic stress,the third invariant of stress deviator and the non-associated flow rule[J].International Journal of Plasticity,2011,27(2):217-231.
[17]Alejano L R,Bobet A.Drucker-Prager criterion[J].Rock Mechanics and Rock Engineering,2012,45(6):995-999.
[18]Zhang Jianzhi,Yu Jin,Cai Yanyan,et al.Viscoelastic-plastic creep solutions and deformation properties of tunnels inswelling rocks under seepage[J].Chinese Journal of Geotechnical Engineering,2014,36(12):2195-2202.[张建智,俞缙,蔡燕燕,等.渗水膨胀岩隧洞黏弹塑性蠕变解及变形特性分析[J].岩土工程学报,2014,36(12):2195-2202.]
[19]Yu Dongming,Yao Hailin,Duan Jianxin,et al.Viscoelastoplastic creep solutions to deep circular tunnels considering intermediate principal stress and shear dilatancy[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(Supp 2):3586-3592.[余东明,姚海林,段建新,等.考虑中主应力和剪胀的深埋圆形隧道黏弹塑性蠕变解[J].岩石力学与工程学报,2012,31(增刊2):3586-3592.]
[20]Hao W U,Qin F,Zhang Y D,et al.Zonal disintegration phenomenon in enclosing rock mass surrounding deep tunnels-Mechanism and discussion of characteristic parameters[J].International Journal of Mining Science and Technology,2009,19(3):306-311.
[21]Park K H,Kim Y J.Analytical solution for a circular opening in an elastic-brittle-plastic rock[J].International Journal of Rock Mechanics and Mining Sciences,2006,43(4):616-622.
[22]Zeng Kaihua,Yang Weihan,Zhang Changguang,et al.Optimal support in soft rock tunnel based on the unified strength theory and steady creep guideline[J].Advanced Engineering Sciences,2018,50(1):62-70.[曾开华,杨维汉,张常光,等.基于统一强度理论和稳定蠕变准则的软岩巷道最优支护[J].工程科学与技术,2018,50(1):62-70.]
[23]Chen Bingrui,Feng Xiating.Universal visco-elasto-plastic combination model and its engineering applications[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(5):1028-1035.[陈炳瑞,冯夏庭.黏弹塑性普适组合模型及其工程应用[J].岩石力学与工程学报,2008,27(5):1028-1035.]
[2]Cui Lan,Zheng Junjie,Miao Chenxi,et al.Coupling analysis of longitudinal deformation profile and ground reaction curve[J].Chinese Journal of Geotechnical Engineering,2014,36(4):707-715.[崔岚,郑俊杰,苗晨曦,等.隧道纵向变形曲线与围岩特征曲线耦合分析[J].岩土工程学报,2014,36(4):707-715.]
[3]Bian Yuewei,Xia Caichu,Xiao Weimin,et al.Viscoelastoplastic solutions for circular tunnel considering stress release and softening behaviour of rocks[J].Rock and Soil Mechanics,2013,34(1):211-220.[卞跃威,夏才初,肖维民,等.考虑围岩软化特性和应力释放的圆形隧道黏弹塑性解[J].岩土力学,2013,34(1):211-220.]
[4]Cai Yanyan,Zhang Jianzhi,Yu Jin,et al.Nonlinear displacement solutions for deep tunnels considering whole process of creep and dilatation of surrounding rock[J].Rock and Soil Mechanics,2015,36(7):1831-1839.[蔡燕燕,张建智,俞缙,等.考虑围岩蠕变全过程与扩容的深埋隧道非线性位移解[J].岩土力学,2015,36(7):1831-1839.]
[5]Manh H T,Sulem J,Subrin D,et al.Anisotropic time-dependent modeling of tunnel excavation in squeezing ground[J].Rock Mechanics and Rock Engineering,2015,48(6):2301-2317.
[6]Wen Sen,Yang Shengqi,Dong Zhengfang,et al.TBM jamming mechanism and control measures in deep buried tunnels[J].Chinese Journal of Geotechnical Engineering,2015,37(7):1271-1277.[温森,杨圣奇,董正方,等.深埋隧道TBM卡机机理及控制措施研究[J].岩土工程学报,2015,37(7):1271-1277.]
[7]Birchall T J,Osman A S.Response of a tunnel deeply embedded in a viscoelastic medium[J].International Journal for Numerical and Analytical Methods in Geomechanics,2012,36(15):1717-1740.
[8]Zhang Changguang,Zeng Kaihua.Comparisons of spatialeffect approaches for tunnel excavation using convergenceconfinement method[J].Rock and Soil Mechanics,2016,37(5):1417-1424.[张常光,曾开华.收敛约束法中隧道开挖面空间效应方法比较[J].岩土力学,2016,37(5):1417-1424.]
[9]Yang Youbin,Zheng Junjie,Lai Hanjiang,et al.A revised method for calculating stress release ratio in tunnel excavation[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(11):2251-2257.[杨友彬,郑俊杰,赖汉江,等.一种改进的隧道开挖应力释放率确定方法[J].岩石力学与工程学报,2015,34(11):2251-2257.]
[10]Cantieni L,Anagnostou G.On a paradox of elasto-plastic tunnel analysis[J].Rock Mechanics and Rock Engineering,2011,44(2):129-147.
[11]Manh H T,Sulem J,Subrin D.Progressive degradation of rock properties and time-dependent behavior of deep tunnels[J].Acta Geotechnica,2016,11(3):693-711.
[12]Vlachopoulos N,Diederichs M S.Improved longitudinal displacement profiles for convergence confinement analysis of deep tunnels[J].Rock Mechanics and Rock Engineering,2009,42(2):131-146.
[13]Zhang Chuanqing,Feng Xiating,Zhou Hui,et al.Study of some problems about application of stress release method to tunnel excavation simulation[J].Rock and Soil Mechanics,2008,29(5):1174-1180.[张传庆,冯夏庭,周辉,等.应力释放法在隧洞开挖模拟中若干问题的研究[J].岩土力学,2008,29(5):1174-1180.]
[14]Zhang Changguang,Zeng Kaihua.Comparisons and applications of displacement release coefficients for a circular rock tunnel subjected to isotropic geostresses[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(3):498-510.[张常光,曾开华.等值地应力下岩质圆形隧道位移释放系数比较及应用[J].岩石力学与工程学报,2015,34(3):498-510.]
[15]Ramoni M,Anagnostou G.The interaction between shield,ground and tunnel support in TBM tunnelling through squeezing ground[J].Rock Mechanics and Rock Engineering,2011,44(1):37-61.
[16]Gao X,Zhang T,Zhou J,et al.On stress-state dependent plasticity modeling:Significance of the hydrostatic stress,the third invariant of stress deviator and the non-associated flow rule[J].International Journal of Plasticity,2011,27(2):217-231.
[17]Alejano L R,Bobet A.Drucker-Prager criterion[J].Rock Mechanics and Rock Engineering,2012,45(6):995-999.
[18]Zhang Jianzhi,Yu Jin,Cai Yanyan,et al.Viscoelastic-plastic creep solutions and deformation properties of tunnels inswelling rocks under seepage[J].Chinese Journal of Geotechnical Engineering,2014,36(12):2195-2202.[张建智,俞缙,蔡燕燕,等.渗水膨胀岩隧洞黏弹塑性蠕变解及变形特性分析[J].岩土工程学报,2014,36(12):2195-2202.]
[19]Yu Dongming,Yao Hailin,Duan Jianxin,et al.Viscoelastoplastic creep solutions to deep circular tunnels considering intermediate principal stress and shear dilatancy[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(Supp 2):3586-3592.[余东明,姚海林,段建新,等.考虑中主应力和剪胀的深埋圆形隧道黏弹塑性蠕变解[J].岩石力学与工程学报,2012,31(增刊2):3586-3592.]
[20]Hao W U,Qin F,Zhang Y D,et al.Zonal disintegration phenomenon in enclosing rock mass surrounding deep tunnels-Mechanism and discussion of characteristic parameters[J].International Journal of Mining Science and Technology,2009,19(3):306-311.
[21]Park K H,Kim Y J.Analytical solution for a circular opening in an elastic-brittle-plastic rock[J].International Journal of Rock Mechanics and Mining Sciences,2006,43(4):616-622.
[22]Zeng Kaihua,Yang Weihan,Zhang Changguang,et al.Optimal support in soft rock tunnel based on the unified strength theory and steady creep guideline[J].Advanced Engineering Sciences,2018,50(1):62-70.[曾开华,杨维汉,张常光,等.基于统一强度理论和稳定蠕变准则的软岩巷道最优支护[J].工程科学与技术,2018,50(1):62-70.]
[23]Chen Bingrui,Feng Xiating.Universal visco-elasto-plastic combination model and its engineering applications[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(5):1028-1035.[陈炳瑞,冯夏庭.黏弹塑性普适组合模型及其工程应用[J].岩石力学与工程学报,2008,27(5):1028-1035.]