考虑残余强度和损伤的岩体应力场—渗流场耦合理论研究及工程应用
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摘要
本文主要依托拟建的京张城际铁路八达岭地下车站工程,以详尽的岩体结构调查统计为基础,以大量的岩石单轴、三轴全应力-应变曲线为支撑,对考虑残余强度和损伤的岩体应力场-渗流场耦合理论作了深入研究,并将理论研究成果应用于八达岭地下车站设计的结构方案优化和环境影响评估以及武广高铁尖峰顶隧道下穿地表高压输电线塔施工控制方案优化。论文的主要创新性的研究方法、手段和研究成果摘要如下：
1、岩体残余强度特征研究
在隧道及地下工程中,研究岩体残余强度及峰后力学性质对工程设计有着非常重要的意义。本文通过以下四个方面对岩体残余强度特征展开研究：(1)岩石在单轴压缩条件下的变形及损伤特征分析；(2)常规三轴压缩试验下岩石的残余强度特征分析；(3)进行单层节理岩体力学特性数值试验研究,重点分析单轴和三轴压缩条件不同结构面倾角的单层节理岩体的强度特征。
2、基于残余强度修正的岩石损伤本构模型
岩石随着围压的增大,残余强度的增加幅度比峰值强度大,残余强度逐渐成为影响岩石全应力-应变曲线峰后段的主要因素,因此,在建立岩石损伤软化统计本构模型时考虑残余强度进行修正是非常有必要的。基于岩石应变强度理论以及岩石微元强度服从Weibull随机分布的假设,本文考虑岩石峰后残余强度对损伤变量进行了修正,在微元破坏符合Hoek-Brown屈服准则条件下,建立了能够反映岩石峰后软化特征的三维损伤统计本构模型；然后,依据岩石试验全应力-应变曲线的几何特征,推导出本构模型参数的数学表达式,并基于花岗岩室内试验数据对模型参数进行探讨,研究了Weibull分布参数与本构模型的关系,探讨了损伤修正系数的取值和岩石累积损伤的扩展过程；最后,将本文建立的本构模型理论曲线与四种岩石(斑状二长花岗岩、细晶大理岩、砂岩和粉砂质泥岩)在不同围压下的常规三轴压缩试验曲线进行对比分析,结果证实该模型能很好的描述岩石破裂过程的全应力-应变关系和表征岩石残余强度特征。这对于岩石损伤软化问题以及岩石加固处理措施的研究均具有重要的意义。
3、岩石损伤本构模型参数取值研究
岩石损伤本构模型的参数是根据岩体地质强度指标(GSI)计算取得。评价岩体地质强度指标时,因其基本要素取值过程存在较大的随机性和模糊性,这就很难用静态模式去准确地衡量每个影响因素。岩体特征参量的模糊性反映了其内在的不确定性,模糊数学理论能为更客观的刻画这种特性提供有力的数学手段。本文首先引入岩体节理组数Jn、节理间距l和岩体完整性系数Kv描述岩体结构特征,再引入大比例尺波形系数Jw、小比例尺光滑系数Js和节理蚀变系数Ja描述结构面状态,然后把多因素模糊综合评判理论应用到GSI系统的评价中去,并利用层次分析法确定模糊评判因素的权重,建立了GSI系统的模糊综合评判模型。工程应用表明,这种方法针对性较强、准确度较高,能够将地质调查勘探结果、试验结果、统计数据以及专家意见有机结合起来,从而减小了研究者决策时主观性。GSI系统的模糊综合评判法为GSI系统量化提供了新的途径。
4、考虑损伤的岩体流固耦合模型研究
应用连续性方程、线动量平衡方程、岩石损伤等效弹性模量方程及相应的物性方程,在合理的基本假设基础上,对饱和状态下渗流场和应力场控制方程分别进行了推导,建立了考虑损伤效应的渗流应力耦合模型。在耦合方程组推导过程中,针对岩体损伤效应,考虑了岩体渗流状态的变化及岩石孔隙率、渗透率变化。结合隧道围岩的初始条件及边界条件,研究了考虑损伤效应的渗流应力耦合模型有限差分求解方法,对求解过程进行了程序设计,以FLAC3D有限差分软件为平台,进行了软件二次开发,程序计算过程简洁、便于实现。
5、工程应用研究
以京张城际铁路八达岭超大规模地下车站修建为例,依据工程区水文地质特征、水压致裂原位应力测量结果,利用有限差分软件FLAC3D建立三维渗流-应力耦合模型,并采用四种方案进行数值模拟：全封堵、全排水、非耦合、注浆限排。并结合理论分析,着重研究在饱水状况下八达岭车站修建前后渗流场变化、涌水量、围岩变形和地表沉降等环境影响负效应因子,对因地下车站修建环境影响效应的显著性、空间分布特征和长期效应进行评价。模拟计算结果对于裂隙发育、富水地层地下工程尤其修建于自然风景区大型地下洞室防排水设计和施工具有指导意义。
偏压富水软岩大断面隧道施工引起的地层变形是多方面影响因素叠加的结果。结合武广高铁尖峰顶隧道下穿地表高压输电线塔的工程实践,首先对隧道施工前后地层变形监测和分析提出控制大变形的工程措施,然后采用综合统计和理论分析,研究地形条件、地层产状、隧道和通道施工、地面荷载、地表坍塌造成的地层变形与建筑物位移的关系,最后以流固耦合数值分析为手段对影响地层变形的关键因素作了量化分析。
This paper relies on the proposed Badaling Underground Project of Jingzhang inter-city railway. The content of the paper,which does a thorough research of the rock mass stress field-seepage field coupling theory which considering residual strength and damage, is based on detail rock mass structure survey statistics and large amount of single and triaxial stress-strain curve of rock. The achievement of the theory is applied to structure optimization and environmental impact assessment of Badaling Underground Project, and this article considers the Jianfengding tunnel on the Wuhan-Guangzhou high-speed railway when electricity pylons are present on the ground surface. The abstract of new research methods and research results are as follows:
Characteristics of the residual strength of rock mass
The residual strength of rock mass and the mechanical response of rock mass after peak strength are undoubtedly significant in tunnel and underground construction. This paper, from the following3aspects, conducts a study of residual strengthof rock mass:(1) the deformation and damage features of rock mass under uniaxial condition,(2) the residual strength of rock mass under tri-axial condition and (3) the numerical simulation of layered rock mass strength especially the influence of dip angle to the rock mass strength under uniaxial and tri-axial condition.
Study on modified damage statistical constitutive model considering residual strength
The increase amplitude of residual strength of rock is larger than the rock peak intensity of rock with the increase of confining pressure. Gradually, residual strength becomes the main factor of complete stress-strain curve of rock at the stage after peak intensity. Therefore, it's necessary to consider the residual strength to modify the damage statistical constitutive model for Rock. Based on the strain strength theory and hypothesis of rock particles intensity obeying Weibull random distribution, a damage statistical constitutive model for rock under triaxial compression, which can describe the characteristics of rock post-peak softening, is established by adopting Hoek-Brown criterion and considering the residual strength to modify the damage parameter in this thesis. Then, all these model parameters analytic solutions are deduced according to the geometric features of rock complete stress-strain curve. On the basis of experimental results of granite specimens, the influences of Weibull distribution parameters on the rock damage constitutive model are studied. At the same time, the value of modified coefficient and the damage process of rock are discussed. Finally, the achieved theoretical curves by the damage model of rock under different confining pressure are comparatively analyzed with the conventional triaxial compression test results of four kinds of rock:porphyaceous adamellite, fine-particle marble, sandstone and silty mudstone.
Fuzzy-synthetical evaluation on the system of geological strength index
When evaluating geologic intensity index, there are great randomness and fuzziness to confirm the value of its basic elements. As a consequence, it is difficult to accurately measure the impact of each influential factor. The fuzziness of the parameters of rock mass characteristics reflects its inherent uncertainty and the fuzzy mathematics theory provides strong measures to depict these characteristics. This article introduces the number of joint sets(Jn), joint spacing(l) and the integrity coefficient of rock mass(Kr) to describe the structure features of rock mass and introduces large-scale waviness(Jw), small-scale smoothness(Js) and Joint altered coefficient(Ja) to describe the conditions of structural planes. Then multifactor fuzzy-synthetical evaluation is applied to the system of geological strength index, meanwhile, analytic hierarchy process is adopted in determining the weight of each factor. As a result, the model of fuzzy-synthetical evaluation on the system of geological strength index is established. Practical project applications prove that this evaluation method has strong pertinence and high accuracy and it can organically combine geological surveys, experiment datum, statistics and expert opinions, so this evaluation method can decrease the subjectivity of researchers' decisions. The method of fuzzy-synthetical evaluation on the system of geological strength index does provide a new approach to quantizing GSI system.
Study on the seepage-stress coupling damage behavior of rock
Based on some reasonable assumption, the seepage field and stress field equations have been derived through continuity equation, momentum conservation equation, rock statistical damage amending equation and some substantial equations. Then the seepage stress coupling damage behavior model is established in saturation state. According to some initial and boundary conditions of tunnel surrounding rock, the finite difference method is explored in seepage-stress coupling damage behavior model.
Engineering applications
In order to access the environmental effects of the Badaling underground station project, numerical analysis for the stability of surrounding rock was done with fast Lagrangian analysis of continua in three-dimension(FLAC3D). Multiple factors were considered including surrounding rock classes, tunnel depths, groundwater tables, construction methods and initial supporting systems. The models are divided into four classes:the exclusion of underground water model, model with underground water seepage flow, model without underground water seepage flow, and a coupling analysis model with grouting reinforcement. According to the results of the displacement of rock mass, the pore pressure distribution and water gushing capacity, the significance, spatial distribution and long-term effects of environmental effects were discussed and the degree of influence were studied as well. The achieved results are successfully applied to the guidance of the tunnel construction for waterproofing of underground station. Furthermore, the study results can provide a theoretical basis for the design of tunnel and underground works in aquifer strata.
The strata deformation of large section water-abundant soft rock shallow-buried tunnel under unsymmetrical pressure passing through existing structures would be effected by several factors. This article considers the Jianfengding tunnel on the Wuhan-Guangzhou high-speed railway when electricity pylons are present on the ground surface. First, the article describes the engineering measures needed as in-situ measured data to control large strata deformation. Second, statistical and theoretical analyses comprehensively studies the relationship between strata deformation and the impact of the existing building as affected by terrain condition, attitude of stratum, tunnelling construction, tunnel cross-hole construction, ground load, and ground collapse. Third, quantitative analysis is performed on strata deformation brought about by several critical factors and based on coupled fluid-mechanical numerical computation.
1、岩体残余强度特征研究
在隧道及地下工程中,研究岩体残余强度及峰后力学性质对工程设计有着非常重要的意义。本文通过以下四个方面对岩体残余强度特征展开研究：(1)岩石在单轴压缩条件下的变形及损伤特征分析；(2)常规三轴压缩试验下岩石的残余强度特征分析；(3)进行单层节理岩体力学特性数值试验研究,重点分析单轴和三轴压缩条件不同结构面倾角的单层节理岩体的强度特征。
2、基于残余强度修正的岩石损伤本构模型
岩石随着围压的增大,残余强度的增加幅度比峰值强度大,残余强度逐渐成为影响岩石全应力-应变曲线峰后段的主要因素,因此,在建立岩石损伤软化统计本构模型时考虑残余强度进行修正是非常有必要的。基于岩石应变强度理论以及岩石微元强度服从Weibull随机分布的假设,本文考虑岩石峰后残余强度对损伤变量进行了修正,在微元破坏符合Hoek-Brown屈服准则条件下,建立了能够反映岩石峰后软化特征的三维损伤统计本构模型；然后,依据岩石试验全应力-应变曲线的几何特征,推导出本构模型参数的数学表达式,并基于花岗岩室内试验数据对模型参数进行探讨,研究了Weibull分布参数与本构模型的关系,探讨了损伤修正系数的取值和岩石累积损伤的扩展过程；最后,将本文建立的本构模型理论曲线与四种岩石(斑状二长花岗岩、细晶大理岩、砂岩和粉砂质泥岩)在不同围压下的常规三轴压缩试验曲线进行对比分析,结果证实该模型能很好的描述岩石破裂过程的全应力-应变关系和表征岩石残余强度特征。这对于岩石损伤软化问题以及岩石加固处理措施的研究均具有重要的意义。
3、岩石损伤本构模型参数取值研究
岩石损伤本构模型的参数是根据岩体地质强度指标(GSI)计算取得。评价岩体地质强度指标时,因其基本要素取值过程存在较大的随机性和模糊性,这就很难用静态模式去准确地衡量每个影响因素。岩体特征参量的模糊性反映了其内在的不确定性,模糊数学理论能为更客观的刻画这种特性提供有力的数学手段。本文首先引入岩体节理组数Jn、节理间距l和岩体完整性系数Kv描述岩体结构特征,再引入大比例尺波形系数Jw、小比例尺光滑系数Js和节理蚀变系数Ja描述结构面状态,然后把多因素模糊综合评判理论应用到GSI系统的评价中去,并利用层次分析法确定模糊评判因素的权重,建立了GSI系统的模糊综合评判模型。工程应用表明,这种方法针对性较强、准确度较高,能够将地质调查勘探结果、试验结果、统计数据以及专家意见有机结合起来,从而减小了研究者决策时主观性。GSI系统的模糊综合评判法为GSI系统量化提供了新的途径。
4、考虑损伤的岩体流固耦合模型研究
应用连续性方程、线动量平衡方程、岩石损伤等效弹性模量方程及相应的物性方程,在合理的基本假设基础上,对饱和状态下渗流场和应力场控制方程分别进行了推导,建立了考虑损伤效应的渗流应力耦合模型。在耦合方程组推导过程中,针对岩体损伤效应,考虑了岩体渗流状态的变化及岩石孔隙率、渗透率变化。结合隧道围岩的初始条件及边界条件,研究了考虑损伤效应的渗流应力耦合模型有限差分求解方法,对求解过程进行了程序设计,以FLAC3D有限差分软件为平台,进行了软件二次开发,程序计算过程简洁、便于实现。
5、工程应用研究
以京张城际铁路八达岭超大规模地下车站修建为例,依据工程区水文地质特征、水压致裂原位应力测量结果,利用有限差分软件FLAC3D建立三维渗流-应力耦合模型,并采用四种方案进行数值模拟：全封堵、全排水、非耦合、注浆限排。并结合理论分析,着重研究在饱水状况下八达岭车站修建前后渗流场变化、涌水量、围岩变形和地表沉降等环境影响负效应因子,对因地下车站修建环境影响效应的显著性、空间分布特征和长期效应进行评价。模拟计算结果对于裂隙发育、富水地层地下工程尤其修建于自然风景区大型地下洞室防排水设计和施工具有指导意义。
偏压富水软岩大断面隧道施工引起的地层变形是多方面影响因素叠加的结果。结合武广高铁尖峰顶隧道下穿地表高压输电线塔的工程实践,首先对隧道施工前后地层变形监测和分析提出控制大变形的工程措施,然后采用综合统计和理论分析,研究地形条件、地层产状、隧道和通道施工、地面荷载、地表坍塌造成的地层变形与建筑物位移的关系,最后以流固耦合数值分析为手段对影响地层变形的关键因素作了量化分析。
This paper relies on the proposed Badaling Underground Project of Jingzhang inter-city railway. The content of the paper,which does a thorough research of the rock mass stress field-seepage field coupling theory which considering residual strength and damage, is based on detail rock mass structure survey statistics and large amount of single and triaxial stress-strain curve of rock. The achievement of the theory is applied to structure optimization and environmental impact assessment of Badaling Underground Project, and this article considers the Jianfengding tunnel on the Wuhan-Guangzhou high-speed railway when electricity pylons are present on the ground surface. The abstract of new research methods and research results are as follows:
Characteristics of the residual strength of rock mass
The residual strength of rock mass and the mechanical response of rock mass after peak strength are undoubtedly significant in tunnel and underground construction. This paper, from the following3aspects, conducts a study of residual strengthof rock mass:(1) the deformation and damage features of rock mass under uniaxial condition,(2) the residual strength of rock mass under tri-axial condition and (3) the numerical simulation of layered rock mass strength especially the influence of dip angle to the rock mass strength under uniaxial and tri-axial condition.
Study on modified damage statistical constitutive model considering residual strength
The increase amplitude of residual strength of rock is larger than the rock peak intensity of rock with the increase of confining pressure. Gradually, residual strength becomes the main factor of complete stress-strain curve of rock at the stage after peak intensity. Therefore, it's necessary to consider the residual strength to modify the damage statistical constitutive model for Rock. Based on the strain strength theory and hypothesis of rock particles intensity obeying Weibull random distribution, a damage statistical constitutive model for rock under triaxial compression, which can describe the characteristics of rock post-peak softening, is established by adopting Hoek-Brown criterion and considering the residual strength to modify the damage parameter in this thesis. Then, all these model parameters analytic solutions are deduced according to the geometric features of rock complete stress-strain curve. On the basis of experimental results of granite specimens, the influences of Weibull distribution parameters on the rock damage constitutive model are studied. At the same time, the value of modified coefficient and the damage process of rock are discussed. Finally, the achieved theoretical curves by the damage model of rock under different confining pressure are comparatively analyzed with the conventional triaxial compression test results of four kinds of rock:porphyaceous adamellite, fine-particle marble, sandstone and silty mudstone.
Fuzzy-synthetical evaluation on the system of geological strength index
When evaluating geologic intensity index, there are great randomness and fuzziness to confirm the value of its basic elements. As a consequence, it is difficult to accurately measure the impact of each influential factor. The fuzziness of the parameters of rock mass characteristics reflects its inherent uncertainty and the fuzzy mathematics theory provides strong measures to depict these characteristics. This article introduces the number of joint sets(Jn), joint spacing(l) and the integrity coefficient of rock mass(Kr) to describe the structure features of rock mass and introduces large-scale waviness(Jw), small-scale smoothness(Js) and Joint altered coefficient(Ja) to describe the conditions of structural planes. Then multifactor fuzzy-synthetical evaluation is applied to the system of geological strength index, meanwhile, analytic hierarchy process is adopted in determining the weight of each factor. As a result, the model of fuzzy-synthetical evaluation on the system of geological strength index is established. Practical project applications prove that this evaluation method has strong pertinence and high accuracy and it can organically combine geological surveys, experiment datum, statistics and expert opinions, so this evaluation method can decrease the subjectivity of researchers' decisions. The method of fuzzy-synthetical evaluation on the system of geological strength index does provide a new approach to quantizing GSI system.
Study on the seepage-stress coupling damage behavior of rock
Based on some reasonable assumption, the seepage field and stress field equations have been derived through continuity equation, momentum conservation equation, rock statistical damage amending equation and some substantial equations. Then the seepage stress coupling damage behavior model is established in saturation state. According to some initial and boundary conditions of tunnel surrounding rock, the finite difference method is explored in seepage-stress coupling damage behavior model.
Engineering applications
In order to access the environmental effects of the Badaling underground station project, numerical analysis for the stability of surrounding rock was done with fast Lagrangian analysis of continua in three-dimension(FLAC3D). Multiple factors were considered including surrounding rock classes, tunnel depths, groundwater tables, construction methods and initial supporting systems. The models are divided into four classes:the exclusion of underground water model, model with underground water seepage flow, model without underground water seepage flow, and a coupling analysis model with grouting reinforcement. According to the results of the displacement of rock mass, the pore pressure distribution and water gushing capacity, the significance, spatial distribution and long-term effects of environmental effects were discussed and the degree of influence were studied as well. The achieved results are successfully applied to the guidance of the tunnel construction for waterproofing of underground station. Furthermore, the study results can provide a theoretical basis for the design of tunnel and underground works in aquifer strata.
The strata deformation of large section water-abundant soft rock shallow-buried tunnel under unsymmetrical pressure passing through existing structures would be effected by several factors. This article considers the Jianfengding tunnel on the Wuhan-Guangzhou high-speed railway when electricity pylons are present on the ground surface. First, the article describes the engineering measures needed as in-situ measured data to control large strata deformation. Second, statistical and theoretical analyses comprehensively studies the relationship between strata deformation and the impact of the existing building as affected by terrain condition, attitude of stratum, tunnelling construction, tunnel cross-hole construction, ground load, and ground collapse. Third, quantitative analysis is performed on strata deformation brought about by several critical factors and based on coupled fluid-mechanical numerical computation.
引文
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