孔扩张理论研究及自钻式旁压试验数值分析
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摘要
旁压试验的基本原理是利用旁压仪对钻孔壁施加横向均匀应力,使孔壁土体发生径向变形直至破坏,量测压力和径向变形的关系,或加压使孔壁膨胀至某孔径时做保持试验,观测超孔隙水压力的消散过程,然后可根据试验结果(压力-体积曲线或超孔隙水压力消散曲线)确定土体的物理力学性质、区分土类及确定地基承载力等。其中,自钻式旁压试验(SBPT)因具有扰动小、测试深度大等优点成为确定土性参数有效的原位测试手段之一。在饱和软黏土层中宜采用SBPT,但利用常用的步骤确定的黏土不排水剪切强度及渗透特性参数与其它高质量的试验结果有差别。因此,分析其在确定黏土不排水剪切强度和渗透性参数时可能产生的误差及修正研究是本论文的研究目的之一。大多数旁压试验的分析方法基于柱形孔扩张理论,其中包含材料特性、旁压仪几何特征和排水条件等重要假设。除了对旁压试验机理解释及反分析确定土体特性参数外,孔扩张理论还是许多其它岩土工程问题研究的基础理论。目前利用较符合实际地描述土体的非脆性软化及剪胀,并考虑中主应力影响的模型进行的孔扩张分析尚少。因此,发展和完善孔扩张理论是本论文研究的另一目的。具体地,论文主要研究内容及所取得的研究成果包括以下方面:
1、回顾SBPT在确定土性参数上的应用,讨论了以孔扩张理论为基础确定的土性参数的误差来源,总结了现有的误差分析方法及误差修正。
2、针对中主应力对孔扩张问题的影响,采用SMP破坏准则及非关联流动法则,并结合Bolton简化的应力-剪胀关系及Bolton模型,以反映砂土的剪胀和应变软化特性,运用塑性区离散分析方法,对不同初始状态下典型石英砂(Ottawa砂)中的柱形孔扩张问题进行了分析及数值计算,不仅得到了砂土中柱孔扩张的应力场、应变场、极限扩孔压力、塑性区半径,还可获得塑性区土体的内摩擦角、剪胀角和孔隙比的变化。该数值方法可同时用来分析零和非零初始孔径的柱形孔扩张问题。通过与基于Mohr-Coulomb破坏准则的计算结果比较分析,探讨了孔扩张问题中的中主应力效应,并阐述了砂土的相对密度、初始应力、临界状态摩擦角对塑性区半径比、极限扩孔压力、剪胀等的影响。比较结果表明基于Mohr-Coulomb破坏准则的解答偏于保守。绘制了一系列不同初始状态和临界状态内摩擦角时Ottawa砂的孔扩张结果图,为确定具有相似性质的砂土中柱孔扩张的极限扩孔压力和塑性区半径提供直接的参考。
3、针对非脆性软化及剪胀的摩擦黏性岩土材料中的柱形孔扩张问题,将土体损伤后的软化特性用材料的力学性能参数下降来描述,引入损伤软化参数。考虑土体的剪胀与内摩擦角、黏聚力以及平均有效应力的相关性和结构性衰减(软化特性)对应力-剪胀关系的影响,将反映结构性衰减的黏聚力下降公式代入Rowe(1971)的应力-剪胀方程,修改了Rowe(1971)的应力-剪胀关系。在塑性区采用对数应变描述土体的大应变特性,在弹性区采用小应变理论,同时使用广义SMP准则和修改的应力-剪胀关系,结合平面应变轴对称问题的控制方程,推导并给出完全排水条件下摩擦黏性岩土材料中的柱形孔扩张问题的求解步骤,得到柱形孔扩张的孔扩张率、塑性流动参数(剪胀)、极限扩孔压力、塑性区变化规律等。进一步,通过损伤软化参数、内摩擦角和黏聚力的变参数计算,探讨了它们对土体剪胀性、塑性区应力、塑性区变化规律及极限扩孔压力的影响;并与基于Mohr-Coulomb准则的解答进行对比分析,研究了中主应力对孔扩张结果的影响。
4、利用通用有限元分析软件ABAQUS模拟黏土中不排水条件下的自钻式旁压加载试验,针对旁压仪探头长径比及应变区间的选择对确定土体不排水剪切强度的影响进行了分析。使用修正剑桥模型模拟土体应力-应变特性,采用低渗透系数控制加载过程中的不排水条件,通过数值计算确定不同长径比、不同应力历史下的旁压加载曲线。根据Gibson等建议的方法,选择几个应变区间,用最小二乘法确定该区间曲线的斜率,该斜率为不排水剪切强度值。当只考虑长径比对确定不排水剪切强度的影响时,以从L/D=∞的旁压曲线确定的不排水剪切强度作为真实值S_u~∞,不同应力历史(OCR)下土体的不排水剪切强度真实值与不同长径比时确定的不排水剪切强度的比值S_u~∞/S_u~(L/D)作为考虑L/D影响的修正系数。通过OCR在1～20,L/D在6～∞范围内的计算,确定了从正常固结到重超固结土体,5种长径比时不排水剪切强度修正系数。应变区间对修正系数有一定影响,对于同一旁压曲线,选择的应变区间越大,修正系数会有所减小,不排水剪切强度的高估量增加。而应变区间的选择对确定不排水剪切强度值的影响显著,随着应变区间的增大,不排水剪切强度明显增加。因此,选择合适的应变区间对测定较准确的不排水剪切强度值至关重要。通过将从有限元模拟的平面应变和不排水条件下的旁压加载曲线确定的不排水剪切强度和Cao等解析解比较,建议了不同应力历史下确定不排水剪切强度的应变区间。
5、以Ducker-Prager理想弹塑性模型为基础,模拟了旁压应变保持试验(SHT),分析旁压仪几何尺寸、加载应变水平、渗透系数、应变加载率对孔扩张过程中排水情况、超孔隙水压力分布及土体固结行为的影响,建议了应变加载率,给出了Randolph解的适用条件,并考虑不同渗透系数、不同应变加载率引起的部分排水的影响,对Randolph解进行修正,建议了误差曲线。为分析土体流变性对SHT过程中超孔隙水压力消散及推求土体固结系数的影响,采用Drucker-Prager理想弹塑性与土体流变的耦合模型描述土体的应力应变强度关系及其对时间的依赖性,利用有限元法模拟SHT过程,分析土体流变性对超孔隙水压力消散的影响。其中,流变时间硬化模型参数由土体流变试验确定。分析发现,土体的流变对超孔隙水压力消散的影响,除了通过应力松弛改变应力水平而使超孔隙水压力下降,还通过改变超孔隙水压力的分布而改变固结速度。考虑流变使不同渗透系数时超孔隙水压力消散过程差异变大。渗透系数越小,土体流变性对超孔隙水压力的消散速度影响越明显。以s_u=48kPa,I_r=156为例,在流变试验确定的参数变化范围内进行变参数计算,分析流变参数变化对超孔隙水压力消散的影响。
Self-boring pressuremeter(SBPT) has been effectively utilized to determine in-situ properties of soils in terms of overcoming soil disturbance to a large extent,especially in saturated soft soil for determination of permeability characteristics and undrained shear strength.However,it is recognized that the undrained strength value and horizontal coefficient of consolidation derived from SBPT are different from those obtained by good laboratory tests and other in situ tests.In order to find the reasons of inaccuracy,the possible factors are analyzed by using finite element methods and quantified by comparing with analytical solutions of cylindrical cavity expansion that are useful interpretation methods which involves important assumptions about material behavior,pressuremeter geometry and drained conditions.Many other geotechnical engineering problems also rely on cavity expansion theory for analyzing,such as pile driving,CPT and anchor working mechanics. And the theory has been progressively refined over the past years.Many research results indicate that it is important for study on cavity expansion theory to choose the reasonable yield criterion and to consider the strain-softening and shear dilatation behavior of geomaterials.Though achievements have been made on the theoretical study,the cavity expansion in non-brittle softening and dilatant soil is in the stage of development.Thus the other purpose of this paper is to present cylindrical cavity expansion analysis in dilatant and elastic-plastic soil,taking non-brittle softening and dilatancy behavior of geomaterials,and the effect of intermediate principle stress on soil strength into account.The main investigations consist of the following portions:
1,The current use of fundamental mechanics in developing rational interpretation methods for deriving soil properties from SBPT is reviewed,and the sources of inaccuracy and modified methods are analyzed and summarized.
2,Considering the effects of intermediate principal stress on material yielding strength, SMP yielding criterion is selected in analysis of cylindrical cavity expansion.Meanwhile, combining Bolton's simplification on the stress-dilatancy relationship and Bolton model to reflect soil shear dilatancy and strain softening behavior this paper analyzes the problem of cylindrical cavity expansion in typical quartz sand(Ottawa sand) by discretizing the plastic zone to determine stress field,strain field,limit cavity pressure,and variation of friction angle, dilatancy angle and void ratio.It is noted that this analysis is applicable to cavity expansions from zero initial radius and finite initial radius simultaneously.The impacts of intermediate principal stress on cavity expansion are examined by comparing the present solutions with results based on Mohr-Coulomb criterion.And the effects of initial state and critical friction angle on ratio of plastic radius,limit pressure,dilatancy etc.are explored.A set of charts have been provided for use in direct estimate of limit pressure and ratio of plastic to cavity radius as a function of soil state(relative density and initial stress state) for soils with the similar properties to Ottawa sands.
3、The extended spatial mobilization plane theory(SMP) is adopted in consideration of the effect of intermediate principal stress on soil shear strength.Damage softening parameter, taken as degradation grads of material mechanics capacity,is introduced to depict the soils softening behavior after yielding.Rowe's Stress-dilatancy equation in combination with cohesion degradation expression by damage softening parameter is rewritten.It can simultaneously consider the bonding component in dilatant response of elastic-plastic soils and softening behavior due to structure degradation for cemented soils during cavity expansion.The cavity expansion problem is formulated in small strain in the elastic zone and large strain in the plastic zone.Based on the extended SMP criterion and stress-dilatancy relation,the governing equations of axisymmetric problem in the plane strain condition and the partial differential equations for the boundary-value problem of cavity expansion in frictional cohesive soils are established.Solutions of radial and hoop stresses and strains around an expanding cavity are obtained by recursive computations.The significance of consideration of the effect of intermediate principal stress is demonstrated by a comparative study between the present solution and current solution based on Mohr-Coulomb criterion. Also the influence of damage softening parameter,cohesion and friction angle is examined by a parametric study.The proposed solution presented here can be of interest for the interpretation of pressuremeter tests or pushing-in piles carried out in cohesive-frictional materials under drained condition.
4,Numerical simulations of self-boring pressuremeter loading tests using ABAQUS are performed to assess the influence of limit length of SBP and strain range on undrained shear strength derived from pressuremeter curves.The numerical models are built where soils behavior is depicted by modified Cam model,and low coefficients of permeability are chosen to control undrained conditions during expansion.The pressuremeter curves are obtained from numerical simulation of SBPTs for ratio of length to diameter L/D values of 6,10,15, 20 and various overconsolidation OCR range from 1 to 20.According to Gibson's analysis, the undrained shear strength using the least squares method is determined from the several chosen strain ranges.The ratio between the undrained shear strength obtained with infinite L/D and the value with various L/D is defined as correction factor,which are obtained from several strain ranges.It is observed that strain range over which the pressuremeter curve is fitted has little influence on derivation of the correction factors,while it has significant influence on undrained shear strength.And further,strain ranges of deriving undrained shear strength are proposed for different overconsolidation ratio by comparing finite element results for L/D=∞with analytical solution(Cao et al.) based on modified Cam clay model.
5,Based on elastic-perfectly plastic Drucker-Prager model,analysis of holding tests using FEM is carried out to illuminate the applied conditions of commonly used a closed-form solution proposed by Randolph and Wroth through investigating the effects of pressuremeter geometry,the strain rate,permeability coefficient and the cavity strain level on partial drainage during cavity expansion,distribution of excess pore pressure,dissipation of excess pressure during SHT.Moreover,based on the results of numerical analyses,strain rate is proposed and the values of time factor T_(50) provided by Randolph el al.to estimate horizontal consolidation coefficient are modified in view of the effects of soil permeability and strain rate on partial undrained.Since stress relaxation during SHTs exists and significantly influences the decay of excess pore pressure,the value of T_(50) deduced by current solutions that ignore the soil theology can be inaccurate.The numerical analysis is performed considering stress relaxation during SHT based on coupling Drucker-Prager and time hardening theology model,where theology parameters are determined by clay rheological test. It is concluded that consideration of soil theology during SHT can speed the decay of excess pore pressure which is the combined results of the emergence of stress relaxation and changing distribution of excess pore pressure that tends to slow down dissipation.For lower coefficient of permeability,soil theology has more significant impact on decay of excess pore pressure.The influence of soil theology is assessed by computation of theology parameters variation within the range by the clay rheological tests for the case that s_u=48kPa,I_r=156.
1、回顾SBPT在确定土性参数上的应用,讨论了以孔扩张理论为基础确定的土性参数的误差来源,总结了现有的误差分析方法及误差修正。
2、针对中主应力对孔扩张问题的影响,采用SMP破坏准则及非关联流动法则,并结合Bolton简化的应力-剪胀关系及Bolton模型,以反映砂土的剪胀和应变软化特性,运用塑性区离散分析方法,对不同初始状态下典型石英砂(Ottawa砂)中的柱形孔扩张问题进行了分析及数值计算,不仅得到了砂土中柱孔扩张的应力场、应变场、极限扩孔压力、塑性区半径,还可获得塑性区土体的内摩擦角、剪胀角和孔隙比的变化。该数值方法可同时用来分析零和非零初始孔径的柱形孔扩张问题。通过与基于Mohr-Coulomb破坏准则的计算结果比较分析,探讨了孔扩张问题中的中主应力效应,并阐述了砂土的相对密度、初始应力、临界状态摩擦角对塑性区半径比、极限扩孔压力、剪胀等的影响。比较结果表明基于Mohr-Coulomb破坏准则的解答偏于保守。绘制了一系列不同初始状态和临界状态内摩擦角时Ottawa砂的孔扩张结果图,为确定具有相似性质的砂土中柱孔扩张的极限扩孔压力和塑性区半径提供直接的参考。
3、针对非脆性软化及剪胀的摩擦黏性岩土材料中的柱形孔扩张问题,将土体损伤后的软化特性用材料的力学性能参数下降来描述,引入损伤软化参数。考虑土体的剪胀与内摩擦角、黏聚力以及平均有效应力的相关性和结构性衰减(软化特性)对应力-剪胀关系的影响,将反映结构性衰减的黏聚力下降公式代入Rowe(1971)的应力-剪胀方程,修改了Rowe(1971)的应力-剪胀关系。在塑性区采用对数应变描述土体的大应变特性,在弹性区采用小应变理论,同时使用广义SMP准则和修改的应力-剪胀关系,结合平面应变轴对称问题的控制方程,推导并给出完全排水条件下摩擦黏性岩土材料中的柱形孔扩张问题的求解步骤,得到柱形孔扩张的孔扩张率、塑性流动参数(剪胀)、极限扩孔压力、塑性区变化规律等。进一步,通过损伤软化参数、内摩擦角和黏聚力的变参数计算,探讨了它们对土体剪胀性、塑性区应力、塑性区变化规律及极限扩孔压力的影响;并与基于Mohr-Coulomb准则的解答进行对比分析,研究了中主应力对孔扩张结果的影响。
4、利用通用有限元分析软件ABAQUS模拟黏土中不排水条件下的自钻式旁压加载试验,针对旁压仪探头长径比及应变区间的选择对确定土体不排水剪切强度的影响进行了分析。使用修正剑桥模型模拟土体应力-应变特性,采用低渗透系数控制加载过程中的不排水条件,通过数值计算确定不同长径比、不同应力历史下的旁压加载曲线。根据Gibson等建议的方法,选择几个应变区间,用最小二乘法确定该区间曲线的斜率,该斜率为不排水剪切强度值。当只考虑长径比对确定不排水剪切强度的影响时,以从L/D=∞的旁压曲线确定的不排水剪切强度作为真实值S_u~∞,不同应力历史(OCR)下土体的不排水剪切强度真实值与不同长径比时确定的不排水剪切强度的比值S_u~∞/S_u~(L/D)作为考虑L/D影响的修正系数。通过OCR在1～20,L/D在6～∞范围内的计算,确定了从正常固结到重超固结土体,5种长径比时不排水剪切强度修正系数。应变区间对修正系数有一定影响,对于同一旁压曲线,选择的应变区间越大,修正系数会有所减小,不排水剪切强度的高估量增加。而应变区间的选择对确定不排水剪切强度值的影响显著,随着应变区间的增大,不排水剪切强度明显增加。因此,选择合适的应变区间对测定较准确的不排水剪切强度值至关重要。通过将从有限元模拟的平面应变和不排水条件下的旁压加载曲线确定的不排水剪切强度和Cao等解析解比较,建议了不同应力历史下确定不排水剪切强度的应变区间。
5、以Ducker-Prager理想弹塑性模型为基础,模拟了旁压应变保持试验(SHT),分析旁压仪几何尺寸、加载应变水平、渗透系数、应变加载率对孔扩张过程中排水情况、超孔隙水压力分布及土体固结行为的影响,建议了应变加载率,给出了Randolph解的适用条件,并考虑不同渗透系数、不同应变加载率引起的部分排水的影响,对Randolph解进行修正,建议了误差曲线。为分析土体流变性对SHT过程中超孔隙水压力消散及推求土体固结系数的影响,采用Drucker-Prager理想弹塑性与土体流变的耦合模型描述土体的应力应变强度关系及其对时间的依赖性,利用有限元法模拟SHT过程,分析土体流变性对超孔隙水压力消散的影响。其中,流变时间硬化模型参数由土体流变试验确定。分析发现,土体的流变对超孔隙水压力消散的影响,除了通过应力松弛改变应力水平而使超孔隙水压力下降,还通过改变超孔隙水压力的分布而改变固结速度。考虑流变使不同渗透系数时超孔隙水压力消散过程差异变大。渗透系数越小,土体流变性对超孔隙水压力的消散速度影响越明显。以s_u=48kPa,I_r=156为例,在流变试验确定的参数变化范围内进行变参数计算,分析流变参数变化对超孔隙水压力消散的影响。
Self-boring pressuremeter(SBPT) has been effectively utilized to determine in-situ properties of soils in terms of overcoming soil disturbance to a large extent,especially in saturated soft soil for determination of permeability characteristics and undrained shear strength.However,it is recognized that the undrained strength value and horizontal coefficient of consolidation derived from SBPT are different from those obtained by good laboratory tests and other in situ tests.In order to find the reasons of inaccuracy,the possible factors are analyzed by using finite element methods and quantified by comparing with analytical solutions of cylindrical cavity expansion that are useful interpretation methods which involves important assumptions about material behavior,pressuremeter geometry and drained conditions.Many other geotechnical engineering problems also rely on cavity expansion theory for analyzing,such as pile driving,CPT and anchor working mechanics. And the theory has been progressively refined over the past years.Many research results indicate that it is important for study on cavity expansion theory to choose the reasonable yield criterion and to consider the strain-softening and shear dilatation behavior of geomaterials.Though achievements have been made on the theoretical study,the cavity expansion in non-brittle softening and dilatant soil is in the stage of development.Thus the other purpose of this paper is to present cylindrical cavity expansion analysis in dilatant and elastic-plastic soil,taking non-brittle softening and dilatancy behavior of geomaterials,and the effect of intermediate principle stress on soil strength into account.The main investigations consist of the following portions:
1,The current use of fundamental mechanics in developing rational interpretation methods for deriving soil properties from SBPT is reviewed,and the sources of inaccuracy and modified methods are analyzed and summarized.
2,Considering the effects of intermediate principal stress on material yielding strength, SMP yielding criterion is selected in analysis of cylindrical cavity expansion.Meanwhile, combining Bolton's simplification on the stress-dilatancy relationship and Bolton model to reflect soil shear dilatancy and strain softening behavior this paper analyzes the problem of cylindrical cavity expansion in typical quartz sand(Ottawa sand) by discretizing the plastic zone to determine stress field,strain field,limit cavity pressure,and variation of friction angle, dilatancy angle and void ratio.It is noted that this analysis is applicable to cavity expansions from zero initial radius and finite initial radius simultaneously.The impacts of intermediate principal stress on cavity expansion are examined by comparing the present solutions with results based on Mohr-Coulomb criterion.And the effects of initial state and critical friction angle on ratio of plastic radius,limit pressure,dilatancy etc.are explored.A set of charts have been provided for use in direct estimate of limit pressure and ratio of plastic to cavity radius as a function of soil state(relative density and initial stress state) for soils with the similar properties to Ottawa sands.
3、The extended spatial mobilization plane theory(SMP) is adopted in consideration of the effect of intermediate principal stress on soil shear strength.Damage softening parameter, taken as degradation grads of material mechanics capacity,is introduced to depict the soils softening behavior after yielding.Rowe's Stress-dilatancy equation in combination with cohesion degradation expression by damage softening parameter is rewritten.It can simultaneously consider the bonding component in dilatant response of elastic-plastic soils and softening behavior due to structure degradation for cemented soils during cavity expansion.The cavity expansion problem is formulated in small strain in the elastic zone and large strain in the plastic zone.Based on the extended SMP criterion and stress-dilatancy relation,the governing equations of axisymmetric problem in the plane strain condition and the partial differential equations for the boundary-value problem of cavity expansion in frictional cohesive soils are established.Solutions of radial and hoop stresses and strains around an expanding cavity are obtained by recursive computations.The significance of consideration of the effect of intermediate principal stress is demonstrated by a comparative study between the present solution and current solution based on Mohr-Coulomb criterion. Also the influence of damage softening parameter,cohesion and friction angle is examined by a parametric study.The proposed solution presented here can be of interest for the interpretation of pressuremeter tests or pushing-in piles carried out in cohesive-frictional materials under drained condition.
4,Numerical simulations of self-boring pressuremeter loading tests using ABAQUS are performed to assess the influence of limit length of SBP and strain range on undrained shear strength derived from pressuremeter curves.The numerical models are built where soils behavior is depicted by modified Cam model,and low coefficients of permeability are chosen to control undrained conditions during expansion.The pressuremeter curves are obtained from numerical simulation of SBPTs for ratio of length to diameter L/D values of 6,10,15, 20 and various overconsolidation OCR range from 1 to 20.According to Gibson's analysis, the undrained shear strength using the least squares method is determined from the several chosen strain ranges.The ratio between the undrained shear strength obtained with infinite L/D and the value with various L/D is defined as correction factor,which are obtained from several strain ranges.It is observed that strain range over which the pressuremeter curve is fitted has little influence on derivation of the correction factors,while it has significant influence on undrained shear strength.And further,strain ranges of deriving undrained shear strength are proposed for different overconsolidation ratio by comparing finite element results for L/D=∞with analytical solution(Cao et al.) based on modified Cam clay model.
5,Based on elastic-perfectly plastic Drucker-Prager model,analysis of holding tests using FEM is carried out to illuminate the applied conditions of commonly used a closed-form solution proposed by Randolph and Wroth through investigating the effects of pressuremeter geometry,the strain rate,permeability coefficient and the cavity strain level on partial drainage during cavity expansion,distribution of excess pore pressure,dissipation of excess pressure during SHT.Moreover,based on the results of numerical analyses,strain rate is proposed and the values of time factor T_(50) provided by Randolph el al.to estimate horizontal consolidation coefficient are modified in view of the effects of soil permeability and strain rate on partial undrained.Since stress relaxation during SHTs exists and significantly influences the decay of excess pore pressure,the value of T_(50) deduced by current solutions that ignore the soil theology can be inaccurate.The numerical analysis is performed considering stress relaxation during SHT based on coupling Drucker-Prager and time hardening theology model,where theology parameters are determined by clay rheological test. It is concluded that consideration of soil theology during SHT can speed the decay of excess pore pressure which is the combined results of the emergence of stress relaxation and changing distribution of excess pore pressure that tends to slow down dissipation.For lower coefficient of permeability,soil theology has more significant impact on decay of excess pore pressure.The influence of soil theology is assessed by computation of theology parameters variation within the range by the clay rheological tests for the case that s_u=48kPa,I_r=156.
引文
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