砂土液化及其判别的微观机理研究
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摘要
砂土液化是土动力学与岩土地震工程研究的重要课题。传统的基于细观材料尺度的研究通常将砂土等岩土颗粒材料视为连续介质,而忽视了其为离散的本质。事实上,液化过程是颗粒与孔隙水复杂相互作用的结果,将岩土颗粒材料的微观结构纳入液化过程的模拟,从微观颗粒尺度揭示砂土液化本质机理已成为是研究的必然趋势。本文在总结国内外颗粒材料微细观力学研究的基础上,针对颗粒微观参数确定、临界状态表征、剪切波速测试、液化机理、抗液化评价等问题,利用颗粒离散单元法(PFC3D)对饱和砂土液化及其判别问题进行了研究,取得如下研究成果：
(1)通过对颗粒材料微细观参数的量纲分析和大量排水条件三轴压缩试验离散元模拟结果的回归整理,分别基于线性接触模型和Hertz模型建立了的颗粒材料微细观参数相关关系。研究表明,Hertz模型能很好地克服了线性接触模型所不能描述颗粒材料应力相关特性的缺点,其初始杨氏模量约与有效围压的1/3方成正比；
(2)开展排水与不排水条件下三轴试验的离散元模拟,通过对颗粒材料在剪切过程中各微观结构量及强弱力对应力比贡献等演化过程的分析,从微观颗粒尺度揭示了临界状态的微观机理。针对不同应力路径、初始组构的分析验证了临界状态的唯一性,给出了基于配位数、接触力等的临界状态微观表征,并建立了基于力学配位数表征的临界状态线。
(3)以颗粒试样内部的颗粒群为激发源和接收源,提出了颗粒离散元模拟中剪切波速的剪切振动和扭转振动测试方法,确定了合理的参数取值范围,并得到了规则排列、随机排列颗粒试样的解析解与均质化理论结果的验证。以剪切振动方法为例,激发频率的选取应保证传播距离与波长之比大于等于2,激发幅值则应以避免摩擦功的产生为宜。
(4)利用剪切振动的剪切波速测试方法,开展不排水条件下等应变幅循环动三轴试验过程中剪切波速的数值测试,通过对比相同有效平均正应力下循环振动前、后的剪切波速,发现了循环应力历史引起小应变剪切模量的衰减和各向异性现象,并从力学配位数、接触刚度等微观颗粒尺度揭示了循环应力历史对小应变剪切模量衰减和各向异性影响的微观机理。
(5)通过开展松散颗粒试样不排水条件下三轴压缩试验的颗粒离散元模拟,分析了剪切过程中颗粒材料的微观结构演化过程,揭示了静态液化时平均法向接触力为零、力学配位数为4的微观机理。针对循环动力液化发生时,其力学配位数下降至4.2,平均法向接触力趋于零点,接触法向、法向接触力、切向接触力和接触滑移都出现显著增长。
(6)通过开展不同初始组构颗粒试样的不排水条件下三轴压缩试验的颗粒离散元模拟,指出初始组构对颗粒材料的力学与变形特性、静态液化等的影响显著。相同初始孔隙比、不同初始组构的颗粒试样沿着不同的应力路径发展,其微观结构可能在相变状态处产生急剧变化。
(7)基于对大量等应力幅循环动三轴试样的模拟和剪切波速测试,分析了颗粒微观参数对颗粒材料抗液化强度、剪切波速、状态参量等的影响,建立了基于微观颗粒尺度的颗粒材料抗液化强度与剪切波速相关关系,并得到了离心机试验结果的验证。对于常见的砂土,其CRR-Vsl经验关系的指数约为5。在此基础上,进一步提出了抗液化强度与状态参量间的相关关系。
Granular materials, which are composed of grains and quite common in nature, are generally treated as continuum in classical framework of geomechanics. However, the static and dynamic behaviors are very complicated due to the complex interactions between particle and particle, particle and its surrounding liquid and/or gas. So even the fundamental mechanisms of some basic and important phenomenon, such as sand liquefaction induced by earchquake, has not been well established. With the recognition that granular material is discrete in nature, rather than continuous, the basic understanding can only be obtained from the particle scale. The complexity in granular materials behavior lies in the fact that the meso-scopic behavior of granular material is determined by not only the interactions operating at contacts, but also how the particles become arranged in space to form an internal structure. This research is aimed to microscopically investigate the mechanism of sand liquefaction and its evaluation, as well as the fundamental mechanism about the critical state. Research results obtained are as follows
(1) For Discrete Element Method (DEM), the key to a successful simulation lies in proper micro-parameters. However, the current way of selecting micro-parameters is often accused of being subjective, unreliable and rendering different simulations incomparable. Controlling criterions on particle number and static loading for both Linear Contact Model and Hertz Model are proposed based on the dimensional analysis. A set of empirical formulas are presented to describe the correlation between macroscopic elastic constants of granular materials and microscopic elastic constants of particles by simulating tri-axial tests with PFC3D and through regression analysis of numerical results. It is found that the Linear Contact Model failed to catch the stress-dependent behavior of granular materials, while Hertz Model can well compensate this defect, e.g. the initial Young's modulus approximately proportional to one third of the confining pressure.
(2) Conventional triaxial tests under both drained and undrained conditions are implemented in DEM simulation. The evolutions of micro-structure of granular materials, including mechanical coordination, anisotropy of fabric, normal contact force, tangential contact force, as well as the different contributions of strong force and weak force to stress ratio are carefully analyzed. The micromechanism of critical state is deposed based on the previous analysis. The uniqueness of the critical state line is verified by performing triaxial tests under different effective stress paths and initial fabrics. A new critical state line is proposed on the basis of mechanical coordination number.
(3) Numerical simulation of shear wave propagation using DEM is implemented by applying a velocity pulse to the transmitter in a certain direction and monitoring the corresponding average velocity of the receiver. The cross-correlation analysis is adopted due to its superiority of both determining the travel time and indentifying similarities between two signals. The shear wave velocity is calculated using the wave travel time and the distance of the travel path, in exactly the same way as in laboratory tests. The influencing factors including excitation frequency, excitation amplitude, size of transmitter and receiver as well as damp are carefully analyzed and reasonable values of the parameters for shear wave modeling are proposed. It is found that the appropriate excitation amplitude should be chosen on the basis of avoiding the generation of frictional work. It is also indicated that fruitful results would be obtained if both the radius of transmitter and receiver are chosen as one half of that of DEM specimen's. The research results are verified through outcomes of even-particle assemblies.
(4) A micromechanical study on the influence of cyclic loading history is attempted by conducting a series of undrained cyclic triaxial tests using Discrete Element Method (DEM). With the implementation of shear wave modeling, the value of small strain shear modulus Gmax of granular soils under the influences of cyclic loading history was investigated by measuring the shear wave velocity at a number of certain effective stresses, and that of Gmax without such effects was examined for comparison. Variations of coordination number, fabric, contact forces as well as contact stiffness are carefully examined to interpret the microscopic mechanism of both reduction and anisotropy of small-strain shear-modulus induced by the effects of cyclic loading.
(5) Static liquefaction on very loose granular materials under undrained condition is simulated in DEM. The micromechanism of this special phenomenon is proclaimed by analyzing the evolution of micro-structures, including mean normal contact force, mechanical coordination number, percentage of rattlers, sliding fraction, anisotropy of contact normal, normal contact force as well as tangential contact force. It shows that the mechanical coordination number will reduce to4or even lower when static liquefaction happens. It seems that the mechanical coordination number will gain very similar situation for cyclic-induced liquefaction.
(6) The influence of initial fabric on the behavior of granular material is revealed by conducting numbers of triaxial tests under undrained condition. In order to create different initial soil fabrics, specimens are subjected to undrained preshearing after isotropically consolidating, and then isotropically reconsolidating back to the initial confining pressure. It is indicated that, specimens with the same initial void ratio but different initial fabrics may follow quite different effective stress paths, and may even induce sharp changes of fabric during phase transformation.
(7) The influences of micro-parameters on Cyclic Resistance Ratio (CRR), shear wave velocity, state parameter are detailedly discussed based on a number of dynamic triaxial tests under undrained condition during constant stress amplitude, as well as the measurement of shear wave velocity. Correlation between cyclic resistance ratio and shear wave velocity of granular materials are estabilished based on paticle-scale analysis, are verified by liquefaction and non-liquefaction data from centrifuge tests. It is indicated that the index number in CRR-Vsl correlation is about5for normal sand. The correlation between cyclic resistance ratio and state parameter is further raised.
(1)通过对颗粒材料微细观参数的量纲分析和大量排水条件三轴压缩试验离散元模拟结果的回归整理,分别基于线性接触模型和Hertz模型建立了的颗粒材料微细观参数相关关系。研究表明,Hertz模型能很好地克服了线性接触模型所不能描述颗粒材料应力相关特性的缺点,其初始杨氏模量约与有效围压的1/3方成正比；
(2)开展排水与不排水条件下三轴试验的离散元模拟,通过对颗粒材料在剪切过程中各微观结构量及强弱力对应力比贡献等演化过程的分析,从微观颗粒尺度揭示了临界状态的微观机理。针对不同应力路径、初始组构的分析验证了临界状态的唯一性,给出了基于配位数、接触力等的临界状态微观表征,并建立了基于力学配位数表征的临界状态线。
(3)以颗粒试样内部的颗粒群为激发源和接收源,提出了颗粒离散元模拟中剪切波速的剪切振动和扭转振动测试方法,确定了合理的参数取值范围,并得到了规则排列、随机排列颗粒试样的解析解与均质化理论结果的验证。以剪切振动方法为例,激发频率的选取应保证传播距离与波长之比大于等于2,激发幅值则应以避免摩擦功的产生为宜。
(4)利用剪切振动的剪切波速测试方法,开展不排水条件下等应变幅循环动三轴试验过程中剪切波速的数值测试,通过对比相同有效平均正应力下循环振动前、后的剪切波速,发现了循环应力历史引起小应变剪切模量的衰减和各向异性现象,并从力学配位数、接触刚度等微观颗粒尺度揭示了循环应力历史对小应变剪切模量衰减和各向异性影响的微观机理。
(5)通过开展松散颗粒试样不排水条件下三轴压缩试验的颗粒离散元模拟,分析了剪切过程中颗粒材料的微观结构演化过程,揭示了静态液化时平均法向接触力为零、力学配位数为4的微观机理。针对循环动力液化发生时,其力学配位数下降至4.2,平均法向接触力趋于零点,接触法向、法向接触力、切向接触力和接触滑移都出现显著增长。
(6)通过开展不同初始组构颗粒试样的不排水条件下三轴压缩试验的颗粒离散元模拟,指出初始组构对颗粒材料的力学与变形特性、静态液化等的影响显著。相同初始孔隙比、不同初始组构的颗粒试样沿着不同的应力路径发展,其微观结构可能在相变状态处产生急剧变化。
(7)基于对大量等应力幅循环动三轴试样的模拟和剪切波速测试,分析了颗粒微观参数对颗粒材料抗液化强度、剪切波速、状态参量等的影响,建立了基于微观颗粒尺度的颗粒材料抗液化强度与剪切波速相关关系,并得到了离心机试验结果的验证。对于常见的砂土,其CRR-Vsl经验关系的指数约为5。在此基础上,进一步提出了抗液化强度与状态参量间的相关关系。
Granular materials, which are composed of grains and quite common in nature, are generally treated as continuum in classical framework of geomechanics. However, the static and dynamic behaviors are very complicated due to the complex interactions between particle and particle, particle and its surrounding liquid and/or gas. So even the fundamental mechanisms of some basic and important phenomenon, such as sand liquefaction induced by earchquake, has not been well established. With the recognition that granular material is discrete in nature, rather than continuous, the basic understanding can only be obtained from the particle scale. The complexity in granular materials behavior lies in the fact that the meso-scopic behavior of granular material is determined by not only the interactions operating at contacts, but also how the particles become arranged in space to form an internal structure. This research is aimed to microscopically investigate the mechanism of sand liquefaction and its evaluation, as well as the fundamental mechanism about the critical state. Research results obtained are as follows
(1) For Discrete Element Method (DEM), the key to a successful simulation lies in proper micro-parameters. However, the current way of selecting micro-parameters is often accused of being subjective, unreliable and rendering different simulations incomparable. Controlling criterions on particle number and static loading for both Linear Contact Model and Hertz Model are proposed based on the dimensional analysis. A set of empirical formulas are presented to describe the correlation between macroscopic elastic constants of granular materials and microscopic elastic constants of particles by simulating tri-axial tests with PFC3D and through regression analysis of numerical results. It is found that the Linear Contact Model failed to catch the stress-dependent behavior of granular materials, while Hertz Model can well compensate this defect, e.g. the initial Young's modulus approximately proportional to one third of the confining pressure.
(2) Conventional triaxial tests under both drained and undrained conditions are implemented in DEM simulation. The evolutions of micro-structure of granular materials, including mechanical coordination, anisotropy of fabric, normal contact force, tangential contact force, as well as the different contributions of strong force and weak force to stress ratio are carefully analyzed. The micromechanism of critical state is deposed based on the previous analysis. The uniqueness of the critical state line is verified by performing triaxial tests under different effective stress paths and initial fabrics. A new critical state line is proposed on the basis of mechanical coordination number.
(3) Numerical simulation of shear wave propagation using DEM is implemented by applying a velocity pulse to the transmitter in a certain direction and monitoring the corresponding average velocity of the receiver. The cross-correlation analysis is adopted due to its superiority of both determining the travel time and indentifying similarities between two signals. The shear wave velocity is calculated using the wave travel time and the distance of the travel path, in exactly the same way as in laboratory tests. The influencing factors including excitation frequency, excitation amplitude, size of transmitter and receiver as well as damp are carefully analyzed and reasonable values of the parameters for shear wave modeling are proposed. It is found that the appropriate excitation amplitude should be chosen on the basis of avoiding the generation of frictional work. It is also indicated that fruitful results would be obtained if both the radius of transmitter and receiver are chosen as one half of that of DEM specimen's. The research results are verified through outcomes of even-particle assemblies.
(4) A micromechanical study on the influence of cyclic loading history is attempted by conducting a series of undrained cyclic triaxial tests using Discrete Element Method (DEM). With the implementation of shear wave modeling, the value of small strain shear modulus Gmax of granular soils under the influences of cyclic loading history was investigated by measuring the shear wave velocity at a number of certain effective stresses, and that of Gmax without such effects was examined for comparison. Variations of coordination number, fabric, contact forces as well as contact stiffness are carefully examined to interpret the microscopic mechanism of both reduction and anisotropy of small-strain shear-modulus induced by the effects of cyclic loading.
(5) Static liquefaction on very loose granular materials under undrained condition is simulated in DEM. The micromechanism of this special phenomenon is proclaimed by analyzing the evolution of micro-structures, including mean normal contact force, mechanical coordination number, percentage of rattlers, sliding fraction, anisotropy of contact normal, normal contact force as well as tangential contact force. It shows that the mechanical coordination number will reduce to4or even lower when static liquefaction happens. It seems that the mechanical coordination number will gain very similar situation for cyclic-induced liquefaction.
(6) The influence of initial fabric on the behavior of granular material is revealed by conducting numbers of triaxial tests under undrained condition. In order to create different initial soil fabrics, specimens are subjected to undrained preshearing after isotropically consolidating, and then isotropically reconsolidating back to the initial confining pressure. It is indicated that, specimens with the same initial void ratio but different initial fabrics may follow quite different effective stress paths, and may even induce sharp changes of fabric during phase transformation.
(7) The influences of micro-parameters on Cyclic Resistance Ratio (CRR), shear wave velocity, state parameter are detailedly discussed based on a number of dynamic triaxial tests under undrained condition during constant stress amplitude, as well as the measurement of shear wave velocity. Correlation between cyclic resistance ratio and shear wave velocity of granular materials are estabilished based on paticle-scale analysis, are verified by liquefaction and non-liquefaction data from centrifuge tests. It is indicated that the index number in CRR-Vsl correlation is about5for normal sand. The correlation between cyclic resistance ratio and state parameter is further raised.
引文
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