基于超塑性力学的软粘土本构理论研究
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摘要
超塑性力学以热力学定律为基础，通过构建耗散函数和自由能函数确定应力应变关系，打破了传统塑性力学通过屈服函数、流动法则和硬化定律确定应力应变关系的理论框架，理论体系更为严密，结构更为严谨。本文对超塑性力学理论进行了概括总结，应用物理元件的组合说明了内变量的物理含义，阐述了Ziegler正交假设和最大熵产生率原理的关系，通过Mises系列模型对超塑性力学构建自由能函数和耗散函数的方法进行了说明。
岩土材料在塑性变形过程中，塑性功不能完全耗散，而是一部分以自由能的形式储存起来。本文分析了最大塑性功原理和最大熵产生率原理的关系和相关联流动法则不适用于岩土材料的原因。弹塑性耦合和耗散函数耦合是使相关联流动法则不适用于岩土材料的主要原因，Drucker公设中初始应力在加载曲线上是可以任选的，因此Drucker公设隐含了耗散函数与应力状态无关的假设，也就隐含了耗散函数不耦合的假设。通过超塑性力学理论得出，考虑弹塑性耦合会使屈服面的位置随所处应力状态的变化而变化，考虑耗散函数耦合会使屈服面从耗散应力空间转换到真实应力空间时形状发生改变。在耗散函数与所处应力状态无关的情况下，如果不考虑弹塑性耦合，Drucker公设仍然对岩土材料适用。
把同一回弹线与正常压缩线和临界状态线交点对应的有效体积应力的比值定义为间隔应力比，原始剑桥模型中间隔应力比的值为2.72，修正剑桥模型中间隔应力比的值为2，实际上间隔应力比是与土性有关的参数，它对土体的力学行为有重要的影响。本文在超塑性力学的框架内讨论了间隔应力比的物理含义和该参数对屈服面形状及应力应变曲线的影响。
原状粘土的压缩曲线有多种表示形式，本文通过拟合13种原状粘土的压缩曲线说明了双对数坐标下双段线形式可以合理的表征原状粘土的压缩特性，并分析了单对数和双对数坐标下塑性体积应变比的差别。
通过分析原状粘土确定结构屈服应力的W-p′方法指出原状粘土颗粒之间的胶结作用可能在结构屈服应力点处有很大一部分发生破坏，通过一些典型的原状粘土的试验数据说明了超过结构屈服应力后原状粘土的间隔应力比可近似取为常数。
因为破坏是变形的最后阶段，所以土的强度和本构具有密不可分的关系。各向异性是天然土体的一个重要特征，本文在超塑性力学的框架内，将真实应力空间的屈服面简化为倾斜的椭圆屈服面，结合临界状态土力学的有关理论给出了轴对称和平面应变条件下K_0固结软粘土不排水强度和上覆压力比值的解析式，并通过试验数据对这些解析式进行了验证。在其他参数一定的条件下，土体的不排水强度比与有效内摩擦角近似呈线性关系，本文根据这个线性关系给出了便于工程应用的临界不排水强度比关于有效内摩擦角的简易表达式。
在超塑性力学的框架内构建了一个适用于粘性土的本构模型，针对粘性土的力学行为构建了一个指数形式的各向异性演化定律，分析了模型参数的物理含义及其对应力应变曲线和屈服面形状的影响，并通过实验进行了验证。
Hyper-plasticity is a new method to construct models of soils, which is basedon the first and second law of thermodynamics, and the stress-strain relations can bedetermined by free energy function and dissipation function. This new method hasbroken the framework of classical plasticity theory. Some physical models have beenused to interpret the internal variables, and the hypothesis of taking plastic strain asthe internal state parameter is analyzed in this paper. Ziegler's orthogonalitypostulate is proved to be equal to the maximum rate of dissipation criterion withLegendre transformation and Euler's theory. The role of free energy function anddissipation function has been analyzed, and the series of Mises models have beenused to explain the method of hyper-plasticity.
Part of plastic work can be interlocked by plastic deformation in the form offree-energy. This point has led to the difference of maximum plastic work theory andmaximum entropy product theory. The relations between the two theories have beenproposed in this paper. Elastic-plastic coupling and dissipative coupling are mainreasons to make the associated flow rule unsatisfied for geomaterials. Dissipativeuncoupling is involved in Drucker postulate as the the choice of initial stress isarbitrary. Yield surface will move with stress state when Elastic-plastic coupling isconsidered, and the shape of yield surface will change when transformed fromdissipative stress space to true stress space when dissipative coupling is considered.
The spacing ratio is defined to be the ratio between volumetric stresses of NCLand CSL on the same unloading line, which has been chosen as 2.72 in OriginalCam-Clay model and 2 in Modified Cam-Clay model. In fact, the spacing ratio is aparameter of soil properties, which has much influence on soil behavior. Based onhyper-plasticity theory, a model has been proposed to take account of the change ofthe spacing ratio, and the influence of spacing ratio on constitutive relations has beenanalyzed.
Bases on the analysis of 13 typical intact clays' compression line, conclusioncan be drawn that the consolidation line of intact clays can be divided into two linearparts in double logarithm space. The compresson index and unloading index havebeen analyzed in both single-logarithm and double-logrithm space. It is proposedthat the spacing ratio can be taken as a constant parameter based on experimentalresult of some typical intact clays.
As failure is the last phase of deformation, there are close relations betweensoil's constitutive model and strength. Anisotropy is an important feature of naturalsoils, it is proved that the inclined ellipsoid is the simplest yield surface shape thatcan take account of anisotropy of soft clays based on hyper-plasticity theory.Companied with critical state soil mechanics, formulas of undrained strength under K_0 consolidation have been proposed, these formulas can be used in triaxial stressconditions and plane strain conditions. Based on a large number of experimental data,the formulas are validated to be true. If we take other parameters as constant, a linearrelation can be got between the undrained strength ratio and the effective frictionalangle. Simplized formulas have been proposed based on this linear relation forengineering application.
A unified model for clays has been proposed within the framework ofhyper-plasticity theory. A rotational hardening rule has been proposed. The physicalmeaning of model parameters and the method to determine them have been putforward.
岩土材料在塑性变形过程中，塑性功不能完全耗散，而是一部分以自由能的形式储存起来。本文分析了最大塑性功原理和最大熵产生率原理的关系和相关联流动法则不适用于岩土材料的原因。弹塑性耦合和耗散函数耦合是使相关联流动法则不适用于岩土材料的主要原因，Drucker公设中初始应力在加载曲线上是可以任选的，因此Drucker公设隐含了耗散函数与应力状态无关的假设，也就隐含了耗散函数不耦合的假设。通过超塑性力学理论得出，考虑弹塑性耦合会使屈服面的位置随所处应力状态的变化而变化，考虑耗散函数耦合会使屈服面从耗散应力空间转换到真实应力空间时形状发生改变。在耗散函数与所处应力状态无关的情况下，如果不考虑弹塑性耦合，Drucker公设仍然对岩土材料适用。
把同一回弹线与正常压缩线和临界状态线交点对应的有效体积应力的比值定义为间隔应力比，原始剑桥模型中间隔应力比的值为2.72，修正剑桥模型中间隔应力比的值为2，实际上间隔应力比是与土性有关的参数，它对土体的力学行为有重要的影响。本文在超塑性力学的框架内讨论了间隔应力比的物理含义和该参数对屈服面形状及应力应变曲线的影响。
原状粘土的压缩曲线有多种表示形式，本文通过拟合13种原状粘土的压缩曲线说明了双对数坐标下双段线形式可以合理的表征原状粘土的压缩特性，并分析了单对数和双对数坐标下塑性体积应变比的差别。
通过分析原状粘土确定结构屈服应力的W-p′方法指出原状粘土颗粒之间的胶结作用可能在结构屈服应力点处有很大一部分发生破坏，通过一些典型的原状粘土的试验数据说明了超过结构屈服应力后原状粘土的间隔应力比可近似取为常数。
因为破坏是变形的最后阶段，所以土的强度和本构具有密不可分的关系。各向异性是天然土体的一个重要特征，本文在超塑性力学的框架内，将真实应力空间的屈服面简化为倾斜的椭圆屈服面，结合临界状态土力学的有关理论给出了轴对称和平面应变条件下K_0固结软粘土不排水强度和上覆压力比值的解析式，并通过试验数据对这些解析式进行了验证。在其他参数一定的条件下，土体的不排水强度比与有效内摩擦角近似呈线性关系，本文根据这个线性关系给出了便于工程应用的临界不排水强度比关于有效内摩擦角的简易表达式。
在超塑性力学的框架内构建了一个适用于粘性土的本构模型，针对粘性土的力学行为构建了一个指数形式的各向异性演化定律，分析了模型参数的物理含义及其对应力应变曲线和屈服面形状的影响，并通过实验进行了验证。
Hyper-plasticity is a new method to construct models of soils, which is basedon the first and second law of thermodynamics, and the stress-strain relations can bedetermined by free energy function and dissipation function. This new method hasbroken the framework of classical plasticity theory. Some physical models have beenused to interpret the internal variables, and the hypothesis of taking plastic strain asthe internal state parameter is analyzed in this paper. Ziegler's orthogonalitypostulate is proved to be equal to the maximum rate of dissipation criterion withLegendre transformation and Euler's theory. The role of free energy function anddissipation function has been analyzed, and the series of Mises models have beenused to explain the method of hyper-plasticity.
Part of plastic work can be interlocked by plastic deformation in the form offree-energy. This point has led to the difference of maximum plastic work theory andmaximum entropy product theory. The relations between the two theories have beenproposed in this paper. Elastic-plastic coupling and dissipative coupling are mainreasons to make the associated flow rule unsatisfied for geomaterials. Dissipativeuncoupling is involved in Drucker postulate as the the choice of initial stress isarbitrary. Yield surface will move with stress state when Elastic-plastic coupling isconsidered, and the shape of yield surface will change when transformed fromdissipative stress space to true stress space when dissipative coupling is considered.
The spacing ratio is defined to be the ratio between volumetric stresses of NCLand CSL on the same unloading line, which has been chosen as 2.72 in OriginalCam-Clay model and 2 in Modified Cam-Clay model. In fact, the spacing ratio is aparameter of soil properties, which has much influence on soil behavior. Based onhyper-plasticity theory, a model has been proposed to take account of the change ofthe spacing ratio, and the influence of spacing ratio on constitutive relations has beenanalyzed.
Bases on the analysis of 13 typical intact clays' compression line, conclusioncan be drawn that the consolidation line of intact clays can be divided into two linearparts in double logarithm space. The compresson index and unloading index havebeen analyzed in both single-logarithm and double-logrithm space. It is proposedthat the spacing ratio can be taken as a constant parameter based on experimentalresult of some typical intact clays.
As failure is the last phase of deformation, there are close relations betweensoil's constitutive model and strength. Anisotropy is an important feature of naturalsoils, it is proved that the inclined ellipsoid is the simplest yield surface shape thatcan take account of anisotropy of soft clays based on hyper-plasticity theory.Companied with critical state soil mechanics, formulas of undrained strength under K_0 consolidation have been proposed, these formulas can be used in triaxial stressconditions and plane strain conditions. Based on a large number of experimental data,the formulas are validated to be true. If we take other parameters as constant, a linearrelation can be got between the undrained strength ratio and the effective frictionalangle. Simplized formulas have been proposed based on this linear relation forengineering application.
A unified model for clays has been proposed within the framework ofhyper-plasticity theory. A rotational hardening rule has been proposed. The physicalmeaning of model parameters and the method to determine them have been putforward.
引文
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