考虑结构性的土体小应变本构模型研究
摘要
在岩土工程中绝大部分土体的变形都在小应变范围内;而在小应变范围内土体具有较高的刚度、逐渐屈服和结构性等变形特性。以剑桥模型为代表的传统土体本构模型难以描述土体的小应变特性。在这种情况下,采用传统土体本构模型分析基坑开挖、地铁施工等岩土工程问题时,预测计算结果将与实际情况相差较大。同时土体是天然地质体,土体结构对包括小应变在内的整个变形过程有强烈的影响。因此,建立考虑结构性的土体小应变本构模型具有重要的理论意义和现实意义。论文以国家自然科学基金项目“土体的小应变本构模型研究”(50309017)和重庆市自然科学基金项目“基于结构扰动的土体本构模型研究”(CSTC2005BB6114)为依托,从土体小应变变形特性的本质原因-土体的结构性入手,对土体的小应变本构模型进行研究。
论文的主要研究工作与结论如下:
①对土体小应变情况下的变形特性及其本构模型、土体结构性及其本构模型和修正剑桥模型等研究进展进行分析,提出了论文研究思路——基于土体的结构性,对修正剑桥模型进行扩展,从而建立土体的小应变本构模型。
②基于非连续介质细观力学,采用理论分析和数值试验两种手段,分别对土体的小应变变形的结构性机理进行分析。
建立了土体的细观模型,利用弹性接触力学理论讨论了胶结结构对土体小应变特性的影响规律。研究表明:在土体的整个变形过程中存在一个由胶结结构控制的变形区域;在该变形区域内,微量的胶结结构(胶结厚度为土体颗粒直径的万分之一)也会使土体宏观的模量增加10余倍。
在颗粒流PFC2D平台上,建立了土体及其三轴试验的颗粒流模型。分别讨论了接触刚度、粘结强度、粘结刚度与半径等细观结构参数对小应变条件下变形特性影响。研究表明:在小应变范围内细观颗粒滑动趋势较小,摩擦力还未得到充分发挥,土体细观颗粒间的摩擦对小应变特性影响较小。细观颗粒间的胶结厚度、胶结半径和胶结模量等对小应变特性影响较大;随着细观颗粒间的胶结厚度、胶结半径和胶结模量的增加,土体宏观变形模量将增大。
在小应变条件,微量胶结也可以使土体颗粒间点接触转换为面接触,从而使土体表现出较高的宏观模量;而当应变进一步增加时,胶结破损,土体细观颗粒间的面接触转换为点接触,从而使土体宏观模量迅速降低。
土体宏观强度参数的粘聚力和摩擦系数两个方面,在小应变范围内主要是粘聚力发挥作用,而摩擦力相对影响较小。
③土体结构的模型及其本构关系研究
对土体的物理结构、宏观变形特性等进行调查,提出了土体结构的材料结构模型和分布结构模型。
将土体变形表现出的超固结划分为材料结构超固结与应力超固结这两种不同性质的超固结;从而使材料结构与应力超固结统一起来。然后对修正剑桥模型进行扩展,模型屈服面的尺寸由材料结构超固结参数和应力超固结参数两者之和共同决定,而屈服面尺寸大小的变化由塑性体积硬化与材料结构损伤共同描述;从而建立了一个可以统一考虑超固结和结构性的土体本构模型。该模型对于描述土体结构性,特别是在大应变范围内的结构性具有较高的适用性。
基于土体的分布结构模型概念,假设土体的一维塑性硬化元件的摩擦滑动元件启动应力参数、塑性模量相互独立,并分别服从某种形式的统计分布;利用统计学和塑性力学理论,推导了基于分布结构模型概念的土体一维弹塑性本构模型。该一维弹塑性模型能够反映土体小应变时的逐渐屈服特征。
④考虑土体的材料结构,利用复合体损伤理论,提出了弹性变形部分的计算方法。在塑性变形部分模型基于土体的分布结构模型,认为塑性变形的内变量不是单一、固定的值,而是在一定区间上遵循统计分布密度函数分布的;扩展修正剑桥模型单一内变量的单个屈服面至尺寸连续的屈服面场,并采用相关联的流动法则,从而提出了可以反映土体小应变特性的土体本构模型。
⑤在有限差分FLAC2D平台上,对论文小应变本构模型进行了fish语言程序化,然后对天府基坑工程案例进行了数值分析。分析表明,基坑开挖工程中绝大部分土体都处于小应变变形情况,土体小应变本构模型有利于准确预测岩土工程的变形;相比修正剑桥模型,本文小应变本构模型更能反映工程土体的变形情况特性。
In the majority of geotechnical engineerings, soils deform in small strain range. And soils display features of high stiffness, progressive yield and so on in the small strain range. But these features are difficult to model by Cam-clay model, which is the typical of traditional soil model. At the same time, soil is a natural geological body; and structure is material basis of deformation and the engineering properties. At present, soil constitutive model in small strain does not reflect the impact of the structure. It is theoretical & practical significance to establish constitutive modelling of soils in small strain considering the influence of structure.
Major work and results of the thesis are as follows:
(1) Investigation and analysis were taken of the soil deformation characteristics and constitutive models in the small strain ranges, of soil structure constitutive model and soil structural theory. It gave out the starting point for research– considering the soil structure, extending modified Cam-Clay model.
(2) Based on non-continuum mechanics, deformation mechanism of soils in small strain ranges was studied by the means of theory and numerical tests respectively.
Studies showed that the friction between soil particles had little effect on the deformation behavior in small strain range, but the particle bulk modulus and strength of contacts between particles, cement and other characteristics of the soils had profound effect on the he deformation behavior in small strain range behavior. In the range controlled by cement structure, just little cement (the thickness of soil cement is 1/10000 of particle‘s diameter size) would also make the modulus of soil increase more than 10 times. And the soil modulus increased with the increasing of the thickness of soil cement.
Microscopic particles of soil contact state and the way had impact on deformation characteristics of soil in small strain ranges. In the initial state, the small amount of cement made contact with soil particles from point contact to surface contact. So soil macro-modulus increased significantly; but when the strain increases further, even the small amount of cement damage, the surface contacts between soil micro particles were changed into point contacts. As the result, soil modulus decreased rapidly.
(3) The soil structure was described by material structure model and distribution structure model.
Material structure was taken as one type of over-consolidation. The over consolidation shown by soil deformation was classified into two parts, over-consolidation induced by the structure and over-consolidation induced by stress. Then material structure and over-consolidation were united together. The model’s yield surface was the same with the modified Cam-Clay models’. And the size of yield surface was decided by the material structure and stress consolidation, and it changed by the volume-hardening and the material structural damage.
By use of theory of plastic, a progressive yield constitutive was established based on the distribution structure model. An element with the composition of coulomb friction & sliding components and a spring was used as the representative volume element to simulate the isotropic elastic-plastic. By the use of statistics and plasticity theory, one-dimensional elastic-plastic soil constitutive model was presented based on the concept of distribution structure model. The result showed that the model can reflect deformation characteristics of soils at small strains.
(4) Based on the concept of disturbing structure and material structure, a progressive yield constitutive model was presented by extending the cam-clay model. The internal variable of yield surface was not just a constant parameter, but it should be treated as a distribution function in a range. The single yield surface of the cam-clay model was extended to a field of yield surface. Then by introduction the progressive yield concept into the Cam-Clay Model, the progressive yield constitutive model was constituted. Only one parameter was added beside the three parameters of the cam-clay, which represented the disturbing structure of the soils. Primary application showed that the model can predict the progressive yield of the soils.
(5) Based FLAC2D platform, the user-define model by fish was given out. And the Tianfu pit was analyzed by the present model and modified cam-clay model. Results showed that the majority of soil in excavation works deform in the small strain. The constitutive model presented in paper could accurately predict the deformation of geotechnical engineering compared to Cam-Clay model.
论文的主要研究工作与结论如下:
①对土体小应变情况下的变形特性及其本构模型、土体结构性及其本构模型和修正剑桥模型等研究进展进行分析,提出了论文研究思路——基于土体的结构性,对修正剑桥模型进行扩展,从而建立土体的小应变本构模型。
②基于非连续介质细观力学,采用理论分析和数值试验两种手段,分别对土体的小应变变形的结构性机理进行分析。
建立了土体的细观模型,利用弹性接触力学理论讨论了胶结结构对土体小应变特性的影响规律。研究表明:在土体的整个变形过程中存在一个由胶结结构控制的变形区域;在该变形区域内,微量的胶结结构(胶结厚度为土体颗粒直径的万分之一)也会使土体宏观的模量增加10余倍。
在颗粒流PFC2D平台上,建立了土体及其三轴试验的颗粒流模型。分别讨论了接触刚度、粘结强度、粘结刚度与半径等细观结构参数对小应变条件下变形特性影响。研究表明:在小应变范围内细观颗粒滑动趋势较小,摩擦力还未得到充分发挥,土体细观颗粒间的摩擦对小应变特性影响较小。细观颗粒间的胶结厚度、胶结半径和胶结模量等对小应变特性影响较大;随着细观颗粒间的胶结厚度、胶结半径和胶结模量的增加,土体宏观变形模量将增大。
在小应变条件,微量胶结也可以使土体颗粒间点接触转换为面接触,从而使土体表现出较高的宏观模量;而当应变进一步增加时,胶结破损,土体细观颗粒间的面接触转换为点接触,从而使土体宏观模量迅速降低。
土体宏观强度参数的粘聚力和摩擦系数两个方面,在小应变范围内主要是粘聚力发挥作用,而摩擦力相对影响较小。
③土体结构的模型及其本构关系研究
对土体的物理结构、宏观变形特性等进行调查,提出了土体结构的材料结构模型和分布结构模型。
将土体变形表现出的超固结划分为材料结构超固结与应力超固结这两种不同性质的超固结;从而使材料结构与应力超固结统一起来。然后对修正剑桥模型进行扩展,模型屈服面的尺寸由材料结构超固结参数和应力超固结参数两者之和共同决定,而屈服面尺寸大小的变化由塑性体积硬化与材料结构损伤共同描述;从而建立了一个可以统一考虑超固结和结构性的土体本构模型。该模型对于描述土体结构性,特别是在大应变范围内的结构性具有较高的适用性。
基于土体的分布结构模型概念,假设土体的一维塑性硬化元件的摩擦滑动元件启动应力参数、塑性模量相互独立,并分别服从某种形式的统计分布;利用统计学和塑性力学理论,推导了基于分布结构模型概念的土体一维弹塑性本构模型。该一维弹塑性模型能够反映土体小应变时的逐渐屈服特征。
④考虑土体的材料结构,利用复合体损伤理论,提出了弹性变形部分的计算方法。在塑性变形部分模型基于土体的分布结构模型,认为塑性变形的内变量不是单一、固定的值,而是在一定区间上遵循统计分布密度函数分布的;扩展修正剑桥模型单一内变量的单个屈服面至尺寸连续的屈服面场,并采用相关联的流动法则,从而提出了可以反映土体小应变特性的土体本构模型。
⑤在有限差分FLAC2D平台上,对论文小应变本构模型进行了fish语言程序化,然后对天府基坑工程案例进行了数值分析。分析表明,基坑开挖工程中绝大部分土体都处于小应变变形情况,土体小应变本构模型有利于准确预测岩土工程的变形;相比修正剑桥模型,本文小应变本构模型更能反映工程土体的变形情况特性。
In the majority of geotechnical engineerings, soils deform in small strain range. And soils display features of high stiffness, progressive yield and so on in the small strain range. But these features are difficult to model by Cam-clay model, which is the typical of traditional soil model. At the same time, soil is a natural geological body; and structure is material basis of deformation and the engineering properties. At present, soil constitutive model in small strain does not reflect the impact of the structure. It is theoretical & practical significance to establish constitutive modelling of soils in small strain considering the influence of structure.
Major work and results of the thesis are as follows:
(1) Investigation and analysis were taken of the soil deformation characteristics and constitutive models in the small strain ranges, of soil structure constitutive model and soil structural theory. It gave out the starting point for research– considering the soil structure, extending modified Cam-Clay model.
(2) Based on non-continuum mechanics, deformation mechanism of soils in small strain ranges was studied by the means of theory and numerical tests respectively.
Studies showed that the friction between soil particles had little effect on the deformation behavior in small strain range, but the particle bulk modulus and strength of contacts between particles, cement and other characteristics of the soils had profound effect on the he deformation behavior in small strain range behavior. In the range controlled by cement structure, just little cement (the thickness of soil cement is 1/10000 of particle‘s diameter size) would also make the modulus of soil increase more than 10 times. And the soil modulus increased with the increasing of the thickness of soil cement.
Microscopic particles of soil contact state and the way had impact on deformation characteristics of soil in small strain ranges. In the initial state, the small amount of cement made contact with soil particles from point contact to surface contact. So soil macro-modulus increased significantly; but when the strain increases further, even the small amount of cement damage, the surface contacts between soil micro particles were changed into point contacts. As the result, soil modulus decreased rapidly.
(3) The soil structure was described by material structure model and distribution structure model.
Material structure was taken as one type of over-consolidation. The over consolidation shown by soil deformation was classified into two parts, over-consolidation induced by the structure and over-consolidation induced by stress. Then material structure and over-consolidation were united together. The model’s yield surface was the same with the modified Cam-Clay models’. And the size of yield surface was decided by the material structure and stress consolidation, and it changed by the volume-hardening and the material structural damage.
By use of theory of plastic, a progressive yield constitutive was established based on the distribution structure model. An element with the composition of coulomb friction & sliding components and a spring was used as the representative volume element to simulate the isotropic elastic-plastic. By the use of statistics and plasticity theory, one-dimensional elastic-plastic soil constitutive model was presented based on the concept of distribution structure model. The result showed that the model can reflect deformation characteristics of soils at small strains.
(4) Based on the concept of disturbing structure and material structure, a progressive yield constitutive model was presented by extending the cam-clay model. The internal variable of yield surface was not just a constant parameter, but it should be treated as a distribution function in a range. The single yield surface of the cam-clay model was extended to a field of yield surface. Then by introduction the progressive yield concept into the Cam-Clay Model, the progressive yield constitutive model was constituted. Only one parameter was added beside the three parameters of the cam-clay, which represented the disturbing structure of the soils. Primary application showed that the model can predict the progressive yield of the soils.
(5) Based FLAC2D platform, the user-define model by fish was given out. And the Tianfu pit was analyzed by the present model and modified cam-clay model. Results showed that the majority of soil in excavation works deform in the small strain. The constitutive model presented in paper could accurately predict the deformation of geotechnical engineering compared to Cam-Clay model.
引文
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