饱和土一维热固结解析理论研究
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摘要
土的热固结理论是当今岩土工程领域颇为关注的研究课题之一,在热能贮存、地热资源开发、核废料处置等方面具有良好的应用背景。本文针对现有热固结问题的研究尚未形成完整的理论体系的不足,较深入系统地开展了饱和土一维热固结解析理论的研究。主要内容和创新工作包括:
(1)在对有关土性温度效应及土体热固结问题等研究现状作了较详尽的回顾和总结的基础上,从传统固结理论、热弹性理论、渗流理论和传热理论等出发,推导了相应应力场、渗流场和温度场的控制方程,在此基础上进行简化,建立了饱和土体的三维、二维、一维热固结方程,并讨论了相应的定解条件,为热固结问题的求解奠定了基础。
(2)对最基本的地表骤然受常温且初始孔压均布的一维热固结问题,分别求得了考虑和不考虑热力耦合的超静孔压和温度增量的解,并通过详细比较,表明可以忽略热固结方程中热力耦合项对固结的影响。在此基础上,应用偏微分方程理论中的有限Fourier变换、分离变量法、冲量定理法等数学求解方法,分别获得了变荷载、初始孔压非均布、地表温度周期性变化等条件下以及综合考虑这些因素的复杂条件下的一维热固结问题的理论解,现有不考虑温度影响的一维传统固结解均为本文解特例。
(3)基于本文理论解,绘制了大量曲线,分析讨论了各种因素对地基超静孔压消散、沉降以及平均固结度发展的影响。分析表明,影响热固结性状的主要因素有:无量纲参数R(反映温度变化大小)、热扩散系数与固结系数之比F(反映热传导与固结速度快慢)、加荷时间因子T_(VO)(反映加荷快慢)、半周期时间因子T_(Vc)(反映温度变化周期)等。一般地,当地基温度升高,超静孔压消散加快,沉降减小;与Terzaghi解相比,温度对超静孔压的影响较小,而对沉降的影响较大;按应力定义和按应变定义的平均固结度是不同的,两者在数值上有较大差异。
本文首次获得了不考虑内热源的多种边界和初始等复杂条件下的一维热固结问题理论解,为饱和土热固结问题的深入研究奠定了良好的基础,也进一步丰富和完善了饱和土的固结解析理论。
Thermal consolidation theory of saturated soil is one of the most important research topics in the field of geotechnical engineering. It bears the important significance in most engineering projects such as heat energy storage, geothermal energy exploration, nuclear waste disposal. To complement the research of thermal consolidation theory of saturated soil, this dissertation gives a systematically study on the analytical theory of one-dimensional thermal consolidation of saturated soil. The main original work are made as follows:
(1) On the basis of reviewing the references about soil properties with temperature and thermal consolidation of soil, thermo-hydro-mechanical governing equations are developed by using traditional consolidation theory for saturated soil, thermoelasticity, seepage theory and heat conduction theory, three-dimensional thermal consolidation equations for saturated soil are constructed, and it can be reduced to the one for one-dimensional thermal consolidation problem.
(2) For the simplist thermal consolidation problem with instantaneous constant surface temperature and uniform initial pore-pressure, analytical solutions of excess pore-water pressure and temperature are derived and compared in detail, respectively. The results show that the thermo-mechanical coupling item in the thermal consolidation equation can be ignored. Based on the above mentioned and considering different conditions, analytical solutions for one-dimensional thermal consolidation problems are derived, respectively. The all traditional one-dimensional consolidation theory without considering temperature so far available are the special case of these solutions.
(3) By using the analytical solutions given herein, a variety of consolidation curves are prepared and the influence of various factors on the dissipation of pore water pressure and the development of settlement and degree of consolidation are dicussed. It has been shown that the main factors affecting thermal consolidation behaviour are: dimensionless parameter R (it indicates temperature increase.), the ratio of heat diffusion coefficient and consolidation coefficient F (it indicates velocity of heat conduction and consolidation.), loading time-factor T_(V0) (it indicates loading time), half-period time-factor T_(vc) (it indicates period of temperature change), etc. Generally, in thermal consolidation, compared with traditional consolidation without temperature effect, excess pore-water pressure dissipates more quickly; settlement decreases; comparing with Terzaghi's one-dimensional consolidation theory, the influence of temperature on excess pore water pressure is smaller than on settlement; two consolidation degrees defined by stress and strain are of great difference in value.
It is in this dissertation that the theoretical solutions for one-dimensional thermal consolidation problem is firstly derived under complicated conditions such as non-uniform initial pore-pressure, time-dependent loading, cycly changing surface temperature. This not only makes a good foundation for future study on the thermal consolidation of saturated soil, but also makes the analytical consolidation theory of saturated soil more perfect.
(1)在对有关土性温度效应及土体热固结问题等研究现状作了较详尽的回顾和总结的基础上,从传统固结理论、热弹性理论、渗流理论和传热理论等出发,推导了相应应力场、渗流场和温度场的控制方程,在此基础上进行简化,建立了饱和土体的三维、二维、一维热固结方程,并讨论了相应的定解条件,为热固结问题的求解奠定了基础。
(2)对最基本的地表骤然受常温且初始孔压均布的一维热固结问题,分别求得了考虑和不考虑热力耦合的超静孔压和温度增量的解,并通过详细比较,表明可以忽略热固结方程中热力耦合项对固结的影响。在此基础上,应用偏微分方程理论中的有限Fourier变换、分离变量法、冲量定理法等数学求解方法,分别获得了变荷载、初始孔压非均布、地表温度周期性变化等条件下以及综合考虑这些因素的复杂条件下的一维热固结问题的理论解,现有不考虑温度影响的一维传统固结解均为本文解特例。
(3)基于本文理论解,绘制了大量曲线,分析讨论了各种因素对地基超静孔压消散、沉降以及平均固结度发展的影响。分析表明,影响热固结性状的主要因素有:无量纲参数R(反映温度变化大小)、热扩散系数与固结系数之比F(反映热传导与固结速度快慢)、加荷时间因子T_(VO)(反映加荷快慢)、半周期时间因子T_(Vc)(反映温度变化周期)等。一般地,当地基温度升高,超静孔压消散加快,沉降减小;与Terzaghi解相比,温度对超静孔压的影响较小,而对沉降的影响较大;按应力定义和按应变定义的平均固结度是不同的,两者在数值上有较大差异。
本文首次获得了不考虑内热源的多种边界和初始等复杂条件下的一维热固结问题理论解,为饱和土热固结问题的深入研究奠定了良好的基础,也进一步丰富和完善了饱和土的固结解析理论。
Thermal consolidation theory of saturated soil is one of the most important research topics in the field of geotechnical engineering. It bears the important significance in most engineering projects such as heat energy storage, geothermal energy exploration, nuclear waste disposal. To complement the research of thermal consolidation theory of saturated soil, this dissertation gives a systematically study on the analytical theory of one-dimensional thermal consolidation of saturated soil. The main original work are made as follows:
(1) On the basis of reviewing the references about soil properties with temperature and thermal consolidation of soil, thermo-hydro-mechanical governing equations are developed by using traditional consolidation theory for saturated soil, thermoelasticity, seepage theory and heat conduction theory, three-dimensional thermal consolidation equations for saturated soil are constructed, and it can be reduced to the one for one-dimensional thermal consolidation problem.
(2) For the simplist thermal consolidation problem with instantaneous constant surface temperature and uniform initial pore-pressure, analytical solutions of excess pore-water pressure and temperature are derived and compared in detail, respectively. The results show that the thermo-mechanical coupling item in the thermal consolidation equation can be ignored. Based on the above mentioned and considering different conditions, analytical solutions for one-dimensional thermal consolidation problems are derived, respectively. The all traditional one-dimensional consolidation theory without considering temperature so far available are the special case of these solutions.
(3) By using the analytical solutions given herein, a variety of consolidation curves are prepared and the influence of various factors on the dissipation of pore water pressure and the development of settlement and degree of consolidation are dicussed. It has been shown that the main factors affecting thermal consolidation behaviour are: dimensionless parameter R (it indicates temperature increase.), the ratio of heat diffusion coefficient and consolidation coefficient F (it indicates velocity of heat conduction and consolidation.), loading time-factor T_(V0) (it indicates loading time), half-period time-factor T_(vc) (it indicates period of temperature change), etc. Generally, in thermal consolidation, compared with traditional consolidation without temperature effect, excess pore-water pressure dissipates more quickly; settlement decreases; comparing with Terzaghi's one-dimensional consolidation theory, the influence of temperature on excess pore water pressure is smaller than on settlement; two consolidation degrees defined by stress and strain are of great difference in value.
It is in this dissertation that the theoretical solutions for one-dimensional thermal consolidation problem is firstly derived under complicated conditions such as non-uniform initial pore-pressure, time-dependent loading, cycly changing surface temperature. This not only makes a good foundation for future study on the thermal consolidation of saturated soil, but also makes the analytical consolidation theory of saturated soil more perfect.
引文
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