考虑起始比降的软土地基一维固结理论研究
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摘要
由于达西渗流定律的获得基于砂土的渗透性试验,其在粘性土中适用性受到了一些学者的质疑,已有渗透试验研究表明：对某些低渗透性饱和粘土而言,存在起始比降,只有当土中某点的水力坡降大于起始比降(又称起始水力坡降、起始水力梯度),该点才会发生渗流。然而,传统的固结理论大都假设土中渗流符合达西定律,对于考虑起始比降的固结问题的研究并不多见。本文在已有研究的基础上,采用解析法和半解析法较深入系统地研究了考虑起始比降的软土地基一维固结问题。主要内容及创新成果包括：
1.分析了初始孔压三种不同分布形式下,即：初始孔压降不小于起始比降、初始孔压降不大于起始比降的负值、初始孔压降绝对值小于起始比降,土中渗流边界的运动规律,建立了相应的固结控制方程,推导了三种不同形式下考虑起始比降的一维固结孔压解及地基平均固结度计算公式,并与已有差分解等进行对比,在此基础上计算分析了起始比降和初始孔压分布形式对渗流边界运动速度、孔压分布、地基平均固结度的影响,讨论了按沉降定义和按孔压定义的地基平均固结度的不同,并编制了初始孔压均布条件下渗流移动边界与时间的关系表。
2.针对工程中加载并非瞬时完成的实际情况,给出了变荷载条件下考虑起始比降一维固结普遍解,以及单级加荷条件下,当加载时间分别大于和小于渗流发展到土层底部所需时间的情况时,渗流移动边界、孔压和地基平均固结度的具体表达式,分析了加载时间等对考虑起始比降后土体一维固结性状的影响。
3.在初始孔压降不小于起始比降的特殊条件下,渗流瞬间在整个土层发生,获得了能考虑起始比降的任意层地基的一维固结解析解及其不同形式下的退化解(包括考虑起始比降的双层地基一维固结解及不考虑起始比降初始孔压非均布条件下的任意层地基一维固结解析解),并编制了相应的计算程序,分析了该特殊条件下考虑起始比降后成层地基的一维固结性状。
4.提出了求解考虑起始比降的任意层地基的一维固结问题的半解析法,编制了相应的计算程序,并通过与已有解的结果对比,对程序的合理性和正确性进行了验证,然后以双层地基为例,分析不同土层起始比降组合对双层地基的一维固结性状的影响。
5.利用半解析法,通过引入土体孔隙比和渗透系数、土体孔隙比和有效应力的对数关系,给出了能同时考虑起始比降、土体自重应力实际分布、渗透系数和压缩系数非线性变化的一维非线性固结半解析解,编制了计算程序,并与已有不考虑起始比降的一维固结非线性解析解进行了结果对比,验证了解和程序的正确性。在此基础上进行了大量的计算,分析了压缩指数和渗透指数的比值、外荷载、起始比降、自重应力分布形式对渗流边界运动速度和地基固结性状的影响。
Up until now. Darcy's law has been incorporated in most conventional theories of consolidation to depict the flow of water through soft soil such as clays. However, Darcy"s law was established from permeability test on sands. It has been widely agreed that deviations from Darcy's law do exist in some clays. Some investigators have revealed evidence indicating deviations of water flow from Darcy's law and demonstrated the existence of a threshold gradient in some fine-grained soils with low permeability. There is no flow in the soil where the hydraulic gradient is less than the threshold gradient, and little research has been reported on consolidation with threshold gradient at present. In order to further improve the theory of consolidation for soft soils with threshold gradient, systematically, studies are made on the basis of previous research. The main original works and innovative achievements include:
(1) The motions of seepage are discussed and the governing equations of consolidation are derived by considering three cases, such as 1). the initial pore pressure gradient is larger than or equal to the threshold gradient;2). the initial pore pressure gradient is less than or equal to the negative value of threshold gradient; 3) the absolute value of initial pore pressure gradient is less than threshold gradient. Analytical solutions for excess pore pressure and average degree of consolidation are obtained with different distribution of initial pore pressure. A comparison is made between the present solution and previous solution for a particular case in which the distribution of the initial excess pore pressure is uniform. Base on the present solution, influences of the threshold gradient and the distribution of initial excess pore pressure on the motion of the moving boundary of seepage, the distribution of excess pore pressure and the average degree of consolidation are analyzed, and the difference between the average degree of consolidation defined by settlement and defined by pore pressure is discussed. At last, computation table describing the motion of moving boundary of seepage with time is provided for the distribution of initial excess pore pressure being uniform.
(2) In light of the application of the external load during construction always takeing some time. A general analytical solution is developed for one-dimensional consolidation with a threshold gradient under time-dependent loading. Moreover, detailed solutions are obtained for the moving boundary of seepage, the excess pore pressure and average degree of consolidation in terms of stress and strain under the single-stage loading, and two different cases are discussed, such as 1). The loading time is larger and equal to the time which the moving boundary takes to the bottom of the layer; 2). The loading time is smaller than the time which the moving boundary takes to the bottom of the layer. Finally, the effect of loading time on the consolidation behaviour is investigated.
(3) By assuming threshold gradients less than the initial pore pressure gradient the flow would occur throughout the whole layer instantaneously, and a analytical solution and its simplified forms are firstly obtained for one-dimensional consolidation of layered systems with threshold gradient. A relevant computation program is developed. Based on the solutions and the corresponding computation program, an example is investigated and the consolidation behavior of layered systems with threshold gradient is analyzed.
(4) Performing discretizations in the time and spatialdomain, a new semi-analytical method is proposed for solving the problem of one-dimensional consolidation of layered systems considering threshold gradient. The corresponding computation program is developed. Then a comparison is made between the result attained from the semi-analytical solution and that obtained from the previous solutions for homogeneous soil. Finally, the effect of different combination of threshold gradients of double-layered ground on consolidation behaviour is discussed.
(5) By incorporating the logarithm relationship between void ratio and permeability coefficient as well as that between void ratio and effective stress, a semi-analytical solution is attained for one-dimensional nonlinear consolidation considering the threshold gradient, the distribution type of self-weight stress, the nonlinear variation of soil's permeability and compressibility. A comparison is made between the present solution and the previous solution without considering threshold gradient with the ratio of compression index permeability index being equal to 1, and the effects of the ratio of compression index permeability index, the external load, the threshold gradient and the distribution type of self-weight stress on the motion of moving boundary and average degree of consolidation are discussed.
1.分析了初始孔压三种不同分布形式下,即：初始孔压降不小于起始比降、初始孔压降不大于起始比降的负值、初始孔压降绝对值小于起始比降,土中渗流边界的运动规律,建立了相应的固结控制方程,推导了三种不同形式下考虑起始比降的一维固结孔压解及地基平均固结度计算公式,并与已有差分解等进行对比,在此基础上计算分析了起始比降和初始孔压分布形式对渗流边界运动速度、孔压分布、地基平均固结度的影响,讨论了按沉降定义和按孔压定义的地基平均固结度的不同,并编制了初始孔压均布条件下渗流移动边界与时间的关系表。
2.针对工程中加载并非瞬时完成的实际情况,给出了变荷载条件下考虑起始比降一维固结普遍解,以及单级加荷条件下,当加载时间分别大于和小于渗流发展到土层底部所需时间的情况时,渗流移动边界、孔压和地基平均固结度的具体表达式,分析了加载时间等对考虑起始比降后土体一维固结性状的影响。
3.在初始孔压降不小于起始比降的特殊条件下,渗流瞬间在整个土层发生,获得了能考虑起始比降的任意层地基的一维固结解析解及其不同形式下的退化解(包括考虑起始比降的双层地基一维固结解及不考虑起始比降初始孔压非均布条件下的任意层地基一维固结解析解),并编制了相应的计算程序,分析了该特殊条件下考虑起始比降后成层地基的一维固结性状。
4.提出了求解考虑起始比降的任意层地基的一维固结问题的半解析法,编制了相应的计算程序,并通过与已有解的结果对比,对程序的合理性和正确性进行了验证,然后以双层地基为例,分析不同土层起始比降组合对双层地基的一维固结性状的影响。
5.利用半解析法,通过引入土体孔隙比和渗透系数、土体孔隙比和有效应力的对数关系,给出了能同时考虑起始比降、土体自重应力实际分布、渗透系数和压缩系数非线性变化的一维非线性固结半解析解,编制了计算程序,并与已有不考虑起始比降的一维固结非线性解析解进行了结果对比,验证了解和程序的正确性。在此基础上进行了大量的计算,分析了压缩指数和渗透指数的比值、外荷载、起始比降、自重应力分布形式对渗流边界运动速度和地基固结性状的影响。
Up until now. Darcy's law has been incorporated in most conventional theories of consolidation to depict the flow of water through soft soil such as clays. However, Darcy"s law was established from permeability test on sands. It has been widely agreed that deviations from Darcy's law do exist in some clays. Some investigators have revealed evidence indicating deviations of water flow from Darcy's law and demonstrated the existence of a threshold gradient in some fine-grained soils with low permeability. There is no flow in the soil where the hydraulic gradient is less than the threshold gradient, and little research has been reported on consolidation with threshold gradient at present. In order to further improve the theory of consolidation for soft soils with threshold gradient, systematically, studies are made on the basis of previous research. The main original works and innovative achievements include:
(1) The motions of seepage are discussed and the governing equations of consolidation are derived by considering three cases, such as 1). the initial pore pressure gradient is larger than or equal to the threshold gradient;2). the initial pore pressure gradient is less than or equal to the negative value of threshold gradient; 3) the absolute value of initial pore pressure gradient is less than threshold gradient. Analytical solutions for excess pore pressure and average degree of consolidation are obtained with different distribution of initial pore pressure. A comparison is made between the present solution and previous solution for a particular case in which the distribution of the initial excess pore pressure is uniform. Base on the present solution, influences of the threshold gradient and the distribution of initial excess pore pressure on the motion of the moving boundary of seepage, the distribution of excess pore pressure and the average degree of consolidation are analyzed, and the difference between the average degree of consolidation defined by settlement and defined by pore pressure is discussed. At last, computation table describing the motion of moving boundary of seepage with time is provided for the distribution of initial excess pore pressure being uniform.
(2) In light of the application of the external load during construction always takeing some time. A general analytical solution is developed for one-dimensional consolidation with a threshold gradient under time-dependent loading. Moreover, detailed solutions are obtained for the moving boundary of seepage, the excess pore pressure and average degree of consolidation in terms of stress and strain under the single-stage loading, and two different cases are discussed, such as 1). The loading time is larger and equal to the time which the moving boundary takes to the bottom of the layer; 2). The loading time is smaller than the time which the moving boundary takes to the bottom of the layer. Finally, the effect of loading time on the consolidation behaviour is investigated.
(3) By assuming threshold gradients less than the initial pore pressure gradient the flow would occur throughout the whole layer instantaneously, and a analytical solution and its simplified forms are firstly obtained for one-dimensional consolidation of layered systems with threshold gradient. A relevant computation program is developed. Based on the solutions and the corresponding computation program, an example is investigated and the consolidation behavior of layered systems with threshold gradient is analyzed.
(4) Performing discretizations in the time and spatialdomain, a new semi-analytical method is proposed for solving the problem of one-dimensional consolidation of layered systems considering threshold gradient. The corresponding computation program is developed. Then a comparison is made between the result attained from the semi-analytical solution and that obtained from the previous solutions for homogeneous soil. Finally, the effect of different combination of threshold gradients of double-layered ground on consolidation behaviour is discussed.
(5) By incorporating the logarithm relationship between void ratio and permeability coefficient as well as that between void ratio and effective stress, a semi-analytical solution is attained for one-dimensional nonlinear consolidation considering the threshold gradient, the distribution type of self-weight stress, the nonlinear variation of soil's permeability and compressibility. A comparison is made between the present solution and the previous solution without considering threshold gradient with the ratio of compression index permeability index being equal to 1, and the effects of the ratio of compression index permeability index, the external load, the threshold gradient and the distribution type of self-weight stress on the motion of moving boundary and average degree of consolidation are discussed.
引文
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