基于指数形式渗流定律的软土一维固结分析

在土中渗流服从指数形式渗流定律的前提下,对软黏土一维固结理论进行分析研究。首先建立考虑指数形式渗流定律的软黏土一维固结微分方程。然后采用相对稳定的Crank-Nicolson差分格式对控制方程进行时间、空间离散,得到了差分方程及其解答,并且将差分计算结果与退化到达西渗流的Terzaghi理论解析解和指数为1.5时的短时间解析解相对比,验证计算程序的可靠性。通过计算分析考虑指数渗流定律情况下的软土地基的一维固结性状,结果表明:考虑指数形式渗流情况下(指数大于1),固结速率在较小的时间因子下要比Terzaghi理论快,而在较大的时间因子下比Terzaghi理论慢,这种现象随着指数值的增大越来越显著;荷载的等效水头与土层厚度的比值对固结性状有显著的影响,比值越小,则固结速率越慢。最后,讨论了达西渗流在实际工程中的适用范围。     

考虑非达西渗流和变荷载影响的软土大变形固结分析

软土中的非达西渗流和大变形特性已为人们所认识,但能考虑土中非达西渗流的软土大变形固结理论还鲜有报道。考虑实际中的变荷载,基于土中的非达西渗流现象在拉格朗日坐标系中建立以超静孔隙水压力为变量的软土一维大变形固结模型。利用有限差分法对所建立的模型进行数值求解,并与特定条件下的解析解对比,以验证数值解的可靠性。最后着重分析非达西渗流模型参数对软土大变形固结性状的影响及大、小应变不同几何假定下非达西渗流固结性状的异同。结果表明非达西渗流模型的参数m及i1值越大,地基的固结速率就越慢;如果小应变固结理论中自重应力的计算也考虑沉积作用,此时尽管软土在大变形几何假定下的固结速率要比小变形假定下快,但大、小应变固结理论计算的地基最终沉降值相等;基于此,鉴于大变形固结理论的复杂性,此种情况下应用小变形代替大变形几何假定所引起的计算误差是可接受的。     

基于指数形式渗流考虑初始有效应力非均匀分布的软土一维非线性固结分析

结合室内固结渗透联合试验资料,考虑实际中的变荷载以及地基中初始有效应力的真实分布,建立基于指数形式渗流定律的一维非线性固结方程,并得到其差分数值解。在指数形式渗流定律退化为达西定律的前提下,将变荷载下假定初始有效应力沿深度均匀分布和固结系数保持不变的解析解与相应的差分解进行对比,验证差分解的可靠性。在此基础上,分析不同参数下的非线性固结性状。结果表明:最终有效应力与初始有效应力平均值的比值较小(≤2)时,随着渗流定律中指数的增加,在较小时间因子下固结速率会加快,而在较大时间因子下会变慢;但是随着最终有效应力与初始有效应力平均值比值的增大,固结曲线在全过程中均会表现出随着指数的增加固结速率加快的性状;初始有效应力沿深度线性增加下的固结速率要比均匀分布下的固结速率快;变荷载的加荷速率越快则固结速率也越快。此外,最终有效应力与初始有效应力平均值的比值以及描述土体非线性固结特性的参数均对非线性固结性状有较大影响。     

考虑初始孔压非均布及起始坡降的黏土流变固结解

外荷载引起的土中初始超静孔压往往沿深度非均匀分布。软黏土的流变特性以及黏性土中渗流存在起始坡降的现象也已被认识。但能同时考虑起始坡降及初始孔压非均布的软黏土流变固结解还鲜见报道。采用Merchant三元件模型描述黏土的流变特性,在初始孔压沿深度非均布条件下建立考虑起始坡降的软黏土一维流变固结控制方程及求解条件,采用拉普拉斯变换方法获得其解析解答。在验证解可靠性的基础上,开展大量的分析计算。结果表明:起始坡降(i_0)越大,渗流移动边界移动速度越慢,土层平均固结度和最终沉降量越小。土层顶面处初始超静孔压(q_T)和底面处初始超静孔压(q_B)的比值(λ)越大,移动边界下移速度越慢,土层固结速率越快,平均固结度最终稳定值越小,土层最终沉降量越大。流变模型中Kelvin体弹簧的弹性模量(E_1)和独立弹簧弹性模量(E_0)的比值(a)在固结前期对固结性状影响很小;固结后期,a值越大,土层固结速率越快,最终沉降量也越大。固结前期,黏滞系数(η_1)的变化对固结性状影响不大;固结后期,η_1值越大,土层固结速率和沉降速率越快,但η_1值的变化并不影响土层的最终沉降量。     

考虑起始水力坡降的超固结土一维非线性固结分析

考虑超固结黏性土中渗流存在的起始水力坡降及变荷载作用,建立超固结土一维非线性固结模型。利用连续条件建立固结模型的控制方程,并采用有限差分法求取该模型的数值解。在此基础上,当回弹再压缩指数ce等于压缩指数cc时,将该文差分解与考虑起始水力坡降的正常固结土非线性固结半解析解对比以验证该文解的可靠性。最后,分析起始水力坡降和超固结应力状态对黏性土固结性状的影响。结果表明:起始水力坡降导致土中超静孔压不能完全消散;当外荷载稳定值qu与起始水力坡降i0、水的重度γw及土层厚度H之积的比值小于1时,单面排水条件下渗流前锋不能至土层底面;起始水力坡降i0越大,土层沉降值越小,按孔压定义的土层平均固结度也越小;相同起始水力坡降下,超固结土层超静孔压的消散速率比正常固结土层快,超固结土层的最终沉降值小于正常固结土层,且前期固结压力越大则最终沉降量越小。     

循环荷载作用下半透水边界一维固结分析

针对单层弹性地基模型,对循环荷载进行傅立叶级数展开,由固结方程求得循环荷载作用下半透水边界地基一维固结解析解,并作固结性状分析,结果表明:在循环荷载作用下,地基中各点的有效应力并不随荷载的变化而同步变化,而是按自身规律滞后发展;半透水层渗透性越大,有效应力振幅就越大,相对的滞后时间越短;土层厚度对固结速度有着较大的影响。     

任意荷载下分数阶导数黏弹性饱和土体一维固结

将分数阶导数理论引入Kelvin–Voigt模型,来描述黏弹性饱和土体的力学行为。对饱和土体一维固结方程和分数阶导数Kelvin–Voigt本构方程实施Laplace变换,联立求解得到变换域内有效应力和沉降的解析解。采用Crump方法实现Laplace数值反演,获得了任意荷载情况下物理空间内一维固结问题的半解析解。并将指数荷载情况下分数阶导数模型退化到黏弹性情形,结果与已有文献解析解相同,验证了本研究提出任意荷载情况下分数阶导数黏弹性解的可靠性。最后,分析了相关参数对固结沉降的影响。研究表明,任意荷载情形下分数阶导数黏弹性饱和土体一维固结发展过程与黏滞系数和分数阶次有关,分数阶次越大,固结沉降发展越快;黏滞系数越大,固结沉降变化越慢;荷载变化趋势与由荷载参数变化引起的沉降变化规律是一致的,且最终沉降量一致。本研究有助于深入认识分数阶黏弹性饱和土体的固结行为。     

指数渗流定律下成层地基一维非线性固结分析

在土中渗流遵循指数形式渗流定律的背景下,考虑实际中的变荷载作用及土体初始有效应力沿深度的线性增加,建立成层软土地基一维非线性固结控制微分方程及求解条件。运用有限差分法获取其数值解并编制相应的计算程序,通过与达西渗流定律下成层地基非线性固结半解析解相对比,验证了该差分解及计算程序的可靠性。最后,结合不同工况下的某四层软土地基一维非线性固结计算实例,分别对土中的超静孔压、按孔压定义的平均固结度以及地基沉降量进行计算分析。     

基于非Darcy渗流的饱和黏土一维固结理论

 按Terzaghi饱和黏土一维固结理论得到的固结度理论值有时与实际值之间存在较大的误差,其原因之一是忽略了某些饱和黏土中孔隙水的渗流对Darcy定律的偏离。引入可以同时考虑低速渗流曲线段和较高速渗流直线段的非Darcy渗流方程,重新推导饱和黏土一维固结方程,并采用有限体积法对该方程进行数值求解。与Terzaghi饱和黏土一维固结理论解析解的对比,证明该方法的有效性。在此基础上,探讨非Darcy渗流参数对固结过程的影响。计算结果表明,非Darcy渗流延缓了饱和黏土中孔隙水压力的消散速度,故使得地基的固结速度比Terzaghi一维固结理论值要慢。同时,除固结系数外,综合直线渗流起始水力梯度i1、土层厚度H、地面荷载p0等3个参数的指标I1也是表征饱和黏土渗透固结特性的一个重要指标。最后,讨论Terzaghi一维固结理论的适用范围。     

散体–柔性桩组合和散体–刚性桩组合复合地基的固结解

 在考虑散体桩涂抹作用非散体桩对下卧层排水通道的减弱作用的基础上,依据应力条件下的平衡方程和连续条件下的固结方程,由假定的无穷级数解,推导出特征方程,进而得到散体桩–柔性桩组合和散体桩–刚性桩组合时的多元复合地基固结解析解,经与实例数值计算结果进行对比表明,该解析解基本与数值解吻合。解析解计算结果表明,土层的固结快慢与各自的渗透系数和压缩模量有关。土层渗透系数越大,刚度越大,则孔压越小,固结越快;桩径比越小,桩体刚度越大,则固结越快。说明该分析方法是可行的,且具有一定的工程应用参考价值。     

One-dimensional consolidation of over-consolidated soil under time-dependent loading

The problem of one-dimensional consolidation of over-consolidated saturated soil under time-dependent loading was studied based on semi-analytical method. The relevant computer code was developed by FORTRAN programming, and one-dimensional consolidation behavior of over-consolidated soil was investigated. It is shown that, unlike this described by traditional Terzaghi’s consolidation theory, the rate of excess pore water pressure dissipation is different from that of settlement developing. The magnitude of load and that of pre-consolidation pressure as well as the loading rate has all significant influence on consolidation. With the increasing of pre-consolidation pressure and loading rate, the rate of consolidation increases correspondingly. However, an increase in load will slow down the consolidation rate.     

One-dimensional consolidation of over-consolidated soil under time-dependent loading

The problem of one-dimensional consolidation of over-consolidated saturated soil under time-dependent loading was studied based on semi-analytical method. The relevant computer code was developed by FORTRAN programming, and one-dimensional consolidation behavior of over-consolidated soil was investigated. It is shown that, unlike this described by traditional Terzaghi’s consolidation theory, the rate of excess pore water pressure dissipation is different from that of settlement developing. The magnitude of load and that of pre-consolidation pressure as well as the loading rate has all significant influence on consolidation. With the increasing of pre-consolidation pressure and loading rate, the rate of consolidation increases correspondingly. However, an increase in load will slow down the consolidation rate.     

Analysis of one-dimensional consolidation of soft soils with non-Darcian flow caused by non-Newtonian liquid

Based on non-Darcian flow caused by non-Newtonian liquid, the theory of one-dimensional (1D) consolidation was modified to consider variation in the total vertical stress with depth and time. The finite difference method (FDM) was adopted to obtain numerical solutions for excess pore water pressure and average degree of consolidation. When non-Darcian flow is degenerated into Darcian flow, a comparison between numerical solutions and analytical solutions was made to verify reliability of finite difference solutions. Finally, taking into account the ramp time-dependent loading, consolidation behaviors with non-Darcian flow under various parameters were analyzed. Thus, a comprehensive analysis of 1D consolidation combined with non-Darcian flow caused by non-Newtonian liquid was conducted in this paper.     

循环荷载作用下软土的一维固结分析

利用受恒载作用下多层地基的一维线性固结问题的解析解,给出了受循环荷载作用下单层地基考虑压缩性变化的一维固结问题的解答。单层地基被平均划分为n层,并把固结时间和荷载也相应的划分为相同的等份,这样在每一微小的时间段内土层的一维固结问题可以处理为恒载线性问题。每一层土体的压缩、回弹状态可以根据该层的有效应力加以判断,通过选择不同的压缩系数并利用现有的多层地基土的固结理论进行分析。编制了相应的计算程序,与不考虑压缩性变化的解析解进行了比较。在证明了该方法的可靠性的基础上,分析了土体受循环荷载作用下的一维固结性状,最后给出了一个工程计算实例。     

One-dimensional consolidation of unsaturated soils considering self-weight: Semi-analytical solutions

For the newly deposited soil, the consolidation will occur under the self-weight and external load jointly if the soil is treated by the stack pre-pressure method. The soil stress caused by self-weight has a significant influence on its consolidation process no matter the soil is either saturated or unsaturated. However, the soil’s self-weight is ignored in the one-dimensional (1D) consolidation theory for unsaturated soils (Fredlund and Hasan, 1979). In this paper, we derived the semi-analytical solutions for excess pressures and normalized settlement in 1D dimensional consolidation of unsaturated soils considering self-weight. The analytical solutions were obtained by Crump’s method (Crump, 1976), through a computing program coupling the calculation of initial excess pore pressures with the inverse Laplace transform of the obtained solutions. Then, the proposed solutions are verified through a degradation case. Several 2D charts are presented to visualize the solutions, and various examples are employed to discuss the key factors that affect one-dimensional consolidation behavior of unsaturated soils when self-weight is considered. It can be found that the relative excess pore pressure will be restrained for the one-dimensional consolidation when considering self-weight.     

考虑自重应力和Hansbo渗流的饱和黏土一维弹黏塑性固结分析

考虑地基土沿深度方向变化的自重应力,引入考虑时间效应的统一硬化(UH)本构模型描述饱和黏土固结过程中的弹黏塑性变形,同时采用Hansbo渗流方程描述固结过程中的非Darcy渗流,对太沙基饱和黏土一维固结方程进行修正,并给出有限体积法数值求解格式。通过与固结试验结果对比,验证了UH模型的适用性。然后探讨了土体自重应力、黏滞性、Hansbo渗流参数、土层厚度及外荷载大小等因素对弹黏塑性固结过程的影响。结果表明:在加载初期,土体的黏滞效应在地基不排水面附近引起了超静孔压升高的现象,且土体自重应力和Hansbo渗流对此均有增强作用,但是随外荷载的增大,这一现象有所减弱;同时,考虑土体自重应力将延缓加载初期饱和黏土地基中超静孔压的整体消散速率,但加快加载中后期饱和黏土地基的固结速率;并且,随着次固结指数、土层厚度及Hansbo渗流参数的增大,饱和黏土地基中超静孔压整体消散滞后,但增大外荷载却加快了饱和黏土地基的固结速率。     

真空联合堆载预压下竖井地基固结解析解

考虑真空度沿竖井的发展是一个深度的函数,同时堆载所引起的附加应力既随时间变化也随深度变化,还考虑了地基的径竖向渗流以及扰动区土体水平渗透系数的3种变化模式,推导了真空联合堆载预压下竖井地基固结度的一个较普遍的解析解,并分析了在真空度沿竖井线性下降,堆载线性施加和附加应力沿深度梯形分布等情况下的地基固结性状。结果表明,荷载线性施加时,真空度对地基固结度有较大影响,真空度越大,沿深度衰减越慢,固结越快;而在荷载瞬时施加时,真空度对固结度没有影响。在地基井径比和水平渗透系数与竖向渗透系数之比较小时,地基的竖向渗流对地基的固结度有较大的影响。