饱和软粘土中沉桩后桩周土体固结分析

假定沉桩过程是一个平面应变圆孔扩张问题, 采用了修正剑桥模型, 给出了软粘土中沉桩过程后初始时刻超孔隙水压力沿桩径分布的解析函数, 并与Cao 等人的数值解以及Gibson 提出的公式进行了比较。根据土骨架的弹性位移特性以及水流的连续性条件, 得到了桩周土体固结的控制方程。运用分离变量法并结合边界条件以及初始条件得到了桩周土中超孔隙水压力消散的级数解答, 该解答可以作为孔压静力触探反求固结系数的一个理论依据。通过2 个算例分析了土体的应力历史以及刚度对桩侧超静孔压消散的影响;算例分析表明, 随着超固结比的增大, 归一化后的塑性区半径以及桩侧超孔隙水压力均在减小;桩侧的超静孔压消散前期较快, 后期较慢。     

内水压作用下粘弹性饱和土-隧洞衬砌相互作用

混凝土衬砌既有粘弹性性质,又有渗透性。实际工程中内水压力值由衬砌和孔隙水共同承担,该文通过引入与孔隙流体体积分数有关的应力系数合理地分配了衬砌和孔隙水分别承担的内水压力值。根据衬砌和土体界面处衬砌中流体速度和土体中流体速度相等以及应力和位移连续性条件建立了部分透水边界条件。将衬砌和土体分别视为多孔粘弹性材料和液固两相介质,采用饱和多孔介质理论和粘弹性理论,在频率域内给出了内水压力作用下粘弹性饱和土-衬砌相互作用时饱和粘弹性土位移、应力和孔压和衬砌的位移和应力解析表达式。进行了参数研究,表明:应力系数以及衬砌和土体相对渗透系数对系统动力响应影响很大。另外,应力系数合理地确定了边界衬砌和孔隙水分别承担的内水压力值。     

由爆炸引起的隧道衬砌与土体相互作用机制的数值模拟分析

为探究爆炸引起的隧道衬砌与土体相互作用机制,基于埋深15 m、含有全饱和颗粒土的单个圆形混凝土线弹性管片组成的隧道模型,对隧道内的管片衬砌与土体在中等幅值的爆破压力脉冲引起的动态变形进行了数值模拟分析.利用有限元程序Abaqus/Standard并结合二维平面应变理论进行建模,同时考虑绝对孔隙压力为零时孔隙水空化,通过精细化单元空间离散,分析了管片衬砌和土体中的应力和变形.研究结果表明:孔隙水空化引起的强非线性对土体性能具有重要影响.具体表现为:孔隙水空化能够显著降低土体的体积模量,并导致大空化带的形成,使得孔隙水从非空化状态向空化状态转变,或从空化状态向非空化状态转变,导致压缩-拉伸过程中土体的应变-应力关系呈现高度非线性,在气蚀区收缩和最终关闭期间,该非线性会在水气混合物溶液中产生高梯度和奇点.     

孔隙水压力作用下盾构隧道开挖面支护力上限研究

基于极限分析上限定理和空间离散技术,构建了适用于在饱和土体中掘进的盾构隧道开挖面上限破坏机制。在此基础上,将孔隙水压力做的功率作为一个外力功率引入上限定理的虚功率方程,通过优化计算,得到了孔隙水压力作用下盾构隧道开挖面支护力的上限解。为了证明上限解的有效性,基于数值模拟技术计算了孔隙水压力作用下隧道开挖面极限支护力的数值解,并将得到的数值解和上限解进行了对比分析,结果表明,上限解和数值解非常接近。最后,分析了参数变化对开挖面支护力和破坏面的影响,分析结果表明:孔隙水压力对支护力上限解影响明显而对开挖面破坏范围的影响不大。     

考虑疏干带非饱和土影响下基坑降水引起地面沉降的计算

大多数基坑底面低于地下水位面,在开挖前需要进行降水工程为施工提供干燥、安全的环境。由于降水历程中孔隙水压力消散和有效应力的增加,周围土体会产生固结压密,同时在基坑周围形成地下水的降落漏斗,最终导致地层的不均匀沉降,对坑周道路、建筑物及地下管线造成危害。在忽略土体的侧向变形及群井效应的前提下,引入非饱和土的有效应力原理,根据裘布依假定求出基坑降水后地下水位的降落曲线方程。采用分层总和法分别计算水位降落曲线上下非饱和土与饱和土的地面沉降量,叠加后得到最终坑周地面沉降量。结合数值模拟计算及工程实例监测数据对比分析,表明该方法具有较高的工程实用价值。     

基于有限元强度折减法路堤稳定性分析

结合工程实例,考虑了土体的渗流和孔隙水压力的消散,应用有限元数值分析软件对一段典型路堤进行了模拟计算,深入地分析了稳态渗流情况下的路堤稳定性问题。     

饱和多孔介质一维瞬态波动问题的解析分析

采用基于混合物理论的多孔介质模型,提出了饱和多孔介质一维动力响应的初边值问题。利用拉氏变换和卷积定理,分别得到了边界自由排水时在任意应力边界条件和任意位移边界条件下瞬态波动过程的解析表达。几种典型的数值算例同时给出了两类边界条件下瞬态波动过程中多孔固体的位移场、应力场和孔隙流体的速度场、压力场。结果表明,饱和多孔介质的波动过程是多孔固体和孔隙流体中以同一速度传播的两种波动的耦合过程,时效特性分析也揭示了饱和多孔介质固有的表观粘弹性性质。     

海洋环境下桩-土相互作用问题的数值解

考虑波压力对海床土体应力状态的影响,基于Biot固结理论及虚拟桩技术对海洋桩-土相互作用体系进行了数学建模,并应用FlexPDE对所建立的数学模型进行了数值求解,得到了作用在桩体上的侧向土压力、桩体周围土体有效正应力以及自由场土体相对水平位移和相对垂直位移的分布,这些结果可为海洋桩基的设计与监测提供依据。     

饱和横观各向同性分数导数黏弹性土中半封闭衬砌振动响应

在频率域内研究了饱和横观各向同性分数导数黏弹性土体中深埋圆形隧道半封闭衬砌振动响应问题。根据土体在长期沉积过程中存在各向异性的特点,将土骨架视为具有分数导数本构关系的横观各向同性黏弹性体,采用饱和多孔介质理论和弹性理论,利用衬砌内边界应力协调以及土体和衬砌界面处应力和位移连续,得到了简谐荷载作用下饱和横观各向同性黏弹性土和弹性衬砌的位移、应力和孔隙水压力解析表达式。考察了饱和经典弹性土、饱和分数导数性黏弹性土和饱和经典黏弹性土三种条件下饱和黏弹性土和衬砌各参数的影响,表明：横观各向同性面的弹性模量和衬砌厚度对系统动力响应的影响与分数导数阶数和土骨架的黏性有关;渗透系数较小时,系统存在明显的共振现象。另外,在三种条件下半封闭衬砌振动响应存在较大差异。     

K_0固结饱和土体柱孔扩张问题一种相似解法

采用能够考虑原状土体实际K_0固结特性弹塑性本构模型的屈服面方程为屈服准则,根据柱孔扩张基本平衡方程和相似解方法,对处于天然状态下的饱和土体柱孔扩张问题进行求解,推导出从零初始孔径柱孔扩张问题在小应变情况下塑性区的有效应力、超静孔隙水压力半解析解答。同时,通过算例对比分析表明:饱和土体在柱孔扩张后其塑性区超静孔隙水压力沿径向呈衰减趋势变化,其大小随着超固结比的增大而增大,孔壁周围土体有效应力下降明显,随着超固结比的增大,有效应力的减小趋势有所降低;考虑K_0固结影响的本文解答所得到的超静孔隙水压力大于修正剑桥模型的解答,扩孔完成后其周围土体有效应力下降大于后者。     

爆炸荷载作用下深埋圆形隧洞饱和土-衬砌系统的动力响应

考虑隧洞衬砌内壁对爆炸波的反射作用及其负压效应,将衬砌视为弹性介质,研究了深埋圆形隧洞饱和土-弹性衬砌耦合系统在隧洞轴线发生爆炸时的轴对称瞬态动力响应。首先,基于Biot理论和弹性理论,考虑边界条件以及弹性衬砌和饱和土接触面处的连续性条件,利用Laplace变换得到饱和土和弹性衬砌位移、应力和孔隙水压力等在Laplace变换域中的解析表达式。在此基础上,利用Laplace数值逆变换得到其时间域的动力响应,数值分析重点考察了不同隧洞模型和不同爆炸载荷模型对饱和土动力响应的影响,并进行了参数研究。结果表明:爆炸波反射产生的负压效应对饱和土体的动力响应有显著影响。同时,饱和土-壳体衬砌系统、饱和土-弹性衬砌系统和无衬砌饱和土隧洞的响应性态基本一致,但响应周期和幅度依次增大。     

粘弹性饱和土中深埋圆形隧道衬砌-土相互作用

基于Biot理论,采用渗流-力学耦合模型研究分析了粘弹性饱和土体中深埋圆形隧道衬砌-土相互作用问题,并考虑了衬砌材料的徐变特性。假定衬砌和土体完全接触,运用积分变换理论在Laplace变换域中得到了衬砌和土体接触面上的应力、变形及衬砌的薄膜力和弯矩。利用Laplace数值逆变换得到时域中的解,并由此分析讨论了衬砌和土体的相对刚度、阻尼比、以及衬砌的相对厚度对隧道衬砌与土体相互作用的影响。数值结果同时也反映了应力、变形、薄膜力和弯矩的随时间变化过程。     

Transfer matrix solutions for three-dimensional consolidation of a multi-layered soil with compressible constituents

In this paper, transfer matrix solutions for three-dimensional consolidation of a multi-layered soil considering the compressibility of pore fluid are presented. The derivation of the solutions starts with the fundamental differential equations of Biot’s three-dimensional consolidation theory, takes into account the compressibility of pore fluid in the Cartesian coordinate system, and introduces the extended displacement functions. The relationship of displacements, stresses, excess pore water pressure, and flux between the ground surface (z = 0) and an arbitrary depth z is established for Biot’s three-dimensional consolidation problem of a finite soil layer with compressible pore fluid by taking the Laplace transform with respect to t and the double Fourier transform with respect to x and y, respectively. Based on this relationship of the transfer matrix, the continuity between layers, and the boundary conditions, the solutions for Biot’s three-dimensional consolidation problem of a multi-layered soil with compressible constituents in a Laplace-Fourier transform domain is obtained. The final solutions in the physical domain are obtained by inverting the Laplace-Fourier transforms. Numerical analysis is carried out by using a corresponding program based on the solutions developed in this study. This analysis demonstrates that the compressibility of pore fluid has a remarkable effect on the process of consolidation.     

A local thermal non-equilibrium model for transversely isotropic porothermoelastic materials

This work presents a local thermal non-equilibrium (LTNE) poroelasticity model for transversely isotropic porous media and applies the model to the problem of a cylindrical hole in an infinite porous medium subjected to convective cooling on the boundary of the cavity. The LTNE thermo-poroelasticity equations are solved using Laplace transform, and numerical examples are presented to examine the effects of LTNE and material anisotropy on the pore pressure and thermal stresses around the cavity. The results show that the thermal pore pressure and the magnitudes of thermal stresses increase significantly with an increase in the thermal expansion coefficient in the transverse direction. However, the elastic modulus anisotropy alone has only a marginal effect on the thermal pore pressure and stresses. The results also confirm that the LTNE effects become more pronounced when the convective heat transfer boundary conditions with moderate Biot numbers are considered.     

饱和分数导数型粘弹性土-深埋圆形隧洞衬砌系统的动力特性

在频率域研究了分数导数型粘弹性饱和土体和深埋圆形隧洞弹性衬砌相互作用的耦合简谐振动。将土骨架视为具有分数阶导数型本构的粘弹性体,基于饱和多孔介质理论和平面弹性理论,分别给出了饱和粘弹性土、弹性衬砌简谐振动的解析解。通过弹性衬砌和饱和土接触面处的连续性条件和衬砌内边界条件,得到了饱和粘弹性土-衬砌系统的稳态动力响应,给出了衬砌和饱和粘弹性土位移、应力和孔隙压力的解析表达式。在此基础上,进行了参数研究,讨论了物理和几何参数对系统响应的影响。研究表明:饱和分数导数型粘弹性土-衬砌系统的动力响应与经典饱和弹性/粘弹性土-衬砌系统的动力响应差异很大。     

State space solution of non-axisymmetric Biot consolidation problem for multilayered porous media

In this paper, the non-axisymmetric Biot consolidation problem for multilayered porous media is studied. Taking stresses, pore pressure and displacements at layer interfaces as basic unknown functions, two sets of partial differential equations, which are independent each other, are formulated. Using Fourier expansion, Laplace transforms and Hankel transforms with respect to the circumferential, time and radial coordinates, respectively, the partial differential equations presented are reduced to the ordinary differential equations. Transfer matrices describing the transfer relation between the state vectors for a finite layer are derived explicitly in the transform space. Using the transfer matrices presented, three cases are studied for the lower surface: (1) permeable rough rigid base, (2) impermeable rough rigid base, and (3) poroelastic half space. The explicit solution in the transform space is presented. Considering the continuity condition at layer interfaces, the solutions of the non-axisymmetric Biot consolidation problems for multilayered semi-infinite porous media are presented in the integral form. The time histories of displacements, stresses and pore pressure are obtained by solving a linear equation system for discrete values of Laplace-Hankel transform inversions.     

Transfer matrix solutions to axisymmetric and non-axisymmetric consolidation of multilayered soils

Transfer matrix solutions are presented in this paper to study the axisymmetric and non-axisymmetric consolidation of a multilayered soil system under an arbitrary loading. Starting with the governing equations for consolidation problems of saturated soils, the relationship of displacements, stresses, excess pore water pressure, and flux between the points at the depth z, and on the ground surface (z = 0) is established in a transformed domain by introducing the displacement functions and using the integral transform technique. Then the transfer matrix method is used with the boundary conditions to obtain the analytical solutions in the transformed domain for the multilayered soil system. Numerical inversion of the integral transform of these analytical solutions results in the solutions for the actual problems. The numerical results for axisymmetric and non-axisymmetric Biot’s consolidation problems of a single layer and a multi-layered soil system are obtained and compared with existing results by others.     

Effects of local thermal non-equilibrium on the pore pressure and thermal stresses around a spherical cavity in a porous medium

In this paper, we use a local thermal non-equilibrium (LTNE) thermo-poroelasticity theory to investigate temperatures, pore pressure and thermal stresses around a spherical cavity in an infinite fluid saturated porous medium. In the LTNE theory, the solid and fluid phases undergo different temperature variations which induce additional pore pressure and thermal stresses. The asymptotic short time solutions of temperature, pore pressure and thermal stresses are obtained using the Laplace transform technique. Numerical results for two porous materials (clay and sandstone) are presented to examine the effects of LTNE on the temperature, pore pressure and thermal stresses around the spherical cavity. The results show that for the clay, the LTNE radial stress has a significantly larger peak value (magnitude) than that of the classical radial stress. The influence of LTNE on the pore pressure and tangential stress, however, are marginal. For the sandstone, both the radial stress (magnitude) and pore pressure are significantly increased by the LTNE effect.