Dynamic responses of unsaturated half‐space soil to a moving harmonic rectangular load

The problem of the dynamic responses of a semi‐infinite unsaturated poroelastic medium subjected to a moving rectangular load is investigated analytical/numerically. The dynamic governing equations are obtained with consideration of the compressibility of solid grain and pore fluid, inertial coupling, and viscous drag as well as capillary pressure in the unsaturated soil, and they can be easily degraded to the complete Biot's theory. Using the Fourier transform, the general solution for the equations is derived in the transformed domain, and then a corresponding boundary value problem is formulated. By introducing fast Fourier transform algorithm, the unsaturated soil vertical displacements, effective stresses, and pore pressures induced by moving load are computed, and some of the calculated results are compared with those for the degenerated solution of saturated soils and confirmed. The influences of the saturation, the load speed, and excitation frequency on the response of the unsaturated half‐space soil are investigated. The numerical results reveal that the effects of these parameters on the dynamic response of the unsaturated soil are significant.     

A closed form analytical solution for two‐dimensional plane strain consolidation of unsaturated soil stratum

This paper discusses the excess pore‐air and pore‐water pressure dissipations and the average degree of consolidation in the 2D plane strain consolidation of an unsaturated soil stratum using eigenfunction expansion and Laplace transformation techniques. In this study, the application of a constant external loading on a soil surface is assumed to immediately generate uniformly or linearly distributed initial excess pore pressures. The general solutions consisting of eigenfunctions and eigenvalues are first proposed. The Laplace transform is then applied to convert the time variable t in partial differential equations into the Laplace complex argument s. Once the domain is obtained, a simplified set of equations with variable s can be achieved. The final analytical solutions can be computed by taking a Laplace inverse. The proposed equations predict the two‐dimensional consolidation behaviour of an unsaturated soil stratum capturing the uniformly and linearly distributed initial excess pore pressures. This study investigates the effects of isotropic and anisotropic permeability conditions on variations of excess pore pressures and the average degree of consolidation. Additionally, isochrones of excess pore pressures along vertical and horizontal directions are presented. It is found that the initial distribution of pore pressures, varying with depth, results in considerable effects on the pore‐water pressure dissipation rate whilst it has insignificant effects on the excess pore‐air pressure dissipation rate. Copyright © 2015 John Wiley & Sons, Ltd.     

The evolution of pore pressure fields around standard and ball penetrometers: influence of penetration rate

Rate effects are examined in the steady pore pressure distribution induced as a result of penetration of standard and ball penetrometers. The incompressible flow field, which develops around the penetrometer is used to define the approximate soil velocity field local to the penetrometer tip. This prescribes the Lagrangian framework for the migration of the fluid saturated porous medium, defining the advection of induced pore pressures relative to the pressure‐monitoring locations present on the probe face. In two separate approaches, different source functions are used to define the undrained pore fluid pressures developed either (i) on the face of the penetrometer or (ii) in the material comprising the failure zone surrounding the penetrometer tip. In the first, the sources applied at the tip face balance the volume of fluid mobilized by the piston displacement of the advancing penetrometer. Alternately, a fluid source distribution is evaluated from plasticity solutions and distributed throughout the tip process zone: for a standard penetrometer, the solution is for the expansion of a spherical cavity, and for the ball penetrometer, the solution is an elastic distribution of stresses conditioned by the limit load embedded within an infinite medium. For the standard penetrometer, the transition from drained to undrained behavior occurs over about two orders of magnitude in penetration rate for pore pressures recorded at the tip (U1) and about two‐and‐a‐half orders of magnitude for the shoulder (U2). This response is strongly influenced by the rigidity of the soil and slightly influenced by the model linking induced total stresses to pore pressures. For the ball penetrometer, the transition from drained to undrained behavior also transits two‐and‐a‐half orders of magnitude in penetration rate, although it is offset to higher dimensionless penetration rates than for standard penetration. Copyright © 2012 John Wiley & Sons, Ltd.     

Permeable piles: An alternative to improve the performance of driven piles

This paper investigates the soil displacements and excess pore pressures induced by driven piles using a combined 3D finite and infinite element approach. The analyses are compared with analytical evaluations and field measurements. Consolidation analysis is conducted to illustrate the variation in pore pressure with time. A technique of drilling drainage holes on the pipe pile is proposed in this paper to accelerate the dissipation of pore pressure to improve the performance of displacement piles. It has been noticed that optimal performance of piles can be obtained by assigning openings in piles within the bottom 50% of the pile length.     

Short-crested wave-induced soil response in a porous seabed of infinite thickness

Waves reflecting obliquely from structures establish short-crested waves which are conducive to scour of the bed adjacent to them. The pore pressures and effective stresses induced by this wave system are derived analytically for an unsaturated, anisotropic soil matrix of infinite depth in a three-dimensional domain. Verification is available by the solutions being readily reduced to the two-dimensional cases of the progressive and standing wave, for which some closed-form solutions are available. It is shown that wave obliquity is coupled with soil permeability. The effects of wave obliquity, relative water depth, soil stiffness and soil permeability on wave-induced pore pressure are discussed in detail.     

Transient response of a circular cavity in a poroelastic medium

This paper considers the transient response of a pressurized long cylindrical cavity in an infinite poroelastic medium. To obtain transient solutions, Biot's equations for poroelastodynamics are specialized for this problem. A set of exact general solutions for radial displacement, stresses, pore pressure and discharge are derived in the Laplace transform space by using analytical techniques. Solutions are presented for three different types of prescribed transient radial pressures acting on the surface of a permeable as well as an impermeable cavity surface. Time domain solutions are obtained by inverting Laplace domain solutions using a reliable numerical scheme. A detailed parametric study is presented to illustrate the influence of poroelastic material parameters and hydraulic boundary conditions on the response of the medium. Comparisons are also presented with the corresponding ideal elastic solutions to portray the poroelastic effects. It is noted that the maximum radial displacement and hoop stress at the cavity surface are substantially higher than the classical static solutions and differ considerably from the transient elastic solutions. Time histories and radial variations of displacement, hoop stress, pore pressure and fluid discharge corresponding to a cavity in two representative poroelastic materials are also presented.     

Probabilistic infinite slope analysis

Research activity in the mechanics of landslides has led to renewed interest in the infinite slope equations, and the need for a more general framework for giving insight into the probability of failure of long slopes involving non-homogeneous vertical soil profiles and variable groundwater conditions. This paper describes a methodology in which parameters such as the soil strength, slope geometry and pore pressures, are generated using random field theory. Within the limitations of the infinite slope assumptions, the paper clearly demonstrates the important “seeking out” effect of failure mechanisms in spatially random materials, and how “first order” methods that may not properly account for spatial variability can lead to unconservative estimates of the probability of slope failure.     

Analytical solution for one‐dimensional consolidation of unsaturated soils using eigenfunction expansion method

This paper introduces an exact analytical solution for governing flow equations for one‐dimensional consolidation in unsaturated soil stratum using the techniques of eigenfunction expansion and Laplace transformation. The homogeneous boundary conditions adopted in this study are as follows: (i) a one‐way drainage system of homogenous soils, in which the top surface is considered as permeable to air and water, whereas the base is an impervious bedrock; and (ii) a two‐way drainage system where both soil ends allow free dissipation of pore‐air and pore‐water pressures. In addition, the analytical development adopts initial conditions capturing both uniform and linear distributions of the initial excess pore pressures within the soil stratum. Eigenfunctions and eigenvalues are parts of the general solution and can be obtained based on the proposed boundary conditions. Besides, the Laplace transform method is adopted to solve the first‐order differential equations. Once equations with transformed domain are all obtained, the final solutions, which are proposed to be functions of time and depth, can be achieved by taking an inverse Laplace transform. To verify the proposed solution, two worked examples are provided to present the consolidation characteristics of unsaturated soils based on the proposed method. The validation of the recent results against other existing analytical solutions is graphically demonstrated. Copyright © 2013 John Wiley & Sons, Ltd.     

半空间饱和土中圆形衬砌对弹性压缩波的散射

借助于Biot 波动理论和弹性波的传播理论,采用复变函数和多级坐标法,对半空间饱和土中圆形衬砌结构对弹性稳态压缩波的散射问题进行求解和分析。利用一个半径很大的圆弧来逼近半空间直边界,将待解问题转化为稳态弹性压缩波在一个大圆孔和一个弹性衬砌结构的散射问题。通过引入势函数,将饱和土的Biot波动方程和衬砌的弹性波动方程解耦成Helmholtz 方程,借助复变函数级数展开便可以预先写出该组Helmholtz方程的通解。然后,通过引用复变量,把饱和土和衬砌结构中的应力、位移及孔压用设定的势函数表示出来,再利用半空间饱和土和衬砌结构的连续性条件和近似直边界的圆弧边界和衬砌内边界的边界条件求解出该组势函数的特解。最后,利用势函数的特解,得到饱和土中的位移,应力和孔压及衬砌结构的位移和应力;变换不同的参数求解衬砌结构内外边界的动应力和孔压的集中系数,通过对算例结果的分析得出一系列有益的结论。     

多级循环泵注水力压裂模拟实验研究

超深储层地层起裂压力较高,水力压裂受现场泵注设备的限制严重,文中重点研究了大尺度水力压裂物模实验水泥样品尺寸（762 mm×762 mm×914 mm）在循环和常规两种泵注条件下的起裂扩展和声发射规律。实验结果显示,（1）相对于普通泵注,采用循环泵注方式进行水力压裂可以有效降低起裂压力,类似于单轴和三轴循环加载岩石力学行为,都是由于循环加载引起疲劳损伤;（2）对于螺旋射孔完井方式,水力压裂裂缝只从最薄弱射孔处起裂,一旦起裂后其他射孔孔眼很难再开启,水力压裂现场应合理选择分段距离和簇间距,实现储层改造效率最优化;（3）循环泵注水力压裂存在Kaiser效应（当加载应力到前次加载最高应力值时出现的声发射信息）。因孔隙流体扩散到岩石并导致孔隙压力的局部上升,破坏模式仍然可以由摩尔圆表示。研究成果对循环泵注条件的裂缝扩展规律研究以及发展新型压裂改造技术具有重要意义。     

沁水盆地煤样静水压力下渗透率实验及模型分析

为研究沁水盆地煤样渗透率演化规律,构建了煤样渗透率测定的瞬态压力脉冲法实验装置,使用N2和CO2在实验室开展了3种试验条件的渗透率测定,应用Connell模型对实验结果进行分析,并讨论了模型预测值和实验值之间差别的原因。结果表明,（1）在恒定孔压变围压条件下渗透率随有效应力增大而减小;在等有效应力条件下,渗透率随孔压增大而减少;在恒定围压变孔压条件下,随孔压增大,渗透率呈先减小后变大的趋势。（2）运用Connell模型预测的恒定围压变孔压条件的渗透率值大于实验值,原因可能是由于裂隙压缩性系数和吸附应变系数存在估计误差。通过开展实验室渗透率实验和模型分析,对指导实验室内二氧化碳封存和气体驱替实验及其模拟研究具有借鉴意义。     

应力、应变与构造超压关系及构造超压控制因素分析

构造应力场引起岩石变形，并使孔隙流体压力发生变化，形成异常流体压力。根据对前人岩石力学实验结果的分析，应力与流体压力间为非线性关系，试件的体积应变与孔隙流体压力间为反相关线性关系。构造异常压力和其他异常压力的形成具有共性特征，都可以抽象为由于孔隙体积和流体体积的相对变化这一个因素。由此也可以将异常压力形成的一般过程概括为：孔隙疲充体饱和的岩石，体积缩小会使饱和流体排出，体积增大会使其周围的流体流入，如果渗透率足够大，流体流动顺畅，这一过程流体压力的变化相对较小。在岩石渗透率较小时，由于流量的限制，流体在这一过程中会产生明显的压力变化，形成异常压力。对于符合达西渗流的流体，异常压力计算时，流量可以用孔隙体积相对变化量替代。这样可以描述构造变形等固体变形所引起的异常压力。根据异常压力的极大值为研究区相应深度的最小主应力和岩石抗张强度之和的特点，可以预测流体封存箱箱壁的最小厚度要求，分析流体封存箱形成的基本条件。构造活动过程中，岩石孔隙的体积应变速率和封存箱壁的渗透率直接控制异常流体压力的大小。高应变速率和低的封存箱壁渗透率是形成构造超压的主要因素。     

Finite element analysis of land subsidence above depleted reservoirs with pore pressure gradient and total stress formulations

The solution of the poroelastic equations for predicting land subsidence above productive gas/oil fields may be addressed by the principle of virtual works using either the effective intergranular stress, with the pore pressure gradient regarded as a distributed body force, or the total stress incorporating the pore pressure. In the finite element (FE) method both approaches prove equivalent at the global assembled level. However, at the element level apparently the equivalence does not hold, and the strength source related to the pore pressure seems to generate different local forces on the element nodes. The two formulations are briefly reviewed and discussed for triangular and tetrahedral finite elements. They are shown to yield different results at the global level as well in a three‐dimensional axisymmetric porous medium if the FE integration is performed using the average element‐wise radius. A modification to both formulations is suggested which allows to correctly solve the problem of a finite reservoir with an infinite pressure gradient, i.e. with a pore pressure discontinuity on its boundary. Copyright © 2001 John Wiley & Sons, Ltd.     

基于MCMC法的非饱和土渗流参数随机反分析

基于贝叶斯理论,以马尔可夫链蒙特卡罗方法（Markov chain Monte Carlo Simulation, MCMC法）的自适应差分演化Metropolis算法为参数后验分布抽样计算方法,建立利用时变测试数据的参数随机反分析及模型预测方法。以香港东涌某天然坡地降雨入渗测试为算例,采用自适应差分演化Metropolis算法对时变降雨条件下非饱和土一维渗流模型参数进行随机反分析,研究参数后验分布的统计特性,并分别对校准期和验证期内模型预测孔压和实测值进行比较。研究结果表明,DREAM算法得到的各随机变量后验分布标准差较先验分布均显著减小;经过实测孔压数据的校准,模型计算精度很高,校准期内95%总置信区间的覆盖率达到0.964;验证期第2～4个阶段95%总置信区间的覆盖率分别为0.52、0.79和0.79,模型预测结果与实测值吻合程度较高。     

An analytical solution for the consolidation around a driven pile

Field studies have shown that the driving of a displacement pile into cohesive soil generates large excess pore pressures in the vicinity of the pile. These pore pressures are often larger than the effective overburden pressure and facilitate the installation of the pile. The subsequent increase in bearing capacity of the pile is largely controlled by the dissipation of the excess pore pressures and a consequent increase in the effective stresses acting on the pile. The paper presents a closed formanalytical solution for the radial consolidation of the soil around a driven pile, assuming that the soil skeleton deforms elastically. This assumption is examined in the light of the predicted effective stress changes in the soil and is shown to lead to, a realistic model for the decay of pore pressure near the pile with time after driving. Although the solution may be applied to any initial distribution of excess pore pressure, attention is focussed on that due to the expansion of a cylindrical cavity in an ideal elastic, perfectly plastic soil. The resulting logarithmic variation of excess pore pressure with radius is considered to be close to that generated around a pile as a result of driving. In addition to giving estimates of the time needed for a driven pile to achieve its maximum strength, the solution may also be used in the analysis of pressuremeter tests to provide in-situ measurements of the coefficient of consolidation of the soil.     

Theory of Volumetric Moving Dislocation in Poroelastic Halfspace and Characterization of Magma Intrusion Events

The undrained change in pore fluid pressure that accompanies dike intrusion may be conveniently represented as a moving volumetric dislocation. The concept of a dilation center was developed to represent the field of undrained pressure change in a saturated linear elastic medium. Since instantaneous pore fluid pressures can be developed to a considerable distance from the dislocation, monitoring the rate of pressure generation and subsequent pressure dissipation in a fully coupled manner enables certain characteristics of the resulting dislocation to be defined. The principal focus of this study is the application of dislocation-based methods to analyze the behavior of the fluid pressure response induced by intrusive dislocations in a semi-infinite space, such as dike intrusion, hydraulic fracturing and piezometar insertion. Partially drained pore pressures result from the isothermal introduction of volumetric moving pencil-like dislocations described as analogs to moving point dislocation within a semi-infinite saturated elastic medium. To represent behavior within the halfspace, an image dislocation is positioned under the moving coordinate frame fixed to the front of the primary moving dislocation, to yield an approximate solution for pore pressure for constant fluid pressure conditions. Induced pore pressures are concisely described under a minimum set of dimensionless parameter groupings representing propagation velocity, and relative geometry. Charts defining induced pore fluid pressure at a static measuring point provide a meaningful tool for determining unknown parameters in data reduction. Two intrusive events at Krafla, Iceland are examined using the type curve matching techniques. Predicted parameters agree favorably with field data.     

支挡结构上的水土压力特性试验研究

针对当前水土压力计算中很少考虑土自身性质对其影响的研究现状,以自制试验槽为研究工具,通过使用3种不同渗透性土样进行的支挡结构上水土压力测试研究,对比了水土压力实测值和由水土压力分算、水土压力合算得到的理论计算值,分析了孔隙水压力和土压力的变化规律。由试验结果可以得到,由水土压力合算得到结果偏小,但在一定条件下尚可以接受,在发生主动位移情况下墙后土体会产生负超孔压,渗透系数影响着负超孔压的消散和孔隙水压力的传递程度,并进一步影响支挡结构上水土压力的分布情况。由试验结果推知,当土体渗透系数小到一定程度时,水土压力合算的方法是合理的。     

破裂面水压对砂板岩峰后强度影响的试验研究

在MTS815 Flex Test GT岩石力学试验系统上进行不同围压下砂板岩三轴压缩全过程试验,并测试破裂岩体试样峰后的天然含水状态强度。对试样破裂面施加4级动水压力和静水压力,分别获得天然含水状态和每级水压下破裂岩体试样的强度。试验结果及分析表明,水对破裂岩体强度影响的作用机制主要表现在饱和软化与水压弱化两方面,即饱和软化作用不随水压的增减而变化和水压力对强度的弱化作用随水压升高而线性增大;主要影响强度参数中的黏聚力,对内摩擦系数的影响较小;裂隙岩体中静水压力的弱化作用强于动水压力。试验与分析还获得水对裂隙岩体的饱和软化以及静水压力综合作用的定量表达,并对这些成果的工程应用进行讨论。     

Effects of driving and subsequent consolidation on behaviour of driven piles

The effects and simulation of driving of structures (piles) into saturated soil media are discussed, and procedures for numerical simulation of driving are proposed. Consolidation caused by changes in stresses and in pore water pressures in the soil mass due to the driving is solved by using a finite element procedure. The changes in stresses and pore water pressures due to driving are obtained on the basis of the cavity expansion approach, and are introduced in the finite element procedure as initial conditions. Stresses and deformations around a pile as consolidation proceeds are plotted and related to the quantities such as a wall friction, and point and total loads relevant to analysis and design.     

Consolidation around a point heat source

When a heat source such as a canister of radioactive waste is buried in a saturated soil the temperature changes that occur will cause the pore water to expand a greater amount than the voids of the soil. The temperature change will thus usually be accompanied by an increase in pore pressure. If the soil is sufficiently permeable these pore pressures will dissipate. This paper develops an analytic solution for the fundamental problem of a point heat source buried deep in a saturated soil.