A Method for Derivation of Compression Equation and Value of Degradation Exponent for Structured Soils

A method to derive a general equation for compression of structured soils is presented. It is shown that the general equation leads to the equation of compression for structured soils as proposed by Liu and Carter (Geotechnique 49(4):43–57, 1999). Using the compression characteristics of the structured and remolded soil, an equation is developed to determine a unique value for the structure degradation exponent term of the Liu-Carter equation. This equation is used to obtain the value of the structure degradation exponent of the Liu-Carter equation from the compression behavior of undisturbed and remolded Mexico City clay. The value of the exponent is used in the Liu-Carter equation to predict the compression behaviour of the clay. Excellent agreement is observed between predictions and experimental data.     

粗粒料的单参数级配方程及其适用性研究

提出了一个适用于描述粗粒料连续级配的单参数级配方程，研究了方程的基本性质，分析了方程对连续级配粗粒料两种典型级配曲线的反映能力，利用多个土石坝工程粗粒料级配曲线验证该方程的适用性，推导了方程表示良好级配的参数范围。结果表明：提出的级配方程能够描述反S形和双曲线形两种典型的粗粒料级配曲线。方程参数? 的范围为(0，1)，当? 值较小时，方程表示的级配曲线为双曲线形；当? 值较大时，方程表示的级配曲线为反S形。提出的级配方程对土石坝工程中各种粗粒料的级配具有较好的适用性。与分形级配方程和连续级配方程相比，该单参数级配方程更具有实用价值。当? >0.13时，方程表示的级配为良好级配，该范围的确定可以为筑坝粗粒料的级配设计提供依据。     

An Analytical Investigation of a Variable-Compliance-type Constitutive Equation

Summary. A constitutive equation is proposed in which the compliance is assumed to monotonically increase as a load is applied. The primary feature of the constitutive equation is that the equation can be applied to various loading conditions such as constant stress rate, constant strain rate, creep, or relaxation. The second feature is that the equation has exact solutions under many loading conditions. The present paper shows the exact solutions for the constitutive equation and investigates the mutual relationships between the exact solutions for the different loading conditions. The third feature is that it is comparatively easy to find the constants in the constitutive equation. The present paper shows how to solve the constitutive equation for the constants, and the constants for some native Japanese rocks. The constitutive equation used in the present paper is extremely simple. Therefore, the equation can be easily implemented in almost any FEM code. It is likely that additional terms of the constitutive equation will prove necessary for practical usage. However, additional terms can be found very easily by finding higher-order approximations of experimental data.     

A generalized advection dispersion equation

This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of the operator are presented. The operator is used to generalize the advection dispersion equation. The generalized equation differs from the standard equation in four properties. The generalized equation is solved via the variational iteration technique. Some illustrative figures are presented.     

Models of geochemical systems from mixture theory: Diffusion

The problem of diffusion of a geochemical component in a natural environment is investigated from the standpoint of mixture theory. The approach here differs from previous diffusion studies in that both the conservation of mass and momentum for the component is considered. This approach avoids parameterizing the diffusive flux in the mass equation by Fick's law. It is shown that when the momentum equation is included with the mass equation, the linear approximation for the space-time distribution of a solute in a binary system is the telegraph equation, well known from electrodynamics. This contrasts with the diffusion equation, which relies on introducing the Fick's law assumption into the conservation of mass equation for the solute. Solutions for both the diffusion and telegraph equation models are obtained and compared for the case of migration of a minor component into the seabed when the sediment-water interface concentration is a prescribed function of time. Although the stationary, steady state solutions of the telegraph and diffusion equations are identical, the former has a transient solution in which fluctuations propagate at finite speed. The Fickian assumption, in contrast, requires an infinite speed of propagation.     

三维溶质运移问题的分步广义迎风解法

对对流占优的三维溶质运移问题提出了分步广义迎风解法，首先利用Ｎ．Ｎ．Ｙａ－ｎｅｎｋｏ对水动力弥散方程分步求解的思想，将原来的一个定解问题分解为两个定解问题即对流定解问题和扩散定解问题，对对流定解问题采用广义迎风对偶单元均衡法求解，对扩散定解问题采用一般的Ｇａｌｅｒｋｉｎ有限元法求解，不仅避免了用一般有限元法和有限差分法求解对流占优的地下水水质数学模型时常出现数值弥散和过量问题，而且避免了求节点速度这一步，节省运算步骤，对井点的浓度变化给出了更合适的求解方法。     

偶数阶微分方程周期解的存在性

讨论了高阶Duffing型微分方程周期解的存在性,此类方程是二阶Duffing型方程的推广,具有重要的理论意义。利用同胚延拓和不动点方法,构造处理了一类比文献所述条件更弱的Duffing型方程。通过构造一个先验界,利用Schaud-er不动点方法得到解的存在性结论,所使用的方法能广泛适用于各种边界条件。     

激光测速粒子对复杂流动的响应研究——Ⅰ颗粒非恒定运动数学模型及其数值方法

流体激光测速的精度与示踪粒子的跟随特性即流体中异质粒子的非恒定运动特性密切相关。首先对粒子非恒定运动方程进行了探讨,着重考虑了在高颗粒雷诺数时该方程的修正问题,简要分析了该方程的数学属性,并构造了这类方程的数值计算方法。分析表明,高颗粒雷诺数下的粒子非恒定运动方程为非线性奇异积分方程,而当颗粒雷诺数小于1时,则线性化为第二类渥尔特拉(Volterra)积分方程。以几种均匀流中球形小颗粒的非恒定运动为算例,计算结果与其解析解及有关实验数据的比较表明,数值方法具有良好的计算精度。     

岩体节理抗剪强度的巴顿方程评价(英文)

根据实验室的抗剪强度试验, 本文对巴顿方程进行新的讨论并提出新的评价方法。实验室完成了一组岩体结构面的抗剪强度 (, )试验后, 利用抗剪强度资料来模拟巴顿方程的三个参数 (, JRC, JCS)在理论上可以用偏导数求解, 但由于巴顿方程的特殊性, 实际上是不可能的。     

Estimation of base settlement from the surface subsidence profile: Plane‐field of displacements

According to Litwiniszyn's theory, subsidence over a yielding underground geo‐structure is seen as a stochastic (Markov) process. This theory leads to a single, linear parabolic differential equation of diffusion–convection type (D–C equation) in the plane‐field of displacements. If the boundary conditions for the governing D–C equation are prescribed along the shear bands, i.e. at ‘moving’ boundaries—it has been observed from small‐scale model experiments that the subsiding process is always confined between a set of inclined shear bands—then the resulting equation is nonlinear. The inverse problem for this nonlinear equation, i.e. the problem of determining the base displacement using the surface subsidence as ‘initial’ condition, is ill‐posed and estimation of the base displacement from a given surface subsidence profile is not possible. In the present paper the domain of integration of the governing D–C equation is fixed (and bounded)—the boundaries are not evolving. Hence, the governing equation remains linear parabolic. The advantage is that this linear differential equation admits an analytical solution, under the trap‐door mechanism assumption, that enables a direct solution to the inverse problem. Copyright © 2008 John Wiley & Sons, Ltd.     

非线性弹性地基上矩形薄板的主参数共振

分析非线性弹性地基上受参数激励小挠度矩形薄板的主参数共振问题,由冯卡门方程和伽辽金方法得到系统的非线性振动方程,它是杜分-马休型方程,应用非线性振动的多尺度法得到平均方程。数值计算结果表明：阻尼系数、地基系数、几何参数对主参数共振曲线影响明显。     

各向异性介质相速度、群速度与克利斯托费尔方程

本文详细回顾了克利斯托费尔方程(Christoffel)的推导.在此基础上,提炼出时空域和频率域克利斯托费尔方程,前者可作正演计算介质的相速度,后者可计算介质的群速度.并计算了横观各向同性介质的相速度和群速度.最后对无损耗各向异性介质的相速度和群速度的关系进行了简单讨论.     

Reynolds控制方程下粗糙节理渗流空腔模型研究

在研究节理的渗流时,渗流控制方程对节理渗流分析结果具有显著影响。首先介绍了节理渗流分析中的控制方程：Navier-Stokes方程、Stokes方程、Reynolds方程和立定定理,并分析了各控制方程在节理渗流分析中的适用性。以Reynolds方程作为渗流分析控制方程,建立了粗糙节理渗流空腔模型。然后以节理试件为研究对象,在实测节理三维表面形貌并计算隙宽分布后,分别进行相同渗流边界条件下的室内渗流试验和空腔模型计算,得到节理在不同接触状态下的渗流量实测值和计算值,并分别将计算结果与立方定理下的空腔模型、将整个节理简化为光滑平行板模型的立方定理以及速宝玉经验公式的计算结果进行比较,结果表明,Reynolds方程下的节理渗流空腔模型计算结果与实测值最为吻合,可以较为准确地反映节理的渗流情况。同时,根据Reynolds方程下空腔模型得到的渗流流量分布可以呈现节理渗流的曲折现象,为从本质上研究节理渗流特性奠定了理论基础。     

Modelling water retention and volume change behaviours of unsaturated soils in non-isothermal conditions

This study presents a simple approach to modelling the effect of temperature on the soil–water retention curves (SWRCs) of deformable soils and takes into consideration the following two aspects: (1) the effect of temperature on the liquid–gas interfacial tension and (2) temperature-induced deformation of the soil skeleton. The first aspect, the temperature effect, can be modelled using an equation proposed by Grant and Salehzadeh [18], but the second aspect is generally neglected in the literature. To quantify the thermo-hydro-mechanical (THM) deformation of unsaturated soils (i.e., the second aspect mentioned above), a simple volume change equation, referred to as the non-isothermal SFG volumetric equation, is proposed on the basis of the original SFG framework [37]. A three-dimensional THM yield surface in the space of net mean stress, suction and temperature is presented here. The proposed volume change equation is integrated into the non-isothermal SWRC by means of a simple hydro-mechanical coupling law [38]. The performance of the non-isothermal SFG volumetric equation and the non-isothermal SWRC equation is investigated through several numerical examples. A number of experimental results reported in the literature are employed to confirm the validity of the proposed non-isothermal SFG volume change equation and the non-isothermal SWRC equation.     

三维地电断面电阻率测深有限元数值模拟

用有限单元法进行了电导率分块均匀的三维点源电场电阻率测深的数值模拟.首先给出了三维构造中点源电场的边值问题、变分问题; 然后, 用有限单元法求解变分问题, 将区域剖分成六面体单元, 在单元中进行三线性函数插值, 将变分方程化为线性代数方程组; 最后解方程组, 得各节点的电位值, 进而计算出地表的视电阻率.对几例较典型的地电模型进行试算, 结果表明本方法是行之有效的      

地下水中多组分平衡化学模型计算方法

将质量作用方程和质量均衡方程组成平衡化学模型,用Newton-Raphon迭代法并辅以曲线逼近法求解多组分系统中全部物种的平衡浓度和活度,本文计算了一套10组分的淡地下水中59种物种的浓度。     

一种新的凝析气藏无因次产能评价方程

凝析气藏在衰竭开发过程中存在复杂的相态变化,凝析油的析出使得地层呈现出油气两相混合渗流状态.针对目前凝析气藏无因次产能评价方程的研究较少的现状,在凝析气藏拟稳态流入动态方程的基础上,利用泰勒级数展开、多项式回归等一系列解析方法建立了一种新的凝析气藏无因次产能评价方程.首先对拟稳态流入动态方程中的拟压力函数定积分进行泰勒级数展开,然后利用稳态定理和多项式回归方法求解出泰勒展开式的各项系数,最后通过解析方法得到了凝析气藏的无因次产能评价方程.应用实例表明,该无因次产能方程与实际系统试井数据基本吻合,能够较好地描述凝析气藏的油气两相流入动态;无因次产能评价法所得到无阻流量比常规干气法低,且考虑高速效应的无因次产能评价法所得到的无阻流量要大于忽略高速流动的无因次产能评价法所得到的结果.      

On the stress-force-fabric equation in triaxial compressions: Some insights into the triaxial strength

The strength of granular materials during triaxial compression is investigated via a grain scale analysis in this paper. A 3D Discrete Element Method (DEM) program provides the triaxial strength data and helps to validate the micromechanical analysis. Some standard methods in statistics are employed first to quantitatively examine the assumptions made when deriving the stress-force-fabric (SFF) equation. After careful validation, a more concise format for the SFF equation is proposed for triaxial compressions. With this SFF equation, the strength is found to be jointly contributed by the magnitudes of the contact force anisotropy and fabric anisotropy. The influence of the initial void ratio, confining pressure and loading direction on the development of contact force anisotropy and fabric anisotropy is examined and presented. With similar techniques, the “force” term in the SFF equation is further decoupled, and an equation is obtained such that it explicitly links the contact force term with the friction coefficient between grains, a tensor defined as a statistic of the normal contact forces and a tensor defined as a statistic of the mobilisation status of contacts. Based on this equation, another equation regarding the stress ratio of granular assembly is obtained, and it clearly indicates two sources that contribute to the phenomenological friction nature of granular assembly. These two sources are caused by the contact force at the grain scale. The first is the anisotropy of the average normal contact forces, and the second is the mobilisation of contacts.     

状态方程法在渗流-应力耦合场求解中的应用

提出了一种计算土体渗流-应力耦合场的状态方程法。按平面应变问题,将描述渗流-应力耦合的平面固结方程进行空间离散,并用状态方程表示了有限元控制方程。利用牛顿-柯特斯公式,导出了当前时间步节点位移向量与前一时间步位移向量之间关系的递推公式。算例表明：状态方程法解决土体渗流-应力耦合问题与传统差分法相比的优势在于用较少的机时即可得到较为精确的解。