低应变下变阻抗薄壁管桩动力响应频域解析解

管桩低应变完整性检测时,桩顶一点受到瞬态集中荷载的作用,其动力响应问题是一个三维波动问题。基于三维波动理论,建立了任意段变阻抗薄壁管桩动力响应的计算模型和波动方程,结合初边值条件,采用Laplace变换法求得了该波动方程的频域解析解,采用Fourier逆变换求得了时域响应。将计算结果与三维有限元结果进行了对比分析,解析解的计算结果和三维有限元结果较为接近,两者在入射波峰、缺陷反射峰和桩底反射峰处都较为吻合,两种方法位移响应曲线基本相同。给出了桩顶不同点的动力响应,并探讨了高频干扰问题。对变截面桩和变模量桩的动力响应特性进行了分析。     

利用任意三个互不平行的截面进行三维应变计算的一种改进算法

进行有限应变测量是构造地质学的一项重要任务,而如何通过平面二维应变计算三维应变椭球就成为有限应变测量中的一个重要问题．现行的由任意三个互不平行的平面上进行计算三维应变椭球需要首先要进行相容性和误差调整,造成了计算过程的复杂性。本文在前人工作的基础上,利用数学方法,将相容性调整和应变椭球系数的计算合二为一,从而简化三维应变的计算。     

软岩巷道弹塑性变形的理论分析

本文采用莫尔－库仑屈服准则和非关联塑性流动法则分析了轴对称软岩巷道的变形规律。从轴对称平面应变问题的基本方程出发，导出了软岩巷道弹塑性变形的位移理论解答，并给出了现有应力与位移理论解的适用条件。通过实例计算结果表明，本文得出的位移理论解与有限元数值解相当吻合。     

小浪底工程边坡稳定性有限元流变分析

采用西原流变模型,给出了初应变法的有限元解析式,编写了平面有限元程序,并对黄河小浪底水利工程出口边坡进行了稳定性分析。     

砂井地基等效平面问题研究

建立并解析了考虑井阻效应、径竖向组合渗流以及土体水平位移的砂墙平面固结等应变模型。以综合考虑各种因素的Tang Xiao-wu均质砂井地基固结理论为前提,根据砂井地基任意深度处平均超静孔压不变的条件,给出了砂井单元向砂墙单元转换的等效公式,使得复杂的砂井空间问题转化为简单的平面问题。采用此种方法,只需调整地基渗透系数,极大地减少了有限元网格中的砂井单元数,降低了计算规模。通过算例,比较了平面应变模型与PDSS（平面应变-空间渗流）情况下的数值解,验证了等效变换公式的有效性和可靠性。     

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。     

平面应变条件下M-C材料屈服时的中主应力公式

基于Mohr-Coulomb准则,通过引入罗德角参数及Mohr-Coulomb准则平面应变等效广义Mises准则,推导了平面应变条件下材料屈服时的中主应力公式,并给出其与基于SMP准则（Spatial Mobiliaztion Piane）的平面应变中主应力公式之间的关系式。对平面应变条件下的条形地基进行了有限元数值模拟,计算结果验证了所推导的平面应变条件下M-C材料屈服时的中主应力公式的正确性,其公式为岩土体的强度和变形分析、中主应力的强度效应的进一步研究,以及Mohr-Coulomb准则的修正提供了有力的基础。     

一种竖井地基竖墙化等效计算方法

考虑井阻作用,推导了等应变条件下竖墙地基水平向固结解析解,并与等应变条件下的竖井地基径向固结解析解进行比较,得到竖墙地基平面应变问题和竖井地基轴对称问题之间的等效方法。该方法转换公式简单,且能保证两种情形下同一深度处平均孔压在任一时刻相等,确保了转换为平面应变有限元分析的准确性。     

起伏地形电导率连续变化的三维激电数据有限元数值模拟

为了模拟起伏地形条件下的地电体,这里给出了电导率连续变化的三维激电数据有限元数值模拟方法.在模拟过程中,采用超松弛预条件共轭梯度法解线性方程组,并探讨了模拟的计算精度和效率问题.最后,对起伏地形下的地电体进行模拟,验证了本文算法的正确性和可行性.     

软土隧道横向抗震分析的简化响应位移法

响应位移法能够反映软土隧道在地震荷载作用下的动力反应特性,是一种简便实用的隧道抗震设计简化分析方法。以方形截面隧道为例,采用地层－结构整体动力有限元方法,验证了响应位移法的准确性与合理性;为了简化响应位移法的计算过程,基于平面应变假定,采用弹性理论的复变函数方法推导了土弹簧刚度的解析表达式,并与有限元解进行了对比分析。将土弹簧刚度的解析表达式应用到响应位移法的计算中,同时采用地层剪应力及自由场地震反应位移的简化计算模式,将简化后的响应位移法和整体动力有限元法进行了对比分析,验证了简化方法的可行性。     

新型卧式土工平面应变仪研制

平面应变仪是一种开发较早但至今尚不完善的一种土工试验仪器,随着国家基础设施建设的发展,平面应变试验及试验方法在许多领域得以应用,显示出了平面应变试验在工程设计和研究中的重要性。通过回顾国内外平面应变仪的发展,提出了开发一种新型的土工平面应变三轴仪的思路,以实现更科学、更精确地进行复杂应力加载条件下土平面应变试验的研究。以此为目的,从压力室结构、加载系统及控制量测系统等方面提出了相应的改善措施,开发了一种新型的土工平面三轴仪。并通过重塑黄土的平面应变试验及改进的真三轴仪平面应变试验对比、以及平面应变试验强度参数与常规三轴试验强度参数对比分析,验证了所研制的新型卧式土工平面应变仪的合理性和研制思路的正确性。最后,通过对该平面应变仪应变试验的黄土破坏特性与改进真三轴平面应变试验的黄土破坏特征的对比分析,验证了本文所开发的平面应变仪在描述土体应变局部化问题的合理性。     

Modelling strain localization in granular materials using micropolar theory: numerical implementation and verification

Implementation and applications for a constitutive numerical model on F‐75 silica sand, course silica sand and two sizes of glass beads compressed under plane strain conditions are presented in this work. The numerical model is used to predict the stress versus axial strain and volumetric strain versus axial strain relationships of those materials; moreover, comparisons between measured and predicted shear band thickness and inclination angles are discussed and the numerical results compare well with the experimental measurements. The numerical model is found to respond to the changes in confining pressure and the initial relative density of a given granular material. The mean particle size is used as an internal length scale. Increasing the confining pressure and the initial density is found to decrease the shear band thickness and increase the inclination angle. The micropolar or Cosserat theory is found to be effective in capturing strain localization in granular materials. The finite element formulations and the solution method for the boundary value problem in the updated Lagrangian frame (UP) are discussed in the companion paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Variational principles and finite element method for stress analysis of porous media

A number of variational principles are established in this paper for the stress analysis of porous media with compressible constituents. A three-dimensional finite element method is proposed based on the variational principle. The finite element method thus established is applied to the study of the temperature, deformation and flow field associated with the water-flood technique in secondary recovery projects for oil exploration. In the study model, the layout of injection wells and production wells is considered to have a regular pattern where symmetry conditions exist. The injection fluid diffuses slowly into the formation through a vertical crack which is initially generated by an explosion. The problem is analysed by a plane strain formulation with the effects of heat conduction and convection included.     

A large strain finite element formulation for one dimensional membrane elements

A finite element formulation suitable for large strain analysis of one-dimensional membranes is described which has applications to the analysis of problems in soil mechanics involving reinforced earth. The finite element equations, which are derived for a plane strain iso-parametric element of arbitrary order, are cast in the familiar small displacement form, but with a modified material stiffness matrix. In this formulation, full account is taken of element rotations during each load step, an effect which is important when stresses cease to be insignificant when compared with the material modulus. The method is illustrated with reference to a large displacement test problem which has a known closed form solution. An example is included demonstrating the application of the formulation to the analysis of a reinforced unpaved road.     

Analysis of triaxial ellipsoids: Their shapes, plane sections, and plane projections

A method is presented for the determination of a triaxial ellipsoid (such as a strain ellipsoid)from three nonparallel plane sections of the ellipsoid. The sections need be neither orthogonal nor central sections of the ellipsoid. Measurement errors are used to adjust the observed plane ellipses so that they are exact sections of the nearest true ellipsoid, whose dimensions and orientation are then found by solution of a system of six linear equations. A solution of the inverse problem is also presented: given a triaxial ellipsoid with known orientation, to determine the shape and orientation of the ellipse on a plane section. The problem is solved by expanding the equation of an ellipsoid with rotated coordinates, then setting one dimension to zero. Also, a method is presented for the projection of a triaxial ellipsoid onto a plane surface. This is solved by taking the derivative of the ellipsoid equation in the direction of the normal to the plane surface.     

非饱和土拟二维平面应变固结问题的解析计算方法

基于Fredlund非饱和土一维固结理论,建立了二维平面应变条件下的固结方程组,并得到了单层非饱和土平面应变条件下的解析解。基于相关理论,假设体变系数和渗透系数都为常量,同时考虑到瞬时加载条件下,沿着土体深度方向上产生均匀或者线性分布的初始超孔隙压力,建立了二阶二元偏微分方程组。求解时,引入函数方法来降低方程的阶数,然后通过分离变量法获得方程的通解。在此基础上,结合一个针对单面排水条件下二维平面应变问题案例,通过与数值解对比,验证了所提方法的正确性。并采用所提方法计算获得了二维平面下超孔隙水压力、气压力沿垂直和水平方向消散的等时线,通过计算对比,分析了不同线性分布情况下,初始超孔隙压力对固结消散过程的影响。研究结果表明：初始超孔隙压力的不同分布对超孔隙气压力消散的影响几乎可以忽略,而对超孔隙水压力消散的影响更大。     

Generalized solution to the anisotropic Mandel's problem

Existing solutions to Mandel's problem focus on isotropic, transversely isotropic, and orthotropic materials, the last two of which have one of the material symmetry axes coincide with the vertical loading direction. The classical plane strain condition holds for all these cases. In this work, analytical solution to Mandel's problem with the most general matrix anisotropy is presented. This newly derived analytical solution for fully anisotropic materials has all the three nonzero shear strains. Warping occurs in the cross sections, and a generalized plane strain condition is fulfilled. This solution can be applied to transversely isotropic and orthotropic materials whose material symmetry axes are not aligned with the vertical loading direction. It is the first analytical poroelastic solution considering mechanical general anisotropy of elasticity. The solution captures the effects of material anisotropy and the deviation of the material symmetry axes from the vertical loading direction on the responses of pore pressure, stress, strain, and displacement. It can be used to match, calibrate, and simulate experimental results to estimate anisotropic poromechanical parameters. This generalized solution is capable of reproducing the existing solutions as special cases. As an application, the solution is used to study the responses of transversely isotropic and orthotropic materials whose symmetry axes are not aligned with the vertical loading direction. Examples on anisotropic shale rocks show that the effects of material anisotropy are significant. Mandel-Cryer's effects are highly impacted by the degree of material anisotropy and the deviation of the material symmetry axes from the vertical loading direction.     

Determination of the principal axes of elliptic cross sections in strain ellipsoids by a variational method

A method is presented for the determination of the shape and orientation of the ellipse on a central plane section across a triaxial ellipsoid (such as a strain ellipsoid) of known orientation and magnitude. Conditional extremal values of longitudinal strain (λ) are obtained in the plane section and these are the principal axes of the strain ellipse. In solving this variational problem, the arbitrary cosntants (two undetermined Lagrange multipliers) are found to have physical meaning in themselves as proved in a complementary geometric solution. The two roots of the first constant directly determine the magnitude of the principal axes of the strain ellipse in terms of the normal to the cross section. The two arbitrary constants together define shear strains and orientation of these axes.

Strain computation uses simple, single-line equations in either frames of strained or unstrained states.     

Mohr–Coulomb MiniCLoE model Uniqueness and localization studies,links with normality rule

This paper is devoted to a parametric study of a plane Mohr–Coulomb CLoE model. As CLoE models are designed with a consistency condition, it is possible to define a normality condition and to study its consequences. The positiveness of the second order work which implies the uniqueness of the solution of a small strain boundary value problem is studied firstly. Then the localization criterion is also studied. It is proved that normality has consequences similar to those for classical elasto plastic models. However if induced anisotropy is introduced in the hypoplastic CLoE model, some conclusions are no longer true. Finally plane strain experimental data are used to identify the parameters of the model. Copyright © 2002 John Wiley & Sons, Ltd.     

二连盆地吉尔嘎朗图凹陷剥蚀量恢复及其对油气藏的影响

吉尔嘎朗图凹陷是二连盆地重要的产油基地之一,早白垩世腾格尔组和赛罕塔拉组沉积末期经历了两次强烈的抬升 剥蚀,沉积地层剥蚀量的恢复对油气成藏评价有重要意义。文章基于钻井泥岩声波时差和镜质组反射率数据对二连盆地吉 尔嘎朗图凹陷腾格尔组和赛罕塔拉组的剥蚀量进行了计算,恢复了其原始沉积厚度及埋藏过程。研究结果表明：研究区腾 格尔组和赛罕塔拉组沉积后受构造反转的控制都经历了不同程度的剥蚀,腾格尔组的剥蚀厚度约为243~1933 m,赛罕塔拉 组的剥蚀厚度约为95~290 m。剥蚀量厚度展布明显受不同方向、不同尺度断层在构造反转期的差异活动性影响,靠近西北 边界断层的罕尼构造带剥蚀量相对较大,向东南缓坡带逐渐减小。区内不同构造部位剥蚀量的差异对油气成藏有直接影 响,断陷区及后期反转控制的大沉积、强烈剥蚀区,烃源岩层生烃时间长。而构造反转形成的与构造走向一致的隆升带的 剥蚀卸压有利于促使油气沿NE断裂面发生垂向和侧向运移,并在断裂面两侧有利的圈闭位置成藏。