饱和土中球空腔的瞬态动力响应

采用工程上通用的饱和土力学模型,考虑流体与固全之间的耦合作用,利用Ｌａｐｌａｃｅ变换求解了饱和土中球空腔的瞬态动力响应问题,得到了变换域内的解析解,借助数值Ｌａｐｌａｃｅ换求解了饱和土中球空腔瞬态动力响应的位移、应力及孔压的变化规律,为分析地下结构瞬态动力响应提供了一种有效的方法,模型符合工程实际,有一定的工程应用价值。     

One-, two-, and three-dimensional solutions for counter-current steady-state two-phase subsurface flow

This paper derives analytical solutions for steady-state one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) two-phase immiscible subsurface flow for a counter-current problem. Since the governing equations are highly nonlinear, 2-D and 3-D derivations are generally difficult to obtain. The primary purpose for the solutions is to test finite difference/volume/element computer programs for accuracy and scalability using architectures ranging from PCs to parallel high performance computers. This derivation is accomplished by first solving for the saturation of water in terms of a function that is a solution to Laplace’s equation to achieve a set of partial differential equations that allows some degree of latitude in the choice of boundary conditions. Separation of variables and Fourier series are used to obtain the final solution. The test problem consists of a rectangular block of soil where specified pressure is applied at the top and bottom of the sample, and no-flow boundary conditions are imposed on the sides. The pressure at the top of the sample is a step function that allows the testing of adaptive meshing or concentration of grid points in action zones.     

Transient responses of porous media under moving surface impulses

Three-dimensional transient responses of porous media under moving surface impulses of finite frequency components are theoretically studied. We discuss three free-surface stiffness conditions, such as fully permeable—‘open pore’, fully impermeable—‘closed pore’, and partially permeable boundaries, that are not explicitly discussed before. The transient responses of the solid vertical displacement and the pore fluid pressure triggered by the moving impulses on the surface are particularly investigated in different typical surface stiffness, moving impulse velocities, material permeabilities and impulse peak frequencies. It is concluded that the R1 surface wave carries the strongest energy as that for stationary source configurations. Moreover, it is more sensitive to surface stiffness condition than body waves represented in the responses of the corresponding wave forms of obvious different amplitudes and arrival time. Furthermore, the apparent velocity of the moving impulse pointing toward the fixed receiver may cause ‘blue shift’ in frequency. The higher velocity triggers more obvious frequency shift. For the moving impulse of low peak frequency, this shift becomes much serious. The lateral velocity of the moving impulse to the receiver may also twist the received wave forms, especially for the impulse of low peak frequency.     

条形荷载下梯度非均匀非饱和土的动力响应分析

基于多孔介质混合物理论, 建立了梯度非均匀非饱和土地基模型, 研究了条形荷载作用下梯度非均匀非饱和土地基的动力响应问题. 通过傅里叶积分变换和Helmholtz矢量分解原理, 获得频域内非饱和土地基动力响应问题的通解, 结合回传射线矩阵法和边界条件, 求解获得了非均匀非饱和土层中位移、应力以及孔隙压力的计算列式. 假设沿深度方向梯度非均匀非饱和土的物理力学性质按幂函数连续变化, 通过数值傅里叶逆变换得到了非均匀非饱和土地基中的应力、位移以及孔隙压力等物理量的数值解, 分析讨论了土体非均匀性对非饱和土介质动力响应的影响规律. 结果表明: 土体非均匀性显著改变了非饱和土中竖向位移、正应力和孔隙压力在其深度方向上的振动模态, 其中孔隙气压在其深度方向的振动频率随着梯度因子的增加而不断增大, 波峰值不断靠近地表处附近; 竖向位移随着梯度因子的增大不断减小; 正应力和孔隙水压随着梯度因子的增大先增大后减小, 并且土体非均匀程度越高, 正应力与孔隙水压的幅值越大.      

剪胀性砂土边界面模型的研究

剪胀性对于砂土,尤其是中密以及密实砂土,是一个非常显著的特性。相变线是剪胀性砂土的特征曲线,能够反映砂土的围压以及初时孔隙比对变形特性的影响。本文在边界面塑性理论的框架内,把相变状态参量引入到剪胀方程以及塑性硬化模量中,建立了一个能够描述砂土剪胀性以及循环特性的本构模型。本模型采用一套参量可以模拟不同初时孔隙比、不同围压、排水(或不排水)条件下单调(或循环)加载的应力-应变特性。验证表明本模型数值计算与试验结果相吻合。     

非饱和土-隧道系统动力响应计算的波函数法

针对非饱和地基土中埋置隧道的三维动力响应计算问题, 提出了波函数法.采用无限长的Flügge薄壁圆柱壳模拟圆形隧道衬砌,采用流、固、气组成的三相介质模拟非饱和地基土体.分别采用分离变量法以及Helmholtz矢量分解定理求解薄壁圆柱壳的振动控制方程与非饱和土的波动方程.根据隧-土交界面与地表面处的应力、位移以及孔隙流体压力等边界条件,利用平面波与柱面波的转换性质,实现了隧道内作用单位简谐载荷时隧道衬砌与土体系统动力响应的耦合求解.通过与既有单相弹性介质2.5维有限元-边界元法、两相饱和多孔介质2.5维有限元-边界元法以及三相非饱和介质Pip in Pip半解析法的计算结果进行对比, 验证了本文计算方法的可靠性. 最后,基于该方法, 通过算例分析了不同饱和度下非饱和土-隧道系统的动力响应特征.结果表明, 饱和度对土体动位移与超孔隙水压力的幅值响应有较大影响.该方法的非饱和地基土参数退化后,也可用来计算和分析饱和地基土或单相弹性地基土与隧道系统的动力响应.      

Hyperelastic Multiphase Porous Media with Strain-Dependent Retention Laws

This article presents poroelastic laws accounting for a retention behavior dependent also on porosity, as suggested by experimental evidence. Motivated by the numerical formulation of the corresponding boundary-value problem presented in a companion article, these constitutive equations employ displacements and fluid pressures as primary variables. The thermodynamic admissibility of the proposed rate laws for stress and fluid contents is assessed by means of symmetry and Maxwell conditions obtained from the Biot theory. In the case of strain-dependent saturation, the two elasticity tensors describing the drained response in saturated and unsaturated conditions, respectively, are proven to be in general not coincident, with their difference depending on capillary pressure and porosity. Furthermore, it is shown that besides the stress decomposition proposed by Coussy, also the stress split proposed by Lewis and Schrefler is consistent with the Biot framework. The former decomposition is obtained for retention laws depending only on capillary pressure, as expected. The Lewis–Schrefler split is proven to be consistent with retention models depending also on porosity. In these developments, the compressibility of all the phases is taken into account, in order to assess the thermodynamic consistency of an extension of the Biot’s coefficient to partially saturated anisotropic porous media.     

黏弹性饱和多孔介质中圆柱孔洞的频域响应

研究了无限黏弹性饱和多孔介质中圆柱孔洞(有衬砌)表面受轴对称简谐荷载和流体压力 作用下的频域响应问题. 引入Carcione提出的本构模型来描述介质的流变和松弛性质. 考 虑衬砌和介质的相对渗透性，孔洞处于半封闭状态，边界半透水. 引入两个势函数，在频域 中得到了应力、位移和超孔隙水压力响应解答. 并进行了算例分析，讨论了反映介质黏弹 性性质的最小质量因子，反映孔洞边界半透水性质的渗透性参数及衬砌和介质的相对刚度对 问题的影响. 分析结果表明：以上参数对圆柱孔洞的频域响应有很大影响.     

Several contributions to soil compactibility induced by cyclic loading test

To investigate the soil compactibility during the cyclic loading, three different kinds of paddy field soils were prepared so as to clarify interrelationships among stress amplitude ratio, bulk density, soil water content and pore water pressure. The presetting values of specimen include the soil water content(percent dry basis) and bulk density of 25% d.b. and 1.1 Mg/m³ respectively. The relation between the number of cyclic loading and axial strain exhibited an asymptotically increasing trend, converging toward a specific value for each experimental condition. Possible effect caused by elastic–plastic characteristics could be recognized, when axial strain for 0.5 Hz excitation becomes greater than the one of 1.0 Hz under same stress amplitude ratio. When the stress amplitude ratio took 0.1, the absolute value of axial strain of 0.5 Hz was greater than the one of 1.0 Hz, whereas its decreasing trend was recognized in the sequence of silt, clay and silty sand. The qualitative relations between pore water pressure and number of cyclic loading were also examined to scrutinize the effect of effective water pressure to the soil compactibility.     

裂隙挤喷流对孔隙介质排水体积模量的影响

实际岩石比如沉积形成的岩石往往是裂隙和孔隙并存的孔隙介质. 由于扁状的裂隙与近似球形或圆管形的孔隙具有不同的可压缩性,当孔隙介质受压时,液体会从易压缩的裂隙中挤出流入不易压缩的孔隙中,这种挤喷流会引起弹性模量的频散和能量的耗散. 着重研究了裂隙挤喷流和液体可压缩性对孔道变形的影响,推导出了动载荷作用下排水体积模量的表达式. 与挤喷流相关的裂隙附加柔度会引起排水体积模量随频率变化,使得孔隙介质呈现黏弹性. 频率越高,模量的实部越大,岩石抵抗变形的能力越强. 而模量的虚部体现了挤喷流对能量的耗散. 裂隙密度主要决定模量频散的幅度以及能量耗散的强度,且裂隙密度越大,模量频散幅度越大,能量耗散也越强. 裂隙的纵横比主要决定模量频散速率最快或能量耗散最强时对应的特征频率. 若孔隙介质中不含有裂隙,即裂隙密度是0时,排水体积模量退化为Biot理论中的排水体积模量.     

Boundary-layer analysis of propagating mode II cracks in porous elastic media

The steady advance of semi-infinite cracks in porous elastic media is examined in the limiting cases of very slow and very rapid propagation. The low-speed limit is the elastic solution representing fully-drained behavior, with no boundary layers present. In the high-speed limit, two boundary layers are identified: one along the crack face and another centered at the crack tip. The zero-order outer solution is the elastic solution representing fully-undrained behavior, with both boundary layers acting as zones of transition to the effectively drained conditions at the crack itself. Closedform expressions are derived for the stresses and pore pressure within the crack-tip boundary layer. The true stress intensity factor is found to be reduced by an amount related to the disparity between the drained and undrained Poisson's ratios of the medium.     

非饱和土半空间Lamb问题及能量传输特性

地球表面绝大多数土层处于非饱和状态, 故采用传统饱和两相介质理论进行动力学分析时, 结果往往与实际情况不符. 针对这一问题, 本文以非饱和半空间作为研究对象, 基于连续介质力学和多孔介质理论, 考虑非饱和多孔介质中各相的质量守恒方程、动量守恒方程、本构方程以及有效应力原理等基本方程, 建立了以骨架位移、孔隙水压力和孔隙气压力为基本未知量的动力学控制方程. 针对非饱和半空间表面在竖向集中简谐荷载作用下的动力学响应及能量传输问题, 建立了频域内经典Lamb问题的轴对称计算模型, 采用Helmholtz分解法, 通过引入势函数Φ和Ψ表示骨架的位移分量, 结合本构方程获得了不同边界条件下半空间表面位移场和能量场等物理量的解析解答, 并通过数值算例对荷载参数(激振频率)、材料参数(饱和度、渗透系数)等影响因素进行了分析与讨论. 结果表明: (1)饱和度的升高或者激振频率下降, 都会提高非饱和半空间的表面位移幅值; (2)当渗透系数下降至一临界值时, 地表位移幅值会趋于一极限值, 并且透水(气)边界与不透水(气)边界条件下渗透系数的影响表现出明显的差异性.      

Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces

An elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces is developed on the basis of soil behavior observed in laboratory tests. This theory is applicable to general three-dimensional stress conditions, but the parameters required to characterize the soil behavior can be derived entirely from results of isotropic compression and conventional drained triaxial compression tests. The theory is shown to predict soil behavior under various loading conditions with good accuracy. Of special interest is its capability of predicting soil behavior under drained as well as undrained conditions over a range of confining pressures where the behavior changes from that typical of dense sand to that typical of loose sand. Work-hardening as well as work-softening is incorporated in the theory.     

Rheology on the drawing zone in glass spinning

This paper describes the work carried out to investigate the pore pressures occurring in secondary consolidation. A theoretical approach and an experimental technique was developed in order to conduct the study. By considering compression to occur only due to water leaving the soil it was possible to derive an expression for the dissipation of pore pressure in the secondary phase. By further simplified assumptions which are based on experimental observations, the above general solution was reduced to a simple formula which predicted the observed behaviour of pore water pressures during secondary consolidation.     

Nonlinear motion equations for a non-Newtonian incompressible fluid in an orthogonal coordinate system

This paper describes the work carried out to investigate the pore pressures occurring in secondary consolidation. A theoretical approach and an experimental technique was developed in order to conduct the study. By considering compression to occur only due to water leaving the soil it was possible to derive an expression for the dissipation of pore pressure in the secondary phase. By further simplified assumptions which are based on experimental observations, the above general solution was reduced to a simple formula which predicted the observed behaviour of pore water pressures during secondary consolidation.     

Pore water pressures in secondary consolidation

This paper describes the work carried out to investigate the pore pressures occurring in secondary consolidation. A theoretical approach and an experimental technique was developed in order to conduct the study.By considering compression to occur only due to water leaving the soil it was possible to derive an expression for the dissipation of pore pressure in the secondary phase. By further simplified assumptions which are based on experimental observations, the above general solution was reduced to a simple formula which predicted the observed behaviour of pore water pressures during secondary consolidation.     

Rhéologie particulière des solutions de polymères en millieus poreux

This paper describes the work carried out to investigate the pore pressures occurring in secondary consolidation. A theoretical approach and an experimental technique was developed in order to conduct the study. By considering compression to occur only due to water leaving the soil it was possible to derive an expression for the dissipation of pore pressure in the secondary phase. By further simplified assumptions which are based on experimental observations, the above general solution was reduced to a simple formula which predicted the observed behaviour of pore water pressures during secondary consolidation.     

Comparison of the time-temperature superposition of the relaxation modulus and time-to-break of preswollen gels

This paper describes the work carried out to investigate the pore pressures occurring in secondary consolidation. A theoretical approach and an experimental technique was developed in order to conduct the study. By considering compression to occur only due to water leaving the soil it was possible to derive an expression for the dissipation of pore pressure in the secondary phase. By further simplified assumptions which are based on experimental observations, the above general solution was reduced to a simple formula which predicted the observed behaviour of pore water pressures during secondary consolidation.     

An extension of Reiner’s “Deborah Number” concept to a wide field of rheological investigations

This paper describes the work carried out to investigate the pore pressures occurring in secondary consolidation. A theoretical approach and an experimental technique was developed in order to conduct the study. By considering compression to occur only due to water leaving the soil it was possible to derive an expression for the dissipation of pore pressure in the secondary phase. By further simplified assumptions which are based on experimental observations, the above general solution was reduced to a simple formula which predicted the observed behaviour of pore water pressures during secondary consolidation.