An analytical solution for a jointed shield‐driven tunnel lining

This paper presents an analytical solution for the prediction of internal forces and displacements of a jointed segmental precast circular tunnel lining. The effects of joint stiffness on the performance of the tunnel lining are discussed. The ‘force method’ is used to determine the internal forces and displacements of jointed tunnel lining. Five shield‐driven tunnel cases are adopted to study the effects of joint stiffness, soil resistance, joint distribution and joint number on the internal forces and displacements of circular tunnels. Laboratory model tests are conducted to verify the proposed analytical solution. Copyright © 2001 John Wiley & Sons, Ltd.     

随机介质热弹性力学模型球坐标问题的解析解

针对随机介质热弹性力学模型,在随机韦泊分布和指数分布下,提出了一种解决随机概率分布用连续函数表示的方法,并推导出该模型球坐标问题的解析解.通过算例,对随机模型与均质模型热应力的区别做了详细研究,结果表明随机概率分布参数m对随机模型的热应力有重要影响.     

An analytical solution for the transient response of saturated linear elastic porous media

The motions of fluid and solid phases in saturated porous media are coupled by inertial, viscous and mechanical interactions as described by Biot's equations. A one-dimensional exact analytical solution of the Biot's equations for the completely general solution of the transient problem in saturated, linear, elastic, porous media is presented. The problem is solved by using the Fourier series. The transient response of porous media is shown for typical material properties of a natural granular deposit and for different degrees of viscous coupling. The analytical results show the mechanics of dispersive wave propagation in saturated porous media and they should provide a useful comparison term for the existing numerical solution methods.     

A meshless method for axisymmetric problems in continuously nonhomogeneous saturated porous media

A meshless method based on the local Petrov–Galerkin approach is proposed to analyze 3-d axisymmetric problems in porous functionally graded materials. Constitutive equations for porous materials possess a coupling between mechanical displacements for solid and fluid phases. The work is based on the u–u formulation and the incognita fields of the coupled analysis in focus are the solid skeleton displacements and the fluid displacements. Independent spatial discretization is considered for each phase of the model, rendering a more flexible and efficient methodology. Both displacements are approximated by the moving least-squares (MLS) scheme. The paper presents in the first time a general meshless method for the numerical analysis of axisymmetric problems in continuously nonhomogeneous saturated porous media. Numerical results are given for boreholes in continuously nonhomogeneous porous medium with prescribed misfit and exponential variation of material parameters in the excavation zone.     

随机介质热弹性平面轴对称问题的解析解

针对随机介质热弹性平面轴对称问题,在随机韦泊分布和指数分布两随机分布下提出了一种解决随机概率分布用连续函数表示的方法,得到了平面应力和平面应变轴对称问题的解析解。通过算例,讨论了热应力随分布参数m的变化规律,结果表明非均质热应力与均质热应力之间的差别很大,而在指数分布下这些差异很小。     

基于幂强化本构模型的轴对称圆巷弹塑性解

轴对称圆巷的弹塑性求解的关键是选择合适的屈服准则。已经有诸多学者选择Mohr-Coulomb准则、Drucker-Prager准则和Hoek-Brown准则等,进行了相应的求解。为了探讨更符合工程实际需要的准则和求解,在考虑岩石材料的应变强化效应的条件下,建立了轴对称圆巷的幂强化本构模型和基于Drucker-Prager屈服准则的幂强化-理想塑性模型,并进行了弹塑性求解。以工程实例为计算条件,将幂强化-理想塑性模型的计算结果与基于Mohr-Coulomb准则、Drucker-Prager准则的理想塑性模型和幂强化模型的计算结果分别进行了对比,分析幂强化参数对围岩弹塑性解的影响。研究表明,应变强化效应对围岩稳定性有较大影响,对于应变强化效应较强的岩石材料,采用幂强化模型分析更接近工程实际。     

饱和土半空间中圆柱形孔洞对平面P波的散射

在 Biot饱和多孔介质动力学理论的基础上,首次建立了求解饱和土半空间中圆柱形孔洞对平面 P 波散射问题的波函数展开法。首先。分析了具有圆柱形孔洞的饱和土半空间场地在平面 P 波入射下产生散射波系,并将入射波和散射波的波函数在圆柱坐标下展开。然后,引入边界条件,求出散射波函数的待定系数,从而,得到饱和土半空间中圆柱形孔洞对平面P波的散射问题的解析解。根据所得的波函数的解,可求解区域内的位移、应力的值,同时,分析了入射波频率、入射角对柱面上的应力集中因子的影响。     

既有路基下浅埋隧道开挖引起地层的位移及应力解析解

在既有公路下进行浅埋隧道开挖会引起地层产生位移,导致地表沉降。为了保证施工安全,快速精确地计算地层位移及应力,有效地控制地表沉降,对浅埋隧道的设计与施工均十分重要。在镜像法原理的基础上,引入等效模量当层法,推导出了在有上覆不同材料下浅埋圆形隧道开挖引起地层位移、应力及地表沉降的解析分布规律。计算结果表明,既有路基下开挖隧道引起地层产生的位移和应力解析解能够很好地体现上层高弹性模量路基对沉降及应力的扩散作用,可以求得隧道开挖后洞周地层包括上覆路基及下卧层中任意位置处的位移、应力以及地表沉降,为在双层地基材料中开挖浅埋隧道引起地层位移及地表沉降的计算提供了一种新的解析方法。     

A frequency-domain analytical solution of Maxwell's equations for layered anisotropic media

An analytical solution of Maxwell's equations for layered anisotropic media is presented in a form which allows estimating the sought parameters by layer stripping without round-off accumulation. The solution in each layer is reduced to the standard procedures of solving a fourth-order algebraic equation, multiplication, addition, and inversion of second-order non-singular matrices. The algorithm has no limitations on layer thickness and is applicable to both very thick and very thin layers. The new numerical code is straightforward and can be easily parallelized.     

Three-dimensional temporally dependent dispersion through porous media: analytical solution

A three-dimensional model for non-reactive solute transport in physically homogeneous subsurface porous media is presented. The model involves solution of the advection-dispersion equation, which additionally considered temporally dependent dispersion. The model also account for a uniform flow field, first-order decay which is inversely proportional to the dispersion coefficient and retardation factor. Porous media with semi-infinite domain is considered. Initially, the space domain is not solute free. Analytical solutions are obtained for uniform and varying pulse-type input source conditions. The governing solute transport equation is solved analytically by employing Laplace transformation technique (LTT). The solutions are illustrated and the behavior of solute transport may be observed for different values of retardation factor, for which simpler models that account for solute adsorption through a retardation factor may yield a misleading assessment of solute transport in ‘‘hydrologically sensitive’’ subsurface environments.     

Explicit meshfree solution for large deformation dynamic problems in saturated porous media

In this paper a new methodology to simulate saturated soils subjected to dynamic loadings under large deformation regime (locally up to 40% in equivalent plastic strain) is presented. The coupling between solid and fluid phases is solved through the complete formulation of the Biot’s equations. The additional novelty lies in the employment of an explicit time integration scheme of the \(u-w\) (solid displacement–relative fluid displacement) formulation which enables us to take advantage of such explicit schemes. Shape functions based on the principle of maximum entropy implemented in the framework of Optimal Transportation Meshfree schemes are utilized to solve both elastic and plastic problems.     

软土一维非线性固结近似解析解

软土非线性固结变形计算目前还主要依赖于数值方法,致使非线性固结理论的工程应用受到极大限制。引入经典的e-lg?' 和e-lgkv非线性关系,在自重应力均匀分布假定下通过变量代换并利用迭代法给出压缩指数Cc与渗透指数Ck比值不等于1时的非线性固结近似解析解。在Cc /Ck趋近1时本文解与其等于1时的差分解及精确解相差无几。但如果Cc /Ck值偏离1,该近似解会存在一定偏差,且偏差值会随Cc /Ck值偏离1的程度和外荷载增加而逐渐增大。在一般工程荷载作用下,如果Cc /Ck值介于0.9～1.1之间,本文解的平均固结度与差分解间最大偏差在2%左右。当Cc /Ck值在0.75～1.25之间时,本文解的平均固结度与差分解最大偏差在5%左右。如果Cc /Ck值在0.5～1.5之间,本文解的平均固结度与差分解间最大偏差在10%左右。当外荷载一定时,土层的非线性固结速率会随着Cc /Ck值的增大而减慢。如果Cc /Ck<1,土层的非线性固结速率会随外荷载的增大而加快;相反,如果Cc/Ck>1,土层的非线性固结速率会随外荷载增大而减慢。     

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.     

二维饱和多孔介质因点汇诱发比奥固结的解析解

给出了有限二维饱和多孔介质因点汇诱发的Biot固结的一个解析解。其中假设多孔介质为均匀各向同性和线弹性,假设孔隙压力场符合第1类边界条件,数学模型采用可压缩多孔介质模型。利用傅里叶和拉普拉斯变换及相应反演获得了双重无穷项级数和形式的精确解。然后特别探讨了定流量点汇诱发的稳态解析解,并用文献现有解析解进行了验证。所提出的解析解适合于验证数值解,并可用于深入分析有限二维多孔介质的流-固耦合行为。     

An analytical solution of one-dimensional consolidation for soft sensitive soil ground

An analytical solution of one-dimensional consolidation for soft sensitive soil ground is presented. The moving boundary is introduced to indicate the notable change of consolidation behaviour of sensitive soil with the increase of stress level. It is assumed that the soil structure of the upper subsoil gradually destroys downwards with the dissipation of pore pressure, and the coefficient of consolidation as well as the coefficient of permeability of the upper subsoil become small, which hinders the dissipation of pore pressure of the lower subsoil. The consolidation degree curve obtained from the present solution is found to lie between the two curves obtained from Terzaghi one-dimensional consolidation solution with the parameters of the undisturbed soil and the remolded soil. The calculated results provide a new explanation for a general phenomenon in the consolidation of soft sensitive soil ground, as that for high loadings the consolidation is longer than for small ones. It should be pointed out from this study that both the deep mixing method and the long vertical drains methods are effective techniques for improving deep sensitive soil ground. Copyright © 2004 John Wiley & Sons, Ltd.     

热-水-力共同作用下圆形洞室弹塑性解析解

基于已有的工作和Mohr-Coulomb屈服准则,建立了热-水-力三场共同作用下的圆形洞室弹塑性解析解,并分别在单力场、热-力场、水-力场、热-水-力场以及改变介质强度参数的条件下计算和比较了围岩中的应力分布、变化及塑性区范围。结果显示,温度场使得塑性区半径有所减小,但总的来看温度作用不明显;与仅有力作用时相比,孔隙水压力使得塑性区半径、径向应力和切向应力有较大幅度增长。     

基于一致性理论的Drucker-Prager材料弹黏塑本构模型

系统地论述了一致性理论的主要内容,推导了相关的黏塑性切线模量,并在前人工作的基础上研究了类Hoffman材料的推广条件及其一般性的推广方法;将线性Drucker-Prager模型(简称D-P)推广到一致性的黏塑性模型;给出了推广后模型的向后欧拉算法的有限元离散列式;最后将数值算例和试验成果进行对比,验证了一致性的线性D-P模型的有效性.     

An analytical solution for modeling thermal energy transfer in a confined aquifer system

A mathematical model is developed for simulating the thermal energy transfer in a confined aquifer with different geological properties in the underlying and overlying rocks. The solutions for temperature distributions in the aquifer, underlying rock, and overlying rock are derived by the Laplace transforms and their corresponding time-domain solutions are evaluated by the modified Crump method. Field data adopted from the literature are used as examples to demonstrate the applicability of the solutions in modeling the heat transfer in an aquifer thermal energy storage (ATES) system. The results show that the aquifer temperature increases with time, injection flow rate, and water temperature. However, the temperature decreases with increasing radial and vertical distances. The heat transfer in the rocks is slow and has an effect on the aquifer temperature only after a long period of injection time. The influence distance depends on the aquifer physical and thermal properties, injection flow rate, and injected water temperature. A larger value of thermal diffusivity or injection flow rate will result in a longer influence distance. The present solution can be used as a tool for designing the heat injection facilities for an ATES system.     

An analytical solution for the settlement of stone columns beneath rigid footings

This paper presents a new approximate solution to study the settlement of rigid footings resting on a soft soil improved with groups of stone columns. The solution development is fully analytical, but finite element analyses are used to verify the validity of some assumptions, such as a simplified geometric model, load distribution with depth and boundary conditions. Groups of stone columns are converted to equivalent single columns with the same cross-sectional area. So, the problem becomes axially symmetric. Soft soil is assumed as linear elastic, but plastic strains are considered in the column using the Mohr–Coulomb yield criterion and a non-associated flow rule, with a constant dilatancy angle. Soil profile is divided into independent horizontal slices, and equilibrium of stresses and compatibility of deformations are imposed in the vertical and horizontal directions. The solution is presented in a closed form and may be easily implemented in a spreadsheet. Comparisons of the proposed solution with numerical analyses show a good agreement for the whole range of common values, which confirms the validity of the solution and its hypotheses. The solution also compares well with a small-scale laboratory test available in the literature.     

土体应变局部化现象的理论解析

引起土体失稳的应变局部化现象是在特定应力状态下,土体本构产生的分叉特性。基于有限变形理论推导了应变局部化产生的三维解析解。基于应变局部化的理论解析,分析了轴对称和平面应变条件下应变局部化现象在弹塑性硬化阶段的存在性以及剪切带的方向性。 理论分析表明,在轴对称条件下,土体应变局部化产生于土体应力-应变的软化阶段,而平面应变条件下,土体应变局部化一般出现在应力-应变的硬化阶段,其剪切带方向角的理论预测与Arthur等[1]建议值较为一致。