考虑椭圆化地层变形影响的浅埋隧道弹性解

研究了浅埋隧道周围地层最终变形的计算问题,提出了考虑椭圆化变形影响的计算模型和浅埋隧道位移边界条件,并利用Airy应力函数得到了该问题弹性解析解。在此基础上,通过算例分析了椭圆化变形对竖向位移和水平位移的影响。结果表明,椭圆化变形对水平位移的影响远大于竖向位移。     

An analytical solution for deforming twin‐parallel tunnels in an elastic half plane

The interaction between twin‐parallel tunnels affects the tunnelling‐induced ground deformation, which may endanger the nearby structures. In this paper, an analytical solution is presented for problems in determining displacements and stresses around deforming twin‐parallel tunnels in an elastic half plane, on the basis of complex variable theory. As an example, a uniform radial displacement was assumed as the boundary condition for each of the two tunnels. Special attention was paid to the effects of tunnel depth and spacing between the two tunnels on the surface movement to gain deep insight into the effect of the interaction between twin‐parallel tunnels using the proposed analytical approach. It is revealed that the influence of twin tunnel interaction on surface movements diminishes with both the increase of the tunnel depth and the spacing between the two tunnels. The presented analytical solution manifests that, similar to most of the existing numerical results, the principle of superposition can be applied to determine ground deformation of twin‐parallel tunnels with a certain large depth and spacing; otherwise, the interaction effect between the two tunnels should be taken into account for predicting reliable ground movement. Copyright © 2014 John Wiley & Sons, Ltd.     

基于边界配点法浅埋隧道开挖引起 周围土体变形的分析

对于浅埋隧道施工引起土层位移的解析解,其边界条件的数学处理上比较困难,因此实际工程的应用中受到限制。为解决这一缺陷,基于弹性力学的Airy应力函数,将半无限平面内土体的应力及位移分布转化为解析函数。然后,采用边界配点的方法,控制地表处的应力边界条件( = 0, = 0)及隧道周边土体的位移边界条件( , )。最后,采用最小二乘法,确定土体应力及位移函数的各项系数,求得浅埋隧道在周边土体产生径向位移的作用下,地表及深层土体位移的半数值半解析解。算例分析表明,该方法可以考虑任意荷载及位移作用的边界条件,能够充分发挥解析法和数值法两者的优点,且计算结果与实测结果较吻合,在预测地表及深层土层位移中具有一定的实用价值,可为进一步采取工程措施控制地层变形提供理论依据。     

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。     

A finite strain closed‐form solution for the elastoplastic ground response curve in tunnelling

The ground response to tunnel excavation is usually described in terms of the characteristic line of the ground (also called ‘ground response curve’, GRC), which relates the support pressure to the displacement of the tunnel wall. Under heavily squeezing conditions, very large convergences may take place, sometimes exceeding 10–20% of the excavated tunnel radius, whereas most of the existing formulations for the GRC are based on the infinitesimal deformation theory. This paper presents an exact closed‐form analytical solution for the ground response around cylindrical and spherical openings unloaded from isotropic and uniform stress states, incorporating finite deformations and linearly elastic‐perfectly plastic rock behaviour obeying the Mohr–Coulomb failure criterion with a non‐associated flow rule. Additionally, the influence of out‐of‐plane stress in the case of cylindrical cavities under plane‐strain conditions is examined. The solution is presented in the form of dimensionless design charts covering the practically relevant parameter range. Finally, an application example is included with reference to a section of the Gotthard Base tunnel crossing heavily squeezing ground. The expressions derived can be used for preliminary convergence assessments and as valuable benchmarks for finite strain numerical analyses. Copyright © 2014 John Wiley & Sons, Ltd.     

上海长江隧道过民房段地表变位预测及控制研究

复杂环境条件下大型泥水盾构施工诱发的地表变位的预测与控制是亟待深入研究的重要课题。结合上海长江隧道超大型泥水盾构推进工程,对其上行线隧道穿越民房段前试验段的地表沉降监测数据进行了分析,并采用随机介质理论预测了2条隧道单独及共同施工引起的横向地表变形和位移,据以制定了民房段施工地表变位控制措施。实例分析证明,预测方法和控制措施具有科学性、有效性,有一定的实用价值。     

挡墙水平变位诱发地表沉降的显式解析解

将基坑看作平面应变边值问题,借助挡墙刚性平移诱发地表沉降的基本解析解,利用微积分思想,推导得到挡墙刚性变位和柔性变位下的地表沉降显式解析解。其中,在挡墙刚性平移影响范围无穷大时,显示解析解与基本解析解形式一致。通过与挡墙刚性平移解析解和绕墙趾转动、绕墙顶转动、三角形变位、抛物线柔性变位模式等几种已有的积分形式解析解作对比,验证了显式解析解的正确性。将显式解析解应用于实际工程,通过与实测数据对比分析,对解析解的适用范围进行了探讨。当围护结构水平位移较小时,显式解析解可较好地预测墙后地表沉降;当围护结构水平位移较大时,由显式解析解计算得到的墙后地表沉降归一化曲线可偏安全地估计墙后地表沉降,说明了该显式解析解的工程实用性。     

路堤荷载下地基的侧向变形计算分析

目前关于路基侧向变形研究,大都是基于现场测试或数值模拟,却鲜有理论上的计算与分析。为深入研究路堤荷载下地基的侧向变形,基于布辛奈斯克等弹性理论解及平面应变问题,推导出无限长线荷载、均布条形荷载、三角形分布条形荷载及梯形分布条形荷载下地基侧向变形解析表达式,并与有限元数值计算结果对比验证了解析解的正确性。在此基础上,重点分析了土体的泊松比、路堤宽度以及路堤边坡宽度等参数对地基侧向位移场的影响。计算结果表明,路堤荷载下地基同一垂直线上土体的侧向变形沿深度呈弓形状,变形最大值在地表下某深度处。泊松比对地基侧向位移有较显著的影响：在坡脚附近地表浅层处,随着泊松比的增加,土体侧向变形的方向由向路堤内逐渐转为向路堤外;另泊松比越大,土体的水平位移也相对越大,且最大位移发生位置逐渐上移。研究结果可为类似路堤工程地基变形分析及稳定性控制监测提供一定理论支撑。     

连拱隧道施工对洞口仰坡影响的三维数值分析

以江西某高速公路一浅埋偏压连拱隧道为例,采用Marc有限元程序对其出口段进行了动态施工的三维数值模拟。从施工过程中的应力集中、塑性区的分布形态和发展规律、仰坡轴向地表位移的分布特征等方面,系统研究了偏压连拱隧道施工对强风化岩体洞口仰坡的影响作用机制。结果表明:在模拟施工过程中塑性区和应力集中区只出现在洞体附近,可能的仰坡失稳往往是隧道施工失稳的累进性响应;洞口仰坡的轴向水平位移前缘大、后缘小,垂直位移后缘大、前缘小;隧道上方和近山脊一侧仰坡位移比近山谷一侧大,仰坡失稳往往从隧道上方和埋深较大一侧开始。     

真空预压加固软土地基变形与固结计算研究

考虑真空度的衰减情况,对真空预压加固软基的变形和固结度计算方法进行了研究。先根据真空预压时砂井的真空压力状态建立了真空预压的空间轴对称变形模型,用位移法推导该模型在等应变条件下的变形及体积应变计算公式。在此基础之上结合Hansbo砂井地基固结理论和真空预压的边界条件,推导了忽略竖向渗流情况下的真空预压加固软土地基的固结解析解。比较文中计算方法与已有计算理论和现场试验实测资料结果表明,体积应变的计算对真空预压的孔压和固结度的计算有较大的影响,而直接引用传统堆载预压的体积应变计算公式计算会导致较大误差。在固结度计算中,采用Hansbo的近似方法能满足计算精度的要求,所得计算结果与实测结果吻合较好     

Solutions for the deformations and stability of elastoplastic hollow cylinders subjected to boundary pressures

In this paper, a closed-form solution is presented for the stress and displacement distributions throughout a hollow cylinder subjected to uniform pressures acting on its internal and external boundary surfaces under plane strain conditions. The material is assumed to be elastoplastic, obeying a Mohr–Coulomb failure criterion, and exhibiting dilatant plastic deformation according to a non-associated flow rule. The newly developed analytical solution is verified through comparison with the solutions obtained from an infinite boundary problem (for which a closed-form solution exists), and numerical analyses using the program FLAC. The solution is also compared with the results of a borehole collapse test on a thick-walled hollow cylinder of synthetic shale. The analytical solution can be used to calculate the stress and displacement distributions around boreholes and other cylindrical cavities under both infinite and finite boundary conditions under both drained and undrained conditions. Copyright © 1999 John Wiley & Sons, Ltd.     

Improved Longitudinal Displacement Profiles for Convergence Confinement Analysis of Deep Tunnels

Summary  Convergence-confinement analysis for tunneling is a standard approach for preliminary analysis of anticipated wall deformation and support design in squeezing ground. Whether this analysis is performed using analytical (closed form) solutions or with plane strain numerical models, a longitudinal displacement profile (LDP) is required to relate tunnel wall deformations at successive stages in the analysis to the actual physical location along the tunnel axis. This paper presents a new and robust formulation for the LDP calculation that takes into account the significant influence of ultimate (maximum) plastic radius. Even after all parameters are appropriately normalized, the LDP function varies with the size of the ultimate plastic zone. Larger yield zones take a relatively longer normalized distance to develop, requiring an appropriately calculated LDP. Failure to use the appropriate LDP can result in significant errors in the specification of appropriate installation distance (from the face) for tunnel support systems. Such errors are likely to result in failure of the temporary support. The equations presented here are readily incorporated into analytical solutions and a graphical template is provided for use with numerical modeling. Correspondence: M. S. Diederichs, Associate Professor, Queen’s University, Ontario, Canada     

基坑挡墙变位诱发地表沉陷的模型试验研究

针对刚性挡墙不同变位模式,对基坑开挖过程中地表沉陷规律进行模型试验研究。开展的模型试验分别模拟了挡墙在平移（T模式）、绕墙趾转动（RB模式）和绕墙顶转动（RT模式）3种基本刚性变位模式下诱发的墙后地表沉陷,得到了土体沉陷曲线的分布规律。结果表明,挡墙平移时,墙后地表沉降呈勺型分布,最大沉降紧靠墙背处;挡墙绕墙趾转动时,墙后地表沉降近似呈三角形分布,最大沉降紧靠墙背处;挡墙绕墙顶转动时,墙后地表沉降近似呈抛物线分布,最大沉降位于距墙背一定距离的位置处。挡墙变位距离相同时,对于绕墙趾和绕墙顶转动模式,墙后土体沉陷的面积基本相等,两者沉陷面积之和近似等于平移模式的土体沉陷面积,另外,挡墙变位面积与墙后土体沉陷面积也近乎一致。将试验观察的沉陷曲线与既有的解析解作了对比分析,验证了二者的一致性。     

考虑注浆材料流变的隧道施工土层变形计算

在盾构隧道施工过程中背后注浆是必不可少的,注浆材料在逐步卸载的压力作用下由流动状态变化到固体状态,注浆材料的变形特性将与恒载作用有区别。针对南京地铁1号线实际工程盾构隧道施工注浆材料,进行了卸载条件和恒载条件下注浆材料的流变试验,得到了非线性流变的试验曲线和拟合的流变方程;在半无限空间圆孔扩张位移理论解和注浆材料的流变试验结果的基础上,推求得到隧道所在土层的位移解,确定了位移的影响范围,讨论了地表沉降计算结果的合理性,初步建议确定隧道施工应保护区域的确定原则。     

A novel analytical approach for predicting the noncylindrical pile penetration‐induced soil displacement in undrained soil by combining use of cavity expansion and strain path methods

Since development of cavity expansion theory and strain path method, almost all the conventional analyses of pile penetration problem have been based on circular cross section penetrometer. However, noncylindrical pile (with noncircular cross section) is also required in geotechnical engineering such as rectangular cross‐sectional pile, X‐sectional cast‐in‐place concrete pile, H‐shaped steel pile, prefabricated vertical drains, and flat dilatometer. This paper presents a novel and general analytical approach for capturing the soil deformation mechanism around the pile with arbitrary cross section. The penetration problem is simulated by a new 2‐dimensional (radial and circumferential) cavity expansion model. Based on the theoretical framework of strain path method, the kinematics (velocity field) of the noncylindrical cavity expansion is reduced to solve the Laplace equation with arbitrary velocity boundary conditions by using the conformal mapping technique. Then, solutions for the strain and displacement, which could consider the large deformation effect, are obtained by the integration of the strain rate and velocity along the streamline. The analytical solution is validated by comparing the degenerate solution of this study with conventional circular (cylindrical) cavity expansion theory. Subsequently, typical numerical examples for the deformation mechanism of elliptical and rectangular cavity expansion are presented to prove the advantage of the proposed new solution particularly in capturing the noncylindrical symmetric displacement field. A brief application of the proposed new analytical solution to the interpretation of the smear effect of prefabricated vertical drain installation confirms its useful in geotechnical engineering.     

软土中盾构法隧道引起的土体移动计算研究

对盾构法隧道施工引起的土体扰动范围进行了分析,根据极限平衡原理,认为Loganathan公式中假定的土体损失边界条件存在误差。考虑到土体内摩擦角对土体移动的影响,认为垂直土体变形区域边界线的水平倾角应等于（45°+? /2）,而不是45°。给出了修正的Loganathan公式,该公式适用于软土地区不排水条件。提出了盾构剪切扰动区范围的计算公式。算例分析表明,与Loganathan公式的计算结果相比,修正公式使沉降槽宽度和土体水平位移有所减小,计算结果与实测数据更加吻合。     

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。     

Analytical study of ground responses induced by the excavation of quasirectangular tunnels at shallow depths

The construction of quasirectangular tunnels at shallow depths is becoming increasingly common in urban areas to efficiently utilize underground space and reduce the need for backfilling. To clarify the mechanical mechanism of the stresses and displacements around the tunnels, this study proposes analytical solutions that precisely account for quasirectangular tunnel shapes, the ground surface, the tunnel depth, and the ground's elastic/viscoelastic properties. The Schwarz alternating method combined with complex variable theory is employed to derive the elastic solution, and convergent and highly accurate solutions are obtained by superposing the solutions in the alternating iterations. Based on the solution and the extended corresponding principle for the viscoelastic problem, the time-dependent analytical solutions for the displacement are obtained for the ground assuming any viscoelastic model. The analytical solutions agree well with the finite element method (FEM) numerical results for models that are completely consistent, and qualitatively agree with field data. Furthermore, based on the stress solution combined with the Mohr-Coulomb failure criterion, the predicted initial plastic zone and propagation directions around the tunnels are qualitatively consistent with those determined by the limit analysis. A parametric study is performed to investigate the influences of the rectangular/quasirectangular tunnel shape, burial depth, and supporting pressure on the ground stresses and displacements.     

挡墙水平变位诱发地表沉降的简化解析解

推导了平移模式下的地表沉降理论显式解,在此基础上提出了任意挡墙变位诱发墙后地表沉降的简化计算方法。分别与平移、绕墙趾及绕墙顶等3种变位模式下的弹性有限元数值解进行对比分析,对简化解析方法进行了验证。最后将这一简化解析方法应用于工程案例预测,与软土地基现场实测结果进行对比,发现理论预测的地表沉降曲线与实测值相吻合,且较准确地预测了最大沉降发生的位置,表明了该简化解析方法的实用性。     

层状地基群桩沉降计算的剪切位移解析算法

考虑群桩的“束缚作用”,基于剪切位移法的理论,提出了竖向荷载作用下用于层状地基大规模群桩沉降分析的简捷实用的解析算法。以单桩位移积分方程为基础,导出了桩顶位移与轴力和桩底位移与轴力之间的关系,考虑桩-桩相互作用,得出了计算群桩沉降的柔度矩阵方程。推导过程中,桩被分成任意n段,因此该方法可以用于地基土任意分层的群桩沉降计算。算例分析表明,该方法与边混合法和界元法有较好的一致性。