黏土中隧道垮落的塑性分析和数值模拟

~~黏土中隧道垮落的塑性分析和数值模拟@谢骏$伦敦南岸大学!伦敦~~     

双平行圆形隧道稳定的塑性极限分析上限解

从塑性极限分析上限法的基本原理出发，通过分析单圆形隧道4种类型垮落机制所获得的稳定率上限解，构建黏土层中双平行圆形隧道的垮落机制，阐述双平行圆形隧道稳定与垮落间的临界稳定分析过程，导出浅土层中双平行圆形隧道稳定率的上限方程。该方程根据隧道间不同距离，综合两隧道重叠（单隧道）、两隧道相接触、相互影响的双隧道以及互不影响的两单隧道的稳定特征。通过该方程进一步讨论土重对双隧道稳定率上限解的影响。最后，由离心模型试验结果证实其上限解的正确性。     

基坑抗隆起稳定的块体集上限分析

采用块体集上限法构造了基坑抗隆起稳定问题的运动许可速度场,分析了各种条件下不排水黏土基坑抗隆起稳定系数和破坏面特性。通过对考虑坑底坚硬土层、挡墙入土深度和基坑外侧地表超载条件下,块体集上限分析结果与已有文献结果的对比,验证了方法的有效性。块体集上限法克服了多块体上限法存在破坏面假设的缺点,不仅适用范围更广,同时可以得到更完整的基坑抗隆起优化破坏面。在考虑支护挡墙入土深度时,块体集上限法所得基坑抗隆起稳定分析结果优于多块体上限法和强度折减有限元法,具有较大优越性。     

Undrained End Bearing Capacity of an Improved Soil Berm in an Excavation

For a wide excavation in soft soil, the excavation can be stabilized by an embedded improved soil berm to increase wall stability and control soil movement. An embedded stiff berm essentially behaves like a horizontal pile subjected to a load applied by the retaining wall and derives its resistance to horizontal movement from both end bearing and interfacial shear resistance on the top and bottom of the berm. This resistance helps to restrain the wall from moving inwards to the excavated side. However, to date, there is no known reported literature on the determination of the undrained ultimate bearing capacity of such a berm, especially for the unit end bearing, q_b. In this paper, the undrained end bearing of an improved berm under a plane strain condition was determined. The undrained end bearing capacity was first derived using a solution from a proposed upper bound analysis based on observations from centrifuge tests and then modified, taking on the basis of an equivalent finite element analyses. The proposed end bearing capacity factor N_c lies between the upper bound and lower bound solutions. The solution showed that the undrained end bearing capacity is not a constant but decreases during the excavation process. Furthermore, it was shown that the existence of an improved soil berm will provide an additional pressure relative to the passive pressure to control the wall displacement.     

非均质黏土地基隧道环向开挖面稳定上限分析

基于多块体极限分析上限法,推导了不排水条件下饱和黏性土地基中隧道环向开挖面稳定支护压力的计算公式。编制相应的计算程序,优化得到了隧道环向开挖稳定的最优上限解答。通过与已有极限分析上限解答的对比,验证了多块体极限分析上限法在隧道开挖稳定性分析的适用性。对照隧道开挖稳定的最优上限解的变化规律及相应破坏面的形状,详细分析了隧道埋深比、土体重度及强度非均质性对开挖面极限支护压力和因隧道开挖产生的滑动面范围和位置的影响。在此基础上,进一步基于隧道失稳的简化破坏模式推导了黏性土地基隧道开挖稳定的极限支护压力的简化上限解。通过与已有离心模型试验的对比验证,指出本文上限解可直接用于工程中初步确定开挖面支护压力,为隧道工程设计提供可靠的理论依据。     

基于块体集上限法的砂土中条形锚板抗拔承载力分析

运用块体集上限法详细分析了砂土中条形锚板的抗拔承载特性。首先分析了砂土中水平条形锚板的抗拔承载力，并与已有文献中的极限分析上限解、极限平衡解和模型试验结果等进行了详细对比，验证了本文分析的有效性。对比结果表明本文块体集上限分析的求解精度要高于多块体上限法和极限分析有限元法，具有较大的优越性。运用块体集上限法分析了条形锚板的破坏面特性，对不同土体内摩擦角和不同锚板埋深比（H/B）条件下砂土中条形锚板的破坏模式及其变化规律进行了详细的分析研究。     

黏土基坑抗隆起稳定分析的多块体上限解

 为了将多块体上限法拓展应用到饱和黏土基坑抗隆起稳定性分析中,提出支护墙体刚性条件下,用于饱和黏土基坑抗隆起稳定分析的多块体相容破坏模式,并给出相应的上限计算能量方程。为检验多块体上限方法的应用情况,结合实际工程案例以及针对基坑宽度、坑底基岩埋置深度、支护墙体与土体间侧摩阻、支护墙体入土深度和土体强度非均质等对抗隆起稳定存在影响的因素进行计算和分析,并将多块体上限法计算结果与基于Terzaghi模式及Prandtl模式的上限解、Faheem强度折减有限元计算结果、Ukritchon的极限分析有限元计算结果做了广泛的对比。通过对比可以发现,所给出的多块体上限解是所讨论上限解中最优的,计算结果与Ukritchon的极限分析上限有限元计算结果较为接近,而多块体上限方法与Ukritchon的极限分析上限有限元相比,更容易实现,计算量也要小得多。通过大量计算以及与其他方法的对比可以发现,多块体上限方法在黏土基坑抗隆起中的应用是比较成功的。     

Undrained stability of a spherical cavity in cohesive soils using finite element limit analysis

A parametric study of undrained stability of a spherical cavity in clays is investigated by finite element limit analysis with an axisymmetric condition.Influences of cover depth ratio of cavity and dimensionless overburden factor on predicted failure mechanisms and dimensionless load factor are examined.It is found that a previously recommended and up-to-date lower bound solution to the problem was significantly inaccurate for practice use.Thus,an accurate approximate solution to the problem is proposed from nonlinear regression analysis of the computed average bound solutions.New cavity stability factors for the soil cohesion and soil unit weight are proposed.New findings are revealed for the threedimensional effect of the cavity shape on these factors between the axisymmetric and plane strain conditions,and their applications to the undrained stability evaluation of cavity problems in practice are described.     

黏土地层隧道开挖面三维稳定性上限分析

对不排水均质黏土地基隧道开挖失稳三维破坏模式进行改进,弥补了目前隧道开挖稳定性问题中三维极限分析上限法的不足。采用截椭圆柱体构造多块体平动破坏模式,克服了现有三维多块体平动破坏模式与隧道开挖面不完全接触的缺陷;进一步针对三维多块体平动破坏模式存在的问题,提出了多块体转动–剪流组合破坏模式,得到了均质黏土地层中隧道开挖稳定的上限解,明显改善了现有的极限分析上限解,并与三维弹塑性有限单元法结果及文献中的离心试验结果进行对比,验证了上限分析方法的有效性。     

隧道工作面稳定性与滑移线网破坏模式研究

针对隧道工作面稳定性和破坏模式问题,从保守角度将其假定为沿隧道纵向中线剖开的二维平面应变模型,采用刚体平动运动单元上限有限元法(UBFEM-RTME)开展分析研究,绘制了土体自重作用下地层临界失稳状态对应的隧道工作面稳定系数N_(cr)图表和有效间断线网(近似滑移线网)破坏模式,探讨了埋深比H/D、内摩擦角j和剪胀角ψ等参数影响规律,给出了N_(cr)与H/D和j影响因素的拟合公式,进一步揭示了有效间断线数目及位置分布等网格参数对计算精度的影响程度。研究表明UBFEM-RTME数值计算配合网格更新策略并保证合理充足的网格密度,能提高N_(cr)上限解精度并捕获高密度有效间断线网破坏模式,其分析结果可用于评价隧道工作面稳定性、揭示极限失稳破坏形态的主要特征,为地层预加固方案制定等工作提供一定理论支撑。     

Realization of uniform deformation of soil specimen under undrained plane strain condition based on soil–water coupled finite deformation analysis considering inertia forces

Based on a soil–water coupled finite deformation analysis, theoretical considerations and numerical calculations were carried out under the undrained plane strain condition in order to reproduce a uniform deformation field. Rather than the “quasi-static” equation of motion, which does not include inertia forces, a dynamic equation of motion which includes inertia forces was used. At first, a theoretical consideration was carried out to realize uniform deformation for a saturated soil that satisfied the element-wise undrained/constant-volume condition. This presents an “infinitely slow loading” case without ignoring the inertia term based on the u–p formulation. In other words, it can be seen that under general slow loading that is not infinitely slow, a gradient in the pore water pressure will always be produced, resulting in the migration of pore water and loss/collapse of uniformity. This first conclusion is useful for verifying numerical analysis code made in the finite deformation regime. Next, the uniform deformation of a plane strain rectangular soil specimen was measured under constant cell pressure and undrained boundary conditions using a dynamic soil–water coupled analysis in which the SYS Cam-clay model was employed as the elasto-plastic constitutive model for the soil skeleton. In addition, the effects of the loading rates as well as loading applications, with/without inertia forces, on the loss of uniformity in deformation were shown to have a significant influence on the inertia term even though the loss itself was extremely small.     

基于组合块体集的浅埋条形锚板上限分析

 基于极限分析法的基本原理以及集成与组合的思路,推导组合块体集的内能耗散和重力做功,运用组合的思想构造斜坡地形下浅埋水平条形锚板的运动许可速度场。首先分析地表水平条件下法向受力水平条形锚板抗拔承载力,并与文献中已有解和模型试验进行对比,验证块体集上限法的优越性。然后详细研究斜坡地形条件下土体重度、不排水抗剪强度、斜坡倾角等因素对条形锚板抗拔承载力和破坏面形状的影响。分析结果表明：重力叠加法并不适用于斜坡地形情况;随着斜坡倾角的增大,锚板的破坏面向坡角方向倾斜;锚板埋深比越大,斜坡倾角的影响也越显著。块体集上限分析方法构造简单,求解快捷,能够为工程设计提供依据。     

Support pressure for circular tunnels in two layered undrained clay

To estimate the required support pressure for stability of circular tunnels in two layered clay under undrained condition,numerical solutions are developed by performing finite element lower bound limit analysis in conjunction with second-order cone programming.The support system is assumed to offer uniform internal compressive pressure on its periphery.From the literature,it is known that the stability of tunnels depends on the overburden pressure acting over it,which is a function of undrained cohesion and unit weight of soil,and cover of soil.When a tunnel is constructed in layered undrained clay,the stability depends on the undrained shear strength,unit weight,and thickness of one layer relative to the other layer.In the present study,the solutions are presented in a form of dimensionless charts which can be used for design of tunnel support systems for different combinations of ratios of unit weight and undrained shear strength of upper layer to those of lower layer,thickness of both layers,and total soil cover depth.     

非线性破坏准则对竖直边坡稳定性分析的影响

在上限分析理论基础上，研究非线性Mohr-Coulomb破坏准则下的竖直边坡稳定性问题。首先，通过“切线法”引进变量；其次，根据上限定理对边坡稳定性问题建立含有变量的速度场，将稳定性问题变为含有多变量的非线性规划问题；最后，根据“序列二次规划算法”求出上限非线性规划问题的最优解。通过上限解和前人的研究成果的比较表明，该方法是有效和正确的。     

K0固结黏土基坑抗隆起稳定性上限分析

软黏土中深基坑开挖支护系统设计一般由不排水稳定控制。考虑基坑开挖引起土体应力主轴旋转和土体不排水抗剪强度的各向异性,首先基于所提出的各向异性本构模型推导了三轴条件下软黏土的不排水强度公式并结合Casagrande和Carillo推荐的能考虑土体应力主轴旋转的软黏土强度公式,提出一种适合于基坑开挖抗隆起稳定分析的K0正常固结软黏土的不排水各向异性抗剪强度。假定Prandtl的土体滑移破坏形式,运用塑性极限分析上限定理推导非均质土层中深基坑开挖的抗隆起稳定公式。研究了基坑开挖土体强度各向异性比、挡墙入土深度、坑底硬土层对抗隆起安全系数的影响。并与基于MIT-E3模型的有限元计算结果及其它文献中的算例进行验证,说明该方法的适用性。     

K_0固结黏土基坑抗隆起稳定性上限分析

软黏土中深基坑开挖支护系统设计一般由不排水稳定控制。考虑基坑开挖引起土体应力主轴旋转和土体不排水抗剪强度的各向异性,首先基于所提出的各向异性本构模型推导了三轴条件下软黏土的不排水强度公式并结合Casagrande和Carillo推荐的能考虑土体应力主轴旋转的软黏土强度公式,提出一种适合于基坑开挖抗隆起稳定分析的K0正常固结软黏土的不排水各向异性抗剪强度。假定Prandtl的土体滑移破坏形式,运用塑性极限分析上限定理推导非均质土层中深基坑开挖的抗隆起稳定公式。研究了基坑开挖土体强度各向异性比、挡墙入土深度、坑底硬土层对抗隆起安全系数的影响。并与基于MIT-E3模型的有限元计算结果及其它文献中的算例进行验证,说明该方法的适用性。     

软土隧道支护压力与稳定性下限有限元分析

隧道开挖面的支护压力计算和稳定性分析至今尚未有比较成熟和简便的计算方法,本文基于岩土塑性极限分析理论,在分析下限有限元方法中引入非线性Power-Law屈服准则,通过对屈服准则的线性化处理,得到平面应变条件下软土隧道开挖面支护压力计算的下限有限元线性规划模型,编制了相应的Matlab有限元计算程序。计算表明:与极限平衡理论和极限分析上限有限元得到的结果比较,可以说明引入非线性Power-Law屈服准则的塑性极限分析下限有限元对隧道开挖面支护压力的计算和稳定性的分析是适用的。同时,总结了隧道埋深系数、土体重度系数等对隧道开挖面支护压力与稳定性的影响。     

考虑土体强度各向异性基坑抗隆起上限分析

软粘土中深基坑开挖支护系统设计一般由不排水稳定控制.考虑基坑开挖引起土体应力主轴旋转和土体不排水抗剪强度的各向异性,采用Casagrande&Carillo推荐的土体不排水各向异性强度公式,假定Terzaghi和Prandtl土体滑移破坏形式,运用塑性极限分析上限定理推导两个基坑开挖的抗隆起稳定公式.研究了基坑开挖土体强度各向异性比、平面几何尺寸、坑底硬土层对抗隆起安全系数的影响及其相互影响,并与Terzaghi方法和Bjerrum&Eide方法进行了比较,最后用文献中的工程实例进行了验证.     

A stable CS-FEM for the static and seismic stability of a single square tunnel in the soil where the shear strength increases linearly with depth

A numerical procedure using a stable cell-based smoothed finite element method (CS-FEM) is presented for estimation of stability of a square tunnel in the soil where the shear strength increases linearly with depth. The kinematically admissible displacement fields are approximated by uniform quadrilateral elements in conjunction with the strain smoothing technique, eliminating volumetric locking issues and the singularity associated with the Mohr–Coulomb model. First, a rich set of simulations was performed to compute the static stability of a square tunnel with different geometries and soil conditions. The presented results are in excellent agreement with the upper and lower bound solutions using the standard finite element method (FEM). The stability charts and tables are given for practical use in the tunnel design, along with a newly proposed formulation for predicting the undrained stability of a single square tunnel. Second, the seismic stability number was computed using the present numerical approach. Numerical results reveal that the seismic stability number reduces with an increasing value of the horizontal seismic acceleration (α_h), for both cases of the weightless soil and the soil with unit weight. Third, the link between the static and seismic stability numbers is described using corrective factors that represent reductions in the tunnel stability due to seismic loadings. It is shown from the numerical results that the corrective factor becomes larger as the unit weight of soil mass increases; however, the degree of the reduction in seismic stability number tends to reduce for the case of the homogeneous soil. Furthermore, this advanced numerical procedure is straightforward to extend to three-dimensional (3D) limit analysis and is readily applicable for the calculation of the stability of tunnels in highly anisotropic and heterogeneous soils which are often encountered in practice.     

底面为曲面基础地基极限承载力上限解

为了解决曲面基础作用于土体的极限承载力问题,改进了 Prandtl 机构和 Hill 机构,利用极限分析理论,得到了底面为曲面基础地基极限承载力的上限解;通过两者的比较,以及与底面为平面基础地基极限承载力的比较,所得的上限解大于处于地基表面的平面基础地基极限承载力的上限解,小于埋深为基础宽度一半的平面基础地基极限承载力的上限解,研究结果可供地基承载力设计及计算参考。