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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。     

Upper-bound stability analysis of a plane strain heading in non-homogeneous clay

This paper investigates the undrained stability of a plane strain tunnel heading in cohesive soil, whose undrained shear strength is assumed to increase linearly with depth. Upper bound stability solutions for a practical range of parameters of geometries and soil conditions are found using the multi-rigid-block upper bound method. The upper bound solutions obtained from the multi-rigid-block mechanisms significantly improve the classical solutions and have good agreement with those of the finite element limit analysis when C/D is small. An improved simple collapse mechanism which intermix inhomogeneous deforming region and rigid blocks translation together is proposed based on the multi-rigid-block upper-bound analysis. An upper bound analytical solution is then obtained in view of the numerical results of both the multi-rigid-block collapse mechanism and the improved simple collapse mechanism. And it predicts the plane strain heading stability relatively accurate for shallow tunnels.     

浅埋软土隧道稳定性极限分析

稳定性分析在浅埋软土隧道工程设计中占有重要位置.本文应用极限分析理论的上限原理及有限元法求解隧道的稳定系数,明显改善了既有的上限分析结果,并且同下限分析结果很接近,因此可以更好地界定准确解的范围.此外,有限元优化的机动可容许破坏速度场有助于理解浅埋软土隧道的破坏机制.本文所用的有限元极限分析方法也适用于研究其他土体结构的总体稳定性.     

Centrifuge Modeling of Granular Soil Response Over Active Circular Trapdoors

The trapdoor problem is a useful model for providing a clearer understanding of stress distribution around basic geotechnical engineering structures such as tunnels, conduits and anchor plates. The interest is mainly directed towards the determination of soil load on the trapdoor, which can be substantially different from the initial geostatic loads, when the trapdoor is moved even slightly. Development of shear bands around the yielding trapdoor is also of interest. A series of centrifuge and 1g model tests were conducted to study active arching in dry granular soil on circular trapdoors. The study was undertaken mainly because of two reasons: (i) limited success in earlier centrifuge modeling studies of a trapdoor problem, and (ii) a lack of understanding of the load-displacement characteristics under axisymmetric conditions. A trapdoor assembly and in-flight precompression technique were developed to perform a series of tests involving different overburden soil thickness on circular doors of different diameters. Correct initial geostatic loads were measured. Greater confidence in the experimental results was obtained because modeling of models type experiments were also successful. A parametric study involving different overburden soil thickness to trapdoor diameter ratios (H/D) ranging from 0.67 to 6 was conducted. The pattern of shear bands in sand above the trapdoor observed in a centrifuge model under a high gravity field differed considerably from that in a 1g model. Maximum arching was completely mobilized at movements of only 1.5% of trapdoor diameter. The minimum load on the trapdoor became constant at H/D equal to 5 regardless of the initial overburden pressure or height of the soil model.     

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.     

Applications of numerical limit analysis (NLA) to stability problems of rock and soil masses

This work presents formulations and results obtained with computer implementations of an alternative to the more standard techniques for the determination of the state of collapse of geotechnical structures in rock or soil masses. Examples of normally available and used techniques for those purposes are limit equilibrium based procedures and elasto-plastic finite elements. As an alternative to these techniques, the present paper describes Numerical Limit Analysis (NLA). The fundamentals for limit analysis, summarized in the so-called bound theorems, have been known for decades. Analytical solutions obtained with limit analysis are however limited in scope and are seldom used in the engineering practice. NLA on the other hand, by solving the limit analysis equations through numerical methods are general and applicable to a wide range of problems. The paper presents a discussion on available alternatives for the formulation of NLA specialized for the determination of collapse load factors of geotechnical structures in/on rock (fractured or not) and soil masses. Rock masses in particular are modelled as standard continua, Cosserat equivalent continua and true discontinua formed by discrete blocks. Finite elements are used for the solution of NLA equations of standard continua and Cosserat continua. The paper presents derivation of the pertinent equations, the numerical formulations used and details of their numerical implementation in computer programs. Attempt was made to validate all the implementations through existing analytical solutions. The obtained results permit to state that NLA is a promising and very often advantageous numerical technique to establish collapse states of geotechnical structures in rock and soil masses.     

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.     

An artificial neural network approach to inhomogeneous soil slope stability predictions based on limit analysis methods

The assessment of soil slope stability is an important task in geotechnical designs. This study uses finite element upper bound (UB) and lower bound (LB) limit analysis (LA) methods to investigate inhomogeneous soil slope stability on the basis of the conventional Mohr–Coulomb parameters. The obtained stability numbers are presented in inhomogeneous soil slope stability charts. In order to minimize manual reading errors when using the chart solutions, an artificial neural network (ANN) is employed to develop a stability assessment tool for the slopes investigated in this paper. The slope stability analysis using the ANN-based tool is convenient, and the predictions it provides are highly accurate.     

Upper-bound solutions for face stability of circular tunnel in purely cohesive soil using continuous rotational velocity field

This paper presents a 2D analysis model based on limit analysis and slip-line theories for the face stability of a circular tunnel in purely cohesive soil. The analysis model depends on the ratio of cover depth C to tunnel diameter D. When C/D is equal to 0.5, the mechanism consists of three blocks, namely, Zone I, Zone II, and Zone III. When C/D is greater than 0.5, the mechanism consists of four blocks, namely, Zone I, Zone II, Zone III, and a possible Zone IV. Zone II is a transition zone satisfying the normality conditions. The possible Zone IV is a Rankine zone that is subjected to the influence of the vertical soil arching effect appearing at the top of Zone III. The criterion for the collapse thickness limit of the tunnel is proposed based on Terzaghi’s theory of relative soil pressure. The results show that significant improvements have been made to the existing solutions using the proposed failure mechanism for the face stability of circular tunnels in purely cohesive soil.     

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。