基于位移控制边界单元法盾构隧道开挖引起分层土体变形分析

 考虑地基土体非均质性的影响,基于弹性层状半空间地基模型,提出分析多层地基中盾构隧道开挖引起周围土体不排水变形的位移控制边界单元法,改变了过去采用简化分析方法仅能在均质地基中进行求解的状况。针对盾构隧道开挖边界引入椭圆化非等量径向土体位移移动模式,建立层状地基中洞周边值问题的边界积分求解方程,并采用高阶等参单元代替低阶常分布单元得到边界离散方程,同时以弹性层状半空间地基模型的基本解代替常规均匀介质体的Kelvin或Mindlin基本解,最终求得隧道洞周给定位移条件下的土体位移场。算例分析表明：位移控制边界单元法在计算均质地基和非均质层状地基中都具有较好的精度;对于非均质层状地基,如果采用以往的将不同土体参数近似折算成平均值进而按照弹性均质地基进行求解会带来较大的计算误差。研究成果可为合理评估盾构隧道施工对周围环境的影响提供一定的理论依据。     

盾构掘进地面沉降虚拟镜像算法

盾构掘进所致地面沉降的准确预估,对于邻近建（构）筑物的保护至关重要。假定土体为均质各向同性半无限空间不可压缩弹性体,基于虚拟镜像技术,推导了在隧道边界土层不同收敛模式下的地面沉降计算公式,计算结果比数值积分算法更接近实测。由于实际土体具有各向异性、成层性和可压缩性,本文算法与数值积分算法均高估了横向地面沉降槽宽度。引入沉降槽宽度修正参数对理论公式进行修正,修正算法计算结果更符合实际,可简单可靠地估算盾构隧道施工地层损失引起的地面沉降。     

Building response to tunnelling

Understanding how buildings respond to tunnelling-induced ground movements is an area of great importance for urban tunnelling projects, particularly for risk management. In this paper, observations of building response to tunnelling, from both centrifuge modelling and a field study in Bologna, are used to identify mechanisms governing the soil–structure interaction. Centrifuge modelling was carried out on an 8-m-diameter beam centrifuge at Cambridge University, with buildings being modelled as highly simplified elastic and inelastic beams of varying stiffness and geometry. The Bologna case study presents the response of two different buildings to the construction of a sprayed concrete lining (SCL) tunnel, 12 m in diameter, with jet grouting and face reinforcement.In both studies, a comparison of the building settlement and horizontal displacement profiles, with the greenfield ground movements, enables the soil structure interaction to be quantified. Encouraging agreement between the modification to the greenfield settlement profile, displayed by the buildings, and estimates made from existing predictive tools is observed. Similarly, both studies indicate that the horizontal strains, induced in the buildings, are typically at least an order of magnitude smaller than the greenfield values. This is consistent with observations in the literature. The potential modification to the settlement distortions is shown to have significant implications on the estimated level of damage. Potential issues for infrastructures connected to buildings, arising from the embedment of rigid buildings into the soil, are also highlighted.     

层状地基中盾构隧道开挖非均匀收敛引起临近管道变形预测

采用弹性层状地基模型来考虑地基土体的非均质性,并针对隧道开挖边界引入椭圆化非等量径向土体位移模式;采用基于位移控制技术的边界单元方法来求解土体自由位移场,提出层状地基中盾构隧道开挖非均匀收敛引起临近管道变形影响的位移控制分析方法。结合位移控制有限元数值模拟和既有离心模型试验结果进行对比分析,验证该方法的有效性。算例分析结果表明,土体自由位移场计算对管道纵向变形性能的评估具有较大影响;对于非均质层状地基,如果采用以往的将不同土体参数近似折算成平均值,进而按照弹性均质地基进行求解会带来较大的计算误差。研究成果可为合理制定城市地铁隧道施工对周围环境影响的保护措施提供一定理论依据。     

分层地基中隧道开挖对邻近刚性桩筏基础竖向影响分析

基于两阶段分析方法：第一阶段采用Loganathan方法计算隧道开挖引起的土体自由场位移,第二阶段采用层状地基中弹性理论法,计算桩和土,桩和桩之间的相互作用,并考虑刚性筏板对桩基的约束作用,提出了一套能够分析层状地基中隧道开挖对刚性筏板群桩基础竖向影响的解析方法。将计算结果与离心试验结果及现有方法计算结果进行对比,得到了较好的一致性,验证了其正确性。并首次对层状地基中桩筏基础承载特性进行了分析,讨论了桩基变形对遮拦效应的削减作用,结果表明此方法意义明确,层状地基模型更符合工程实际情况,适于推广使用。     

浅埋隧道围岩应力及位移的显式解析解

浅埋隧道施工引起的地层位移将传递至地表进而形成地表沉降,施工前准确预测地层位移是有效控制地表沉降的前提。基于复变函数法,利用逆映射函数求解z平面复势函数的级数形式,并结合柯西-黎曼方程（C-R条件）对Verruijt提出的浅埋隧道围岩应力及位移隐式解析解中的解析函数求导,得出了浅埋隧道应力及位移函数的级数显式表达式;与Verruijt隐式解析解相比,该显式解析解直观,便于被工程人员使用,其编程计算量也较小;为确定显式解析解中的未知系数,基于浅埋隧道洞室变形产生的原因,提出了3种隧道洞室边界的变形模式和2种变形比率,合理调整变形比率可以实现多种边界条件组合。工程实测地层位移与显示解析解的计算结果吻合度高,验证了所提显式解析解的正确性和实用性。     

Effect of building stiffness on tunnelling-induced ground movement

The progressive response of two–three storey masonry buildings to bored tunnelling on the Jubilee Line Extension in London is investigated in order to determine the effect of building stiffness on tunnelling-induced ground movement. The masonry buildings, at Moodkee Street and Keetons Estate, were affected by tunnelling with earth pressure balance machines on Contract 105 of the Jubilee Line Extension. Bending deformations and axial strain induced in these structures are compared to greenfield ground deformations and strain in order to infer the effect of building stiffness. The modifying influence of the stiffness of these buildings on ground movement is interpreted using the Potts and Addenbrooke [Potts D.M., Addenbrooke, T.I., 1997. A structure’s influence on tunnelling induced ground movements. Proc. Inst. Civ. Eng. Geotech. Eng. 125 (2), 109–125] method, which is based on a series of finite element analyses. The inferred building stiffness that can be used for design purposes with the Potts and Addenbrooke method is compared to an estimation for a Class A [Lambe, T.W., 1973. Predictions in geotechnical engineering. Geotechnique 23 (2), 149–202] prediction exercise by Mair and Taylor [Mair, R.J., Taylor, R.N., 2001. Settlement predictions for Neptune, Murdoch and Clegg Houses and adjacent masonry walls. Building response to tunnelling – case studies from construction of the Jubilee Line Extension, London. In: Burland, J.B., Standing, J.R., Jardine, F.M. (Eds.), Projects and Methods, vol. 1. CIRIA SP200, pp. 217–228 (CIRIA and Thomas Telford, 2001). ISBN: 0 7277 30177] using the same method. As a result an alternative approach is proposed for estimating the relative bending stiffness of masonry structures for future use with the Potts and Addenbrooke method when making simple predictions.     

Analytical solution for tunnelling-induced ground movement in clays

Elastic solutions are presented to predict the tunnelling-induced undrained ground movements for shallow and deep circular tunnels in soft ground, by imposing the oval-shaped ground deformation pattern as the boundary condition of the displacement around the tunnel opening. The gap parameter is used to describe the displacement at the opening. The difference between uniform radial and oval-shaped ground deformation patterns on ground deformations is investigated and different definitions for ground loss are discussed. The applicability of the proposed analytical solutions is checked with five case studies. Generally good agreement of the predicted ground deformations can be seen with field observations for tunnels in uniform clay.     

Evaluation of ground settlement in response to shield penetration using numerical and statistical methods: a metro tunnel construction case

Shield tunnelling can cause ground settlement, which poses significant risks to adjacent structures or facilities. To understand complex soil behaviour in response to shield penetration, a model that can establish the shield–ground relationship and accurately predict tunnelling-induced ground settlement is necessary. The aim of this paper is to combine numerical methods and statistical methods for settlement prediction in the Wuhan (China) metro project. During the pre-construction stage, due to the lack of instrumentation data, the numerical method was applied to simulate the tunnelling process. The relevant factors influencing ground settlements were identified by examining the model’s sensitivity to each parameter. After the shield launch, data of the relevant factors and field measurements were collected. Using these data, a statistical model based on an adaptive relevance vector machine (aRVM) was trained for real-time prediction of the ground settlement development. The simulation results show that a number of factors, including geometrical, geological and shield operational parameters, contribute to ground settlement, and the aRVM model can accurately and effectively predict settlement development. The example application demonstrates that the method is a practical tool for settlement prediction and can be widely used in metro projects.     

Finite element analysis of tunnel–soil–pile interaction using displacement controlled model

Significant additional loads could be induced in pile foundations adjacent to new tunnels. Accurate prediction of magnitude and shape of the ground displacements, which define curvature changes, is crucial for the computation of tunnelling induced bending and axial stresses in pile foundations. The finite element simulation of tunnelling by removing forces corresponding to initial stress-state, tend to predict incorrect shape of ground displacement profiles, hence incorrect forces in pile foundations adjacent to tunnels. To overcome this difficulty, this paper describes the development and application of a simple and useful displacement controlled model (DCM) to predict the effects of tunnel excavation on adjacent pile foundations. The DCM simulates tunnelling by applying displacements to the tunnel boundary. A method to determine magnitude and direction of tunnel boundary displacements, based on convergence patterns observed in field and centrifuge test results, is proposed. Back analyses of numerous greenfield tunnel case histories using the DCM indicate good agreement between computed displacement profiles and field/test data. The suitability of the DCM in modelling tunnel–soil–pile interaction problems is demonstrated through back analysis of a centrifuge test and a field case study.     

考虑弧长和法向应力修正的基坑抗隆起稳定计算方法

目前抗隆起稳定计算方法多是基于均质土推导得出安全系数计算公式,将其应用于分层土地基时,通常将各土层的抗剪强度指标按土层厚度加权平均,这种方法既没有考虑滑动面实际经过各土层的弧长也没有考虑滑动面上法向应力大小。分析了分层土地基中土层分布影响抗隆起稳定性的因素,针对均质土中的抗隆起稳定验算公式提出了两种修正方法,按弧长加权平均法和按弧长与滑动面法向应力加权平均法。通过工程实例计算分析表明,传统层厚加权平均法得到的安全系数与精确解法得到的安全系数相差较大,不能合理反映各土层的抗隆起贡献;而两种修正方法,尤其是第二种,所得到的安全系数接近精确解法得到的结果,可以合理地反映不同深度土层对抗隆起稳定的贡献及基坑抗隆起稳定安全系数随土层分布变化的变化规律,并且计算简便,易于工程技术人员使用。此外,针对土层分布变化对抗隆起稳定的影响研究得出,滑动面下部土层对基坑稳定性影响最显著,因此在工程实践中,应尽可能将全部或部分支护结构的底端嵌入较好的土层中。     

Influence zones for 2D pile–soil-tunnelling interaction based on model test and numerical analysis

In the congested urban areas, tunnelling close to existing structures or services often occurs due to the lack of surface space. Consequently, tunnelling-induced ground movements may cause a serious damage to the adjacent structures. This study focussed on two-dimensional laboratory model test for the pile–soil-tunnelling interaction using a close range photogrammetric technique and numerical analysis. Model testing equipments and procedures were introduced, particularly the use of aluminium rods regarded as the frictional granular material. The normalised pile tip movements were identified by both the model test and finite element analysis. The model test results found to be in good agreement with the finite element analysis. Based on the normalised pile tip settlements due to tunnelling adjacent to a line of loaded piles, influence zones were proposed in this study. The proposed influence zones are relatively wider and deeper than those proposed in previous studies. The authors believe that it will be useful to decide the reasonable location of tunnel construction in the planning stage.     

层状地基中隧道开挖对临近既有隧道的影响分析

首次采用弹性层状半空间地基模型,建立了多层地基中隧道开挖对临近既有隧道影响的连续弹性分析方法,改变了过去采用简化分析方法仅能在均质地基中求解此类工程问题的状况。首先,采用Laplace积分变换得到了直角坐标系下单层地基应力和位移的初始函数,在此基础上,运用矩阵递推技术,给出了竖向荷载作用下层状地基中应力和位移的解析表达式并将其作为分析该问题的基本解。然后,采用弹性层状半空间地基模型将既有隧道视为Euler-Bernoulli梁,地基土体连续位移采用弹性层状半空间体系的基本解进行计算,并引入临近隧道开挖引起的土体自由位移场影响建立该问题的连续弹性求解方程,从而可以求得隧道纵向位移和内力。最后,结合离心模型试验和有限元数值模拟算例进行分析,验证了本文方法的有效性。此外,为考察地基土成层性对既有隧道性状的影响,还对几种典型层状地基中的隧道进行了参数分析。成果可为合理制定地下工程施工对临近既有隧道的保护措施提供一定的依据。     

Response of clay soil to three-dimensional tunnelling simulation in centrifuge models

Tunnelling-induced ground movements are complicated and investigations into them normally require some simplifications. This paper provides a brief literature review which highlights the advantages of adopting simplifications in physical modelling and addresses some of the deficiencies in the assessment of soil deformation due to a simulated tunnel excavation. A set of centrifuge tests modelling a tunnel heading located at different depths in clay was carried out at 125g. The tunnel was modelled by a semi-circular cavity partly supported by a stiff lining. The unlined tunnel heading was supported by a thin rubber bag supplied with compressed air pressure. Tunnel excavation was simulated by reducing air pressure. The induced ground movements at the subsurface and surface were measured by a 2D image analysis and a new, novel 3D imaging system. The results show that the experiment successfully reproduced key aspects of tunnelling-induced soil deformation in practice. In addition, a new equation to predict horizontal displacements in the longitudinal direction is proposed.     

Effects of tunnelling on pile foundations

An efficient analysis method is presented for estimating the effects induced by tunnelling on existing pile foundations. The method is based on a two-stage procedure: (1) an estimate of the free-field ground movements caused by the tunnel excavation, and (2) an analysis of the pile group subjected to the computed free-field ground movements. The first step may be carried out using alternative approaches, ranging from empirical methods to 3D numerical analyses. The second step is performed by PGROUPN, a computer program for pile-group analysis based on a non-linear boundary element solution. The validity of the approach is assessed by comparing it with alternative numerical solutions and field measurements. The results indicate that the method is capable of generating reasonable predictions of pile response for many cases of practical interest, thus offering substantial cost savings over a complete 3D analysis of tunnel–soil–pile interaction.     

层状地基中单桩的扭转变形分析

研究了扭矩作用下单桩的扭转变形。采用积分变换和传递矩阵方法求解成层土在内部环形荷载作用下的基本解;利用此基本解并考虑桩土位移协调条件,提出了层状地基中单桩扭转变形的半解析方法;通过一匀质地基算例验证了该理论方法的正确性,并给出了双层地基模型的数值分析结果。     

Back analysis for tunnelling induced ground movements and stress redistribution

Analysing tunnelling process in 2D plane strain conditions is widely used method to calculate tunnelling induced settlement profiles as well as soil structure interactions. Possibility of damage to the surface and/or underground structures can be estimated using powerful finite difference method (FDM) and finite element method (FEM) of analysis. However, setting up a realistic model that would be able to achieve this goal is rather difficult. In this paper, 2D FDM analysis has been conducted to assess tunnelling induced settlement, stress redistribution phenomena along with movements around shallow soft ground tunnels excavated in accordance with the New Austrian Tunnelling Method. Measurements recorded during construction of the Heathrow Express Trial Tunnel in London Clay were compared with the predicted values to validate numerical estimations. As a soil model, the Mohr–Coulomb plasticity model has been used in the FDM analysis. Results obtained from 2D FEM are also included in this paper for comparison purposes to evaluate performance of both numerical analysis procedures. Predictions from both FDM and FEM analyses proved to be procedures used within this work can be a tool in practical engineering applications to simulate tunnelling operations.     

Evaluating the effect of soil structure on the ground response during shield tunnelling in Shanghai soft clay

When evaluating tunnel-induced ground response in Shanghai soft clay, the soil structure and its degradation behaviour of natural Shanghai soft clay during shield tunnelling should be properly considered. In this paper, a constitutive model that considers the initial soil structure and its destructuration is formulated within the framework of critical-state soil mechanics. The model is successfully calibrated and used to simulate the undrained behaviour of natural Shanghai soft clay. Based on the proposed model, finite-element analyses are conducted to simulate the short- and long-term ground responses induced by tunnelling at Shanghai metro line 2. The comparisons between numerical results and field measurements reported in literature indicate that the soil structure and the tunnel-induced destructuration significantly affects the magnitude and shape of the short-term surface settlement trough and horizontal displacement in Shanghai soft clay. The pore pressure variations around the tunnel are also affected by soil structure, which will significantly influence the long-term ground consolidation settlement in Shanghai soft clay.     

A study on the effects of overlying soil strata on the stresses developing in a tunnel lining

Shield tunnel lining in soft ground is usually designed based on empirical and analytical methods. These methods are convenient and easy to use; however, they are based on simplifying assumptions related to soil homogeneity around and above the excavated tunnel. The effects of overlying stiffer layers on the tunnelling induced settlement has been investigated by several researchers and was found to significantly influence ground movements. This study evaluates the effects of overlying stiff layers above a tunnel excavated in soft ground on the stresses developing in the tunnel lining. Laboratory investigation is conducted to study how the presence of these layers influence bending stresses in a model tunnel constructed in soft clay and overlain by a coarse sand layer located at different heights above the tunnel. Validation using the experimental results, elasto-plastic finite element analyses are then performed to explain the role of the relative stiffness between the overlying layer and the soft soil deposit hosting the tunnel. Depending on the thickness and location of the overlying stratum, the presence of a stiff layer above the tunnel can have a significant impact on the stresses developing in the tunnel lining.     

隧道开挖对层状地基中邻近管道影响的 DCBEM-FEM 耦合方法

目前,在城市地铁隧道施工中常常遇到邻近市政管线的影响。而较多的研究集中在隧道施工引起的周围地层变形上,考虑邻近管线 作用的隧道开挖理论分析方法并不多见。为此,针对隧道洞周引入椭圆化非等量径向土体位移控制模式,将邻近管线视为 Euler-Bernoulli 梁,同时将层状地基土体视为弹性层状地基模型,提出了 层状地基中隧道开挖引起邻近管道纵向变形的 DCBEM-FEM （位移控制边界元与有限元） 耦合分析方法。最后结合现场实测数据和位移控制有限元数值模拟进行分析,验证了本文方法的有效性。研究表明： DCBEM-FEM 耦合 方法可以较好的体现隧道开挖所引起的地层损失问题,同时本文方法在考虑邻近管线作用时具有较好的计算精度。研究成果可为合理制定城市地铁隧道施工对邻近管线的保护措施提供一定的理论依据。