Analytical approach for circular-jointed shield tunnel lining based on the state space method

This paper presents a new analytical solution to the circular segmental tunnel lining subjected to overburden and surrounding earth pressures. The governing equations are derived by adopting the curved Euler beam theory and the principle of minimum potential energy. Based on the state space method, the displacements and the relevant energy-conjugated internal forces are treated as the fundamental unknown state vector and can be obtained by solving the state function. The inter-segment joints on the lining are modeled by a set of linear springs, including shear, compression, and rotation. The presented method allows for the arbitrary distribution of the segmented joints and loads along the circumferential direction. The most striking advantages of the proposed method include the rigid body displacement treatment, lining-displacement-dependent soil reaction, and internal force direction dependency of the joint stiffness. Using this method, the displacements and internal forces of the entire lining can be obtained conveniently and simultaneously under the arbitrary loading and joint distribution conditions. The verification of the analytical solutions is provided by several examples.     

考虑接头力学特性的盾构隧道衬砌结构计算方法研究

基于盾构隧道衬砌结构接头的构造特征,建立了接头的力学模型,将接头位置管片间的相互作用离散为一系列由剪切弹簧和法向弹簧组成的组合弹簧,根据得到的节点弹簧应力或法向位移在计算过程中动态调整弹簧刚度参数,将接头模型应用到衬砌结构计算中。该方法可以综合考虑衬砌结构的横向和纵向结构性能,计算管片和接头的内力与变形以及接缝的张开量。采用上海长江隧道衬砌结构整环试验结果对计算模型进行了验证,结果表明该模型能比较合理地模拟衬砌结构的变形特性。     

简谐荷载作用下饱和土体中圆形衬砌隧道三维动力响应分析

研究了全空间饱和土体中圆形衬砌隧道在径向简谐点荷载作用下的三维动力响应,将衬砌用无限长圆柱壳来模拟,土体用Biot饱和多孔介质模型来模拟,引入两类势函数来表示土骨架的位移和孔隙水压力,并利用修正Bessel方程来求解各势函数,结合边界条件,得到频率-波数域内衬砌和土骨架位移、孔隙水压力的解答,最后进行Fourier逆变换得到时间-空间域内的响应。通过算例分析了荷载振动频率和土体渗透性对土体和衬砌位移响应及土体孔压的影响。结果表明,饱和土体和弹性土体的位移响应具有明显区别。随着荷载频率的增大,土体和隧道位移幅值减小,土体孔压幅值增大;随着土体渗透性增大,土体位移及孔压幅值减小。     

节理岩体中隧道开挖与支护的数值模拟

由于节理、断层等不连续面的存在造成岩体变形的不连续性,并且这些不连续面对岩体变形、应力等力学行为造成重要影响。对已有的非连续变形分析程序进行了两点改进,应用改进的程序模拟了节理岩体中隧洞开挖与支护的过程,研究了不同节理倾角岩体的应力分布特性、开挖后隧洞围岩的变形和应力分布规律以及支护后衬砌的变形与应力特点。研究结果表明,节理倾角对节理岩体系统的应力和变形有着直接的影响,并且影响着隧洞开挖后的内空收敛效应;隧洞开挖顺序对围岩的变形和稳定也有重要影响。改进后的非连续变形分析方法和程序可以用来分析复杂节理岩体系统中隧洞的开挖与支护。     

盾构隧道管片衬砌的平板壳-弹性铰-地基系统模型

从Reissner-Mindlin板单元入手,研究了盾构隧道管片衬砌结构之间的连接特征及土层与管片衬砌结构的共同作用,提出了盾构隧道管片衬砌结构的平板壳-弹性铰-地基系统模型,在此基础上研制了相应的有限元计算程序。该模型考虑了管片衬砌本身的弯曲、剪切和薄膜作用,考虑了纵向接缝在正负弯矩作用下的转动刚度差异和环向结缝对结构刚度的削弱作用,以及土层与衬砌结构的共同作用。能解决盾构隧道管片衬砌结构的三维受力分析,并能计算出结构的内力和变形,弥补了二维计算模型的某些不足。验证了程序的可靠性,最后给出了工程算例的三维计算分析结果。     

大断面宽幅盾构管片三维内力分布分析

以武汉长江隧道工程为例,采用三维壳-弹簧计算模型,对不同幅宽和不同环间接头剪切刚度的管片衬砌结构力学分布进行了分析,并与梁-弹簧模型结果在量值上做了全面比较。研究表明,全环最大弯矩发生在幅宽边缘部位;环间接头剪力对幅宽边缘影响较大,而对幅宽中央影响偏小;当环间接头剪切刚度为非无穷大时,壳模型的幅宽边缘最大弯矩值略微大于梁弹簧模型相应结果,而当无穷大时两者数值则基本相等;壳模型的幅宽中央的最大弯矩值介于梁模型错缝与通缝拼装的数值之间,并随幅宽加大而趋于接近通缝拼装的结果;大幅宽条件下,不宜将梁-弹簧模型的环间最大剪力结果作为环间接头抗剪设计的计算依据。     

隧道支护结构荷载作用的随机反演

提出荷载－结构模式进行随机反分析方法，从隧道支护结构变形反算对应的荷载作用，可反推围岩抗力系数和覆土荷载的分布情况，以及作用于支护结构上各部位的外荷载。提出了以实测位移为基础的样条函数插值．以插值位移补充大量的实测值，满足了反分析所需众多的已知位移数。通过一施工实例对该方法的可行性进行了检验。     

Analytical model for the beam action of a tunnel lining during construction

Measurements on a 14.5‐m diameter bored tunnel have shown that the mechanised assembly of a segmented tunnel lining results in a permanent longitudinal bending moment in the tunnel lining. An analytical model for the beam action of the tunnel lining during the construction phase of bored tunnels is presented. The model incorporates many of the essentials in staged beam construction. It takes into account the influence of forces from the TBM, the loading of the tunnel lining by the grout in the liquid phase, and linear elastic properties of the tunnel lining and soil. Calculations are compared with measurements at the Groene Hart Tunnel (GHT), 20 km south of Amsterdam: the bending moment curve and vertical inclination of tunnel lining segments were compared. The measured bending moment curve is well reproduced. The measured vertical inclination of the lining segments is found to be governed by the beam action of the tunnel lining plus the influence of shear force in the lining. Copyright © 2011 John Wiley & Sons, Ltd.     

A new numerical approach to the hyperstatic reaction method for segmental tunnel linings

This paper proposes a numerical approach to the hyperstatic reaction method (HRM) for the analysis of segmental tunnel linings. The influence of segmental joints has been considered directly using a fixity ratio that is determined on the basis of the rotational stiffness. The parameters necessary for the calculation are presented. A specific implementation has been developed using a FEM framework. This code is able to consider the three‐dimensional (3D) effect of segment joints in successive rings on the tunnel lining behaviour. The present HRM allows one to take an arbitrary distribution of segment joints along the tunnel boundary into consideration. In addition, the rotational stiffness of segment joints has been simulated using nonlinear behaviour, as it is closer to the true behaviour of a joint than linear or bilinear behaviour. The numerical results of three hypotheses on ring interaction, which allow the 3D effect of a segmental tunnel lining to be taken into account, have been compared with data obtained from the shield‐driven tunnel of the Bologna–Florence high‐speed railway line project. The numerical results presented in the paper show that the proposed HRM can be used to effectively estimate the behaviour of a segmental tunnel lining. Copyright © 2014 John Wiley & Sons, Ltd.     

爆炸荷载作用下深埋圆形隧洞的饱和黏弹性土-衬砌系统动力响应

假定土骨架服从标准线性固体黏弹性本构关系,研究了深埋圆形隧洞的饱和黏弹性土-弹性衬砌耦合系统在轴对称爆炸作用下的瞬态动力响应。首先,基于饱和土的Biot模型和衬砌的弹性理论,通过引入势函数和Laplace变换,利用弹性衬砌和饱和黏弹性土界面处的连续性条件以及边界条件,得到饱和黏弹性土体和弹性衬砌位移、应力和孔隙水压力等在Laplace变换域中的解析解。其次,利用Laplace数值Crump逆变换得到耦合系统在时间域的动力响应,数值分析了不同土体模型下土体-衬砌耦合系统的径向位移和环向应力以及土体孔隙水压力等。结果表明：对不同土体模型的土体-衬砌耦合系统,其在爆炸载荷作用下的动力响应性态基本一致,但动力响应的振动周期和幅值等具有明显的差异。同时,对于饱和黏弹性土-弹性衬砌系统,土体黏性参数对土体径向位移和孔隙水压力有明显的影响,但对土体环向应力影响较小。     

水工隧洞钢筋混凝土衬砌外水压力取值方法研究

外水压力是隧洞衬砌承受的主要荷载之一,也是控制其建设与运行或检修过程中衬砌结构安全的关键因素。目前外水压力的取值仍然以经验公式为主,存在很大的局限性和不准确性。首先分析对比了衬砌外水压力的折减系数法、理论解析方法和数值分析方法几种取值方法,然后进行了不同渗透环境和衬砌支护条件下的衬砌外水压力计算。结果表明,随着围岩渗透性和衬砌厚度的增大,衬砌外表面的水压力越大;对于渗流数值计算,模型范围应取距离隧洞中心不小于30倍洞径;考虑渗流场的时间效应,开挖完成10 d后隧洞的渗流场趋于稳定,衬砌支护20 d后衬砌外侧水压力分布趋于稳定。     

隧道斜交穿越地裂缝的模型试验研究

西安地区由北向南间隔分布有十多条近东西走向的地裂缝,建设中的多条地铁线路与地裂缝呈斜交状态。为了揭示地铁隧道斜交穿越地裂缝时受地裂缝活动而产生的力学性状变化,采用50:1几何相似比尺的物理模型试验仪,在合理模拟围岩地层、衬砌结构、应力条件、地裂缝与洞轴线交角及其错动位移基础上,开展了斜交地裂缝活动条件下隧道衬砌结构与围岩相互作用的物理模型试验研究,并与正交地裂缝活动下的测试结果进行了对比分析。表明斜交地裂缝活动对地铁隧道的影响范围更大,各变形缝均有明显的沉降差发展;邻近斜交地裂缝的衬砌结构易处于“悬臂梁”受力状态,衬砌结构不均匀沉降使其产生旋转位移,围岩土压力变化使衬砌结构内力产生显著变化;随着地裂缝错动位移的发展,上盘内拱顶和下盘拱顶、拱底出现围岩作用的加强,而上盘拱底出现围岩作用的松弛。与隧道正交穿越地裂缝的情况比较,斜交穿越地裂缝时围岩土压力和衬砌结构内力变化更大,易出现拉裂破坏。     

火灾作用下隧道衬砌结构变形理论分析模型

火灾作用下衬砌材料力学性能的劣化会引起隧道结构的损伤,变形量的增大,危害隧道运营安全。基于几何和材料非线性理论,综合考虑火灾作用下衬砌结构中温度的非线性分布,材料力学性能的高温劣化及热膨胀等因素的影响,提出用于描述火灾作用下隧道衬砌结构变形行为的理论分析模型。在此基础上,给出半圆形隧道在火灾作用下截面转角及径向变形的解析解,分析火灾持续时间对衬砌变形行为的影响规律,可为隧道结构防火设计及灾后评估提供理论依据。     

翔安海底公路隧道陆域段变形控制措施研究

翔安隧道是我国第一条大跨公路海底隧道,其两端陆域段位于富水的强风化岩层中,地质条件极为复杂。隧道施工期间,部分断面发生了较大变形,超过了预留变形量,给二次衬砌的施工造成了影响,而且过大的变形有时还会导致隧道围岩失稳,应寻求一套合理的变形控制措施。基于现场监测数据和施工记录,并结合数值方法,对隧道施工过程中所采取的工程措施的作用效果进行了研究。结果表明,增设锁脚锚管、加强临时支护及管井降水等工程措施都可以在一定程度上减小隧道支护结构的变形,但在地质条件较差的富水强风化岩层中修建大跨公路隧道时,将两种或多种工程措施的组合起来使用效果更佳。例如,在采用降水（连续墙）＋加强临时支护＋锁脚锚管的组合方案后,隧道的拱顶下沉减小了46 %～60 %,水平收敛也减小了约30 %。这些措施可为今后类似工程提供一定的参考。     

隧道围岩特性曲线数值模拟与分析

由于围岩特性曲线中只有圆形坑道才有解析解,对马蹄形坑道只能近似地将其转换成圆形[1],加上其它因素,如围岩原始数据、原始应力场、初始位移等的确定问题,使得特征曲线法在一般衬砌设计,特别是衬砌标准图设计中难以应用。笔者采用弹塑性有限元方法绘制了不同埋深、各种围岩级别下的铁路标准设计单、双线毛洞的围岩特征曲线,得出不同围岩级别、不同埋深、不同洞形和尺寸下围岩特性曲线的变化规律。对特性曲线法在隧道衬砌设计中的应用有实际意义。     

深埋圆形隧道弹塑性位移统一解及其比较分析

基于统一强度理论和非关联线性流动法则,考虑塑性区的真实弹性应变,推导了深埋圆形隧道弹塑性位移统一解。位移统一解合理地考虑了中间主应力效应和围岩剪胀特性的影响,具有广泛的理论意义。经与文献简化位移解析解比较分析知,围岩塑性区的弹性应变对隧道位移影响显著,简化解析解所得结果偏小,简化解析解和文中统一解之间的差异与中间主应力效应和围岩剪胀特性密切相关;考虑中间主应力的影响,能更加充分发挥围岩的强度潜能;隧道支护设计应考虑围岩剪胀特性的重要影响     

移动环形荷载作用下饱和土中圆形衬砌隧洞动力响应研究

基于Biot理论,研究了饱和土中带有衬砌的圆形隧洞在移动环形荷载作用下的动力响应。假定衬砌为弹性体,土体为饱和多孔介质,引入两类势函数来表示土体、孔隙水和衬砌的位移,使隧洞的控制方程解耦。结合边界条件及连续条件,通过傅立叶变换得到频率-波数域中衬砌和土体的应力、位移和孔隙水压力解答,最后用傅立叶积分逆变换得到时-空域中的数值解。计算并比较了3种隧洞模型（弹性土体隧洞、饱和土体隧洞和饱和土衬砌隧洞）的动力响应分析。数值分析结果说明：（1）移动荷载速度对3种隧洞动力响应均具有较大影响;（2）弹性土体隧洞和饱和土体隧洞的动力响应具有明显区别,所以在富水地区的隧洞动力响应中土体应该视为饱和土体;（3）衬砌对隧洞动力响应有较大影响,故隧洞的动力分析中不能忽略衬砌作用。     

水底隧道饱水地层衬砌作用荷载研究

与山岭隧道所不同,采用矿山法修建水底隧道,二次衬砌将承受很大外水压力,特别是穿越饱水破碎地层时,具有很大的施工风险。以厦门翔安海底隧道为工程背景,针对F4风化深槽地层,研究不同水位条件下,衬砌荷载与排放流量及排放方式之间相关关系。研究得出：当控制排放量为全排条件流量1/3左右时,可卸掉80%外水压力;从环境和经济角度考虑,可将出现拐点折减系数0.2作为水底隧道限量排放的设计基准值;从支护结构体系组成考虑,对于F4强风化深槽破碎围岩,必须施作注浆圈,才可以保证在水压、土压共同作用下衬砌结构安全,结果显示施作注浆圈能够减少衬砌作用荷载30%～40%,提高安全系数几乎一倍;从主体结构受力特征看,水底隧道最不利受力位置在墙脚和仰拱,因此,无论是防水型还是排水型隧道,均应对仰拱形式及支护参数加强设计。     

正交各向异性岩体中非圆形水工隧洞的解析解

将围岩和衬砌分别视作均质、连续的线弹性正交各向异性和各向同性体,并充分考虑衬砌的支护滞后效应和隧洞运行时的内水压力作用,运用复变函数方法中的幂级数解法,提出了正交各向异性岩体中任意形状水工隧洞的力学解析方法。以直墙半圆拱形水工隧洞为例,所获得的解析解可精确满足衬砌内边界的应力边界条件以及围岩与衬砌接触面的应力、位移连续条件,同时还将解析结果与ANSYS数值结果对比分析,吻合良好。利用获得的解析解,讨论了围岩开挖面上不同的各向异性程度、不同的弹性对称面角度以及隧洞内不同的水压荷载对衬砌以及围岩上应力和位移分布的影响。     

Stresses around Pressure Tunnels with Semi-permeable Liners

Summary. The liner of a pressure tunnel needs to be designed such that it can withstand the loads from the ground, the internal pressure, and minimize the development of significant pore pressures at the liner-ground interface. Pore pressures behind the liner reduce the effective stresses in the ground immediately in contact with the liner and can ultimately produce loss of support from the ground. Deformations and loads of the liner are intimately connected to the interplay that exists between liner, ground, and pore pressures in the ground. A closed-form analytical solution has been derived that accounts for the inter-relation between liner, ground, and pore pressures. Elastic response of the liner and ground, and plane strain conditions at any cross-section of the tunnel are assumed. The solution shows that stresses in the ground depend on the following dimensionless factors: relative stiffness of the ground and liner, ground Poisson’s ratio, surface slope angle, coefficient of earth pressure at rest, relative tunnel depth, and magnitude of the pore pressure behind the liner relative to the internal pressure. The minimum ground effective tangential stresses at the ground-liner interface increase with the relative stiffness of the liner, with the coefficient of earth pressure at rest, and with tunnel depth. They decrease with increasing surface slope angle and pore pressures behind the liner. As leakage through the liner increases, the pore pressures in the ground increase. This results in a decrease of effective radial and tangential stresses in the ground while displacements and loads of the liner are relatively less affected.