复合式衬砌结构中衬砌分担围岩压力比例的研究

复合式衬砌结构中衬砌分担围岩压力的评价方法是隧道工程技术的重要研究课题之一。依托某新建铁路隧道工程,提出了一种基于监测位移反分析评价围岩和支护应力,进而计算初期支护和衬砌背后压力的方法。根据监测位移和衬砌施作时间,确定初期支护的已发生变形和剩余变形。通过有限元反分析求出与已发生变形和剩余变形相对应的围岩和支护应力,得到初期支护和衬砌背后压力。对比初期支护背后压力及衬砌背后压力的现场监测和反分析的计算结果,两者比较一致,说明了该方法的可行性。该新建隧道初期支护闭合95 d后施作衬砌,计算得到衬砌背后压力约0.04～0.06 MPa,衬砌分担围岩压力比例约13%～16%。研究成果对复合式衬砌结构的设计具有一定的参考意义。     

Analytical Solutions for the Construction of Deeply Buried Circular Tunnels with Two Liners in Rheological Rock

The construction of underground tunnels is a time-dependent process. The states of stress and strain in the ground vary with time due to the construction process. Stress and strain variations are heavily dependent on the rheological behavior of the hosting rock mass. In this paper, analytical closed-form solutions are developed for the excavation of a circular tunnel supported by the construction of two elastic liners in a viscoelastic surrounding rock under a hydrostatic stress field. In the solutions, the stiffness and installation times of the liners are accounted for. To simulate realistically the process of tunnel excavation, a time-dependent excavation process is considered in the development of the solutions, assuming that the radius of the tunnel grows from zero until its final value according to a time-dependent function to be specified by the designers. The integral equations for the supporting pressures between rock and first liner are derived according to the boundary conditions for linear viscoelastic rocks (unified model). Then, explicit analytical expressions are obtained by considering either the Maxwell or the Boltzmann viscoelastic model for the rheology of the rock mass. Applications of the obtained solutions are illustrated using two examples, where the response in terms of displacements and stresses caused by various combinations of excavation rate, first and second liner installation times, and the rheological properties of the rock is illustrated.     

复杂条件下隧道断面形状和支护参数优化

通过有限差分法（FLAC3D）数值计算和现场试验对马蹄形断面和大曲率边墙、似圆形断面形式下隧道的支护受力和围岩变形特征进行了对比分析,得出采用似圆形断面可以有效地控制围岩的变形量和变形速率,尤其是水平收敛变形;现场变形量测时的丢失位移所占总位移比例较大,其中下台阶丢失位移比例最大;通过现场试验,对不同支护刚度下围岩压力、锚杆受力、钢架、混凝土应力以及二次衬砌分担的围岩压力和模筑混凝土受力情况进行分析,结合洞室变形的现场量测,得出二次衬砌接触压力及分担围岩压力比呈现出随着初支刚度增大而增大的规律,并综合确定了板岩段合理的支护参数。该结论对在构造应力发育的软岩地区修筑隧道提供了有益的工程经验     

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。     

流变性软土地基模型的时效性分析与刚度计算

建立了线性粘弹性半空间地基模型,并给出了地基柔度矩阵和刚度矩阵的计算公式。文中以上海香港广场北块地库深基坑工程为例,对基坑围护结构的变形和内力,将原设计的理论计算值、实测值与本文采用时效性地坛模型的理论计算值进行了对比分析。结果表明,时效性地基模型的理论计算值与实测值较吻合,反映出该地基模型在流变性软土地落中对基坑围护结构的变形和受力分析具有较好的适用性。     

粘弹-塑性岩体中衬砌与围岩的共同作用问题

在许多类型的岩层中(比如粘土质的沉积岩、岩盐以及其他较软弱的岩质等)地下洞室在开挖完成之后,其围岩的变形特性,强度特性以及整体的稳定性有明显的时间效应.因此,近年来在国内外的研究工作中已有不少人致力于时间因素对围岩稳定性影响的研究.     

黏弹性节理岩体的位移不连续模型研究

选用三参数标准线性固体作为岩石本构,提出了一种考虑岩体黏弹性的位移不连续模型;根据一维黏弹性波的特征线法,推导了节理处质点速度、应力和应变递推公式。首先,基于分离式霍普金森压杆（SHPB）对砂层进行试验,得到其应力-应变关系,并换算出砂层节理的法向刚度;接着,通过一维强间断黏弹性波的波速公式、高频波衰减系数以及任一频率下的衰减系数,确定出数值算法中的三参数。最后,基于自制的摆锤装置,探讨了一维应力波在节理岩体中的传播规律,试验中以两根长1 000 mm、直径为68.50 m的岩杆作为入射和透射杆,以3 mm砂层模拟节理。试验和数值结果吻合度良好,进一步验证了该方法的可靠性。     

Elastic Solution for Deep Tunnels. Application to Excavation Damage Zone and Rockbolt Support

Summary  A new formulation is presented for deep circular tunnels in rock with cylindrical anisotropy. The formulation is an exact solution since it satisfies equilibrium, strain compatibility, and the anisotropic constitutive model. Complete solutions have been found for two scenarios: tunnel with excavation damage zone, and tunnel with rockbolt support. The solution is based on the assumption of a deep, circular tunnel in a medium with two homogeneous zones: an inner zone surrounding the tunnel, which is either isotropic or anisotropic, and an outer zone, for the remainder of the medium, which is isotropic. Plane strain conditions, elastic response of rock, rockbolts and support, and simultaneous excavation and support installation are also assumed. For tunnels surrounded by an excavation damage zone with reduced rock properties, the tangential stresses and the radial deformations at the tunnel wall are very sensitive to both the magnitude of stiffness reduction of the damaged rock and the size of the damaged zone. The effect of the rockbolts on the rock is approximated by treating the rockbolt-rock composite as a material with cylindrical anisotropy with stiffnesses related to the properties of the rock and rockbolts, and spacing of the rockbolts. Comparisons between the analytical solution and a numerical method show small differences and provide confidence in the approach suggested.     

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。     

TBM隧道回填层-管片受力特征模型试验研究

回填层作为围岩和管片之间的连接部分,起到稳定衬砌、传递荷载、吸收变形等作用。护盾式TBM隧道施工过程中,回填层存在未注浆松散、注浆固结两个主要状态。回填层状态不同,回填层作用及管片受力特点也不同。研究采用相似模型试验分析不同状态下的回填层作用机制,通过研究得到了以下结论：回填层未注浆松散状态下,由于碎石的径向压缩与环向移动,围岩传递到管片上的荷载量值降低且分布较为均匀,此时回填层作为“可压缩层”,具有让压和均匀荷载的作用,能明显降低管片的受力和变形;回填层注浆固结后,回填层虽然能够承担少量的荷载与变形,但承载能力有限,主要作为围岩与管片之间的“传递层”,传递荷载与变形;对于挤压性围岩护盾式TBM隧道施工可适当应用回填层未注浆时的“可压缩性”,减小施工过程中管片受力与变形;对于浅埋及地铁隧道则应尽早注浆,使衬砌与围岩形成稳定的受力体系;回填层弹性模量的增加可提高回填层-管片组合体系支护刚度,但增加效果不明显。     

A method of time-dependent analysis using elastic solutions for nonlinear materials

The formulation of viscoelastic solutions from elastic equations using the ‘correspondence principle’ and an inverse Laplace transform has been discussed extensively in the literature. Because this method has been developed, many time-dependent solutions can be obtained from closed form elastic solutions and conditions have been delineated in which the ‘quasi-elastic’ approximation of the viscoelastic solution is within acceptable tolerance. This communication shows the feasibility of the application of these methods to formulate approximate nonlinear viscoelastic solutions with nonlinear stress-strain materials, and for want of a specific nonlinear model to demonstrate this, the hyperbolic model was selected. The ‘power law’ is used to model the relaxation modulus of the viscoelastic materials. There are five related development that are discussed here using a simple numerical example to illustrate each of them and they are: (1) a linear elastic solution, (2) a linear viscoelastic solution, (3) a nonlinear elastic solution, (4) a nonlinear viscoelastic solution and finally, (5) a ‘regression’ approximation of the nonlinear viscoelastic solution which is suggested by the series form of the elastic solution. All of these are related to one another and each provides an acceptably accurate solution of the problem it addresses. The latter is of particular practical interest since it can be used to provide answers to problems involving nonlinear viscoelastic materials while requiring only very small calculation times. The problem used as an example is the calculation of the displacement of a circular hole in an infinite plate made of a material with a nonlinear time-dependent stress-strain relationship. The nonlinear elastic form of the solution was developed by matching results from nonlinear finite element analysis.     

恒载作用下轴对称圆巷围岩的流变变形方程求解

建立围岩-支护相互作用流变变形机制的数学力学模型是解决岩石地下工程支护问题的有效途径,其关键问题是,在围岩产生流变变形的过程中支护是如何对围岩进行作用的。根据基于Levy-Mises本构关系及D-P屈服准则的轴对称圆巷的理想弹塑性解、一维蠕变曲线的等时曲线相似的假设以及三维流变试验结果,推导出了原岩应力和被动支护反力均为恒载,且巷道围岩为三维应力状态下的蠕变方程及轴对称圆巷围岩的非线性黏弹塑性流变变形计算公式。与前人的工作相比,文中推导的公式中含有对围岩流变变形起决定作用的2个参数,即原岩应力 和岩石材料的单轴塑性屈服应力 ,因此公式推导的理论基础更加完备、可信度更高。     

复合式衬砌在围岩蠕变过程中的受力规律研究

为了分析隧道复合式衬砌在围岩蠕变过程中的受力规律,利用有限元程序ANSYS建立计算模型,采用广义开尔文本构关系,分别分析了二次衬砌在不同支护时机和不同刚度下,复合式衬砌的受力规律。分析结果表明:在不同的时机施加二衬,其受力都有一个逐步增大并趋于稳定的过程,初支与二衬受力随二衬支护时机的变化趋势是相反的;二衬支护越早,其受力越大。通过早施作二衬,来转移初支上的应力是不合适的。当二衬刚度增加时,其所分担的围岩压力将增大,而初支分担的围岩压力有一定的减小。结合云腾岭隧道进行具体分析,得出该隧道二次衬砌的最佳支护时间为开挖后第40天。另外,通过对该隧道现场监控量测分析发现,二衬的受力—历时曲线与有限元分析相吻合。     

基于西原模型的圆形隧道黏弹-黏塑性解析解

基于西原模型,假设黏塑性体的偏应变张量的一阶导数与瞬态偏应力张量和稳态偏应力张量之差成正比,得到围岩黏塑性区的本构方程。采用拉普拉斯变换与逆变换,推导了圆形隧道黏弹-黏塑性解析解。当 时,该解退化成线弹性本构模型的解答;当 时,该解退化成理想弹塑性本构模型的解答。通过工程实例,分析了围岩位移场、应力场和黏塑性区半径随时间的变化规律。当支护力保持不变时,围岩不同位置位移、围岩黏塑性区半径将随时间增长而持续增大并趋于稳定;围岩黏弹-黏塑性特征对径向应力和黏弹性区切向应力影响较小,对黏塑性区切向应力影响较大,越靠近洞壁处,切向应力随时间变化越剧烈。此外,不同支护力作用下洞壁处的切向应力在支护初期均较大,因此应采用及时支护的策略;考虑到围岩黏弹-黏塑性特征对支护力的影响,建议采取让压支护技术以保证围岩和衬砌的稳定性。     

应变软化模拟与圆形隧道衬砌分析

在岩土工程中,有许多类岩体呈现应变软化特性。在应变软化过程中,如果多个材料强度参数分析发生变化,就很难给出软化问题的解析解。已有的文献研究表明,在经典的弹塑性理论框架下,模拟岩土介质的应变软化过程依然值得深入研究。利用应变软化材料强度参数随塑性应变增加而弱化的特点,提出了将应变软化过程简化为一系列的脆性应力跌落与塑性流动过程的思想,应变软化行为的模拟转化为一系列脆塑性过程的分析。将这种模拟应变软化过程的思想方法用于求解均匀初始应力场中应变软化介质内的圆形隧道开挖问题,研究了衬砌对减少岩土开挖扰动的作用以及考虑应变软化对衬砌内力的影响。数值结果表明,对于应变软化岩土材料,忽略其强度软化的行为是偏于危险的。     

Analysis of undrained cavity expansion in elasto‐plastic soils with non‐linear elasticity

A large strain analysis of undrained expansion of a spherical/cylindrical cavity in a soil modelled as non‐linear elastic modified Cam clay material is presented. The stress–strain response of the soil is assumed to obey non‐linear elasticity until yielding. A power‐law characteristic or a hyperbolic stress–strain curve is used to describe the gradual reduction of soil stiffness with shear strain. It is assumed that, after yielding, the elasto‐plastic behaviour of the soil can be described by the modified Cam clay model. Based on a closed‐form stress–strain response in undrained condition, a numerical solution is obtained with the aid of simple numerical integration technique. The results show that the stresses and the pore pressure in the soil around an expanded cavity are significantly affected by the non‐linear elasticity, especially if the soil is overconsolidated. The difference between large strain and small strain solutions in the elastic zone is not significant. The stresses and the pore pressure at the cavity wall can be expressed as an approximate closed‐form solution. Copyright © 2001 John Wiley & Sons, Ltd.     

A new concept for sinking freeze shafts into great depths

For Ruhrkohle AG, the largest mining company of the Federal Republic of Germany, nine shafts are presently being sunk. In late 1978, Gewerkschaft Walter, Essen, obtained the contract for the construction of the Voerde shaft from Bergbau AG Niederrhein, a subsidiary of Ruhrkohle AG.

The requirements to be met regarding the quality of the lining in terms of loads to be absorbed from rock pressure, hydraulic pressure, tension, etc. are very high. Up to a depth of 600 m, this shaft will be sunk through soft and water-bearing strata such as formations of Tertiary, Cretaceous, Bunter Sandstone and Permian. The freezing method therefore has to be employed.

The high requirements with regard to the quality of the lining can only be fulfilled if the lining is constructed in the form of an absolutely watertight tube, not connected to the surrounding ground and resting on a ring foundation below the frozen part of the shaft.

During sinking of the shaft, the icewall will normally absorb the load of both rock pressure and hydraulic pressure. Because of the depth of the frozen part of this shaft and for economical reasons, a yielding outer lining has to be constructed. This will serve on one hand as an auxilliary lining during sinking as a support for the icewall and, as part of the final lining on the other hand, will absorb the rock pressure. This auxilliary lining can only be of the yielding type, its flexibility must correspond to the behavior of the surrounding frozen rock. The determination of the thickness of the icewall and the outer lining was based upon results of tests carried out on frozen and non-frozen drilling cores by Prof. Jessberger's Institute at the Ruhr-University of Bochum.

Taking an outside shaft diameter of approximately 9 m, the diameter of the freezingpipe circle is 18.5 m, the number of freezing pipes is 38.

Considering an icewall-thickness of 8 m (on average) and using the data for friction and cohesion for the different rock formations resulting from the above mentioned tests, the lining dimensions for the different rock formations were calculated. The determined dimensions were widely varying. It also had to be considered, that the outer lining would have to bear the load of the rock pressure once the frozen core of the shaft had been finished.     

Analysis of Inflatable Rock Bolts

An inflatable bolt is integrated in the rock mass through the friction and mechanical interlock at the bolt–rock interface. The pullout resistance of the inflatable bolt is determined by the contact stress at the interface. The contact stress is composed of two parts, termed the primary and secondary contact stresses. The former refers to the stress established during bolt installation and the latter is mobilized when the bolt tends to slip in the borehole owing to the roughness of the borehole surface. The existing analysis of the inflatable rock bolt does not appropriately describe the interaction between the bolt and the rock since the influence of the folded tongue of the bolt on the stiffness of the bolt and the elastic rebound of the bolt tube in the end of bolt installation are ignored. The interaction of the inflatable bolt with the rock is thoroughly analysed by taking into account the elastic displacements of the rock mass and the bolt tube during and after bolt installation in this article. The study aims to reveal the influence of the bolt tongue on the contact stress and the different anchoring mechanisms of the bolt in hard and soft rocks. A new solution to the primary contact stress is derived, which is more realistic than the existing one in describing the interaction between the bolt and the rock. The mechanism of the secondary contact stress is also discussed from the point of view of the mechanical behaviour of the asperities on the borehole surface. The analytical solutions are in agreement with both the laboratory and field pullout test results. The analysis reveals that the primary contact stress decreases with the Young’s modulus of the rock mass and increases with the borehole diameter and installation pump pressure. The primary contact stress can be easily established in soft and weak rock but is low or zero in hard and strong rock. In soft and weak rock, the primary contact stress is crucially important for the anchorage of the bolt, while in hard and strong rock it is the secondary contact stress that plays a vital role.     

Prediction of tunnel lining loads using correction factors

A design method for the prediction of lining loads should include the decrease of lining loads due to the stress release before lining installation and the increase of lining loads due to development of ground yielding. Schwartz and Einstein included both factors in their original closed form solutions in the form of a support delay factor λ_d and a yield factor λ_y respectively. The validity of the design method is reviewed by comparing the loads calculated using the methods with the field measurements obtained from several tunnels. The possible causes of the load discrepancy between measurements and predictions are presented.

Schwartz and Einstein's proposed method gives reasonable results for tunnels with short delay lengths. However, the method could not be used reliably for tunnels either with long delay lengths or with voids between the soil and TBM due to the difficulties finding the pre-support ground movements and therefore λ_d.     

管道衬砌内水外渗对边坡稳定影响的数值模拟

根据钢筋混凝土受拉开裂特性，通过混凝土开裂后钢筋和混凝土联合承载原理，提出了在内水压作用下混凝土衬砌开裂的裂缝宽度估算公式。根据开裂衬砌内水外渗的规律，提出了高压管道内水外渗与混凝土衬砌裂缝宽度相互影响的有限元迭代计算分析方法。该方法将内水压荷载分解为起裂荷载和破坏荷载，对混凝土衬砌起裂荷载采用一次加载，对破坏荷载采用分级加载迭代，由此较好地反映衬砌开裂和渗流耦合作用效应。根据渗流荷载对边坡的破坏作用，提出了对边坡稳定判断的思路。通过对实际工程的分析计算，论证了高压管道内水外渗对边坡的稳定影响, 为内水外渗与应力场耦合分析提供了一种有效的计算方法。