平行双孔水工隧道相互作用的时效解答

地下工程中常遇到流变岩体中双线近距离隧道施工问题。隧道施工位移的预测和控制,特别是新建隧道的施工对既有隧道产生的影响,是工程中面临的重要问题。针对流变岩体中深埋双圆形水工隧道的问题,笔者采用复变函数方法和Laplace变换技术建立了考虑施工过程时黏弹性应力、位移与弹性复位势之间的关系,然后运用黏弹性叠加原理得到了整个施工过程各个阶段围岩应力和位移全量和增量理论解答,并据此进行新建隧道对既有隧道的影响分析。为验证解答的正确性,对一算例进行了有限元解答和理论解答的比对,两者吻合很好。与数值与实验方法相比,本文解答可以较为便利地对岩体应力、位移进行参数分析,进一步可以指导工程的初步设计。     

Evaluation of deformation response for adjacent tunnels due to soil unloading in excavation engineering

A major challenge in the design and construction of soil excavation and foundation pit engineering in urban areas is the protection of adjacent underground structures, such as existing tunnels. Excavation-induced soil unloading can adversely affect and even damage the tunnels in the vicinity. A simplified analytical approach is presented to analyze the deformation response for adjacent tunnels due to excavation-induced soil unloading in excavation engineering. Firstly, the green soil unloading stress due to adjacent excavation is estimated at the existing tunnel location. Secondly, the deformation response of the tunnel subjected to green soil unloading stress is calculated by the Galerkin’s method, which can be used to obtain the finite element equation converted from the differential equation. The accuracy of the proposed method is verified by comparisons with 3D finite element numerical simulation, centrifuge model tests provide by Kusakabe et al. (1985) and measured data in situ. Finally, the parametric analysis for deformation influence factors of the existing tunnel, including the tunnel buried depth, the distance from the excavation site, the soil geo-characters and the outer diameter of the tunnel, is presented to demonstrate the performance of the proposed method. This proposed method may provide certain basis to make protective measures of existing tunnels influenced by excavation engineering and enables a quick estimate of the deformation behavior of excavation-induced adjacent tunnels, resulting in savings in time and costs.     

Polyaxial strength criterion and closed-form solution for squeezing rock conditions

In this paper,a nonlinear strength criterion is proposed using the average of intermediate(σ_2) and minor(σ_3) principal stresses in place of σ_3 in Ramamurthy(1994)'s strength criterion.The proposed criterion has the main advantages of negligible variation of strength parameters with confining stress and ability to link with conventional strength parameters.Additionally,a new closed-form solution based on the proposed criterion is derived and validated for Chhibro Khodri tunnel.Further,analytical solutions including Singh's elastoplastic theory,Scussel's approach,and closed-form solutions based on conventional and modified Ramamurthy(2007) criteria are compared with the results of proposed approach.It is shown that the in situ squeezing pressure predictions made by the proposed approach are more accurate.Also,a parametric study of the present analytical solution is carried out,which displays explicit dependency of tunnel stability on internal support pressure and tunnel depth.The influence of tunnel geometry is observed to be dependent on the applied support pressure.     

New analytical method for predicting stresses around rectangular tunnels under arbitrary stress boundary conditions

Rectangular tunnels are often encountered in geotechnical engineering. To clarify the mechanical mechanism of the stresses around tunnels, this study presents new analytical approximant solutions for evaluating stresses around tunnels under arbitrary stress boundary conditions. The solutions consist of two parts: one is the solution for a half-plane before excavation, and the other is the solution for a half-plane with tunnels. The second part can be further decomposed into solutions of a half-plane without tunnels subjected to virtual tractions along the ground surface and solutions of an infinite plane with tunnels loaded by virtual tractions along tunnel boundaries. An efficient iterative procedure is proposed for determining the two sets of unknown virtual tractions, which are transformed into equivalent concentrated forces to simplify the computational process. The solutions agree very well with the results obtained by the finite element method. A parametric study is finally performed to investigate the influences of the tunnel buried depth, the tunnel shape, and surcharge loads on the stresses along the ground and around tunnels. The new proposed solutions potentially provide a potential alternative approach for preliminary designs of future rectangular tunnels.     

Effect of underground tunnel on the ground surface acceleration

A series of dynamic centrifuge tests was designed and conducted to study the seismic behavior of buried box tunnels. In this study, numerical simulations of the same tests were also performed using a finite difference software. The simulation results were in very good agreement with the results observed in the centrifuge tests. Subsequently, verified numerical model was used to perform parametric studies on the effect of an underground box tunnel on the ground surface acceleration. The results of parametric studies revealed that an underground tunnel could have either positive or negative effect on the ground surface acceleration. Presence of the tunnel amplifies long periods and deamplifies short periods of the motion. Therefore, it is concluded that the effect of an underground structure on the acceleration at the ground surface may be significant and hence, should be taken into account for seismic zonation of urban areas.     

挤压性围岩隧道大变形机理及分级标准研究

结合高地应力条件下挤压性大变形隧道--乌鞘岭隧道工程实例,通过变形的现场量测结果,分析了挤压性围岩隧道大变形的基本特征。采用室内试验及现场量测等手段,综合分析确定了围岩物理力学参数,定量分析了洞室周边产生塑性区的条件、塑性区及洞壁位移的影响因素、塑性区半径与洞壁位移的关系。以现场量测数据为依托,结合理论计算,参考以往类似隧道经验,分别考虑了围岩的相对变形、强度应力比、原始地应力、弹性模量作为分级指标,并提出了综合系数α指标,采用综合指标判定法给出了大变形的分级标准,以及相应的防治措施。     

平行隧道开挖引起上方既有隧道的纵向变形研究

城市地铁隧道大多数采用平行双洞的布置形式作为隧道设计施工方案,根据不同的地层条件等因素采用盾构法或暗挖法施工。由于城市地下空间变的越来越拥挤,研究新建平行双洞隧道施工过程中对邻近既有隧道的影响程度问题显得尤为重要。本文基于两阶段分析方法研究预测平行双洞隧道开挖引起上方已建隧道的纵向变形的简化解析方法。首先,采用两高斯曲线叠加,计算新建平行双洞隧道施工引起的作用在既有隧道上的附加荷载。然后,将既有隧道考虑为Winkler 地基上的Timoshenko梁,建立既有隧道纵向变形的基本微分方程,并基于Galerkin 法进行求解。将本文提出的简化解析方法得到的结果与工程沉降实测数据进行对比以验证本文提出的预测方法的合理性。最后,进行了参数敏感性分析,研究了不同隧道相互位置、地层损失率、相对抗弯刚度和地层土性参数等对结果的影响规律。     

Numerical Studies on Thermally-Induced Air Flow in Sloping Tunnels with Experimental Scale Modelling Justifications

Study of smoke movement or air flow due to fire in sloping tunnels is important in designing smoke control systems. In contrast to a horizontal tunnel, there is an acceleration along the longitudinal axis due to smoke buoyancy. This phenomenon together with thermal radiation would lead to a complicated heat transfer mechanism of the ceiling jet in sloping tunnels. In the present work, thermally induced air flow arising from fire in sloping tunnels was studied via numerical simulations using the Computational Fluid Dynamics code FLUENT. Prior to the application of FLUENT in simulating the air flow under different conditions, scale model experiments were carried out and the results were compared with simulation results, to establish the reliability of FLUENT in simulating fires in sloping tunnels. For this purpose, a tunnel section model of length 3 m, width 0.8 m and height 1 m was constructed, with a 1.5 kW electrical heating source to model fire. Hot air movement pattern driven by the electric heater was studied with the tunnel inclined at 0°, 10°, 20° and 30° to the horizontal. Four cases of the same configuration as the scale tunnel experiments were simulated using FLUENT, with predicted results agreeing well with experimental results. Having established the suitability of FLUENT in simulating air flow due to fire in sloping tunnels, numerical simulations were carried out to study air flow in sloping tunnels with different scenarios, that is, for tunnels with different gradients and with fire located at different positions in the tunnel. Macroscopic number on heat transfer, including the Rayleigh number Ra, the average and local Nusselt number Nu_ave for sloping tunnels were also studied from the measured results. The correlation between Nu_ave and Ra, which shows the effect of hydrodynamic properties on relative dominance of heat transfer in tunnel fire, was also discussed.     

行波效应下曲线隧道动力响应解析解

隧道曲率变化段是制约隧道结构抗震安全性的关键控制区段,但目前隧道抗震设计仅以横断面剪切变形为主,未考虑隧道沿纵向的曲率半径变化,缺乏针对曲线隧道的纵向抗震简化分析方法。将曲线隧道沿纵向简化为作用在黏弹性地基上的变曲率有限长均质Euler-Bernoulli梁,基于Hamilton原理及黏弹性地基梁理论建立了结构的微分动力控制方程及边界条件,并通过模态叠加法进行求解,推导出任意动载作用下曲线隧道的位移、速度、加速度、弯矩、剪力等动力响应的解析表达式,以行波荷载为例,给出行波效应下曲线隧道动力响应的退化解答。通过与有限元基准模型在相同条件下的对比分析,验证了所推导解析解的正确性。最后应用该解析公式进行参数敏感性分析,揭示了隧道曲率半径、行波波速、行波频率及地层–结构相对刚度比等关键因素对曲线隧道结构动力响应的影响规律。     

Mechanical properties and associated seismic isolation effects of foamed concrete layer in rock tunnel

Foamed concrete has a good energy absorption capability and can be used as seismic isolation material for tunnels. This study aims to investigate the mechanical properties and associated seismic isolation effects of foamed concrete layer in rock tunnel. For this, a series of uniaxial/triaxial compression tests was conducted to understand the effects of concrete density, confining stress and strain rate on the mechanical properties of foamed concrete. The direct shear tests were also performed to investigate the effects of concrete density and normal stress on the nonlinear behaviors of foamed concrete layer-lining interface. The test results showed that the mechanical properties of foamed concrete are significantly influenced by the concrete density. The foamed concrete also has high volumetric compressibility and strain-rate dependence. The peak stress, residual stress, shear stiffness and residual friction coefficient of the foamed concrete layer-lining interface are influenced by the foamed concrete density and normal stress applied. Then, a crushable foam constitutive model was constructed using ABAQUS software and a composite exponential model was also established to study the relationship between shear stress and shear displacement of the interface, in which their parameters were fitted based on the experimental results. Finally, a parametric analysis using the finite element method (FEM) was conducted to understand the influence of foamed concrete layer properties on the seismic isolation effect, including the density and thickness of the layer as well as the shear stiffness and residual friction coefficient of the interface. It was revealed that lower density and greater thickness in addition to smaller shear stiffness or residual friction coefficient of the foamed concrete layer could yield better seismic isolation effect, and the influences of the first two tend to be more significant.     

破碎千枚岩隧道施工期位移安全控制基准研究

 随着以千枚岩为主的软岩隧道的大量兴建,建立针对性的位移安全控制基准已成为工程界亟待解决的难题之一。以横跨5.12震区的广(元)甘(肃)高速公路杜家山隧道为工程背景,采用室内模型试验及现场试验相结合的研究手段,通过对以V级围岩为主的破碎千枚岩隧道在不同埋深、施工工法及支护参数等条件下位移变形规律的研究,揭示埋深、施工工法、支护与隧道位移间的关联性,结果表明较之工法、支护参数而言,埋深对隧道变形的影响更为显著。并以拱顶沉降作为主要控制指标,以衬砌裂损的出现作为隧道稳定性的判别标志,结合依托工程现场统计数据的系统分析,建立破碎千枚岩隧道中埋深在300 m以内、三台阶法(核心土)以及F3～F5支护方式下的施工期位移安全控制基准。     

Linearization of the Hoek and Brown rock failure criterion for tunnelling in elasto-plastic rock masses

We present a novel methodology for estimation of equivalent Mohr–Coulomb strength parameters that can be used for design of supported tunnels in elasto-plastic rock masses satisfying the non-linear empirical Hoek–Brown failure criterion. We work with a general adimensional formulation of the Hoek–Brown failure criterion in the space of normalized Lambe's variables for plane stress, and we perform linearization considering the stress field in the plastic region around the tunnel. The procedure is validated using analytical solutions to a series of benchmark test cases. Numerical solutions are also employed to validate the procedure in cases for which analytical solutions are not available. Results indicate that the stress field in the plastic region around the tunnel, as well as the linearization method employed and the quality of the rock mass, has a significant impact on computed estimates of equivalent Mohr–Coulomb strength parameters. Results of numerical analyses also show that our proposed linearization method can be employed to estimate loads and moments on the tunnel support system. We recommend the equating model responses (EMR) method to compute equivalent Mohr–Coulomb strength parameters when the tunnel support pressure is accurately known, and we further show that our newly introduced linearization method can be employed as an alternative to the best fitting in the existing stress range (BFe) and best fitting in an artificial stress range (BFa) methods, providing performance estimates that are generally better than estimates of the BFe and BFa methods when differences with the response of the Hoek–Brown rock mass are of engineering significance (say more than 10%).     

Stability of long unsupported twin circular tunnels in soils

The stability of two long unsupported circular parallel tunnels aligned horizontally in fully cohesive and cohesive–frictional soils has been determined. An upper bound limit analysis in combination with finite elements and linear programming is employed to perform the analysis. For different clear spacing (S) between the tunnels, the stability of tunnels is expressed in terms of a non-dimensional stability number (γ_maxH/c); where H is tunnel cover, c refers to soil cohesion, and γ_max is maximum unit weight of soil mass which the tunnels can bear without any collapse. The variation of the stability number with tunnels’ spacing has been established for different combinations of H/D, m and ϕ; where D refers to diameter of each tunnel, ϕ is the internal friction angle of soil and m accounts for the rate at which the cohesion increases linearly with depth. The stability number reduces continuously with a decrease in the spacing between the tunnels. The optimum spacing (S_opt) between the two tunnels required to eliminate the interference effect increases with (i) an increase in H/D and (ii) a decrease in the values of both m and ϕ. The value of S_opt lies approximately in a range of 1.5D–3.5D with H/D = 1 and 7D–12D with H/D = 7. The results from the analysis compare reasonably well with the different solutions reported in literature.     

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。     

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。     

Analytical solution for long lined tunnels subjected to travelling loads

An analytical solution is derived for dynamic response of long lined tunnels subjected to travelling loads. For the derivation, the long lined tunnel is assumed to be infinitely long with a uniform cross-section resting on a viscoelastic foundation. Fourier and Laplace transforms are utilized to simplify the governing equation of the tunnel to an algebraic equation, so that the solution can be conveniently obtained in the frequency domain. The convolution theorem is employed to convert the solution into the time domain. Final solutions of tunnel responses investigated are deflection, velocity, acceleration, bending moment, and shear force. The proposed solution is verified by providing comparisons between its results and those from the Finite Element program ABAQUS. Further parametric analysis, such as the influence of wave velocity and frequency on dynamic responses of the tunnel is presented with the analytical solution. These relationships can be an effective tool for practitioners.     

Risk of shear failure and extensional failure around over-stressed excavations in brittle rock

The authors investigate the failure modes surrounding over-stressed tunnels in rock.Three lines of investigation are employed:failure in over-stressed three-dimensional(3D) models of tunnels bored under 3D stress,failure modes in two-dimensional(2D) numerical simulations of 1000 m and 2000 m deep tunnels using FRACOD,both in intact rock and in rock masses with one or two joint sets,and finally,observations in TBM(tunnel boring machine) tunnels in hard and medium hard massive rocks.The reason for 'stress-induced' failure to initiate,when the assumed maximum tangential stress is approximately(0.4-0.5)σ_c(UCS,uniaxial compressive strength) in massive rock,is now known to be due to exceedance of a critical extensional strain which is generated by a Poisson's ratio effect.However,because similar 'stress/strength' failure limits are found in mining,nuclear waste research excavations,and deep road tunnels in Norway,one is easily misled into thinking of compressive stress induced failure.Because of this,the empirical SRF(stress reduction factor in the Q-system) is set to accelerate as the estimated ratio σ_(θmax)/σ_c 0.4.In mining,similar 'stress/strength' ratios are used to suggest depth of break-out.The reality behind the fracture initiation stress/strength ratio of '0.4' is actually because of combinations of familiar tensile and compressive strength ratios(such as 10) with Poisson's ratio(say0.25).We exceed the extensional strain limits and start to see acoustic emission(AE) when tangential stress σθ≈ 0.4σc,due to simple arithmetic.The combination of 2D theoretical FRACOD models and actual tunnelling suggests frequent initiation of failure by 'stable' extensional strain fracturing,but propagation in 'unstable' and therefore dynamic shearing.In the case of very deep tunnels(and 3D physical simulations),compressive stresses may be too high for extensional strain fracturing,and shearing will dominate,both ahead of the face and following the face.When shallower,the concept of 'extensional strain initiation but propagation' in shear is suggested.The various failure modes are richly illustrated,and the inability of conventional continuum modelling is emphasized,unless cohesion weakening and friction mobilization at different strain levels are used to reach a pseudo state of yield,but still considering a continuum.     

近距离交叠隧道施工影响的数值模拟

由于地质条件的限制及地下空间的综合开发利用,在工程中有时不可避免地产生近距离交叠隧道.对于这种型式的隧道,新建隧道是在既有隧道完成之后修建的,新建隧道的施工势必影响既有隧道结构的受力状态,引起既有隧道变形.本文应用ANSYS有限元程序采用三维弹塑性数值计算方法对某新建铁路隧道下穿既有高速公路隧道的施工过程进行了模拟,揭...     

Three-dimensional FDEM numerical simulation of failure processes observed in Opalinus Clay laboratory samples

This study presents the first step of a research project that aims at using a three-dimensional(3D) hybrid finite-discrete element method(FDEM) to investigate the development of an excavation damaged zone(EDZ) around tunnels in a clay shale formation known as Opalinus Clay. The 3D FDEM was first calibrated against standard laboratory experiments, including Brazilian disc test and uniaxial compression test. The effect of increasing confining pressure on the mechanical response and fracture propagation of the rock was quantified under triaxial compression tests. Polyaxial(or true triaxial) simulations highlighted the effect of the intermediate principal stress(s2) on fracture directions in the model: as the intermediate principal stress increased, fractures tended to align in the direction parallel to the plane defined by the major and intermediate principal stresses. The peak strength was also shown to vary with changing σ2.     

The effect of principal stress orientation on tunnel stability

In order to investigate the effect of principal stress orientation on the stability of regular tunnels and cracked tunnels, experiments by using square specimens with a centralized small tunnel were conducted, and the corresponding numerical study as well as photoelastic study were implemented. Two kinds of materials, cement mortar and sandstone, were used to make tunnel models, and three types of tunnel models were studied, i.e. (1) regular tunnel models loaded by different orientation’s principal stresses, (2) tunnel models with various orientation’s radial cracks in the spandrel under compression, and (3) tunnel models with a fixed radial crack loaded by various orientation’s principal stresses. In the numerical study, the stress intensity factors of the radial cracks were calculated, and the results agree well with the test results. For regular tunnels, when the angle θ between the major principal stress and the tunnel symmetrical axis is 45°, the corresponding tunnel is the most unfavorable; for tunnels with a radial crack in the spandrel, when the angle β between the crack and the tunnel wall is 135°, the corresponding tunnel is the most unfavorable; for tunnels with a β = 130° radial crack, when θ = 0° or θ = 70°, the compressive strengths of the tunnel models are comparatively low, whereas when θ = 90°, it is the highest.