任意圆弧形凸起地形中隧洞对入射平面SH波的影响

借助辅助函数的思想， 采用波函数展开法给出了圆弧形凸起地形中隧洞对入射平面SH波影响问题的一个解析解．数值结果表明，凸起地形中隧洞的存在以及隧洞大小，对凸起地形表面运动，以及凸起地形中的隧洞的动应力集中均具有显著影响．      

Diffraction of anti-plane SH waves by a semi-circular cylindrical hill with an inside concentric semi-circular tunnel

A closed-form analytic solution of two-dimensional scattering and diffraction of plane SH waves by a semicylindrical hill with a semi-cylindrical concentric tunnel inside an elastic half-space is presented using the cylindrical wave functions expansion method. The solution is reduced to solving a set of infinite linear algebraic equations. Fourier expansion theorem with the form of complex exponential function and cosine function is used. Numerical solutions are obtained by truncation of the infinite equations. The accuracy of the presented numerical results is carefully verified.     

Conversion between solid and beam element solutions of finite element method based on meta-modeling theory: development and application to a ramp tunnel structure

In this study, a new method for conversion of solid finite element solution to beam finite element solution is developed based on the meta-modeling theory which constructs a model consistent with continuum mechanics. The proposed method is rigorous and efficient compared to a typical conversion method which merely computes surface integration of solid element nodal stresses to obtain cross-sectional forces. The meta-modeling theory ensures the rigorousness of proposed method by defining a proper distance between beam element and solid element solutions in a function space of continuum mechanics. Results of numerical verification test that is conducted with a simple cantilever beam are used to find the proper distance function for this conversion. Time history analysis of the main tunnel structure of a real ramp tunnel is considered as a numerical example for the proposed conversion method. It is shown that cross-sectional forces are readily computed for solid element solution of the main tunnel structure when it is converted to a beam element solution using the proposed method. Further, envelopes of resultant forces which are of primary importance for the purpose of design, are developed for a given ground motion at the end.     

Approximate evaluation of stresses in degraded tunnel linings

This paper uses numerical and analytical methods to examine the static and seismic response of tunnels with intact and degraded segmental concrete tunnel liners. Concrete degradation is simulated using a non-linear finite element (FE) model that accounts for soil-structure interaction and the non-linear stress–strain response of the soil and concrete. The non-linear FE model is used to calculate radial stresses in tunnel linings with local concrete delaminations and that are subject to both static and seismic loads. Then, the FE results are compared with an analytical solution for jointed tunnel linings in order to assess the accuracy of the solution for predicting stresses in degraded liners. The analyses and results presented in this paper illustrate a simple method for estimating and evaluating the effect of concrete degradation on the distribution of thrust and moment in segmental tunnel linings subject to either static or seismic loads.     

3-D seismic response analysis of long lined tunnels in half-space

The dynamic response of infinitely long lined tunnels with a uniform cross-section buried into an elastic or viscoelastic half-space to body and surface harmonic seismic waves is numerically determined by a special direct boundary element method in the frequency domain. The waves have an arbitrary direction of propagation with respect to the axis of the tunnel and this renders the problem three-dimensional. However, this problem is effectively reduced to a two-dimensional one by a coordinate transformation and appropriate integration of the full-space dynamic fundamental solution along the direction of the tunnel axis. Quadratic isoparametric boundary line elements and advanced numerical integration techniques for the treatment of singular integrals produce results of high accuracy. Numerical results are presented for the case of an infinitely long lined tunnel of circular cross-section and compared against those of a full three-dimensional boundary element analysis, as well as those of other methods. Thus the proposed method is illustrated and its merits demonstrated.     

Circular tunnels in sand: dynamic response and efficiency of seismic analysis methods at extreme lining flexibilities

The paper discusses the seismic response of circular tunnels in dry sand and investigates the efficiency of current seismic analysis methods at extreme lining flexibilities. Initially, a dynamic centrifuge test on a flexible circular model tunnel, embedded in dry sand, is analyzed by means of rigorous full dynamic analysis of the coupled soil–tunnel system, applying various non-linear soil and soil–tunnel interface models. The numerical results are compared to the experimental ones, aiming to better understand the recorded response and calibrate the numerical models. Then a series of numerical analyses are conducted using the validated numerical model, in order to investigate the effect of the tunnel lining rigidity on the dynamic response of the soil–tunnel system. In parallel, the accuracy of currently used simplified analysis methods is evaluated, by comparing their predictions with the results of the a priori more accurate and well validated numerical models. The comparative analyses allow us to highlight and discuss several crucial aspects of the soil-tunnel system seismic response, including (1) the post-earthquake residual values of the lining forces, which are amplified with the increase of the flexibility of the tunnel and (2) the importance of the soil-tunnel interface conditions. It is finally concluded that simplified analysis methods may provide a reasonable framework for the analysis at a preliminary stage, under certain conditions.     

圆形隧洞对地下地震动的影响:SH波入射

地下结构对地震波的散射改变了场地的动力特性,无论是地上建筑还是地下结构的安全评价和抗震设计中,目前均没有很好的考虑由于地下结构的存在对原场地地震动尤其是地下地震动的影响。基于弹性波动理论,运用波函数展开法和镜像原理,分析了弹性半空间中圆形隧洞对柱面SH波的散射问题,得到了含圆形隧洞的弹性半空间位移解析解。通过数值算例分析了圆形隧洞对原场地地震动的影响,重点考察了隧洞埋深、隧洞半径和围岩衬砌模量比等参数的影响规律。结果表明,地下结构对沿线场地的动力特性有着显著的影响,对其自身以及沿线工程结构的抗震设计提供一定参考价值。     

An Analytical Method for Groundwater Inflow into a Drained Circular Tunnel

Groundwater inflow estimation is essential for the design and construction of tunnel and the assessment of the environmental impacts. Analytical solutions used in current engineering practice do not adequately account for the effect of the excavation‐induced drawdown, which leads to significant change in pore water pressure distribution and reductions of the water level beyond tunnel. Based on the numerical analysis results, this article proposes semianalytical method to predict the height of lowered water level and groundwater tunnel inflow. The tunnel problem is conceptualized as two‐dimensional flow in a plane perpendicular to the tunnel axis. The analytical formula, considering the effect of the excavation‐induced drawdown, provides a better prediction of the tunnel inflow compared to the existing analytical formulas, even for the cases with inclined groundwater level.     

棋盘石隧道断裂破碎带地震动力响应分析

以棋盘石穿越断层破碎带段隧道为背景,采用理论计算与数值模拟相结合的方法,对棋盘石隧道在汶川波作用下的地震响应分析进行了系统研究。探讨了断层破碎带衬砌在地震荷载作用下的破坏方式,并且把数值模拟结果与汶川特大地震震害的公路隧道进行对比分析。结果表明:用松动圈折减系数法估算出衬砌最大弯矩和剪力的数值与数值模拟的结果基本一致,验证了MIDAS/GTS-NX模拟隧道地震时程分析的可行性;同时根据对有限元模型进行时程分析的结果,探讨了断层破碎带处衬砌的破坏方式,并提出合理可行的防治及加固措施。     

Dynamic stress concentration of an elliptical cavity in a semi-elliptical hill under SH-waves

The method of wave-function expansion in elliptical coordinates,elliptical cosine half-range expansion and Mathieu function were applied to obtain an exact analytical solution of the dynamic stress concentration factor(DSCF)around an elliptical cavity in a shallow,semi-elliptical hill.An infinite system of simultaneous linear equations for solving this problem was established by substituting the wave expression obtained by the Mathieu function including the standing wave expression of elliptical lining given herein into the boundary condition obtained by the region-matching method.The finite equations system with unknown coefficients obtained by truncation were solved numerically,and the results in the case of an ellipse degenerating into a circle were compared with previous results to verify the accuracy of the method.The effects of different aspect ratios,incident wave angles and aperture ratios on the dynamic stress concentration around the elliptical cavity were described.Some numerical results,when the elliptical hill was changed into a circular one,were analyzed and compared in detail.In engineering,this model can be regarded as a semi-cylindrical hill with an elliptical cylindrical unlined tunnel under the action of SH waves,and the results are significant in aseismic design.     

考虑进洞高程效应的黄土隧道洞口段地震动力响应特征研究

通过大型振动台模型试验并采用Midas-GTS有限元软件进行模拟计算,研究黄土隧道洞口段在地震作用下的动力响应特征、破坏过程和地震波在模型中的传递规律,分析影响黄土隧道洞口段地震动力响应的主要因素。结果表明:边坡沿弧形开裂面的垮塌受坡脚剪切和坡顶拉裂的共同作用;边坡会对其卓越频率内的地震波产生明显放大效应,且在1/2坡高以上放大效应出现饱和现象;隧道临空面是影响隧道洞口段地震动力响应的主要因素。考虑进洞高程效应时隧道洞口段抗震设防长度可取距洞口5倍洞径范围。振动台模型试验与数值计算在位移、加速度、应力三个响应特征上吻合较好,证明二者结果合理可靠。研究成果可为隧道工程设计和地下结构抗震理论研究提供有益参考。     

On Inflow to a Tunnel in a Fractured Double-Porosity Aquifer

Inflow to a tunnel is a great public concern and is closely related to groundwater hydrology, geotechnical engineering, and mining engineering, among other disciplines. Rapid computation of inflow to a tunnel provides a timely means for quickly assessing the inflow discharge, thus is critical for safe operation of tunnels. Dewatering of tunnels is another engineering practice that should be planned. In this study, an analytical solution of the inflow to a tunnel in a fractured unconfined aquifer is obtained. The solution takes into account either the spherical or slab-shaped matrix block and the unsteady state interporosity flow. The instantaneous drainage water table and anisotropic hydraulic conductivities of the fractures network are also considered. Both uniform flux and uniform head boundary condition are considered to simulate the constant head boundary condition in the tunnel. The effects of the hydraulic parameters of the fractured aquifer on the inflow variation of the tunnel are explored. The application of the presented solution to obtain the optimum location and discharge of the well to minimize the inflow to a tunnel is illustrated.     

Scattering of plane SH waves by a cylindrical canyon of circular-arc cross-section

A closed-form solution of two-dimensional scattering of plane SH waves by a cylindrical canyon of circular-arc cross-section in a half-space is studied using the wave functions expansion method. The solution is reduced to solving infinite linear algebraic equations using the Graf's addition theorem in an appropriate form. Numerical results of the solution are obtained by truncation of the infinite equations and accuracies of the truncation are checked by the extent to which the numerical results fit the boundary condition and by convergence of the numerical results with the truncation order. Complicated effects of the depth-to-width ratio of the canyon on surface ground motion are shown by the numerical results for typical cases.     

Wind flow and wind loads on the surface of a towershaped building: Numerical simulations and wind tunnel experiment

Flow structure and wind pressure distribution caused by obtuse obstacles are usually the focuses in Computational Wind Engineer researches (CWE). By solving the non-hydrostatical dynamic equations, PUMA model (Peking University Model of Atmospheric Environment) was developed and applied to simulating the flow structure and wind pressure distribution around a tower-shaped building. Evaluation about the wind environment and wind loads around the building was obtained through the analysis of the numerical simulation results and wind tunnel data. Comparisons between the simulation and wind tunnel study indicate that numerical simulation results agree well in the flow field and wind pressure distribution around the tower-shaped building. On the other hand, the horizontal grid interval of 2 m and the vertical grid of 3 m were still too crude to simulate the flow structure and wind pressure distribution on the building surface more exactly in detail; and the absence of suitable pressure perturbation parameterization scheme between the solid and the adjacent space also limits the accuracy of the numerical simulation. The numerical simulation model can be used to evaluate the wind environment and wind load around high buildings.     

Dynamic response of an eccentrically lined circular tunnel in poroelastic soil under seismic excitation

An exact analysis for two-dimensional dynamic interaction of monochromatic progressive plane compressional and shear seismic waves with a permeable circular tunnel lining of circumferentially varying wall thickness buried in a boundless porous elastic fluid-saturated formation is presented. The novel features of Biot dynamic theory of poroelasticity in conjunction with the translational addition theorems for cylindrical wave functions, along with the appropriate wave field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in form of infinite series. The analytical results are illustrated with numerical examples in which an air-filled and water-saturated permeable tunnel lining of variable wall thickness, embedded within water-saturated surrounding formations of distinct frame properties (soft, stiff, and stiff viscoelastic soil), is insonified by fast compressional or shear waves at selected angles of incidence. The effects of liner eccentricity, interface permeability, formation material type, incident wave frequency, and angle of incidence on the hoop stress amplitude are evaluated and discussed for representative values of the parameters characterizing the system. Limiting cases are considered and good agreements with the solutions available in the literature are obtained.     

隧道工程勘察中的超前预报成像方法研究

针对地下工程领域隧道超前预报地震波波场传播与成像中存在的问题,通过数值模拟,构建二维含低速异常的隧道介质模型,研究隧道弹性波场传播规律和异常体边界成像准确性.首先,利用一阶速度-应力波动方程和高阶交错网格有限差分计算方法,导出隧道超前预报数值模拟的稳定性条件和边界条件,对上述隧道模型进行数值模拟,识别波场特征;其次,利用叠前逆时偏移成像方法,对压制噪音干扰后的波场在互相关成像条件下,对隧道模型中的异常体边界进行逆时偏移成像.研究结果表明：采用高阶交错网格有限差分正演获得异常体边界清晰的反射波和角点产生的散射波;逆时偏移算法获得隧道内异常体准确成像结果,从而大大提高隧道超前预报的分辨率与准确性;靠近掌子面单一震源、多道接收观测系统对异常体成像效果最佳,为隧道内高效数据采集提供理论依据.     

Analytical model for computing residence times near a pumping well

An analytical solution for calculating the residence time of fluid flowing toward a pumping well in an unconfined aquifer has been developed. The analytical solution was derived based on a radial, steady-state, Dupuit-Forchheimer flow model. The resulting integral expression involved computing the imaginary error function, for which a simple series expansion is proposed. The validity of the analytical expression is demonstrated by testing its results against numerical results for an example problem. The analytical solution compared favorably with the numerical approximation.     

盾构施工对不同刚度桩体影响的数值分析

针对苏州轻轨一号线盾构隧道的施工情况,采用三维有限元数值模型,研究了盾构施工对不同刚度桩体的影响。计算结果表明：当盾构施工时,不同刚度桩体均偏向隧道移动,在隧道轴线处的横向位移均为最大。桩身横向位移最大值、竖向位移随桩体刚度增大而变小,桩身轴力、弯矩则随桩体刚度增大而逐渐增大,桩身最大负弯矩均出现在隧道轴线位置处。在盾构正下方穿越单桩过程中,桩身沿隧道轴向位移近似为一条直线。当桩体弹性模量为0.5 GPa时,柱顶和桩底处竖向位移相差较大;当桩体弹性模量大于0.5 GPa时,桩身竖向位移急剧增大。桩身轴力沿桩身两端大、中间小。桩身弯矩随桩体弹性模量增大而明显增大。     

A semi-analytical solution based on a numerical solution of the solute transport of a conservative and nonreactive tracer

In the evaluation of potential risk from ingestion of groundwater near an impacted site, numerical simulation of fate and transport processes of chemicals of concern is often required. If there is potential concern about multiple chemicals, numerical simulation of each chemical separately is often needed. In this paper, a semi-analytical solution is presented based on a numerical solution of the transport of a conservative and nonreactive tracer. When multiple chemicals undergoing sorption and first-order degradation need to be modeled, we can avoid performing individual numerical simulations for each chemical by applying the semi-analytical solution. Numerical test runs were conducted to verify the semi-analytical solution; simulation results reveal that the concentrations derived from the semi-analytical solution are identical to those derived from the individual numerical fate and transport model simulations. The semi-analytical solution requires steady-state flow conditions, no continuing contaminant source, and similar initial source concentration distributions.     

Application of a new analytical method to a model of non-Darcian consolidation in clay soils

A model of consolidation in clay soil is studied by analytical means and the results compared with a recent numerical solution. Good agreement is obtained when the soil is only weakly non-Darcian. As the non-Darcian behavior of the soil becomes more pronounced the numerical solution is shown to be in error.