Seismic analysis of underground tunnels by the 2.5D finite/infinite element approach

A procedure for the seismic analysis of underground tunnels using recorded free-field earthquakes based on the 2.5D finite/infinite element approach is presented. The near and far fields of the half space are modeled by finite and infinite elements, respectively. Using the 1D wave theory, the nodal force and displacement on the near-field boundary are computed for each spectral frequency of the earthquake. Then, equivalent seismic forces are computed for the near-field boundary for the earthquake spectrum. By assuming the soil-tunnel system to be uniform along the tunnel axis, the 2.5D approach can account for the wave transmission along the tunnel axis, which reduces to the 2D case for infinite transmission velocity. The horizontal and vertical components of the 1999 Chi-Chi Earthquake (TCU068) are adopted as the free-field motions in the numerical analysis. The maximal stresses and distribution patterns of the tunnel section under the P- and SV-waves are thoroughly studied by the 2.5D and 2D approaches, which should prove useful to the design of underground tunnels.     

Train-induced wave propagation in layered soils using finite/infinite element simulation

In this paper, the transmissibility of soils for vibrations induced by trains moving at different speeds is studied. The 2.5 D finite/infinite element approach adopted herein allows us to consider the load-moving effect of the train in the direction normal to the two-dimensional profile of the soils considered, and, therefore, to obtain three-dimensional responses for the soils using only plane elements. The moving train is simulated by a sequence of moving wheel loads that may vibrate with certain frequency. Two train speeds are considered, one is smaller and the other is greater than the Rayleigh wave speed of the layered soils, to represent the effects of speed in the sub-critical and super-critical ranges. In order to evaluate the effect of each parameter on the ground response induced by moving trains, parametric studies are conducted for the following parameters: the shear wave speed, damping ratio and stratum depth of the supporting soils, and the moving speed and vibration frequency of the traveling trains. Conclusions concerning the mechanism of wave propagation in layered soils are drawn from the parametric studies, which should prove useful to practicing engineers.     

Simulations and analyses of train-induced ground vibrations in finite element models

Analyses of the actual vibration measurements and the results from the mathematical and numerical models have been performed in both the frequency and time domains. The conclusions from these analyses were that two-dimensional models could be used in order to study certain effects of train-induced ground vibrations, but that three-dimensional analyses are necessary to achieve a better simulation of the problem. All these analyses were linear elastic. It was, however, found in the three-dimensional analyses that relatively large shear strains existed in the embankment and in the soft soil layers just beneath the railway embankment. These shear strains were taken into consideration through iterative reduction of the shear modulus of the materials where large shear strains were calculated.     

Attenuation of ground vibrations due to different technical sources

The attenuation of technically induced surface waves is studied theoretically and experimentally.In this paper, nineteen measurements of ground vibrations induced by eight different technical sources including road and rail traffic, vibratory and impulsive construction work or pile driving, explosions, hammer impulses and mass drops are described, and it is shown that the technically induced ground vibrations exhibit a power-law attenuation v～r-q where the exponents q are in the range of 0.5 to 2.0 and depend on the source types.Comparisons performed demonstrate that the measured exponents are considerably higher than theoretically expected.Some potential effects on ground vibration attenuation are theoretically analyzed.The most important effect is due to the material or scattering damping.Each frequency component is attenuated exponentially as exp(-kr), but for a broad-band excitation, the sum of the exponential laws also yields a power law but with a high exponent.Additional effects are discussed, for example the dispersion of the Rayleigh wave due to soil layering, which yields an additional exponent of 0.5 in cases of impulsive loading.     

3D seismic response of a limited valley via BEM using 2.5D analytical Green's functions for an infinite free-rigid layer

This paper presents analytical solutions for computing the 3D displacements in a flat solid elastic stratum bounded by a rigid base, when it is subjected to spatially sinusoidal harmonic line loads. These functions are also used as Greens functions in a boundary element method code that simulates the seismic wave propagation in a confined or semi-confined 2D valley, avoiding the discretization of the free and rigid horizontal boundaries.The models developed are then used to simulate wave propagation within a rigid stratum and valleys with different dimensions and geometries, when struck by a spatially sinusoidal harmonic vertical line load. Simulations are performed in the frequency domain, for varying spatial wave numbers in the axial direction of the valley. Time results are obtained by means of inverse Fourier transforms, to help understand how the geometry of the valley may affect the variation of the displacement field.     

Analysis on effect of surface fault to site ground motion using finite element method

Dynamic contact theory is applied to simulate the sliding of surface fault.Finite element method is used to analyze the effect of surface fault to site ground motions.Calculated results indicate that amplification effect is obvious in the area near surface fault,especially on the site that is in the downside fault.The results show that the effect of surface fault should be considered when important structure is constructed in the site with surface fault.     

Analysis of train-induced vibrations and vibration reduction schemes above and below critical Rayleigh speeds by finite element method

This paper simulates soil vibration under the train speed below and over the soil Rayleigh speed using the three-dimensional finite element method. Two vibration isolation schemes were studied including the soil improvement around the railway and the concrete slab constructed between the rail and soil. Numerical results indicate that the vibration increases considerably and decays slowly when the train speed exceeds the soil Rayleigh speed. The wave direction and dominant frequencies are the simple functions of the train speed, the soil Rayleigh speed and the train compartment length. When the train speed exceeds the shear wave speed, the vibration magnitude is critical and not sensitive to the train speed. To reduce this vibration, the two isolation schemes investigated in this study are useful for the train speed over the soil Rayleigh speed, but they are not efficient for the train speed below the soil Rayleigh speed.     

Prediction of railway ground vibrations: Accuracy of a coupled lumped mass model for representing the track/soil interaction

Recent advances in railway-induced ground vibrations showed that the track/soil interaction plays an important role in the low frequency range. This paper contributes to the numerical analysis of train/track/foundation dynamics by presenting the accuracy of a coupled lumped mass (CLM) model devoted to the railway foundations and to the track/soil coupling. Following a summary of the background and the advantages of the CLM model, the coupling strategy is quantified through two application cases. Firstly, the dynamic track deflection is calculated for different railway lines considering various degrees of complexities of foundations. Then, the foundation responses are compared depending on whether detailed coupling is introduced or not. The benefit of the proposed model is emphasized by presenting free-field ground vibration responses generated by a tram and a high-speed train, obtained by a revisited two-step prediction model developed by the authors.     

基于自适应有限元的复电阻率法2.5维复杂构造电磁场模拟

复电阻率法在矿产、油气勘探调查中发挥着重要作用.为了认识复杂构造的复电阻率法电磁场的变化规律,本文基于自适应有限元方法,采用非结构化网格,引入Cole-Cole模型,实现了电偶源2.5D复电阻率法电磁场正演,可以模拟复杂地形和地电结构,正演结果更符合野外实际地质情况.通过将本文的计算结果与半空间模型解析解、层状介质和起伏模型结果进行对比,验证了本文算法的正确性.最后,基于复杂地电模型,通过正演模拟,系统分析了地形、激电参数、复杂构造对复电阻率法电磁场的影响特征.

     

Transient analysis of 1D inhomogeneous media by dynamic inhomogeneous finite element method

The dynamic inhomogeneous finite element method is studied for use in the transient analysis of one dimensional inhomogeneous media. The general formula of the inhomogeneous consistent mass matrix is established based on the shape function. In order to research the advantages of this method, it is compared with the general finite element method. A linear bar element is chosen for the discretization tests of material parameters with two fictitious distributions. And, a numerical example is solved to observe the differences in the results between these two methods. Some characteristics of the dynamic inhomogeneous finite element method that demonstrate its advantages are obtained through comparison with the general finite element method. It is found that the method can be used to solve elastic wave motion problems with a large element scale and a large number of iteration steps.     

某正倾滑断层引起的近断层强地面运动的有限元数值模拟

本文使用与文献[1]相同的数值模拟方法,预测了某城市设定矩震级为MW=6.75的活断层产生的近断层强地面运动。主要定性计算结果是:正倾滑断层(倾角δ=75°)产生的近断层强地面运动也不同程度地存在上盘效应、F ling Step效应、速度大脉冲效应和竖向效应。表明本文采用的震源模型和计算方法可以实际应用于预测城市近断层强地面运动影响场。     

Numerical modeling of vibrations induced by railway traffic in tunnels: From the source to the nearby buildings

In this paper, a numerical approach for the prediction of vibrations induced in buildings due to railway traffic in tunnel is proposed. The numerical method is based on a sub-structuring approach, where the train is simulated by a multi-body model; the track–tunnel–ground system is modeled by a 2.5D FEM–PML approach; and the building by resource to a 3D FEM method. The coupling of the building to the ground is established taking into account the soil–structure-interaction (SSI). The methodology proposed allows dealing with the three-dimensional characteristics of the problem with a reasonable computational effort. Using the proposed model, a numerical study is developed in order to better discern the impact of the use of floating slabs systems for the isolation of vibrations in the tunnel on the dynamic response of a building located in the surrounding of the tunnel. The comparison between isolated and non-isolated scenarios allowed concluding that the mats stiffness is a key parameter on the efficiency of floating slab systems. Furthermore, it was found that the selection of the stiffness of the mats should be performed carefully in order to avoid amplification of vertical vibrations of the slabs of the building.     

Mitigation of railway induced ground vibration by heavy masses next to the track

The effectiveness of heavy masses next to the track as a measure for the reduction of railway induced ground vibration is investigated by means of numerical simulations. It is assumed that the heavy masses are placed in a continuous row along the track forming a wall. Such a continuous wall could be built as a gabion wall and also used as a noise barrier. Since the performance of mitigation measures on the transmission path strongly depends on local ground conditions, a parametric study is performed for a range of possible designs in a set of different ground types. A two-and-a-half dimensional coupled finite element–boundary element methodology is used, assuming that the geometry of the problem is uniform in the direction along the track. It is found that the heavy masses start to be effective above the mass–spring resonance frequency which is determined by the dynamic stiffness of the soil and the mass of the wall. At frequencies above this resonance frequency, masses at the soil׳s surface hinder the propagation of surface waves. It is therefore beneficial to make the footprint of the masses as large and stiff as possible. For homogeneous soil conditions, the effectiveness is nearly independent of the distance behind the wall. In the case of a layered soil with a soft top layer, the vibration reduction strongly decreases with increasing distance from the wall.     

3D Response analysis of an instrumented hill at Matsuzaki, Japan, by a spectral method

Strong ground motion observed at an instrumented hill site is first analysed through the standard (SSR) and the horizontal-to-vertical (HVSR) spectral ratio techniques. A reasonable agreement is found between these approaches. The observations are then compared with 3D numerical simulations, performed with a highly efficient numerical code based on a spectral method, that allowed for reasonable computer times also on a PC. The observed amplification is significantly higher than that computed with a 3D homogeneous model of the mountain, suggesting that local response is governed by large-scale and small-scale soil heterogeneities rather than by topographic site effects. The introduction of a local near-surface inclusion of nonhomogeneous soil material under one of the recording stations has not significantly improved the numerical results. The observed data are also compared with the results of simplified simulations, either using 2D homogeneous models or coupling the 3D response with a 1D local soil profile. The results of such simplified approaches are discussed and their usefulness is emphasised.