Experimental validation of a numerical prediction model for free field traffic induced vibrations by in situ experiments

This paper deals with the validation of a numerical model for traffic induced vibrations. Road unevenness subjects the vehicle to vertical oscillations that cause dynamic axle loads, which generate waves propagating in the subsoil. A 2D vehicle model is used for the calculation of the axle loads from the longitudinal road profile. The free field soil response is calculated with the dynamic Betti–Rayleigh reciprocity theorem, using a transfer function between the road and the receiver that accounts for dynamic road–soil interaction. The validation relies on the measured response of the vehicle's axles and the soil during the passage of a truck on an artificial unevenness with speeds varying from 30 to 70 km/h. The agreement between the numerical and the experimental results is good: the influence of the vehicle speed and the distance from the road is well predicted, while the ratio of the predicted and the measured PPV is less than two.     

The effect of road unevenness on the dynamic vehicle response and ground-borne vibrations due to road traffic

In this paper, the relation between road unevenness, the dynamic vehicle response, and ground-borne vibrations is studied. In situ measurements of road unevenness and the dynamic vehicle response for six roads with different types of pavement are supplemented by numerical predictions of ground vibrations. The predictions are performed in two stages. In the first stage, the dynamic vehicle response is computed based on the measured road unevenness. The vehicle model is validated by comparing the predicted and measured vehicle response and subsequently used to predict the dynamic vehicle loads. In the second stage, the dynamic road–soil interaction problem is considered and the transfer functions between the road and the soil are computed. The effect of the pavement type (continuous, jointed, or composed of individual pavers) on the road–soil transfer functions is investigated and the free field vibrations are calculated using the dynamic vehicle loads computed in the first stage. The predicted free field vibrations are validated by measurements at one of the measurement sites before and after rehabilitation of a deteriorated concrete pavement. Finally, the results are used to investigate the relation between indicators of road unevenness such as the ISO 8608 road class, the International Roughness Index, and the coefficient of evenness on one hand, and the dynamic vehicle response and level of ground-borne vibration on the other hand.     

Pile response and free field vibrations due to low strain dynamic loading

This paper presents the results of in situ measurements during dynamic pile testing at a construction site in Louvain-la-Neuve. Main objectives are the investigation of the pile response and the free field vibrations due to low strain dynamic loading on a single cast in situ pile with a 5.5 kg hammer impact on the pile head. Whereas low strain testing is usually performed to assess the integrity of the pile as a structural member, this study focuses on both pile and ground vibrations. The pile head response and ground motions are measured with accelerometers during different blows with the impact hammer. The dynamic characteristics of the soil are determined with a SASW test. Experimental results are compared with predictions obtained with a coupled finite element–boundary element model. The computed pile head and free field response show a good correspondence with the measured response. In addition, the static stiffness of the pile estimated by means of the mobility function shows a very good agreement with the value calculated by an analytical formulation.     

A 2.5D coupled FE-BE model for the prediction of railway induced vibrations

Ground vibrations induced by railway traffic at grade and in tunnels are often studied by means of two-and-half dimensional (2.5D) models that are based on a Fourier transform of the coordinate in the longitudinal direction of the track. In this paper, the need for 2.5D coupled finite element-boundary element models is demonstrated in two cases where the prediction of railway induced vibrations is considered. A recently proposed novel 2.5D methodology is used where the finite element method is combined with a boundary element method, based on a regularized boundary integral equation. In the formulation of the boundary integral equation, Green's functions of a layered elastic halfspace are used, so that no discretization of the free surface or the layer interfaces is required. In the first case, two alternative models for a ballasted track on an embankment are compared. In the first model, the ballast and the embankment are modelled as a continuum using 2.5D solid elements, whereas a simplified beam representation is adopted in the second model. The free field vibrations predicted by both models are compared to those measured during a passage of the TGVA at a site in Reugny (France). A very large difference is found for the free field response of both models that is due to the fact that the deformation of the cross section of the embankment is disregarded in the simplified representation. In the second case, the track and free field response due to a harmonic load in a tunnel embedded in a layered halfspace are considered. A simplified methodology based on the use of the full space Green's function in the tunnel–soil interaction problem is investigated. It is shown that the rigorous finite element-boundary element method is required when the distance between the tunnel and the free surface and the layer interfaces of the halfspace is small compared to the wavelength in the soil.     

Torsional response of a rigid circular foundation on a saturated half-space to SH waves

An analytical approach is used to study the torsional vibrations of a rigid circular foundation resting on saturated soil to obliquely incident SH waves. Biot’s poroelastic dynamic theory is considered to characterize the saturated soil below the foundation, which is solved by Hankel transform later. In order to consider the scattering phenomena caused by the existence of the foundation, the total wave field in soil is classified into free-field, rigid-body scattering field and radiation scattering field. According to the classification of wave field and the mixed boundary-value conditions between the soil and the foundation, torsional vibrations of the foundation are formulated in two sets of dual integral equations. Then, the dual integral equations are reduced to Fredholm integral equation of the second kind to be solved. Combining with the dynamic equilibrium equations of the foundation, the expressions for the torsional vibrations of the foundation are obtained. Numerical results are presented to demonstrate the influence of excitation frequency, incident angle, the torsional inertia moment of the foundation and permeability of the saturated half-space on the torsional vibrations of the foundation.     

Experimental and numerical evaluation of the effectiveness of a stiff wave barrier in the soil

This paper discusses the design, the installation, and the experimental and numerical evaluation of the effectiveness of a stiff wave barrier in the soil as a mitigation measure for railway induced vibrations. A full scale in situ experiment has been conducted at a site in El Realengo (Spain), where a barrier consisting of overlapping jet grout columns has been installed along a railway track. This barrier is stiff compared to the soil and has a depth of 7.5 m, a width of 1 m, and a length of 55 m. Geophysical tests have been performed prior to the installation of the barrier for the determination of the dynamic soil characteristics. Extensive measurements have been carried out before and after installation of the barrier, including free field vibrations during train passages, transfer functions between the track and the free field, and the track receptance. Measurements have also been performed at a reference section adjacent to the test section in order to verify the effect of changing train, track, and soil conditions over time. The in situ measurements show that the barrier is very effective: during train passages, a reduction of vibration levels by 5 dB is already obtained from 8 Hz upwards, while a peak reduction of about 12 dB is observed near 30 Hz immediately behind the barrier. The performance decreases further away from the jet grouting wall, but remains significant. The experimental results are also compared to numerical simulations based on a coupled finite element–boundary element methodology. A reasonable agreement between experiments and predictions is found, largely confirming the initially predicted reduction. This in situ test hence serves as a ‘proof of concept׳, demonstrating that stiff wave barriers are capable of significantly reducing vibration levels, provided that they are properly designed.     

Soil–structure interaction in resonant railway bridges

This paper explores dynamic soil–bridge interaction in high speed railway lines. The analysis was conducted using a general and fully three-dimensional multi-body finite element–boundary element model formulated in the time domain to predict vibrations caused by trains passing over the bridge. The vehicle was modelled as a multi-body system, the track and the bridge were modelled using finite elements and the soil was considered as a half-space by the boundary element method. The dynamic response of bridges to vehicle passage is usually studied using moving force and moving mass models. However, the multi-body system allows to consider the quasi-static and dynamic excitation mechanisms. Soil–structure interaction was taken into account by coupling finite elements and boundary elements. The paper presents the results obtained for a simply supported short span bridge in a resonant regime under different soil stiffness conditions.     

Prediction of free field vibrations due to pile driving using a dynamic soil–structure interaction formulation

This paper presents a numerical model for the prediction of free field vibrations due to vibratory and impact pile driving. As the focus is on the response in the far field where deformations are relatively small, a linear elastic constitutive behaviour is assumed for the soil. The free field vibrations are calculated by means of a coupled FE–BE model based on a subdomain formulation. First, the case of vibratory pile driving is considered, where the contributions of different types of waves are investigated for several penetration depths. In the near field, the soil response is dominated by a vertically polarized shear wave, whereas in the far field, body waves are importantly attenuated and Rayleigh waves dominate the ground vibration. Second, the case of impact pile driving is considered. A linear wave equation model is used to estimate the impact force during the driving process. Apart from the response of a homogeneous halfspace, it is also investigated how the soil stratification influences the ground vibration for the case of a soft layer on a stiffer halfspace. When the penetration depth is smaller than the layer thickness, the layered medium has no significant influence on ground vibrations. However, when the penetration depth is larger than the layer thickness, the influence of the layered medium becomes more significant. The computed ground vibrations are finally compared with field measurements reported in the literature.     

Experimental and numerical analyses of vibrations induced by high-speed trains on the Córdoba–Málaga line

This paper has two main purposes. One is to present and analyse soil and structural vibration data obtained experimentally during certification testing of the high-speed train line between Córdoba and Málaga (Spain) that was opened on December 2007. The second is to show the capabilities of a three-dimensional boundary element method (BEM)/finite element method (FEM) numerical approach for the analysis of train induced vibrations. The model can represent local soil conditions, discontinuities such as underpasses, as well as structures placed next to the rail track. Vibrations in those structures can be computed taking into account, in a rigorous way, dynamic soil–structure interaction and local soil properties. Experimental and numerical results at several points near the track are compared. Results for an overhead contact support structure are also evaluated. The comparison of numerically predicted and recorded results shows that the model is reliable for predicting the amplitude of vibrations produced in the soil and nearby structures by high-speed trains.     

Shinkansen high-speed train induced ground vibrations in view of viaduct–ground interaction

Train viaduct behavior and nearby ground motion under the high-speed train passage have been studied in this paper. First, the findings from the field measurement alongside the high-speed Shinkansen railway in Japan are interpreted. Then, the computer simulation is made based on the soil-foundation-viaduct interaction analysis under moving axle loads. The solution method is to apply the dynamic substructure method in the frequency domain. The viaduct girders including track structure and pier supports are modeled by the three-dimensional beam-column elements. The supporting pile foundation and nearby field are discretized by the axisymmetric three-dimensional finite elements and analyzed in a semi-analytical way, with a transmitting boundary replacing the far field based on the thin layer element method. Nearby ground motion during train passage on a viaduct have been calculated by superimposing the effects from neighboring pile foundations.The main parameters affecting viaduct vibrations are discussed by taking environmental vibration into consideration. The nearby ground motion along the viaduct is recomputed by applying the above determined forces to the foundation tops. The results from numerical studies are compared with the field test data, thus proving the present simulation to be effective and reliable.     

Numerical modelling of ground borne vibrations from high speed rail lines on embankments

A three dimensional numerical model is presented capable of modelling the propagation and transmission of ground vibration in the vicinity of high speed railways. It is used to investigate the effect of embankment constituent material on ground borne vibration levels at various distances from the track.The model is a time domain explicit, dynamic finite element model capable of simulating non-linear excitation mechanisms. The entire model, including the wheel/rail interface is fully coupled. To account for the unbounded nature of the soil structure an absorbing boundary condition (infinite element) is placed at the truncated interfaces. To increase boundary absorption performance, the soil structure is modelled using an elongated spherical geometry.The complex geometries associated with the track components are modelled in detail thus allowing a highly realistic simulation of force transmission from vehicle to embankment. Lastly, quasi-static and dynamic excitation mechanisms of the vehicle locomotives are described using a multi-body approach which is fully coupled to the track using non-linear Hertzian contact theory.The resulting model is verified using experimental ground borne vibration data from high speed trains, gathered through field trials. It is then used to investigate the role of embankments in the transmission of vibration. It is found that soft embankments exhibit large deflections and act as a waveguide for railway vibrations which are trapped within the structure. This results in increased vibration levels both inside the embankment and in the surrounding soil. In contrast it is found that embankments formed from stiffer material reduce vibrations in the near and far fields.     

Dynamic effects of moving loads on road pavements: A review

This review paper deals with the dynamic response of road pavements to moving loads on their surface. The road pavement can be modeled as a beam, a plate, or the top layer of a layered soil medium. The foundation soil can be modeled as a system of elastic springs and dashpots or a homogeneous or layered half-space. The material behavior of the pavement can be elastic or viscoelastic, while that of the foundation layers elastic, viscoelastic, water-saturated poroelastic or even inelastic. The loads are concentrated or distributed of finite extent, may vary with time and move with constant or variable speed. The analysis is done by analytical, analytical/numerical and purely numerical methods, such as finite element and boundary element methods, under conditions of plane strain or full three-dimensionality. A number of representative examples is presented in order to illustrate the problem and the methods of analysis, demonstrate the dynamic effects of moving loads on the layered soil medium and indicate the implications of the results on road and airport pavement design.     

SV波在饱和土体自由表面的反射

基于饱和两相介质弹性波动方程分析SV波在饱和土体自由表面的反射问题,引入波动方程的势函数解答,求解出二维问题中SV波入射情况下饱和土体自由场的位移、速度、加速度和应力响应。在饱和土体自由场响应解析解基础上,建立SV波入射下饱和土体自由场静、动力有限元模型。建模中考虑了如下几方面因素:(1)在不同分析步,对土体单元赋予不同材料本构。通过*model change命令进行单元生死设定,从而实现在初始应力场平衡的静力状态下采用DuncanChang本构模型,而地震波动输入时采用Davidenkov动力本构模型;(2)采用多孔介质黏弹性人工边界条件,在人工边界上分别施加固相和液相介质的弹簧和阻尼来模拟饱和土体中能量的传播;(3)将地震波转化为作用在人工边界上的等效地震荷载,施加到人工边界节点上;(4)土体单元采用4结点平面应变孔压单元(CPE4P)。有限元计算与解析解比较结果表明:SV波在垂直入射和掠入射时,竖向位移响应为零;在45°左右入射时,水平位移响应最大;60°左右入射时,竖向位移响应最大。这些结论与解析解吻合较好,本文模型为建立土-结构动力相互作用模型打下良好的基础。     

Transient dynamic response of fluid-saturated soil under a moving cyclic loading

Based on the Theory of Porous Media (TPM), a mathematical model of a two-dimensional incompressible fluid-saturated elastic soil is established, and the periodic boundary conditions are presented to analyze the transient dynamic response of this soil under a moving cyclic loading. The differential quadrature method (DQM) and the second-order backward difference scheme are applied to discretize the governing equations on the spatial and temporal domains, respectively. As application, a typical two-dimensional wave-induced transient problem with a seabed of finite thickness is analyzed, and the numerical results are compared with the analytical results presented in the present work. In addition, a transient dynamic response of fluid-saturated soil under limit moving vehicle loadings is studied. The effects of the velocity of vehicle and the volume fraction on the settlement and the pore water pressure are studied.     

Centrifugal modelling of dynamic soil-structure interaction

This paper presents a centrifuge model that is capable of realistically representing soil-structure systems subjected to earthquake-like excitation. The model is validated by performing (i) free field soil tests, (ii) dynamic soil-structure interaction tests and (iii) a numerical analysis of the experimental results. The free field experiments show that the simulated earthquake, which is generated by the hammer-exciter plate method, is similar in amplitude and frequency content to a real earthquake. The experiments also demonstrate that a confined soil sample can satisfactorily model a horizontal soil stratum of infinite lateral extent when the containment walls are lined with an absorptive material to attenuate wave reflections that would otherwise occur. Measurements of the acceleration at different locations on the free soil surface indicate that the surface motion is fairly uniform over a relatively large area. This is further confirmed by a comparison made between the measured free and scattered field motions for a surface foundation. Next, a series of soil-structure interaction tests are performed which examine the dependence of radiation damping on the natural frequencies of the structure relative to the fundamental frequency of the soil stratum. The experimental results are shown to be consistent with established theories. Finally, the experimental results are used to compute the stiffness and damping parameters of a two degree of freedom numerical model of the soil-structure system. The experimental parameters are shown to be in good agreement with calssical text book formulae. This study demonstrates that the centrifuge model consistently behaves as expected for simple, but realistic, dynamic soil and soil-structure systems, and can, therefore, be used with confidence to examine more complicated systems that are not yet fully understood.     

Blind identification of soil–structure systems

Surrounding soil can drastically influence the dynamic response of buildings during strong ground shaking. Soil’s flexibility decreases the natural frequencies of the system; and in most cases, soil provides additional damping due to material hysteresis and radiation. The additional damping forces, which are in non-classical form, render the mode shapes of the soil–structure system complex-valued. The response of a soil-foundation system can be compactly represented through impedance functions that have real and imaginary parts representing the stiffness and damping of the system, respectively. These impedance functions are frequency-dependent, and their determination for different configurations been the subject of a considerable number of analytical, numerical, and experimental studies. In this paper, we first develop a new identification technique that is capable of extracting complex mode shapes from the recorded free or ambient vibrations of a system. This technique is an extension of the second-order blind identification (SOBI) method, which is fairly well established in a number of other areas including sound separation, image processing, and mechanical system identification. The relative ease of implementation of this output-only identification technique has been the primary source of its appeal. We assess the accuracy and the utility of this extended SOBI technique by applying it to both synthetic and experimental data. We also present a secondary procedure, through which the frequency-dependent soil-foundation impedance functions can be easily extracted. The said procedure has a practical appeal as it uses only free or ambient responses of the structure to extract the foundation impedance functions, whereas current techniques require expensive and time-consuming forced-vibration tests.     

Seismic behaviour of circular tunnels accounting for above ground structures interaction effects

Tunnels are commonly designed under seismic loading assuming “free field conditions”. However, in urban areas these structures pass beneath buildings, often high-rise ones, or are located close to them. During seismic excitation, above ground structures may cause complex interaction effects with the tunnel, altering its seismic response compared to the “free field conditions” case. The paper summarizes an attempt to identify and understand these interaction effects, focusing on the tunnel response. The problem is investigated in the transversal direction, by means of full dynamic time history analyses. Two structural configurations are studied and compared to the free field conditions case, consisting of one or two above ground structures, located over a circular tunnel. Above ground structures are modeled in a simplified way as equivalent single-degree of freedom oscillators, with proper mechanical properties. Several parameters that are significantly affecting the phenomenon are accounted for in this parametric study, namely the soil to tunnel relative flexibility, the tunnel dimensions, the tunnel burial depth and the soil properties and nonlinearities during shaking. Tunnels response characteristics are compared and discussed, in terms of acceleration, deformations and lining dynamic internal forces. Internal forces are also evaluated with analytical closed form solutions, commonly used in preliminary stages of design, and compared with the numerical predictions. The results indicate that the presence of the above ground structures may have a significant effect on the seismic response of the tunnel, especially when the latter is stiff and located in shallow depths.     

砂土自由场地震响应的离心机试验研究

离心机模型试验是研究岩土地震工程问题的有效手段。本文使用层状剪切箱,通过干落法制备了均匀的砂土模型,进行了离心机振动试验;观测了振动过程中孔隙水压力的发展,土体的加速度响应、侧向变形以及竖向沉降。结果表明,土体的运动和变形与孔隙水压力的发展密切相关,但离心机中的试验现象和现场观测的现象存在显著区别。研究结果增强了对振动过程中土-水之间相互作用机理的理解,同时为自由场地震响应分析方法的验证提供了基础数据。     

轨道附近地面振动模型中的饱和地层动力格林函数

列车引起场地振动的建模需要能够表达地层的动力格林函数.本文兼顾饱和土的流固两相耦合性、场地土的分层性和波动的三维传播性,构建了半解析的场地动力格林函数.首先,基于Biot方程,在傅里叶变换域求解固体骨架和流体的位移和应力.然后采用传递矩阵方法建立地表位移和应力间的关系,得到格林函数矩阵.进而讨论矩阵的一些固有特征,提出改善竖向位移计算效率的措施.最后利用推导的格林函数计算了几个典型算例.数值结果与文献中其他方法得到的结果十分接近,与场地振动的现场观测试验基本符合.软土场地振动的计算结果高于饱和砂土场地,高速列车场地振动强度高于低速列车.当车速接近场地瑞利波速,模拟结果中显示出马赫锥.数值结果还显示,即使车速略低于瑞利波速,马赫锥也可能出现.本文推导的格林函数将有助于深入理解列车等移动激励作用下层状饱和土场地的振动特征.     

Effects of wave passage on the relevant dynamic properties of structures with flexible foundation

An evaluation of the wave passage effects on the relevant dynamic properties of structures with flexible foundation is presented. A simple soil–structure system similar to that used in practice to take into account the inertial interaction effects by the soil flexibility is studied. The kinematic interaction effects due to non‐vertically incident P, SV and Rayleigh waves are accounted for in this model. The effective period and damping of the system are obtained by establishing an equivalence between the interacting system excited by the foundation input motion and a replacement oscillator excited by the free‐field ground motion. In this way, the maximum structural response could be estimated from standard free‐field response spectra using the period and damping of the building modified by both the soil flexibility and the travelling wave effects. Also, an approximate solution for the travelling wave problem is examined over wide ranges of the main parameters involved. Numerical results are computed for a number of soil–structure systems to identify under which conditions the effects of wave passage are important. It comes out that these effects are generally negligible for the system period, but they may significantly change the system damping since the energy dissipation within the soil depends on both the wave radiation and the diffraction and scattering of the incident waves by the foundation. Copyright © 2001 John Wiley & Sons, Ltd.