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.     

Numerical modelling of free field traffic-induced vibrations

This paper deals with the numerical modelling of free field traffic-induced vibrations during the passage of a vehicle on an uneven road. The road unevenness subjects the vehicle to vertical oscillations that cause dynamic axle loads. The latter are calculated from the vehicle transfer functions and the frequency content of the road profile as experienced by the vehicle axles. A transfer function between the source and the receiver that accounts for the dynamic interaction between the road and the soil is used to calculate the free field response. Its calculation is based on a dynamic substructure method, using a boundary element method for the soil and an analytical beam model for the road. The methodology is validated with analytical results and is finally illustrated by a numerical example where the free field vibrations during the passage of a vehicle on a traffic plateau are considered.     

Vibrations induced by HST passage on ballast and non-ballast tracks

The use of ballastless slab track is significantly increasing in HST line technology. This development is due to some structural and operational advantages over ballasted track. In addition, floating slab tracks can be used to control ground-borne vibrations generated by surface and underground rail transportation systems. In this paper, a general and fully three dimensional multi-body-finite element-boundary element model is used to study vibrations due to train passage on ballast and non-ballast tracks. The vehicle is modelled as a multi-body system, the track, in both cases, using finite elements and the soil is represented using boundary elements. The three components of the load are considered; the quasi-static excitation (force generated by moving axle loads), the parametric excitation due to discrete supports of the rails and the excitation due to wheel and rail roughness and track unevenness. Track receptances are computed for both track systems and vibrations induced by high-speed train passage at the track and the free-field are evaluated for different train speeds. Soil behaviour changes significantly with the track system. Finally, a floating slab track is studied to show how this type of solution leads to a significant vibration reduction for surface tracks.     

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.     

Building vibrations and dynamic pavement loads induced by transit buses

The purpose of this study was to investigate the effect of bus suspension systems on building vibrations and dynamic pavement loads. Building vibrations and pavement loads induced by two instrumented buses having different characteristics were measured simultaneously under controlled field conditions. Field tests were performed at several vehicle speeds, normal and reduced tire pressures, and with roads having good surface condition as well as abrupt surface irregularities. Tests were carried out at two vibration complaint sites in Montréal. The level and frequency content of vibrations and loads induced by the two buses were evaluated and compared. The results show that the dynamic component of pavement loads induced by the two buses were significantly different but the difference in building vibration levels was not as significant.     

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.     

Reduction of ground vibration by means of barriers or soil improvement along a railway track

Trains running in built-up areas are a source to ground-borne noise. A careful design of the track may be one way of minimizing the vibrations in the surroundings. For example, open or infilled trenches may be constructed along the track, or the soil underneath the track may be improved. In this work, the influence of the track design and properties on the level of ground vibration due to a vehicle moving with subsonic speed is examined. A coupled finite element-boundary element model of the track and subsoil is employed, adopting a formulation in the moving frame of reference following the vehicle. The computations are carried out in the frequency domain for various combinations of the vehicle speed and the excitation frequency. The analyses indicate that open trenches are more efficient than infilled trenches or soil stiffening–even at low frequencies. However, the direction of the load is of paramount importance. For example, the response outside a shallow open trench may change dramatically when horizontal load is applied instead of vertical load.     

Bridge response with tractor-trailer vehicle loading

A method for the calculation of dynamic response and loading of single span multigirder bridges due to vehicle loads is described. The analysis takes account of vehicle acceleration or braking, road surface roughness and eccentric placement of the vehicle on the bridge. The analysis is presented for a three-axle tractor-trailer vehicle and the bridge is modelled as an orthotropic plate using higher order finite strips. As an example application, the loadings produced with braking of the three-axle vehicle and a nominally equivalent two-axle vehicle on a bridge were computed. Previous theoretical studies of bridge loading with vehicle braking had employed a two-axle idealization of a three-axle vehicle. The results of the present study show that this approximation is not valid for braking studies as the behaviour of the two vehicle models is significantly different. The loadings produced by a three-axle vehicle are generally less severe than those due to an ‘equivalent’ two-axle vehicle.     

Experimental investigation of railway train-induced vibrations of surrounding ground and a nearby multi-story building

In this paper, a field experiment was carried out to study train-induced environmental vibrations. During the field experiment, velocity responses were measured at different locations of a six-story masonry structure near the Beijing-Guangzhou Railway and along a small road adjacent to the building. The results show that the velocity response levels of the environmental ground and the building floors increase with train speed, and attenuate with the distance to the railway track. Heavier freight trains indu...     

Numerical prediction of ground vibrations induced by high-speed trains including wheel–rail–soil coupled effects

A simplified analytical model including the coupled effects of the wheel–rail–soil system and geometric irregularities of the track is proposed for evaluation of the moving train load. The wheel–rail–soil system is simulated as a series of moving point loads on an Euler–Bernoulli beam resting on a visco-elastic half-space, and the wave-number transform is adopted to derive the 2.5D finite element formulation. The numerical model is validated by published data in the literature. Numerical predictions of ground vibrations by using the proposed method are conducted at a site on the Qin-Shen Line in China.     

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.     

Fully coupled finite element model for dynamics of partially saturated soils

Understanding the response of partially saturated earth structures under various static and dynamic loads is important for the design and construction of economical and safe geotechnical engineering structures. In this study, the numerical approach is used to understand the dynamics of partially saturated soils. The mathematical equations governing the dynamics of partially saturated soils are derived based on the theory of mixtures and implemented within a finite element framework. The stress–strain behavior of the soil is represented by an elasto-plastic constitutive model for unsaturated soil based on bounding surface concept and the moisture-suction behavior is modeled using van Genuchten model. Fully coupled finite element simulations are performed to study the response of partially saturated soil embankment under earthquake loading and validated with centrifuge test results available in the literature. The predicted displacement responses are in good agreement with the measured responses. The pore water pressure, pore air pressure, matric suction, the degree of saturation in various elements and the response of the embankment under different initial moisture content are also discussed.     

Numerical evaluation of the dynamic response of pipelines to vibrations induced by the operation of a pavement breaker

This paper studies the response of pipelines to vibrations induced by the operation of a pavement breaker during the rehabilitation of concrete pavements. An efficient two-and-a-half-dimensional (2.5D) formulation is employed, where the geometry of the structure and the soil is assumed to be invariant in the longitudinal direction, allowing for a Fourier transform of the longitudinal coordinate y along the structure to the wavenumber k_y. The dynamic soil–structure interaction problem is solved by means of a 2.5D coupled finite element–boundary element (FE–BE) method using a subdomain formulation. The numerical model is verified by means of results available in the literature for a buried pipeline subjected to incident P- and SV-waves with an arbitrary angle of incidence. The presented methodology is capable to incorporate any type of incident wave field induced by earthquakes, construction activities, traffic, explosions or industrial activities. The risk of damage to a high pressure steel natural gas pipeline and a concrete sewer pipe due to the operation of a pavement breaker is assessed by means of the 2.5D coupled FE–BE methodology. It is observed that the stresses in the steel pipeline due to the operation of the pavement breaker are much lower than those induced by the operating internal pressure. The steel pipeline behaves in the linear elastic range under the combined effect of the loadings, indicating that damage to steel pipelines close to the road due to the operation of a pavement breaker is unlikely. The maximum principal stress in the concrete pipe, on the other hand, remains only slightly lower than the specified tensile strength. The decision to use a pavement breaker should hence be taken with care, as its operation may induce tensile stresses in concrete sewer pipes which are of the same order of magnitude as the tensile strength of the concrete. Assessing the risk of damage by means of vibration guidelines based on the peak particle velocity (PPV) gives, for the particular cases considered, qualitatively similar results.     

车辆荷载作用下山西路基重塑黄土的动力特性研究

针对车辆荷载对山西高速公路路基土体影响研究不足的现状,从试验角度出发,研究车辆荷载水平、波形、干密度和围压对路基土体的动力特性响应。研究表明:路基土体的体变随波形比的增大而增大,随车辆荷载的增大而增大;路基土体的动弹性模量随干密度的增大而增大,随围压的增大而增大,阻尼比随围压的增大而减小。     

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.     

Effect of ground-motion asynchronism on the equivalent acceleration of earth dams

Under seismic loads the deformability of an earth dam may induce several effects, including ground-motion amplification and asynchronism between different points of the dam embankment. The paper analyses the asynchronous effects occurring in two existing earth dams, representing well-documented case histories: the El Infiernillo Dam (Mexico) and the Camastra Dam (Italy). Asynchronous effects are analysed by theoretical predictions of the dam seismic response by adopting an advanced dynamic approach, which takes into account the main features that dam soils exhibit under cyclic loading conditions. For different potentially unstable masses within the dam embankment, equivalent accelerations were computed as the ratio between the resultant of the inertial forces and the weight of the volume V associated to the unstable mass. With the exception of very cortical sliding surfaces – not significant for dam stability – in most of the analysed cases the equivalent seismic coefficients do not exceed the peak acceleration at the dam base.     

A simplified model for lateral response of large diameter caisson foundations—Linear elastic formulation

The transient response of large embedded foundation elements of length-to-diameter aspect ratio D/B=2–6 is characterized by a complex stress distribution at the pier–soil interface that cannot be adequately represented by means of existing models for shallow foundations or flexible piles. On the other hand, while three-dimensional (3D) numerical solutions are feasible, they are infrequently employed in practice due to their associated cost and effort. Prompted by the scarcity of simplified models for design in current practice, we here develop an analytical model that accounts for the multitude of soil resistance mechanisms mobilized at their base and circumference, while retaining the advantages of simplified methodologies for the design of non-critical facilities. The characteristics of soil resistance mechanisms and corresponding complex spring functions are developed on the basis of finite element simulations, by equating the stiffness matrix terms and/or overall numerically computed response to the analytical expressions derived by means of the proposed Winkler model. Sensitivity analyses are performed for the optimization of the truncated numerical domain size, the optimal finite element size and the far-field dynamic boundary conditions to avoid spurious wave reflections. Numerical simulations of the transient system response to vertically propagating shear waves are next successfully compared to the analytically predicted response. Finally, the applicability of the method is assessed for soil profiles with depth-varying properties. The formulation of frequency-dependent complex spring functions including material damping is also described, while extension of the methodology to account for nonlinear soil behavior and soil–foundation interface separation is described in the conclusion and is being currently investigated.     

高速铁路路基动土压力测试信号的小波分析

阐述了小波分析的基本原理与方法,选用Daubechies小波对某高速铁路路基土压力的现场振动测试信号进行分析处理。由此对高速列车荷载作用下,路基动土压力产生的机理及其土压力的构成进行较深入的研究。     

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.     

Bridge dynamic loading due to road surface irregularities and braking of vehicle

Single span highway bridges of composite construction are idealized as beams as well as orthotropic plates. A standard HS–20–44 highway vehicle is represented by a planar, two-axle, sprung mass system with frictional device. The response equations are derived in terms of the natural modal co-ordinates of the bridge and of displacement co-ordinates of the vehicle. The road surface irregularities, generally found at the junctions of the approach road and bridge ends, are idealized as a 45° ramp. The maximum impact factors for bending moment and deflection are obtained due to the ramp and in combination with the braking of vehicle for symmetric as well as essentric loading of the vehicle.