Train-induced Vibration Research Articles

Efficient time–frequency approach for prediction of subway train-induced tunnel and ground vibrations

In this paper, an efficient time–frequency approach is presented for the prediction of subway train-induced tunnel and ground vibrations. The proposed approach involves two steps. In the first step, a time domain simulation of the vehicle–track subsystem is used to determine the track–tunnel interaction forces and, in the second step, the resulting forces are then applied to a 2.5 D FEM–PML model of the tunnel–soil system. There are two main aspects to the novelty and contribution of this work: First, the errors of the linearized Hertzian wheel–rail contact models in the calculation of the track–tunnel interaction forces are quantified by a comparison with the nonlinear Hertzian contact model. The results show that the relative errors are less than 2%. Second, an efficient time–frequency analysis framework is proposed, including the use of a strongly coupled model in the time domain solution and a 2.5 D FEM–PML model in the frequency–wavenumber domain solution. Finally, the accuracy and efficiency of the proposed approach are verified by comparison with a time-dependent 3 D approach, where three types of soil, i.e. soft, medium, and hard, are considered.

Identifying the influence of a large alluvial valley on train-induced vibration propagation in Rome by an integrated approach

In recent decades, the number of tunnels has increased within city centres worldwide due to the construction of new underground train lines, thus instigating subsequent issues related to an increase in the amount of vibrations affecting pre-existing buildings and infrastructures; therefore, more studies have been devoted to investigating the interactions between underground train lines and buildings within the framework of a site-city interaction (SCI) scheme. The already designed layout of line C of the Rome Metro was chosen as the research object of a case study focusing on underground train-induced vibration propagation in the city centre of Rome (Italy). Numerical modelling was carried out to analyse the propagation of future vibrations within the large buried alluvial valley and to assess the spatial extension of the induced vibration resentment.Two different subsoil models were considered for this study area: i) a homogeneous model (HoM), in which a homogeneous filling of Tiber alluvia was considered, and ii) a heterogeneous model (HeM), where the Tiber alluvia was distinguished within various lithotechnical units. Specific geophysical measurements were performed to i) record vibrations induced by accelerating, braking and regularly transiting trains to provide input for numerical modelling and ii) define the typical ambient vibration noise of the investigated area. Numerical modelling was then performed using the CESAR-LCPC code, which adopts a finite element method (FEM) solution in the time domain, to simulate the propagation of train-induced vibrations within the Tiber River valley in both the HoM and HeM simulations.The simulation outputs reveal a negligible deamplification effect up to approximately 2 Hz with respect to the considered solicitation in the area located above the tunnels and a maximum effect with respect to the reference ambient vibration noise within 5 and 10 Hz along the valley. The vibrations induced by the accelerating trains can be associated with the highest resentment at the free surface of the valley. A more intense effect generally results in the HeM simulation, which highlights the nonnegligible role of the heterogeneities present within the Tiber alluvia in propagating train-induced vibrations. The numerical outputs highlight that the train-induced vibrations can propagate hundreds of metres away from the underground train location, i.e., up to 400 m astride the axis of the designed tunnels in the case study considered here, and can be distinguished with respect to the regular ambient vibration level.

Impact of train vibration on physical and mechanical properties of epoxy asphalt concrete in the road-railway bridge

In the road-railway bridge (RRB) reconstruction, the significant train-induced vibration excitation poses a potential risk to the epoxy asphalt concrete (EAC) during the paving process on the road deck bridge. This paper aimed to investigate the effect of train-induced vibration on the physical and mechanical behaviors of EAC paving on the road bridge. In the following study, we determined the typical vibration condition refer to the vibration load obtained by in-situ monitoring, designed and conducted a series of indoor tests to explore the impacts of train-induced vibration on the mixture segregation, Marshall stability (MS), immersion MS, and dynamic stability (DS) of EAC by using a self-developed vibration simulation device (SVSD). The results confirm that EAC shows obvious segregation under the train-induced vibration and then declined the Marshall stability (MS) and uniformity of mixture. The initial MS decreases by 9.4%, ultimate MS by 4.9%. Frequency and duration are the major factors. Train-induced vibration could only impact the physical properties of EAC, but the chemical cured, thus EAC still retains high performances under the disturbance. It is found that EAC is vulnerable at the initial stage of paving construction, so the breakdown rolling process should be conducted immediately to reduce the vibration impact in the field. In the aspect of material design, a rapid-curved EAC is expected better under the train-induced vibration.

Vibration transmissions and predictions within low-rise buildings above throat area in the metro depot

Train-induced feelable vibrations can bring side effects to people living or working in the building, as well as to operation of precise equipment. As massive construction of over-track buildings above metro depots prevails in megacities, impacts from train-induced feelable vibration take more concern. Four standard-designed 4-story steel-framed offices above the throat area in the Qianhai metro depot in Shenzhen, China, are studied in this research. The field measurements were conducted to investigate the influences of track alignment and track location in the throat area on vibration responses of over-track buildings. Detailed vibration analyses using the finite element method have been conducted. Train-induced floor vibration assessments on human comfort are carried out based on a total of 54 train pass-bys operated in the morning and evening and on different tracks. It can be found that the track alignment primarily affected the higher frequency components of train-induced vibrations, where curved trackinduced vibrations have larger amplitudes. The variance of train-induced building vibrations among pass-bys on different track locations was reduced compared with that of ground vibrations because of the averaging effects caused by multiple transmitting paths within the massive platform and stiff transfer structures. Train-induced acceleration levels at mid-floor can be 20–25 dB larger than those near columns at floor resonance frequencies which are dependent on the structural design. This research gives a comprehensive insight into train-induced vibrations within low-rise steel-framed buildings above the throat area in the metro depot, which is a valuable reference for assessments before the construction of future similar over-track communities.

Vibration Isolation of a Rubber-Concrete Alternating Superposition In-Filled Trench for Train-Induced Environmental Vibration Based on 2.5D Indirect Boundary Element Method

A new train-induced vibration isolation measure of rubber-concrete alternating superposition in-filled trench is presented in this paper. For analyzing the vibration isolation effect of the new measure, this paper establishes a 2.5D train-track-layered foundation-filled trench model to analyze the dynamics of track and layered foundation with the in-filled trench. The correctness of the model is verified by using the measured data of the Sweden X-2000 high-speed train. The vibration isolation effect of the rubber-concrete alternating superposition in-filled trench is calculated by using the actual soft soil foundation parameters of the X-2000 high-speed train, and the vibration isolation effect is also compared with that of the empty trench, rubber in-filled trench, and concrete in-filled trench. The results show that the vibration isolation effect of the rubber-concrete alternating superposition in-filled trench proposed in this paper is better than that of the C30 concrete in-filled trench, especially the impact on displacement. Compared with low-frequency vibrations generated by the lower train speed, the rubber-concrete alternating superposition in-filled trench has a better vibration isolation effect on high-frequency vibrations caused by higher-speed trains. The rubber-concrete alternately superposition in-filled trench has the frequency band characteristics of elastic waves. Elastic waves in the passband frequency range can propagate without attenuation, while the elastic waves in the forbidden frequency range will be filtered out.

Measurement research on vibro-acoustic characteristics of large-span plate-truss composite bridge in urban rail transit

Large-span plate-truss composite bridge (LPCB) is developing more and more rapidly in urban rail transit. Nevertheless, the bridges are often close to residential buildings, and some even pass through residential areas directly. Compared with small span bridges and ordinary concrete viaducts, the train-induced vibration and noise of LPCB are larger and last longer, and have a greater impact on the residents along the line. Therefore, it is necessary to study the train-induced vibro-acoustic characteristics of LPCB. However, the current research on LPCB mainly focuses on the aspects of bridge structure design, construction, traffic safety and comfortable capability etc, and usually only cares about the global mechanical behavior of bridge structure and train-track-bridge coupling vibration. In order to study the vibro-acoustic characteristics of large-span and complex bridge structures such as LPCB, it is extremely important to obtain and analyze the field measured data. In this paper, the vibration and noise filed measurement of LPCB has been carried out by the authors. The vibration characteristics of track and bridge system have been measured by means of acceleration sensors, which were arranged on the rails, track slab, the center of bridge deck, longitudinal web and transverse web. The noise characteristics of wheel-rail and bridge structure system have been measured by mans of noise sensors, which were arranged beside the track structure and under the bridge structure. Based on the measurement date, the vibro-acoustic characteristic of the LPCB were analyzed in the present paper. It is found that the response of track structures are mainly affected by wheelsets periodic excitation, while the response of bridge structures are determined both by wheelsets periodic excitation and wheel-rail irregularity; the rail and slab are decoupled after beyond the natural frequency of the rail-fastener system (100 Hz); the vibration energy in high frequency band can be effectively suppressed to downward transmission by damping pad floating slab track; the overall vibration level of rail, track slab and bridge are about 130 dB, 114 dB and 118 dB respectively, the overall sound pressure level of track-side and bridge structure are approximately 82 dB(A) and 83 dB(A) respectively.

Experimental validation of a simplified numerical model to predict train-induced ground vibrations

This study evaluates the effect of high-speed train (HST)-induced environmental vibrations using simplified computational models and validates the test results in full-scale field conditions. Experimental investigations and in-situ measurements were performed at the Istanbul-Ankara high-speed railway section to examine the effect of ground vibrations from HSTs on the surrounding residential lands. In this study, ground-borne free-field surface motion at different distances from the railway track was realized using accelerometers. The experimental results of vertical and horizontal ground vibration accelerations induced by HSTs with a velocity of 250 km/h were analyzed. In the first part of the study, a two-dimensional (2D) numerical model based on finite element method (FEM) was used to investigate ground vibrations and validate the experimental results. To minimize artificial reflections and dissipate vibrational energy at the boundaries, the lateral extension of an infinite domain was modeled with viscous absorbing boundaries. A dynamic analysis of the proposed railway-soil coupled model was performed in the time domain under plain-strain conditions using Plaxis 2D, a commercial FEM software. For the verification, the experimental results were compared with those obtained from the numerical analysis. The simplified computational model validated by the test results may help researchers determine further investigation strategies to develop cost-effective mitigation measures for structures with sensitive devices near the railway track and significantly contribute to understanding complex wave propagation problems. In the second part of the study, train-induced environmental ground vibrations were analyzed for different types of soil conditions using a 2D FE model. Computational analyses were performed with four types of soil: soft, medium, dense, and rock, based on the Turkish Earthquake Code. The HST was used as a dynamic source to observe the differences in vibration generation and wave transmission in different types of soil. The HST load on the slab track was simulated to study the effect of operational loads on ground-borne vibrations. Based on the dynamic analysis results, the response of the free-field motion was investigated to obtain the relative acceleration time histories for different points of soil. According to the results, the peak acceleration values of train-induced vibrations at soft, medium, and dense soil sites increased dramatically when compared to the rock site. Vibration measurement data collected from parametric experiments with a simple numerical model for various soil characteristics can be particularly useful when planning residential and industrial facilities at new locations near railroads, to avoid the adverse effects of environmental vibrations caused by HSTs.

Analytical modeling for the calculation of underground train-induced vibrations in inhomogeneous soils with uncertainty

In this paper, an analytical wave function method was used to calculate the underground train-induced vibrations with the inhomogeneous soils taken into account. The wave function method is suitable for solving dynamic problems of multi-layered soils; therefore, inhomogeneous soils with uncertainty could be achieved by assigning different soil parameters to each soil layer. Based on the method, a half-space dynamic model with a viscoelastic cylinder tunnel was established. The dynamic shear modulus of the soil was the main uncertain variable in this study, and models with different load frequencies are compared to analyze the effect caused by the uncertainty. According to the numerical results, the relationship between the uncertainty of the soil modulus and the dynamic response of the model was given. When the dynamic shear modulus changes randomly with the range of 20%, the vertical displacement of the surface can be from 1.02 to 1.12 times to that in the model where the soil is homogeneous, while the displacement of the tunnel vault is 1.03–1.1 times.

A hybrid methodology for predicting train-induced vibration on sensitive equipment in far-field buildings

The prediction of train-induced vibration on far-field buildings is a challenging issue in the transportation environment communities. In this work, a hybrid prediction method is put forward utilizing the idea of substructure analysis, which can high-effectively calculate the train-induced vibration under different operation conditions. Based on vehicle-track coupled dynamics theory, wavenumber finite element theory (2.5D FEM) and Green’s function method, this method could comprehensively analyze vibration characteristics of the source, propagation path and sensitive target/vibration receiver by appropriately considering the boundary conditions between each part. The proposed model possesses the advantages of 2.5D FEM in calculation efficiency and could consider the dynamic interaction between vehicle and track system more elaborately. In addition, the vibration response under different operation conditions can be high-efficiently obtained by updating the track supporting forces without repeatedly solving the Green’s functions of the system. On this basis, this work predicts the vibration impact of subway train operation on the sensitive equipment in a far-field large-scale building, and uses the generic vibration criteria for sensitive equipment to evaluate the vibration responses. Further, to mitigate the impact of train-induced vibration, floating slab track is adopted to achieve the vibration attenuation in the concerned frequency. Results show that the train-induced vibration on the monolithic bed track exceeds the limit specified in the standard in some frequency bands. The use of floating slab track can effectively reduce the vibration response of the building and ensure the routine use of sensitive equipment.

Vibration suppression of bridges under moving loads using the structure-immittance approach

This paper presents the possibility of suppressing the train-induced vibration on bridges using a linear passive vibration suppression device incorporating inerter. The inerter is a two-terminal mechanical element with the property that the applied force is proportional to the relative acceleration across its terminals. The inerter has been applied to various engineering structures where performance benefits have been identified. However, currently these studies are either limited to simple network configurations with moderate performance improvement, or resulted in complicated configurations with a large number of elements which are impractical for real-life applications. In addition, the potential of using inerter-based absorbers for suppressing the train-induced bridge vibrations has not been taken into consideration. In this paper, a simplified bridge model equipped with a vibration suppression device subjected to series of moving forces is presented. The structure-immittance approach, which can cover all networks with pre-determined numbers of each element type, is adopted for the identification of the optimal absorber configurations. Numerical studies for two bridges, the THSR and the Kum-gang, under three types of railway excitations, the French T.G.V., the German I.C.E. and the Japanese S.K.S. are conducted. It is demonstrated that the overall performance of the bridge can be improved by using the proposed inerter-based configuration. It is also checked that the absorber stroke is much smaller than the inner space of bridge box girder, indicating the practical installation of the absorber. Furthermore, the robustness of the proposed absorber is verified by sensitivity analysis subjected to the change of bridge parameters and the device component values.

An efficient prediction model for vibrations induced by underground railway traffic and experimental validation

This study proposes an efficient prediction model for the vibration generated by underground railways. The proposed model is based on an analytical approach for a tunnel in a horizontally multi-layered half-space, showing the advantage of high computational efficiency and accuracy. Three alternative modelling strategies regarding hypotheses about the cross-section behavior of the slab and the connection condition between the slab and tunnel are introduced. A multi-body vehicle model is subsequently coupled with the track-tunnel-ground system in the moving frame of reference to determine the train-induced vibration. The predicted vibrations on the track, tunnel, and ground surface induced by the passage of trains are compared with the measured vibrations from an underground railway line in London from the literature. The predicted results for the double-beam track model with uniform support and the continuum track model exhibit a good agreement with the site measurements. The cross-section deformation of the track can be ignored and has little influence on the responses of the tunnel and ground. However, the assumption of the one-line connection between the slab and tunnel results in an overestimation of the track vibration, up to 20 dB, and an underestimation of the tunnel and ground vibration, up to 10 dB.

Real-time hybrid testing for efficiency assessment of magnetorheological dampers to mitigate train-induced vibrations in bridges

ABSTRACT The dynamic response of railway bridges is important to consider, as the high velocity loading from the trains increases the risk of resonance. Increasing train speeds and loads result in a need for adaptable properties for railway bridges. One solution is to install magnetorheological dampers, as the response of the structure originating from moving loads could be controlled by alternating the input current to the damper. However, the complexity of such devices results in difficulties to accurately model their behaviour. From this context, real-time hybrid simulations, consisting of a numerical bridge model and a full-scale physical magnetorheological damper in a test frame, are presented in this paper. The novelty of the present paper is the application of RTHS in railway bridge engineering and the substructure combination with magnetorheological dampers. The results from the real-time hybrid simulations show that the bridge deck responses can be reduced to permissible levels.

Attenuation Law of Train-Induced Vibration Response of Subgrade in Beijing–Harbin Railway

To investigate environmental vibration in the case of railway subgrade in seasonally frozen regions, field experiments were conducted on the Beijing–Harbin railway subgrade of China in autumn and winter. Vibration acceleration and vibration level attenuation law were analysed based on monitoring results. Accordingly, the influence of the subgrade freeze-thaw states, vehicle load, train formation, and running speed on the subgrade surface environmental vibration was analysed. The vibration response of the subgrade decreased with an increase in the distance from the track. The attenuation curve of the vibration acceleration can be fitted using the negative exponential function, and the attenuation curve of the vibration level can be fitted using the linear function. Additionally, the subgrade vibration response during the frozen period was greater than that during the unfrozen period owing to increased strength and rigidity and decreased damping ratio after subgrade freezing, which increased the vibration response. Moreover, the vibration intensity of the subgrade increased with increase in the vehicle load and formation and decreased with an increase in the driving speed within a particular speed range. The findings of this study provide an objective basis for railway subgrade design and disaster assessment in cold regions of China.

Finite element analysis of multistory structures subjected to train-induced vibrations considering soil-structure interaction

Due to the expansion of cities through megaprojects and the increase in populations in large cities, many buildings are constructed beside train tracks. Trains passing nearby buildings cause ground vibrations that may affect the structures and their foundations. In this research, a detailed 3-D finite element analysis is conducted on a ten-story reinforced concrete framed structure resting on a raft foundation using ABAQUS. The soil profile consists of silty clay for 10 m followed by dense sand for 40 m. The soil block considered in the analysis has plan dimensions of 100m × 100m. The train loads are modeled using moving point loads. The train track is considered at different distances from the building. The effect of the train speed and its track distance from the building on the response of the structure with its foundations are investigated. Mitigation techniques including open trenches and in-filled foam trenches are considered in order to mitigate the effect of vibrations induced by trains on the adjacent building. The results showed that these techniques are efficient in reducing the train-induced vibrations transmitted to the soil and the adjacent building. The average reduction percentage in acceleration was 61.29 % and 57.39 % when using in-filled foam trench and open trench mitigation techniques, respectively.

Effect of longitudinal joint on train-induced vibrations from subway shield-driven tunnels in a homogeneous half-space

With the rapid increase of urban rail transit networks, the environmental problems induced by vibrations from subway traffic become more and more prominent. Most subway tunnels are constructed by the shield machine, which are assembled by tunnel linings connected by joints. This study investigates the effect of the tunnel longitudinal joints on the train-induced vibrations from a subway shield-driven tunnel in a homogeneous half-space. The shield-driven tunnel is considered as an elastic lining ring connected by longitudinal joints, while the ground is simplified as a homogeneous elastic half-space. The general solution for the tunnel and the ground are derived by using the thin-shell theory and the elastic continuum theory, respectively. By satisfying the boundary conditions on the tunnel-ground interface, the tunnel is coupled to the ground in a half-space domain. The responses during the running of a metro train are calculated by coupling the tunnel-ground model with the vehicle-track model. The longitudinal joint has a significant impact on ground vibrations, which increases the running RMS values of the vertical velocity by 20% ∼ 70% and of the horizontal verticity by 10% ∼ 20%. As the stiffness of the longitudinal joint decreases, the ground vibrations increase.

Three-dimensional dynamic analysis of ancient buildings with novel high damping isolation trenches

To improve the efficiency of conventional isolation trench and lighten the impact of the excavation on neighbor buildings, a novel high damping isolation trench is proposed. The viscoelastic braces equipped in the high damping isolation trench can dissipate the energy of ground-borne vibration while providing supporting force to ensure the stability of the soil on both sides. According to two actual ancient buildings, two types of high damping isolation trenchs with the plane shape of U and L are designed to solve the potential damages caused by long-term train-induced vibration. First, three-dimensional finite/infinite models based on these two buildings are established, respectively. Then, the energy dissipation characteristics are obtained by experiments. Through calculation, the control effects of the high damping isolation trenchs for these two buildings are investigated. The results indicate that the viscoelastic braces possess high energy dissipation capacity. After setting the high damping isolation trenchs around the structures, even at a small excavation depth, the acceleration and velocity responses of the two buildings are reduced significantly. Furthermore, the selected U-shaped and L-shaped trenches also show superiority compared with the conventional linear-shaped trench in this project.

Experimental study on ground vibration induced by double-line subway trains and road traffic

Rail transit and highway transportation have flourished in the process of urbanization by virtue of their respective advantages, facilitating people’s travel but also producing harmful environmental vibrations. For an accurate analysis of source characteristics and propagation laws of train-induced vibrations, a field measurement was carried out in Shenzhen, China, where a double-line subway passes directly under the main urban road. The rail acceleration at the straight track and the point of fixed frog in the tunnel as well as ground vibrations caused by double-line subway and road traffic under different operating conditions were measured. A special attention was paid to the vibration response of each measurement point on the ground when the subway train and road vehicles passed through simultaneously. Measurement shows that horizontal acceleration cannot be ignored in the area close to the subway line, and vibration amplification phenomenon exists in the free field, due to the difference of the local geological conditions that leads to different vibration levels. Compared with the ground vibration caused by only the near-line train passage, when a near-line train passes the test section with a far-line train is about to arrive, the ground vibration intensifies in the frequency band of 50–63 Hz. When a far-line train passes the test section with a near-line train just left, the vibration level of each measuring point shows different degrees of reduction in various frequency bands, and reduction amount of horizontal acceleration in the frequency 10–16 Hz reaches 12 dB. Ground vibration aggravates significantly when the near-line train and bus pass simultaneously, the horizontal vibration is more sensitive to the superposition influence of road traffic. The measured data can not only guide the work of vibration environment assessment in the stage of subway design and planning but also can validate possible numerical models for predicting train-induced vibrations.

Experimental study on the characteristics of train-induced vibration in a new structure of metro depot.

In order to improve the utilization rate of expensive and very limited urban land, a new structure system, underground metro depot, has been developed and applied in several cities in China. The underground metro depot, which is built underground, can be multiple stories, and allows other developments on top, has become increasingly popular in recent years. Since there are other developments on top, the vibration induced by the trains frequently entering and exiting the depot cannot be ignored. To better understand the characteristics of the train-induced vibration in the underground metro depot, a series of field tests were conducted on a two-story underground depot which is the largest underground metro depot in Asia. The results show that the main frequency components of vibration source are between 50 and 200 Hz and the level of that in the first floor underground is larger than that in the second floor underground due to the train floor structure interaction when the train running on the first floor underground. The vibration in the top platform decreases linearly with the distance from the measuring point to the center line of the track. When the train is running on the track at the edge area, the linear attenuation rate was about 0.2dB/m. It is easy to excite the vibration mode of the floor structure when the train is running on the first floor underground, so the vibration in the top platform induced by the train running on the first floor underground was much larger than the train running on the second floor underground. In the future design, if the underground depot has more than one floor, the structural dynamic behavior of over-track buildings induced by the train running on the floor slab underground should be the focus. The throat area has many rail joints and turnouts which can lead to a larger vibration level, the level easy to exceed the limit given for human vibration comfort. If developments are proposed on top of the throat area, the vibration level should be carefully checked in the area within 30 m from the track to avoid potential later vibration problem.

Safety of buildings against train induced structure borne noise

Construction and operation of subways in crowded zones cause structure borne noise (SBN) which is sometimes annoying to the residents of nearby buildings. This is a serious challenge in the development of subways in large cities. Although various methods have been proposed to protect buildings against SBN, the amount of train-induced vibrations which cause impermissible SBN is not clearly known. Since train induced vibration is a criterion in the design and construction of subways, there is a need to find correlations between train-induced vibrations and SBN in order to take SBN into the subway and buildings design approaches. In response to this need, influences of train-induced vibration on SBN were studied in this research, leading to drive conditions for safety of buildings against train induced structure borne noise. For this purpose, a vibroacoustic model of building was developed and validated, using results of field tests carried out in this research. Buildings parameters were classified based on their structural and non-structural properties. Through parametric analysis of the model, effects of building structural and acoustic parameters on SBN were investigated. A prediction model was developed by which the allowable amount of train induced vibration acceleration beneath building foundations as a function of building conditions is derived. The model was used as a guideline for design and construction of safe buildings against SBN. The applicability and effectiveness of the results/model were illustrated by several field tests.

Evaluating vertical conditions of bridge substructures of heavy-haul railway lines based on dynamic stiffness and pier vibration response

When it is necessary to increase the freight volume, the related increase in the train axle loads can potentially affect the bearing capacity of bridge substructures. Therefore, the structural integrity of bridge substructures should be evaluated, and their capacities need to be estimated. Existing studies have only investigated the lateral health condition of piers and foundations of bridges. To evaluate the vertical condition of bridge substructures, in this study, a dynamic transient response method (TRM) was developed using newly designed equipment. The vertical dynamic stiffness of a bridge foundation was employed as the main evaluation index. Subsequently, in situ experiments were performed on 62 bridge foundations of a heavy-haul railway line, including three types of foundations. Train-induced vertical and lateral vibration responses on the pier tops were also measured. The relationship between the vertical dynamic stiffness of the foundations and the train-induced vibration amplitudes on the pier tops was analysed. Subsequently, the support vector machine (SVM) method was employed to predict the dynamic stiffness of the bridge foundations when the TRM test could not be performed and the train-induced vertical vibration response on pier tops could be tested. Finally, a three-step evaluation strategy was proposed to comprehensively assess the vertical conditions of bridge substructures using the above methods. The study indicates the following: (1) The redundancy of the vertical bearing capacity is completely different from that of the horizontal vibration amplitude. There may be a certain error in the evaluation of a pier foundation when only the horizontal vibration amplitude is used to analyse its health condition. (2) The dynamic stiffness obtained by the TRM can effectively reflect the vertical condition of a bridge substructure and can be employed as an index in the detailed evaluation stage. (3) Using SVM, the dynamic stiffness of a foundation can be predicted with the measured amplitudes of the train-induced vertical vibration on the pier tops. The amplitudes of train-induced vibration and SVM-based prediction of dynamic stiffness can be used as early warning indicators in the scoping evaluation stage.