interaction and ground borne vibration Excitation mechanisms of train/track Structural Mechanics, Department of Civil Engineering, KU Leuven

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1 RIVAS Training Workshop 9//23, Hotel Bloom, Brussels, Belgium "Reducing railway induced ground vibration by controlling the source" Excitation mechanisms of train/track interaction and ground borne vibration Geert Lombaert, Stijn François, Geert Degrande bwk.kuleuven.be/bwm Structural Mechanics, Department of Civil Engineering, KU Leuven RIVAS Training Workshop 9//23

Outline Transmission path (ISO 4837-:25). Loads applied by the vehicle on the track. 2. Dynamic track-soil interaction. 3. Transmission of vibrations through the soil. 4. Dynamic soil-structure interaction.

2 Outline Transmission path (ISO 4837-:25). Loads applied by the vehicle on the track. 2. Dynamic track-soil interaction. 3. Transmission of vibrations through the soil. 4. Dynamic soil-structure interaction. v urw ub fw K t L ui ur (ut, tt) y 5. Vibration (-8 Hz) and re-radiated noise (6-25 Hz) in the building. RIVAS Training Workshop 9//23 2

3 Wave propagation in the soil Relevant characteristics Transient response of a homogeneous halfspace (left), a single layer on bedrock (center), and a single layer on a halfspace (right), representing different simplified layered ground models. RIVAS Training Workshop 9//23 3

Wave propagation in the soil Relevant characteristics The soil is assumed to be a horizontally layered medium as its formation is governed by large scale processes (erosion, sediment

4 Wave propagation in the soil Relevant characteristics The soil is assumed to be a horizontally layered medium as its formation is governed by large scale processes (erosion, sediment transport,...). Each layer is characterized by (a) shear and (b) dilatational wave velocities Cs, Cp, material damping ratios βs, and βp, and its density ρ. (a) (b) RIVAS Training Workshop 9//23 4

5 Wave propagation in the soil Relevant characteristics The dynamic soil characteristics differ significantly from one site to another with wave velocities typically ranging from: Cs [m/s] Cp [m/s] Soft soil as peat Medium stiff soil 5 3 Stiff soil 4 8 In situ geophysical tests are required to identify dynamic soil characteristics and assess the transmission of vibrations at a given site. RIVAS Training Workshop 9//23 5

train and passages of Thalys High Speed Train (HST).

6 Case study Site at Lincent (Belgium), along line L2 Brussels - Köln Measurements during homologation of L2 (9/22) for passsages of InterCity train and passages of Thalys High Speed Train (HST). Elaborate tests to identify dynamic track and soil characteristics. RIVAS Training Workshop 9//23 6

7 Case study Dynamic soil characteristics Setup Setup Depth [m] Depth [m] No. 4 No. 5 RIVAS Training Workshop 9// S wave velocity [m/s] S wave velocity [m/s] Drilling B8 SASW SCPT Soft layer (Cs = 5 m/s, Cp = 3 m/s) with thickness of 3 m on top of stiffer halfspace (Cs = 28 m/s, Cp = 56 m/s). Density ρ = 2 kg/m 3 and material damping ratio β =.3 assumed for both.

8 Moving loads Wave field generated by a moving load with constant amplitude Vertical response of a layered elastic halfspace for a load of constant amplitude travelling at different load speeds v. x 8 x 8 x 8 Displacement [m] Displacement [m] Displacement [m] x [m] y [m] x [m] y [m] x [m] 25 v = v < min CR v > min CR 25 y [m] Trans-Rayleigh speeds only in case of high speed trains (v 8 km/h) travelling on tracks supported by very soft soil (Cs 5 m/s). RIVAS Training Workshop 9//23 8

9 Moving loads Wave field generated by a moving load with harmonic time variation Vertical response of a layered elastic halfspace for a load of harmonic amplitude travelling at different load speeds v. x 8 x 8 x 8 Displacement [m] Displacement [m] x [m] y [m] x [m] y [m] x [m] 25 y [m] RIVAS Training Workshop 9// Displacement [m] v = v < min CR v > min CR A moving harmonic load generates propagating surface waves regardless of the load speed.

10 Excitation mechanisms Excitation mechanisms of ground-borne vibration x 8 x 8 Displacement [m] Displacement [m] x [m] y [m] x [m] y [m] For a subcritical train speed, the response due to the static train load (quasi-static excitation) is a sequence of bowl shaped deflections. The response due to the dynamic load component (dynamic excitation) consists of waves emitted by the train that travel into the free field. The importance of both contributions to the free field response is illustrated by means of numerical simulations for the site at Lincent. RIVAS Training Workshop 9//23

Case study Numerical models for vibrations induced by traffic at grade FACULTY OF ENGINEERING DEPARTMENT OF CIVIL ENGINEERING STRUCTURAL MECHANICS KASTEELPARK ARENBERG 4

2 BUILD 9 OCTOBER 29 REPORT BWM-29-23 MATTIAS SCHEVENELS STIJN FRANÇOIS GEERT DEGRANDE The Matlab toolbox TRAFFIC has been developed at KU Leuven for the prediction of

11 Case study Numerical models for vibrations induced by traffic at grade FACULTY OF ENGINEERING DEPARTMENT OF CIVIL ENGINEERING STRUCTURAL MECHANICS KASTEELPARK ARENBERG 4 B-3 LEUVEN h z x y x3 3 2 b x4 4 d EDT ELASTODYNAMICS TOOLBOX FOR MATLAB SITE AMPLIFICATION SURFACE WAVES FORCED VIBRATION PROBLEMS USER S GUIDE EDT VERSION 2.2 BUILD 9 OCTOBER 29 REPORT BWM MATTIAS SCHEVENELS STIJN FRANÇOIS GEERT DEGRANDE The Matlab toolbox TRAFFIC has been developed at KU Leuven for the prediction of ground vibrations due to railway traffic. The software has been successfully benchmarked by comparing results from TRAFFIC and the software TGV developed at ISVR. RIVAS Training Workshop 9//23

12 Case study Track characteristics UIC6 rail. Precast prestressed monoblock sleepers (spacing d =.6 m). Pandrol E239 rail fastening system. Pandrol medium stiff resilient rubber railpads type 597 with a thickness of mm. Soft to medium stiff ballast layer (calibre 25/5, d =.35 m). Sub-ballast porphyry layer (calibre /32, d =.6 m). Improved soil layer (d =. m). RIVAS Training Workshop 9//23 2

13 Case study Cross section of model Rail Railpad The cross section of the track is assumed to be translationally invariant. Rails: Euler-Bernoulli beams. Railpads: Distributed spring-damper connection. Sleeper: Distributed mass, rigid in cross-section plane. Ballast: Elastic continuum. Soil: Layered elastic halfspace. z x Sleeper Ballast Soil RIVAS Training Workshop 9//23 3

14 Case study InterCity train Carriage length Lt, bogie spacing Lb, axle distance La, total axle mass Mt, sprung mass Ms, and unsprung mass Mu of all carriages of the InterCity train. Axles Lt Lb La Mt Ms Mu [-] [m] [m] [m] [kg] [kg] [kg] Locomotive Central coaches End coach Total mass Mt carried by each axle defines the static load component, unsprung mass Mu is used to compute the dynamic load component. RIVAS Training Workshop 9//23 4

15 Excitation mechanisms Quasi-static contribution to the sleeper velocity due to an InterCity train passing at a speed of 56 km/h: time history (left) and narrow-band spectrum (right) for a single axle (up) and the entire train (below). x Velocity [m/s] Velocity [m/s/hz] Time [s] Frequency [Hz].5.2 Velocity [m/s] Time [s] Velocity [m/s/hz] Frequency [Hz] RIVAS Training Workshop 9//23 5

Excitation mechanisms Mechanisms of dynamic

2-24) Dynamic axle loads are due to vehicle-track

Impact excitation due to rail joints and wheel flats.

16 Excitation mechanisms Mechanisms of dynamic excitation (ISO ) Dynamic axle loads are due to vehicle-track interaction caused by: Wheel and track unevenness. Impact excitation due to rail joints and wheel flats. Parametric excitation due to spatial variation of support stiffness. RIVAS Training Workshop 9//23 6

17 Excitation mechanisms Dynamic excitation Since excitation characterized by a wavelength λy is experienced by the train at a frequency f = v/λy, the relevant range of wavelengths depends on the train speed v. Ground-borne vibration Ground-borne noise Train speed/frequency Hz 8 Hz 6 Hz 25 Hz v = 72 km/h 2 m.25 m.25 m.8 m v = 36 km/h m.25 m 6.25 m.4 m RIVAS Training Workshop 9//23 7

18 Excitation mechanisms Dynamic excitation Data from track recording cars (wavelengths between a few metres and 2 to 3 m) needs to be supplemented by data obtained from other measurement devices such as trolleys. A track recording car measures a loaded track profile, however, and therefore includes a contribution from parametric excitation. RIVAS Training Workshop 9//23 8

19 Train-track interaction Dynamic excitation In numerical predictions, the dynamic load component is usually computed assuming a perfect contact between the train and the track: ût(ω) ûa(ω) = ûw/r(ω) where ua(ω) and ut(ω) are the displacements of the axles and uw/r(ω) is the combined wheel and rail unevenness. Rewriting ua(ω) and ut(ω) in terms of the dynamic load ĝd(ω) gives: [Ĉt (ω) + Ĉ v (ω) ] ĝd(ω) = ûw/r(ω) where Ĉ t (ω) and Ĉ v (ω) are the track and vehicle compliance. RIVAS Training Workshop 9//23 9

20 Train-track interaction Dynamic excitation Simplifying for a single axle, taking the track compliance as the inverse of the track stiffness /kt and keeping only the unsprung mass Mu of the wheelset leads to: [ k tmuω 2 ] ĝdk(ω) = û k kt Muω w/r(ω) 2 The denominator on the right hand side becomes zero at the frequency ω = kt/mu where "resonance" of the unsprung mass on the track stiffness (sometimes known as P2 resonance) occurs. RIVAS Training Workshop 9//23 2

21 Case study Time history (left) and one-third octave band spectra (right) of ground velocity at 6 m (up) and 32 m (below) due to an InterCity train at 56 km/h: total (solid), quasi-static (dashed) and dynamic (dotted) response. 2 x 3 Velocity [m/s] Time [s] Velocity [db ref 8 m/s] 2 Frequency [Hz] 2 x 3 Velocity [m/s] Time [s] Velocity [db ref 8 m/s] 2 Frequency [Hz] RIVAS Training Workshop 9//23 2

22 Conclusions Conclusions Railway induced ground vibration is usually dominated by dynamic excitation, arising from train-track interaction due to wheel and track unevenness, impact excitation, and parametric excitation. The transmission of vibration at a particular site is highly depending on local site conditions and dynamic soil characteristics. Within RIVAS, mitigation measures at the source and on the transmission path are investigated, fully accounting for the layered nature of soil. We are looking forward to welcoming you at the RIVAS final conference on 2//23 in Brussels where more results will be presented! RIVAS Training Workshop 9//23 22

Railway induced ground vibration

RIVAS Training Workshop 23/5/213, Die Schmiede, Berlin, Germany "Reducing railway induced ground vibration by interventions on the transmission path" Railway induced ground vibration Geert Lombaert, Stijn