RIVAS Final Conference "Vibrations Ways out of the annoyance" Royal Flemish Academy of Belgium, Brussels, 21 November 213 Determination of dynamic soil characteristics and transfer functions to support the evaluation of the efficiency of vibration mitigation measures H. Verbraken 1, V. Cuellar 2, B. Stallaert 3, G. Lombaert 1 and G. Degrande 1 1 Department of Civil Engineering, KU Leuven, Belgium 2 Laboratoria de Geotecnia, CEDEX, Spain 3 D2S International, Belgium RIVAS Final Conference, 21 November 213 1
Transfer functions Numerical prediction [Many authors] x z y x g k (t) x v(x, t) = n a k=1 t H T v (x k (τ), x, t τ)g k (τ)dτ (1) RIVAS Final Conference, 21 November 213 2
Transfer functions Empirical prediction (e.g. FRA and FTA [Hanson et al., 25, 26]) Prediction of the ground vibration velocity level in one-third octave bands: L v = L F + TM L (2) Impact locations z x y Rail alignment Measurement line TM L = 1 log 1 (h n 1 TM Pk 1 ) (3) k=1 RIVAS Final Conference, 21 November 213 3
Transfer functions Insertion loss for vibration mitigation measures [Stiebel al., 212] Test site Reference site Before TM tb P C 1 TM rb P E 2 C 2 After TM ta P E 1 TM ra P Vibration isolation efficiency: E = TM ta P TM tb P }{{} E 2 E = TM ta P TM ra P }{{} E 1 rb + TM P TM ra P (4) }{{} C 2 rb + TM P TM tb P (5) }{{} C 1 RIVAS Final Conference, 21 November 213 4
Dynamic soil characteristics (a) Dilatational and (b) shear wave in an elastic medium. (a) (b) Dilatational and shear wave velocity: C p = λ + 2µ ρ = M ρ (6) C s = µ ρ (7) RIVAS Final Conference, 21 November 213 5
Dynamic soil characteristics (a) τ γ curve under cyclic excitation and (b) shear modulus degradation curve and (b) material damping ratio for Toyoura sand (Kokusho, 198): (a) (b) Material damping ratio (correspondence principle): (λ + 2µ) = (λ + 2µ)(1 + 2β p i) (8) (µ) = µ(1 + 2β s i) (9) (c) RIVAS Final Conference, 21 November 213 6
Dynamic soil characteristics 1. Archive records and test information. Geological maps, results of previous geotechnical investigation. Estimation of the soil layering and the dynamic characteristics of each layer. Use of empirical relations cannot replace in situ or laboratory testing! 2. Classical soil mechanics tests on (undisturbed) soil samples. At least one sample per soil layer; lateral sampling. Mass density, void ratio, degree of saturation, plasticity index,.... 3. Non-intrusive geophysical tests at small strain levels. Combined surface wave - seismic refraction test. Measure input force. 4. Intrusive geophysical tests at small strain levels. Seismic cone penetration test (SCPT). Down hole or cross hole test. 5. Dynamic laboratory experiments on (undisturbed) soil samples. Resonant column test. Cyclic triaxial test. Bender element test. RIVAS Final Conference, 21 November 213 7
Dynamic soil characteristics Spectral Analysis of Surface Waves Signal Analyzer Impulse Load Near Receiver Far Receiver RIVAS Final Conference, 21 November 213 8
Dynamic soil characteristics Shear wave velocity: frequency-wavenumber analysis [Rix et al., JGGE, 2; Lai et al., SDEE, 22] Phase velocity C E R(ω) from peaks of the transfer function H E zz(k r, ω):: H E zz(k r, ω) = Ĥ E zz(r, ω)j (k r r)r dr (1) (a) Transfer function H E zz(k r, ω), (b) phase velocity C E R(ω), and (c) shear wave velocity profile:: Phase velocity [m/s] 3 2 1 Depth [m] 1 2 3 4 (a) (b) 2 4 6 8 Frequency [Hz] (c) 5 1 2 3 4 5 Shear wave velocity [m/s] RIVAS Final Conference, 21 November 213 9
Dynamic soil characteristics Material damping ratio: Arias intensity [Badsar, 212] Arias intensity I E zz(r): I E zz(r) = π 2g a 2 z(r, t)dt (11) (a) Displacement u z (r, t), (b) Arias intensity I E zz(r) and (c) material damping ratio profile: (a) (b) Normalized Arias intensity [ ] 1 5 1 1 5 2 4 6 8 1 Distance [m] (c) Depth [m] 1 2 3 4 5.5.1 Material damping ratio [ ] RIVAS Final Conference, 21 November 213 1
Dynamic soil characteristics Seismic refraction test t 1 impact direct wave first x c refracted wave first t 2 θ c θ c t 12 C p1 t 11 t 3 C p2 > C p1 t 4 t 5 t 6 t 7 t 8 t 9 t 1.1.8 Arrival time [s].6.4.2 2 4 6 8 Distance [m] RIVAS Final Conference, 21 November 213 11
Dynamic soil characteristics Soil profile at the site in Lincent (Belgium) (a) Soil stratification, (b) shear wave velocity (SASW and SCPT), (c) dilatational wave velocity (seismic refraction) and (d) material damping ratio (SASW and SCPT) profile. Simplified Stratification of Drilling B118.m Silt 1.2 Fine Sand (Clayey Sand) 3.2 1. Quaternary Deposits 1 SCPT1 SCPT2 SASW1 SASW2 1 SR1 SR2 1 SCPT2(MH) SCPT2(SH) SASW1 SASW2 (a) Mean Groundwater 1.4 m Sequence of Arenite/ Clay (Sandy Clay to Silty Clay) 7.5 Clay (Silty Clay) 8.5 Fine Sand 1. Sequence of FineSand/Clay (Silty Clay) 15. 13. Formation of Hannut (Tertiary Deposit) Formation of Heers (Tertiary Deposit) (b) Depth [m] 2 3 4 5 6 7 8 1 2 3 4 5 Shear wave velocity [m/s] (c) Depth [m] 2 3 4 5 6 7 8 5 1 15 2 Longitudinal wave velocity [m/s] (d) Depth [m] 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 1 Material damping ratio [%] RIVAS Final Conference, 21 November 213 12
El Realengo test site Test and reference site Conventional railway line (ADIF) between Murcia and Alicante. Low Segura river flood plain. S592 commuter train, S599 medium distance train and Talgo VI train. Construction of a new HST line between Madrid and Levante. Installation of a jet grouting wall next to track as a vibration mitigation measure. RIVAS Final Conference, 21 November 213 13
El Realengo test site Test and reference site RIVAS Final Conference, 21 November 213 14
Dynamic soil characteristics Shear wave velocity Spectral Analysis of Surface Waves (falling weight deflectometer, CEDEX). Seismic Cone Penetration Test (down-hole test, CEDEX). RIVAS Final Conference, 21 November 213 15
Dynamic soil characteristics Longitudinal wave velocity Seismic refraction test (CEDEX). Identified soil profile Layer h C s C p β s β p ρ [m] [m/s] [m/s] [ ] [ ] [kg/m 3 ] 1.3 27 56.25.25 18 2 1.2 15 47.25.25 175 3 8.5 15 156.25.25 175 4 1. 475 156.25.25 19 5 55 23.25.25 19 RIVAS Final Conference, 21 November 213 16
Dynamic soil characteristics Material damping ratio Measured Arias intensity at the test (red line) and reference (green line) section and predicted Arias intensity (a) before and (b) after updating of the material damping ratio [Badsar, 212]. 1 11 1 11 Arias intensity [m/s] 1 12 1 13 1 14 1 15 1 16 Arias intensity [m/s] 1 12 1 13 1 14 1 15 1 16 (a) 1 17 1 2 3 4 5 6 7 Distance [m] (b) 1 17 1 2 3 4 5 6 7 Distance [m] Identified soil profile (update) Layer h C s C p β s β p ρ [m] [m/s] [m/s] [ ] [ ] [kg/m 3 ] 1.3 27 56.123.123 18 2 1.2 15 47.112.112 175 3 8.5 15 156.14.14 175 4 1. 475 156.1.1 19 5 55 23.1.1 19 RIVAS Final Conference, 21 November 213 17
Free field transfer functions Measurement setup (a) Measurement setup, (b) falling weight deflectometer, (c) force during a single impact, and (d) velocity stacked for 5 impacts. (a) (b) (c) Force [N] 3.5 2.5 2 1.5 1.5 4 x 15 3.5 1 2 3 4 5 Time [s] (d) Distance [m] 64 48 32 24 16 12 8 6 234 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 Time [s] RIVAS Final Conference, 21 November 213 18
Free field transfer functions Numerical model for benchmarking 3D coupled finite element boundary element method. Rigid foundation: finite element method. Layered elastic soil: boundary element formulation. Model and parameter uncertainty. RIVAS Final Conference, 21 November 213 19
Free field transfer functions Free field transfer functions Measured and predicted transfer function (narrow band) at (a) 8 m, (b) 16 m, (c) 32 m, and (d) 64 m. Measured results are shown for the test (red line) and reference (green line) section. Predicted results are shown for initial (grey line) and updated (black line) soil parameters. (a) (c) Mobility [db ref 1 8 m/s/n] Mobility [db ref 1 8 m/s/n] 5 25 25 5 5 1 15 2 5 25 25 Frequency [Hz] 8m 5 5 1 15 2 Frequency [Hz] 32m (b) (d) Mobility [db ref 1 8 m/s/n] Mobility [db ref 1 8 m/s/n] 5 25 25 5 5 1 15 2 5 25 25 Frequency [Hz] 16m 5 5 1 15 2 Frequency [Hz] 64m C 2 m 3 m 4 m 6 m 8 m 12 m 16 m 24 m 32 m FF48C FF64C RIVAS Final Conference, 21 November 213 2
Track free field transfer functions Track characteristics RN 45 rails: EI r = 3. 1 6 Nm 2 and ρa r = 44.8 kg/m. Bi-block reinforced concrete sleepers: m sl = 2 kg and spacing d =.6 m. Rubber rail pads with a thickness of 4.5 mm and stiffness of 3 kn/mm. Ballast layer (d =.5 m, C s = 25 m/s, ν =.2 and ρ = 16 kg/m 3 ). Embankment (d =.5 m, C s = 2 m/s, ν =.35 and ρ = 17 kg/m 3 ). RIVAS Final Conference, 21 November 213 21
Track free field transfer functions Measurement setup (a) Measurement setup, (b) force during a single impact, and (c) velocity along line C stacked for 98 impacts. 3 x 14 2.5 2 Force [N] 1.5 1.5 (b).5.5 1 1.5 2 Time [s] 64 Distance [m] 48 32 24 16 1 (a) (c).2.4.6.8 1 1.2 1.4 1.6 1.8 2 Time [s] RIVAS Final Conference, 21 November 213 22
Track free field transfer functions Variation along the track at the test section Comparison of the free field response for all impact locations and corresponding measurement lines at (a) 1 m, (b) 16 m, (c) 24 m, and (d) 32 m from the track. (a) (c) Mobility [db ref 1 8 m/s/n] Mobility [db ref 1 8 m/s/n] 5 25 25 5 5 1 15 2 5 25 25 Frequency [Hz] 1m 5 5 1 15 2 Frequency [Hz] 24m (b) (d) Mobility [db ref 1 8 m/s/n] Mobility [db ref 1 8 m/s/n] 5 25 25 5 5 1 15 2 5 25 25 Frequency [Hz] 16m 5 5 1 15 2 Frequency [Hz] 32m RIVAS Final Conference, 21 November 213 23
Track free field transfer functions Numerical model 2.5D coupled finite element boundary element method [François et al., CMAME, 21]. Track: finite element method. rail and rail pad: Euler-Bernoulli beam and continuous spring-damper connection; sleeper: beam, rigid in plane of cross section; ballast: elastic continuum. Layered elastic soil: boundary element formulation. Model and parameter uncertainty. RIVAS Final Conference, 21 November 213 24
Track free field transfer functions Transfer functions Measured and predicted transfer function (narrow band) at (a) 1 m, (b) 16 m, (c) 32 m, and (d) 64 m along line C. Measured results are shown for the test (red line) and reference (green line) section. Predicted results are shown for initial (grey line) and updated (black line) track parameters. C 1 m 16 m (a) (c) Mobility [db ref 1 8 m/s/n] Mobility [db ref 1 8 m/s/n] 5 25 25 5 5 1 15 2 5 25 25 Frequency [Hz] 1C 5 5 1 15 2 Frequency [Hz] 32C (b) (d) Mobility [db ref 1 8 m/s/n] Mobility [db ref 1 8 m/s/n] 5 25 25 5 5 1 15 2 5 25 25 Frequency [Hz] 16C 5 5 1 15 2 Frequency [Hz] 64C 24 m 32 m 48 m 64 m RIVAS Final Conference, 21 November 213 25
El Realengo test site Installation of the jet grouting wall (November 213) RIVAS Final Conference, 21 November 213 26
Conclusion Determination of dynamic soil characteristics. In situ geophysical techniques to determine the shear and dilatational wave velocity and material damping ratio profile. Deliverable D1.1 "Test procedures for the determination of the dynamic soil characteristics" (December 211). Quantification of uncertainty on identified dynamic soil characteristics. Benchmark problems as a validation tool. Free field and track free field transfer functions. Deliberable D1.11 "Benchmark tests for soil properties, including recommendations for standards and guidelines" (December 213). Quantification of uncertainty on model predictions. Assessment of vibration isolation efficiency of mitigation measures: Sheet pile wall at Furet (Sweden). Jet grouting wall at El Realengo (Spain). Visit our website www.rivas-project.eu RIVAS Final Conference, 21 November 213 27