SASW – an in situ method for determining shear modulus

1. SASW – an in situ method for determining shear modulus Soil Dynamics Ph.D.-course at NTNU, 2003. Håkon Heyerdahl

2. Methods for determining shear modulus • Shear modulus G is often indirectly measured by measuring shear wave velocity Vs • In situ methods • Refraction seismics • Cross-hole or down-hole (up-hole) seismic methods • Seismic CPT-cone • SASW (uses the Rayleigh wave) • Laboratory methods • Bender elements (S-wave propagation) • Resonant column

3. SASW development • Spectral Analysis of Surface Waves • Development started in 1930’s in Germany • DEGEBO (1933) • Foundation response of steady-state vibration • 1940’s: State of the art • Terzaghi (1943) and Hvorslef (1949) • Continuous vibratory motion on surface from mechanical device • 1950’s and 1960’s: Intermittent development of method • Several references, pavement tests and site characterization.

4. SASW development • Rapid development only recently • Transient excitation and advanced signal analysis • Heisey et al (1982): First mentioning of the concept SASW • Applications • Geodynamic site characterization • Construction monitoring • Determination of pavement elastic properties • Extended to offshore applications and detection of gas hydrates, Stokoe et al (1990), Sedighi-Manesh et al (1992)

5. Advantages of SASW • In situ method • Non-destructive method • No expensive boreholes needed • May be done at different times at low cost • May catch change in effective stress due to ground water fluctuations (NB: G is stress dependent!) • Consolidation / compaction effects • Mexico city: Large settlements due to pumping, stiffness increases with time (12th Europ. Earthq. Conf. 2002)

6. Description of the method • Sinusoidal excitation u in a point on ground surface • u0(t)=u0 sinωt (ω = 2f) • Other point on ground surface: Time lag • u(t)=u sinω(t- /ω) • Time lag equals •  = (2fx)/Vr in which x is distance, Vr is Rayleigh wave distance • Vr is 0.874 to 0.955 Vs depending on 

7. Waves arriving at two sensors

8. Seismic Surface Wave method • Steady-state vibration with known frequency • Moved sensor to find positions with same phase (e.g. two successive peaks • Wavelength is determined! • Calculation of Vr from frequency and distance. • Change frequency of vibrator • Different value of Vr • Result: Dispersion curve (relation Vr and Lr)

9. Penetration of Rayleigh wave

10. Penetration of Rayleigh wave

11. Interpretation of Vs from dispersion curve (= inversion) • Rayleigh-waves penetrate to ca. 1.5 Lr • Solution for two-layered space (Stokoe at al. 1994) • No change in measured Vr until Lr > thickness of top layer • Effective depth: 1/2 to 1/3 of Lr • Often used to give crude estimate of Vs with depth • Surface wave method may be time consuming ->SASW method

12. Two-layered soil

13. SASW • Field work - data collection • Data processing - surface wave dispersion curve • Inversion of dispersion curve to obtain profile for Vs

14. Data collection • Receivers on ground surface • Equal distances around imaginary centre line • Typical pattern: 0.5 - 1 - 2 - 4 - 8 - 16 - 32 - 64 m • Sufficient for depths down to 50 m • May reduce number of sensors: e.g. 1 - 4 - 16 - 64 m • Also one-directional sensor arrays are used • May be combined with seismic refraction. • Limitation on sensor spacing d: • 2d < Lr < 3d (Sheu et al,1988, Tokimatsu, 1995) • Wave filtering (excluding longer waves than desired)

15. Sensor array

16. Energy sources • Increasing energy necessary for longer sensor spacing • Small distance: • Hammer • 2-8 m: • Sledge hammer • Drop weights of 20-70 kg

17. Energy sources (cont.) • Larger distances • Drop weights up to 900 kg • Vehicles - bulldozers • Weights used for dynamic compaction • Small buried explosives (50-100 g) • Very large wave lengths • Mictrotremors (passive source)

18. Data processing - dispersion curve • Frequency domain • Auto power spectra • Cross power spectra • Coherence function • Phase and coherence function are key parameters

19. Dispersion curve • Coherence: Signal-to-noise ratio • Value around 1 indicates appropriate frequency range for calculation of dispersion curve • Phase of cross power spectrum: • Phase difference of motion of two receivers • Unwrapped phase angle (not restricted to 0-2) • Phase spectrum • Dispersion curve from phase spectrum • Each set of receiver spacing gives dispersion curve for a certain range of wave lengths • Final dispersion curve ”patched” from individual curves

20. Unwrapped phase angle

21. Dispersion curve and WinSasw

22. Interpretation - inversion • Several mathematical algorithms • Still under development • Forward modelling (2-D) • Nazarian and Stokoe (1984) • Theoretical dispersion curve for known profile with experimental dispersion curve • Iterative procedure until match is ok • Based on stiffness matrices of the layered soil for discrete frequencies • Limitation: Only first mode shape of surface wave is included. • Not suit|able if stiff soil above soft soil

23. Example of 2D forward modelling

24. 3-D Forward modelling • Green’s function of layered soil • Displacements of vertical disk load on ground surface • Most complete solution • All waves included • Not limited by type of soil profile • Forward modelling • Time consuming • Especially in layered soils with large stiffness contrasts • Automation • Generate a trial profile, adjust until difference between trial profile and experimental profile

25. Numerical solutions

26. Numerical solutions