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 Applications
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 to 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: m
Sufficient for depths down to 50 m
May reduce number of sensors: e.g 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 kg

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