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SASW – an in situ method for determining shear modulus. Soil Dynamics Ph.D.-course at NTNU, 2003. Håkon Heyerdahl. Methods for determining shear modulus. Shear modulus G is often indirectly measured by measuring shear wave velocity V s In situ methods Refraction seismics

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sasw an in situ method for determining shear modulus

SASW – an in situ method for determining shear modulus

Soil Dynamics

Ph.D.-course at NTNU, 2003.

Håkon Heyerdahl

methods for determining shear modulus
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
sasw development
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.
sasw development4
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)
advantages of sasw
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)
description of the method
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 
seismic surface wave method
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)
interpretation of v s from dispersion curve inversion
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
slide13
SASW
  • Field work - data collection
  • Data processing - surface wave dispersion curve
  • Inversion of dispersion curve to obtain profile for Vs
data collection
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)
energy sources
Energy sources
  • Increasing energy necessary for longer sensor spacing
    • Small distance:
      • Hammer
    • 2-8 m:
      • Sledge hammer
      • Drop weights of 20-70 kg
energy sources cont
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)
data processing dispersion curve
Data processing - dispersion curve
  • Frequency domain
    • Auto power spectra
    • Cross power spectra
    • Coherence function
  • Phase and coherence function are key parameters
dispersion curve
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
interpretation inversion
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
3 d forward modelling
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