norges geotekniske institutt norwegian geotechnical institute sasw – an in situ method for...

Norges Geotekniske InstituttNorwegian Geotechnical Institute

SASW – an in situ method for determining shear modulus

Soil Dynamics

Ph.D.-course at NTNU, 2003. Håkon Heyerdahl


• 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

Methods for determining shear modulus


• 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 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)

SASW development


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

• Sinusoidal excitation u in a point on ground surface

– u0(t)=u0 sinωt (ω = 2f)• Other point on ground surface: Time lag

– u(t)=u sinω(t- /ω)

• Time lag equals = (2fx)/Vr in which x is distance, Vr is Rayleigh wave

distance – Vr is 0.874 to 0.955 Vs depending on


Waves arriving at two sensors


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)


Penetration of Rayleigh wave


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


Two-layered soil


SASW

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

Vs


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)


Sensor array


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.)

– 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

• Frequency domain – Auto power spectra

– Cross power spectra

– Coherence function

• Phase and coherence function are key parameters


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


Unwrapped phase angle


Dispersion curve and WinSasw


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


Example of 2D 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


Numerical solutions

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