Norges Geotekniske Institutt Norwegian Geotechnical Institute SASW – an in situ method for...
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Transcript of 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
Norges Geotekniske InstituttNorwegian Geotechnical Institute
• 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
Norges Geotekniske InstituttNorwegian Geotechnical Institute
• 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
Norges Geotekniske InstituttNorwegian Geotechnical Institute
• 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
Norges Geotekniske InstituttNorwegian Geotechnical Institute
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)
Norges Geotekniske InstituttNorwegian Geotechnical Institute
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
Norges Geotekniske InstituttNorwegian Geotechnical Institute
Waves arriving at two sensors
Norges Geotekniske InstituttNorwegian Geotechnical Institute
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)
Norges Geotekniske InstituttNorwegian Geotechnical Institute
Penetration of Rayleigh wave
Norges Geotekniske InstituttNorwegian Geotechnical Institute
Penetration of Rayleigh wave
Norges Geotekniske InstituttNorwegian Geotechnical Institute
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
Norges Geotekniske InstituttNorwegian Geotechnical Institute
Two-layered soil
Norges Geotekniske InstituttNorwegian Geotechnical Institute
SASW
• Field work - data collection• Data processing - surface wave dispersion curve• Inversion of dispersion curve to obtain profile for
Vs
Norges Geotekniske InstituttNorwegian Geotechnical Institute
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)
Norges Geotekniske InstituttNorwegian Geotechnical Institute
Sensor array
Norges Geotekniske InstituttNorwegian Geotechnical Institute
Energy sources
• Increasing energy necessary for longer sensor spacing
– Small distance: • Hammer
– 2-8 m: • Sledge hammer • Drop weights of 20-70 kg
Norges Geotekniske InstituttNorwegian Geotechnical Institute
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)
Norges Geotekniske InstituttNorwegian Geotechnical Institute
Data processing - dispersion curve
• Frequency domain – Auto power spectra
– Cross power spectra
– Coherence function
• Phase and coherence function are key parameters
Norges Geotekniske InstituttNorwegian Geotechnical Institute
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
Norges Geotekniske InstituttNorwegian Geotechnical Institute
Unwrapped phase angle
Norges Geotekniske InstituttNorwegian Geotechnical Institute
Dispersion curve and WinSasw
Norges Geotekniske InstituttNorwegian Geotechnical Institute
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
Norges Geotekniske InstituttNorwegian Geotechnical Institute
Example of 2D forward modelling
Norges Geotekniske InstituttNorwegian Geotechnical Institute
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
Norges Geotekniske InstituttNorwegian Geotechnical Institute
Numerical solutions
Norges Geotekniske InstituttNorwegian Geotechnical Institute
Numerical solutions