G

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Low-Strain Dynamic Properties of Soils
Gmax
Initial Shear Modulus
G
?
Peak Energy During Cycle, W
Material Damping Ratio
?
Energy Dissipated in one cycle, ?W
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Low-Strain Dynamic Properties of Soils
Influence of Gmax in Site Response Analysis
SD 5
(from Lai, 1998)
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Low-Strain Dynamic Properties of Soils
Influence of D in Site Response Analysis
SD 5
(from Lai, 1998)
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The Resonant Column
Brief History Device Configuration Experimental
Setup Model Assumptions Determination of Dynamic
Properties Shear Modulus Material Damping
Ratio Shear Strain Amplitude
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The Resonant Column
Brief History

• 1930s Ishimoto and Iida begin research
  by on dynamic soil properties using a
  resonant column device.
• 1930s Birch and Bancroft study the
  dynamic properties of rock with similar
  device.
• 1960 Shannon, Yamane, Wilson, and
  Dietrich develop system capable
  of applying isotropic confining pressure.
• 1960s Hall and Richart develop new
  fixed-free apparatus.
• 1960s Hardin and Music develop new
  apparatus capable of applying axial
  loads (Hardin device).
• Late 1960s Drnevich reduces the distribution
  of angular rotation along the specimen
  to nearly uniform by adding a top mass
  (Drnevich device).

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The Resonant Column
Brief History (continued)

• 1970s Drnevich and Richart modify RC
  in order to accommodate hollow
  specimens.
• 1970s Drnevich and Richart increase
  torque capacity of the device to allow
  for the generation of shearing strains amplitudes
  above 0.1.
• Late 1970s Stokoe develops more practical
  Stokoe device.
• 1978 Drnevich proposes standardized
  resonant column testing procedures
• 1980 RC testing procedures are
  standardized by ASTM (ASTM 4015-92).

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The Resonant Column
Confining Chamber
Drains
Confinement Pressure
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The Resonant Column Experimental Setup

Frequency response function
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The Resonant Column
Idealization Kelvin-Voigt Model
Assumptions
At low strains, behavior
of specimen material is linear viscoelastic. Visco
us damping coefficient c, and stiffness G, are
independent of frequency.
Linear vibrations are considered correct
for cases where the peak strain amplitude of
vibration is less than the elastic threshold
strain. Dynamic properties
of soils are considered independent of strain
below elastic threshold strain.
Kelvin-Voigt Model
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The Resonant Column Shear Modulus Determination

I
dx
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The Resonant Column Damping Ratio Determination

Half Power Bandwidth Method
Vibration Decay Method
Amax
0.707 Amax
fr
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The Resonant Column Shear Strain Determination

Displacement at accelerometer, Xa
Shear Strain, ?

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Measurement of Vs Seismic Cone

• Impulse Source at Surface (Sledge Hammer)
• Horizontally Polarized Vertically Propagating
  Shear Waves

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Measurement of Vs Seismic Cone
Strike Plate
First Peak
First Arrival
t 0
First Trough
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Measurement of Vs Seismic Cone

• Selection of first arrivals from successive wave
  forms
• Strain Level determined for DHT (plane wave) as
• gs PPV / Vs

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Measurement of Vs Seismic Cone

• Subtract sequential distances
• Subtract sequential time intervals
• Vs distance / time DD / Dt

DD D2 - D1
D1
Dt
D2
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Measurement of Vs Seismic Cone
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using Bender Elements
Wykeham Farrance International
Introduce their new method for the
Measurement of Shear Modulus in soil(Gmax)
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Measurement of shear modulus (Gmax) using
Bender Elements
Top Cap
Sample
Transmitter
Gmax Vs². p
where
Gmax Vs².p
Bender Elements
Vs Velocity
p Density
Receiver
Pedestal
Triaxial Cell Base
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Bender Elements Manufacturer Piezo Systems,
Inc. Products 2-L Piezo Transucer PSI-4H4E,
X-Poled Size 0.50.3150.026
www.piezo.com/benders.html
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Directivity
Electrical cross talk Directivity Frequency
response Travel time
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Transverse directivity (specimen
size)Santamarina and Lee, 2002
P-wave
P-wave
S-wave
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Resonant frequencySantamarina and Lee, 2002
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Operating Frequency ComparisonSantamarina and
Lee, 2002

• Experimental Results

• Analytical Results

Controlling parameter Short cantilever length ?
Bender element Long cantilever length ? Soil
properties
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First arrival? Santamarina and Lee, 2002
A First deflection B First inflection C Zero
after first inflection D Second inflection
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Multiple Reflections Santamarina and Lee, 2002

• Goals
• High R-boundaries
• No P-wave from side walls
• No uncertainty in length
• No uncertainty in time

BE
L
1st event
2nd event
Soil
BE