Soil Mechanics – Dynamic systems
WF Resonant Column Apparatus
Combined Resonant Column (RC) & Torsional Cyclic Shear (TCS) Test
apparatus to determinate with saturated soil :
• Shear Modulus
• Damping Modulus
versus Shear Strain
Soil Mechanics – Dynamic systems
WF Resonant Column Apparatus
The base pedestal is fixed (the same as a standard triaxial) but the
specimen top cap is free to rotate.
A rotational force (torque) is applied to the specimen top by electromagnetic system which applies the stress or strain loading in
frequency up to 250 Hz.
Ideal for Research
Conforming to ASTM D 4015
Soil Mechanics – Dynamic systems
The aim
The WF-Resonant Column allows the investigation of stress-strain behavior in
the small shear strains level field
Typically small and medium strain levels
High accuracy testing systems, suitable for that
levels of strains
Soil Mechanics – Dynamic systems
The aim
Causes of Vibrations
Dynamic System Ranges
This bottom half graph shows the range of strain encountered from machines or natural
causes. The top half shows test systems that can perform these range of strains
Dynatriax - Cyclic Triaxial
Bender Element
Cyclic Simple Shear
TCS-Torsional Cyclic Shear
RC-Resonant Column
Small Strain Triaxial
10 - 4
10 - 3
10 - 2
10 - 1
1
10
10 - 1
1
10
Machine Foundations
Ocean Wave Loading
Earthquake
10 - 4
10 - 3
10 - 2
(% Strain)
Soil Mechanics – Dynamic systems
The aim
Stress conditions of soil sample during earthquake
before
throughout
Soil Mechanics – Dynamic systems
The aim
Soil response to cyclic vibrations
Soil Mechanics – Dynamic systems
The aim
Secant shear modulus
Secant shear modulus
Damping ratio
Soil Mechanics – Dynamic systems
The aim
Strain level and mechanical
behaviour
Small strain level behaviour
Medium strain level behaviour
Big strain level behaviour
Soil Mechanics – Dynamic systems
The aim
Strain-dependent shear modulus and damping ratio
G0 or Gmax
Soil Mechanics – Dynamic systems
The aim
Local Seismic Response of a real soil
Change of D and G against depth, due to different
density g of the soil layers and to different
geostatical stress levels
Layer 1
Layer 2
Layer 3
Soil Mechanics – Dynamic systems
The aim
Typical range of G/Go curves against shear
strain g for gravels, sands and clays
Soil Mechanics – Dynamic systems
The aim
Range of strain
Soil strains on site
Micro strains
Small
strains
Large strains
Conventional triaxial tests
Local measurement of strains
Dynamic tests
Soil Mechanics – Dynamic systems
WF Resonant Column Apparatus
The test procedure includes a series of measurements of the
resonance frequency against the increasing levels of shear strains,
in order to define the diagram (g – G).
For each level of strain, once the resonance frequency has been
measured, the damping ratio is also calculated, in order to define
the diagram (g – D).
Soil Mechanics – Dynamic systems
The System
Soil Mechanics – Dynamic systems
The Cell
External perspex cell wall
• double coaxial perspex cell,
Axial transducer
Proxy transducers support
• electromagnetic system:
8 coils encircling 4 magnets
connected to the sample upper
end,
• measuring system (axial
transducer, proxy transducers,
pressure transducers, volume
change system)
coils
magnet
specimen
Internal lexan cell wall
Soil Mechanics – Dynamic systems
The Cell Parts
Electromagnetic
system: fixed part
Magnets supporting frame and
top cap: moving part
Double cell
Proxy transducers
motion system
Soil Mechanics – Dynamic systems
The Cell
• Electromagnetic drive
system connects to the
specimen top cap
• Double cell system
Soil Mechanics – Dynamic systems
How does it work ?
•
The electromagnetic drive consists of eight coils mounted on a drive plate with
four magnets positioned on the specimen top cap assembly. When a sinusoidal
current is applied to the coils, it pulls the magnets in one direction and reverses
the direction as the sine wave changes from positive to negative. The actual
rotational movement of the top cap is determined by the stiffness of the specimen
being tested.
•
The double cell is to allow us to have water in the inner cell up to the top cap with
a layer of silicon oil on top of the water. The outer cell confining pressure is air.
The water in the inner cell is to prevent air diffusion through the specimen
membrane and the silicon oil is to prevent air entering the water.
Soil Mechanics – Dynamic systems
The Cell
Electromagnetic system
fixed to the inner cell top
Magnets supporting frame and
top cap: free to rotate
Soil Mechanics – Dynamic systems
The Cell
• The top picture shows the electromagnetic drive system which is
attached to the top of the inner cell.
• The bottom picture shows the top cap with the four magnets. This is
attached to the specimen with a membrane and o rings, the same as a
standard triaxial set up. This assembly is free to rotate.
Soil Mechanics – Dynamic systems
The Cell
• The inner cell containing the
specimen is filled with water with a
silicon oil top to prevent air diffusion
through the membrane.
• The outer cell pressure is air which
acts on the water producing
equal pressure to the inner & outer cell.
Double cell
• We use a double cell to separate the
air and water when applying cell
pressure. The electromagnetic drive
system can only run in air. If we used
air around the specimen we can have
air diffusion through the membrane.
This happens in long term tests, so we use
de-aired water as in our standard
triaxial tests.
Soil Mechanics – Dynamic systems
The Measurements
• Two proximity transducers
are mounted on the electromagnetic drive system to
monitor the rotation of the
top cap assembly.
• Proximity transducers are
non contact transducers
which do not interfere with
the rotation of the top cap.
Therefore they have no
influence on the recorded data.
Soil Mechanics – Dynamic systems
The Control Box
Soil Mechanics – Dynamic systems
The Control Box
Power
Main switch
GND
Ground
Accel
Accelerometer
Axial
Connection to LVDT for measurement of axial compression of the specimen
Aux 1
Auxiliary input for further appplications
Prox
Connection to the couple of the proximity transducers
Cell, Pore e Back pressure
Serie of 3 connectors for the relevant pressure transducers
Volume Connection to the volume change transducers or differential pressure
Motion
Connection to the motor drivers of the proximity transducers
Aux2
Auxiliary input for further appplications
Coils
Uscita per il collegamento delle bobine del motore di coppia.
USB
Connection to PC
Each cable is fitted with a specific connector for easy installation of the transducers
inside the cell body, near the sample.
Soil Mechanics – Dynamic systems
Performing the test
The test is performed on a cylindrical sample
(50 mm dia, 70 mm available on request), either undisturbed or remoulded
The RC system software has the following stages:
1. Saturation
2. Isotropic Consolidation
3. Resonant Frequency
4. Torsional shear
As in all standard triaxial tests, we start by saturating the
specimen and applying the in-situ effective stress.
Then we choose to determine the resonant frequency or the
torsional shear strength.
Soil Mechanics – Dynamic systems
Performing the test
Performing the test:
Saturation
Consolidation
Measurements
Same as in the triaxial test
Same as in the triaxial test
An excitation current is applied to the electromagnetic drive
system, to generate a constant torque to the top end of the soil
sample. The frequency of this current is increased until the
fundamental resonance frequency of the system is achieved.
Resonance frequency and relevant acceleration are measured.
From these data the G modulus is calculated
The damping ratio D is also measured during the “free vibration
decay” procedure.
Further measurements are performed during torsional tests,
where higher levels of excitation current and torque are applied.
Soil Mechanics – Dynamic systems
Performing the test
The dynamic behavior of soils is represented by the Shear modulus G,
the Damping ratio D and the Shear Strain g
G shear modulus and D damping ratio, are of key importance to determine the
mechanical behaviour of soils under small strain cyclic loading conditions
Soil Mechanics – Dynamic systems
Resonant frequency
The excitation Voltage is fixed and the frequency increased in automatic
increments or steps.
The system records the shear strain and calculates the Fundamental
Resonant Frequency corresponding to the maximum shear strain.
Soil Mechanics – Dynamic systems
Resonant frequency
fr Fundamental Resonant Frequency
f1 & f2 are the band width frequencies at which the amplitude 0.707
times the amplitude of the fundamental resonant frequency fr
Stokoe et al. 1999
Shear strain,
(%) g (%)
Shear gstrain,
G   VS2
Frequency, f (Hz)
VS 
2   fr  L
F
D
f 2  f1
2  fr
Soil Mechanics – Dynamic systems
Torsional shear
The test (undrained conditions):
1. Saturation
2. Isotropic consolidation
3. The frequency of the cyclic Torsional shear (sinusoidal, <2 Hz) is constant while
amplitude is increased.
1. The system records the Torsional stress & strain values for each amplitude and
displays Hysteresis cycle from witch G and D are determined.
g is measured through
proximity transducers the
shear strength t is
evaluated through the
applied torque
Soil Mechanics – Dynamic systems
Resonant frequency
Soil Mechanics – Dynamic systems
Resonant frequency
From the frequency sweep graph the fundamental resonant
frequency and Modulus of damping can be determined.
In the resonant column test the half power bandwidth method can
be used to measure the material damping
The bandwidth is the frequency difference between the upper and
lower frequencies for which the power has dropped to half of its
maximum, the frequencies F1 and F2 at which the amplitude is 0.707
times the amplitude at the resonance frequency Fr.
Soil Mechanics – Dynamic systems
Saturation and consolidation
Graph showing consolidation curve
Soil Mechanics – Dynamic systems
Torsional shear
Torsion Shear Test at 0.1Hz, Amplitude 1 Volt