Resonant column & Torsional shear Tests
2022-11-14
Cambridge University, November 2022
Introduction
Two well known laboratory tests, resonant column and
torsional shear tests, are used to measure dynamic properties
of Huston sand.
Tests are performed on:
- Dry sample, 7 & 8 November.
- Saturated sample in drained condition, 09 November.
- Dry sample, 10 November.
- Saturated with Methyl Cellulose, viscosity around 56cp, 11 November.
Tests are performed on 4 samples, at different confining pressures
between 30 and 700 kPa, at various shear strains.
Steps of the test
These steps are followed for each sample:
Stage 1:
Applying the desired confining pressure.
Selecting a range of frequencies, amplitude and duration to apply a chirp on the sample.
Detecting the most probable resonant frequency and modifying previous step.
Performing the resonant column (RC) test.
stage 2:
Automatic adjustment of the relative position of magnets for torsional shear test.
Selecting the frequency, amplitude and number of cycles.
Performing the torsional shear (TS) test.
stage 3:
- Modifying the confining pressure and repeating the above stages at
low amplitudes to be sure sample is not degraded.
The capacity of the equipment allowed increasing the confining pressure up to 700 kPa.
Stage 4:
Applying a confining pressure (usually 50 or 100 kPa).
Performing stage 2 at successive increasing amplitudes to obtain the stiffness degradation curve.
Relative density
The tests are performed on the samples with relative density around
40%; small variation in the relative density had occurred because of
loosing small quantities of sand during sampling specially in saturated
tests.
This is the measurements/calculations related to relative density:
Among the two options, the porous stone with diameter equal to 50 mm is used as bigger sample is more representative. Next figure shows variation of the diameter along different tests; clearly there are some unusual values which diameter is reported to be almost twice the initial value (=50 mm). Such an anomaly is not detected in sample´s height; the conclusion was that sample is OK and there is some problem with instruments so tests with unusual diameter just filtered out.
Mentioned anomaly was detected during the test as the measured
stiffness dropped considerably. The cause is unknown; there are not so
many variables to dictate the machine during the test. As above figure
shows the anomaly had happened at the beginning of the second day which
confining pressure had been around 600 kPa. Lets look at the measured
stiffness at the second day and compare it with the applied confining
pressure:
Above figure shows although confining pressure is high at the beginning of the test, measured stiffness is not high so something is wrong. If the sample height show unusual changes, the conclusion would be degradation of the sample. Next figure evaluate the sample´s height. It seems that variation in the height of the sample are logic so the reported values for diameter can not be real. At the end of the test when the sample was going to be removed, the shape of the sample was normal as well.
Above figure shows by increasing the confining pressure, dry samples
(day= 07 & 08) show increase in the height while in the saturated
sample (day=09) confining pressure squeezes the water out and solids
shrink (?).
The test which is performed on 9th Nov. should be considered as a
drained test on saturated sample because porous stones was not saturated
before the test and sudden increase in water pressure did not occured as
sample failed under high strains.
Total number of resonant column tests is 102; removing the ones with
diameter larger than 55 mm, 80 is remained. Next figures show the
results of these tests.
—————————————————————————–
Resonant column (RC) test
Stiffness
Beside the range of stiffness, below figures show as confinement
increases, stiffness increases as well.
Damping (RC test)
Except an outlier (file:RX_ELA20221107171116, damping=55% & G=1.3 MPa),
other measurements show more or less the same values for damping:
Above figure shows the range of damping quantity. Furthermore, it
shows damping decreases as confining pressure increase although at the
same confinement and shear strain, measured values has considerable
variance.
By separating the saturated and dry tests, interpretation becomes
easier; drained tests at strains less that 0.002% behave strange while
in larger strains similar to saturated tests, at higher confinement,
lower damping is measured.
Above figure does not show clear trend of variation of damping with confining pressure.
—————————————————————————–
Torsional shear (TS) test
Torsional shear tests are performed on the same samples as resonant
column tests so those anomalies in diameter and probably other variables
may be repeated in torsional shear test as well. Next figure approves at
the second day of testing (day=08) unusual variations had registered in
the diameter of the sample.
In spite of unusual measured values in RC test that just increased
diameters are registered, here we can see considerable reduction in
diameter are registered as well. These had happened for the same sample
and approximately at the same time so, maybe a control over the machine
becomes necessary although reproduction of the values is almost
impossible!
The figure also shows higher performance level of an expert; the test
which is performed by Gianmario (day=11) shows min. scatter in measured
diameter so, human error may have a role as well. It should be noted
that just two resonant column tests are performed on the last sample
which was saturated by Methyl Cellulose; beside the role of experience
in performing the tests accurately, less degradation may have some role
as well.
The same approach is followed and data set is filtered regarding the
acceptable values in sample dimensions.
Next figure shows the height of the sample has acceptable variations
(less than 1 mm) in all the tests.
Tests with diameter more than 45mm and less than
55mm are kept and remains are filtered out. In the next
sections these outliers are investigated separately as well. The
variation in the diameter of the cleaned data set are as follow:
Total number of torsional shear tests is 254; removing the ones with unusual diameter, 218 are remained.
Measured values of stiffness and damping according to the torsional shear test are as follow. It should be noted that strain is reported as peak to peak value in data files; as the cycles are symmetric, half the reported strain is used to have a more meaningful comparison with the results of resonant column test.
Stiffness (TS)
Above figure shows high strains (up to around 1%) are applied on the
sample in torsional shear test while it was impossible in resonant colum
test.
It also shows stiffness decreases as strain increases. As a general rule
it approves that increasing the confinement causes increase in stiffness
although there are 9 measurements at day=07 which are exceptions.
Referring to the results at day=07 (below figure) the direct relation
between confining pressure and stiffness is approved but the specific
sample at that day frequently shows stiffnesses which are higher than
the measured values on similar samples at higher confinements.
Saturated samples (day=09 & 11) show lower stiffnesses compared to
the dry ones.
There is an outlier in the measurements (negative value). It is filtered
out in the next figures.
Comparing the above figure with the one which is prepared for resonant column test shows measured values in torsional shear test are much higher than measured stiffnesses in resonant colum while estimations in torsional shear are based on higher strains and should lead to lower strains!
Just to have a check, the next figures represent the measured
stiffnesses that are cleaned up from the data set. All the values are
registered at day=08. Range of the measured stiffness is quite different
for diameters larger than initial value and the ones less than initial
diameter so they are presented in two separate figures.
Comparing these two figures, at higher confinement pressures smaller
values for G is measured which does not seem to be true.
Both the figures approve expected decrease in G as strain increases although magnitude of G (at confinement=100kPa) are very high (below table).
Characteristics of the tests with outlier results
Normalised degradation curve of G vs. strain
In torsional shear test a variety of torques can be applied on the sample; it causes a range of strains. As strain increases stiffness decrease and normalized degradation curve can be produced. As Part of the test this procedure is followed and the results are presented in the following sections.
Damping (TS)
It seems that at low strains damping decreases (or does not change) with increasing the strain while at higher strains, they change together. It was noticed in measurements by direct shear test as well.
——————————————————————————
Comparing the results
The max. strain which is applied in resonant column test was measured
as 0.0232% while cleaning the data set, it reduces to 0.0083%.
In torsional shear test larger strains are applied; the max. magnitude
of strain in cleaned data set is registered as 0.8464%.
To compare the results of the two method, max strain is restricted to 0.0083% which both the tests cover it.
There are 107 torsional shear test in this range of strains and 78 record from the resonant column test. The measured values of stiffness and damping are compared as in the next figures.
Mean of the G values at arbitrary ranges of strains are as follow:
| gama (%) | Mean_G (MPa)_RC | Var_G (MPa)_RC | Mean_G (MPa)_TS | Var_G (MPa)_TS |
|---|---|---|---|---|
| (0,0.0005] | 94 | 5797 | 93 | 67 |
| (0.0005,0.001] | 121 | 2119 | 152 | 3805 |
| (0.001,0.0015] | 101 | 3023 | 90 | 1457 |
| (0.0015,0.002] | 82 | 1991 | 90 | 2285 |
| (0.002,0.0025] | 84 | 3139 | 121 | 466 |
| (0.0025,0.003] | 81 | 2204 | 87 | 470 |
| (0.003,0.0035] | 59 | NA | 107 | 3013 |
| (0.0035,0.004] | 66 | 254 | 92 | 1691 |
| (0.004,0.0045] | 54 | NA | 51 | 13 |
| (0.0045,0.005] | 34 | NA | 90 | 160 |
| (0.005,0.0055] | 54 | 1318 | NA | NA |
| (0.0055,0.006] | 96 | 0 | 164 | NA |
| (0.006,0.0065] | NA | NA | 74 | 1332 |
| (0.0065,0.007] | NA | NA | 78 | 1060 |
| (0.0075,0.008] | 75 | 726 | 60 | 222 |
| NA | 82 | 462 | 83 | NA |
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It seems that by the resonant column test smaller values are measured
for the stiffness of the same sample. In contrary, trend of the measured
G values is more logic in RC test compare to the TS!
This is the results at the same confining pressures:
Trend of the measurements in the above figure shows as strain increases, damping decrease! ** should be checked**
Next figures are based on repeating the torsional shear test at
increasing input voltage (amplitude) to see variation of both the
stiffness and damping with shear strain at fixed confining pressure.
