JGS 0542-2020

Japanese Geotechnical Society Standard (JGS 0542-2020）
Method for cyclic triaxial test to determine deformation properties of
soils
1

Scope

This standard specifies a test method to determine the deformation properties of soils in isotropic or anisotropic
stress states when subjected to cyclic loading, using a triaxial testing apparatus under drained or undrained
conditions. The standard applies to sandy soils, cohesive soils and gravelly soils.
Note 1:This test method applies to specimens in the saturated, air dried state, and unsaturated state.

Note 2:This test method may apply to other geomaterials.

2

Normative references

The following standards shall constitute a part of this standard by virtue of being referenced in this standard.
The latest versions of these standards shall apply (including supplements).
JGS 0520 Preparation of soil specimens for triaxial tests
JGS 0530 Preparation of specimens of coarse granular materials for triaxial tests
For matters not prescribed in this standard in connection with carrying out this test, refer to the following related
codes and standards.
JGS 0522 Method for consolidated-undrained triaxial compression test on soils
JGS 0523 Method for consolidated-undrained triaxial compression test on soils with pore water pressure
measurements
JGS 0524 Method for consolidated-drained triaxial compression test on soils
JGS 0541 Method for cyclic undrained triaxial test on soils

3

Terms and definitions

In addition to those specified in JIS A 0207, the main terminology and definitions used in this standard shall be
as follows.

3.1

Cyclic triaxial test to determine deformation properties

A test in which a constant amplitude and symmetric cyclic axial load is applied to a specimen under isotropic or
anisotropic stress conditions for a constant period, under constant cell pressure and drained or undrained
conditions.

3.2

Deformation properties

The equivalent Young’s modulus obtained from the cyclic deviator stress amplitude and the cyclic axial strain
amplitude, and the hysteresis damping factor obtained from the hysteresis curve of the deviator stress and theaxial strain.

3.3

Axial stress

The stress acting on the specimen in the cylinder axis direction.

3.4

Lateral stress

The stress acting in the radial direction of the specimen.
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JGS 0542-2020

3.5

Deviator stress

The difference between the two stresses in the cyclic loading process. The stress value shall be defined at the
mid-height of the specimen.

3.6

Back pressure

The pressure applied to the pore water within the test specimen (JIS A 1227).
Note: In this standard, the back pressure means the pore water pressure applied to the specimen to achieve a higher
degree of saturation of the specimen while maintaining a constant effective stress.

3.7

Anisotropic consolidation stress ratio

The effective lateral stress at completion of consolidation divided by the effective axial stress.

3.8

Consolidation stress

The stress of soil element that induces consolidation.
Note:

In this Standard, the consolidation stress means the difference between the externally applied stress on the test

specimen and the back pressure during the consolidation process.

3.9

Axial consolidation stress

The value of consolidation stress in the axial direction of the specimen.

3.10 Lateral consolidation stress
The value of consolidation stress in the lateral direction of the specimen.

4

Equipment

The cyclic triaxial testing apparatus shall include a triaxial cell, a cell pressure and back pressure supply device,
an axial loading device or an axial displacement loading device, and load, displacement, volume change, porewater pressure measuring and recording devices, and shall satisfy the following conditions. An example of acyclic triaxial testing apparatus is shown in Figure 1.
a)

The test equipment shall have sufficient capacity and load resistance with respect to the maximum cellpressure, back pressure, the maximum axial compressive load and the maximum axial tensile load on thespecimen. The triaxial cell shall be fixed to a loading platform or similar, so that the triaxial cell is not raised
up when the maximum tension axial load is acting. In order to produce a triaxial extensive stress state
during cyclic loading, and ensure that there is no play between the loading piston and the cap, apparatus
in which the load piston and the cap are rigidly connected before setting the specimen in the triaxial cellshall be used (see Figure 2(a) of JGS 0522 Method for consolidated undrained triaxial compression test
on soils).

b)

The specimen shall be covered with the cap, pedestal, and a rubber sleeve. The apparatus shall be capableof to applying the required cell pressure, back pressure, and axial load, and it shall be capable of supplying
and draining water at the top and bottom ends of the specimen. The diameter of the cap and pedestal shallbe the same as the diameter of the specimen as standard, and the two surfaces of the cap and pedestal
shall be flat and parallel to each other, and shall be normal to the load piston. A porous plate with sufficientwater permeability shall be used on the water drainage surfaces, and if necessary, an appropriate filter
paper shall be used. However, if filter paper is placed on a hard specimen, take care with the measurementof displacement. Also, if a cyclic loading test is carried out in the undrained state on a saturated specimen,
the volume change of the pore water pressure measurement route due to water pressure changes shall be
sufficiently small.

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JGS 0542-2020

Note:

The volume change of the pore water pressure measurement route due to water pressure changes should be inaccordance with Note of Section 4b) of JGS 0541 Method for cyclic undrained triaxial test on soils.

c)During isotropic or anisotropic consolidation, the apparatus shall be capable of continuously applying therequired cell pressure, back pressure, and axial stress within a range of fluctuation of ±2 kN/m2 forpressures less than 200 kN/m2, and ±1.0% for pressures 200 kN/m2 and higher. Also, during consolidation
it shall be capable of measuring the axial displacement and volume change of the specimen with anallowable tolerance in the height of the specimen and the volume of 0.02% and 0.05% respectively. The
volume change of the specimen shall be measured using a burette or other device with equal or better
performance.

Note:

The burette shall have a structure to enable the back pressure to be applied, and should have a structure so thatthe water level in the burette does not change due to changes in the back pressure.

d)

The following conditions on the axial load or axial displacement shall be always satisfied.
1)

In the drained or undrained state after isotropic or anisotropic consolidation, the apparatus shall becapable of continuously applying a constant amplitude cyclic axial load or cyclic axial displacementfrom a single amplitude axial strain (εa)SA during a loading cycle as defined in Section 5.4 of 0.001%
or less to 0.1% or more.

2)

The wave form shall be a sine wave or triangular wave with a frequency of 0.05 to 1.0 Hz as standard,
while other wave forms may be used if it has been confirmed that the measurement accuracy indicatedin this standard can be satisfied. Apart from a sine wave or a triangular wave, however, a rectangularor trapezoidal wave shall not be used.

3)

In tests in which cyclic axial load is controlled and applied, the following conditions shall always besatisfied.

3.1)

The fluctuation in the sum of the single amplitude compressive load PC and the single amplitude
extensive load PE defined from the stress state when cyclic loading is started (PC+PE) shall be 10%
or less.

3.2)

0.8≦PC／PE≦1.2

where the single amplitude of the compressive load PC and the single amplitude of the extensive load
PE shall be defined from the stress state prior to cyclic loading as shown in Figure 2. In both cases the
positive value shall be taken. ΔP (=PC+PE) is the double amplitude of the cyclic axial load. In Figure 2,
P0 is the axial load difference (the product of the deviator stress and the cross-sectional area of thespecimen) under the stress state prior to cyclic loading.
4)

In tests in which cyclic axial displacement is controlled and applied, the following conditions shallalways be satisfied.

4.1)

The fluctuation in the sum of the single amplitude compressive displacement ΔLC and the single
amplitude extensive displacement ΔLE defined from the stress state when cyclic loading is started(ΔLC+ΔLE) shall be 10% or less.

4.2)

0.8≦ΔLC／ΔLE≦1.2

where the compressive axial displacement single amplitude ΔLC and the extensive axial displacement
single amplitude ΔLE shall be defined from the state prior to cyclic loading, as shown in Figure 3. In
both cases they shall be the positive value. ΔL (=ΔLC+ΔLE) is the double amplitude axial displacement.
e)During cyclic loading, the apparatus shall be capable of continuously applying the required cell pressure towithin a range of fluctuation of pressure of ±2 kN/m2 for pressures less than 200 kN/m2, and ±1.0% forpressures 200 kN/m2 and higher.

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JGS 0542-2020f)

During cyclic loading, the apparatus shall be capable of continuously measuring the cell pressure (and thepore water pressure for an undrained cyclic loading test on a saturated specimen) to within an allowable
tolerance of 2 kN/m2 for pressures less than 200 kN/m2, and 1.0% for pressures 200 kN/m2 and higher.

g)

In measuring the axial load during cyclic loading, the following conditions shall be satisfied.
1)

For cyclic loading at single amplitude axial strains (εa)SA of 0.01% or more, the apparatus shall becapable of continuously measuring the cyclic axial load acting on the specimen to within an allowable
tolerance of 1.0% of the double amplitude of the prescribed load, using a load cell installed within thetriaxial pressure cell whose hysteresis properties can be ignored.

2)

An electrical load cell that is capable of measuring the compressive load and the tension load and thatis installed within the triaxial cell shall be used for measurement of the cyclic loading.

3)

The output of the load cell shall not change due to a change in the cell pressure. Also, it shall not beaffected by moments or horizontal forces due to eccentric axial loads. In addition, during each wave
of cyclic loading, during cyclic loading in which the single amplitude axial strain (εa)SA is 0.01% there
shall be no drift in excess of or equal to 1% of the measured value and no change in the calibration
value of 1% or more.

4)

Using a dummy specimen for calibration that has no viscous damping, the hysteresis property hLC for
cyclic loading shall be evaluated based on the relationship between the load cell output and the actualload for static loading and unloading obtained by the method shown in Figure 4. The value of hLC shallbe not more than 5% of the hysteresis damping factor h of the specimen when the single amplitude
strain (εa)SA is 0.01%. The maximum value of the load applied to the load cell shall be the maximum
value of the load applied in the actual test.
Load cell hysteresis property hLC=(1/2π)∙ΔX/X

h)4

In measuring the axial displacement during cyclic loading, the following conditions shall be satisfied.
1)

For cyclic loading with a single amplitude axial strain (εa)SA of 0.01% or more, the apparatus shall becapable of continuously measuring the axial displacement of the specimen to within an allowable
tolerance of 1.0% of the double amplitude of the prescribed axial displacement, using a displacementgauge for which the hysteresis property can be ignored. However, for single amplitude axial strains(εa)SA less than 0.1%, it shall be capable of directly measuring the axial displacement of the cap witha displacement gauge installed within the triaxial cell. For single amplitude axial strains (εa)SA equal to
0.1% or more, displacements shall be measured with a displacement gauge installed outside thetriaxial cell. If the axial displacement of the specimen is obtained from the axial displacement of thecap, as a rule a displacement gauge of non-contact type shall be used.

2)

If measurement of the axial displacement during cyclic loading is performed by an electric
displacement gauge installed outside the triaxial cell, the deformation of the load piston, load cell, etc.,
located between the displacement meter and the specimen, the deformation of the fixing position of
the axial displacement gauge, etc., shall be 1.0% of the axial displacement or less when the single
amplitude axial strain (εa)SA is 0.1%.

3)

If it is estimated that the difference between the average axial strain of the specimen and the axial
strain obtained from the axial displacement of the cap or the load piston is 5% or more, and that theerror in the hysteresis damping factor h defined in Section 5.4 is estimated to be 5% or more of themeasured value, due to incomplete contact between the top and bottom ends of the specimen andthe cap and pedestal, or slack at the top or bottom ends of the specimen due to filter paper, etc., theaxial displacement of the specimen shall be measured at the side surface of the specimen by anappropriate method. In this case, the axial displacement ΔLlocal shall be measured between two points
on lines on the rubber sleeve parallel to the specimen axis at the position of the two ends of thespecimen in the radial direction, referring to Figure 5. The measurement length of ΔLlocal shall be 50© JGS 2016 – All rights reserved

JGS 0542-2020

to 80% of the height of the specimen, and sliding between the rubber sleeve and the specimen shallnot affect the measured value of the axial displacement. Also, the measuring instrument shall notaffect the deformation of the specimen.
4)

The output of the displacement gauge shall not change due to a change in the cell pressure. Also,
during each wave of cyclic loading, during cyclic loading in which the single amplitude axial strain(εa)SA is 0.01% there shall be no drift in excess of or equal to 1% of the measured value and no change
in the calibration value of 1% or more.

5)

Using a dummy specimen for calibration that has no viscous damping, evaluate the hysteresis property
hDT for cyclic loading by the method shown in Figure 6, based on the static relationship between theaxial displacement gauge output and the displacement applied to the axial displacement gauge thatis measured with a micrometer for increasing and decreasing displacement, including cases in which
the axial displacement is measured on the side surface of the specimen. Confirm that when the single
amplitude axial strain (εa)SA is 0.01%, the value of hDT is 5% of the hysteresis damping factor h of thespecimen or less. The maximum value of displacement applied shall be the maximum value of axial
displacement actually applied in the test.
Displacement gauge hysteresis property hDT=(1/2π) ∙ΔY/Yi)

On data recording during cyclic loading, the following conditions shall be satisfied.
1)

It shall be possible to continuously and simultaneously record the cyclic axial load and the cyclic axial
displacement during cyclic loading. If necessary, it shall be possible to continuously record the porewater pressure.

2)

The measured values of the axial load, the axial displacement, and if necessary, the measured cellpressure and the pore water pressure during cyclic loading shall be continuously recorded using anelectrical recording device such as a digital data recorder, etc. However, the number of data points in
one cycle shall be 40 or more, so that it will be possible to sufficiently interpolate between two
consecutive digital measurement values.

3)

Using a dummy specimen for calibration that has no viscous damping, confirm that the error in thehysteresis damping factor due to the phase shift between measured results for the axial load and theaxial displacement is 5% of the hysteresis damping factor of the specimen or less when the single
amplitude axial strain (εa)SA is 0.01%. As shown in Figure 7, if the hysteresis damping factor linearly
increases (decreases) with an increase in frequency, there is a time delay (advance) between the load
P and the displacement D.

5

Test method

5.1

Preparation and installation of the specimen

Preparation and installation of the specimen shall be in accordance with JGS 0520 Preparation of soil specimens
for triaxial tests. The diameter of the specimen shall be 50 mm or more for a sandy soil, and 35 mm or more fora cohesive soil. The diameter of a gravelly soil specimen prepared in the laboratory shall be 10 times the
maximum grain size or more as standard, but it may be up to about 5 times in the case of a soil withcomparatively wide range of grain size with a uniformity coefficient of 5 or more. The specimen height shall be
1.5 to 2.5 times the diameter. However, there shall be little disturbance on the top and bottom end surfaces ofthe specimen, and the smoothness, flatness, and parallelism of the top and bottom surfaces of the specimen
shall satisfy the following values.
a)The error in the height of any point on the top end surface relative to the bottom end surface of the specimen
as standard shall be 0.5% of the height of the specimen or less.

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JGS 0542-2020b)

The angle formed between the top end surface of the specimen when it is set on the pedestal and thebottom end surface of the cap shall be 0.5 or less.

c)

The distance of the center of the top and bottom end surfaces of the specimen from the center of theloading axis shall be 1% of the height of the specimen or less.

5.2

Confirming the degree of saturation

If necessary, before consolidation or after consolidation, the pore pressure coefficient B (B value) shall bemeasured. If the B value is obtained, it shall be measured in accordance with the method described in Section
5.2 of JGS 0541 Method for cyclic undrained triaxial test on soils. However, for anisotropic consolidation, it shallbe obtained immediately before anisotropic consolidation.

5.3

Consolidation process

Carry out either isotropic consolidation or anisotropic consolidation depending on the objective of the test.
Measure the change in axial displacement ΔHC (mm) of the specimen due to consolidation, and for a saturated
specimen measure the volume change ΔVC (mm3) in the specimen due to consolidation. Determine completionof primary consolidation of the specimen in accordance with the method indicated in Section 5.2d) of JGS 0522
Method for consolidated-undrained triaxial compression test on soils.
a)b)Isotropic consolidation process
1)

Carry out consolidation with a constant back pressure by applying the prescribed isotropic stress within
the triaxial cell.

2)

Consolidation shall continue at least until primary consolidation is completed.

Anisotropic consolidation process
Under drained conditions, apply the axial stress that will satisfy the required anisotropic consolidation stressratio corresponding to the effective lateral stress under the initial isotropic consolidation state. Increase theanisotropic stress state in stages with the combination of the lateral stress and the axial stress to give therequired anisotropic consolidation stress ratio until the final anisotropic consolidation stress state is reached.
Consolidation shall be continued until at least primary consolidation is completed.
1)

Anisotropic consolidation shall be carried out by the following method as standard.

1.1)

Apply the axial stress that will satisfy the required anisotropic consolidation stress ratio
corresponding to the effective lateral stress under the initial isotropic consolidation state.

1.2)

Set Δσr so that the difference between the effective lateral stresses at the initial consolidation stressstate and the final consolidation stress state is divided equally into 5 or more. However, Δσr shallnot exceed 20 kN/m2.

1.3)

Increment the lateral stress by just Δσr.

1.4)

Increment the axial stress to achieve the required anisotropic stress ratio.

1.5)

Check that the rate of change in axial strain is 0.1%/min or less.

1.6)

Repeat the operations in 1.3), 1.4), and 1.5) above until the final consolidation stress state isreached.

2)

If the following simplified consolidation method can be applied, it may be used.

2.1)

6

Carry out isotropic consolidation up to the effective lateral stress under the final consolidation stressstate (= lateral consolidation stress σ'rc).

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JGS 0542-2020

5.4

2.2)

Divide the difference between the effective axial stress at the final consolidation stress state (=axial consolidation stress σ'ac) and the lateral effective stress σ'rc into 5 equal increments to obtain
Δq.

2.3)

With the specimen in the drained state, increment the axial stress by Δq. During this time theloading rate shall be such that the excess pore water pressure in the specimen Δu is always 10%of σ'rc or less.

2.4)

Check that the rate of change of axial strain is 0.1%/min or less.

2.5)

Repeat the operations in 2.3) and 2.4) above until the final consolidation stress state is reached.

Cyclic loading process

The test shall be performed in accordance with the following requirements for the cyclic loading process.
a)

Confirm the required isotropic or anisotropic stress state.

b)

Apply the cyclic axial load or the cyclic axial displacement in accordance with the following requirements.
For saturated specimens, the conditions shall be drained or undrained, and for unsaturated or air dried
specimens, the conditions shall be water drainage or air drainage conditions. In drained tests, carry out thecyclic loading with a range so that under the peak stress state in the triaxial extensive stress state the total
axial stress does not become negative. The back pressure can be increased with the objective of increasing
the range of cyclic loading amplitude applied to the specimen.

Note 1:

The maximum cyclic axial load amplitude or axial displacement amplitude may be determined as appropriate inaccordance with the condition of the specimens and the objectives of the test.
Note 2:

1)

An example of cyclic triaxial test record is shown in Figure 8.

First loading

1.1)

For an undrained test, close the drainage valve.

1.2)

Apply 11 waves of cyclic axial load or cyclic axial displacement as a sine wave or a triangular wave,
at a constant amplitude and a constant frequency between 0.05 to 1.0 Hz, so that the single
amplitude axial strain (εa)SA is about 0.001% or less. During loading continuously record the axial
load and axial displacement, and if necessary the pore water pressure.

1.3)

Measure the change in height of the test specimen due to the cyclic loading (in the case of adrained test on a saturated specimen, measure the volume change also). During cyclic loading, inthe case of undrained conditions, after completion of cyclic loading the conditions shall be changed
to drained, and the resulting change in height and the volume change of the specimen shall bemeasured.

2)

Second loading

2.1)

For an undrained test, close the drainage valve, while checking that the rate of change of the axial
strain in 0.01%/min. or less.

2.2)

Carry out loading by repeating the same loading as the first loading, so that the single amplitude
axial strain (εa)SA is about double that in the first loading.

2.3)

Measure the change in height of the test specimen due to the cyclic loading (in the case of adrained test on a saturated specimen, measure the volume change also). During cyclic loading, inthe case of undrained conditions, after completion of cyclic loading the conditions shall be changed
to drained, and the resulting change in height and the volume change of the specimen shall bemeasured.

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JGS 0542-2020

3)

Third and subsequent loadings
Apply the loading is the same way as the second loading. The loading shall repeat this loading stage
as much as possible.

c)

Observe and record the specimen deformation state, etc.

d)Measure the specimen oven-dried mass ms (g).

6Processing test results

6.1

Condition of the specimen before consolidation

The specimen volume V0 (mm3) and specimen height H0 (mm) before consolidation shall be calculated from thefollowing equation.
V0 = Vi - ΔVi
H0 = Hi - ΔHi
where
Vi :
Initial volume of the specimen (mm3)Hi :Initial height of the specimen (mm)
ΔVi : Volume change of the specimen from the initial state to before consolidation (mm3), where volume
reduction is defined to be positive
ΔHi : Axial displacement of the specimen from the initial state to before consolidation (mm), wherecompression is defined to be positive

6.2

Pore pressure coefficient B

The B value of the specimen before consolidation shall be calculated from the following equation, which shallbe rounded to two significant digits.
B=

∆u
∆σ

where
Δσ:
Δu:

6.3

Increment of isotropic stress (kN/m2)
Increment of pore water pressure associated with Δσ (kN/m2)

Consolidation process

The calculation and processing method for the consolidation process shall be as follows.
a)Calculate the volume of the specimen Vc (mm3) after consolidation from the following equation.
Vc = V0 − Vc

where
ΔVc : Volume change of the specimen due to consolidation (mm3), where volume reduction is defined
to be positive
Note 1:

If the specimen is not saturated, the volume change of the specimen ΔVc (mm3) due to isotropic consolidation shallbe calculated from the following equation.

Vc =

8

3H c
V0
H0
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JGS 0542-2020

where
ΔHc : Axial displacement due to consolidation (mm), where compression is defined to be positive
V0 : Volume of the specimen before consolidation (mm3)H0 : Height of the specimen before consolidation (mm)Note 2:

If the specimen is not saturated, calculate the volume change of the specimen due to anisotropic consolidation by

an appropriate method.

b)

Calculate the height of the specimen after consolidation Hc (mm) from the following equation.
Hc = H0 − Hc

where
ΔHc: Axial displacement due to consolidation (mm), where compression is defined to be positivec)Calculate the cross-sectional area Ac (mm2) of the specimen after consolidation from the following equation.

Vc
Hc

Ac =

d)

Calculate the dry density ρdc (Mg/m3) of the specimen after consolidation from the following equation, whichshall be rounded to two digits after the decimal point.
ρdc =

ms
× 1000
Vc

where
ms :
Note 1:Oven-dried mass of the specimen (g)The values of densities that have been expressed conventionally with a unit of g/cm 3 are the same as thoseexpressed with a unit of Mg/m3.
Note 2: If necessary, the void ratio ec and the relative density Drc (%) of the specimen after consolidation shall be calculated
from the following equations.

ec =

ρs
−1
ρdc

Drc =

emax − ec
× 100
emax − eminwhereρs : Soil particle density (Mg/m3)
emax : Void ratio of the specimen from a minimum density test
emin : Void ratio of the specimen from a maximum density test

6.4

Cyclic loading process

The calculation and processing method for the cyclic loading process shall be as follows.
Note:

If the axial strain of the specimen is 1% or less, normally it is not necessary to correct σd for the force acting on therubber sleeve.
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9JGS 0542-2020

a)Calculate the volume Vn (mm3), height Hn (mm), and cross-sectional area An (mm2) of the specimen at thestart of each loading stage carried out by constant amplitude cyclic axial loading or axial displacement.

Note 1:

If necessary, the void ratio en at the start of each loading stage shall be calculated from the following equation.

en =Vn /1000 × ρs
−1
ms

where
ms:
ρs:

Oven-dried mass of the specimen (g)Soil particle density (Mg/m3)

However, the void ratio en at the start of the initial cyclic loading stage is equal to the void ratio after
consolidation ec.
1)

Calculate the volume of the specimen Vn (mm3) at the start of each loading stage from the following
equation.
Vn = Vc − Vn

where
ΔVn: Volume change of the specimen from completion of consolidation to the start of each loading
stage (mm3), where volume reduction is defined to be positive
Note 1: If isotropic consolidation is carried out on the specimen when the specimen is not saturated, the volume changeof the specimen ΔVn due to cyclic loading may be calculated from the following equation.

Vn =

3Hn
Vc
Hc

where
ΔHn: Axial displacement from completion of consolidation to the start of each loading stage (mm),where compression is defined to be positive
Vc:
Volume of the specimen at completion of consolidation (mm3)Hc:
Height of the specimen at completion of consolidation (mm)Note 2:

If anisotropic consolidation is carried out on the specimen when the specimen is not saturated, the volume changeof the specimen ΔVn due to cyclic loading shall be calculated by an appropriate method.

2)

Calculate the height of the specimen Hn (mm) at the start of each loading stage from the following
equation.
Hn = Hc − Hn

where
ΔHn: Axial displacement from completion of consolidation to the start of each loading stage (mm),where compression is defined to be positive3)

The cross-sectional area of the specimen An (mm2) at the start of each loading stage shall becalculated from the following equation.
An =

10

Vn
Hn
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JGS 0542-2020b)

Every 5th and 10th loading cycle in each cyclic loading stage of constant amplitude cyclic axial loading oraxial displacement, the single amplitude deviator stress σd (kN/m2), the single amplitude axial strain(εa)SA(%), the equivalent Young’s modulus Eeq (MN/m2), and the hysteresis damping factor shall be calculated.

Note 1:

In tests with constant amplitude cyclic axial loading, if there is a deviation in the axial displacement ΔH (mm) of thespecimen between two consecutive cycles as shown in Figure 9, and if the amount of deviation α (mm) is equal to 2% ormore of the axial displacement double amplitude ΔL (mm), then ΔL (mm) shall be corrected by the following method.

1)

If the specimen has been compressed by consecutive cycles (Figure 9(a))(Corrected ΔL in the Nth cycle) = (ΔL measured in the Nth cycle) + α/2

2)

If the specimen has been extended by consecutive cycles (Figure 9(b))(Corrected ΔL in the Nth cycle) = (ΔL measured in the Nth cycle) - α /2Note 2: In tests with constant amplitude cyclic axial displacement, if the cyclic axial load P (N) on the specimen between two
consecutive cycles has deviated as shown in Figure. 10, and if the amount of deviation β (N) is 2% of the double amplitude
axial load ΔP (N) or more, ΔP (N) shall be corrected by the following method.

1)

If the specimen axial load has been reduced by consecutive cycles (Figure 10(a))(Corrected ΔP in the Nth cycle) = (ΔP measured in the Nth cycle) - β/22)

If the specimen axial load has been increased by consecutive cycles (Figure 10(b))(Corrected ΔP in the Nth cycle) = (ΔP measured in the Nth cycle) + β/2

Note 3:Calculate the equivalent Young’s modulus and hysteresis damping factor at loading cycles other than the 5th andthe 10th, in accordance with the objectives of the test.

1)

The single amplitude cyclic deviator stress σd (kN/m2) shall be calculated from the following equation,
which shall be rounded to three significant digits. If the precision of the measurement device is not
sufficient, two significant digits shall be used.
σd =Pc + PE
× 10002An

wherePC, PE: The single amplitude cyclic axial load on the compression side and the extension side inthat cycle (N) (both positive values)An:
Specimen cross-sectional area at the start of that cyclic loading stage (mm2)2)

The single amplitude axial strain (εa)SA (%) shall be calculated from the following equation, which shallbe rounded to three significant digits. If the precision of the measurement device is not sufficient, twosignificant digits shall be used.
(εa )SA =

∆L
× 100
2Hn

where
ΔL:
Hn:
Note 1:

Double amplitude axial displacement of the specimen ΔH in that cycle (mm)Specimen height at the start of that cyclic loading stage (mm)If the axial displacement of the cap of the specimen is measured by several non-contact displacement gauges, thevalue of ΔL shall be obtained from their average value.

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JGS 0542-2020

Note 2:

If the axial compression ΔLlocal1 and ΔLlocal2 are measured between 2 points on lines on the rubber sleeve that areparallel to the axis of the specimen at positions on the diagonal of the diameter of the specimen (Figure 5), the double
amplitude ΔL (mm) of the specimen axial displacement ΔH shall be calculated from the following equation.

L = ((Llocal1) / L1n ) + ((Llocal 2) / L2n ) / 2 Hn
where
L1n, L2n:3)

The equivalent Young’s modulus Eeq (MN/ m2) shall be calculated from the following equation, whichshall be rounded to three significant digits. If the precision of the measurement device is not sufficient,
two significant digits shall be used.
Eeq =

Note:

Average distance (mm) between the two points on the specimen side surface at the
specimen diagonal positions respectively at the start of that loading cycle

σd1×(εa )SA 10

Figure 11 is an example of hysteresis curve drawn from the axial stress difference and the axial strain obtained using

the specimen height and volume at the start of that cyclic loading, and it explains the equivalent Young’s modulus
Eeq (MN/m2).

4)

The hysteresis damping factor h (%) shall be calculated from the following equation, which shall be
rounded to three significant digits. If the precision of the measurement device is not sufficient, twoeffective significant shall be used.

h=

1 W
 100

2 W

where
ΔW:
W:
W=

The damping energy in that cycle, and is the area of the hysteresis curve prepared from theaxial load difference P and the axial displacement ΔH (N∙mm)
Equivalent elastic energy in that loading cycle, calculated from the following equation.
(Pc + PE )L
4

Note 1:Figure 12 is a diagram that explains the hysteresis damping factor h=(1/2π)∙ΔW/W

Note 2:

If the hysteresis curve does not close, as shown in Figure 13, the sum of the areas of the compression side

hysteresis curve gbh and the extension side hysteresis curve hdf shall be taken to be ΔW (N∙mm). Also, the value of W
(N∙mm) shall be calculated from the following equation.

1)

Test with constant cyclic axial load amplitudeW =1
P  L
4

where
ΔP:
ΔL:
2)

12

Measured value (N)Value corrected in accordance with the method described in Section 6.4b）Note 1 (mm)Test with constant cyclic axial displacement amplitude© JGS 2016 – All rights reserved

JGS 0542-2020

W=

1∆P ∙ ∆L
4

where
ΔL:
ΔP:

7

Measured value (mm)Value corrected in accordance with the method described in Section 6.4b）Note 2 (N)Reporting

The following items of the test results shall be reported.
a)Method of preparing the specimensb)

Dimensions of the specimens before consolidationc)

If an undrained cyclic load test has been carried out on a saturated specimen, the magnitude of the backpressure (kN/m2) and the B value and its measurement methodd)Volume change (mm3) and axial displacement (mm) due to consolidatione)Oven-dried mass of the specimen, and dry density after consolidation (Mg/m3)

Note: If necessary, the void ratio and relative density after consolidation shall be reported.

f)

Axial consolidation stress (kN/m2) and lateral consolidation stress (kN/m2)

g)

Loading frequency and loading wave form, drainage conditions during cyclic loadingh)Method of measurement of axial load (N) and axial displacement (mm) during cyclic loading

Note:

The position of the load cell and displacement gauge within the triaxial cell shall be reported. If the axial displacement

is measured on the specimen side surface, the method shall be reported.

i)

Specimen dimensions at the start of each of the second to final cyclic loadingj)

Axial load (N) and axial displacement (mm) time histories and the axial load (N) and axial displacement(mm) hysteresis curve at the 5th and 10th cycles in each cyclic loading stage

Note:

k)

The axial stress and axial strain time history and the hysteresis curve may also be reported.

The equivalent Young’s modulus Eeq (MN/m2), the hysteresis damping factor h (%), and the corresponding
single amplitude axial strain (εa)SA (%) at the 5th and 10th cycles in each cyclic loading stage

Note:

If necessary, the equivalent Young’s modulus Eeq (MN/m2), the hysteresis damping factor h (%), and thecorresponding single amplitude axial strain (εa)SA (%) at each cycle from the 2nd to the 10th cycle in each cyclic loading
stage shall be reported.

The logarithmic relationship between the equivalent Young’s modulus Eeq (MN/m2), the hysteretic damping
factor h (%), and the corresponding single amplitude axial strain (εa)SA (%) at the 5th and 10th cycles

l)

Note:

Figure 14 shows a standard example of summary of the series of test results.

m) If a method that partially differs from this standard was used, details of the points of differencen)Other reportable mattersAn outline description of the testing apparatus, the method of saturating the specimen, the hysteresis
property of the load cell and displacement gauge, synchronization of the axial load and axial displacement
records, the rubber sleeve material and thickness shall be reported.
The alternation of strata state of the specimen, and the failure state such as necking, etc., shall be reported.

© JGS 2016 – All rights reserved

13

JGS 0542-2020

Cyclic axial
loading cylinder

Axial displacement gauge

Loading
frame

Cell pressure(air pressure)
Load cell

Back pressure(air pressure)Non-contact
displacement
gauge

Double tube buretteCap

Specimen

Water

Rubber sleeve

Pore waterpressure gauge

Pedestal

Loading platform

Figure 1 Example of a standard cyclic triaxial testing apparatus

Time

Figure 2 Definition of compressive load single amplitude PC and extensive load single amplitude PE forsine wave cyclic axial loading

14© JGS 2016 – All rights reserved

JGS 0542-2020

Time

Figure 3 Definition of compressive axial displacement single amplitude ΔLC and extensive axial
displacement single amplitude ΔLE for a sine wave cyclic axial displacement

Load cell output
X = [Area of Δabc] + [Area of Δdae]

Load applied to load cell

Hysteresis area ΔX

Figure 4 Definition of the hysteresis property of the load cellCap
Measurement length of axial
displacement of specimen
Length L1
Axial displacement

ΔLlocal1

Specimen

Length L2
Axial displacement

ΔLlocal2

Pedestal

Figure 5 Example of measurement of axial displacement of the specimen at the side surface of thespecimen© JGS 2016 – All rights reserved

15

JGS 0542-2020
Displacementgauge output
Y = [Area of Δabc] + [Area of Δdae]

Displacement measured by
micrometer
Hysteresis area ΔY

Figure 6 Definition of hysteresis property of axial displacement gauge

Displacement
recording delayed

Load recording
delayedFigure 7 Apparent load frequency dependence of the measured hysteresis damping factor due tophase shift between the measured results for load and displacement when h does not depend on
frequency f (h0 is a positive value, hd is the apparent value at f1)

16© JGS 2016 – All rights reserved

JGS 0542-2020

Axial strain

εa (%)

Deviator stressq (kN/m2)

Toyoura sand, Air-pluviation method, ec=0.688,
σc'=98 kN/m2, f =0.1 Hz, H=170 mm, D=70 mm

Figure 8 Example of cyclic triaxial test record with constant cyclic loading amplitude and a sinusoidal
wave form

Nth cycle

Nth cycle(Measuredvalue)(Measuredvalue)

Nth cycle(Measured value)(Measured value)

Figure 9 Explanation of the amount of deviation  of the axial displacement in 2 consecutive cycles

Nth cycle

Figure 10 Explanation of the amount of deviation  of the axial load in 2 consecutive cycles© JGS 2016 – All rights reserved

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JGS 0542-2020

Deviator stressq (kN/m2)

10th cycle incyclic loading

Axial strain εa (%)

Figure 11 Example of typical hysteresis curve

Cyclic axial load acting on
specimen P (N)W = [Area of abc] +[Area of dae]= P ・ L
4

Axial displacement of specimen ΔH (mm)Hysteresis area ΔW

Figure 12 Explanatory diagram for hysteresis damping factor h (diagram for the case where PC and PE
are equal)

18© JGS 2016 – All rights reserved

JGS 0542-2020

ΔP (Measured value)

Cyclic axial load acting
on specimen P (N)Axial displacement of specimen
ΔH (mm)Hysteresis area ΔW

ΔL (Measured value)

Toyoura sand, Air-pluviation method, ec=0.688,
σc’=98 kN/m2, f =0.1 Hz, H=170 mm, D=70 mm
Cyclic triaxial test (drained loading)○: 10th cycle in cyclic loading△: 5th cycle in cyclic loading

Hysteresis damping factorh (%)

Equivalent Young's modulus
Eeq (MN/m2)

Figure 13 Explanatory diagram for hysteresis damping factor h when the hysteresis curve does not
close (diagram for the case where PC and PE are equal)

Single amplitude strain (εa)SA (%)

Figure 14 Example of summary of the series of test results© JGS 2016 – All rights reserved

19