Cyclic Behavior of Sand
and Cyclic Triaxial Tests
Hsin-yu Shan
Dept. of Civil Engineering
National Chiao Tung University
Causes of Pore Pressure Buildup
due to Cyclic Stress Application
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Stress are due to upward propagation of
shear waves in a soil deposit during
earthquake
Structure of the cohesionless soil tends to
become more compact Æ
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Transfer of stress to the pore water
Reduction in stress on the soil grains
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Soil grain structure rebounds to the extent
required to keep the volume constant
Volume reduction and soil structure rebound
determines the magnitude of the increase in
pore water pressure increase
As the pore water pressure approaches a
value equal to the applied confining pressure
Æ the sand begins to undergo deformations
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If the sand is loose:
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Pore pressure increase suddenly to a value equal
to the applied confining pressure
The sand will rapidly begin to undergo large
deformations with shear strains exceeding around
20% or more
If the sand will undergo unlimited deformations
without mobilizing significant resistance to
deformation Æ it can be said to be liquefied
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If the sand is dense:
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It may develop a residual pore water pressure (a
peak cyclic pore pressure ratio of 100%)
When the cyclic stress is reapplied on the next
stress cycle, or if the sand is subjected to
monotonic loading Æ
The soil will tend to dilate
Pore pressure will drop if the sand is undrained
The soil will ultimately develop enough resistance
to withstand the applied stress
Large deformation will develop during the process
Effect of Partial Drainage
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There will be some drainage in the field
Add some margin of safety against cyclic
mobility or liquefaction
To ignore the effect of partial drainage is on
the conservative side
Evaluating Liquefaction or
Cyclic Mobility Potential
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Methods based on observation of
performance of sand deposit in previous
earthquake
Method based on stress conditions in field
and laboratory determinations of stress
conditions causing cyclic mobility or
liquefaction of soils
Observation Method
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Based on the location of the points
representing the data set (N1, τ/σ’0) relative
to the curve representing the lower bound for
sites where liquefaction occurred
N1 is the corrected SPT-N value
τ
σ 0′
= cyclic ratio causing liquefaction
τ av
amax σ 0
rd
≈ 0.65
σ 0′
g σ 0′
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amax = maximum acceleration at the ground surface
σ0 = total overburden pressure on sand layer under
consideration
σ’0 = effective overburden pressure on sand layer
under consideration
rd = a stress reduction factor varying from a value of
one at the ground surface to a value of 0.9 at a
depth of 10 m
Experience with the Method
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The lower bound curve is strongly supported
by abundant data from Japan and China
Works satisfactorily with the data from 921
earthquake
Conservative for earthquakes with lesser
magnitudes involving shorter duration of
shaking
Limitations of the Method
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Need for additional reliable data points to
better define the lower bound of causing
cyclic mobility or liquefaction at high values of
τav/σ’0
Need to understand more about the
significant factors affecting cyclic mobility or
liquefaction
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Duration of shaking, magnitude of earthquake
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Penetration resistance may not be an
appropriate index of the cyclic mobility
characteristics of soils
The standard penetration resistance of a soil
is not always determined with reliability in the
field and its value may vary significantly
depending on the boring and sampling
conditions
Factors Affecting the Cyclic
Mobility Characteristics of Sand
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Density or relative density ↑
Grain structure or fabric ↑
Length of time the sand subjected to
sustained pressures ↑
Value of K0 ↑
Prior seismic or other shear strains ↑
Factors Affecting the N Value
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The use of drilling mud vs. casing for
supporting the walls of the drill hole
The use of a hollow stem auger vs. casing
and water
The size of the drill hole
The number of turns of the rope around the
drum
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The use of a small or large anvil
The length of the drive rods
The used of nonstandard sampling tubes
The depth range over which the penetration
resistance is measured
Evaluating Liquefaction or
Cyclic Mobility Potential
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Methods based on observation of
performance of sand deposit in previous
earthquake
Method based on stress conditions in
field and laboratory determinations of
stress conditions causing cyclic mobility
or liquefaction of soils
Methods Based on Field/Lab
Stress Conditions
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An evaluation of the cyclic stresses induced
at different levels in the deposit by the
earthquake shaking
A laboratory investigation to determine the
cyclic stresses which, at given confining
pressures representative of specific depths in
the deposit, will cause the soil to develop a
peak cyclic pore pressure ratio of 100% or
undergoes various degrees of cyclic strain
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Compare the results of the two evaluation:
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The cyclic stresses induced in the field with the
stresses required to cause a peak cyclic pore
pressure ratio of 100%
An acceptable limit of cyclic strain in
representative samples in the lab
5 Basic Procedures Need to be
Developed
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Suitable analytical procedures for evaluating
stresses developed in an earthquake
Suitable procedure for representing the
irregular stress history produced by the
earthquake by an equivalent uniform cyclic
stress series
Suitable test procedure for measuring the
cyclic stress conditions causing a peak pore
pressure ratio of 100% or intolerable level of
strain in the soil sample
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Understanding of all the factors having a
significant influence on the cyclic mobility or
liquefaction characteristics of soils
Understanding of the effects of sample
disturbance on the in-situ properties of
natural deposits
Methods for Evaluating Stresses
Induced by Earthquake Shaking
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Ground response analysis that neglects the
pore pressure buildup
Procedure that takes into account the pore
pressure generated in the soil
Simplified procedure based on a knowledge
of the maximum ground surface acceleration
Deconvolution of a known ground surface
motion
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Ignoring pore pressure build up during
earthquake may not be particularly significant
May lead to somewhat conservative results in
some cases
Converting Irreg. Stress His. into
Equiv. Unif. Cyclic Stress Series
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Because it is usually more convenient to
perform lab tests using uniform cyclic stress
applications than to reproduce the actual field
stress history
There were three methods can be used and
their differences have little effect on the final
results
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Three basic methods:
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By estimation from a visual inspection of the
irregular time history involved
By a weighting procedure for individual stress
cycles – use an experimentally-determined pore
pressure response
A cumulative damage approach based on Miner’s
law and involving the natural period of the deposit
and the duration of earthquake shaking
Suitable Test Procedures
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Cyclic simple shear tests
Multidirectional shaking in simple shear tests
Cyclic triaxial compression tests
Cyclic Direct Simple Shear
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DSS Roscoe-type
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Four plates
Pure shear is applied to horizontal and vertical
plane
Difficulties
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Preparation of representative samples
Development of uniform shear strains throughout the
samples
Application of uniform stress conditions
Avoidance of stress concentrations
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Very long and shallow samples
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Stress concentrations are limited to small areas at
the ends
Longer samples Æ less affected by the stiffness
of the walls of the sample container
Cyclic Triaxial Compression
Tests
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Equipment less complicated and more
available than DSS
Do not reproduce correct initial stress
conditions for NC soils or in a simple shear
test
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Other limitations
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Stress concentrations at the cap and base
A 90° rotation of the direction of major principal
stress during the two halves of the loading cycle
Necking may develop and invalidate the test data
beyond this point in the test
Intermediate principal stress does not have the
same relative value during the two halves of the
loading cycle
Difficult to achieve a high degree of accuracy for
stress ratio not representative of field values
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Cyclic triaxial stress ratio is higher than that
for simple shear condition
 σ dc 
 τh 

 
= cr 
 2σ 3  triaxial
 σ c′ simple shear
cr = correction factor ranging from 0.5 – 1.0,
increases with K0
Factors Influencing Cyclic Mobility
or Liquefaction Characteristics
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Grain characteristics
Relative density
Method of soil formation (soil structure)
Period under sustained load
Period under sustained load
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Previous strain history
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Lateral earth pressure coefficient and
overconsolidation
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Increase the stress ratio
Larger K0 Æ higher stress ratio
Cyclic mobility and liquefaction
characteristics of in-situ deposits
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Disturbance Æ lower the stress ratio