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Liquefaction Analysis in Grenoble Basin
by In Situ and Laboratory Tests
Draft of Master Dissertation Msc in Engineering Seismology
ALPEREN SEYFI
Supervisor: Prof. PIERRE FORAY
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1.
INTRODUCTION
2.
MECHANICS OF LIQUEFACTION
In this chapter, general concepts on liquefaction, definitions of different types of
liquefaction and the main factors which are effecting liquefaction are presented. These
concepts help us to understand in which conditions liquefaction occurs.
2.1
Terminology and Definitions
In common usage, liquefaction refers to the loss of strength in saturated, cohesionless
soils due to the build-up of pore water pressures during the dynamic loading.
A more precise definition of soil liquefaction is given by Sladen et al. (1985). They state
“Liquefaction is phenomenon wherein a mass of soil loses a large percentage of its shear
resistance, when subjected to monotonic, cyclic, or shock loading, and flows in a manner
resembling a liquid until the shear stresses acting on the mass are as low as the reduced
shear resistance”.
Liquefaction results from the tendency of soils to decrease in volume when subjected to
shearing stresses. When loose, saturated soils are sheared, the soil grains tend to
rearrange into a more dense packing, with less space in the voids, as water in the pore
spaces is forced out. If drainage of pore water is impeded, pore water pressures increase
progressively with the shear load. This leads to transfer of stress from the soil skeleton to
the pore water precipitating a decrease in effective stress and shear resistance of soil. If
the shear resistance of the soil becomes less than the static, driving shear stress, the soil
can undergo large deformations and is said to liquefy (Martin et al. 1975; Seed and Idriss
1982).
Figure 2.1 Liquefaction in Nigata, Japon (1964) and in Adapazari, Turkey (1999)
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In terms of effective stress and pore-water pressure, Seed et al. [1979] recognize different
conditions on the behavior of saturated sands:
Liquefaction: A soil will undergo continued deformation at constant low residual stress
or with no residual resistance due to the build up and maintenance of high pore-water
pressures, which reduce the effective confining pressure to a very low value. Porepressure build up leading to this type of liquefaction may be due to either static or cyclic
stress application.
Initial Liquefaction: During the course of cyclic stress applications, the residual porewater pressure becomes equal to the applied confining pressure on completion of any full
stress cycle. The development of initial liquefaction has no implications concerning the
magnitude of the deformations that the soil might subsequently undergo. However, it
defines a condition that is a useful basis for assessing various possible forms of
subsequent soil behavior.
Initial Liquefaction with limited strain potential: This corresponds to a condition in
which cyclic stress applications develop a condition of initial liquefaction and subsequent
cyclic stress applications cause limited strains to develop, either because of the remaining
resistance of the soil to deformation or because the soil dilates, the pore-pressure drops,
and the soil stabilizes under applied loads.
On the other hand, Kramer [1996] distinguishes two main groups in which liquefaction
can be divided depending on the nature and characteristics of soil shear stress:
Flow Liquefaction: This type of liquefaction occur when the static shear stress is greater
than the shear strength of the soil in its liquefied state. Once triggered, the large
deformations produced by flow liquefaction are actually driven by static shear stresses,
which bring the soil to an unstable state with a drop in strength that is enough to allow the
static stresses to produce flow failure. Flow liquefaction is characterized by its sudden
nature, the speed with which it develops and the large distance over which the liquefied
material moves.
Cyclic Mobility: Contrary to flow liquefaction, cyclic mobility occurs when the static
shear stress is less than shear strength of the liquefied soil. The deformations produced by
cyclic mobility failure develop incrementally during earthquake shaking. Different from
flow liquefaction, the deformations produced by cyclic mobility, called lateral spreading,
are driven by both cyclic and static shear stresses. Level-ground liquefaction is a special
case of cyclic mobility, in which failure is caused by the upward flow of water, which
occurs when the seismically induced excess pore-pressure dissipates. Level-ground
liquefaction failure may occur even after ground shaking has ceased depending on the
lapse of time required to reach the hydraulic equilibrium. The presence of sand boils and
excessive vertical settlement with consequent flooding of low-lying land is characteristic
of the Level-Ground liquefaction failure.
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Figure 2.2
Sand Boils
Level Ground Liquefaction: Level ground liquefaction is a subset of cyclic mobility that
occurs when the static shear stress is zero. Because static horizontal shear stress that
could drive lateral deformations do not exist, level-ground liquefaction can produce large,
chaotic movement known as ground oscillation during earthquake shaking, but produces
little permanent lateral soil movement. Level ground liquefaction failures are caused by
the upward flow of water that occurs when seismically induced excess pore pressures
dissipate. Depending on the length of time required to reach hydraulic equilibrium, levelground liquefaction failure may occur well after ground shaking has ceased (Kramer
1996). This form of liquefaction typically occurs in loose to medium-dense soils, but may
occur in dense soils if the loading is strong enough and of sufficient duration and fiels
conditions are favorable.
As the excess porewater pressure increases during seismic or cyclic loading, shear
stiffness decreases. If the loading is of sufficient strength and duration, the soil can cycle
through momentary periods of zero effective stress. Since there is no driving stress,
permanent lateral deformations are often relatively small; however, large vertical
settlements may develop during the dissipation of seismically-induced excess porewater
pressure. These settlements can create large downdrag forces on deep foundations. If
level ground liquefaction occurs below a surface cap soil (soil of lower permeability), the
cap soil can be hydraulically fractured resulting in sand blow formation and loss of
ground (Obermeier 1996). A cap soil also may separate from an underlying liquefied
layer allowing potentially large ground oscillations and large, chaotic vertical
displacements to develop (Youd 1995).
Roberson and Fear (1996) suggested a fairly complete classification system to define
“soil liquefaction”. The latest of version of this system can be summarized as:
Flow liquefaction, used for the undrained flow of a saturated, contractive soil when the
static shear stress exceeds the residual strength of the soil. Failure may be triggered by
the cyclic or monotonic shear loading.
Cyclic softening, used to describe large deformations occurring cyclic shear due to pore
pressure build-up in soils that would tend to dilate in undrained, monotonic shear. Cyclic
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softening, in which deformations do not continue after cyclic loading ceases, can be
further classified as;
•
•
Cyclic liquefaction, which occurs when cyclic shear stresses exceed the initial,
static shear stress to produce a stress reversal. A condition of zero effective stress
may be achieved during which larger deformations may occur.
Cyclic mobility, in which cyclic loads do not yield a shear stress reversal and a
condition of zero effective stress does not develop. Deformations accumulate in
each cycle of shear stress.
During cyclic undrained loading almost all saturated cohesionless soil develop positive
pore water pressures due to the contractive response of the soil at small strains. If there is
shear stress reversal, the effective stress state can progress to the point of essentially zero
effective stress, as illustrated in the figure 1. When the soil element reaches the condition
of essentially zero effective stress, the soil has very little stiffness and large deformations
can occur during cyclic loading. If there is no shear stress reversal, the stress state may
not reach zero effective stress. (Robertson and Wride 1996)
2.2
Liquefaction Susceptibility
Liquefaction is most commonly observed in shallow, loose, saturated deposits of
cohesionless soils subjected to strong ground motions in large-magnitude earthquakes.
Unsaturated soils are not subjected to liquefaction because volume compression does not
generate excess pore pressures. Liquefaction and large deformations are more likely with
contractive soils while cyclic softening and limited deformations are associated with
dilative soils. Other factors affecting liquefaction susceptibility of different soil types are
discussed in this section.
2.2.1 Factors Affecting Liquefaction
2.2.1.1 Moment Magnitude and Epicentral Distance
Based on historical registers, Ambraseys [1988] compiled worldwide data from shallow
earthquakes in order to estimate a limiting epicentral distance beyond which liquefaction
has not been observed in earthquakes of different magnitudes. Figure 2.3 shows that
distance to which liquefaction can be expected increases dramatically with increasing
magnitude. Ambraseys reported that deep earthquakes with focal depth greater than 50
km have produced liquefaction at greater distances.
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Figure 2.3 Limiting Epicentral Distance [Ambraseys, 1988]
2.2.1.2 Geologic Criteria
Since liquefaction is associated with the tendency for soil grains to rearrange when
sheared, anything that impedes the movement of soil grains will increase the liquefaction
resistance of soil deposit. Particle cementation, soil fabric, and aging all related to the
geological formation of a deposit are important factors that can hinder particle
rearrangement (Seed 1979). Soils deposited prior to the Holocene epoch (more than
10.000 years old) are usually not prone to liquefaction (Youd and Perkins 1978).
Geological processes may form loose soils with uniform-size grain distribution such as
fluvial, saturated colluvial and saturated Aeolian deposits, which have high liquefaction
susceptibility. Man-made loose fills badly compacted or without compaction are very
likely to be susceptible to liquefaction, and even well compacted fills have some risk of
liquefaction due to the initial relative density of the soil.
2.2.1.3 Soil Composition
The characteristics that imply volume-change potential are normally associated with
liquefaction susceptibility, including particle size, shape and gradation [Kramer, 1996].
Based on the result of sieve analyses on soils that did or did not liquefy during past
earthquakes, Tsuchida [1970] proposed the grain size distribution boundary curves shown
in Figure 2.4 in order to identify susceptible and non-susceptible to liquefaction soils.
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Figure 2.4 Limits in gradation curves for liquefiable and unliquefiable soils
[Tsuchida, 1970]
More recently [Ishirara, 1985], these boundaries have broadened, since liquefaction of
non-plastic silts has been observed indicating that the plasticity characteristics, rather
than the grain size alone, influence the liquefaction occurrence in fine-grained soils.
Figure 2.5 contains the ranges of grain sizes for tailing slimes with low resistance to
liquefaction proposed by Ishihara.
Figure 2.5 Ranges of grain sizes with low resistance to liquefaction [Ishihara, 1985]
Plastic fines in sandy soils usually create sufficient adhesion between the sand grains to
limit the ability of larger particles to move into a denser arrangement. Consequently, soils
with significant plastic fines content are rarely observed to liquefy in earthquakes. In
contrast, as discussed by Ishihara (1993), non-plastic soil fines with a dry surface texture
do not create adhesion and do not provide significant resistance to a particle
rearrangement and liquefaction.
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Permeability also affects the liquefaction characteristics of a soil deposit. When pore
water movement within a liquefiable deposit is retarded by a low permeability, pore
pressures are more likely to accumulate during cyclic loading. Consequently, soils with
large non-plastic fines content may be more susceptible to liquefaction because the fines
inhibit drainage of excess pore pressures.
2.2.1.4 Initial Relative Density
Initial relative density is one of the most important factors controlling liquefaction
[Prakash, 1981]. Up to a relative density of 70-80%, the undrained cyclic resistance
increases almost proportionally to relative density. Beyond this value, the cyclic
resistance increases faster than the relative density. Typical stress-strain curves for dense
sands (initial void ratio e0 = 0.605) and loose sands (e0 = 0.834) for an applied pressure
σ 3 = 207 kPa are shown in Figure 2.6. The slope of the stress-strain curve, a measure of
the rigidity of the soil, is smaller for loose sands than those for dense sand. Consequently,
sands having smaller initial relative density undergo larger strains and larger settlements
than those having higher relative density. Therefore, probability of liquefaction and
excessive settlement are hence reduced with increased relative density.
Figure 2.6 Typical triaxial compression tests on sand [ Prakash, 1981]
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2.2.1.5
Confining Pressure
The frictional resistance between soil grains is proportional to effective confining stress.
Consequently, the liquefaction resistance of a soil deposit increases with depth as the
effective overburden pressure increases. For this reason, soil deposited deeper than about
15m are rarely observed to liquefy (Krinitzsky et al. 1993). In figure 2.7 (a), curves of
cyclic stress required for three different confining pressures are presented. Positions of
the curves are governed by the initial effective confining pressure. As the confining
pressure increases, the curves become steeper and shift upward on the diagram. In Figure
2.7 (b), it is seen that the pulsating shear stress required to cause liquefaction for a given
number of cycles increases linearly with increasing confining pressure.
Figure 2.7 Effects of confining pressure on sand liquefaction [Peacock and Seed,
1968]
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2.2.1.6 Cyclic Loading
The level of pore-pressure excess required to initiate liquefaction is related to the
amplitude and duration of earthquake-induced cyclic loading. The amount of damage to
structures on soils undergoing liquefaction depends on how long the sand remains in a
liquefied state [Prakash, 1981]. Seed [1976] concluded that the multidirectional shaking
is more sever than one-directional loading in terms of pore pressure. Pore water pressure
build up faster under multidirectional stress conditions than under unidirectional stress
conditons. Densification of soil is expected as a result of cyclic loading since the soil
particles are rearranged during the back-and-forth straining [Youd, 1972]. As cycling
continues, the pore-pressure increases progressively until finally it reaches, during part of
each subsequent cycle, the total stress acting upon the sand.
In figure 2.8, results of typical cyclic simple-shear test are presented. Initial liquefaction
(σ’=0) occurs when the pore-pressure equals the vertical total stress. The pore pressure
continues to cycle after first reaching the σ’=0 condition, which can only occur in the
absence of shear stress.
Figure 2.8 Typical simple cyclic shear test on a loose sand [Seed and Idriss, 1982]
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2.3
Ground Failures Resulting from Soil Liquefaction
Eight types of failure commonly associated with soil liquefaction in earthquakes:
•
•
•
•
•
•
•
•
Sand boils, which usually result in subsidence and relatively minor damage.
Flow failures of slopes involving very large down-slope movements of a soil
mass.
Lateral spreads resulting from the lateral displacement of gently sloping ground.
Ground oscillation where liquefaction of a soil deposit beneath a level site leads
to back and forth movements of intact blocks of surface soil.
Loss of bearing capacity causing foundations failures.
Buoyant rise of buried structures such as tanks.
Ground settlement, often associated with some other failure mechanism.
Failure of retaining walls due to increased lateral loads from liquefied backfill
soil or loss of support from liquefied foundation soils.
The nature and severity of liquefaction damage is a function of the reduced shear strength
and the magnitude of the static shear loads supported by soil deposit (Ishihara et al.
1991). Castro (1987) classifies the possible consequences of liquefaction, as shown in
table 2.1, based on the relative magnitude of static driving shear stresses that may be
present due to a surface slope or a foundation bearing load. When the driving shear loads
are greater than the reduced strength of a liquefied soil deposit, a loss of stability can
result in extensive ground failures or flow slides. However, if the driving shear stresses
are less than the shear strength (perhaps due to dilatation at large strains) only limited
shear deformations are likely. On level ground with no driving shear stresses, excess pore
pressures may break through to the surface to form sand boils; while the venting of
liquefied soil may cause settlements, damages are usually not extensive in the absence of
static shear loads.
Table 2.1 Classification of soil liquefaction consequences (after Castro1987)
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Ground failures associated with liquefaction under cyclic loading can be classified as
(Robertson et al. 1992):
(1) Flow failures, occurring when the liquefaction of loose, contractive soils (that do
not gain strength at large shear strains) results in very large deformations.
(2) Deformation failures, occurring when a liquefied soils gains shear resistance at
large strains, yielding limited deformations without loss of stability.
2.4
Behavior of Saturated, Cohesionless Soils in Undrained Shear
During an earthquake, the upward propagation of shear waves through the ground
generates shear stresses and strains that are cyclic in nature (Seed and Idriss 1982). If a
cohesionless soil is saturated, excess pore pressures may accumulate during seismic
shearing and lead to liquefaction.
A loose soil tends to compact when sheared and, without drainage, pore water pressures
increase. As indicated in Figure2.9a, a contractive soil sheared monotonically reaches a
peak shear strength and then softens, eventually achieving a residual shear resistance. If
the residual shear strength is less than the static driving shear, liquefaction flow failure
results. If the same soil is sheared cyclicly, excess pore pressures are generated with each
cycle of load. Without drainage, pore pressures accumulate and the effective stress path
moves toward failure. If the shear strength falls below the static driving stress, a flow
failure results and deformations continue after cyclic loading stops. For a liquefaction
flow failure to occur, a saturated soil with a tendency to contract must undergo undrained
shear of sufficient magnitude, or sufficient number of load cycles, for the shear resistance
to become less than the static driving load. Under these conditions, tremendous
deformations may occur before equilibrium conditions are re-established at the reduced
shear strength.
Shearing of dense, dilative soils will also produce some excess pore pressure at small
strains. However, at larger strains, the pore pressures decrease and can become negative
as the soil grains, moving up and over one another, tend to cause an increase in soil
volume (dilation). Consequently, as shown in Figure 2.9b, monotonic shearing of a
dilative soil results in an increasing effective stress and shear resistance. Figure 2.9b also
shows the response of the same dilative soil to dynamic loading. In this case, pore
pressures are generated in each shear cycle resulting in an accumulation of excess pore
pressure and deformation. However, beyond some point the tendency to dilate and
develop negative pore pressures limits further straining in additional load cycles. As
indicated in the bottom of figure 2.9b, the effective stress path moves to the left but never
reaches the failure surface. If the soil is sheared after the cyclic load ceases, the soil will
develop the full strength that would be observed in a monotonic shear test. While
significant strains can occur during cyclic loading, the very large deformations associated
with a flow failure do not develop in dense, dilative soils. Hence, cyclic shear of dilative
soils does not result in flow failures because, with undrained conditions, the shear
strength remains greater than the static driving shear stress.
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Figure 2.9 Response of (a) contractive and (b) dilative saturated sands to undrained
shear.
Robertson and Wride (1998) defined the behavior of a granular soil in undrained
monotonic triaxial compression in terms of strain hardening and strain softening
behaviors. Figure 2.10 shows a summary of the behavior of a granular soil loaded in
undrained monotonic triaxial compression. In void (e) and mean normal effective stress
(p’) space, a soil with an initial void ratio higher than ultimate state line (USL) will strain
soften (SS) at large strains, eventually reaching an ultimate condition often referred to as
critical or steady state. However a soil with an initial void ratio lower than USL will
strain harden (SH) at large strains towards its ultimate state. It is possible to have a soil
with an initial void ratio higher than but close to USL. For this soil state, the response can
show limited strain softening (LSS) to a quasi steady state (QSS) (Ishihara 1993), but
eventually, at large strains, the response strain hardens to ultimate state. During cyclic
undrained loading (e.g., earthquake loading), almost all saturated cohesionless soils
develop positive pore pressures due to the contractive response of the soil at small
strains(Robertson and Wride 1998).
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Figure 2.10 Schematic of undrained monotonic behavior of sand in triaxial
compression (after Robertson 1994).
If there is shear stress reversal, the effective stress state can progress to the point of
essentially zero effective stress, as illustrated in Fig. 2.11 for shear stress reversal to
occur, ground conditions must be generally level or gently sloping; however, shear stress
reversal can occur in steeply sloping ground if the slope is of limited height (Pando and
Robertson 1995).
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When a soil element reaches the condition of essentially zero effective stress, the soil has
very little stiffness and large deformations can occur during cyclic loading. However,
when cyclic loading stops, the deformations essentially stop, except for those due to local
pore-pressure redistribution. If there is no shear stress reversal, such as in steeply sloping
ground subjected to moderate cyclic loading, the stress state may not reach zero effective
stress. As a result, only cyclic mobility with limited deformations will occur, provided
that the initial void ratio of the sand is below the USL and the large strain response is
strain hardening (i.e. the material is not susceptible to a catastrophic flow slide).
However, shear stress reversal in the level ground area beyond the toe of a slope may
lead to overall failure of the slope due to softening of the soil in the toe region
(Robertson and Wride 1998).
Figure 2.11 Schematic of undrained cyclic behavior of sand illustrating cyclic
liquefaction (after Robertson 1994) qcy, cyclic shear stress, qst, static gravitational
shear stress.
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Figure 2.12 represents a flow chart (after Robertson 1994) for the evaluation of
liquefaction.
According to flow chart in Figure 2.12, the first step is to evaluate the material
characteristics in terms of a strain-softening or strain-hardening response. If the soil is
strain softening, flow liquefaction is possible if the soil can be triggered to collapse and if
the gravitational shear stresses are larger than ultimate or minimum strength. The trigger
mechanism can be either monotonic or cyclic. If the soil is strain hardening, flow
liquefaction generally not occur. If extensive shear stress reversal occurs, it is possible for
the effective stress to reach zero and, hence, cyclic liquefaction can take place. When the
condition of essentially zero effective stress is achieved, large deformations can result. If
shear stress reversal does not take place, it is generally not possible to reach condition of
zero effective stress and deformations will be smaller, i.e., cyclic mobility will occur.
Earthquake-induced flow liquefaction movements tend to occur after cyclic loading
ceases due to the progressive nature of the load redistribution. Cyclic liquefaction, on the
other hand, tends to occur during the cyclic loading, since it is the intertial forces that
drive the phenomenon. (Robertson and Wride 1998)
Figure 2.12 Suggested flow chart for evaluation of soil liquefaction (after Robertson
1994).
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CHAPTER 3
EVALUATION OF LIQUEFACTION
A number of approaches to evaluation of the potential for initiation of liquefaction have
developed over the years. Simplified procedures (e.g., Seed and Idriss 1971, Dobry et al.
1982, Law et al. 1990, Kayen and Mitchell 1997) are commonly used in engineering
practice. There are two approaches for the simplified procedures: (1) the cyclic stress
approach and (2) the cyclic strain approach.
3.1 Cyclic Stress Approach
The cyclic stress approach was developed by Seed and Idriss (1967) after Niigata
Earthquake. In this approach, liquefaction is evaluated based on the earthquake-induced
shear stresses and shear stresses required to cause liquefaction.
The earthquake-induced shear stresses at different depth within the soil deposit are
determined either from site response analysis or from the peak ground acceleration
expected at the site. Although the actual shear stress-time history generated by the
earthquake is not uniform, the liquefaction analysis converts these non-uniform shear
stress cycles into an equivalent number of uniform stress cycles. The equivalent cycles
are given an amplitude equal to approximately 65% of the computed maximum shear
stress and the number uniform cycles are related to earthquake magnitude. The amplitude
of the earthquake-induced shear stress is plotted versus depth within the soil deposit
(Figure 3.1).
Figure 3.1 Cyclic stress approach for the evaluation of liquefaction potential (Seed
et al. 1975)
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Seed et al. (1985) proposed boundary lines that separate conditions causing liquefaction
from conditions not causing liquefaction in sandy soils, as shown in Figures 3.2 and 3.3,
for an earthquake magnitude (M) of 7.5. These correlations remain the standard of
practice for the evaluation of level ground liquefaction resistance using the standard
penetration test (SPT) in many parts of the world.
Figure 3.2 Relationship between cyclic stress ratio triggering level ground
liquefaction and (N1)60 values for clean sand and M=7.5 earthquakes (after Seed et
al. 1985)
Figure 3.3 Relationship between cyclic stress ratio triggering level ground
liquefaction and (N1)60 values for clean sand and silty sand and M=7.5 earthquakes
(after Seed et al. 1985)
3.1.1 Evaluation of Cyclic Stress Ratio
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Seed et al. (1985) used equivalent cyclic stress ratio CSReq, to represent the intensity of
earthquake loading. Since CSReq pertains to a certain number of equivalent laboratory
loading cycles corresponding to a given earthquake magnitude, Stark and Mesri (1992)
proposed the term seismic (shear) stress ratio, SSR, to describe earthquake loading. They
suggested that SSR is more descriptive of field earthquake loading than equivalent cyclic
stress ratio.
Seed and Idriss (1971) proposed the “simplified” equation to estimate the equivalent
cyclic shear stress ratio (or seismic shear stress ratio) induced by an earthquake. The
resulting seismic (shear) stress ratio is defined as:
SSR = CS Re q =
τave
τ max
a max σvo
≈ 0.65
≈ 0.65
rd
σ ' vo
σ ' vo
g σ ' vo
(3.1)
where the τave is the average earthquake-induced shear stress, τmax is the maximum
earthquake-induced shear stress, σ’vo is the vertical effective stress, amax is the maximum
earthquake acceleration at the ground surface, g is the acceleration of gravity, σvo is the
vertical total stress, and rd is a depth reduction factor to account for the flexibility of the
soil column.
3.2
Cyclic Strain Approach
The cyclic strain approach for evaluating the liquefaction potential was first introduced
by Dobry et al. (1982). In this approach, shear strain, rather than shear stress, is the main
parameter that controls both densification and liquefaction in sands. Dobry et al. (1982)
found a strong relationship between cyclic shear strain and pore water pressure
generation, as presented in Figure 3.4. The data shown in Figure 3.4 were obtained from
cyclic strain-controlled triaxial tests performed on two types of clean sands. The pore
water pressure response of both sands after ten loading cycles revealed the existence of a
cyclic threshold shear strain of approximately 0.01%, below which no densification of the
soil (if allowed to drain) or pore water pressure generation occurs. The trend of these data
also showed that approximately 10 cycles of 1% cyclic shear strain would generate a pore
water pressure ratio of 1.0, which corresponds to zero effective stress and thus initial
liquefaction of the specimen.
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Figure 3.4 Measured pore water pressure in saturated sands after ten loading cycles
in strain-controlled cyclic triaxial tests (Dobry et al. 1982)
3.2.1 Evaluation of Cyclic Shear Strain (γc)
The evaluation of liquefaction potential in the cyclic strain approach is based on the
prediction of pore water pressures from the earthquake-induced cyclic shear strain and
the expected number of strain cycles. The cyclic shear strain, γc, is calculated by:
γc =
a max σvo
τav
= 0.65
rd
G (γc)
g G (γc)
(3.2)
where amax is the peak horizontal acceleration at the ground surface; g is the acceleration
of gravity; σvo is the initial total vertical stress at the depth of interest; G (γc) is the shear
modulus of the soil at shear strain level, γc, and rd is the stress reduction factor at the
depth of interest to account for the flexibility of the soil column. Equation 3.2 must be
used iteratively, as the value of G is based on the computed value of γc. A modulus
reduction curve (e.g., Darendeli and Stokoe 2001) can be used along with a measured
value of Gmaxto predict G as a function of γc.
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3.3
Characterization of Liquefaction Resistance
The liquefaction resistance of an element of soil depends on how close the initial state of
the soil is to the state corresponding to “failure” and on the nature of the loading required
to move it from the initial state to the failure state (Kramer, 1996). Two basic approaches
have been used to predict the liquefaction potential of soil strata (De Alba et al. 1976;
Seed 1979; Seed et al. 1983):
(1) Evaluations based on a comparison of the stresses induced by an earthquake and
the stress conditions causing liquefaction in cyclic laboratory tests on soil
samples.
(2) Empirical methods based on measurements of in situ soil strength and
observations of field performance in previous earthquakes.
3.3.1
Characterization of Liquefaction Resistance Based on Laboratory Tests
In the field, prior to the dynamic earthquake loading, the soil is assumed to be in the at
rest (Ko) condition, as represented in Figure 3.5a. The upward propagation shear waves
produce an irregular, yet cyclic, history of dynamic shear stresses on the horizontal and
vertical planes. The duration of the cyclic loading is usually assumed to be short enough
that the water cannot dissipate and thus the soil responds undrained during dynamic
loading. In laboratory testing, it is important to duplicate the in situ loading conditions as
accurately as possible. There are three major types of laboratory tests used to study
liquefaction. These are: (1) triaxial tests, (2) torsional shear tests, and (3) direct simple
shear tests. The extend to which these tests are capable of simulating the stress state
induced by a seismic event depends on the nonuniformities of stresses and strains
induced in the sample, the rotation of the principal stress axes, and duplication of the
plane strain condition. Also, each testing method imposes a slightly different stress
condition on the specimen, which leads to different testing results. For this study cyclic
triaxial test is used to evaluate liquefaction susceptibility at the HMG site, which is in the
university campus of Grenoble. Details of cyclic triaxial test are explained here.
(a) Idealized field loading conditions
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(b) Shear stress variation determined by response analysis
Figure 3.5 Cyclic shear stresses beneath level ground during seismic loading (Seed
1979)
3.3.1.1 CYCLIC TRIAXIAL TESTING
Cyclic triaxial testing for liquefaction evaluation was first performed by Seed and Lee
(1966). In this type of testing, a cylindrical soil specimen formed in a latex membrane is
contained in a cell. The sample is initially consolidated under an effective confining
pressure σo’ and then subjected to a cyclic axial stress of σd under undrained conditions
until initial liquefaction occurs or a specified axial strain level is reached. The stresses on
a plane of 45° through the sample are analogous to those produced on a horizontal plane
in situ during an earthquake. A typical triaxial configuration and simulation of the
stresses during a cyclic triaxial test are shown in Figures 3.6 and 3.7, respectively. An
increase of σd in the axial stress induces a shear stress of σd/2 on the 45° plane. When the
direction of the axial stress is reversed, the direction of the shear stress on the 45° plane is
also reversed. Hence, the 45° plane is subjected to a cyclic shear stress of σd/2 in the
opposite direction.
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Figure 3.6 Diagram of triaxial test equipment (after Bishop and Bjerrum, 1960)
Figure 3.7 Cyclic stresses in a cyclic triaxial test (Ishihara 1996)
24
Cyclic triaxial tests have been successfully used to determine the liquefaction resistance
of granular soils. As a result of many studies, it has been shown that the liquefaction
resistance of reconstituted sand specimens is primarily influenced by initial confining
stress, intensity of shaking, the number of loading cycles, and void ratio (Ishihara 1996).
The effects of initial confining stress and cyclic stress ratio are usually combined in terms
of the cyclic stress ratio, CSR=τ/σo’=σd/2σo’, where σd is deviator stress and σo’ is the
initial effective confining pressure. Hence, the cyclic strength of sand can be
characterized by varying the density of samples and measuring the number of cycles to
liquefaction for various cyclic stress ratios. Figure 3.8 presents such measurements from
cyclic triaxial test performed on undisturbed and reconstituted sand specimens.
Figure 3.8 Cyclic strength of sands in terms of cyclic stress ratio versus number of
loading cycles (Yoshimi et al. 1989)
25
3.3.2
Characterization of Liquefaction Resistance Based on In Situ Tests
To evaluate the liquefaction resistance (shear stress required to cause liquefaction in a
number of loading cycles), cyclic laboratory testing on representative samples can be
performed or the liquefaction resistance can be correlated with in situ tests such as the
Standard Penetration Test (SPT). When performing laboratory tests, the tests provide data
regarding the shear stress level that causes liquefaction in the number of expected
earthquake loading cycles. This is sometimes called cyclic strength. When using in situ
correlations, the shear stress level required to cause liquefaction in a given number of
cycles is empirically related to in situ test parameters such as SPT blow count (N1,60; Seed
et al. 1985), the Cone Penetration Test (CPT) tip resistance (qc1n; Robertson and Wride
1998) or soil shear wave velocity (Vs1; Andrus and Stokoe 2000).
Unfortunately, liquefaction assessments based on laboratory tests are hindered by
limitations in the ability of laboratory equipment to reproduce field stress conditions in
small soil samples. Even more problematic, disturbance of filed samples is nearly
impossible to avoid and very difficult to quantify in laboratory tests (Seed 1979). As a
result, early evaluations based on laboratory tests were often overly conservative in
predicting liquefaction (Peck 1979). Because the empirical correlations are simple and
incorporate a limited number of parameters, the simplified procedure is widely used in
practice.
3.3.2.1 Method Based on the Standard Penetration Test
Seed et al. (1985) investigated sites that did and did not experience liquefaction during
earthquakes. The empirical chart published by Seed et al. (1985) is based on a
standardized SPT blowcount, (N1)60, and the cyclic stress ratio (CSR). To get (N1)60, the
measured NSPT is corrected for the energy delivered by different hammer systems and
normalized with respect to overburden stress. Seed et al. found that for the same stresscorrected penetration resistance, (N1)60, the liquefaction resistance increases with
increasing fine content (Figure 3.9).
26
Figure 3.9 Relationship between stress ratio causing liquefaction and (N1)60 values for
silty sand for event of magnitude M=7.5(Seed et al. 1985)
3.3.2.1.1
Evaluation of SPT Penetration Resistance
Seed et al. (1985) used corrected blowcount (N1)60 to represent soil resistance to
porewater pressure increase because of the variability of SPT systems. The corrected
blowcount, (N1)60, is defined as the SPT blowcount at a vertical effective stress of 100kPa
and an energy level equal to 60% of the theoretical free-fall hammer energy applied to
the drill stem. Seed et al. (1985) proposed a “standard” blowcount, N60, which
corresponds to a transfer of approximately 60% of the theoretical free-fall hammer
energy. Seed et al. (1985) suggested the following equation to correct various SPT energy
ratios to energy ratio of 60% for use in liquefaction analyses:
⎛ ER ⎞
N 60 = N .⎜
⎟
⎝ 60 ⎠
(3.3)
where ER is the energy ratio (percent of the theoretical free-fall energy) of the SPT
hammer system and N is the field blowcount. The value of N60 is corrected to a vertical
effective stress of approximately 100 kPa by multiplying N60 by the overburden
correction factor, CN, which (as presented below) is slightly modified from Liao and
Whitman (1986):
27
⎛ Pa ⎞
( N1)60 = N 60.Cn = N 60.⎜
⎟
⎝ σ ' vo ⎠
n
(3.4)
where Pa is one atmosphere of pressure in the units of σ’vo and n is equal to 0.5 for
sands. The value of (N1)60 must then be corrected for borehole diameter, rod length, and
sampling spoon configuration (Youd and Idriss 1997).
3.3.2.2 Method Based on the Cone Penetration Test
Because the SPT is subject to numerous corrections including energy ratio, overburden
correction, borehole diameter, rod length, and sampling method (Youd and Idriss, eds.,
1997), several researchers (e.g., Robertson and Campanella 1985, Seed and de Alba
1986, Shibata and Teparaksa 1988, Stark and Olson 1995, etc.), have investigated the use
of the cone penetration test to estimate the level ground liquefaction resistance of sandy
soils.
The CPT has 5 main advantages over the usual combination of boring, sampling and
standard penetration testing:
1. it can be more economical to perform than the SPT, which allows a more
comprehensive subsurface investigation.
2. the test procedure is simpler, more standardized, and more reproducible than the
SPT.
3. it provides a continuous record of penetration resistance throughout a soil deposit,
which provides a better description of soil variability and allows thin (greater than
15 cm in thickness) liquefiable sand or silt to be located and properly
characterized. This is particularly important in sands and silts because of the
natural non-uniformity of these deposits.
4. it avoids the disturbance of ground associated with boring and sampling,
particularly that which occurs with Standard Penetration Test (SPT).
5. it is faster by a factor of 10.
Based on these advantages, it is desirable to develop relationships between CPT tip
resistance and liquefaction resistance, rather relying on a conversion from SPT
blowcount to CPT tip resistance to develop CPT based liquefaction resistance
relationships.
The main reasons why the CPT has not been used extensively for liquefaction
assessment are:
•
•
•
The lack of a sample for soil classification and grain size analysis.
A limited amount of CPT based field data pertaining to liquefaction resistance
was available
Limited availability of cone penetration test equipment in some locales.
28
During a CPT, an electrical cone on the end of a series of rods is pushed into the ground
at a constant rate of 2cm/s. Continuous measurements are made of resistance to
penetration of the cone tip (qc) and the frictional resistance (fs), or adhesion, on a surface
sleeve set immediately behind the cone end assembly. Measurements can also be made of
other soil parameters using more specialized cones such as poer water pressure
(piezecone), electrical conductivity, shear wave velocity (seismic cone), and
pressuremeter cone.
The CPT has three main applications;
1. To determine the soil profile and identify the soil present
2. To interpolate ground conditions between control boreholes.
3. To evaluate the engineering parameters of the soils and to asses the bearing
capacity and settlement of foundations.
In this third role, in relation to certain problems, the evaluation is essentially preliminary
in nature, preferably supplemented by borings and other tests, either in situ or in the
laboratory. In this respect, the CPT provides guidance on the nature of such additional
testing, and helps to determine the positions and levels at which in situ tests or sampling
should be undertaken. Where the geology is fairly uniform and predictions based on CPT
results have been extensively correlated with building performance, the CPT can be used
alone in investigation for building foundations.
Even in these circumstances it is preferable that CPTs be accompanied by, or followed
by, borings for one or more of the following reasons:
1.
2.
3.
4.
To assist where there is difficulty in the interpretation of the CPT result.
To further investigate layers with relatively low cone resistance.
To explore below the maximum depth attainable by CPT.
If the project involves excavation, where samples may be required for laboratory
testing and knowledge of ground water levels and permeability is needed.
3.3.2.2.1 Evaluation of CPT ¨Penetration Resistance
Penetration resistance from CPT, similar to SPT blowcount, is influenced by soil density,
soil structure, cementation, aging, stress state, and stress history, and thus can be used to
estimate liquefaction resistance (Robertson and Campenalla 1985). The corrected CPT tip
resistance qc1N, is obtained as follows:
qc1
⎛ qc ⎞
qc1N = ⎜
⎟Cq =
Pa 2
⎝ Pa 2 ⎠
(3.5)
(
where qc is the measured cone tip penetration resistance; Cq = Pa
σ ' vo )
n
is a correction
for overburden stress; the exponential n is typically equal to 0.5; Pa is a reference
pressure in the same units as σ ' vo (i.e., Pa=100 kPa if σ ' vo is in kPa); and Pa2 is a
reference pressure in the same units as qc (i.e., Pa2 =0.1 Mpa if qc is in MPa)
29
The recommended cyclic resistance ratio for clean sands under level ground conditions
by Robertson and Wride (1998) is seen in Figure 10, corrected CPT tip resistance, qc1N
versus cyclic resistance ratio.
Figure 10. Recommended cyclic resistance ratio (CRR) for clean sands under level
ground conditions based on CPT.γ1, limiting shear strain. Corrected CPT tip penetration
versus CRR. Robertson and Wride (1998)
3.3.2.3 Piezocone (CPTU)
The Piezocone is a CPT including a pore-pressure transducer allowing the measurement
of the pore-pressure changes close to the point induced by the penetration. Pore pressure
changes ∆u;
•
•
•
is a local measurement generally just behind the tip, and is extremely sensitive to
small changes in the soil. Very thin layers of potentially liquefiable sand can be
detected from the pore pressure data.
∆u can give an indication of the dilative (∆u<0) or contractive (∆u>0) behavior of
the soil.
dissipation test can be performed after a given penetration, giving an assessment
of the horizontal permeability of the soil and evaluation of the drainage conditions
in an earthquake situation.
30
The cone penetrometer consists of the cone, friction sleeve, any other sensors and
measuring systems, as well as the connections to push rods. Most commonly are used the
tip resistance + sleeve friction (CPT) and the tip resistance, sleeve friction + pore water
pressure (CPTU) Figure 3.11.
For the evaluation liquefaction susceptibility a piezocone test and Cone Penetration Test
(CPT) were carried out at the site of the Engineering School of Hydraulics and
Mechanics of Grenoble (HMG). Method for evaluating liquefaction susceptibility using
cone penetration test is explained in the next chapter
FIGURE EKLE
Figure 3.11 Cone Penetrometer
31
3.3.2.4 Soil Identification by CPT and CPTU
In the recent years, charts have been developed to estimate soil type from CPT data
(Olsen and Malone 1988; Olsen and Koester 1995; Robertson and Campanella 1988;
Robertson 1990). Experience has shown that the CPT friction ratio (ratio of the CPT
sleeve friction to the cone tip resistance) increases with increasing fines fines content and
soil plasticity. Hence, grain characteristics such as apparent fines content of sandy soils
can be estimated directly from CPT data using any of these soil behavior charts, such as
that by Robertson (1990) shown in Figure 3.12.
Figure 3.12 Soil behavior type classification chart based on normalized CPT/CPTU data
(after Robertson, 1990). Soil types: 1, sensitive, fine grained; 2, peats; 3, silty clay to
clay;4, clayey silt to silty clay; 5, silty sand to sandy silt; 6,clean sand to silty sand; 7,
gravelly sand to dense sand; 8, very stiff
where:
u 2 − u0
Bq =
qt − σv0
F = [ fs / (qc − σvo )]100 is the normalized friction ratio, in percent.
fs is the CPT sleeve friction stress;
Qt =
qt − σvo
σ ' vo
u2 = pore pressure measured between the cone and the friction sleeve
u0 = equilibrium pore pressure
σv0 = total overburden stress
qt = cone resistance corrected for unequal end area effects
σ ' vo = effective overburden stress
(3.6)
(3.7)
(3.8)
32
CHAPTER 4
Evaluation of Liquefaction Susceptibility in Grenoble Basin Using Cone Penetration
Test (CPT)
4.1. Seismotectonic Frame of the Grenoble Valley
4.1.1 Geography of the Y-shaped Grenoble Valley
Grenoble is settled on Quarternary loose fluvial deposits at the junction of 3 large
valleys of the French external Alps (Figure 4.1). This junction mimics the letter Y
(the so-called Grenoble Y), with three legs:
1. The N.30-40 trending Gresivaudan valley corresponds to the northeastern branch of the Y and extends from Grenoble to Montmelian.
The Isere River there flows to the SSW. The Combe-de-Savoie Valley
continues the Gresivaudan valley north of Montmelian.
2. The N.150 trending north-western branch is called Cluse-de-l’Isere
from Grenoble to Moirans. There the Isere Rivers flows to the NW.
3. The N.10 trending leg of the Y corresponds to the plain of the Drac
River, spanning 15 km south of Grenoble.
There three valleys delineate three massifs. The Belledone external crystalline massif lays
east of the Gresivaudan valley and the Drac plain. The N.30 trending sub alpine
sedimentary Chartreuse massif lays between the Gresivaudan and the Cluse-de-l’Isere
valleys. The subalpine sedimentary Vercors massif is located SW of the Cluse-de-l’Isere
and west of the Drac plain.
4.1.2 Structure of the Isere Valley
From 110 km, from Albertville in the NE to Rovon west of the Vercors massif, the Isere
valley (Gresivaudan, Cluse-de-l’Isere, basse-Isere) is flat, with slowly decreasing
altitudes (330m in Albertville, 211m in Grenoble, 180m in Rovon). Its morphology with
asymmetrical inclined sides and longitudinal moraines on the glacial shoulders indicates
that glaciers contributed to shape the present topography. These glaciers (Isere glacier,
local glaciers of the Belledonne massif, Drac-Romanche glacier) followed the fluvial
valley of the Isere River created as early as the end of the Tertiary. The geometry of the
glacial through beneath the flat surface constituted by the post-glacial infilling sediments
is still poorly known.
33
Figure 4.1 Grenoble topographic and tectonic framework. Light grey: sedimentary
Mesozoic cover of Vercors, Chartreuse, Bauges massifs and Belledone border hills.
Dark grey with crosses: Paleozoic crystalline basement. Dotted: bas-Dauphine
Tertiary and Quaternary depositis. White: Quaternary alluvium of the Isere valley.
Thick dashed line: Belledone Border Fault trace. BMF: Belledone Middle Fault
34
4.2Seismicity of the Grenoble Area
The western Alps (Fig 4.2) result from the Europe-Africa convergence and from the
indentation of the European margin by the Adria microplate (e.g. Tapponnier, 1977; Platt
et al., 1989; Lemoine et al., 2000). The Penninic Frontal Thrust- the main tectonic
boundary between the outer (French) Alps and the inner (Italian) Alps- and the L-shaped
wedge of the external crystalline massifs still express this collision. The resulting
seismicity is moderate, with only one ML> 3.5 event per year.
Figure 4.2 Schematic map of the western Alps, with the external crystalline
massifs (shaded) and the Penninic Frontal (barbed line). CH= Switzerland; F=
France, I= Italy; A.R=Aiguilles Rouges, Mt Bl.= Mont Blanc.
The Grenoble area has been known for centuries as prone to earthquakes, although
intensities larger than VIII MSK were never observed (Thouvenot et al., 2003). Two
largest damaging earthquakes struck in 1962 and 1963. The Correncon earthquake (25
April 1962, ML=5.3) occurred in the north-eastern part of the Vercors massif. On 25
April 1963 the ML=4.9 Monteynard earthquake reached a maximum intensity of VII.
35
Seismicity maps of the Grenoble area for 1989-2004 and 1356-1988 periods are seen in
the Figure 4.3 (a) and (b), respectively. In Figure 4.3(a), seismic stations are shown by
triangles, (black= permenant; grey= temporary); BBF= Belledone Border Fault; Laffrey
EQ = position of the most recent damaging earthquake on the BBF (Laffrey Earthquake,
1999, ML=3.5). In Figure 4.3(b) historical seismicity for the 1356-1988 period is seen,
after Thouveno et al. (2003); circles= good quality; hexagons= low quality. For Figure
4(b), maximum intensities converted to magnitude using the relation M=0.44Im + 1.96
derived from Levre et al. (1996).
Figure 4.3 Seismicity maps of the Grenoble area. (a) Instrumental seismicity for the
1989-2004 period. (b) Historical seismicity for the 1356-1988 period, after Thouveno
et al. (2003).
Geology and seismicity studies indicate the possibility of earthquakes as large as M5-5.5
in the Grenoble area. A right-lateral, strike-slip event is likely to occur on the fault
located along the Belledone massif to the east of the basin (N30). An overthrusting
structure corresponding to subalpine mountain ranges, located just beneath the city of
Grenoble, is also capable of producing a significant event. For this study, liquefaction
potential in the Grenoble basin was calculated by taking into account Mw= 5.25
earthquake.
36
4.3
Evaluation of the Liquefaction Susceptibility in the Grenoble Basin
For the evaluation of liquefaction susceptibility a piezecone test and Cone Penetration
Test (CPT) were carried out at the site of the Engineering School of Hydraulics and
Mechanics of Grenoble (HMG). CPT and piezecone tests were done until 6.8 meters
depth, below which dense gravel layer prevented penetration. Intact samples were
obtained by drilling from 1.7 to 2.8 meters and from 3.0 to 4.3 meters. Intact samples are
used to obtain cyclic resistance ratio of the soil by cyclic triaxial test. Initially water table
is assumed at the depth of 3.6 meters, thus piezecone profile begins at 3.6 meters depth.
11 dissipation tests were carried out at 3.71m, 3.98m, 4.18m, 4.42m, 4.77m, 5.26m,
5.55m, 5.87, 6.19m, 6.32m, 6.68m depths to obtain t50 values.
4.3.1
Evaluation of Liquefaction Susceptibility using Cone Penetration Test
For this study, the proposed integrated method by Robertson and Wride (1998) is applied
using magnitude-dependent stress reduction factor (rd) and magnitude scaling factor
(MSF) which are defined by Idriss and Boulanger (2004) for the evaluation of
liquefaction potential. Liquefaction potential in the Grenoble basin was calculated by
taking into account Mw= 5.25 earthquake. The proposed integrated method by Robertson
and Wride (1998) is summarized in Figure 4.5 in the form of a flow chart.
∆u and t50 values are obtained using piezecone. ∆u and t50 are the excess pore water
pressure due to penetration and, the time in which 50% of the over pore water pressure is
dissipated during a dissipation test, respectively. ∆u=u-u0, u0 is the hydrostatic pore water
pressure.
The CPT cone tip resistance, (qc) and friction ratio (F) are used to estimate soil grain
characteristics in terms of “soil behaviour type index” (Ic). Ic was calculated by iteration.
The final continuous profile of CRR at N=15 cycles (M=7.5) is calculated from the
equivalent clean sand values of qc1N (i.e., (qc1N)cs=Kcqc1N)
Cyclic stress ratio for Mw=5.25 earthquake is calculated by using simplified procedure
by Seed and Idriss (1971);
CSR =
⎛ a max ⎞⎛ σvo ⎞
τav
⎟⎟⎜
= 0.65⎜⎜
⎟rd
σ ' vo
⎝ g ⎠⎝ σ ' vo ⎠
(4.1)
where τav is the average cyclic shear sress; amax is the maximum horizontal acceleration
at the ground surface; g is the acceleration due to the gravity; σvo and σ ' vo are the total
and effective vertical overburden stresses, respectively; and rd is the stress reduction
factor.
rd stress reduction coefficient, magnitude scaling coefficient, MSF, cyclic resistance ratio,
CRR, soil type index, Ic, and apparent fines content are calculated as explained in the
following sections.
37
Figure 4.5 Flow chart illustrating the application of the integrated CPT method of
evaluating cyclic resistance ratio (CRR) in sandy soils.
38
4.3.1.1 Stress Reduction Coefficient, rd
Seed and Idriss (1971) introduced the stress reduction coefficient rd as a parameter
describing the ratio of cylic stresses for a flexible soil column to cylic stresses for a rigid
soil column. Idriss (1999), in extending the work of Golesorkhi (1989), performed
several hundred parametric site response analyses and concluded that for the conditions
of most practical interest, the parameter rd could be adequately expressed as a function of
depth and earthquake magnitude (M). The following relation was derived using those
results;
Ln(rd ) = α ( z ) + β ( z ) M
(4.2a)
⎛ z
⎞
+ 5.133 ⎟
⎝ 11.73
⎠
α ( z ) = −1.012 − 1.126 sin ⎜
⎛ z
⎞
+ 5.142 ⎟
⎝ 11.28
⎠
β ( z ) = 0.106 + 0.118 sin ⎜
(4.2b)
(4.2c)
in which z is depth in meters and M is moment magnitude. Plots of rd calculated using
equation 4.2 for M= 5.5, 6.5, 7.5 and 8.0 are presented in Figure 4.5. Also shown in this
figure is the average of the range published by Seed and Idriss in 1971 (Idriss and
Boulanger 2004).
Figure 4.5 Variations of stress reduction coefficient with depth and earthquake
magnitude (from Idriss 1999).
39
4.3.1.2 Calculation of Magnitude Scaling Factor, MSF
The magnitude scaling factor, MSF, has been used to adjust the induced CSR during
earthquake magnitude M to an equivalent CSR for an earthquake magnitude, M = 7.5.
The MSF is thus defined as:
MSF = CSRM/CSRM=7.5
Thus, MSF provides an approximate representation of the effects of shaking duration or
equivalent number of stress cycles.
The MSF relation was expressed by Idriss (1999) as:
⎛−M ⎞
MSF = 6.9 exp⎜
⎟ − 0.058
⎝ 4 ⎠
MSF ≤ 1.8
(4.3a)
(4.3b)
The values of MSF obtained using equation 4.3 are presented in figure 4.6, together with
those proposed by others (Idriss and Boulanger 2004).
Figure 4.6 Magnitude scaling factor, MSF, values proposed by various investigators
40
4.3.1.3 Calculation of Cyclic Resistance Ratio, CRR
The CRR-qc1N relation is expressed by Idriss and Boulanger (2004) as:
⎧⎪ qc1Ncs ⎛ qc1Ncs ⎞ 2 ⎛ qc1Ncs ⎞ 3 ⎛ qc1Ncs ⎞ 4
⎫⎪
+⎜
CRR = exp⎨
(4.4)
⎟ −⎜
⎟ +⎜
⎟ − 3⎬
⎪⎩ 540
⎪⎭
⎝ 67 ⎠ ⎝ 80 ⎠ ⎝ 114 ⎠
where qc1N is the dimensionless normalized cone penetration resistance, corrected for a
vertical effective stress of 100 kPa. qc1N in equation (4.4) refers to clean sand data (fines
content < 5%).
qc1
⎛ qc ⎞
qc1N = ⎜
(4.5)
⎟Cq =
Pa 2
⎝ Pa 2 ⎠
qc1Ncs = Kcqc1N
(4.6)
Kc: CPT grain characteristics correction factor
If Ic ≤ 1.64
Kc = 1
(4.6a)
If Ic > 1.64
Kc = −0.403Ic 4 + 5.581Ic 3 − 21.63Ic 2 + 33.75Ic − 17.88
(4.6b)
(
where qc is the measured cone tip penetration resistance; Cq = Pa
)
n
σ ' vo
is a correction
for overburden stress; the exponential n is typically equal to 0.5; Pa is a reference
pressure in the same units as σ ' vo (i.e., Pa=100 kPa if σ ' vo is in kPa); and Pa2 is a
reference pressure in the same units as qc (i.e., Pa2 =0.1 Mpa if qc is in MPa)
This CRR-qc1N relation is compared in Fig 4.7 to those by Shibata and Teparaksa,
Robertson and Wride, Suzuki et al., and the 5% probability curve by Moss as
summarized in Seed et al. (Idriss and Boulanger 2004).
Figure 4.7 CPT-based case histories and recommended relation for clean sand with
relations proposed by others (Idriss and Boulanger 2004).
41
4.3.1.4 Grain Characteristics from the CPT and the Calculation of Ic “Soil Type
Index”
Using the CPT chart by Robertson (1990), the soil behaviour type index, Ic, can be
defined as follows;
[
Ic = (3.47 − Q ) + (log F + 1.22)
2
⎛ qc − σvo ⎞⎛ Pa ⎞
where Q = ⎜
⎟⎜
⎟
⎝ Pa 2 ⎠⎝ σ ' vo ⎠
]
2 0.5
(4.7a)
n
(4.7b)
Q is the normalized CPT penetration resistance (dimensionless); the exponent n is
typically equal to 1.0; F = [ fs / (qc − σvo )]100 is the normalized friction ratio, in percent;
fs is the CPT sleeve friction stress; σvo and σ ' vo are the total and effective overburden
stresses, respectively; Pa is a reference pressure in the same units as σ ' vo (i.e., Pa=100
kPa if σ ' vo is in kPa); and Pa2 is a reference pressure in the same units as qc and σvo (i.e.,
Pa2=0.1 MPa if qc and σvo are in MPa).
Figure 4.8. Normalized CPT soil type chart, as proposed by Robertson (1990). Soil
types: 1, sensitive, fine grained; 2, peats; 3, silty clay to clay;4, clayey silt to silty
clay; 5, silty sand to sandy silt; 6,clean sand to silty sand; 7, gravelly sand to dense
sand; 8, very stiff sand to clayey sand (heavily overconsolidated or cemented); 9,
very stiff, fine grained (heavily overconsolidated or cemented). OCR,
overconsolidation ratio; ϕ ' , friction angle.
42
Ic is calculated iteratively. It is recommended to use first n=1 to calculate Q and,
therefore, an initial value of Ic for CPT data. If Ic>2.6, the data should be plotted directly
on the Robertson chart (and assume qc1N=Q). However, if Ic ≤ 2.6, the exponent to
calculate Q should be changed to n=0.5 and Ic should be recalculated based on qc1N and
F. if the recalculated Ic remains less than 2,6, the data should be plotted on the Robertson
chart using qc1N based on n=0.5. if, however, Ic iterates above and below a value of 2.6,
depending which value of n is used, a value of n=0.75 should be selected to calculate qc1N
And plot data on the Robertson chart. The boundaries of soil behavior type are given in
terms of the index, Ic, as shown in table 4.1.
Table 4.1 Boundaries of soil behavior type (after Robertson 1990)
Soil behavior type index increases with increasing apparent fines content and soil
plasticity (Figure 4.9). Soil behavior type index is linked to fines content as follows;
if Ic < 1.26 apparent fines content FC(%) = 0
if 1.26 ≤ Ic ≤ 3.5 apparent fines content FC(%) =
if Ic > 3.5 apparent fines content FC(%) = 100
1.75Ic
3.25
− 3.7
(4.8a)
(4.8b)
(4.8c)
43
Figure 4.9 Variation of CPT soil behavior type index (Ic) with apparent fines content by
Robertson (1990). PI, plasticity index.
4.3.1.5 Evaluation of Factor of Safety
In evaluating the liquefaction potential of a saturated sand deposit under some postulated
earthquake conditions, it is customary to express the results in terms of a factor of safety
(FS) against liquefaction;
CRR
(4.7)
CSR
As a general guideline, acceptable factors of safety range from about 1.25 to 1.5, though
values outside this range may sometimes be accepted (Seed and Idriss 1982). For this
study factor of safety =1.3 is chosen to identify the layers which have liquefaction
potential in HMG site.
FS =
44
4.3.2
Results of Evaluation of Liquefaction Susceptibility by CPT in HMG site
4.3.2.1 Identification of Soil Layer using CPT and CPTU Results
Figure 4.10 presents the result of the cone penetration test. qc for the CPT, F (friction
ratio) and qc for the piezocone test are seen in this figure. Soil layers were classified in
terms of “soil type index” (Ic). There is silty sand between depths of 1.3m and 2.9m with
average fines content of 28%. Between depths of 2.9m and 3.6m there is a sandy silt
layer with a small thickness of clayey silt with average fines content of 18%. Between
3.6m and 4.5m silty sand layer with average fines content of 15% is identified. This is
followed by a dense sandy gravel layer between 4.5m and 5.4m. After 5.4m, there is a
heterogeneous layer which consists of loose silty sand and silty clay layers between 5.4m
and 6.4m. Between the last 6.4m and 6.8m sandy gravel layer is identified.
qc (Mpa), F(%)
0
5
10
15
20
0
1
2
Silty Sand
Depth (m)
3
Clayey Silt, Sandy Silt
4
5
6
Silty Sand
qc
F
piezecone
Sandy Gravel
Silty Clay, Silty Sand
Sandy Gravel
7
8
Figure 4.10 Plot of qc, F for CPT and qc for piezecone test.
In this figure 4.10, it is also seen that qc profiles from CPT and piezocone are consistent
with each other after 3.6 meters.
45
Soil classification is also done with CPTU result. Soil layers are classified by using
Bq- Qt relation, Figure 4.11 Robertson (1990). The changes in Bq value with depth is
seen in Figure 4.12. There is a silty sand layer between 3.6m and 4.5m. From 4.5m to
5.4m there is a heterogeneous layer consists of sandy gravel, silty sand layer and this is
followed by silty clay layer between 5.6m and 6.4m. From 6.4m to 6.8m there is another
heterogeneous layer with silty sand, gravelly sand stratifications.
It can be concluded that the results of soil classifications which are obtained by using
friction ratio (F) in terms of “soil type index Ic” and the results obtained by using Bq
value are consistent.
Bq-Qt
300
250
Depth 3.6m-4.5m
Depth 4.5m-5.4m
Dept 5.6m-6.4m
Depth 6.4m-6.8m
Qt
200
150
100
50
0
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Bq
Figure 4.11 Soil behavior type classification chart based on normalized CPTU data
(after Robertson, 1990). Soil types: 1, sensitive, fine grained; 2, peats; 3, silty clay to
clay;4, clayey silt to silty clay; 5, silty sand to sandy silt; 6,clean sand to silty sand; 7,
gravelly sand to dense sand; 8, very stiff
46
Bq
-0,05
-0,04
-0,03
-0,02
-0,01
0
0,01
0,02
0,03
0,04
0,05
3,5
Silty Sand
4
4,5
Sandy Gravel
5
Bq
5,5
Silty Clay, Silty Sand
6
6,5
Sandy Gravel
7
Figure 4.12 Changes in Bq ( Bq =
u 2 − u0
) with depth
qt − σv0
Using the piezecone test which was carried out at 0.5 meter horizontal distance from the
CPT test, total pore water pressure between 3.6m and 6.8m were obtained. In figure 4.13
the total pore water pressure (u), hydrostatic water pressure (u0) are seen with respect to
depth. In this plot we also see the type of soil layers which were defined using Ic for
corresponding depth intervals. Initially water table is assumed at the depth of 3.6 meters,
thus piezecone profile begins at 3.6 meters depth.
U and Uo (kPa)
-50
0
50
100
3,5
Silty Sand
4
4,5
Sandy Gravel
5
U
U0
Dissipation Test
5,5
Silty Clay, Silty Sand
6
6,5
Sandy Gravel
7
Figure 4.13 Changes in Pore water pressure, hydrostatic water pressure
47
Figure 4.14 is showing the changes in excess pore pressure during CPTU test. As it is
seen in Figure 4.14, in the layers from 3.6m to 4.5m and from 4.5m to 5.4m, excess pore
water pressures are negative. At the depth of 4.2m to 4.3m positive excess pore water
pressures are seen. At the depth of 5.66m, 6.0m, and 6.32m negative excess pore
pressures are observed while at 5.87 and 6.26m positive excess pore water pressures are
met. At 6.32 m there is a strong negative excess pore water pressure, which may be
because of the existing dense gravel layer and impermeability of the clayey layer above
the gravel layer. There are positive spikes at 5.87m, which corresponds to thin layer of
sandy silt and another positive spike in excess pore pressure at 6.19m, which corresponds
to a thin clayey silt layer.
Between the 4.5m and 5.4m excess pore water pressures are very close to zero, which
may result from the high permeable sandy gravel layer.
From the result of the excess pore water pressure, dilative behavior of the soil is expected
in the layers where ∆u<0, and on the other hand, contractive behavior of the soil is
expected in the layers where ∆u>0. Since the liquefaction is precisely related to
contractive behavior of the soil, we can assume that the soil is susceptible to flow
liquefaction when ∆u>0 if there is a strong enough disturbance to move the effective
stress path from its initial point to flow liquefaction surface (FLS).
∆U
-50
0
50
100
3,5
Silty Sand
4
Depth (m)
4,5
Sandy Gravel
5
Delta U = U - Uo
5,5
Silty Clay, Silty Sand
6
6,5
Sandy Gravel
7
Figure 4.14 Excess pore water pressure during CPTU.
48
11 dissipation tests were carried out at average intervals of 30cm to obtain t50 parameter,
which is the time in which 50% of the excess pore water pressure is dissipated during a
dissipation test (Figure 4.15). t50 values are shown in table 4.2 with respect to
corresponding depths. These results are consistent with the permeable nature of the
profile.
depth(m)
t50(s)
3.71
3.98
4.18
5.55
5.87
6.19
6.32
3
1.7
1.1
2
15
8.4
1.6
Table 4.2 t50 values at different depths.
Pore Water Pressure Dissipation
60
t50=15s
50
t50=8.4s
40
t50=1.6s
30
t50=2s
u (kPa)
20
t50=1.1s
t50=1.7s
10
t50=3s
0
1
10
100
-10
-20
-30
-40
Time (s)
Figure 4.15 Dissipation test for different depths
1000
3,71 Silty Sand
3,98 Silty Sand
4,18 Silty Sand
5,55 Silty Clay
5,87 Silty Clay
6,19 Silty Clay
6,32 Silty Clay
49
4.3.2.2 Liquefaction Analysis
In Figure 4.16 the plot of cyclic stress ratio (CSR) versus cyclic resistance ratio (CRR) is
seen. CRR is calculated using equation (4.4) and CSR is calculated with an estimated
amax=0.16g for the Grenoble area. As it is seen in Figure 4.16, CSR is very close to CRR
at depth intervals between 2.3m and 2.9m, 3.6m and 4.5m, and 5.5m and 6.2m. In
addition to CSR-CRR plot, we can see the plot of factor of safety against assumed factor
of safety Fs = 1.3 in Figure 4.14. Also in figure 4.14 we see that factor of safety for Mw
= 5.25 earthquake is lower than the factor of safety Fs = 1.3 at depth intervals between
2.3m and 2.9m, 3.6m and 4.5m, and 5.5m and 6.2m. Also, these depth intervals
corresponds to the regions where ∆u<0 and sandy silt layers. Consequently, we can
expect cyclic liquefaction in the layers from 2.3m to 2.9m, from 3.6m to 4.5m, and from
5.5m to 6.2m provided that there is shear stress reversal during cyclic loading.
CSR-CRR Mw=5.25
0
0.5
1
1.5
0
1
2
Liquefaction Possible
Depth
3
4
Liquefaction Possible
CRR for Mw=5.25
CSR Mw=5.25
5
6
Liquefaction Possible
7
8
Figure 4.16 CSR-CRR for Mw = 5.25, regions susceptible to liquefaction are seen.
50
Factor of Safety for Mw=5.25
0
1
2
3
4
5
6
7
8
9
10
0
1
2
Fs<1.3
Liquefaction Possible
Depth
3
4
Fs<1.3
Liquefaction Possible
Fs for Mw=5,25
Fs=1,3
5
6
Fs<1.3 Liquefaction Possible
7
8
Figure 4.17 Factor of safety for Mw = 5.25 against factor of safety Fs = 1.3.