Cent. Eur. J. Eng. • 4(3) • 2014 • 226-249
DOI: 10.2478/s13531-013-0165-y
Central European Journal of Engineering
Prediction of liquefaction potential and pore water
pressure beneath machine foundations
Research Article
Mohammed Y. Fattah1∗ , Mohammed A. Al-Neami2 , Nora H. Jajjawi3
1 Professor, Building and Construction Engineering Department
University of Technology, Baghdad, Iraq.
2 Assistant Professor, Building and Construction Engineering Department
University of Technology, Baghdad, Iraq.
3 Assistant Lecturer, Building and Construction Engineering Department
University of Technology.
Received 20 March 2013; accepted 22 March 2014
Abstract: The present research is concerned with predicting liquefaction potential and pore water pressure under the dynamic loading on fully saturated sandy soil using the finite element method by QUAKE/W computer program.
As a case study, machine foundations on fully saturated sandy soil in different cases of soil densification (loose,
medium and dense sand) are analyzed. Harmonic loading is used in a parametric study to investigate the effect of
several parameters including: the amplitude frequency of the dynamic load. The equivalent linear elastic model is
adopted to model the soil behaviour and eight node isoparametric elements are used to model the soil. Emphasis
was made on zones at which liquefaction takes place, the pore water pressure and vertical displacements develop during liquefaction. The results showed that liquefaction and deformation develop fast with the increase of
loading amplitude and frequency. Liquefaction zones increase with the increase of load frequency and amplitude.
Tracing the propagation of liquefaction zones, one can notice that, liquefaction occurs first near the loading end
and then develops faraway. The soil overburden pressure affects the soil liquefaction resistance at large depths.
The liquefaction resistance and time for initial liquefaction increase with increasing depths. When the frequency
changes from 5 to 10 rad/sec. (approximately from static to dynamic), the response in displacement and pore
water pressure is very pronounced. This can be attributed to inertia effects. Further increase of frequency leads
to smaller effect on displacement and pore water pressure. When the frequency is low; 5, 10 and 25 rad/sec.,
the oscillation of the displacement ends within the period of load application 60 sec., while when ω = 50 rad/sec.,
oscillation continues after this period.
Keywords: Dynamic • finite elements • sand • liquefaction • machine foundation
© Versita sp. z o.o.
1.
∗
E-mail: [email protected].
Introduction
Soil liquefaction is a major cause of damage during earthquakes. "Modern" engineering treatment of liquefaction
related issues evolved initially in the wake of the two
devastating earthquakes of the 1964 and 2011 Japan.
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Over the nearly four decades that have followed, a significant progress has occurred. Initially, this progress was
largely confined to improve the ability to assess the likelihood of initiation of liquefaction in clean, sandy soils.
Additional potential problems associated with both silty
and gravelly soils, and the important additional issues
of post-liquefaction strength and stress deformation behaviour also began to attract increased attention [1].
2.
Liquefaction Mechanisms
Liquefaction has been used to define two mainly related
but different soil behaviours during earthquakes, namely
flow liquefaction and cyclic softening. Since both phenomena can have quite similar consequences, it is difficult to distinguish between them. However, the mechanisms behind them are rather different. Flow liquefaction
is a phenomenon in which the equilibrium is destroyed by
static or dynamic loads in a soil deposit with low strength,
which is defined as the strength of soils under large strain
levels (critical state). Static loading, for example, can be
applied by new buildings on a slope that exert additional
forces on the soil beneath the foundations. Earthquakes,
blasting, and pile driving are all examples of dynamic
loads that could trigger flow liquefaction. Once triggered,
the strength of a soil susceptible to flow liquefaction is
no longer sufficient to withstand the static stresses that
were acting on the soil before the disturbance. Failures
caused by flow liquefaction are often characterized by
large and rapid movements which can lead to disastrous
consequences [2]. Cyclic softening is another phenomenon,
triggered by cyclic loading, occurring in soil deposits with
static shear stresses lower than the soil strength. Deformations due to cyclic softening develop incrementally
because of static and dynamic stresses that exist during
an earthquake. Two main engineering terms can be used
to define the cyclic softening phenomenon, as follows [2]:
cyclic liquefaction requires undrained cyclic loading during which shear stresses reversals occur or zero shear
stress can develop; i.e. occurs when in-situ static shear
stresses are low compared to cyclic shear stresses. At the
point of zero effective stress, no shear stress exists. When
shear stress is applied, pore water pressure drops as the
material tends to dilate, but a very soft initial stress strain
response can develop resulting in large deformations. Deformations during cyclic loading can accumulate to large
values, but generally stabilize when cyclic loading stops.
The first step in engineering assessment of the potential
for initiation of soil liquefaction is the determination of
whether or not soils of "potentially liquefiable nature" are
present at a site. This, in turn, raises the important ques-
tion regarding which types of soils are potentially vulnerable to soil liquefaction. It has long been recognized that
relatively "clean" sandy soils, with few fines, are potentially vulnerable to the seismically induced liquefaction.
There has, however, been significant controversy and confusion regarding the liquefaction potential of silty soils
(and silty/clayey soils), and also of coarser, gravelly soils
[1]. The most widely criteria used for defining potentially
liquefiable soil is "Modified Chinese Criteria" [3]. According to these criteria, fine (cohesive) soils that plot above
the A-line (in plasticity chart) are considered to be of potentially liquefiable type and character if:
1. There are less than 15% "clay" fines (based on the
Chinese definition of "clay" sizes as less than 0.005
mm),
2. A liquid limit (LL) ≤ 35%, and
3. In-situ water content greater than or equal to 90%
of the liquid limit.
Sitharam et al. (2004) studied methods of determining the
dynamic properties as well as potential for liquefaction of
soils [4]. Parameters affecting the dynamic properties and
liquefaction have been brought out. A simple procedure of
obtaining the dynamic properties of layered ground has
been highlighted. Results of a series of cyclic triaxial
tests on liquefiable sands collected from the sites close
to the Sabarmati river belt have been presented. Simple method was used to obtain the equivalent modulus of
layered system. Cyclic strain-controlled triaxial tests to
evaluate the dynamic properties and liquefaction potential of sands have been carried out. It has been brought
out that the material immediately beneath the foundation
plays a dominant role in controlling the dynamic response.
Material at a depth greater than twice the width of the
foundation plays an insignificant role. A major reduction
in the shear modulus and a corresponding increase in the
damping of sand occur in the large shear strain range.
As the initial densities of sand increase, the shear modulus shows clearly an increasing trend. However, more or
less the same values of shear modulus occur beyond 0.5%
shear strain level irrespective of their initial density. As
a result of application of cyclic loads on the soils, pore
water pressure builds up steadily and reaches initially
applied confining pressure depending on the magnitude
of cyclic shear strain as well as the density of the soil.
At higher cyclic shear strain amplitudes, the pore water
pressure builds up fast and there is triggering of liquefaction at lower cycles. Jin et al. (2008) tested samples
of saturated loose sand under bi-directional cyclic loading to characterize liquefaction and cyclic failure, by using an advanced soil static and dynamic universal triaxial
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Prediction of liquefaction potential and pore water pressure beneath machine foundations
and torsional shear apparatus [5]. Tests were performed
with two cyclic components involving the horizontal shear
stress (torsional shear stress) and the vertical shear stress
(stress difference between vertical normal stress and horizontal normal stress) to provide an approximate presentation of wave or seismic loading conditions. Samples were
consolidated under various initial static horizontal shear
stresses and subsequently subjected to a specified level
of dynamic loading. Three stress levels of dynamic load
were concerned. Results showed that the developed pore
water pressure decreases linearly as initial static horizontal shear stress increases and decreases exponentially as
consolidation stress ratio increases. Worthen (2009) carried out a study on the characterization of the liquefaction
potential of fine-grained soils, based on plasticity characteristics using the Chinese criteria [6]. Recent research
showed that such criteria are ineffective. In addition, the
current liquefaction models do not account for the confining pressure of in-situ soil or the strength of the earthquake. The study used the critical state soil mechanics
framework, which emphasizes that the shear strength and
deformation behaviour of soil depends on changes in volume and confining stress. Lu et al. (2010) investigated
the responses of saturated sand under horizontal vibration
loading induced by a bucket foundation [7]. The saturated
sand liquefies gradually since the vibration loading is applied on. The maximum displacement on the surface of
sand layer occurs near the loading end and in this zone;
the sand is compressed and moves upwards. The liquefaction zone was developed from the upper part near the loading side and stopped gradually under the vibrating loading on one side of the saturated sand; liquefaction occurs
first near the loading end and then develops faraway. The
deformation becomes up-heave near the loading end and
degrades faraway gradually. It was found that the liquefaction and the deformation develop fast with the increase
of the loading amplitude and the frequency and the decrease of the modulus. The liquefaction may occur under
vibration loading on the side from the foundation side to a
finite distance. It needs to be considered in the design of
platform. However, the generation of pore water pressure
will reduce the effective stresses and, therefore the deformation will increase. In cases near the surface, this is even
more critical as the effective stresses can be reduced to
almost zero and, therefore, increasing deformations. Fattah and Nsaif (2010) carried out coupled dynamic analysis
on zoned earthdam subjected to earthquake excitation in
which displacements and pore water pressure are calculated [8]. The finite element method is used. Al-Adhaim
dam which is an earthdam is analyzed as a case study.
A parametric study was carried out to investigate the effect of some parameters on the general response of the
dam to earthquakes, and emphasis was made on zones at
which liquefaction takes place. It was found that as the
maximum horizontal component of the input acceleration
increases, liquefaction zones within the dam and its foundation become larger. The maximum stresses and pore
water pressure occur at a time after the earthquake shock
and not on or in the vicinity of the time of the peak ground
acceleration as was concluded by conventional dynamic
stress analyses. Vivek and Ghosh (2012) studied dynamic
interaction of two closely spaced embedded strip foundations under the action of machine vibration [9]. One of the
footings was excited with a known vibration source placed
on the top of the footing, called the active footing. The
objective was to study the effect of dynamic excitation of
active footing on the nearby passive footing through a homogeneous c-φ soil medium. The analysis was performed
numerically by using finite element software, PLAXIS 2D.
The soil profile was assumed to obey the Mohr-Coulomb
yield criteria. The analysis was performed under two different loading conditions; sinusoidal dynamic loading with
constant amplitude and varying amplitude. Under the dynamic excitation, the settlement behavior of interacting
footings is studied by varying the spacing between the
footings. In addition, the variation of normal and shear
stress developed below the passive footing was also explored. The response of the adjoining passive structure
was found to be significant up to a spacing of 2B (B is
foundation width) from the actual excited structure. It was
concluded from previous studies on liquefaction that most
of them concentrated on earthquake induced liquefaction
and that little studies talked about liquefaction caused by
machine vibrations. Some equipment or heavy machines
used during construction particularly on saturated sandy
soil might cause some vibration and consequently, a loose
soil may be susceptible to liquefaction.
3.
Description of the Problem
A saturated porous foundation soil 30 m wide and 20 m
deep is modelled by a finite element analysis. A 2 m wide
footing is placed at the middle of the top surface. The
foundation will be subjected to dynamic load of harmonic
excitation described by the following equation:
F (t) = ao sin(ω, t)
(1)
Where:
ao is the load amplitude
ω is the load frequency, and
t is the time
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M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi
Figure 1.
Typical finite element mesh.
The duration of this dynamic load is 60 sec. with a time
step ∆t = 0.1 sec. In order to study the pore water pressure changes under such loading condition, the soil is
assumed to be saturated; i.e. the water table level coincides with the ground surface. The properties of the
sand are summarized in Table 1. The plane strain problem is analyzed using the QUAKE / W (2004) program
which is a geotechnical finite element software product
used for the dynamic analysis of earth structures subjected to earthquake shaking and other sudden impact
loading. QUAKE/W is part of GeoStudio and is, consequently, the integration of QUAKE/W and other products within GeoStudio greatly expands the type and range
of problems that can be analyzed beyond what can be
done with other geotechnical dynamic analysis software.
It is formulated for two- dimensional plane strain problems. The finite element mesh used for the analysis is
shown in Figure 1. The mesh consists of 8 noded quadrilateral isoparametric elements. The side boundaries are
allowed to move vertically only while the bottom boundary
is restricted horizontally and vertically. The top surface is
free draining while the other boundaries are impermeable.
Equivalent linear elastic model is used in the analysis.
The time of the analysis is taken as 100 sec with ∆t =
0.1 sec. The analysis is repeated for three types of soils;
loose, medium and dense sand. The results are presented
at selected points A, B, C, D and E at different depths
below the foundation in order to study the depth of soil
affected by the dynamic load.
The relationships used for the equivalent linear elastic
model include the shear modulus reduction function of
Figure 2, the relationship between the cyclic number ratio
and pore pressure ratio of Figure 3 and the cyclic deviator
stress with number of cycles as given in Figure 4.
Figure 2.
Shear modulus reduction function (Seed and Idriss, 1970)
[16].
Figure 3.
Cyclic number ratio N/NL versus pore pressure ratio ru
(Seed and Booker, 1977) [17].
4.
Effect of load frequency
The harmonic load is applied at the surface as shown in
Figure 1. The load is changed to different values by considering different values of frequency; 5, 10, 25 and 50
rad/sec. with damping ratio equals 0.05 and the load
amplitude equals 10 kN. The results are presented in
figures which include; vertical displacement, pore water
pressure, surface displacement and liquefaction zones, for
loose, medium and dense sandy soils:
• Vertical displacement and pore water pressure are
presented at three points A, B and C located at
depths 1, 5 and 10 m, respectively.
• Surface displacement is drawn at different times 40,
50, 55 and 60 sec.
• The liquefaction zones are inspected at time 10 sec.
Figures 5 to 8 show the results for loose sand with amplitude of harmonic load (ao = 10 kN) at different values
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Prediction of liquefaction potential and pore water pressure beneath machine foundations
Figure 4.
Cyclic test results on Sacramento River Sand (Kramer,
1996) [18].
of load frequency (ω = 5, 10, 25 and 50 rad/sec.), while
Figures 9 to 12 show the results for medium sand. Figures 13 to 16 show the results for dense sand with the
same amplitude of harmonic load and values of load frequency. For loose sand, it can be noticed in Figures 5
to 8 that when the frequency of dynamic load increases
from (ω = 5 to 10 rad/sec.), the maximum vertical displacements at points A, B and C in the foundation soil
increases by about 2101, 1393 and 1243 %, respectively.
This result is in agreement with the results obtained by
Lu et al. (2010) [7] who stated that the development of
displacement becomes large with the increase of loading
frequency.
On the other hand, the increase in the frequency from ω
= 5 to 10 rad/sec. leads to increase in the maximum pore
water pressure at points A, B and C depending on the
amplitude of load (103, 23 and 10%), respectively. When
the frequency is further increased to 25 or 50 rad/sec.,
the pore water pressure is approximately unchanged, because that liquefaction takes place at all points under
such frequencies. The pore pressure in the saturated sand
increases gradually and the strength of sandy layer decreases gradually. At last, liquefaction occurs. These
results are consistent with the conclusion of Seed et al.
(1976) [10] who stated that during the period of earthquake shaking (or dynamic load application), there would
be no significant dissipation or redistribution of pore water pressure in the soil mass. When the frequency is low;
5, 10 and 25 rad/sec., the oscillation of the displacement
ends within the period of load application 60 sec., while
when ω = 50 rad/sec., oscillation continues after this period. When the frequency is low; ω = 5 rad/sec., liquefaction is not taking place at points A, B and C , while when
the frequency increases to 10 rad/sec. liquefaction occurs
at points A and B at a short time 10 sec. and the pore
water pressure continues to increase at point C. When the
frequency ω = 25 and 50 rad/sec., liquefaction occurs at
points A, B and C at time 10 sec. This means that liq-
uefaction may propagate to a point at a depth of about
five times the foundation width. This conclusion overrides
the conclusion of Sitharam et al. (2004) [4] who stated
that material at a depth greater than twice the width of
the foundation plays an insignificant role. For medium
sand, from Figures 9 to 12, it can be noticed that when
the frequency of dynamic load increases from ω = 5 to 10
rad/sec., the maximum vertical displacement at points A,
B and C in the foundation soil increases by about 1433,
1139 and 1065 %, respectively. Further increase in the
frequency to 25 and 50 rad/sec. causes increase in the
maximum displacement at points A, B and C, the increase
is about 36, 67 and 83 %, respectively. On the other hand,
the increase in the frequency from ? = 5 to 10 rad/sec.
leads to increase in the maximum pore water pressure at
points A and B depending on the amplitude of load; 95
and 30 %, respectively, while at point C the pore water pressure is approximately unchanged . When the frequency is further increased to 25 rad/sec., the pore water
pressure is approximately unchanged, but when the frequency reached to the 50 rad/sec, the pore water pressure
is slightly increased at points B and C while still constant
at point A. When the frequency is low; ω = 5 rad/sec., liquefaction is not taking place at any point, while when the
frequency increases to 10 rad/sec. liquefaction occurs at
point A only in a short time 10 sec. and the pore water
pressure continues to increase at point B slightly. When
the frequency becomes 25 rad/sec., liquefaction still occurs at point A at 10 sec. and point B at time 50 sec. This
means that the increase of load frequency increases the
liquefaction potential and causes liquefaction at shorter
times. When the frequency ω = 50 rad/sec., liquefaction
occurs at points A, B at time 10 sec., liquefaction is not
taking place at point C. For dense sand, Figures 13 to
16, reveal that, when the frequency of dynamic load increases from ω = 5 to 10 rad/sec., the maximum vertical
displacement at points A, B and C in the foundation soil
increases by about 1209, 1005 and 949 %, respectively.
Further increase in the frequency to 25 and 50 rad/sec.
causes increase in the maximum displacement at points A,
B and C, the increase is about 15, 24 and 32 %, respectively. On the other hand, the increase in the frequency
from ω = 5 to 10 rad/sec. leads to increase in the maximum pore water pressure at point A depending on the
amplitude of load 95%, while the pore water pressure at
points B and C is approximately unchanged . When the
frequency is further increased to 25 or 50 rad/sec., the
pore water pressures at points A, B and C are approximately unchanged. This conclusion agrees well with Lu
et al. (2004), who stated that the rate of the liquefaction
increases with the increase of the initial void ratio (or decrease of density) or amplitude and frequency of loading,
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Figure 5.
Dynamic response of the foundation to harmonic load, ao = 10 kN, ω = 5 rad/sec., constructed over loose sand.
and increases with decrease of the modulus [7]. The pore
pressure increases slowly at the beginning and then increases fast up to the maximum which is equal to the sum
of the initial pore pressure and the initial effective stress
(after liquefaction, the fluctuating pore pressure caused
by the loading is not considered). The increase rates of
the pore pressure become faster and faster with increase
of the loading amplitude. Also, at all values of frequency,
liquefaction is not taking place at any elective points except point A, liquefaction occurs at frequency equals to 10,
25 and 50 rad/ sec. in a short time 10 sec. Similar results
were found by Kumar (2008) who concluded that the dense
sand has greater resistance for liquefaction [11]. It would
require higher deviator cyclic stress amplitude or more
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Prediction of liquefaction potential and pore water pressure beneath machine foundations
Figure 6.
Dynamic response of the foundation to harmonic load, ao = 10 kN, ω = 10 rad/sec., constructed over loose sand.
number of cycles of deviator cyclic stress to cause initial
liquefaction as compared to same soil in loose state. The
deformation development becomes large with the increase
of loading frequency; the deformation becomes larger and
larger with time. The increase in velocity of the excess
pore pressure is faster; this means that the duration developing to liquefaction is shorter. For very loose soils,
as initial cyclic pore pressure induced softening leads to
monotonic accumulation of shear deformations, and these,
in turn, lead to further pore pressure increases. For very
dense soils, the presence of non-zero initial static driving shear stresses can lead to reduction in the rate of
generation of pore pressures during cyclic loading. As
each cycle of loading produces an incremental increase in
pore pressure, and some resultant reduction in strength
and stiffness, the driving shear stresses then act to pro-
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M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi
Figure 7.
Dynamic response of the foundation to harmonic load, ao = 10 kN, ω = 25 rad/sec., constructed over loose sand.
duce shear deformations that cause dilation of the soil, in
turn reducing pore pressures [1]. To simplify comparison
between the results for three states of sandy soil (loose,
medium and dense). It is noticed that when the frequency
changes from 5 to 10 rad/sec. (approximately from static
to dynamic), the response in displacement and pore water pressure is very pronounced. This can be attributed
to inertia effects. Further increase of frequency leads to
smaller effect on displacement and pore water pressure.
5.
Effect of load amplitude
The effect of load amplitude is studied by aplying the
harmonic load on the foundation,. Three values of load
amplitude; 20, 40 and 60 kN (where ao =10 kN is stud233
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Prediction of liquefaction potential and pore water pressure beneath machine foundations
Figure 8.
Dynamic response of the foundation to harmonic load, ao = 10 kN, ω = 50 rad/sec., constructed over loose sand.
ied in the previous section) with load frequency equals 5
rad/sec. Figures 17 to 19 show the results for medium
sand with frequency of harmonic load ω = 5 rad/sec at
different values of load amplitude; ao = 20, 40, 60 kN,
while Figures 20 to 22 show the results for dense sand
with the same frequency of harmonic load and values of
load amplitude.
For loose sand, it was found that when the amplitude of
dynamic load increases from ao = 20 to 40 kN, the maximum vertical displacement at points A, B and C in the
foundation soil increases by about 288, 248 and 212 %,
respectively. Further increase in the amplitude to 40 and
60 kN causes increase in the maximum displacement at
points A, B and C, the increase is about 107, 125 and 116
%, respectively. No change in the maximum pore water
pressure at points A, B and C is recorded with the in-
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M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi
Figure 9.
Dynamic response of the foundation to harmonic load, ao = 10 kN, ω = 5 rad/sec., constructed over medium sand.
crease in the amplitude, because liquefaction takes place
at all points under such amplitudes and the pores between
the soil grains are filled with water which cannot drain
sufficiently, to generate excess pore pressure. When the
amplitude of dynamic load increases from ao = 20 to 40
and 60 kN, the time required for liquefaction to take place
becomes 10 sec. at points A, B and C. These results are
compatible with those of Sitharam et al. (2004) [4] who
stated that at higher cyclic shear strain amplitudes, the
pore water pressure builds up fast and there is trigging
of liquefaction at lower cycles. For medium sand, Figures 17 to 19 reveal that when the amplitude of dynamic
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Prediction of liquefaction potential and pore water pressure beneath machine foundations
Figure 10.
Dynamic response of the foundation to harmonic load, ao = 10 kN, ω = 10 rad/sec., constructed over medium sand.
load increases from ao = 20 to 40 kN, the maximum vertical displacement at points A, B and C in the foundation
soil increases by about 248, 185 and 150 %, respectively.
Further increase in the amplitude to 40 and 60 kN causes
increase in the maximum displacement at points A, B and
C, the increase is about 90, 70 and 58 %, respectively.
Due to the increase in the amplitude from ao = 20 to 40
kN, the maximum pore water pressure is unchanged at
points A and B, at time 10 sec., while at amplitude equals
20 kN, the pore water pressure at point C causes smaller
increase, because the pore water pressure at this deep
point is still in the development stage compared to point
B which is located at shallower depth, and when ao = 40
kN, no significant change occurs at this point. When the
amplitude is further increased 40 to 60 kN, the pore water
pressure is approximately unchanged at points A, B and
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M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi
Figure 11.
Dynamic response of the foundation to harmonic load, ao = 10 kN, ω = 25 rad/sec., constructed over medium sand.
C because that liquefaction takes place under such amplitude. When the amplitude of dynamic load is ao = 20
kN, the time required for liquefaction to take place is 10
sec. at points A and B, while at point C, the increase in
the pore water pressure continues to time 61 sec. When
the amplitude of dynamic load is ao = 40 and 60 kN, the
time required for liquefaction to take place is 10 sec. at
points A, B and C. For dense sand, from Figures 20 to 22,
it can be concluded that, when the amplitude of dynamic
load increases from ao = 20 to 40 kN, the maximum vertical displacement at points A, B and C in the foundation
soil increases by about 223, 156 and 132 %, respectively.
Further increase in the amplitude to 40 and 60 kN causes
increase in the maximum displacement at points A, B and
C by about 80, 55 and 46 %, respectively. On the other
hand, upon the increase in the amplitude from ao = 20
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Prediction of liquefaction potential and pore water pressure beneath machine foundations
Figure 12.
Dynamic response of the foundation to harmonic load, ao = 10 kN, ω = 50 rad/sec., constructed over medium sand.
to 40 kN, the maximum pore water pressure is unchanged
at points A and C, while at point B, the increase in the
amplitude leads to increase in the maximum pore water
pressure depending on the amplitude of load. When the
amplitude is further increased to 40 to 60 kN, the pore
water pressure at points A and C is approximately unchanged, while at point B, the pore water pressure is de-
creased by 5%. This may be attributed to cyclic mobility
which tends to stabilize the pore water pressure after liquefaction occurrence. When the amplitude is ao = 20 kN,
liquefaction takes place only at point A, while when the
amplitude increases to 40 and 60 kN, liquefaction occurs
at points A and B in a short time 10 sec., while liquefaction is not taking place at point C, because the pore
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M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi
Figure 13.
Dynamic response of the foundation to harmonic load, ao = 10 kN, ω = 5 rad/sec., constructed over dense sand.
water pressure continues to decrease at point C till time
100 sec. In dense sand, the soil tends to dilate at failure resulting in negative pore water pressure therefore,
the pore water pressure decreases as shown in Figure 22.
With the increase of the sand density, the affected area
and the settlement are decreased. This may be explained
by the fact that, the strength of sandy layer increases
with the increase of the density. This means that the ratio of the loading amplitude to the sandy layer strength
decreases, therefore, the affected area decreases. When
the density increases to some value, the response caused
by the applied loading is elastic; therefore, the affected
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Prediction of liquefaction potential and pore water pressure beneath machine foundations
Figure 14.
Table 1.
Dynamic response of the foundation to harmonic load, ao = 10 kN, ω = 10 rad/sec., constructed over dense sand.
Properties of the sandy soil used in the parametric study.
Material Properties
Loose sand Medium sand Dense sand
Modulus of elasticity,
E (kN/m2 )
20000
40000
Poisson’s ratio, υ
0.2
0.3
0.4
Unit weight γt , (kN/m3 )
14.0
17.0
22.0
60000
area does not occur. This is compatible with the findings
of Kumar (2008) [11] who found that the dense sand has
greater resistance for liquefaction. It would require higher
deviator cyclic stress amplitude or more number of cycles
of deviator cyclic stress to cause initial liquefaction as
compared to same soil in loose state. When the loading
amplitude was small enough, there is no obvious response,
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M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi
Figure 15.
Dynamic response of the foundation to harmonic load, ao = 10 kN, ω = 25 rad/sec., constructed over dense sand.
with the increase of loading amplitude, even if no liquefaction occurred, the sandy layer surrounding the foundation
settled gradually. There is no liquefaction occurring when
the amplitude is smaller than a critical value [12]. Fattah et al. (2013) showed that liquefaction occurs faster
at shallow depths due to low overburden pressure [13].
Also, liquefaction zones and deformation occur faster with
the increase of dynamic loading amplitude. The analysis
marked that increasing the amplitude pressure accelerates the occurrence of initial liquefaction and increases
the pore water pressure. Based on the results obtained,
it can be concluded that:
• " During loading, the pore pressure increases at the
first stage and then decreases gradually. The reason is that, at the first stage the sand layer intents
to contract, but the water is difficult to drain, the
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Prediction of liquefaction potential and pore water pressure beneath machine foundations
Figure 16.
Dynamic response of the foundation to harmonic load, ao = 10 kN, ω = 50 rad/sec., constructed over dense sand.
strength of the sand decreases, so the sand begins
to compress and the pore pressure decreases gradually.
• The soil overburden pressure affects the soil liquefaction resistance at large depths. The liquefaction
resistance and time for initial liquefaction increase
with increasing depths.
• At large amplitude of dynamic load, liquefaction can
occur at virtually any depth.
• Liquefaction occurs faster at shallow depths for all
ranges of frequency and amplitude. This finding
does not comply with that of (Amini and Duan,
2002) [14] who, during his numerical study on the
liquefaction resistance of soil at high confining
pressure, found that at a lower frequency, liquefaction occurs faster at large depths.
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M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi
Figure 17.
Dynamic response of the foundation to harmonic load, ao = 20 kN, ω = 5 rad/sec., constructed over medium sand.
• Liquefaction zones increase with the increase of
load frequency and amplitude. Tracing the propagation of liquefaction zones, it is noticed that, liquefaction occurs first near the loading end and then
develops far away as was concluded by (Lu et al.,
2010) [7].
• The liquefaction and deformation develop fast when
the loading amplitude and frequency increase.
• The liquefaction zone develops from the upper part
near the loading side and stops gradually under the
vibrating loading on one side of the saturated sand;
liquefaction occurs first near the loading end and
then develops faraway. The deformation becomes
up-heave near the loading end and degrades far243
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Prediction of liquefaction potential and pore water pressure beneath machine foundations
Figure 18.
Dynamic response of the foundation to harmonic load, ao = 40 kN, ω = 5 rad/sec., constructed over medium sand.
away gradually.
• The maximum displacement on the surface of sandy
layer occurs near loading end, after this point the
soil is compressed and surface displacement is begin to decrease till reaching zero with increasing
distance away from the end of vibration loading.
For this reason it is important to take the effect of
vibration on a finite distance from the side of reason
of disturbance in foundation design.
• Maximum displacement increases with decrease the
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M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi
Figure 19.
Dynamic response of the foundation to harmonic load, ao = 60 kN, ω = 5 rad/sec., constructed over medium sand.
modulus of elasticity (the soil changes from dense
to loose sand) this conclusion is compatible with
the finding of Lu et al. (2010) [7], who found that
the sand surface near the loading side becomes
up-heave first and then develops to faraway, the
deformation degrades from the loading side to far
away and the deformation became larger when the
modulus of elasticity of sandy layer is smaller The
smaller the modulus is, the faster the development
of the liquefaction zone is.
6.
Conclusions
As a result of the finite elements analysis carried out in
this study and discussion presented, the following conclu245
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Prediction of liquefaction potential and pore water pressure beneath machine foundations
Figure 20.
Dynamic response of the foundation to harmonic load, ao = 20 kN, ω = 5 rad/sec., constructed over dense sand.
sions could be made:
1. At large amplitude of dynamic force, liquefaction
can occur at virtually any depth, but liquefaction
occurs faster at shallow depths for all cases of frequency and amplitude. Liquefaction mostly occurs
within the top 10 m below the ground surface, although, it can occur up to about 20 m deep.
2. Liquefaction and deformation occur faster with the
increase of loading amplitude and frequency, when
the foundation is constructed over loose saturated
sand. The time of initial liquefaction decreases as
the frequency of dynamic load increases.
3. For loose sand, no change in pore water pressure due to increase in the load amplitude take
place after the initial liquefaction has occurred but
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M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi
Figure 21.
Dynamic response of the foundation to harmonic load, ao = 40 kN, ω = 5 rad/sec., constructed over dense sand.
when the sand density increases, limited increase
or (sometimes a slight decrees) occurred in pore
water pressure as a result of increasing of load amplitude.
4. The soil overburden pressure affects the soil liquefaction resistance at large depths. Liquefaction
resistance and time for initial liquefaction increase
with increasing depth. Liquefaction may propagate
to a point at depth of about five times the foundation width.
5. Liquefaction zones increase with the increase of
load frequency and amplitude. Tracing the propagation of liquefaction zones, one can notice that
liquefaction occurs first near the loading end and
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Prediction of liquefaction potential and pore water pressure beneath machine foundations
Figure 22.
Dynamic response of the foundation to harmonic load, ao = 60 kN, ω = 5 rad/sec., constructed over dense sand.
then develops faraway.
6. When the frequency changes from 5 to 10 rad/sec.
(approximately from static to dynamic), the response in displacement and pore water pressure
is very pronounced. This can be attributed to inertia effects. Further increase of frequency leads
to smaller effect on displacement and pore water
pressure. When the frequency is low; 5, 10 and 25
rad/sec., the oscillation of the displacement ends
within the period of load application 60 sec., while
when ω = 50 rad/sec., oscillation continues after
this period.
7. The deformation development becomes large with
the increase of loading frequency; the deformation
becomes larger and larger with time. The increase
in velocity of the excess pore pressure is faster; this
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M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi
means that the duration developing to liquefaction
is shorter. For very loose soils, as initial cyclic
pore pressure induced softening leads to monotonic
accumulation of shear deformations, and these, in
turn, lead to further pore pressure increases.
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