10th Asian Regional Conference of IAEG (2015)

Normalized Pore Water Pressure Ratio and Post-Cyclic Settlement of Saturated Clay
Subjected to Undrained Uni-Directional and Multi-Directional Cyclic Shears
TRAN Thanh Nhan(1), Hiroshi MATSUDA(2), Hiroyuki HARA(2) and Hidemasa SATO(3)(1) Hue University of Sciences, Vietnam
E-mail: nhan_hueuni@yahoo.com(2) Yamaguchi University, Japan, (3) Fukken Co. Ltd, Japan
Abstract
In this paper, normalized excess pore water pressure ratio (D(Udyn/’v0)) andnormalized post-cyclic settlement in strain (Dv), which are defined as the ratio of thoseinduced by multi-directional cyclic shear to the ones induced by uni-directional cyclic shear,
were used to show the effect of cyclic shear direction on the post-earthquake deformation ofa cohesive soil layer. It is shown from the experimental results that, for the shear strain
amplitude ( ) in the range from 0.1 % to 3.0 %, the tendencies of the normalized pore waterpressure ratio are different from those of the normalized post-cyclic settlement: thenormalized excess pore water pressure ratio reaches its maximum (D(Udyn/’v0)max) at  =0.1% and then consecutively decreases, meanwhile the normalized post-cyclic settlement
firstly increases up to their peaks (Dvmax) at  = 0.3 % - 0.4 % then, decreasing. Thesetendencies are independent of the number of cycles (n). For the Kaolinite clay used in thisstudy, the maximum normalized excess pore water pressure ratio and the maximum
normalized post-cyclic settlement are at about D(Udyn/’v0)max = 2.19 - 2.45 and Dvmax =2.25 - 2.73, respectively.
Keywords: Pore water pressure, saturated clay, settlement, undrained cyclic shear
1.

Introduction1980) and Nihon-kai Chubu earthquake in 1983, ormajor slopes in quick clay area, which were recordedin Alaska earthquake in 1964.
It is well known that the ground vibration during
the earthquake is caused by the so-called P-waves andS-waves which propagate vertically and horizontally,
respectively. For the soil deposits which is commonly
considered to be horizontally stratified, verticalmotions produced by P-waves only generate
temporary increase in pore water pressure or in otherwords, no pore water pressure accumulation insaturated soil are caused by such P-waves. Therefore,
practically, an attention is usually paid on the effectof one-dimensional S-wave propagation. In such a
condition, the behavior of soil element deformation
can be directly simulated in the laboratory by
undrained cyclic direct simple shear tests, provided
that lateral strains are prevented or largely reduced(Matasovic and Vucetic, 1992; 1995). Among which,the multi-directional cyclic shear strains induced byan earthquake can only be simulated by using themulti-directional cyclic simple shear test device.
Therefore, in this study, by using themulti-directional cyclic simple shear test apparatus,
normally consolidated Kaolinite clay was subjected toWhen a saturated soil specimen is subjected tocyclic shear, the pore water pressure is generally
produced. In the case of short-term cyclic loading ofan earthquake during which the accelerations
mobilize the multi-directional irregular cyclic shear
strains with high frequency, cohesive soils cantherefore be considered to be under undrained
conditions, which leads the pore water pressure
accumulation up to very high level. After earthquakes,
the dissipation of cyclically induced-pore waterpressures may lead to instantaneous and long-term
ground settlements which have been typicallyobserved after the Mexico earthquake in 1957
(Zeevaert, 1983), the Miyagi-ken Oki earthquake in1978 (Suzuki, 1984) or Hyogo-ken Nanbu earthquake
in 1995 (Matsuda, 1997). In the case of the ground on
which structures are constructed, the stiffness
deteriorates and elastic or immediate settlement
damaged the structures such as building founded onclay in the 1985 Mexico earthquake (Mendoza andAuvinet, 1988), road and river embankments founded
on clay deposits with seated slope failures in
Miyagi-ken Oki earthquake in 1978 (Sasaki et al.,1

10th Asian Regional Conference of IAEG (2015)

phase difference of multi-directional tests was at  =200, 450, 700 and 900; and the number of cycles was
fixed as n = 10, 20, 50, 100 and 200. The wave formof the cyclic shear strain was sinusoidal (two way
cyclic strain) with the period 2 s (frequency of 0.5
Hz) and so the cyclic loading durations were of from
20 seconds to 400 seconds.

the uni-directional and multi-directional cyclic simple
shears with different cyclic shear directions, shear
strain amplitudes and number of cycles. The effectsof these cyclic shearing conditions on the excess porewater pressure build-up during undrained cyclic shear
and the vertical settlement after cyclic shear wereobserved. The effects of cyclic shear direction on thepore water pressure accumulation and the post-cyclic
settlement were investigated in relation to phasedifference, shear strain amplitude and number ofcycles.
2.

3.

Results and Discussions

3.1. Excess pore water pressure during undrained
uni-directional and multi-directional cyclic simple
shearsAs a result of undrained cyclic shear, excess porewater pressure (Udyn) increases with the number ofcycles. Typical records of the excess pore waterpressure ratio which is defined by Udyn/’v0, where
’v0 is the initial effective stress, during undrained
uni-directional and multi-directional cyclic shear tests
are shown in Figure 1 for shear strain amplitude  =0.1 %, 0.4 % and 2.0 %. The observed results of
uni-directional tests in this figure as well as any otherfigures will be symbolized as “uni”. The differencesin the build-up rate and the level of excess porewater pressure are apparently seen in Figure 1,
indicating the effects of cyclic shear direction(uni-direction and multi-direction), phase difference( = 200, 450, 700 and 900), shear strain amplitude ()and the number of cycles (n). In addition, since therelations between the cyclically induced-pore waterpressure and the cyclic degradation of cohesive soil
have been shown by a number of models such as
those proposed by Matasovic and Vucetic (1995), thehigher level of excess pore water pressure obviously
relates to the higher degradation of soil specimens
subjected to the multi-directional cyclic shear.
Therefore, these results confirm the significant effectof the cyclic shear direction on the undrained
behavior of cohesive soils.
As shown in Figure 1, the discrepancies in theexcess pore water pressure ratio between
uni-directional and multi-directional cyclic shears (= 200, 450, 700 and 900) are dissimilar for different
shear strain amplitude and number of cycles. These
discrepancies still remain after large number of cycles
as shown in Figure 2, in which although noises
caused by the measuring system are seen, the excess
pore water pressure ratio induced by uni-directional
cyclic shear and multi-directional one with  = 900
are shown for shear strain amplitude  = 2.0 % andthe number of cycles from n = 100 to 500. Thisbehavior is completely different from those of
Toyoura sand which shows that the effect of cyclic
shear direction on the effective stress reduction
becomes negligible when the shear train amplitude islarger than 0.3 % (Matsuda et al., 2011 and 2012).

Material and Specimen

The soil used in this study is Kaolinite clay, index
properties of which are specific gravity Gs = 2.71,
liquid limit wL = 47.80 %, plastic limit wp = 22.30 %,plasticity index Ip = 25.50 and compression index Cc= 0.31. In order to prepare the specimen, dried
Kaolinite powder was mixed with the de-aired water
to form slurry having a water content of about 80 %.
After keeping the water content constant for one day,the slurry was de-aired in the vacuum cell for about
half an hour, and then poured into a rubber membrane
placed in the shear box of the multi-directional cyclic
simple shear test apparatus.
The slurry was pre-consolidated under the verticalstress v0 = 49 kPa with the consolidation duration of
about 14 minutes. This consolidation period was
decided based on the 3t method (JGS, 2000) which
has been introduced for closing the consolidation
period in laboratory tests and also based on therecord of the excess pore water pressure dissipation
with time. The dimensions of specimen after the
pre-consolidation are about 20 mm in height and 75
mm in diameter. Then the void ratio is in the rangeof about 1.11 - 1.19. The B-value of the specimen
before undrained cyclic shear B > 0.95 was
confirmed by applying the load increment to satisfy
the required saturation degree of undrained cyclic
shear test. After pre-consolidation is completed, thespecimen was subjected to cyclic shear for
pre-determined number of cycles (n), shear strain
amplitude () and phase difference () under theundrained conditions. Since the specimen isprevented from the radial and vertical strains during
cyclic shear, the constant-volume condition aresatisfied. Such a constant-volume test procedure
simulates undrained conditions. Following theundrained cyclic shear, drainage was allowed by
opening the valve and the pore water pressuresgenerated during cyclic loading were dissipated. The
settlements and the pore water pressure were thenmeasured with time.
In this study, the specimens were subjected to thestrain-controlled uni-directional and multi-directional
cyclic simple shears. The shear strain amplitude waschanged in the range from  = 0.1 % to 3.0 %; the2

10th Asian Regional Conference of IAEG (2015)
3(a) Kaolin; n = 10

2.5
2

=900
=700
=450
=200

1.5
1

0
3 0

11

22

(b) Kaolin; n = 20

=900
=700
=450
=200

1
1

22

2.5

Fig. 1 Relations of excess pore water pressure ratio(Udyn/’v0) induced by uni-directional andmulti-directional cyclic shears versus number ofcycles (n) for shear strain amplitude  = 0.1 %, 0.4 %and 2.0 %2

Normalized excess pore water pressure ratio, D(Udyn/’v0)

33

1.5
1
0
3 0

(c) Kaolin; n = 50

2.5
2

=900
=700
=450
=200

1.5

Fig. 2 Excess pore water pressure ratio induced byuni-directional cyclic shear and multi-directional one
with the phase difference  = 900 versus number ofcycles for  = 2.0 %1122(d) Kaolin; n = 100

=900
=700
=450
=200

11

22

(e) Kaolin; n = 200

=900
=700
=450
=200

1

2

2.5
2

3.2. The normalized excess pore water pressure
ratio of saturated clay subjected to undrained
uni-directional and multi-directional cyclic shears
For further detail of the effect of cyclic shear
direction on the excess pore water pressure behavior
of cohesive soils, the normalized excess pore waterpressure ratio, D(Udyn/’v0) is used. This parameter isdefined by the ratio of those induced bymulti-directional cyclic shear ((Udyn/’v0)M) to theones induced by the uni-directional cyclic shear((Udyn/’v0)U) and can be expressed by Equation (1).
D(Udyn/’v0) = (Udyn/’v0)M /(Udyn/’v0)U

1
0
3 0

1.5
1

3

00

2.5
2

(1)

1.5

The changes of D(Udyn/’v0) with shear strain
amplitude () are shown in Figures 3(a) to 3(e) for
various phase differences and number of cycles.

1

00

1
Shear strain amplitude,
 (%) 2

Fig. 3 Normalized excess pore water pressure ratio
versus shear strain amplitude for various phasedifferences and number of cycles

310th Asian Regional Conference of IAEG (2015)

It is seen in these figures that, at the same shear
strain amplitude, the normalized excess pore waterpressure ratio increases with the phase difference,and this value is significantly affected by the shear
strain amplitude as firstly D(Udyn/’v0) reaches its
peak at the shear strain amplitude of about DUmax =0.1 % (for simplification, the shear strain amplitude atwhich D(Udyn/’v0) reaches maximum value
D(Udyn/’v0)max is denoted hereinafter as DUmax) andsecondly consecutively decreases, and this tendency
is independent of the number of cycles.

3.0

=900
=700
=450
=200

11
22
(b) Kaolin; n = 20

33

2.0

1.0

3.0

3.3. The normalized settlement of saturated clay
pre-subjected to undrained uni-directional andmulti-directional cyclic shears
The normalized post-cyclic settlements obtained
from multi-directional and uni-directional cyclic
shears (Dv) by using Equation (2) are plotted against
shear strain amplitude in Figures 4(a) to 4(e) for
different number of cycles.

00

2.0

Normalized post-cyclic settlement, Dv

Dv = vM /vU(a) Kaolin; n = 10

1.0

(2)

3.0

Where vM and vU are the post-cyclic settlements
induced by undrained multi-directional anduni-directional cyclic shears, respectively.
It is seen from Figures 4(a) to 4(e) that thenormalized settlement (Dv) generally increases withthe phase difference for every number of cycles. The
variations of Dv with the shear strain amplitude (),however, are definitely different: Dv firstly increases
with  and reaches its peak at the shear strain
amplitude of about Dmax = 0.3 % - 0.4 % (the shear
strain amplitude at which Dv reaches maximum
value Dvmax is denoted hereinafter as Dmax) and then,decreasing.

00

11(c) Kaolin; n = 50

22
=900
=700
=450
=200

00

11

22

(d) Kaolin; n = 100

=900
=700
=450
=200

11

22

2.0

1.0

3.0

2.0

3.4. The tendency of normalized excess pore waterpressure ratio and post-cyclic settlement withnumber of cycles
In order to show the tendencies about the numberof cycles for the relation of D(Udyn/’v0) and Dv
versus shear strain amplitude, results for the phasedifference  = 900 are shown in Figures 5(a) and 5(b),respectively. Although some scatterings are seen,
D(Udyn/’v0) and Dv decrease with the number ofcycles, regardless of the shear strain amplitude and atendency that the larger the number of cycles
increases, the smaller the value D(Udyn/’v0) and Dv,
except for the small shear strain amplitude in Figure5(b) as around 0.3%, where Dv for n = 200 becomeslarger compared with small number of cycles. Thismeans that when the shear strain amplitude is small,the effect of the multi-directional shear on the
degradation of the structure becomes relatively
large.

1.0
3.0

00

(e) Kaolin; n = 200 =900
=700
=450
=200

2.0

1.0

=900
=700
=450
=200

00

11
22
Shear strain amplitude,  (%)

Fig. 4 Normalized post-cyclic settlement versus shear
strain amplitude for various phase differences andnumber of cycles

410th Asian Regional Conference of IAEG (2015)

By using stress-controlled cyclic direct simple
shear tests on normally consolidated Drammen clay,
Yasuhara and Andersen (1991) confirmed that thesoil structure is disturbed even under theuni-directional cyclic shearing conditions and that thesettlement of cohesive soil in re-compression stage isaffected not only by the level of cyclicallyinduced-pore water pressure but also by this
disturbance of soil structure. Therefore, the result in
Figure 5(b) suggests that the clay structure would
suffer from the higher disturbance under themulti-directional cyclic shearing conditions.

3.0

Kaolin2.0

D(Udyn/’v0)max
DVmaxDUmax1.0

Dmax0.00Normalized excess pore waterpressure ratio, D(Udyn/’v0)

3.0
3.0

(a) Kaolin;  = 900

2.0
2.0

11

22

(b) Kaolin;  = 900

n = 10n = 20n = 50n = 100n = 200

1

2

Normalized post-cyclic
settlement, Dv

1.0
1.0
00
3.0
3.0

n = 10n = 20n = 50n = 100n = 200

2.0
2.0

Shear strain amplitude,  (%)

100

150

Number of cycles, n

200

Fig. 6 The tendency of D(Udyn/’v0)max, Dvmax, DUmaxand Dmax with number of cycles
4.

Conclusions

By using the multi-directional cyclic simple test
apparatus, normally consolidated samples of
Kaolinite clay were tested under undrained
uni-directional and multi-directional cyclic shears
followed by drainage, the effect of cyclic shear
direction on the pore water pressure andre-compression characteristics was investigated inrelation to another cyclic shearing parameter. The
main conclusions are as follows:
The normalized pore water pressure ratio andpost-cyclic settlement between multi-directional
cyclic shear and uni-directional one generally
decrease with the number of cycles. For the numberof cycles from n = 10 to 200, the maximum values ofnormalized pore water pressure ratio are at about 2.19
- 2.45 and slightly smaller than those of post-cyclic
settlement being at Dvmax = 2.25 - 2.73. These values
are obtained at the shear strain amplitude of DUmax =0.1 % and Dmax = 0.3 % - 0.4 %, respectively.

1.0
1.0
0

50

Fig. 5 Normalized excess pore water pressure ratio
and post-cyclic settlement between multi-directional
cyclic shear with  = 900 and uni-directional cyclic
shear versus shear strain amplitude for various
number of cycles

Acknowledgements
Authors would like to express gratitude toVietnam National Foundation for Science andTechnology Development (NAFOSTED) for
financialsupportunder
Grant
number105.99-2014.04.

Finally, in Figure 6, the maximum normalized
excess pore water pressure ratio and post-cyclic
settlement and their corresponding shear strain
amplitudes (DUmax and Dmax) are plotted against the
number of cycles. For the number of cycles from n =10 to 200, the maximum values of normalized excess
pore water pressure ratio fluctuate between
D(Udyn/’v0)max = 2.19 and 2.45, being slightly smaller
than those of the post-cyclic settlement which are in
the range between Dvmax = 2.25 and 2.73 (Fig. 6).
Meanwhile, the shear strain amplitude for the
maximum normalized pore water pressure ratio andpost-cyclic settlement are almost unchanged at DUmax= 0.1 % and Dmax = 0.3 % - 0.4 %, respectively.

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510th Asian Regional Conference of IAEG (2015)

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