The Influence Of Dynamic Acceleration Of Sinusoidal Loads To The Landslide Surface Of Cantilever Retaining Walls.
Proceedings of Slope 2015, September 27-30 th 2015
THE INFLUENCE OF DYNAMIC ACCELERATION OF SINUSOIDAL LOADS TO
THE LANDSLIDE SURFACE OF CANTILEVER RETAINING WALLS
Anissa M.Hidayati 1, Sri Prabandiyani RW 2 and I Wayan Redana 3
ABSTRACT: The dynamic acceleration is one of dynamic parameters will be taken into consideration in the
analysis of the safety of retaining wall construction due to dynamic loads beside other parameters such as: (1) the
dynamic frequency, (2) the density of soils and (3) the amplitude of vibration. This research aims to study the
role of dynamic acceleration to the landslide surface of retaining walls of cantilecer type due to dynamic load.
This study was done by a small scale model test of cantilever retaining wall type of 18 centimeters in height, 9
centimeters in width and loaded by using shaking table to simulate dynamic loads. The dynamic load was given
with the variation of the frequency and amplitude of vibration to obtain the acceleration of dynamic response.
The dynamic acceleration response was measured by using accelerometer. Dry sand with three densities
variations were used in this experiment. The movements of the sand grains were recorded during experiment to
be able to show the change of the sliding surface of the retaining wall. The results showed that there was the
difference in the dynamic acceleration response generated due to differences in the dynamic frequency and
amplitude of vibration. There was also a relation ship between the value of dynamic acceleration response to the
shape of the landslide surface.
Keywords: dynamic acceleration response, landslide surface, soils density, cantilever type
INTRODUCTION
Landslides occur on a regular basis throughout
the world as part of the ongoing evolution of
landscapes. Many landslides occur in natural slopes,
but slides also occur in man-made slopes from time
to time. At any point in time, then, slopes exist in
states ranging from very stable to marginally stable.
When earthquake occur, the effects of earthquakeinduced ground shaking is often sufficient to cause
failure of slopes that were marginally to moderately
stable before the earthquake. The resulting damage
can range from insignificant to catastrophic
depending on the geometric and material
characteristics of the slope. Construction of retaining
wall construction is one way to anticipate the slopes
damage due to earthquake load.
In the last two decades had developed innovative
system which was used to anticipate the damage of
slopes caused by the earthquake. In general, ground
anchoring system for seismic design purposes can be
divided into three main categories: gravity walls,
cantilever walls and braced walls. Each type of wall
posses different assumption in evaluating lateral soil
pressure.
Retaining walls can fail in many difference ways.
Cantilever walls fail by sliding, overturning, or gross
instability also fail in bending. The magnitude and
distribution of dynamic wall pressures were
influenced by the mode of wall movement, e.g.,
translation , rotation about the base, or rotation about
the top (Sherif, A. M., and Fang, Y - S. 1984).
Okabe (1924) and Mononobe & Matsuo (1929)
developed the basis of pseudo-static analysis of earth
pressure on the wall of the load due to the earthquake
which was then known as Mononobe-Okabe method.
Mononobe-Okabe method is a development of
Coloumb theory that follows the principle of
equilibrium limit (limit equilibrium). The problem of
stability of retaining walls was solved used a
combination of rigid displacement-based analytical
solutions (walls are allowed to experience the
rotation at the top of the wall) and the experimental
method utilized shaking table to determine the
distribution of dynamic active pressure on a gravity
1
Student, Udayana University, anissamh@yahoo.com, INDONESIA
Professor, Diponegoro University, wardani_spr@yahoo.com, INDONESIA
3 Professor, Udayana University, iwayanredana@yahoo.com, INDONESIA
2
X1-1
walls (Sherif and Fang 1984). The experimental
results showed that the distribution of dynamic active
earth pressure as a function of acceleration. Dynamic
active ground pressure distribution obtained from the
value of soil pressure of observe by using transducer,
hence pressure did not calculating by using the real
movement of soil particle of the experiment.
Dynamic active pressure increased with the increased
in acceleration. Ishibashi and Fang (1987) completed
the rigid retaining wall stability issues using a
combination of analytical methods based on
displacement and experimental methods. The
experiments carried out used a shaking table with
model of gravity wall. The experiments were done on
dry soils and non-cohesive, while the walls were
allowed to experience a variety of movements such
as translation, rotation of the bottom wall, the
rotation at the top of the wall, and combinations
thereof. When the rotation at the base of the wall, the
pressure distribution is not linear. In the area near the
base of the wall, there is a high residual stress due to
displacement of the wall, hence the capture point of
active pressure is lower than a third of the wall height.
When the rotation at the top of the wall, the pressure
distribution is not linear. There are areas that had a
high stress near the top of the wall as a result of the
tapered land, and the area had a low voltage at the
base of the wall due to a shift in the wall.
Consequently, capture point total active dynamic
pressure was higher than a third of the wall height.
Dynamic lateral earth pressure distribution obtained
from observations on the value of soil pressure
transducer.
LITERATURE REVIEW
Construction of the building both inside or on the
surface of the ground, not only accepted static load
but also dynamic load. Dynamic load acting on the
land or building structures could be derived from
natural or man-made. If the dynamic loads worked on
the ground, it would caused the movement of soil
grain, consequently the structure which was
supported by the soil would experienced instability.
Dynamic Response of retaining wall ranging from
even the simplest to quite complex. Movement and
pressure of the wall depends on the response of the
soil which underlying of walls, the response of the
back-fill, the response of inertia and flexibility of the
wall itself, and the nature of the input motion
(Kramer, Steven L. 1996).
The problem of retaining soil is one of the oldest
in geotechnical engineering; some of the earliest and
most fundamental principles of soil mechanics were
developed to allow rational design of retaining walls.
X1-2
Many different approaches to soil retention have
been developed and used successfully.
Seismic design of retaining walls is generally
based on seismic pressure or allowable displacement.
In the former approach, pseudo-static or pseudodynamic analysis are used to estimate seismically
induced wall pressure, and the wall is designed to
resist those pressure without failing or causing failure
of the surrounding soil. The latter approach involves
designing the wall such that its seismically induced
permanent displacement does not exceed a
predetermined allowable displacement.
Modeling experiments in the laboratory can be
done with the aim to study the movement of sand and
retaining wall caused by vibration (dynamic load)
using cantilevered retaining wall models that are
supported by dry sand with provided dynamic load
(sinusoidal) with variations of the vibration
acceleration and the density of the sand.
The objects that perform accelerated uniformly
motion, has fixed acceleration, this means that the
object is always working with pattern that remains
both direction and magnitude. If it’s force is always
changing, the acceleration is olso changing.
Repetitive motion in the same time interval called a
periodic motion. This periodic motion occurs on a
regular basis and motive force is proportional to the
amplitude. Easy to understand that the smaller the
amplitude is also smaller the driving force. The
largest amplitude is called amplitude of vibration (A).
Periodic motion can be expressed in sine or cosine
function, therefore periodic motion is called
harmonic motion. The periodic motion that moves
back and forth through the same trajectory so-called
vibration or oscillation and is also known as a simple
harmonic motion. The time needed to take the path
back and forth is called the period, while the number
of vibrations per unit time is called frequency. The
relationship between the period (T) and frequency (f)
according to this statement is expressed as the
equation 1.
T
1
f
[sec]
(1)
The frequency (f) or the amount of vibration in each
unit time is expressed in equation 2.
f
1
T
[ cps ]
(2)
While the mathematical function from objects
called harmonic motion/vibration (Prakash, S., 1981)
and be expressed as equation 3.
x Asin ( t )
(3)
where x is the displacement of a trajectory in function
of time (t); A is the amplitude (equal to the maximum
displacement); ω is the angular frequency of the
trajectory [radians/sec]; t is the time [seconds]. The
harmonic motion repeated every 2π radians with
fixed angular velocity and maximum displacement is
value of A, referred to as amplitude (Figure 1.).
By taking into account the movement of grain
movement graphic results, it can be calculated the
area of landslide behind the retaining wall
construction due to the sinusoidal dynamic load (see
Figure 3.).
Figure 2. Representation of displacement, velocity
and acceleration
Figure 1. Representation fo harmonic motion.
A cycle of motion is completed when the movement
reached one full rotation as described in equation 4.
2 f
[radians / sec]
(4)
with f is frequency of vibration.
From equation 4., values of obtained f as defined in
equation 5.
f
cps
2
(5)
To determine the velocity of simple harmonic motion,
differentiate equation 3. with respect to time (t) in
order to obtain equation 6 (Prakash, S., and Puri, V.
K., 1988).
x
dx
dt
d
dt
( A sin t ) A cos ( t )
d x
dt
d
dt
( A cos ( t )) A 2 sin( t ) 2 x a
The area bounded by 2 (two) curves y1 and y2 which
as function of x and x = 0 and x = x1, it can be
calculated:
The area below of curve y1, x = 0 and x = x1 is
expressed as equation 8.
A1 y1 dx
x1
(6)
(8)
0
where x is the velocity of simple harmonic motion
equation. Then, to obtain the acceleration of simple
harmonic motion by differentiating equation 6. with
respect to time (t) thus produce equation 7.
x
Figure 3. The area bounded by curve y1 = f(x), y2 =
f(x), x = 0 dan x = x1
(7)
where x is the acceleration of simple harmonic
motion equation, also denoted as a . The displacement
path, velocity and acceleration of motion was
described in Figure 2.
The area below of curve y2, x = 0 and x = x1 is
defined in equation 9.
A1 y2 dx
x2
(9)
0
So the area bounded by the intersection of the two
curves are expressed as equation 10.
X1-3
A A1 A2 y1 dx y2 dx
x1
x2
0
0
(10)
See the segment of y x dx. Then the centroid segment
against X-axis and Y-axis is C ( x ; y ). The of
coordinates centroid C can be obtained by using
equation 11 and equation 12.
x. y dx
x2
x
0
x2
(11)
y dx
0
y1 y2
. y dx
2
0
Figure 4 The equipment of retaining walls model test
on sinusoidal dynamic load (not scaled) (Hidayati et
al. 2015)
x2
y
y dx
DATA COLLECTION AND DISCUSSION
(12)
x2
0
EXPERIMENT
The retaining wall model test was performed in
The Laboratory Soil Mechanics of Civil Engineering
Faculty, Udayana University, Bali, Indonesia. The
model of retaining wall was made of concrete placed
on dry sand. Model test was performed using dry
sand material with a grain size through No. 4 of sieve
and retained No.100 sieve of loose sand density (DR
= 30 %), medium sand density (DR = 55 %) and
dense sand density (DR = 70 %). The model of
retaining wall was designed as a cantilever type of 18
centimeters in height (H), 9 centimeters in width (B).
The model retaining wall was loaded by sinusoidal
speed and amplitude variations. Dynamic response
was recorded using recording devices vibration
acceleration (accelerometer). During experiment the
movement of sand grains recorded.
The model tests was made in the glass box of 2
meters in length, 0.4 meter in width and 1 meter in
height. Thick of glass box was 10 millimeters. The
glass box was placed on a vibrating table (shaking
table) supported by four wheels. Shaking table was
driven by an electric motor through two pulleys that
drive the crank shaft that was connected to the
connecting rod that was prepared as shown in Figure
4. Shaking table moved back and forward
horizontally with a given variant of speed (inverter).
A model experiment was carried out as many as 6
units with details of 2 experiments with low density
DR 30%, 3 experiments were the medium density
DR = 55% and an experiment with high density Dr =
70%. The shaking table vibrated with speed variation.
In the experiment of 30% in density (DR = 30 %)
with variations of the amplitude and frequency
obtained dynamic acceleration response graphics as
shown in Figure 5, Figure 6 and Figure 7.
The Results of recorded of the shaking table
movement was obtained in the form of the dynamic
acceleration response graphics. The graph further
idealized by using equation 1. through equation 7.,
also to obtain the value of the maximum dynamic
acceleration response that occured. The first
experiments carried out of 0.005 meter in the
amplitude of vibration and one cicle per second in the
frequency of vibration.
Figure 5. Dynamic acceleration response graph of
cantilever model of A= 0,005m, DR = 30 %
Figure 5. shows that of 0.005 meter in amplitude, one
cicle per second in frequency and DR = 30 % in
density obtained of 0.19737 g in the maximum
dynamic acceleration. The second experiment
X1-4
conducted by using the same density that DR = 30%
and the results are shown in Figure 6.
Figure 6. Dynamic acceleration response graph of
cantilever model of A= 0,0081m, DR = 30 %
Figure 6. shows that of 0.0081 meter in amplitude
and 0.83 cicle per second in frequency obtained of
0.22029 g in the maximum dynamic acceleration. It
shows that the increase in the amplitude of vibration
with decrease in the frequency of vibration can lead
to a decrease in the maximum dynamic acceleration
vibration. Then next experiments carried out
additional of 15 percents in frequency with 0.005
meter in amplitude and the results are presented in
Figure 7.
Figure 8. The graph of the dynamic acceleration
response with amplitude, frequency variations to
density of DR = 30 %
Figure 8. shows that by increasing the amplitude of
vibration by 62 percent accompanied by lowering the
vibration frequency of about 17 percent then the
maximum dynamic acceleration increased 11.61
percent. Dynamic acceleration increased 18.5 percent
if the vibration amplitude decreased 38.3 percent but
the vibration frequency increased 38.5 percent. If the
vibration frequency is increased to 15 percent by the
amplitude remains the maximum dynamic
acceleration increased 32.26 percent.
Experiment with medium density DR = 55%,
with the amplitude and frequency variations obtained
the dynamic acceleration response graph as shown in
Figure 9, figure 10 and Figure 11.
Figure 7. Acceleration response graph of cantilever
model of A= 0,005m, DR = 30 %
Figure 7. shows that if the results of the experiment
in figure 5. compared to experimental results of
0.005 meter in amplitude and 1.15 cicles per second
in frequency as in figure 7. with 0.26105 g in
maximum dynamic acceleration indicates that the
increase of 15 percent in frequency with the same
amplitude resulted an increase of maximum dynamic
acceleration about 32.32 percent. This indicates that
the maximum dynamic acceleration is only
influenced by the frequency of vibration. The role of
the vibration frequency and amplitude of vibration to
the dynamic acceleration response presented in
Figure 8
Figure 9. Acceleration response graph of cantilever
model of A= 0,005m, DR = 55 %
Figure 9. shows that of 0.005 meter in the amplitude
of vibration, of 1.15 cicles per second in frequency of
vibration and DR = 55% in density obtained the
maximum dynamic acceleration 0.26104 g. If the
amplitude and frequency of each plus then the
maximum dynamic acceleration also increases as
shown in Figure 10.
X1-5
Figure 10. Acceleration response graph of cantilever
model of A= 0,0055 m, DR = 55 %
Figure 10 shows that the maximum dynamic
acceleration reached 0.35742 g with increased the
amplitude of vibration becomes 0.0055 meter and the
vibration frequency to 1.3 cicles per second.
In the next experiment with increasing the
amplitude becomes 0.0104 meters but the frequency
was reduced to 0.95 cicle per second obtained the
maximum dynamic acceleration by 0.37767 g as
shown in Figure 11.
Figure 12. shows that by increasing the amplitude of
vibration by 10 percent accompanied by increasing
the vibration frequency about 13 percent then the
maximum dynamic acceleration increased 36.54
percent. Dynamic acceleration increased about 6
percent if the vibration amplitude increased but the
vibration frequency decreased respectively about 27
percent. If the vibration frequency is increased to 112
percent but the amplitude decreased to about 17
percent then the maximum dynamic acceleration
increased about 45 percent.
The last experiment with high density DR = 70 %
had done of 0.0165 in the vibration amplitude and
0.95 cicle per second in the vibration frequency as
shown in Figure 13.
Figure 13. Acceleration response graph of cantilever
model of A= 0,0165 m, DR = 70 %
Figure 11. Acceleration response graph of cantilever
model of A= 0,0106 m, DR = 55 %
The influence of vibration amplitude and
frequency of vibration to the maximum dynamic
acceleration with a density of DR = 55% can be seen
in Figure 12.
Figure 12. The graph of the dynamic acceleration
response with amplitude, frequency variations to
density of DR = 55 %
X1-6
Figure 13. shows that with gave of 0.0165 meter in
amplitude of vibration and 0.95 cicle per second in
frequency of vibration to DR = 70 % in high density
obtained 0.56948 g in maximum dynamic
acceleration. The maximum dynamic acceleration
values obtained from all of experiments with density,
amplitude and frequency variations is shown in tables
1.
Table 1. Dynamic acceleration response of the tests
No of
test
1
2
3
4
5
6
7
DR
[%]
30
30
30
55
55
55
70
A [m]
f [cps]
amax [g]
0.005
0.0081
0.005
0.005
0.0055
0.0106
0.0165
1
0.83
1.15
1.15
1.3
0.95
0.95
0.19737
0.22029
0.26105
0.26104
0.35642
0.37767
0.56948
Results recorded the movement of sand grains
during experiment were analyzed for further drawn
landslide form. By using equations 8 - 10. the areas
of landslide obtained. Furthermore, to get centroid of
landslides areas used equations 11. The shape of
landslide and the centroid coordinates of landslide to
experiment of DR = 30 % in density is presented in
the Figure 14, DR = 55 % in density in the Figure 15
and DR = 70 % in density in Figure 16.
Figure 15 shows that increasing the maximum the
dynamic acceleration provides greater the bandwidth
due to landslide but smaller than the density of DR =
30%. Centroid coordinates trends tend vertical
direction. Next, the form of landslides areas and
coordinates of landslides areas to experiment with a
density DR = 70% is presented in Figure 16.
Figure 14. The graph of shape and centroid of slide
surface, DR = 30 %
Figure 14. shows that increasing the maximum the
dynamic acceleration of 18.5% gives a result of the
greater bandwidth landslide five-times. Centroid
coordinates trends tend toward the horizontal.
Furthermore, the shape of coordinates of landslides
areas and the centroid of landslide areas to
experiment with DR = 55% in density is presented in
Figure 15.
Figure 16. The graph of shape and centroid of slide
surface, DR = 70 %
Figure 16 shows that by provides maximum dynamic
acceleration of 0.56948 g, the bandwidth of landslide
that occurs very small compared to other experiments
with the maximum dynamic acceleration which is
smaller.
The equation of landslides, the areas of landslides,
the height of landslides areas, the width of landslides
areas and the centroid of landslides areas are
presented in Table 2.
Figure 15. The graph of shape and centroid of slide
surface, DR = 55 %
Table 2. Area of landslides of the tests
No
of
test
DR
[%]
Slide function
Area
[cm2]
1
2
3
4
5
6
7
30
30
30
55
55
55
70
y = 181.9569
y =6E-07x3+0.001x2–0.057x +141.5
y =0.168x +97.95
y =0.002x2-0.135x +106.4
y = 0.002x2-0.115x +48.31
y =6E-10x4-3E-07x3+0.196x+0.156
y =0.001x2–0.051x +111.5
0
32.50
202.19
109.04
249.45
564.01
146.58
Height
[h] of
slide
(x H)
0.1407
0.4091
0.3878
0.7317
1.0056
0.4139
Width
[b] of
slide
(x H)
0.9674
2.3118
1.2477
1.5069
2.3656
1.5661
Centroid of
slide [mm];
(xc, yc)
68.71; 155.38
156.24; 153.08
85.16; 144.29
106.52; 121.03
187.3; 105.4
110.9; 153.1
X1-7
CONCLUSION
REFERENCES
Based on the data which obtained during this
experiment, the following conclusions can be drawn
about the influence of dynamic acceleration of
sinusoidal loads to the landslide surface of cantilever
retaining walls:
1. Dynamic Acceleration is a function of
vibration frequency and amplitude of vibration. So
the value of dynamic acceleration is directly
proportional to the frequency of vibration and
amplitude of vibration
2. Increasing the percentage of vibration
frequency with fixed vibration amplitude resulting in
increasing of the percentage of the maximum
dynamic acceleration in double of the vibration
frequency percentage
3. Addition of the percentage of the amplitude of
vibration with remained in vibration frequency
resulting in increasing of the maximum dynamic
acceleration which equal to the percentage of
increasing the amplitude of vibration
4. The size of landslides area that occurred during
experiment showing direct proportion to the
maximum dynamic acceleration which is given at a
certain density
5. The form of landslides area that occurred
showing direct proportion to the dynamic
acceleration which is given at a certain density
6. Centroid coordinates followed the pattern of
landslides area
7. By increasing of 18.5% in the maximum the
dynamic acceleration with density of sands DR =
30 %.gives a result of the greater area of landslide
five-times and centroid coordinates trends tend to
more flat
8. By increasing to DR = 55 % and by increasing
the maximum of the dynamic acceleration provides
greater of the size of landslide, however the size of
landslide is smaller compere to the density of DR =
30 % as expected. The centroid coordinates trends
tend incline toward vertical.
Hidayati, A. M., Prabandiyani, S. RW., and Redana,
I.W. Laboratory Tests on Failure of Retaining
Walls Caused by Sinusoidal Load. Applied
Mechanics and Materials Vol 776 (2015) pp 4146, © (2015) Trans Tech Publications,
Switzerland,
doi:10.4028/www.scientific.net
/AMM.776.41.
Ishibashi, I. and Fang, Y – S ., 1987. Dynamic Earth
Pressures with Different Wall Movement Modes.
Soils And Foundations, Vol. 27, N0. 4, 11-22,
Dec. 1987, Japanese Society Of Soil Mechanics
And Foundation Engineering.
Kramer, Steven L. 1996. Geotechnicl Earthquake
Engineering. Upper Saddle River, New Jersey
07458: Prentice Hall, Inc.
Mononobe, N., and Matsuo, H., 1929. On
Determination of Earth Pressure during
Earthquake. Proccedings World Engineering
Conference, Tokyo, Japan, Vol. 9.
Okabe, S., 1924. General Theory of Earth Pressure
and seismic Stability of Retaining Wall and Dam.
Journal of Japanese Soc. of Civil Engineering,
Vol. 10, No. 6.
Prakash, S., 1981. Soil Dynamics. McGraw-Hill, Inc.
Prakash, S., and Puri, V. K., 1988. Foundations for
Machines : Analysis and Design. John Wiley &
Sons, Inc.
Sherif, A. M., and Fang, Y - S., 1984. Dynamic Earth
Pressures On Walls Rotating About The Top,
Soils And Foundation, Vol. 24, No. 4, 109-117,
Japanese Society of Soil Mechanics And
Foundation Engineering (paper).
X1-8
THE INFLUENCE OF DYNAMIC ACCELERATION OF SINUSOIDAL LOADS TO
THE LANDSLIDE SURFACE OF CANTILEVER RETAINING WALLS
Anissa M.Hidayati 1, Sri Prabandiyani RW 2 and I Wayan Redana 3
ABSTRACT: The dynamic acceleration is one of dynamic parameters will be taken into consideration in the
analysis of the safety of retaining wall construction due to dynamic loads beside other parameters such as: (1) the
dynamic frequency, (2) the density of soils and (3) the amplitude of vibration. This research aims to study the
role of dynamic acceleration to the landslide surface of retaining walls of cantilecer type due to dynamic load.
This study was done by a small scale model test of cantilever retaining wall type of 18 centimeters in height, 9
centimeters in width and loaded by using shaking table to simulate dynamic loads. The dynamic load was given
with the variation of the frequency and amplitude of vibration to obtain the acceleration of dynamic response.
The dynamic acceleration response was measured by using accelerometer. Dry sand with three densities
variations were used in this experiment. The movements of the sand grains were recorded during experiment to
be able to show the change of the sliding surface of the retaining wall. The results showed that there was the
difference in the dynamic acceleration response generated due to differences in the dynamic frequency and
amplitude of vibration. There was also a relation ship between the value of dynamic acceleration response to the
shape of the landslide surface.
Keywords: dynamic acceleration response, landslide surface, soils density, cantilever type
INTRODUCTION
Landslides occur on a regular basis throughout
the world as part of the ongoing evolution of
landscapes. Many landslides occur in natural slopes,
but slides also occur in man-made slopes from time
to time. At any point in time, then, slopes exist in
states ranging from very stable to marginally stable.
When earthquake occur, the effects of earthquakeinduced ground shaking is often sufficient to cause
failure of slopes that were marginally to moderately
stable before the earthquake. The resulting damage
can range from insignificant to catastrophic
depending on the geometric and material
characteristics of the slope. Construction of retaining
wall construction is one way to anticipate the slopes
damage due to earthquake load.
In the last two decades had developed innovative
system which was used to anticipate the damage of
slopes caused by the earthquake. In general, ground
anchoring system for seismic design purposes can be
divided into three main categories: gravity walls,
cantilever walls and braced walls. Each type of wall
posses different assumption in evaluating lateral soil
pressure.
Retaining walls can fail in many difference ways.
Cantilever walls fail by sliding, overturning, or gross
instability also fail in bending. The magnitude and
distribution of dynamic wall pressures were
influenced by the mode of wall movement, e.g.,
translation , rotation about the base, or rotation about
the top (Sherif, A. M., and Fang, Y - S. 1984).
Okabe (1924) and Mononobe & Matsuo (1929)
developed the basis of pseudo-static analysis of earth
pressure on the wall of the load due to the earthquake
which was then known as Mononobe-Okabe method.
Mononobe-Okabe method is a development of
Coloumb theory that follows the principle of
equilibrium limit (limit equilibrium). The problem of
stability of retaining walls was solved used a
combination of rigid displacement-based analytical
solutions (walls are allowed to experience the
rotation at the top of the wall) and the experimental
method utilized shaking table to determine the
distribution of dynamic active pressure on a gravity
1
Student, Udayana University, anissamh@yahoo.com, INDONESIA
Professor, Diponegoro University, wardani_spr@yahoo.com, INDONESIA
3 Professor, Udayana University, iwayanredana@yahoo.com, INDONESIA
2
X1-1
walls (Sherif and Fang 1984). The experimental
results showed that the distribution of dynamic active
earth pressure as a function of acceleration. Dynamic
active ground pressure distribution obtained from the
value of soil pressure of observe by using transducer,
hence pressure did not calculating by using the real
movement of soil particle of the experiment.
Dynamic active pressure increased with the increased
in acceleration. Ishibashi and Fang (1987) completed
the rigid retaining wall stability issues using a
combination of analytical methods based on
displacement and experimental methods. The
experiments carried out used a shaking table with
model of gravity wall. The experiments were done on
dry soils and non-cohesive, while the walls were
allowed to experience a variety of movements such
as translation, rotation of the bottom wall, the
rotation at the top of the wall, and combinations
thereof. When the rotation at the base of the wall, the
pressure distribution is not linear. In the area near the
base of the wall, there is a high residual stress due to
displacement of the wall, hence the capture point of
active pressure is lower than a third of the wall height.
When the rotation at the top of the wall, the pressure
distribution is not linear. There are areas that had a
high stress near the top of the wall as a result of the
tapered land, and the area had a low voltage at the
base of the wall due to a shift in the wall.
Consequently, capture point total active dynamic
pressure was higher than a third of the wall height.
Dynamic lateral earth pressure distribution obtained
from observations on the value of soil pressure
transducer.
LITERATURE REVIEW
Construction of the building both inside or on the
surface of the ground, not only accepted static load
but also dynamic load. Dynamic load acting on the
land or building structures could be derived from
natural or man-made. If the dynamic loads worked on
the ground, it would caused the movement of soil
grain, consequently the structure which was
supported by the soil would experienced instability.
Dynamic Response of retaining wall ranging from
even the simplest to quite complex. Movement and
pressure of the wall depends on the response of the
soil which underlying of walls, the response of the
back-fill, the response of inertia and flexibility of the
wall itself, and the nature of the input motion
(Kramer, Steven L. 1996).
The problem of retaining soil is one of the oldest
in geotechnical engineering; some of the earliest and
most fundamental principles of soil mechanics were
developed to allow rational design of retaining walls.
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Many different approaches to soil retention have
been developed and used successfully.
Seismic design of retaining walls is generally
based on seismic pressure or allowable displacement.
In the former approach, pseudo-static or pseudodynamic analysis are used to estimate seismically
induced wall pressure, and the wall is designed to
resist those pressure without failing or causing failure
of the surrounding soil. The latter approach involves
designing the wall such that its seismically induced
permanent displacement does not exceed a
predetermined allowable displacement.
Modeling experiments in the laboratory can be
done with the aim to study the movement of sand and
retaining wall caused by vibration (dynamic load)
using cantilevered retaining wall models that are
supported by dry sand with provided dynamic load
(sinusoidal) with variations of the vibration
acceleration and the density of the sand.
The objects that perform accelerated uniformly
motion, has fixed acceleration, this means that the
object is always working with pattern that remains
both direction and magnitude. If it’s force is always
changing, the acceleration is olso changing.
Repetitive motion in the same time interval called a
periodic motion. This periodic motion occurs on a
regular basis and motive force is proportional to the
amplitude. Easy to understand that the smaller the
amplitude is also smaller the driving force. The
largest amplitude is called amplitude of vibration (A).
Periodic motion can be expressed in sine or cosine
function, therefore periodic motion is called
harmonic motion. The periodic motion that moves
back and forth through the same trajectory so-called
vibration or oscillation and is also known as a simple
harmonic motion. The time needed to take the path
back and forth is called the period, while the number
of vibrations per unit time is called frequency. The
relationship between the period (T) and frequency (f)
according to this statement is expressed as the
equation 1.
T
1
f
[sec]
(1)
The frequency (f) or the amount of vibration in each
unit time is expressed in equation 2.
f
1
T
[ cps ]
(2)
While the mathematical function from objects
called harmonic motion/vibration (Prakash, S., 1981)
and be expressed as equation 3.
x Asin ( t )
(3)
where x is the displacement of a trajectory in function
of time (t); A is the amplitude (equal to the maximum
displacement); ω is the angular frequency of the
trajectory [radians/sec]; t is the time [seconds]. The
harmonic motion repeated every 2π radians with
fixed angular velocity and maximum displacement is
value of A, referred to as amplitude (Figure 1.).
By taking into account the movement of grain
movement graphic results, it can be calculated the
area of landslide behind the retaining wall
construction due to the sinusoidal dynamic load (see
Figure 3.).
Figure 2. Representation of displacement, velocity
and acceleration
Figure 1. Representation fo harmonic motion.
A cycle of motion is completed when the movement
reached one full rotation as described in equation 4.
2 f
[radians / sec]
(4)
with f is frequency of vibration.
From equation 4., values of obtained f as defined in
equation 5.
f
cps
2
(5)
To determine the velocity of simple harmonic motion,
differentiate equation 3. with respect to time (t) in
order to obtain equation 6 (Prakash, S., and Puri, V.
K., 1988).
x
dx
dt
d
dt
( A sin t ) A cos ( t )
d x
dt
d
dt
( A cos ( t )) A 2 sin( t ) 2 x a
The area bounded by 2 (two) curves y1 and y2 which
as function of x and x = 0 and x = x1, it can be
calculated:
The area below of curve y1, x = 0 and x = x1 is
expressed as equation 8.
A1 y1 dx
x1
(6)
(8)
0
where x is the velocity of simple harmonic motion
equation. Then, to obtain the acceleration of simple
harmonic motion by differentiating equation 6. with
respect to time (t) thus produce equation 7.
x
Figure 3. The area bounded by curve y1 = f(x), y2 =
f(x), x = 0 dan x = x1
(7)
where x is the acceleration of simple harmonic
motion equation, also denoted as a . The displacement
path, velocity and acceleration of motion was
described in Figure 2.
The area below of curve y2, x = 0 and x = x1 is
defined in equation 9.
A1 y2 dx
x2
(9)
0
So the area bounded by the intersection of the two
curves are expressed as equation 10.
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A A1 A2 y1 dx y2 dx
x1
x2
0
0
(10)
See the segment of y x dx. Then the centroid segment
against X-axis and Y-axis is C ( x ; y ). The of
coordinates centroid C can be obtained by using
equation 11 and equation 12.
x. y dx
x2
x
0
x2
(11)
y dx
0
y1 y2
. y dx
2
0
Figure 4 The equipment of retaining walls model test
on sinusoidal dynamic load (not scaled) (Hidayati et
al. 2015)
x2
y
y dx
DATA COLLECTION AND DISCUSSION
(12)
x2
0
EXPERIMENT
The retaining wall model test was performed in
The Laboratory Soil Mechanics of Civil Engineering
Faculty, Udayana University, Bali, Indonesia. The
model of retaining wall was made of concrete placed
on dry sand. Model test was performed using dry
sand material with a grain size through No. 4 of sieve
and retained No.100 sieve of loose sand density (DR
= 30 %), medium sand density (DR = 55 %) and
dense sand density (DR = 70 %). The model of
retaining wall was designed as a cantilever type of 18
centimeters in height (H), 9 centimeters in width (B).
The model retaining wall was loaded by sinusoidal
speed and amplitude variations. Dynamic response
was recorded using recording devices vibration
acceleration (accelerometer). During experiment the
movement of sand grains recorded.
The model tests was made in the glass box of 2
meters in length, 0.4 meter in width and 1 meter in
height. Thick of glass box was 10 millimeters. The
glass box was placed on a vibrating table (shaking
table) supported by four wheels. Shaking table was
driven by an electric motor through two pulleys that
drive the crank shaft that was connected to the
connecting rod that was prepared as shown in Figure
4. Shaking table moved back and forward
horizontally with a given variant of speed (inverter).
A model experiment was carried out as many as 6
units with details of 2 experiments with low density
DR 30%, 3 experiments were the medium density
DR = 55% and an experiment with high density Dr =
70%. The shaking table vibrated with speed variation.
In the experiment of 30% in density (DR = 30 %)
with variations of the amplitude and frequency
obtained dynamic acceleration response graphics as
shown in Figure 5, Figure 6 and Figure 7.
The Results of recorded of the shaking table
movement was obtained in the form of the dynamic
acceleration response graphics. The graph further
idealized by using equation 1. through equation 7.,
also to obtain the value of the maximum dynamic
acceleration response that occured. The first
experiments carried out of 0.005 meter in the
amplitude of vibration and one cicle per second in the
frequency of vibration.
Figure 5. Dynamic acceleration response graph of
cantilever model of A= 0,005m, DR = 30 %
Figure 5. shows that of 0.005 meter in amplitude, one
cicle per second in frequency and DR = 30 % in
density obtained of 0.19737 g in the maximum
dynamic acceleration. The second experiment
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conducted by using the same density that DR = 30%
and the results are shown in Figure 6.
Figure 6. Dynamic acceleration response graph of
cantilever model of A= 0,0081m, DR = 30 %
Figure 6. shows that of 0.0081 meter in amplitude
and 0.83 cicle per second in frequency obtained of
0.22029 g in the maximum dynamic acceleration. It
shows that the increase in the amplitude of vibration
with decrease in the frequency of vibration can lead
to a decrease in the maximum dynamic acceleration
vibration. Then next experiments carried out
additional of 15 percents in frequency with 0.005
meter in amplitude and the results are presented in
Figure 7.
Figure 8. The graph of the dynamic acceleration
response with amplitude, frequency variations to
density of DR = 30 %
Figure 8. shows that by increasing the amplitude of
vibration by 62 percent accompanied by lowering the
vibration frequency of about 17 percent then the
maximum dynamic acceleration increased 11.61
percent. Dynamic acceleration increased 18.5 percent
if the vibration amplitude decreased 38.3 percent but
the vibration frequency increased 38.5 percent. If the
vibration frequency is increased to 15 percent by the
amplitude remains the maximum dynamic
acceleration increased 32.26 percent.
Experiment with medium density DR = 55%,
with the amplitude and frequency variations obtained
the dynamic acceleration response graph as shown in
Figure 9, figure 10 and Figure 11.
Figure 7. Acceleration response graph of cantilever
model of A= 0,005m, DR = 30 %
Figure 7. shows that if the results of the experiment
in figure 5. compared to experimental results of
0.005 meter in amplitude and 1.15 cicles per second
in frequency as in figure 7. with 0.26105 g in
maximum dynamic acceleration indicates that the
increase of 15 percent in frequency with the same
amplitude resulted an increase of maximum dynamic
acceleration about 32.32 percent. This indicates that
the maximum dynamic acceleration is only
influenced by the frequency of vibration. The role of
the vibration frequency and amplitude of vibration to
the dynamic acceleration response presented in
Figure 8
Figure 9. Acceleration response graph of cantilever
model of A= 0,005m, DR = 55 %
Figure 9. shows that of 0.005 meter in the amplitude
of vibration, of 1.15 cicles per second in frequency of
vibration and DR = 55% in density obtained the
maximum dynamic acceleration 0.26104 g. If the
amplitude and frequency of each plus then the
maximum dynamic acceleration also increases as
shown in Figure 10.
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Figure 10. Acceleration response graph of cantilever
model of A= 0,0055 m, DR = 55 %
Figure 10 shows that the maximum dynamic
acceleration reached 0.35742 g with increased the
amplitude of vibration becomes 0.0055 meter and the
vibration frequency to 1.3 cicles per second.
In the next experiment with increasing the
amplitude becomes 0.0104 meters but the frequency
was reduced to 0.95 cicle per second obtained the
maximum dynamic acceleration by 0.37767 g as
shown in Figure 11.
Figure 12. shows that by increasing the amplitude of
vibration by 10 percent accompanied by increasing
the vibration frequency about 13 percent then the
maximum dynamic acceleration increased 36.54
percent. Dynamic acceleration increased about 6
percent if the vibration amplitude increased but the
vibration frequency decreased respectively about 27
percent. If the vibration frequency is increased to 112
percent but the amplitude decreased to about 17
percent then the maximum dynamic acceleration
increased about 45 percent.
The last experiment with high density DR = 70 %
had done of 0.0165 in the vibration amplitude and
0.95 cicle per second in the vibration frequency as
shown in Figure 13.
Figure 13. Acceleration response graph of cantilever
model of A= 0,0165 m, DR = 70 %
Figure 11. Acceleration response graph of cantilever
model of A= 0,0106 m, DR = 55 %
The influence of vibration amplitude and
frequency of vibration to the maximum dynamic
acceleration with a density of DR = 55% can be seen
in Figure 12.
Figure 12. The graph of the dynamic acceleration
response with amplitude, frequency variations to
density of DR = 55 %
X1-6
Figure 13. shows that with gave of 0.0165 meter in
amplitude of vibration and 0.95 cicle per second in
frequency of vibration to DR = 70 % in high density
obtained 0.56948 g in maximum dynamic
acceleration. The maximum dynamic acceleration
values obtained from all of experiments with density,
amplitude and frequency variations is shown in tables
1.
Table 1. Dynamic acceleration response of the tests
No of
test
1
2
3
4
5
6
7
DR
[%]
30
30
30
55
55
55
70
A [m]
f [cps]
amax [g]
0.005
0.0081
0.005
0.005
0.0055
0.0106
0.0165
1
0.83
1.15
1.15
1.3
0.95
0.95
0.19737
0.22029
0.26105
0.26104
0.35642
0.37767
0.56948
Results recorded the movement of sand grains
during experiment were analyzed for further drawn
landslide form. By using equations 8 - 10. the areas
of landslide obtained. Furthermore, to get centroid of
landslides areas used equations 11. The shape of
landslide and the centroid coordinates of landslide to
experiment of DR = 30 % in density is presented in
the Figure 14, DR = 55 % in density in the Figure 15
and DR = 70 % in density in Figure 16.
Figure 15 shows that increasing the maximum the
dynamic acceleration provides greater the bandwidth
due to landslide but smaller than the density of DR =
30%. Centroid coordinates trends tend vertical
direction. Next, the form of landslides areas and
coordinates of landslides areas to experiment with a
density DR = 70% is presented in Figure 16.
Figure 14. The graph of shape and centroid of slide
surface, DR = 30 %
Figure 14. shows that increasing the maximum the
dynamic acceleration of 18.5% gives a result of the
greater bandwidth landslide five-times. Centroid
coordinates trends tend toward the horizontal.
Furthermore, the shape of coordinates of landslides
areas and the centroid of landslide areas to
experiment with DR = 55% in density is presented in
Figure 15.
Figure 16. The graph of shape and centroid of slide
surface, DR = 70 %
Figure 16 shows that by provides maximum dynamic
acceleration of 0.56948 g, the bandwidth of landslide
that occurs very small compared to other experiments
with the maximum dynamic acceleration which is
smaller.
The equation of landslides, the areas of landslides,
the height of landslides areas, the width of landslides
areas and the centroid of landslides areas are
presented in Table 2.
Figure 15. The graph of shape and centroid of slide
surface, DR = 55 %
Table 2. Area of landslides of the tests
No
of
test
DR
[%]
Slide function
Area
[cm2]
1
2
3
4
5
6
7
30
30
30
55
55
55
70
y = 181.9569
y =6E-07x3+0.001x2–0.057x +141.5
y =0.168x +97.95
y =0.002x2-0.135x +106.4
y = 0.002x2-0.115x +48.31
y =6E-10x4-3E-07x3+0.196x+0.156
y =0.001x2–0.051x +111.5
0
32.50
202.19
109.04
249.45
564.01
146.58
Height
[h] of
slide
(x H)
0.1407
0.4091
0.3878
0.7317
1.0056
0.4139
Width
[b] of
slide
(x H)
0.9674
2.3118
1.2477
1.5069
2.3656
1.5661
Centroid of
slide [mm];
(xc, yc)
68.71; 155.38
156.24; 153.08
85.16; 144.29
106.52; 121.03
187.3; 105.4
110.9; 153.1
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CONCLUSION
REFERENCES
Based on the data which obtained during this
experiment, the following conclusions can be drawn
about the influence of dynamic acceleration of
sinusoidal loads to the landslide surface of cantilever
retaining walls:
1. Dynamic Acceleration is a function of
vibration frequency and amplitude of vibration. So
the value of dynamic acceleration is directly
proportional to the frequency of vibration and
amplitude of vibration
2. Increasing the percentage of vibration
frequency with fixed vibration amplitude resulting in
increasing of the percentage of the maximum
dynamic acceleration in double of the vibration
frequency percentage
3. Addition of the percentage of the amplitude of
vibration with remained in vibration frequency
resulting in increasing of the maximum dynamic
acceleration which equal to the percentage of
increasing the amplitude of vibration
4. The size of landslides area that occurred during
experiment showing direct proportion to the
maximum dynamic acceleration which is given at a
certain density
5. The form of landslides area that occurred
showing direct proportion to the dynamic
acceleration which is given at a certain density
6. Centroid coordinates followed the pattern of
landslides area
7. By increasing of 18.5% in the maximum the
dynamic acceleration with density of sands DR =
30 %.gives a result of the greater area of landslide
five-times and centroid coordinates trends tend to
more flat
8. By increasing to DR = 55 % and by increasing
the maximum of the dynamic acceleration provides
greater of the size of landslide, however the size of
landslide is smaller compere to the density of DR =
30 % as expected. The centroid coordinates trends
tend incline toward vertical.
Hidayati, A. M., Prabandiyani, S. RW., and Redana,
I.W. Laboratory Tests on Failure of Retaining
Walls Caused by Sinusoidal Load. Applied
Mechanics and Materials Vol 776 (2015) pp 4146, © (2015) Trans Tech Publications,
Switzerland,
doi:10.4028/www.scientific.net
/AMM.776.41.
Ishibashi, I. and Fang, Y – S ., 1987. Dynamic Earth
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Soils And Foundations, Vol. 27, N0. 4, 11-22,
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And Foundation Engineering.
Kramer, Steven L. 1996. Geotechnicl Earthquake
Engineering. Upper Saddle River, New Jersey
07458: Prentice Hall, Inc.
Mononobe, N., and Matsuo, H., 1929. On
Determination of Earth Pressure during
Earthquake. Proccedings World Engineering
Conference, Tokyo, Japan, Vol. 9.
Okabe, S., 1924. General Theory of Earth Pressure
and seismic Stability of Retaining Wall and Dam.
Journal of Japanese Soc. of Civil Engineering,
Vol. 10, No. 6.
Prakash, S., 1981. Soil Dynamics. McGraw-Hill, Inc.
Prakash, S., and Puri, V. K., 1988. Foundations for
Machines : Analysis and Design. John Wiley &
Sons, Inc.
Sherif, A. M., and Fang, Y - S., 1984. Dynamic Earth
Pressures On Walls Rotating About The Top,
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Japanese Society of Soil Mechanics And
Foundation Engineering (paper).
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