Gsp dynamic responseofmodelfootingonreinforcedsand

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Dynamic Response of Model Footing on Reinforced Sand
Conference Paper · June 2018
DOI: 10.1061/9780784481486.021
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Geotechnical Earthquake Engineering and Soil Dynamics V GSP 293 199
© ASCE
Dynamic Response of Model Footing on Reinforced Sand
Raghvendra Sahu1
; Ramanathan Ayothiraman2
; and G. V. Ramana3
1
Ph.D. Scholar, Dept. of Civil Eng., IIT Delhi, New Delhi-16. E-mail:
sahu.raghvendra@gmail.com
2
Associate Professor, Dept. of Civil Eng., IIT Delhi, New Delhi-16. E-mail:
araman@civil.iitd.ac.in
3
Professor, Dept. of Civil Eng., IIT Delhi, New Delhi-16. E-mail: ramana@civil.iitd.ac.in
ABSTRACT
The free vibration tests were conducted on model footing resting on unreinforced and
reinforced. The sand was reinforced with the human hair fibers and geogrids (PET and HDPE).
The fiber inclusion was considered as 0.5% by dry weight of sand. The sand bed was filled in 8
layers, and each layer was compacted using a calibrated plate vibrator to achieve the desired
relative density (80%). The free vibration tests were conducted in model test tank by varying the
depth of reinforcement (dr) by keeping the width of reinforcement (wr) as constant. The results
indicate that the hair fiber reinforcement and geogrid reinforcement could improve the natural
frequency of the soil-foundation system. Damping is found to reduce with the inclusion of both
reinforcing materials.
INTRODUCTION
Dynamic loads transmitted to machine foundations are limited to 20% of static load to avoid
the nonlinear behavior of soil (Prakash and Puri 1988). While designing machine foundation, the
critical design requirement such as resonance criteria (operating frequency, ω ≠ natural
frequency, ωn) and limiting amplitude criteria should be fulfilled (Permissible amplitude: 20 to
200 µm depending on the type of machines and their operating frequencies). Because excessive
amplitude may induce the large strains and eventually it may damage the machine components
(Richart 1962). In cases, when the above said criteria is not fulfilled, deep foundation such as
pile foundation or ground improvement techniques such as reinforcement, grouting and heavy
compaction are usually adopted. Ground improvement enhances the strength of soil and hence
limits the dynamic parameters within the permissible range. Significant works had been
conducted on the soil-foundation system (Layered/reinforced soil) subjected to machine-induced
dynamic loads to investigate the effects of various parameters such as embedment depth,
saturation, reinforcement through model tests (Mandal & Baidya 2004; Samal 2011; Khati et al.
2012; Clement et al. 2015) and in-situ tests (Boominathan et al. 1991).
Ground improvement using different reinforcing materials (metal strips, geosynthetics or
fibers) had been successfully implemented in different applications under static loading.
However, it has been noticed that the use of fibers and geosynthetics as reinforcing material with
the soil under machine foundations is not explored much (Boominathan et al. 1991; Khati et al.
2010; Samal 2011; Clement et al. 2015).
In the last decade, the use of human hair fibers as reinforcing material was investigated
through lab tests to check the improvement in the strength properties of soil (Akhtar et al. 2008;
Akhtar and Ahmad 2009; Pillai and Ayothiraman 2012; Ayothiraman et al. 2014; Butt et al.
2016; Sahu et al. 2016, 2018). Their use as reinforcing material could be an eco-friendly and
economical solution. However, the use of human hair fibers as reinforcing material under
Geotechnical Earthquake Engineering and Soil Dynamics V
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dynamic loading is not studied so far. Studies on the reinforced soil-foundation system under
dynamic load are also limited. Therefore, the present study focuses on the use of reinforcing
material (human hair fibers and geogrids) to investigate the dynamic behavior of soil. 1-g model
free vibration tests were conducted on a small-scale footing resting on unreinforced sand and
reinforced sand.
CHARACTERIZATION OF MATERIALS
Soil: The sand used in the present study was collected from the banks of Yamuna River,
Delhi, India. This sand contains mainly fine sand (80%), medium to coarse sand (16.9%) and
silt/clay (3.1%) and is classified as poorly graded sand (SP) (ASTM D2487 − 11).
Reinforcing materials: Human Hair Fibers (HHF) shown in Fig. 1a, are the natural waste
material generated from the barber shops which are usually dispose-off to landfills. (Gupta 2014)
reported the potential uses of human hair fibers in several applications as reinforcement material
similar to other commercially available fibers, owing to its fibrous nature, tensile strength, bulk
availability, and economy. The diameter of used hair fiber samples was measured through
different SEM images and found in the range of 50 to 114 µm (micron) (Akhtar and Ahmad
2009; Pillai and Ayothiraman 2012; Sahu et al. 2016, 2018). Tensile strength tests were
conducted on randomly selected hair fiber samples and found that the tensile strength of different
hair fibers tested varied widely and calculated values lie in the range of 124-150 MPa.
Polyethylene Terephthalate (PET) biaxial geogrid (aperture = 28.7×27.6 mm) and extruded
High-Density Polyethylene (HDPE) biaxial geogrid (aperture = 38.7×36.4 mm) were used in this
study and are shown in Fig. 1b and 1c respectively.
FREE VIBRATION TESTS
Scaling of footing: The dimensions of the model footing were scaled down from the
dimensions of test block used in IS: 5249 (1992) considering the scaling laws (Wood 2004). The
arrived dimensions of footing (100 × 100 × 44 mm) using following scaling parameters yielded
mass ratio of 2.2.
m m
l
p p
l B 1
Length ratio, n = = =
l B n
m
E
p
E 200
Young's modulus ratio, n = =
E 20
G α
1
Stiffness ratio, n = Where, α = 0.5 for sand
n
m G
3
h l
p E
t n
Thickness ratio, n = = n
t n
wherein lm and lp, Em and Ep, tm and tp are the length, Young’s modulus and thickness of model
footing and test block of IS: 5249 (1992) respectively.
Test tank: In this study, the experimental program was established such that the
reinforcement could be placed right below the foundation varying the depth/vertical extent of
reinforcement (dr) and the no. of geogrid layers. Since the present study was focused on the
dynamic response of foundation subjected to free vibration tests in the test tank, the reflection of
waves from tank wall was a major concern. Therefore, a larger size model test tank (1240 mm ×
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900 mm × 800 mm) was used in this study along with the absorbing medium. In this study, 50
mm thick sheet of thermocol (Gazetas and Stokoe 1991) was used as absorbing medium between
the rigid tank wall and sand. The typical schematic representation of model test arrangement and
view of inducing the free vibration is shown in Fig. 2.
Figure 1. Reinforcing materials (a) HHF (b) PET geogrid (c) HDPE geogrid
Figure 2. (a) Typical arrangement of test tank and free vibration tests (b) View of inducing
free vibration by hitting model foundation
Sand bed preparation: The relative density tests were carried out on unreinforced sand (UR
sand), and Hair Fiber-Reinforced sand (HFR sand) (random mixing of 0.5% unsorted fibers) as
per IS: 2720 (Part-14). It was very difficult to mix the fibers with sand in a dry condition, hence
to make a uniform mix of sand and fibers, an initial water content of 2-3% by dry weight of the
sand was added. The typical view of sand-hair fiber matrix after thorough mixing is shown in
Fig. 3. The maximum, minimum and density at 80% relative density, of unreinforced sand and
fiber-reinforced sand, are summarized in Table 1.
The sand was compacted in layers using a calibrated vibratory compactor (Fig. 4) in both
unreinforced and reinforced conditions. The model experiments were conducted on the sand bed
prepared at 80% relative density to simulate the very dense condition. In case of fiber-reinforced
sand, due to cohesionless properties of sand, it was not possible to excavate the area which was
to be reinforced because the sides may collapse. To resolve this issue a stainless steel cage (Fig.
5) was fabricated for separating the unreinforced and fiber-reinforced sand in the model test tank.
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The thickness of the cage used to demarcate the reinforced and unreinforced zone is only 2 mm
thick with a very smooth surface and enough care was exercised while withdrawing the cage.
This may not significantly affect the density of the prepared sand bed in both zones.
Table 1. Variation in Density of Fiber-Reinforced Sand
Fiber Content (%)
Maximum Dry Density
(kg/m3
)
Minimum Dry
Density (kg/m3
)
Dry Density at RD =
80% (kg/m3
)
UR sand 1700 1290 1590
0.5% HFR sand 1660 1290 1570
Figure 3. Typical Hair fiber-reinforced sand mixture
Figure 4. Mini Plate Vibrator
In case of preparation of geogrid-reinforced sand, the geogrids were placed according to the
different configuration used in different tests. The geogrid layers were placed such that the center
of geogrid, model foundation, and model test tank matches concentrically. The first geogrid was
placed at a depth of 0.3B below the model footing, and further, the spacing between the geogrids
was kept as 0.3B.
Test procedure and test program: The free vibration was created by hitting the model
foundation with a hammer. The time history of acceleration was measured using high precision
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(Sensitivity = 400 mV/g) calibrated accelerometer in free vibration tests. The signals of the
accelerometer were recorded at sampling frequency of 2400 using a Data Acquisition System
(DAS) consisting of the 8-channel universal data logger and a computer.
Figure 5. Stainless steel cage
Test program
The free vibration tests were conducted on both, unreinforced sand and reinforced sand in
model test tank varying the fiber content and extent of fiber-reinforced sand. The free vibration
tests were repeated five times to confirm the repeatability of the results, and the same results
were obtained.
Table 2. Experimental Program
Reinforcing
Material
Variable Parameters
No. of
Tests
UR sand N/A 1
HHF
Fiber content (%) 0.5
4
Vertical extent of fiber-reinforcement
(dr)
0.25B, 0.5B, 0.75B, B
PET geogrid
No. of geogrid 2,3,4
3
(dr)
0.6B, 0.9B, 1.2B
HDPE geogrid
No. of geogrid 2,3,4
3
(dr)
0.6B, 0.9B, 1.2B
Total Tests 11
B*_Width of model footing
RESULTS AND DISCUSSIONS
Time histories and FFT analysis. The typical time-histories of acceleration measured by the
free vibration tests in the unreinforced sand, HFR sand and geogrids reinforced sand (PET and
HDPE) are shown in Fig. 6. It can be observed from Fig. 6 that the vibration initially decreases
up to few cycles (2 to 3 cycles). After these few cycles, there is an increase in the amplitude of
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vibration observed for another few cycles which subsequently died down permanently. This may
be due to the reflection of waves from the tank boundary in spite of having an absorbing
medium. However, the magnitude of increase in vibration amplitude is only marginal, but it has
affected the time period. A similar observation was reported by Dobry et al. (1986) from free
vibration tests conducted on model footings in test tanks where the reflected waves arrive after
few cycles (1.5 cycles). Hence, Dobry et al. (1986) recommended that the time history data
recorded for initial few cycles only to be used for calculations. Therefore, in the present study,
the time history data of initial 2 to 3 cycles was used for obtaining the natural frequency and
damping. The Fast Fourier Transform (FFT) was done to convert the response of time domain to
frequency domain for all the cases, and typical FFT plots are shown in Fig. 7.
Figure 6. Typical acceleration-time histories of free vibration tests conducted on (a) UR
sand and (b) HFR sand (dr/B = 0.25) (c) PET geogrid-reinforced sand (dr/B = 0.6) and (d)
HDPE geogrid-reinforced sand (dr/B = 0.6)
It can be observed from Fig. 7 that the predominant frequency in FFT of unreinforced sand is
102.2 Hz, fiber-reinforced sand is about 109.0 Hz, and geogrid reinforced sand is about 107.5.
Similar FFT plots were made for all the tests conducted, and the natural frequency of soil-
foundation system was interpreted, and results are presented in Table 3. The damping ratio was
determined using the fundamentals of vibration of a Single Degree of Freedom (SDOF) system
from the measured time-history of acceleration for different tests. The natural frequency and
1.56 1.58 1.60 1.62 1.64 1.66 1.68
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
UR sand
Acceleration
(g)
(a)
1.26 1.28 1.30 1.32 1.34 1.36 1.38
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
(b)
0.25B_0.50% HF
Acceleration
(g)
1.84 1.86 1.88 1.90 1.92 1.94 1.96
-1.2
-0.8
-0.4
0.0
0.4
0.8
(c)
2G_PET
Acceleration
(g)
1.24 1.26 1.28 1.30 1.32 1.34 1.36
-1.2
-0.8
-0.4
0.0
0.4
0.8
(d)
Time (sec.)
Time (sec.)
Time (sec.)
2G_HDPE
Time (sec.)
Acceleration
(g)
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damping ratio obtained from free vibration tests are discussed below.
Figure 7. Typical FFT curves of (a) UR sand and (b) HFR sand (dr/B = 0.25) (c) PET
geogrid-reinforced sand (dr/B = 0.6) and (d) HDPE geogrid-reinforced sand (dr/B = 0.6)
Natural frequency and damping: The natural frequency and damping ratio obtained from
free vibration tests are presented in Table 3. It is observed from Table 3 that natural frequency of
reinforced sand is increased as compared to unreinforced sand whereas the damping ratio is
decreased for reinforced sand as compared to unreinforced sand. The natural frequency of model
foundation obtained from free vibration tests was scaled-up to determine the natural frequency of
in-situ test block using scale factor, n (Wood 2004). It is observed from Table 3 that the
extrapolated natural frequencies for in-situ test block lie in the range of 22 to 25 Hz. Clement et
al. (2015) conducted model tests on the geogrid-reinforced sand and found a similar range of
natural frequencies from forced vibration tests (23-30 Hz). The lower value of 23 Hz was
reported for unreinforced very dense Badarpur sand, and the similar value of natural frequency
was observed for very dense Yamuna sand in this study. This confirms that the natural
frequencies obtained for identically same model foundation mass are almost same even though
the gradation characteristics of sands are different.
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
107.5 Hz
107.5 Hz
109.0 Hz
UR sand
Fourier
amplitude
102.2 Hz
(a)
0.000
0.002
0.004
0.006
0.008
(b)
0.25B_0.5% HF
0 20 40 60 80 100 120 140
0.000
0.005
0.010
0.015
0.020
0.025
(c)
2G_PET
Fourier
amplitude
Frequency (Hz)
0 20 40 60 80 100 120 140
0.000
0.005
0.010
0.015
0.020
(d)
2G_HDPE
Frequency (Hz)
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Table 3. Free Vibration Test Results on Reinforced Sand
Type of
Reinforcement
Lateral
Extent (wr)
Vertical
Extent (dr)
Natural Frequency (Hz) Damping
Ratio, ξ (%)
fnm fnp
UR sand NA NA 102.2 22.7 18.2
0.50%
HFR sand
B
0.25B 109.0 24.2 6.0
0.5B 108.1 24.0 10.6
0.75B 109.9 24.4 8.6
B 109.5 24.3 9.6
HDPE
Geogrid
B
0.6B 107.5 23.9 8.7
0.9B 107.5 23.9 7.5
1.2B 107.5 23.9 8.4
PET
Geogrid
B
0.6B 107.5 23.9 9.7
0.9B 111.3 24.7 8.8
1.2B 107.5 23.9 11.9
CONCLUSIONS
The following conclusions are drawn from the interpreted test data:
1. The natural frequency of the model foundation resting on reinforced sand has
increased compared to that of unreinforced sand.
2. Mixing of about 0.5% human hair fibers with the sand can increase the natural
frequency of the soil-foundation system.
3. Damping ratio measured in the reinforced sand is less than that of unreinforced sand.
4. Improving the ground with the random mixing of fibers up to a depth of about 0.25 B
to 0.50 B may be sufficient to achieve an increased natural frequency.
5. The natural frequency is increased for geogrids-reinforced sand compared to
unreinforced sand. However, the maximum increase in natural frequency is observed
with 3 layers of PET geogrids.
It is recommended to conduct in-situ block vibration tests on large size foundation resting on
reinforced sand, for enhancing the confidence on the conclusions arrived and assessing any
construction related issues of handling a relatively large reinforced-mass.
ACKNOWLEDGEMENTS
The authors appreciate M/s Strata Geosystems (India) Pvt. Ltd. for providing the geogrids for
the experimental work carried out in this study
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