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50
th
IGC
50th INDIAN GEOTECHNICAL CONFERENCE
17th – 19th DECEMBER 2015, Pune, Maharashtra, India
Venue: College of Engineering (Estd. 1854), Pune, India
INFLUENCE OF STRIP FOOTINGS SUBJECTED TO LATERAL DYNAMIC FORCES
Sanjay Paul1
ABSTRACT
The major objective of this paper is to present laboratory observations on small-scale strip footings subjected to harmonic excitation for determination of the seismic factor of safety and criticalaccelerations for the various modes of footing movement. A foundation must be stable against failure due to static loading as well as dynamic loading. The dynamic loads are generated by earthquakes, wind, traffic, blasting or neighboring machinery and are transmitted to the foundation either through a structural system or through the soil. The bearing capacity of soil under seismic forces , commonly known as seismic bearing capacity was studied by several researchers. These studies used a limit equilibrium analysis with various assumptions on the shape of the failure surface.
In the present study, experimental works were conducted with strip footings of different widths subjected to a periodic horizontal force. The model footings were placed on a sand bed kept in a fabricated steel tank. Representative sample of sand was collected from Silchar town of northeast India. Different parameters like coefficient of horizontal acceleration coefficient, angle of internal friction, embedment ratio, width of footing, etc. affecting seismic factor of safety were studied. Critical horizontal acceleration for which seismic factor of safety is equal to 1.0 was also evaluated. An attempt has been made to show the failure surface mechanism at critical acceleration. Seismic effects on shallow foundations are usually analyzed by the pseudo-static approach in which the effects of earthquake forces are accounted by constant horizontal and vertical accelerations attached to the inertia. The static bearing capacity or ultimate load that a strip footing can sustain is usually calculated by superposition where the contributions from soil cohesion, soil unit weight, angle of internal friction of soil and surcharge loading are added together. The seismic bearing capacity that a strip footing can sustain actually depends on the values of coefficients of the horizontal and vertical pseudo-static accelerations. The critical acceleration is the horizontal acceleration at which the allowable seismic bearing capacity approaches to the allowable static bearing capacity.
Experiments were conducted at three different relative densities of sand sample corresponding to three different values of angle of internal friction. Three mild steel strip footings of different sizes were used in the present study at different embedment conditions. The acceleration-time histories of footing under
1Sanjay Paul, Assistant Professor, Department of Civil Engineering, N.I.T. Agartala, India, [email protected]
Sanjay Paul
different lateral periodic loading were recorded with the help of FFT analyzer. The acceleration –time histories were recorded by the accelerometers at three different relative densities of soil sample.
From the present study important conclusions were drawn. The parameters that affect the bearing capacity under seismic conditions include the angle of internal friction of soil, the embedment ratio of footing and width of footing, horizontal and vertical acceleration coefficients, the static factor of safety and the amplitude of horizontal vibration. Seismic factor of safety values decrease with the increase of horizontal and vertical acceleration coefficients. Seismic factor of safety values increase with the increase of angle of internal friction, embedment ratio and static factor of safety. The effect of vertical acceleration coefficient is more prominent at higher values of horizontal acceleration coefficient. The critical acceleration coefficient value increases with the increase of embedment ratio, but decreases with the increase of vertical acceleration coefficient. Foundation failure surface mechanism shows that the depth of failure block under seismic loading is less than that under static loading.
Keywords: Horizontal acceleration coefficient; Vertical acceleration coefficient; Seismic bearing
capacity; Seismic factor of safety; Critical acceleration.
50
th
IGC
50th INDIAN GEOTECHNICAL CONFERENCE
17th – 19th DECEMBER 2015, Pune, Maharashtra, India
Venue: College of Engineering (Estd. 1854), Pune, India
INFLUENCE OF STRIP FOOTINGS SUBJECTED TO LATERAL DYNAMIC FORCES
Sanjay Paul, Assistant Professor, Department of Civil Engineering, N.I.T. Agartala, [email protected]
ABSTRACT: The aim of the paper is to present laboratory results on a small-scale model strip footings under horizontal dynamic force to find seismic factor of safety, critical acceleration coefficients, etc. The model strip footings of mild steel were placed on a sand bed inside a mild steel tank. Representative sand sample was collected from Silchar town of northeast India. Seismic effects on shallow footings are usually analyzed by pseudo-static approach. Seismic bearing capacity of strip footing depends on angle of internal friction of soil, embedment ratio and width of footing, horizontal and vertical pseudo-static acceleration coefficients, static factor of safety, etc.
INTRODUCTIONThe major objective of this paper is to present laboratory observations on small-scale strip footings subjected to harmonic excitation for determination of the seismic factor of safety and critical accelerations for the various modes of footing movement. Seismic Bearing Capacity of SoilThe bearing capacity of soil under seismic forces , commonly known as seismic bearing capacity was studied by several researchers [1, 2, 3, 4, 5]. These studies used a Limit equilibrium analysis with various assumptions on the shape of the failure surface.A foundation must be stable against failure due to static loading as well as dynamic loading. The dynamic loads are generated by earthquakes, wind, traffic, blasting or neighboring machinery and are transmitted to the foundation either through a structural system or through the soil. The seismic bearing capacity can be expressed by the following expressions:
EqEcEuE NBqNcNq 12
1 (1)
where, NqE, NcE, NγE are the seismic bearing capacity factors.
Seismic Factor of Safety and Critical AccelerationThe value of factor of safety was found to be a major control variable for the design of any Civil
Engineering Structures. The critical acceleration is the horizontal acceleration that is applied by the seismic shaking at which the footing will start to move down inside the soil mass. At the critical acceleration the allowable seismic bearing capacity (qaE) reduces to the allowable static bearing capacity (qaS), i.e.,
aSaE qq (2)
In Eq. 1, denoting the static safety factor with FsS, and substituting qaS by quS/ FsS and replacing qaE
by quE/FsE, then
S
uS
E
uE
Fs
q
Fs
q (3)
where, quS = is the ultimate bearing capacity,quE = the ultimate seismic bearing capacity
and FsE = the seismic safety factor,
when FsE = 1 at the critical acceleration, then from Eq. 3,
uS
suEE q
FsqFs
(4)
EXPERIMENTAL SET-UPIn the present study, experimental works were conducted with strip footings of different widths subjected to a periodic horizontal force [6, 7]. The model footings were placed in a sand bed kept in a fabricated mild steel tank of inside dimensions 1.50 m (length) × 0.60 m (width) × 0.90 m (height) with wall thickness of 4 mm (Fig.1). The tank is connected to a three-phase A.C. motor having 1.5
Sanjay Paul
H.P. capacity with a slider crank mechanism. The speed of the motor and that of the sinusoidal movement of the tank are observed to be 1440 rpm and 32 rpm respectively, the corresponding frequencies of motor and tank are respectively 24.00 Hz and 0.53 Hz. The amplitude of movement of the tank can be regulated by pinning the slider arm at different slots on a 30.5 cm diameter wheel connected to the motor. In the present study the amplitude of the to and fro movement of tank (i.e., stroke length) is maintained at 12 cm, 22 cm and 29 cm respectively in the horizontal direction. The thickness of dry sand layer in each experiment was taken as 0.62 m.
Fig. 1 Model tank used in the experiments
The width of the tank was made equal to four the length of the rectangular footing, in order to minimize the boundary effects (Fig.2). For the footings a clear gap of 3.5 cm was maintained between the tank wall and the edge of the footing considering the actual field problems, where, either the strip footing butts to the original ground stratum or is restrained due to cross strip footings. However, little effects in the observed values due to secondary waves from reflection at the boundaries are admitted in the present study.
Fig.2 Plan of footing inside the Tank
H.P. capacity with a slider crank mechanism. The speed of the motor and that of the sinusoidal movement of the tank are observed to be 1440 rpm and 32 rpm respectively, the corresponding frequencies of motor and tank are respectively
4.00 Hz and 0.53 Hz. The amplitude of movement of the tank can be regulated by pinning the slider arm at different slots on a 30.5 cm diameter wheel connected to the motor. In the present study the amplitude of the to and fro movement of tank (i.e.,
length) is maintained at 12 cm, 22 cm and 29 cm respectively in the horizontal direction. The thickness of dry sand layer in each experiment was
Model tank used in the experiments
The width of the tank was made equal to four times the length of the rectangular footing, in order to minimize the boundary effects (Fig.2). For the footings a clear gap of 3.5 cm was maintained between the tank wall and the edge of the footing considering the actual field problems, where, either
strip footing butts to the original ground stratum or is restrained due to cross strip footings. However, little effects in the observed values due to secondary waves from reflection at the boundaries are admitted in the present study.
Representative sample of sand was collected from Silchar town of northeast India. size distribution of sand sample is shown in Table 3.1 gives the other The physical properties of the samples is presented in Table 1.
Fig.3 Particle size distribution of the sand sample used in the study
Table 1 Physical properties of the sand samplePhysical propertiesSpecific GravityNatural moisture content (%)Bulk unit weight (kN/m3)D10 (mm)D30 (mm)D60 (mm)Cu
Cc
The experiments were carried out with strip footings of different dimensions. Detailed dimensions of the footings are shown in Table 2 and Fig.4.
Table 2 Dimensions and weights of different mild steel strip footing models used in the study
B(m)
h (m)
t1 (m)
t2 (m)
0.125 0.110 0.015 0.010 0.0100.100 0.080 0.012 0.010 0.0060.075 0.053 0.010 0005 0.005
* Notations B, t1, t2, t3 are shown in Fig.4
Representative sample of sand was collected from Silchar town of northeast India. Typical particle size distribution of sand sample is shown in Fig.3.Table 3.1 gives the other The physical properties of
ble 1.
Particle size distribution of the sand sample
Physical properties of the sand sampleValues2.648
Natural moisture content (%) 2219.50.190.260.351.841.02
The experiments were carried out with strip footings of different dimensions. Detailed dimensions of the footings are shown in Table 2
Dimensions and weights of different mild steel strip footing models used in the study *
t3 (m)
Weight (kN)
0.010 0.0790.006 0.0630.005 0.037
, t1, t2, t3 are shown in Fig.4
50
th
IGC
50th INDIAN GEOTECHNICAL CONFERENCE
17th – 19th DECEMBER 2015, Pune, Maharashtra, India
Venue: College of Engineering (Estd. 1854), Pune, India
Fig.4 Mild steel footing dimensions(The values of B, h, t1, t2, t3 are shown in Table 2)
The acceleration – time histories of footing and tank were recorded for 5 seconds duration by the accelerometers connected to FFT analyzer [8] for the different values of width (B), embedment ratio (D/B), angle of internal friction () and stroke length. Typical acceleration – time history graphs are shown Figs.5 - 6.
Fig.5 Typical horizontal acceleration –time histories of footing and tank
Fig.6 Typical horizontal and vertical components of footing acceleration
In the present study a total of 99 number of vibration tests have been performed using sand sample (Table 3).
Table 3 Different variables used in the vibration tests on sand samples
Variables ValuesB (cm) 7.5 / 10 / 12.5D/B 0.00 / 0.10 /
0.25 / 0.50 0.75 (Degrees) 31/ 32 / 35Stroke length (cm) 12 / 22 / 29Relative density (%) 35.83 / 45.57 / 65.00Void ratio 0.82 / 0.80 / 0.76
Horizontal and Vertical Displacements of Footing due to Dynamic LoadsTotal horizontal and vertical displacements(settlement) of footings due to a dynamic load depend upon several parameters like, size of footing, void ratio of soil deposit and embedment ratio of the footing, etc. The horizontal and vertical displacements (δH and δV respectively) were measured manually along the centre line of each footing at the end of each test.
Horizontal Displacement of FootingFig.7 shows the horizontal displacement of different footings at different D/B ratios and void ratios. It is observed that, the horizontal displacement of footing reduces with the increase of embedment ratio, due to higher overburden pressure of soil. As expected, the displacement increases with the increase in void ratio.
Settlement of FootingFig.8 shows the vertical displacement of different footings at different embedment ratios and void ratios. It is observed that the settlement of footing reduces with the increase of embedment ratio, due to higher overburden pressure of soil. This displacement increases with the increase of void ratio for most of the cases.
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
0 2 4 6 8 10
Acc
eler
atio
n [g
]
Time [s]
Sand Surface Acceleration
Tank Acceleration
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
0.00 1.00 2.00 3.00 4.00 5.00
Acc
eler
atio
n (g
)
Time (sec)
Horizontal AccelerationVertical Acceleration
Sanjay Paul
Fig.7 Variation of horizontal displacements of typical strip footing with different void ratio and embedment ratio values
Fig.8 Variation of settlements of typical footing with void ratio and embedment ratio
Correlation between the Horizontal and Vertical Displacements of FootingFig.9 shows the correlation between net horizontal footing displacement (δH) and net vertical footing displacement (settlement) (δV) of a footing in the different experiments. The correlation between δH and δV can be expressed as:
δV = 0.13 δH + 0.15 (1)
Fig.9 Correlation between horizontal and vertical footing displacements due to horizontal dynamic loads
Variation of Seismic Factor of Safety (FSE)Considering FSS = 3, equation(4) has been solved numerically to find FSE for different values of horizontal acceleration coefficient (kh), vertical acceleration coefficient (kv), angle of internal friction of soil (),embedment ratio (D/B), static factor of safety (FSS) and degree of saturation (Sr). The results are presented in Figs. 10 – 13.
Variation of FSE and kc against kh and kv
FSE values decrease with the increase of kh and kv. In Fig. 10, the values of kc are determined graphically and found as kc = 0.179 ( for kv ≠ 0) and 0.207 (for kv = 0) .
Fig.10 Variation of FSE with kh for different kv
values, for B = 12.5 cm, = 350, D/B = 0.25, FSS = 3, stroke length = 12 cm
0
5
10
15
20
25
0.00 0.10 0.20 0.30 0.40 0.50 0.60D/B
Hor
z. F
ootin
g D
isp.
(cm
)
e = 0.76e = 0.80e = 0.82
0.00
0.50
1.00
1.50
2.00
2.50
3.00
0.00 0.10 0.20 0.30 0.40 0.50 0.60D/B
Ver
t. Fo
otin
g D
isp.
(cm
)
e = 0.76e = 0.80e = 0.82
δV = 0.13.δH + 0.15
R 2 = 0.96
0.00
0.20
0.40
0.60
0.80
1.00
0.00 1.00 2.00 3.00 4.00 5.00
δH (cm)
δV (
cm)
0.01
0.1
1
10
0.00 0.20 0.40 0.60 0.80 1.00
FS E
kh
kv ≠ 0
kv = 0
kc = 0.179 (kv ≠ 0) = 0.207 (kv = 0)
50
th
IGC
50th INDIAN GEOTECHNICAL CONFERENCE
17th – 19th DECEMBER 2015, Pune, Maharashtra, India
Venue: College of Engineering (Estd. 1854), Pune, India
Variation of FSE against kh and The Fig.11 shows that, FSE value decreases with the increase of kh, but increases with the increase of . The effect of is more prominent at higher values of kh
Fig.11 Variation of FSE with kh for different values, for kv = 0, B = 12.5 cm, D/B = 0.00, FSS = 3, stroke length = 29 cm
Variation of FSE against kh and D/BThe Fig.12 shows that, FSE value decreases with the increase of kh, but increases with the increase of D/B. The effect of D/B is more prominent at higher values of kh.
Fig.12 Variation of FSE with kh for different D/B values, for kv = 0, B = 12.5 cm, =350, FSS = 3, stroke length = 29 cm
Variation of FSE against kh and FSS
The Fig.13 shows that, FSE value decreases with the increase of kh, but increases with the increase of FSS values. It is also observed that, all curves are parallel for any value of kh.
Fig.13 Variation of FSE with kh for different FSS
values, for kv = 0, D/B = 0.00, B = 12.5 cm, =350, stroke length = 29 cm
Variation of FSE against kh and Sr
FSE value increases with the increase of degree of saturation (Sr) of the soil. Fig.14 shows the variation of FSE with kh and Sr.
Fig.14 Variation of FsE with kh for different values of Sr for kv = 0, FSS = 3 with B = 12.5 cm, D/B = 0.00, stroke length = 29 cm
0.01
0.1
1
10
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80
k h
FS E
φ = 35 degφ = 32 ,,φ = 31 ,,
0.01
0.1
1
10
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80
k h
FS E
D/B = 0.00D/B = 0.10D/B = 0.25D/B = 0.50D/B = 0.75
0.01
0.1
1
10
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80
k h
FS E
FSs = 3.0FSs = 4.0FSs = 5.0FSs = 6.0FSs = 7.0
Sanjay Paul
Variation of Critical Acceleration Coefficient (kc)The critical acceleration coefficient of footing is likely to be depended upon the different parameters like the angle the ratio embedment ratio (D/B), vertical acceleration coefficient (kv), etc.
Variation of kc against D/B and kv
The Fig.15 shows that, kc value increases with the increase of D/B, but decreases with the increase of kv.
Fig.15 Variation of kc with D/B for kv = 0 and kv ≠ 0, FSS = 3, B = 12.5 cm, =320, stroke length =
22 cm
Variation of kc against Sr
The Fig.16 shows the effect of degree of saturation (Sr) on critical acceleration (kc). With the increase of Sr value, kc value remains almost constant at higher values of Sr.
Fig.16 Variation of kc with Sr at kv = 0, FSS = 3 with B = 12.5 cm, D/B = 0.00, stroke length = 29 cm
Correlation between Average Horizontal Acceleration of Footing (aavgH) and Critical Acceleration Coefficient (kc)Fig.17 shows the correlation between average horizontal acceleration of footing (aavgH) and the corresponding critical acceleration (kc) for different vibration experiments on footing. The following correlation was obtained between aavgH and kc :kc = 0.06 exp(3.09 aavgH) (5)
Fig.17 Correlation between aavgH and the corresponding kc values at kv ≠ 0 for the different
experiments on footing
Variation of Ultimate Seismic Bearing Capacity of Soil at Critical Acceleration (quE*)The value of quE* is likely to be depended upon the different parameters like the embedment ratio (D/B), the angle of internal friction of soil () and maximum horizontal acceleration values of the footing (amaxH). The results are presented in Figs.18 – 21.
Variation of quE* against embedment ratio (D/B)and angle of internal friction of soil ()The ultimate seismic bearing capacity values have been calculated for different values of D/B and . Fig.18 shows that, quE* value increases with the increase of both D/B and .
0.05
0.10
0.15
0.20
0.25
0.30
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80
D/B
k c
kv ≠ 0kv = 0
kc = 0.06.exp(3.09.aavgH)R2 = -0.99
0.01
0.1
1
0.20 0.25 0.30 0.35 0.40 0.45 0.50k c
aavgH (g)
50
th
IGC
50th INDIAN GEOTECHNICAL CONFERENCE
17th – 19th DECEMBER 2015, Pune, Maharashtra, India
Venue: College of Engineering (Estd. 1854), Pune, India
Fig.18 Variation of quE* with D/B for kv ≠ 0, FSS = 3, B = 12.5 cm, stroke length = 22 cm
Variation of quE* against maximum horizontal acceleration values of footing (amaxH) Fig.19 shows the variation of ultimate seismic bearing capacity at critical acceleration (quE*)against maximum horizontal acceleration values offooting (amaxH). The correlation obtained between quE* and amaxH is:
quE * = 0.32 exp(3.66 amaxH) (7)
Fig.19 Variation of quE* against amaxH for kv ≠ 0
Failure Surface Mechanism at Critical AccelerationThe wedge angles of Prandtl and Coulomb failure mechanism of shallow footing under seismic condition can be obtained analytically using the criteria given by Richards et. al. (1993). Fig.20shows the typical failure surface mechanism at critical acceleration for a footing having B = 12.5
cm, = 350, D/B = 0.00 with stroke length as 12 cm. In this example, the values of wedge angles are obtained as : ρAE* = 520, ρA = 650, ρPE* = 180, ρP = 200.Fig. 21 shows the Variation of wedge angle ratio (ρAE / ρA) against critical acceleration coefficient(kc) for the different experiments on footing in the following form:
ρAE* = 1.56.ρA.exp(-3.80.kc) (8)
Fig.20 Failure surface mechanism at critical acceleration for B = 12.5 cm, = 350,
for D/B = 0.00 with stroke length of horizontal motion = 12 cm, FSS = 3
(All dimensions are in millimeters)
Fig.21 Variation of wedge angle ratio (ρAE / ρA)against critical acceleration coefficient (kc) for the
different experiments on footing
CONCLUSIONSBased on the experimental works done, the important findings from the present study are:● Total horizontal and vertical displacements
(settlement) of footings due to a dynamic load
0
5
10
15
20
25
30
35
40
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80
D/B
q uE*
(kPa
)
φ = 35 degφ = 32 ,,φ = 31 ,,
quE * = 0.32.exp(3.66.a maxH )
R 2 = 0.75
1
10
100
0.80 0.90 1.00 1.10 1.20 1.30 1.40
a maxH (g)
q uE
* (
kPa)
ρ AE * = 1.56. ρ A. exp(-3.80.kc)
R 2 = -0.98
0.1
1
10
0.00 0.05 0.10 0.15 0.20 0.25
k c
ρ AE*/
ρ A
Sanjay Paul
depend upon several factors like, size of footing, void ratio of soil deposit and embedment ratio of the footing, etc.
● The horizontal displacement of footing reduces with the increase of embedment ratio.
● The displacement of footing increases with the increase in void ratio.
● The settlement of footing reduces with the increase of embedment ratio.
● Footing displacement also increases with the increase of void ratio.
● The linear correlation exists between net horizontal footing displacement and net vertical footing displacement (settlement).
● Seismic factor of safety values depends upon the values of horizontal acceleration coefficient, vertical acceleration coefficient, angle of internal friction of soil, embedment ratio of footing, static factor of safety and degree of saturation of soil.
● Seismic factor of safety values decrease with the increase of horizontal and vertical seismic acceleration coefficients.
● Seismic factor of safety values increase with the increase of angle of internal friction of soil.
● Seismic factor of safety values decrease with the increase of embedment ratio of soil.
● Seismic factor of safety values decrease with the increase of static factor of safety.
● Seismic factor of safety values increase with the increase of degree of saturation of soil.
● Critical acceleration coefficient values increase with the increase of embedment ratio of footing.
● Critical acceleration coefficient values remains almost constant at higher values of degree of saturation.
● There is an exponential correlation exits between average horizontal acceleration of footing and the corresponding critical acceleration values.
● The values of ultimate seismic bearing capacity of soil depends on the different factors like the footing embedment ratio, the angle of internal friction of soil, maximum horizontal acceleration values of the footing, etc.
● The ultimate seismic bearing capacity values at critical acceleration increase with the increase of embedment ratio of footing.
● The ultimate seismic bearing capacity values at critical acceleration increase with the increase of angle of internal friction of soil.
● There is an exponential correlation exits between ultimate seismic bearing capacity at critical acceleration and maximum horizontal acceleration values of footing.
● There is an exponential correlation exits between wedge angle ratio and critical acceleration coefficient.
REFERENCES
1. Sarma, S. K., and Iossifelis, I. S. (1990), Seismic Bearing Capacity Factors of Shallow Strip Footings, Geotechnique, 40 (2), 265-273.
2. Richards, R., Elms, D.G., and Budhu, M. (1993), Seismic Bearing Capacity and Settlement of Foundations, Journal of Geotechnical Engineering., v. 119, no. 4, ASCE, pp. 662-674.
3. Al-Karni A. A. (1993), Seismic Settlement and Bearing Capacity of Shallow Footing on Cohesionless Soil, Ph.D. Dissertation, University of Arizona, Tucson, Arizona 85712, USA.
4. Choudhury, D. and Subba Rao, K.S. (2006): “Seismic Bearing Capacity of Shallow Strip Footings Embedded in Slope,” International Journal of Geomechanics, A.S.C.E., v. 6, no. 3, pp. 176 – 184.
5. Knappett, J.A., Haigh, S.K. and Madabhushi (2006): “Mechanisms of Failure for Shallow Foundations under Earthquake Loading”, Journal of Soil Dynamics and Earthquake Engineering, v. 26, nos. 2-4, pp. 91-102.
6. Paul, S. and Dey, A.K. (2009): “An Experimental Study of Horizontal Vibration of Footing on Dry Cohesionless Soil”, Indian Geotechnical Journal, v. 39, no. 4, October, pp. 424 – 435.
7. Paul, S. (2010), Characterization of Soil at Silchar under Dynamic Loading, Ph.D. Thesis, Department of Civil Engineering, National Institute of Technology, Silchar.
8. Brüel & Kjaer Sound and Vibration Measurement A/S PULSE, (2003): ‘Getting Started’ User Manual.
