Dynamic Analysis and Comparative Study of Three Piles and Four … · 2019-03-04 · Modelling & Analysis The modelling is performed using a finite element software, STAAD Pro. V8i

Journal for Research | Volume 05 | Issue 1 | March 2019

ISSN: 2395-7549

All rights reserved by www.journal4research.org

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Dynamic Analysis and Comparative Study of

Three Piles and Four Piles

Kushal M. Panchal Sunil M. Rangari

Research Scholar Professor & Head of Department

Department of Civil Engineering Department of Civil Engineering

Saraswati College of Engineering Saraswati College of Engineering

Abstract

This research works gives an idea about the behaviour of the pile foundation which are 3 piles, 4 piles, 3 piles arranged at triangular

corners and 4 piles arranged at square corners, against the lateral load induced in this pile due to the dynamic effect of earthquake

acting on this pile system. The pile foundation is assumed to be subjected below a bridge pier and enclosed within cohesion-less

soil and soil properties are considered randomly and the load applied is using basic data and calculated using IRC 6, 2014. The

models are analysed in the finite element method based software naming STAAD Pro. for deflection, axial force, shear force and

bending moment for piles. It is observed that the piles arranged in series shows higher value of deflection, axial force, shear force

and bending moment compare to non-series piles.

Keywords: Group Piles, Pile cap, laterally loaded piles, STAAD Pro, Deflection, Axial force, Shear Force, Bending Moment

_______________________________________________________________________________________________________

I. INTRODUCTION

A pile is basically a long cylinder of a strong material such as concrete that is pushed into the ground to act as a steady support for

structures built on top of it. Pile foundations are used in the situations when there is a layer of weak soil at the surface. Pile

foundation is required when the soil bearing capacity is not sufficient for the structure to withstand. This layer cannot support the

weight of the building, so the loads of the building have to bypass this layer and be transferred to the layer of stronger soil or rock

that is below the weak layer. And also, when a building has very heavy, concentrated loads, such as in a high-rise structure, bridge,

or water tank.

In the recent years, a variety of approaches for predicting lateral load behaviour of piles have been developed, including linear

subgrade reaction analysis, nonlinear subgrade reaction analysis, elastic continuum analysis and finite element analysis. The

subgrade reaction analysis is based on Winkler’s hypothesis, according to which, soil is replaced by a series of infinitely closely

spaced, independent and elastic springs. In the elastic continuum analysis, the pile is represented as an infinitely thin linearly elastic

strip, embedded in elastic soil media. Shear stresses developed at the pile soil interface are not taken into account. The finite

element method enables a more rigorous solution to be achieved comparatively, as the pile is modelled more accurately. Also,

heterogeneous soil conditions are readily and correctly modelled.

Lateral loads on piles are developed both by the superstructure and by the wave propagation through the soil. The dynamic loads

due to the horizontal movement of the superstructures are mainly generated by wind effects, machine vibrations, impact of vehicles

or boats; the loads due to the wave propagation is primarily because of earthquakes. Therefore, the total forces are the result of two

types of interaction: an inertial one from the movement of the superstructure and a kinematical one from the soil motion.

II. METHODOLOGY

The primary aim of the present study is to analyse the piles in group under dynamic condition.

Data Considered

Fig. 1. shows the animated top view of the pile cases considered for the research study. This pile foundations are considered to be

placed below a pier bearing service load on it.

Dynamic Analysis and Comparative Study of Three Piles and Four Piles (J4R/ Volume 05 / Issue 1 / 001)


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Fig. 1: Arrangement of Piles in Group

The pile diameter is considered as 1 m with spacing between piles as 3 m centre to centre of the piles. The length of pile is

considered to be 10m, from the pile – pile cap connection till the end of the pile.

The soil details considered for the analysis of the model is cohesion-less soil and properties considered are

Spring coefficient (k) – 3500 KN/m

Density of soil (ρ) – 20 KN/m3

Modelling & Analysis

The modelling is performed using a finite element software, STAAD Pro. V8i. The model consists of 3 piles in series, 4 piles in

series, 3 piles arranged in triangular corner position and 4 piles arranged in square corner position with pile to pile spacing as 3D,

where D is diameter of pile shown in Fig. 2. which shows typical STAAD Pro. model for mentioned cases.

(a)



3

(b)

(c)

(d)

Fig. 2: (a) 3 piles in series, (b) 4 piles in series, (c) 3 piles arranged in triangular corners position and (d) 4 piles arranged in square corners

position.



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Load Applications

The load application on the model is considered as per IRC - 6, 2014. The loads are considered as Dead load, Live load and Seismic

load.

For Dead load, as per clause 203 of IRC – 6, 2014, the various loads considered are self-weight of the sub-structure elements

like pile cap, pier and pier cap; self-weight of superstructure girders, deck weight, wearing coat, crash parapet, loading of noise

barrier and services.

For Live load, cases considered for analysis is carried on with the help of clause 204 of IRC: 6-2014 which is “Standard

specifications and code of practice for road bridges” section II: Loads and Stresses. The load acting between kerb to kerb widths

was considered using:

1) Class A - 2 lanes …… (IRC: 6 – 2014, Table 2: Live Load Combination)

2) Class 70R - 1 lanes.

For seismic load the earthquake load in x direction i.e. EQx and earthquake load in y direction i.e. EQy is considered as per clause

219 of IRC – 6, 2014. (As per "Design data")

Following shows the basic considerations for seismic load calculation:

Zone = III

Zone factor = 0.16

Importance factor = 1.2 (As per Table 8 of IRC: 6-2014.)

Response Reduction Factor= 3

Load Combinations

Following basic load combinations are considered using the above loads. The load combinations are considered form IS 875 - 1987

and IS 456 - 2000 Table – 1

Loads and Loads Combinations

LOAD COMBINATION

SELF WEIGHT+DEAD LOAD

LIVE LOAD

SEISMIC LOAD IN (+ X) DIRECTION

SEISMIC LOAD IN (+ Z) DIRECTION

SELF WEIGHT+DEAD LOAD+LIVE LOAD

SELF WEIGHT+DEAD LOAD+EARTHQUAKE LOAD(+X) DIRECTION

SELF WEIGHT+DEAD LOAD+EARTHQUAKE LOAD(+X) DIRECTION

SELF WEIGHT+DEAD LOAD+LIVE LOAD+EARTHQUAKE LOAD(+X) DIRECTION

SELF WEIGHT+DEAD LOAD+LIVE LOAD+EARTHQUAKE LOAD(+Z) DIRECTION

III. RESULTS & DISCUSSIONS

Results obtained after analysis are mentioned below in graphs and tables format. The results for piles are considered for

displacement, axial force, shear force and bending moment. From the load cases in Table - 2 the critical combination obtained that

is Self-weight + Dead Load + Live Load + Earthquake Load (+X) direction for analysis to obtain the results.

Deflection Details

Table - 2 and Fig. 3. shows the deflection details of 3 piles arranged in series. The details are explained for central pile and corner

piles. The percentage difference between central piles and corner piles is 21%. Table – 2

Deflection value for 3 piles in series

Length (m) 0 1 2 3 4 5 6 7 8 9 10

Deflection(mm)

Central Pile 0 9.66 16.25 20.37 22.58 23.38 23.19 22.35 21.13 19.73 18.26

Deflection(mm)

Corner Pile 0 12.31 20.56 25.83 28.69 29.60 29.36 28.31 26.88 24.95 23.18



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Fig. 3: Deflection variation for 3 piles throughout the pile length

Table - 3 and Fig. 4. shows the deflection details of 4 piles arranged in series. The table shows the details of central piles and

corner piles as the piles in centre and corner shows similar deflection value. The percentage difference between central piles and

corner piles is 16% respectively. Table – 3

Deflection value for 4 piles in series

Length(m) 0 1 2 3 4 5 6 7 8 9 10

Deflection(mm)

Central Piles 0 6.88 11.58 14.51 16.08 16.66 16.52 15.93 15.06 14.06 13.02

Deflection(mm)

Corner Piles 0 8.19 13.78 17.27 19.15 19.83 19.66 18.95 17.92 16.73 15.49

Fig. 4: Deflection variation for 4 piles throughout the pile length

Table - 4 and Fig. 4. shows the deflection of 3 piles arranged in triangular positions with spacing 3D between them. It can be

seen that the nature of graph is similar to the graphs of pile connected in series. All the three piles show different deflection values.

The 3rd pile shows minimum deflection while 1st pile shows maximum deflection. Difference in deflection between 1st pile and 2nd

pile is 1% and between 2nd and 3rd pile is 3% respectively. Table – 4

Deflection value for 3 piles arranged in triangular corners position

Length (m) 0 1 2 3 4 5 6 7 8 9 10

1st Pile 0 10.52 17.69 22.17 24.58 25.45 25.24 24.33 23.06 21.48 19.88

2nd Pile 0 10.43 17.54 21.99 24.37 25.24 25.04 24.13 22.81 21.29 19.71

3rd Pile 0 9.82 16.51 20.69 22.94 23.75 23.56 22.70 21.46 20.04 18.55



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Fig. 5: Deflection variation for 3 piles arranged in triangular corners position

Table - 5 and Fig. 6. shows the deflection value for 4 piles arranged in square corner position. The analysis showed that 1st pile

and 3rd pile shows the same deflection value while 2nd pile and 4th pile shows same as per pile numbering mentioned in Fig 2.1.

Pile 2nd and 4th shows more deflection comparing to that of 1st pile and 3rd pile. The deviation in deflection varies from 10% to

14% throughout the length of the pile. Table – 5

Deflection value for 4 piles arranged in square corner position

Length(m) 0 1 2 3 4 5 6 7 8 9 10

1st Pile 0 3.912 6.576 8.243 9.138 9.462 9.385 9.046 8.552 7.984 7.391

2nd Pile 0 3.915 6.582 8.25 9.146 9.47 9.393 9.053 8.559 7.99 7.397

3rd Pile 0 3.176 5.34 6.694 7.421 7.684 7.621 7.345 6.945 6.401 5.783

4th Pile 0 3.173 5.335 6.687 7.413 7.676 7.613 7.338 6.937 6.455 5.776

Fig. 6: Deflection variation for 4 piles arranged in square corner position

Deflection Comparison

The comparison of deflection of 3 piles in series and 3 piles arranged in triangular corner position at spacing 3D is disscussed. It

is noticed that the percentage difference in maximum deflection is calculated as 14%, while the difference in deflection for

minimum deflection between 3 piles in series and 3 piles at triangular corner position is calculated as 2%. While for 4 piles in

series and 4 piles arranged at square corner position, the percentage difference between the piles with maximum deflection is

calculated as 52%. Whereas minimum deflection between for 4 piles in series and 4 piles arranged at square corner, difference of

54% is observed.



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Axial Force, Shear Force and Bending moment Details

Table - 6 and Fig. 7. shows the Axial force, Shear force and Bending moment details of 3 piles arranged in series. It can be seen

that the Axial force, Shear force and Bending moment variation of central pile is more compare to corner piles. The percentage

difference of axial force between central pile and corner pile is about 4% to 11%, while that of shear force and bending moment is

20%. Table – 6

Axial Force, Shear Force and Bending Moment of 3 piles in series

Beam

No.

Central Pile Corner Piles

Axial force

(KN)

Shear force

(KN)

Bending Moment

(KNm)

Axial force

(KN)

Shear force

(KN)

Bending Moment

(KNm)

1 116.05 863.688 4115.2 102.776 689.135 3283.635

2 138.256 821.295 3295.137 124.982 655.31 2629.221

3 160.463 750.021 2546.002 147.189 598.44 2031.433

4 182.669 660.683 1885.857 169.395 527.158 1504.674

5 204.875 561.641 1324.432 191.601 448.133 1056.703

6 227.082 459.087 865.288 213.807 366.306 690.354

7 249.288 357.37 507.645 236.014 285.147 405

8 271.494 259.331 247.882 258.22 206.922 197.75

9 293.7 166.639 80.707 280.426 132.963 64.378

10 315.907 80.106 0 302.633 63.918 0

(a)

(b)



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(c)

Fig. 7: 3 Piles in Series (a) Axial force, (b) Shear Force and (c) Bending Moment

Table - 7 and Fig. 8. shows the Axial force, Shear force and Bending moment details of 4 piles arranged in series. The percentage

difference of axial force between central pile and corner pile varies from 10% to 58%, while that of shear force and bending

moment is 10%. It can be seen that the Axial force, Shear force and Bending moment variation of central pile is more compare to

corner piles. Table – 7

Axial Force, Shear Force and Bending Moment of 4 piles in series

Beam No.

Central Piles Corner Piles

Axial force (KN) Shear force (KN) Bending Moment

(KNm) Axial force (KN) Shear force (KN)

Bending Moment

(KNm)

1 42.405 580.431 2799.15 17.683 519.825 2477.495

2 64.612 551.941 2214.629 39.889 494.309 1983.439

3 86.818 504.042 1710.927 62.095 451.412 1532.254

4 109.024 444.005 1267.146 84.302 397.644 1134.77

5 131.23 377.448 889.794 106.508 338.037 796.803

6 153.437 308.531 581.237 128.714 276.317 520.466

7 175.643 240.176 340.93 150.921 215.1 305.263

8 197.849 174.291 166.424 173.127 156.096 148.998

9 220.056 111.997 54.153 195.333 100.306 48.473

10 242.262 53.841 0 217.539 48.221 0



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(b)

(c)

Fig. 8. 4 Piles in Series (a) Axial force, (b) Shear Force and (c) Bending Moment

Table - 8 and Fig. 9. shows the details of 3 piles arranged at triangular corner positions spaced at spacing 3D between them. It

is observed that the 3rd pile shows the maximum axial force, while the behaviour of 1st pile is maximum in shear force and bending

moment. Table – 8

Axial Force, Shear Force and Bending Moment of 3 piles arranged at triangular corner

Beam

no.

1st PILE 2nd PILE 3rd PILE

Axial

force

Shear

force

Bending

moment

Axial

force

Shear

force

Bending

moment

Axial

force

Shear

force

Bending

moment

1 83.203 750.26 3575.09 149.126 743.96 3544.39 220.658 699.99 3334.27

2 105.409 713.435 2862.49 171.332 707.443 2838.25 242.864 665.64 2670.33

3 127.615 651.521 2211.59 193.538 646.049 2193.11 265.071 607.874 2063.61

4 149.821 573.917 1638.06 215.744 569.094 1624.56 287.277 535.465 1528.82

5 172.028 487.883 1150.34 237.951 483.781 1140.99 309.483 455.189 1073.89

6 194.234 398.799 751.495 260.157 395.441 745.492 331.689 372.067 701.757

7 216.44 310.442 440.845 282.363 307.824 437.402 353.896 289.623 411.822

8 238.647 225.28 215.234 304.57 223.375 213.612 376.102 210.163 201.18

9 260.853 144.76 70.059 326.776 143.532 69.567 398.308 135.039 65.556

10 283.059 69.59 0 348.982 68.998 0 420.515 64.913 0



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(a)

(b)

(c)

Fig. 9. 3 piles arranged in triangular corners position (a) Axial Force, (b) Shear Force and (c) Bending Moment

Table - 9 and Fig. 10. describes the details of axial force, shear force and bending moment of 4 piles arranged at square corner

position spaced at the spacing of 3D between the piles. 1st and 2nd piles and 3rd and 4th piles show similar value in axial force, shear

force and bending moment. Comparatively 3rd and 4th pile shows higher axial force value then 1st and 2nd while 1st and 2nd pile in

shear force and bending moment are maximum.



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Table – 9

Axial Force, Shear Force and Bending Moment of 4 piles arranged at square corner

Bea

m

no.

1st PILE 2nd PILE 3rd PILE 4th PILE

Axial

force

Shear

force

Bending

moment

Axial

force

Shear

force

Bending

moment

Axial

force

Shear

force

Bending

moment

Axial

force

Shear

force

Bending

moment

1 92.618 278.91

2

1329.01

3 93.217

279.14

5 1330.12

140.60

4

226.48

1

1079.03

2

141.20

2

226.24

9

1077.92

3

2 120.37

6

265.22

2

1064.14

9

120.97

5

265.44

3

1065.03

6

168.36

1

215.36

4 864.062 168.96

215.14

4 863.175

3 148.13

4

242.20

4 822.214

148.73

3

242.40

7 822.901

196.11

9

196.67

4 667.672

196.71

8

196.47

2 666.988

4 175.89

2

213.35

4 609.031

176.49

1

213.53

2 609.54

223.87

7

173.24

6 494.599

224.47

6

173.06

9 494.092

5 203.65 181.36

9 427.732

204.24

9

181.52

1 428.09

251.63

5

147.27

4 347.395

252.23

4

147.12

3 347.04

6 231.40

8

148.25

1 279.462

232.00

7

148.37

4 279.697

279.39

3 120.38 226.996

279.99

2

120.25

7 226.764

7 259.16

6

115.40

3 163.967

259.76

4

115.49

9 164.105

307.15

1 93.706 133.201 307.75 93.61 133.066

8 286.92

3 83.743 80.076

287.52

2 83.813 80.143

334.90

9 67.998 65.064

335.50

7 67.928 64.998

9 314.68

1 53.81 26.079 315.28 53.855 26.101

362.66

6 43.692 21.198

363.26

5 43.647 21.176

10 342.43

9 25.867 0

343.03

8 25.889 0

390.42

4 21.003 0

391.02

3 20.981 0

(a)

(b)



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(c)

Fig. 10. 4 piles arranged in square corners position (a) Axial Force, (b) Shear Force and (c) Bending Moment

Axial Force, Shear Force and Bending Moment Comparison

Comparison of axial force, shear force and bending moment is carried out for 3 piles in triangular corner and 3 piles in series. The

maximum axial force of 3 piles in series when compared to that of 3 piles arranged in triangular corner the difference obtained is

around 25% to 47%, while when compared to minimum axial force the difference calculated is around 6% to 19%. Shear force

and bending moment show similar percentage difference, i.e. when maximum and minimum values of shear force and bending

moment of 3 and 4 piles in series compared to 3 piles arranged in triangular corner and 4 piles arranged at square corner, the

percentage difference obtained is 13% for maximum and 2% for minimum value respectively.

Comparison of axial force, shear force and bending moment values for 4 piles in triangular corner having 1st, 2nd, 3rd and 4th pile

with 4 piles in series having central and corner piles. The percentage difference in minimum axial force of 4 piles in square corners

compared to minimum axial force of series in piles is varying from 36% to 81%, while maximum axial force of 4 piles in square

corners are compared to maximum axial force value of 4 piles in series, the difference varies from 38% to 70%. Minimum shear

force and bending moment for 4 piles in square corners when compared to the minimum shear force and bending moment of 4

piles in series, it shows a percentage difference of 56%. When maximum shear force and bending moment for 4 piles in square

corners when compared to the maximum shear force and bending moment of 4 piles in series, it shows a percentage difference of

52%.

IV. CONCLUSION

1) The deflection increases up to certain length and then it decreases for the remaining length.

2) For piles in series, central piles show higher value in Deflection, Axial force, Shear force and Bending moment compare to

corner piles.

3) 1st pile in 3 piles arranged in triangular corners and 1st and 2nd pile in 4 piles arranged in square corners shows higher value of

Deflection, Axial force, Shear force and Bending moment.

4) From comparison between series piles and non- series piles, it is noticed that piles in series shows higher value compare to

non-series piles arrangement.

5) Maximum percentage difference is 14%, when deflection of 3 piles in series compares to 3 piles in triangular corners.

6) Maximum percentage difference is 52%, when deflection of 4 piles in series compares to 4 piles in square corners.

7) Maximum percentage difference is 47%, when axial force of 3 piles in series compares to 3 piles in triangular corners.

8) Maximum percentage difference is 70%, when axial force of 4 piles in series compares to 4 piles in square corners.

9) Maximum percentage difference is 13%, when shear force of 3 piles in series compares to 3 piles in triangular corners.

10) Maximum percentage difference is 52%, when shear force of 4 piles in series compares to 4 piles in square corners.

11) Maximum percentage difference is 13%, when bending moment of 3 piles in series compares to 3 piles in triangular corners.

12) Maximum percentage difference is 52%, when bending moment of 4 piles in series compares to 4 piles in square corners.

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Documents

Dynamic Analysis and Comparative Study of Three Piles and Four … · 2019-03-04 · Modelling & Analysis The modelling is performed using a finite element software, STAAD Pro. V8i