671017.pdf

Table 1: Comparison of FE, BDWF, and the present simplified approach for dimensionless maximum kinematic pile bending

푀

max

(휔

)/휌 1

푑푑
4

̈

푈

푔

during the harmonic excitation.

Case

퐿/푑 퐸

/퐸푝

푎

퐻

/퐻푎

푏

푉

/푉푎

푏

Previous

휔

푑/푉 1

푎

Computed

휔^1

푑/푉

푎

FE method

훿comp

BDWF method

Error1: %

Simplified results

Error2: %

1

10

500

1

0.58

0.0964

0.0968

709

2.21

760

7.2

752

6.0

2

20

0.0482

0.0484

1253

2.41

1282

2.3

1326

5.8

3

40

0.0241

0.0242

2088

2.63

2196

5.2

2313

10.8

4

10

5000

1

0.0964

0.0968

1854

1.66

1623

−12.5

1921

3.6

5

20

0.0482

0.0484

7718

1.81

8019

3.9

7735

0.2

6

40

0.0241

0.0242

13120

1.97

13320

1.5

13406

2.2

7

20

1000

3

1.5

0.0916

0.0910

508

2.27

515

1.4

555

9.2

8

20

10000

1/3

0.1164

0.1159

1113

1.42

1097

−1.4

1119

0.6

9

20

1

0.1058

0.1056

931

1.55

1070

14.9

663

−28.8

10

20

3

0.0913

0.0910

1482

1.70

1433

−3.3

1547

4.4

11

10

500

1

1.73

0.2310

0.2293

86

2.05

79

−8.1

96

11.6

12

20

0.1155

0.1147

269

2.24

253

−5.9

315

17.2

13

40

0.0578

0.0573

656

2.44

577

−12.0

778

18.7

14

10

5000

1

0.2310

0.2293

273

1.54

266

−2.6

265

−2.9

15

20

0.1155

0.1147

998

1.68

860

−13.8

963

−3.5

16

40

0.0578

0.0573

3054

1.83

2825

−7.5

3144

3.0

17

20

1000

3

3

0.1017

0.1009

1046

2.17

1075

2.8

1331

27.3

18

20

10000

1/3

0.2117

0.2094

875

1.35

896

2.4

1217

39.1

19

20

3

0.1415

0.1403

2949

1.48

3042

3.2

3470

17.7

20

20

3

0.1019

0.1009

4867

1.63

4911

0.9

5608

15.2

21

20

1000

3

6

0.1042

0.1037

1486

2.07

1480

−0.4

2077

39.7

22

20

10000

1/3

0.2897

0.2849

1128

1.29

1274

12.9

1827

62.0

23

20

1

0.1535

0.1526

3809

1.42

4193

10.1

5073

33.2

24

20

3

0.1045

0.1037

6730

1.55

6831

1.5

8675

28.9

(1) Values of previous

휔^1

푑/푉

,FE푎

,훿

comp

, and BDWF computed form a proposed simple analytical expression [

19

].

(2) Error1: percentage error in the BDWF moment compared with the FE moment. Error2: percentage error in the elastic moment compared with the FE moment

.

(3) The values of computed

휔^1

푑/푉

푎

are associated with the computed time interval.