This article describes a novel approach for deciding optimal horizontal extent of soil domain to be used for finite element based numerical dynamic soil structure interaction (SSI) studies. SSI model for a 12 storied building frame, supported on pile foundation-soil system, is developed in the finite element based software framework, OpenSEES. Three different structure-foundation configurations are analyzed under different ground motion characteristics. Lateral extent of soil domain, along with the soil properties, were varied exhaustively for a particular structural configuration. Based on the reduction in the variation of acceleration response at different locations in the SSI system (quantified by normalized root mean square error, NRMSE), the optimum lateral extent of the soil domain is prescribed for various structural widths, soil types and peak ground acceleration levels of ground motion. Compared to the past studies, error estimation analysis shows that the relationships prescribed in the present study are credible and more inclusive of the various factors that influence SSI. These relationships can be readily applied for deciding upon the lateral extent of the soil domain for conducting precise SSI analysis with reduced computational time.
computational time required for analysis (in hours)
motion 1 (M1)
motion 2 (M2)
motion 3 (M3)
TY-I
TY-II
TY-III
TY-I
TY-II
TY-III
TY-I
TY-II
TY-III
15
753
12.23
15.35
15.38
8.23
8.51
8.50
44.58
43.63
42.41
681
8.00
11.81
14.56
6.57
8.91
7.63
35.86
33.82
33.65
603
7.86
9.00
11.00
5.13
8.03
7.52
27.57
26.51
26.25
543
5.40
7.02
8.09
5.15
7.27
6.23
22.53
18.02
21.93
483
4.00
5.56
4.91
4.23
6.58
5.42
18.46
17.89
17.66
423
3.28
4.13
3.46
3.15
4.53
3.69
14.96
13.61
14.25
363
2.50
3.06
2.63
2.75
3.64
2.79
12.03
10.78
11.28
303
1.75
2.23
1.86
1.68
2.65
2.12
9.08
8.08
8.58
243
1.42
1.55
1.47
1.18
1.18
1.18
6.26
5.75
5.95
183
0.83
1.03
0.83
0.78
0.83
0.83
4.07
3.83
3.97
153
0.75
0.75
0.75
0.55
0.55
0.55
3.19
3.07
3.05
123
0.53
0.56
0.54
0.27
0.27
0.27
2.23
2.18
2.16
93
0.46
0.48
0.47
0.23
0.23
0.23
1.58
1.52
1.45
75
0.33
0.35
0.34
0.17
0.17
0.17
1.28
1.12
1.08
63
0.21
0.23
0.22
0.12
0.12
0.12
1.03
0.96
0.87
45
0.14
0.13
0.12
0.06
0.06
0.06
0.61
0.60
0.57
33
0.05
0.05
0.05
0.03
0.03
0.03
0.41
0.41
0.36
27
1353
34.23
33.78
32.50
32.23
29.155
33.90
282.33
245.17
201.22
1215
29.68
28.96
27.68
24.16
24.56
26.36
218.90
190.46
155.42
1083
24.56
23.93
23.27
20.17
20.39
20.84
166.00
142.59
116.70
975
20.56
19.34
19.92
16.23
17.42
17.79
120.63
107.35
90.45
867
17.26
15.56
15.67
13.56
13.88
14.34
106.20
82.81
66.52
759
10.25
8.37
7.69
8.56
6.03
8.59
78.35
56.18
42.13
651
8.56
5.13
6.31
6.75
4.76
6.32
56.65
38.35
35.52
543
6.58
3.74
4.57
4.49
3.43
4.14
38.56
26.82
24.89
435
4.56
2.68
3.02
2.09
2.25
2.71
24.35
18.35
17.59
327
2.36
1.74
1.82
1.55
1.13
1.64
15.63
11.33
11.46
273
1.56
1.29
1.22
1.16
0.87
1.00
12.36
8.72
8.78
219
1.15
0.64
0.60
0.71
0.67
0.74
10.63
6.17
6.52
165
0.96
0.45
0.43
0.48
0.45
0.48
6.35
3.97
4.73
135
0.65
0.36
0.36
0.34
0.35
0.21
4.35
2.93
3.15
111
0.43
0.29
0.28
0.14
0.16
0.17
2.48
2.19
2.45
81
0.23
0.15
0.20
0.10
0.12
0.12
1.15
1.38
1.53
57
0.10
0.06
0.13
0.06
0.07
0.07
0.15
0.83
0.92
45
2253
117.5
114.98
371.28
123.18
104.24
96.10
197.26
252.97
207.12
2025
87.66
82.60
244.26
99.5
75.06
71.24
139.37
199.74
147.73
1803
65.44
58.72
145.82
73.30
48.96
51.27
100.56
152.36
109.61
1623
50.72
42.82
129.82
59.83
50.26
60.58
76.64
116.56
80.93
1443
37.34
37.08
95.40
46.89
40.71
24.92
58.35
87.25
61.66
1263
29.73
30.00
49.21
35.26
29.87
24.24
43.48
62.12
48.69
1083
23.80
23.97
49.65
15.63
18.45
19.22
30.15
41.07
35.27
903
16.84
18.17
26.78
10.90
10.04
13.70
19.33
27.14
25.65
723
10.71
11.66
20.00
5.57
7.24
9.20
12.17
16.96
15.21
543
5.78
6.33
10.26
3.16
4.78
3.90
7.72
8.66
7.23
453
2.40
3.63
7.13
2.33
3.58
2.55
5.19
5.03
5.13
363
1.75
2.34
5.23
1.41
1.53
1.99
3.13
4.22
3.28
273
1.24
1.47
3.50
0.89
1.01
1.17
2.53
2.21
2.13
225
0.98
0.89
2.97
0.59
0.80
0.88
1.21
1.14
1.17
183
0.76
0.64
2.33
0.47
0.60
0.59
0.51
0.50
0.48
135
0.51
0.43
2.02
0.30
0.25
0.36
0.30
0.31
0.29
93
0.33
0.26
1.44
0.19
0.16
0.20
0.12
0.18
0.15
Tab.4
Fig.4
Fig.5
Fig.6
Fig.7
Fig.8
Fig.9
Fig.10
structural width, W
soil type
ground motion
Ω
15 m
TY-I
M1
-0.0860
1.0862
-0.0052
0.2819
0.91
0.90
9.95
TY-I
M2
-0.0474
0.4663
-0.0044
0.1862
0.97
0.93
6.51
TY-I
M3
-0.0221
0.1813
-0.0016
0.0698
0.98
0.96
5.44
TY-II
M1
-0.0929
1.1503
-0.0058
0.4058
0.95
0.91
8.55
TY-II
M2
-0.0410
0.4015
-0.0034
0.1515
0.97
0.97
6.65
TY-II
M3
-0.0205
0.1774
-0.0017
0.0715
0.97
0.93
5.63
TY-III
M1
-0.0775
1.1087
-0.0063
0.4815
0.90
0.93
8.81
TY-III
M2
-0.0446
0.4056
-0.0037
0.1651
0.97
0.95
5.88
TY-III
M3
-0.0258
0.1894
-0.0016
0.0679
0.99
0.90
5.02
27 m
TY-I
M1
-0.1492
1.235
-0.0054
0.3088
0.92
0.90
6.44
TY-I
M2
-0.0522
0.4586
-0.0045
0.1885
0.91
0.90
5.62
TY-I
M3
-0.0208
0.1631
-0.0016
0.0758
0.96
0.91
4.55
TY-II
M1
-0.1279
1.2095
-0.0054
0.4646
0.91
0.92
6.08
TY-II
M2
-0.0416
0.3696
-0.0038
0.1704
0.90
0.94
5.23
TY-II
M3
-0.0181
0.1518
-0.0018
0.0736
0.91
0.90
4.80
TY-III
M1
-0.1037
1.1712
-0.0062
0.5201
0.93
0.92
6.68
TY-III
M2
-0.0362
0.3288
-0.0034
0.1461
0.91
0.85
5.57
TY-III
M3
-0.0197
0.1541
-0.0016
0.0651
0.91
0.81
4.92
45 m
TY-I
M1
-0.1341
1.2002
-0.0044
0.4036
0.90
0.80
6.14
TY-I
M2
-0.0695
0.5572
-0.0040
0.1742
0.98
0.75
5.85
TY-I
M3
-0.0305
0.2224
-0.0017
0.0769
0.98
0.91
5.19
TY-II
M1
-0.1019
1.1841
-0.0036
0.5955
0.96
0.91
5.98
TY-II
M2
-0.0475
0.4484
-0.0035
0.2076
0.99
0.71
5.47
TY-II
M3
-0.0252
0.1998
-0.0017
0.0732
0.97
0.78
5.38
TY-III
M1
-0.1079
1.1702
-0.0063
0.5331
0.85
0.80
6.27
TY-III
M2
-0.0454
0.4183
-0.0035
0.1749
0.98
0.81
5.81
TY-III
M3
-0.0120
0.1337
-0.0017
0.0771
0.98
0.88
5.49
Tab.5
Fig.11
Fig.12
Fig.13
structure width, W
PGA
W
W× W (m)
difference in peak acceleration, %
computational time*
soil node
pile node
structure node
15 m
0.82g
10.00
150
2
9
5
4.3%
0.43g
7.06
106
4
4
7
3.5%
0.22g
5.53
83
1
2
4
2.0%
27 m
0.82g
8.81
238
5
7
4
3.3%
0.43g
6.70
181
4
6
1
2.2%
0.22g
5.52
149
1
4
6
1.0%
45 m
0.82g
7.00
315
2
4
1
1.0%
0.43g
6.15
277
8
6
4
0.9%
0.22g
5.51
248
9
9
9
0.8%
Tab.6
Fig.14
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