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Elastic characteristics of the superstructure_
| ρst (kg/m3) | Est (MPa) | vst | ξst (%) | Mass (t) |
|---|---|---|---|---|
| 2500 | 8000 | 0.3 | 2 | 350 |
Influence of the spacing inter-bridge on the seismic response of three dissimilar parallel bridges system_
| S (m) | ast (m/s2) | acap (m/s2) | Internal forces | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Central piles | Corner piles | |||||||||||
| Pile (2) (Mst = 350 t) | Pile (16) (Mst = 700 t) | Pile (1) (Mst = 350 t) | Pile (7) (Mst = 700 t) | |||||||||
| Mmax (kN m) | Tmax (kN) | Mmax (kN m) | Tmax (kN) | Mmax (kN m) | Tmax (kN) | Mmax (kN m) | Tmax (kN) | |||||
| One bridge (Mst = 350 t and S = 0) | 23.02 | 14.39 | 2244 | 1218 | 2189 | 1604 | ||||||
| One bridge (Mst = 700 t and S = 0) | 18.09 | 14.9 | 1640 | 1134 | 1732 | 1233 | ||||||
| S (m) | Bridge (Mst = 350 t) | Bridge (Mst = 700 t) | Three dissimilar parallel bridges | |||||||||
| ast | acap | ast | acap | Pile (2) (Mst = 350 t) | Pile (16) (Mst = 700 t) | Pile (1) (Mst = 350 t) | Pile (7) (Mst = 700 t) | |||||
| 20 | 11.5 | 6.61 | 8.45 | 5.78 | 1981 | 1169 | 1123 | 998 | 1824 | 1310 | 1218 | 1090 |
| 30 | 11.8 | 6.88 | 8.63 | 5.94 | 2021 | 1200 | 1156 | 1006 | 1870 | 1273 | 1222 | 1118 |
| 40 | 12 | 7.1 | 8.81 | 6.05 | 2035 | 1242 | 1176 | 1037 | 1935 | 1361 | 1278 | 1157 |
Properties of cohesive soil_
| ρs (kg/m3) | Eos (MPa) | υs | Ko | ζs (%) | C (kPa) | φ (0) | Ψ (0) |
|---|---|---|---|---|---|---|---|
| 1700 | 8 | 0.3 | 0.5 | 5 | 150 | 0 | 0 |
Influence of inter-bridge spacing on the seismic response of three dissimilar parallel bridges system
| S (m) | ast (m/s2) | acap (m/s2) | Internal forces | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Central piles | Corner piles | |||||||||||
| Pile (2) (Mst = 350 t) | Pile (15) (Mst = 1050 t) | Pile (1) (Mst = 350 t) | Pile (7) (Mst = 1050 t) | |||||||||
| Mmax (kN m) | Tmax (kN) | Mmax (kN m) | Tmax (kN) | Mmax (kN m) | Tmax (kN) | Mmax (kN m) | Tmax (kN) | |||||
| One bridge (Mst = 350 t and S = 0) | 20.1 | 11.5 | 3979 | 1268 | 4093 | 1330 | ||||||
| One bridge (Mst = 1050 t and S = 0) | 20.53 | 12.49 | 2196 | 1325 | 2061 | 1294 | ||||||
| S (m) | Bridge (Mst = 350 t) | Bridge (Mst = 1050 t) | Three dissimilar bridges | |||||||||
| Ast | acap | Ast | acap | Pile (2) (Mst = 350 t) | Pile (15) (Mst = 1050 t) | Pile (1) (Mst = 350 t) | Pile (7) (Mst = 1050 t) | |||||
| 20 m | 11.6 | 11.6 | 5.78 | 4.58 | 2091 | 1189 | 1260 | 294.8 | 1929 | 1236 | 1496 | 426.3 |
| 30 m | 12.1 | 12.2 | 5.95 | 4.79 | 2166 | 1271 | 1322 | 305.4 | 1969 | 1283 | 1517 | 428 |
| 40 m | 12.7 | 12.7 | 6.15 | 5.12 | 2241 | 1360 | 1392 | 316 | 2017 | 1333 | 1552 | 433 |
Influence of different positioning of three dissimilar bridges on the seismic response system_
| Position | ast (m/s2) | acap (m/s2) | Internal forces | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Central piles | Corner piles | |||||||||||
| Pile (2) (Mst = 350 t) | Pile (15) (Mst = 1050 t) | Pile (1) (Mst = 350 t) | Pile (7) (Mst = 1050 t) | |||||||||
| Mmax (kN m) | Tmax (kN) | Mmax (kN m) | Tmax (kN) | Mmax (kN m) | Tmax (kN) | Mmax (kN m) | Tmax (kN) | |||||
| One perpendicular bridge (Mst = 350 t) | 20.1 | 11.5 | 3979 | 1268 | 4093 | 1330 | ||||||
| One perpendicular bridge (Mst = 1050 t) | 20.53 | 12.49 | 2196 | 1325 | 2061 | 1294 | ||||||
| Position | Bridge (Mst = 350 t) | Bridge (Mst = 1050 t) | Three dissimilar bridges | |||||||||
| ast | acap | ast | acap | Pile (2) (Mst = 350 t) | Pile (15) (Mst = 1050 t) | Pile (1) (Mst = 350 t) | Pile (7) (Mst = 1050 t) | |||||
| Parallel | 11.6 | 11.6 | 5.78 | 4.58 | 2091 | 1189 | 1260 | 294.8 | 1929 | 1236 | 1496 | 426.3 |
| Perpendicular | 0.54 | 6.47 | 2.81 | 1.17 | 411.8 | 113.4 | 1580 | 282.7 | 388 | 130.5 | 1578 | 456.2 |
| Crossing | 0.51 | 6.3 | 5.67 | 2.39 | 370.2 | 110.6 | 1042 | 589.7 | 360.8 | 123.2 | 2412 | 1274 |
Response of a group of (4x3) piles for Kocaeli earthquake (1999)_
| C (kPa) | ast (m/s2) | acap (m/s2) | Internal forces | |||
|---|---|---|---|---|---|---|
| Central piles | Corner piles | |||||
| Mmax (kN m) | Tmax (kN) | Mmax (kN m) | Tmax (kN) | |||
| 150 | 18.09 | 14.9 | 1411 | 837.8 | 1732 | 1233 |
Elastic characteristics of the pile materials_
| Material | Diameter (m) | Mass density ρ (kg/m3) | Young's modulus E (MPa) | Poisson's ratio ν | Damping ratio ξ (%) | Height (m) |
|---|---|---|---|---|---|---|
| Pile | 0.8 | 2500 | 20,000 | 0.3 | 2 | 10 |
Response of a group of (2 × 3) piles for Kocaeli earthquake (1999)_
| C Cohesion (kPa) | ast (m/s2) | acap (m/s2) | Internal forces | |||
|---|---|---|---|---|---|---|
| Central piles | Corner piles | |||||
| Mmax Bending moment (kN m) | Tmax Shear force (kN) | Mmax Bending moment (kN m) | Tmax Shear force (kN) | |||
| 150 | 23.02 | 14.39 | 2244 | 1218 | 2189 | 1604 |
Response of a group of (6×3) piles for Kocaeli earthquake (1999)_
| C (kPa) | ast (m/s2) | acap (m/s2) | Internal forces | |||
|---|---|---|---|---|---|---|
| Central piles | Corner piles | |||||
| Mmax (kN m) | Tmax (kN) | Mmax (kN m) | Tmax (kN) | |||
| 150 | 11.99 | 10.82 | 2363 | 623.3 | 2947 | 1007 |