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Validation and comparison of α for groups of two, three, and four GP–GPR systems_
| PARAMETERS | SETTLEMENT INTERACTION FACTOR, α | REFERENCES |
|---|---|---|
| L/d=10, s/d=3, νs= 0.5, Kgp=10000 | 0.494 | Present analysis for 2GPs |
| L/d=10, s/d=3, νs= 0.5, Kgp=∞ | 0.493 | Poulos (1968) |
| L/d=25, s/d=3, νs= 0.5, Kgp=10000 | 0.584 | Present analysis for 2GPs |
| L/d=25, s/d=3, νs= 0.5, Kgp=∞ | 0.582 | Poulos (1968) |
| L/d=25, s/d=3, νs= 0, Kgp=10000 | 0.631 | Present analysis for 2GPs |
| L/d=25, s/d=3, νs= 0, Kgp=∞ | 0.630 | Poulos (1968) |
| L/d=25, s/d=10, νs=0.5, Kgp=10000 | 0.299 | Present analysis for 2GPs |
| L/d=25, s/d=10, νs=0.5, Kgp=1000 | 0.26 | Kitiyodom and Matsumoto (2003) |
| L/d=25, s/d=10, νs=0.5, Kgp=1000 | 0.265 | Present analysis for 2GPs |
| L/d=25, s/d=10, νs= 0.5, Kgp=∞ | 0.31 | Poulos (1968) |
| L/d=25, s/d=10, νs=0.5, Kgp=10000 | 0.596 | Present analysis for 3GPs |
| L/d=25, s/d=10, νs= 0.5, Kgp=∞ | 0.589 | Poulos (1968) |
| L/d=25, s/d=10, νs=0.5, Kgp=10000 | 0.829 | Present analysis for 4GPs |
| L/d=25, s/d=10, νs= 0.5, Kgp=∞ | 0.81 | Poulos (1968) |
| L/d=10, D/d=2, s/d=4, νs=0.5, Kgp=10000 | 0.42 | Present analysis for 2GPRs |
| L/d=10, D/d=2, s/d=4, νs=0.5, Kgp=∞ | 0.41 | Davis and Poulos (1972) |
| L/d=10, D/d=2, s/d=6, νs=0.5, Kgp=10000 | 0.311 | Present analysis for 2GPRs |
| L/d=10, D/d=2, s/d=6, νs=0.5, Kgp=∞ | 0.31 | Davis and Poulos (1972) |
| L/d=25, D/d=2, s/d=4, νs=0.5, Kgp=10000 | 0.51 | Present analysis for 2GPRs |
| L/d=25, D/d=2, s/d=4, νs=0.5, Kgp=∞ | 0.50 | Davis and Poulos (1972) |
| L/d=25, D/d=2, s/d=6, νs=0, Kgp=10000 | 0.471 | Present analysis for 2GPRs |
| L/d=25, D/d=2, s/d=6, νs=0, Kgp=∞ | 0.47 | Davis and Poulos (1972) |
Calculated α Values for 2GPR, 3GPR, and 4GPR at Different Kgp Values_
| Kgp | Ssingle GPR | S2GPRs | α2 | S3GPRs | α3 | S4GPRs | α4 |
|---|---|---|---|---|---|---|---|
| 10 | 0.28896019 | 0.44372244 | 0.5354 | 0.57710092 | 0.9974 | 0.66499219 | 1.3012 |
| 20 | 0.24921961 | 0.37804292 | 0.517 | 0.4909663 | 0.9707 | 0.57116472 | 1.2923 |
| 40 | 0.21146596 | 0.32215436 | 0.5237 | 0.42253469 | 0.9977 | 0.49794194 | 1.3545 |
| 60 | 0.19295914 | 0.29693231 | 0.5392 | 0.3930989 | 1.037 | 0.46686672 | 1.4202 |
| 80 | 0.18191326 | 0.28252547 | 0.5527 | 0.37668362 | 1.0703 | 0.44965581 | 1.4722 |
| 100 | 0.17456244 | 0.27319766 | 0.5653 | 0.36620857 | 1.0974 | 0.43871883 | 1.5138 |
| 200 | 0.15786745 | 0.25275908 | 0.6007 | 0.34367319 | 1.1776 | 0.41531357 | 1.6311 |
| 300 | 0.15160321 | 0.24534996 | 0.6177 | 0.33564417 | 1.2138 | 0.40701624 | 1.6848 |
| 400 | 0.14831981 | 0.24152163 | 0.6284 | 0.33152454 | 1.2357 | 0.40276757 | 1.7154 |
| 500 | 0.14629833 | 0.23918332 | 0.6355 | 0.32901799 | 1.2489 | 0.40018538 | 1.7365 |
| 600 | 0.1449285 | 0.23760681 | 0.6402 | 0.32733219 | 1.2588 | 0.39844994 | 1.7517 |
| 700 | 0.14393894 | 0.23647197 | 0.6434 | 0.32612074 | 1.2667 | 0.39720341 | 1.7627 |
| 800 | 0.1431906 | 0.23561598 | 0.6455 | 0.3252081 | 1.2727 | 0.3962647 | 1.7703 |
| 900 | 0.14260485 | 0.23494732 | 0.6468 | 0.32449587 | 1.2774 | 0.39553232 | 1.7757 |
| 1000 | 0.14213391 | 0.23441055 | 0.6476 | 0.32392456 | 1.2811 | 0.39494498 | 1.7797 |