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Based on the Biot’s poroelastic model and the Euler-Bernoulli beam equations，the dynamic response of extended helical pile foundations with multiple helixes is studied. The equivalent stiffness model is used to simulate the helixes on the helical pile. With the utilization of the integral transform，the variable separation methods，and the impedance matrix transfer method，the analytical solution to the dynamic response of helical piles with multiple helixes is derived. Through the comparisons with the simplified analytical solutions and the experimental results，the correctness of the proposed model is justified. Finally，with the presentation of a comprehensive parametric study，some dominant impact factors on the dynamic responses are revealed，and the optimal design scheme is suggested accordingly. The main conclusion of this study can be concluded as：An increase of the extension ratio of helix will increase the complex impedance and resonance frequency at the pile top of the helical pile. An increase of the ratio of helix spacing to width will increase the complex impedance of the pile top，but the effect on the resonance frequency is not significant. An increase of the vertical static load at the top of the pile will significantly reduce the complex impedance and resonance frequency at the pile top. The helix inclination has an optimal range in the effect of complex impedance of the pile top.
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| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |
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