Effects of topography on dynamic responses of single piles under vertical cyclic loading

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This paper describes model tests of single piles subjected to vertical cyclic compressive loading for three kinds of topography: sloping ground, level ground, and inclined bedrock. Comprehensive dynamic responses involving cyclic effects and vibration behaviours are studied under various load combinations of dynamic amplitude, mean load, frequency and number of cycles. Test results show that permanent settlement can generally be predicted with a quadratic function or power function of cycles. Sloping ground topography produces more pronounced settlement than level ground under the same load condition. For vibration behaviour, displacement amplitude is weakly affected by the number of cycles, while load amplitude significantly influences dynamic responses. Test results also reveal that increasing load amplitude intensifies nonlinearity and topography effects. The strain distribution in a pile and soil stress at the pile tip are displayed to investigate the vibration mechanism accounting for sloping ground effects. Furthermore, the dynamic characteristics among three kinds of topography in the elastic stage are studied using a three-dimensional finite method. Numerical results are validated by comparing with experimental results for base inclination topography. An inclined soil profile boundary causes non-axisymmetric resultant deformation, though a small difference in vertical displacement is observed.

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pmax, pmin :

Maximum and minimum dynamic load

Eamp, pmin, F :

Half load amplitude, average and frequency of the dynamic load

P[number1] _E[number2]_F [number3]:

Combined load featuring Pmean =[number1] kN, Eamp = [number2] kN, and F= [number3] Hz

S_H, S_G, S_B:

Topography symbols for the horizontal soil site, sloping soil site and the soil site with inclined bedrock, respectively.

D :

Pile diameter

Ep, Es :

Pile and soil Young’s modulus

α, β :

Mass, stiffness proportion of Rayleigh damping

υs, qc :

Poisson’s ratio and cone resistance in cone penetration test of soil


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This work was supported by the National Science Foundation of China (51622803), Technology Research and Development Project of CHINA RAILWAY (2017G008-H), and ChinaScholarship Council (File No: 201806050121) for financial support to visit Purdue University, the United States.

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Correspondence to Xuan-ming Ding.

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Qu, L., Ding, X., Wu, C. et al. Effects of topography on dynamic responses of single piles under vertical cyclic loading. J. Mt. Sci. 17, 230–243 (2020).

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  • Pile
  • Model test
  • Dynamic response
  • Permanent settlement
  • Vibration displacement
  • Topography effects