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Lateral Bearing Behaviors of Slightly Inclined Single Pile with Different Pile Head Restraint Under Combined Loads

  • Research Article-Civil Engineering
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Abstract

For a laterally loaded pile with its head keyed into the cap, pile head actually rotates in spite of the restraint of the cap. Being aware of this fact, some parameters were put forward to represent the degree of rotational restraint at pile top, and many calculation methods of lateral pile responses were then developed. However, the presented solutions are only for piles under pure lateral loads. In fact, they are usually under the vertical loads simultaneously, caused by the weights of themselves and superstructures. Besides, the slight initial inclination of pile shaft is inevitable in engineering. Some researchers raised solutions of lateral responses of the slightly inclined single pile under combined vertical and lateral loads, but the partially fixed-head condition and the elastoplasticity of soil were not considered. In this study, elastoplastic semi-analytical solutions of lateral responses of the slightly inclined single pile under combined vertical and lateral loads were deduced, in which the rotational restraint coefficient was used to represent the degree of rotational restraint at pile top, and the three-parameter model of the coefficient of subgrade reaction was employed. The computer program was developed thereafter. The effectiveness and advantage of the obtained solutions were validated by the comparison among existing solutions, presented solutions and model test results. Sensitivity analysis was carried out for parameters such as the initial inclination angle of pile shaft, the rotational restraint coefficient, and the vertical load. Eventually, effects of each parameter on lateral pile responses were presented and discussed.

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Abbreviations

N p :

Vertical load (kN)

Q p :

Horizontal load (kN)

M p :

Bending moment at pile top (kN m)

u p :

Horizontal displacement of pile shaft at pile head (mm)

φ p :

Rotation angle of pile shaft at pile head (rad)

θ :

Initial inclination angle of pile shaft (rad)

\(u_{*}\) :

Yielding displacement of soil (mm)

H 0, H 1, H 2 :

Pile length (m)

H :

Total pile length (m)

K m :

Rotational restraint coefficient (kN m/rad)

q :

Distributed load acting on pile shaft above ground (kN/m)

q 0, Δq :

Coefficient of distributed load acting on pile shaft above ground (kN/m)

N G, N S, N E :

Axial force of pile shaft (kN)

f 0, f 1 :

Coefficient of axial load of pile shaft (kN/m)

\(u_{\text{G}}^{\text{t}}\), \(u_{\text{S} }^{\text{t}}\), \(u_{\text{E} }^{\text{t}}\) :

Abscissa value of longitudinal axis of pile shaft

u G, u S, u E :

Horizontal displacement of pile shaft (mm)

u free :

Horizontal displacement at pile top with free-head condition (mm)

u vp :

Horizontal displacement at the top of the vertical pile (mm)

\(\varphi_{\text{G}}\), \(\varphi_{\text{S}}\), \(\varphi_{\text{E}}\) :

Rotation angle of pile shaft (rad)

\(M_{\text{G} }\), \(M_{\text{S}}\), \(M_{\text{E}}\) :

Bending moment of pile shaft (kN m)

M max :

Maximum bending moment under ground (kN m)

M fixed :

Bending moment at pile top with fixed-head condition (kN m)

M vmax :

Maximum bending moment under ground of the vertical pile (kN m)

\(Q_{\text{G} }\), \(Q_{\text{S}}\), \(Q_{\text{E}}\) :

Shear force of pile shaft (kN)

p, p u :

Soil resistance (kN/m)

b :

Pile width (m)

k 0 :

Coefficient of soil resistance in plastic zone (kN/m3)

k 1 :

Coefficient of subgrade reaction in elastic zone of soil (kN/m3)

m :

Scale factor in coefficient of subgrade reaction (kN/m3+n)

n :

Index in coefficient of subgrade reaction

z 0 :

A parameter standing for soil resistance at ground level (m)

z m :

Distance between maximum bending moment and pile top (m)

EI :

Flexural stiffness of pile (kN m2)

E :

Modulus of elasticity of pile (kPa)

I :

Moment of inertia of pile cross section (m4)

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Acknowledgements

This work was funded by the National Natural Science Foundation of China (Grant No. 51508455), and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2019JM-232).

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Authors and Affiliations

  1. School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an, Shaanxi Province, 710055, China

    Lei Zhang

  2. Shaanxi Key Laboratory of Geotechnical and Underground Space Engineering, Xi’an University of Architecture and Technology, Xi’an, 710055, Shaanxi Province, China

    Lei Zhang

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Zhang, L. Lateral Bearing Behaviors of Slightly Inclined Single Pile with Different Pile Head Restraint Under Combined Loads. Arab J Sci Eng 46, 4593–4602 (2021). https://doi.org/10.1007/s13369-020-05026-z

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