Numerical analysis of bearing behaviors of single batter piles under horizontal loads in various directions

doi:10.1007/s11709-022-0914-1

Front. Struct. Civ. Eng.

2023, Vol. 17

Issue (2) : 224-237 https://doi.org/10.1007/s11709-022-0914-1

RESEARCH ARTICLE

Numerical analysis of bearing behaviors of single batter piles under horizontal loads in various directions

Shuang ZHAO¹, Kuihua WANG¹(

), Yuan TU¹, Weiqiu CHEN², Juntao WU¹

¹. College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
². School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310013, China

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Abstract

The horizontal bearing behavior of a single batter pile (SBP) is vital to its application in practical engineering; however, the horizontal responses of SBPs change with the directions of horizontal loads, and this phenomenon is rarely investigated. Therefore, the directional differences in the horizontal bearing behaviors of SBPs are investigated in this study. Four model tests are conducted to preliminarily examine the effects of the skew angle of horizontal loads on the horizontal bearing capacities and distributions of the bending moments of the SBPs. Subsequently, the differences in the responses of the SBPs under horizontal loads in various directions at full scale are analyzed comprehensively via finite-element (FE) analysis. The effects of the skew angle on SBP-soil interaction are discussed. Moreover, an empirical design method is proposed based on the FE analysis results to predict the bearing ratios of SBPs in medium-dense and dense sand while considering the effects of the skew angle, batter angle, and pile diameter. The method is confirmed to be effective, as confirmed by the close agreement between the predicting results with the model test (reported in this study) and centrifuge model test results (reported in the literature).

Keywords single batter pile skew horizontal load model test finite-element analysis empirical design method

Corresponding Author(s): Kuihua WANG

Just Accepted Date: 07 December 2022 Online First Date: 08 March 2023 Issue Date: 03 April 2023

Cite this article:

Shuang ZHAO,Kuihua WANG,Yuan TU, et al. Numerical analysis of bearing behaviors of single batter piles under horizontal loads in various directions[J]. Front. Struct. Civ. Eng., 2023, 17(2): 224-237.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-022-0914-1
https://academic.hep.com.cn/fsce/EN/Y2023/V17/I2/224

Fig.1 Diagram showing SBP and skew horizontal load.

Fig.2 Schematic illustration of the model piles (unit: cm).

Fig.3 Setup for the static load test.

Fig.4 Schematic illustration of static load test (unit: cm).

Fig.5 H–w curves for SBPs in the model tests.

Fig.6 Values of

H u

for SBPs in the model tests.

Fig.7 Pile bending moment profiles for SBPs in the model tests under H = 150 N.

Fig.8 M_max–H curves for SBPs in the model tests.

Tab.1 Detailed simulation conditions for the full-scale modeling

Fig.9 FE model used in current study.

Fig.10 Details of reinforcements in the piles illustrated using embedded shell elements.

soil	unit weight γ_s′ (kN/m³)	material parameters		Poisson’s ratio $υ$	internal friction angle φ (° )	dilation angle $ψ$ (° )	cohesion c (kPa)
soil	unit weight γ_s′ (kN/m³)	λ	κ	Poisson’s ratio $υ$	internal friction angle φ (° )	dilation angle $ψ$ (° )	cohesion c (kPa)
medium-dense sand (D_r = 50%)	11	600	0.6	0.25	35.0	5.0	0.1
dense sand (D_r = 80%)	11	1000	0.5	0.25	37.5	7.5	0.1

Tab.2 Default parameters of sand used in modeling

soil	unit weight (kN/m³)	elastic modulus E_p (MPa)	Poisson’s ratio $υ$	internal friction angle φ (° )	dilation angle $ψ$ (° )	cohesion c (kPa)
sand	15.386	17.0	0.3	34.1	0	0.34

Tab.3 Default parameters of sand in the model-scale modeling

Fig.11 Comparison of H–w curves of piles obtained from model tests and FEM results.

soil	unit weight γ_s′ (kN/m³)	material parameters		Poisson’s ratio $υ$	internal friction angle φ (° )	dilation angle $ψ$ (° )	cohesionc (kPa)
soil	unit weight γ_s′ (kN/m³)	λ	κ	Poisson’s ratio $υ$	internal friction angle φ (° )	dilation angle $ψ$ (° )	cohesionc (kPa)
sand	9.45	560	0.6	0.21	34.8	2.9	0.1

Tab.4 Default parameters of sand used in centrifuge model test [36]

Fig.12 Comparison of H–w curves for piles obtained from centrifuge model test and FEM results.

Fig.13 Typical

H u

–δ curves of SBPs in full-scale modeling.

Fig.14 Distribution of M_p vs. Z based on H = 600 kN.

Fig.15 β–δ curves of SBPs in sand of various relative densities: (a) θ = 15°; (b) θ = 25°.

Fig.16 β–δ curves of SBPs of various lengths and diameters in medium-dense sand: (a) various pile lengths; (b) various pile diameters (The FE model for 15° SBP at D = 1.5 m and δ = 150° was not convergent when w = 0.1D).

Fig.17 Distributions of normal deflection (y) vs. Z for 15° SBP and vertical pile under 600 kN horizontal loads.

Fig.18 Distributions of p vs. Z for 15° SBP and vertical pile under H = 600 kN.

Fig.19 p–y curves for 15° SBP and vertical pile: (a) Z = 1D; (b) Z = 2D; (c) Z = 3D.

Fig.20 β vs. δ.

Fig.21 Values of a, b, and c for sand of various relative densities.

Fig.22 Values of normalized parameters (k_c/k_50%, m_c/m_50%, and n_c/n_50%) vs. D_r.

Fig.23 Values of normalized parameters (

a d

a 1

b d

b 1

, and

c d

c 1

) vs. D.

Fig.24 β values for SBPs yielded by proposed method and obtained from FEM results.

Fig.25 β values for SBPs yielded by the proposed method and obtained from model test results: (a) model tests; (b) centrifuge model test [1].

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