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Seismic response of single piles in liquefiable soil considering P-delta effect

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Abstract

Dynamic analyses of piles subjected to both vertical and horizontal loading under seismic conditions are of great significance to geotechnical and practicing engineers and the numerical methodology proposed in the present study fills the existing research gap. A finite difference based computer program FLAC3D is used to model a single pile and obtain the deflection and bending moment behaviour along the depth of the pile, under earthquake loading conditions in both non-liquefiable and liquefiable soil. The various earthquake motions considered in the current analysis includes 1989 Loma Gilroy, 1995 Kobe, 2001 Bhuj and 2011 Sikkim motions The bending moment is maximum at the interface of the liquefying and non-liquefying soil layers due to shear strain in the soil being discontinuous across the interface of the layers. The free field ground surface displacement is observed to initially increase with time, reaching the maximum at some instant during shaking and thereafter it remains constant with time, due to local failure of the liquefiable soil around the pile foundation. The combination of vertical load and lateral load on the pile top is varied to obtain the P-delta curves under dynamic loading conditions which are important factors for peak pile bending moment, when there is lateral spreading due to liquefaction causing displacement of the pile head, and inertial load from the superstructure is present. Hence a thorough evaluation of both horizontal and vertical inertial interactions and kinematic interactions due to free field motions, is necessary for considering the behaviour of piles in liquefiable soil and under combined loading situations.

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(Modified after Abdoun et al. 2003)

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Abbreviations

l :

Pile length

d :

Pile diameter

x :

Deflection in pile

M :

Moment generated in the pile

M max :

Maximum bending moment generated in the pile

δ :

Interface friction angle

θ :

Angle between the ground surface with the horizontal

ϕ :

Soil friction angle

k n :

Normal stiffness

k s :

Shear stiffness

G :

Low strain shear modulus

L liq :

Thickness of the liquefiable soil layer

r o :

Radius of the pile

μ :

Poisson’s ratio

V :

Vertical load applied at the pile top

H :

Pseudo-static horizontal inertial load acting at the pile top

D r :

Relative density of the soil

L 1, L 2 :

Hysteresis default model parameters

M w :

Moment magnitude of the earthquake

a max :

Bedrock level acceleration

f :

Amplification factor

E p :

Young’s modulus of elasticity of pile

E s :

Young’s modulus of elasticity of soil

ρ :

Density

e max :

Maximum void ratio

e min :

Minimum void ratio

G s :

Specific gravity

c u :

Cohesion

k :

Coefficient of permeability

γ :

Unit weight

C 1, C 2 :

Byrne model parameters

\(\Delta \in_{vd}\) :

Incremental volume decrease,

\(\in_{vd}\) :

Irrecoverable volumetric strain

V ult :

Ultimate pile capacity

V all :

Allowable capacity of a single pile

P-Δ :

Load-deflection

P :

Axial load in the pile at a particular depth

A :

Cross sectional area of the pile

I :

Moment of inertia of the pile

y :

Maximum distance from the neutral axis

σ max :

Maximum stress generated in the pile

σ per :

Permissible tensile stress at yield

r u :

Excess pore water pressure ratio

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Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    Kaustav Chatterjee

  2. Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India

    Deepankar Choudhury & Vansittee Dilli Rao

  3. Coffey Geotechnics Pty. Ltd, Sydney, Australia

    Harry G. Poulos

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  1. Kaustav Chatterjee
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  2. Deepankar Choudhury
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  3. Vansittee Dilli Rao
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  4. Harry G. Poulos
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Correspondence to Kaustav Chatterjee.

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Chatterjee, K., Choudhury, D., Rao, V.D. et al. Seismic response of single piles in liquefiable soil considering P-delta effect. Bull Earthquake Eng 17, 2935–2961 (2019). https://doi.org/10.1007/s10518-019-00588-2

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