Bearing and uplift capacities of under-reamed piles in soft clay underlaid by stiff clay using lower-bound finite element limit analysis

doi:10.1007/s11709-021-0708-x

Front. Struct. Civ. Eng.

2021, Vol. 15

Issue (2) : 537-551 https://doi.org/10.1007/s11709-021-0708-x

RESEARCH ARTICLE

Bearing and uplift capacities of under-reamed piles in soft clay underlaid by stiff clay using lower-bound finite element limit analysis

Mantu MAJUMDER, Debarghya CHAKRABORTY(

)

Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India

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Abstract

Ensuring a safe foundation design in soft clay is always a challenging task to engineers. In the present study, the effectiveness of under-reamed piles in soft clay underlaid by stiff clay is numerically studied using the lower-bound finite element limit analysis (LB FELA). The bearing and uplift capacities of under-reamed piles are estimated through non-dimensional factors N_cul and F_cul, respectively. These factors increased remarkably and marginally compared to N_cul and F_cul of the piles without bulbs when the bulb is placed in stiff and soft clay, respectively. For a given ratio of undrained cohesion of stiff to soft clay (c₂/c₁), the factors N_cul and F_cul moderately increased with the increase in the length-to-shaft-diameter ratio (L_u/D) and adhesion factors in soft clay (α_s1) and stiff clay (α_s2). The variation of radial stress along the pile–soil interface, distribution of axial force in the under-reamed piles, and state of plastic shear failure in the soil are also studied under axial compression and tension. The results of this study are expected to be useful for the estimation of the bearing and uplift capacities of under-reamed piles in uniform clay and soft clay underlaid by stiff clay.

Keywords bearing capacity uplift capacity under-reamed pile clay limit analysis

Corresponding Author(s): Debarghya CHAKRABORTY

Just Accepted Date: 03 March 2021 Online First Date: 20 April 2021 Issue Date: 27 May 2021

Cite this article:

Mantu MAJUMDER,Debarghya CHAKRABORTY. Bearing and uplift capacities of under-reamed piles in soft clay underlaid by stiff clay using lower-bound finite element limit analysis[J]. Front. Struct. Civ. Eng., 2021, 15(2): 537-551.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-021-0708-x
https://academic.hep.com.cn/fsce/EN/Y2021/V15/I2/537

Fig.1 Details of the domain, boundary conditions, and mesh. (a) Typical domain and boundary conditions of the under-reamed pile for the bulb in stiff clay; (b) typical finite element mesh of the under-reamed pile for the bulb in stiff clay; (c) typical domain and boundary conditions of the under-reamed pile for bulb in soft clay; (d) typical finite element mesh of the under-reamed pile for the bulb in soft clay.

Tab.1 Comparison of Q_cl,base/(A_sc₁) for the pile without bulb with the available literature

Tab.2 Comparison of Q_ul,base/(A_sc₁) for the pile without bulb with the available literature

Fig.2 Variation of N_cul with c₂/c₁. (a) L_u/D = 5; (b) L_u/D = 10; (c) L_u/D = 15; (d) L_u/D = 20.

Fig.3 Variation of F_cul with c₂/c₁. (a) L_u/D = 5; (b) L_u/D = 10; (c) L_u/D = 15; (d) L_u/D = 20.

Tab.3 Effects of α_s1 and α_s2 on N_cul for the bulb in stiff clay

Tab.4 Effects of α_s1 and α_s2 on F_cul for the bulb in stiff clay

Fig.4 Distributions of the normalized radial stress (σ_r/c₁) along the pile–soil interface under axial compression and tension. (a) Different h_b/D_u, L_u/D = 20, c₂/c₁ = 1, compression; (b) different h_b/D_u, L_u/D = 20, c₂/c₁ = 100, compression; (c) different L_u/D, c₂/c₁ = 100, bulb in stiff clay, compression; (d) different h_b/D_u, L_u/D = 20, c₂/c₁ = 1, tension; (e) different h_b/D_u, L_u/D = 20, c₂/c₁ = 100, tension; (f) different L_u/D, c₂/c₁ = 100, bulb in stiff clay, tension.

Fig.5 Distributions of the normalized axial force in the under-reamed pile under axial compression and tension. (a) Different h_b/D_u, L_u/D = 20, c₂/c₁ = 1, compression; (b) different h_b/D_u, L_u/D = 20, c₂/c₁ = 100, compression; (c) different L_u/D, c₂/c₁ = 100, bulb in stiff clay, compression; (d) different h_b/D_u, L_u/D = 20, c₂/c₁ = 1, tension; (e) different h_b/D_u, L_u/D = 20, c₂/c₁ = 100, tension; (f) different L_u/D, c₂/c₁ = 100, bulb in stiff clay, tension.

Fig.6 Selected failure patterns of the pile without bulb and under-reamed pile under axial compression. (a) L_u/D = 20, c₂/c₁ = 1, without bulb; (b) L_u/D = 20, c₂/c₁ = 100, without bulb; (c) L_u/D = 20, c₂/c₁ = 1, h_b/D_u = 0.55; (d) L_u/D = 20, c₂/c₁ = 100, bulb in stiff clay; (e) L_u/D = 20, c₂/c₁ = 1, h_b/D_u = 1.15; (f) L_u/D = 20, c₂/c₁ = 100, bulb in soft clay; (g) L_u/D = 5, c₂/c₁ = 100, bulb in stiff clay; (h) L_u/D = 5, c₂/c₁ = 100, bulb in soft clay.

Fig.7 Selected failure patterns of the pile without bulb and under-reamed pile under axial tension. (a) L_u/D = 20, c₂/c₁ = 1, without bulb; (b) L_u/D = 20, c₂/c₁ = 100, without bulb; (c) L_u/D = 20, c₂/c₁ = 1, h_b/D_u = 0.55; (d) L_u/D = 20, c₂/c₁ = 100, bulb in stiff clay; (e) L_u/D = 20, c₂/c₁ = 1, h_b/D_u = 1.15; (f) L_u/D = 20, c₂/c₁ = 100, bulb in soft clay; (g) L_u/D = 5, c₂/c₁ = 100, bulb in stiff clay; (h) L_u/D = 5, c₂/c₁ = 100, bulb in soft clay.

Tab.5 Comparison of Q_cl/(A_sc₂) for the pile without bulb with the available literature

Tab.6 Comparison of the computed bearing capacity of the under-reamed pile with the available literature

Tab.7 Comparison of the computed uplift capacity of the under-reamed pile with the available literature

a: a component of the equation representing the Mohr–Coulomb yield criteria

A_s: area of the cross-section of the shaft

c: undrained cohesion of soil

c₁: undrained cohesion of soft clay

c₂: undrained cohesion of stiff clay

d: a component of the equation representing the Mohr–Coulomb yield criteria

dr_i, dz_i: radial and vertical distances between the lower and upper nodes of the ith edge along the shaft and surfaceof bulbs, respectively

D: shaft diameter

D_u: bulb diameter

e_base: number of edges at the pile base

e_s,1, e_s,2: total edges along the shaft below and above the bulb, respectively

e_bs,1, e_ts,1: total edges along the bottom and top surfaces of the bulb, respectively

F_cul: non-dimensional uplift capacity factor for the layered clay

h_b: distance of the centre of the bulb from the pile base

LB FELA: lower-bound finite element limit analysis

L₁: depth of the soft clay (top) layer

L₂: depth of the stiff clay (bottom) layer

L_h: horizontal domain extent from the pile surface

L_u: depth of embedment of the under-reamed pile from the ground level

L_v: vertical domain extent below the pile base

N_cul: non-dimensional bearing capacity factor for the layered clay

Q_cl: ultimate collapse load under axial compression for the layered clay

Q_cl,base: resistance from the base under axial compression

Q_cl,bulb: resistance from the bulb under axial compression

Q_cl,shaft: resistance from the shaft under axial compression

Q_ul: ultimate collapse load under axial tension for the layered clay

Q_ul,base: resistance from the base under axial tension

Q_ul,bulb: resistance from the bulb under axial tension

Q_ul,shaft: resistance from the shaft under axial tension

r_i, r_i₊₁: radial distance of the ith and (i+1)th nodes along the pile base from the pile center

r_l,_i, r_u,_i: radial distance of the lower and upper nodes of the ith edge along the bottom and top surfaces of the bulb

α_b: adhesion factor at the pile base

α_s: pile–soil adhesion factor along shaft

α_s1, α_s2: pile–soil adhesion factor of soft and stiff clay, respectively

β: angle of the bulb surface with respect to the horizontal plane (under-ream angle)

γ: unit weight of soil

σ_r: normal stress in the r-direction

σ_z: normal stress in the z-direction

τ_nt: tangential stress along the surface of the bulb

τ_rz: shear stress in the r-z plane

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