Bearing capacity of tapered piles in clay under undrained condition

ABSTRACT

Based on the lower bound limit analysis, the bearing capacity of a tapered pile in clay is computed. The numerical analysis is performed for various parameters such as embedment length to base diameter ratio (L_p/D₀), taper angle (β), a factor m for the linear variation of cohesion, and adhesion factors (α_b and α_s). The results are presented in the form of bearing capacity factors N_ct^b, N_ct^s and N_ct which represent resistances due to pile base, shaft and total load carrying capacity, respectively. The factor N_ct^b is found to be decreasing, while the factors N_ct^s and N_ct are increasing, due to an increase in β. The increases in N_ct^s and N_ct are found to be significant for smaller β (between 1–3°) and larger L_p/D₀. The bearing capacity factors are significantly affected by undrained cohesion. It is expected that the results of the present analysis will be helpful to the practicing engineers.

KEYWORDS:

• Tapered pile
• limit analysis
• clay
• bearing capacity
• plasticity

List of notations

[A]	=	global matrix for linear equality constraint in Equation (6)(6) $[A]\left\{\sigma \right\}=\left\{B\right\}$(6)
a	=	one part of the equation of two-dimensional Mohr-Coulomb yield criteria
{B}	=	global vector for linear equality constraint in Equation (6)(6) $[A]\left\{\sigma \right\}=\left\{B\right\}$(6)
[C]	=	global matrix for linear inequality constraint in Equation (7)(7) $[C]\left\{\sigma \right\}\le \left\{D\right\}$(7)
c	=	cohesion at any depth below the ground surface
c0	=	cohesion at the ground surface
cb	=	cohesion at pile base
cs	=	cohesion at any depth along the pile shaft
[D]	=	global vector for linear inequality constraint in Equation (7)(7) $[C]\left\{\sigma \right\}\le \left\{D\right\}$(7)
d	=	other part of the equation of two-dimensional Mohr-Coulomb yield criteria
D0	=	diameter of pile base
dri	=	base of the triangular element for ith edge along the pile shaft
dzi	=	height of the triangular element for ith edge along the pile shaft
{g}	=	global vector of objective function coefficients
Lp	=	depth of embedment of the tapered pile
m	=	a constant for the variation of undrained cohesion with depth
Nctb	=	bearing capacity factor for the base resistance
Ncts	=	bearing capacity factor for the shaft resistance
Nct	=	bearing capacity factor for the total collapse load
Qu	=	total collapse load due to base and shaft resistance
Qub	=	collapse load due to the base resistance
Qus	=	collapse load due to the shaft resistance
r0	=	radius of the pile base
rl,i	=	radius of the lower node at ith edge along the pile shaft
ru,i	=	radius of the upper node at ith edge along the pile shaft
s	=	number of edges along the pile shaft
αb	=	adhesion factor at the pile base
αs	=	adhesion factor along the pile shaft
β	=	taper angle
{σ}	=	global stress vector
σr	=	normal stress component along the r-direction
σz	=	normal stress component along the z-direction
σθ	=	normal stress component along the θ-direction
τnt	=	tangential stress component along the pile shaft
τrz	=	shear stress component in the r-z plane
ϕ	=	the angle of internal friction of soil

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Mantu Majumder

Mr. Mantu Majumder is a research scholar in the Department of Civil Engineering, Indian Institute of Technology Kharagpur. He has pursued his Master of Technology in Civil Engineering from Indian Institute of Technology Gandhinagar. He has done his Bachelor of Technology in Civil Engineering from National Institute of Technology Agartala.

Debarghya Chakraborty

Dr. Debarghya Chakraborty is an Assistant Professor in the Department of Civil Engineering, Indian Institute of Technology Kharagpur. He has received his Ph.D degree in Civil Engineering from the Indian Institute of Science Bangalore. He has completed his Master of Technology in Civil Engineering (Specialization: Geotechnical Engineering) from Indian Institute of Technology Bombay. He has done his Bachelor of Technology in Civil Engineering from the Jalpaiguri Government Engineering Collage.