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 (Lp/D0), taper angle (β), a factor m for the linear variation of cohesion, and adhesion factors (αb and αs). The results are presented in the form of bearing capacity factors Nctb, Ncts and Nct which represent resistances due to pile base, shaft and total load carrying capacity, respectively. The factor Nctb is found to be decreasing, while the factors Ncts and Nct are increasing, due to an increase in β. The increases in Ncts and Nct are found to be significant for smaller β (between 1–3°) and larger Lp/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.
List of notations
[A] | = | global matrix for linear equality constraint in EquationEquation (6) |
a | = | one part of the equation of two-dimensional Mohr-Coulomb yield criteria |
{B} | = | global vector for linear equality constraint in EquationEquation (6) |
[C] | = | global matrix for linear inequality constraint in EquationEquation (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 EquationEquation (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.