A Simplified Analytical Method of Lateral Bearing Capacity of Rigid Single Pile Considering All Soil Reactions in Sand

Acknowledgments

Notation

A_b

sectional area of pile;

a

depth of rotation point;

b

depth of soil-yielding;

c

depth of soil-yielding;

d

pile diameter;

E

Young’s modulus of soil.

E_pI_p

bending stiffness of the pile;

e

height of lateral load;

F_b

lateral resistance at the pile tip;

F_bu

ultimate lateral resistance at the pile tip;

f_i

vertical friction resistance on an elemental area;

H

lateral load;

K_p

coefficient of passive earth pressure;

K₀

coefficient of static earth pressure;

k_bF

initial stiffness of lateral resistance;

k_bM

initial stiffness of moment;

k_h

modulus of horizontal subgrade reaction;

L

pile length;

M

moment at groundline induced by lateral load;

M_b

moment at the pile tip;

M_bu

ultimate moment at the pile tip;

M_s

shaft-resisting moment per unit length;

M_s1

shaft-resisting moment per unit length induced by initial compressive soil pressure;

M_s2

shaft-resisting moment per unit length induced by incremental compressive soil pressure;

$M_s^{\mathrm{\prime }}$

sum of $M_{s1}^{\mathrm{\prime }}$ and $M_{s2}^{\mathrm{\prime }}$;

$M_{s1}^{\mathrm{\prime }}$

total moment induced by M_s1;

$M_{s2}^{\mathrm{\prime }}$

total moment induced by M_s2;

n

constant of horizontal subgrade reaction;

n_max

maximum constant of horizontal subgrade reaction;

P

soil resistance;

P_u

ultimate soil resistance;

q_bu

ultimate resistance of soil;

x_i

distance between the center point of the circular arc i and the axis AC;

y

pile displacement;

y_b

lateral displacement at the pile tip;

y₀

groundline displacement of the pile;

z

depth;

α₀

angle around the pile;

δ

frictional angle of the pile–soil interface;

γ′

effective unit weight of soil;

μ_v

coefficient of vertical friction resistance;

θ

rotation angle of the pile;

θ_b

rotation at the pile tip;

φ

internal friction angle;

φ′

soil’s effective internal friction angle;

σ₀

static earth pressure;

Δσ_pr,i

increment of compressive soil pressure;

Δσ_pr,max

maximum increment of compressive soil pressure;

σ_pr,max

ultimate compressive soil pressure;

σ_v

effective vertical stress;

τ_bu

ultimate friction resistance at the pile tip;

τ_v,i

vertical friction resistance of the circular arc i;

ξ

coefficient to describe variation of σ_pr,max versus P; and

υ

Poisson’s ratio of soil.

References