Theoretical Analysis on Reduction of Load-Induced Excess Pore-Water Pressures in Roads with Geogrids

Data Availability Statement

Notation

A₁–A₃

unknown variant;

a

radius of the applied pressure;

B₁–B₃

unknown variant;

c

parameter regarding M and k;

E

elastic modulus;

E_b

elastic modulus of base course;

E_g

elastic modulus of geogrid;

E_gh_g

geogrid stiffness;

E_s

elastic modulus of subgrade;

e

volumetric strain;

f(r, z, t)

function;

$\overline{f}(\xi ,z,s)$

Laplace-Hankel transform of a function f(r, z, t);

G

shear modulus;

h

thickness of base course;

h_g

thickness of geogrid;

J₀

Bessel function in Order 0;

J₁

Bessel function in Order 1;

k

permeability of soil;

M

parameter regarding shear modulus and Poisson’s ratio;

m

order of the Hankel transform;

N_r

tensile force of the geosynthetic in the radial direction;

N_φ

tensile force of the geosynthetic in the transverse direction;

p

applied pressure;

Q

volume of water through a unit area;

q

parameter;

q_zg

vertical support stress provided by geogrid;

r

radial distance from the centerline;

r_d

distance from the centerline to the inflection point;

s

transformed variant of t;

s_rg

lateral confinement stress provided by geogrid;

t

time;

u

lateral elastic displacement of soil;

u*

permanent lateral deformation of a road layer that mobilizes a geogrid;

V₁–V₃₀

parameters;

w

vertical elastic displacement of soil;

w*

permanent vertical deformation of a road layer that mobilizes a geogrid;

z

vertical distance from the interface;

β

stress distribution angle;

γ_w

unit weight of water;

δ

vertical displacement of geogrid;

ɛ

vertical strain;

ɛ

vertical permanent strain at the bottom of the base course;

η

reduction factor;

λ_e

elastic coefficient;

λ_p

plastic coefficient;

μ

Poisson’s ratio;

μ_g

Poisson’s ratio of geogrid;

ξ

transformed variant of r;

σ

excess pore pressure;

σ_b

excess pore pressure at the bottom of the base course;

σ_r

total normal stresses in the vertical direction;

${\sigma }_r^{\mathrm{\prime }}$

effective normal stresses in the radial direction;

${\overline{\sigma }}_{r0}$

Laplace–Hankel transformed component of radial stress in Order zero;

${\overline{\sigma }}_{r1}$

Laplace–Hankel transformed component of radial stress in Order 1;

σ_s

excess pore pressure at the top of the subgrade;

σ_s,max

maximum vertical stress at the top of the subgrade;

σ_z

total normal stresses in the transverse direction;

${\sigma }_z^{\mathrm{\prime }}$

effective normal stresses in the vertical direction;

${\sigma }_{zb}^{\mathrm{\prime }}$

effective normal stresses at the bottom of the base course;

${\sigma }_{zs}^{\mathrm{\prime }}$

effective normal stresses at the top of the subgrade;

${\sigma }_{\theta }$

total normal stresses in the radial direction;

${\sigma }_{\theta }^{\mathrm{\prime }}$

effective normal stresses in the transverse direction;

τ_zr

shear stress;

τ_rb

shear stress at the bottom of the base course;

τ_rs

shear stress at the top of the subgrade;

$\mathrm{\nabla }$

Laplacian operator for the axisymmetric problem;

subscript of s

parameters regarding subgrade;

subscript of b

parameters regarding base course; and

subscript of g

parameters regarding geogrid.

References