Large-Deformation Finite-Element Analysis of Square Foundations in Spatially Variable Sediments

Data Availability Statement

Notation

A

bottom area of square foundation;

B

foundation width;

D_max

maximum probability difference between the sample and the referred distribution;

E

Young’s modulus of sediment;

F

penetration resistance of square foundation in uniform sediment;

F_ran

penetration resistance of square foundation in random sediment;

f

field variable in Eulerian formulation;

h_min

minimum mesh size;

k

shear strength gradient;

k₀

geostress coefficient;

N

number of Monte Carlo simulation;

N_c

bearing capacity factor in uniform sediment;

N_c,ran

bearing capacity factor considering random sediment;

p

probability of failure;

q_u

bearing pressure;

S

source term of Eulerian equation;

s_u

random sediment strength;

s_u0

uniform sediment strength;

s_ui(x, y, z)

lognormal random strength field at an arbitrary point (x, y, z);

s_u(x, y, z)

nonstationary random strength field at an arbitrary point (x, y, z);

s_u0,U

strength at penetration depth of U in uniform sediment;

U

penetration depth of square foundation;

$u_{s_{um}}$

mean strength at the mudline;

$u_{s_{uU}}$

mean strength at depth of U;

$u_{s_{uz}(Z)}$

mean strength at depth of z;

V

penetration velocity of square foundation;

z

sediment depth;

γ′

effective sediment unit weight;

Θ_H

horizontal autocorrelation length;

Θ_V

vertical autocorrelation length;

${\mu }_{\ln N_{c,\mathrm{ran}}}$

mean value of the logarithmic N_c,ran;

${\mu }_{N_{c,\mathrm{ran}}}$

mean value of N_c,ran;

ν

Poisson’s ratio;

${\sigma }_{\ln N_{c,\mathrm{ran}}}$

standard deviation of the logarithmic N_c,ran;

${\sigma }_{N_{c,\mathrm{ran}}}$

standard deviation of N_c,ran;

Φ

cumulative normal function;

φ

friction angle;

ϕ

flux function in Eulerian formulation; and

ψ

dilatancy angle.

References