Prediction of the Maximum Tensile Load in Reinforcement Layers of a MSE Wall Using ANN-Based Response Surface Method and Probabilistic Assessment of Internal Stability of the Wall

Data Availability Statement

Notation

A_c

cross-section area of a single reinforcement strip after corrosion;

b

width of reinforcement strip;

C_i, C_Ks

constants used in ANN response surface;

COV_Rn, COV_Qn, COV_λR, COV_λQ

coefficient of variation of nominal resistance, nominal load, resistance bias, and load bias, respectively;

D_tmax

distribution factor for T_max;

d_zo

initial zinc thickness;

E_c

corroded strip thickness at the end of design life;

E_n

initial nominal (before corrosion) thickness of steel;

E_s

sacrificial (after corrosion) thickness of steel;

e

eccentricity due to the earth pressure;

F_n

nominal factor of safety;

F*

dimensionless interaction factor between soil and reinforcement layer;

F_y

initial or noncorroded yield strength of the steel;

f¹(•)

logistic sigmoid transfer function;

H

total wall height;

h

number of hidden neurons;

H_ref

reference height equal to 6 m;

K

ratio of loss of steel yield strength to average loss of steel thickness;

K_a

coefficient of active earth pressure;

K_s

horizontal component of active lateral earth pressure coefficient;

K₀

coefficient of earth pressure at-rest;

${\tilde{K}}_s$

approximate value of K_s;

L

reinforcement length;

L_e

anchorage length of the reinforcement layer in the passive zone;

m

number of levels for each factor in UDM;

n

number of random variables;

P_c

the maximum pullout capacity of the reinforcement layer;

P_f

probability of failure;

p

maximum number of columns of the uniform design table;

Q_m, Q_n

measured and nominal load terms, respectively;

q

surcharge pressure;

R_c

coverage ratio of the reinforcement layer equal to b/S_h;

R_m, R_n

measured and nominal resistance terms, respectively;

S

surcharge height;

S_h

horizontal spacing of reinforcement layer;

S_v

tributary vertical spacing of reinforcement layer;

T_al

nominal long-term design strength of reinforcement per unit width;

T_max

maximum tensile load in a steel strip;

T_max,m, T_max,c

measured and computed values of T_max, respectively;

t_dep

time to deplete the zinc coating that protects the steel strip from corrosion;

t_des

design lifetime of the reinforcement from time of construction;

t₁

duration of Stage 1 corrosion;

V_s

rate of loss of average thickness at the surface of steel strip;

V_z1

zinc depletion rate for Stage 1 corrosion;

V_z2

zinc depletion rate for Stage 2 corrosion;

w¹, b¹

weights and bias between input and hidden layer, respectively;

w², b²

weights and bias between hidden and output layer, respectively;

x_i

original value of input variable;

x_i,max

maximum value of original input variable;

x_i,min

minimum value of original input variable;

$x_i^{\mathrm{\prime }}$

normalized value of input variable;

$x_{i,max}^{\mathrm{\prime }}$

maximum value of normalized input variable equal to 1;

$x_{i,min}^{\mathrm{\prime }}$

minimum value of normalized input variable equal to −1;

z

depth below crest of wall;

β

reliability index;

β₀, β₁, and β₂

regression coefficient used in LM5;

γ

unit weight of the soil;

λ_i, λ_Ks

coefficients used in ANN response surface;

λ_Q

load bias;

λ_R

resistance bias;

μ_Rn, μ_Qn, μ_λR, μ_λQ

mean values of nominal resistance, nominal load, resistance bias, and load bias, respectively;

ϕ

friction angle of the soil;

Φ_c

soil cohesion factor;

Φ_fb

facing batter factor;

Φ_fs

facing stiffness factor;

Φ_g

global stiffness factor;

Φ_local

local stiffness factor;

ρ_n

nominal correlation coefficient between nominal resistance and load terms;

ρ_Q

Pearson’s correlation coefficient between nominal load and load bias value;

ρ_R

Pearson’s correlation coefficient between nominal resistance and resistance bias value; and

σ_v

vertical overburden pressure of the soil.

References