Prediction of Peak Shear Strength of Rock Joints Based on Back-Propagation Neural Network

Acknowledgments

Notation

A₀

maximum contact area ratio;

$A_{{\theta }^{*}}$

effective contact area ratio;

a_j

selected parameters in the input layer;

b_j

activation value of the hidden layer;

C

dimensionless roughness parameter;

d

shear displacement (mm);

l

number of neurons in the output layer;

MSE

global error exists between the actual output y_t and expected output y_t*;

m

number of neurons in the hidden layer;

N

number of samples;

n

number of input neurons;

P

input vector;

p

pth adjustment;

s_j

input of the jth neuron in the hidden layer;

v_jt

weight between neurons in the hidden layer and output layer;

w_ij

weight between neurons in the input layer and the hidden layer;

Y

output vector;

y_t

output of the tth neuron in output layer;

$y_t^{*}$

expected output of the tth neuron in output layer;

α

learning speed between the hidden and the output layers;

β

learning speed between the input and the hidden layers;

γ_t

threshold between neurons in the hidden layer and output layer;

δ

error δ of the actual data τ_p and predicted data ${\tau }_p^{*}$;

θ_j

threshold between neurons in the input layer and the hidden layer;

${\theta }_{\max }^{*}$

maximum effective inclination along the shear direction (°);

${\theta }_{\max }^{*}/(C+1)$

3D roughness parameter;

${\theta }^{*}$

effective apparent inclination angle (°);

σ_n

normal stress (MPa);

σ_t

tensile strength (MPa);

${\overline{\sigma }}_{\mathrm{avg}}$

average estimation error;

τ_p

peak shear strength (MPa);

τ_mes

measured peak shear strength (MPa);

τ_est

estimated peak shear strength (MPa);

${\tau }_p^{*}$

predicted value of peak shear strength (MPa); and

φ_b

basic friction angle (°).

References