Risk assessment of water inrush in karst tunnels excavation based on normal cloud model

Abstract

Water inrush in karst tunnels is a dynamic process in which internal and external factors are involved. The evaluation of this process is fuzzy, complex, and uncertain. In the current research, few articles give full consideration to the fuzziness and randomness of the water inrush evaluation with useful dynamic feedback. A new assessment method has been proposed for the water inrush evaluation based on a combination of the weighting method and normal cloud model. Specifically, an evaluation index system is forged and each index is quantitatively classified into four grades. A synthetic weighted algorithm combining the analytic hierarchy process, entropy method, and statistical methods is proposed to assign the index weight rationally. Based on the cloud generator algorithm, three numerical characteristics are calculated and a sufficient number of cloud droplets are generated. The membership degree of each index belonging to each grade is constructed and the integrated certain grades are determined. In this paper, the multi-factor normal cloud assessment method is applied to the risk assessment of the Qiyueshan tunnel. The assessment result of the risk grade is accurate, that is, the water inrush risk of different samples at the same risk grade can be reflected in figures. The results not only show high consistency with other assessment methods but are also in good agreement with the excavation results. The proposed cloud model method demonstrates good practical reference for risk assessment of tunnel construction in karst areas and can be applied to tunneling, mining, and other engineering practices in the future.

Appendix

A. The Normal Cloud Generator

Input: Three numerical characteristics of the cloud model (Ex, En, He) and the number of cloud drops N;

Output:N cloud drops and their certainty degree μ(x_i).

Steps:

• (a) Generate a normally distributed random number E_n^' with expectation En and standard deviation He: En^'~N(En, He²);

• (b) Generate a normally distributed random number x_i with expectation Ex and standard deviation E_n^': x_i~N(Ex, En'²);

• (c) Calculate the certainty degree: $\mu \left({x}_i\right)={e}^{-\frac{{\left({x}_i-{E}_{xi}\right)}^2}{2{\left({E_n}^{\hbox{'}}\right)}^2}}$;

• (d) Generate a cloud drop with the certainty degree μ(x_i) and the normally random number x_i;

• (e) Repeat steps (a) to (d) until n required cloud drops are generated.

B. The subjective weight calculation program based on AHP

clear.

close all.

clc

tic

disp(‘please input Matrix A’).

A = input(‘A = \n’);

[n,n] = size(A);

x = ones(n,100);

y = ones(n,100);

m = zeros(1100);

m(1) = max(x(:,1));

y(:,1) = x(:,1);

x(:,2) = A*y(:,1);

m(2) = max(x(:,2));

y(:,2) = x(:,2)/m(1);

p = 0.0001;

i = 2;

k = abs(m(2)-m(1));

while k > p;

i = i + 1;

x(:,i) = A*y(:,i-1);

m(i) = max(x(:,i));

y(:,i) = x(:,i)/m(i);

k = abs(m(i)-m(i-1));

end

a = sum(y(:,i));

w = y(:,i)/a;

t = m(i);

disp(‘w = ‘).

disp(w).

%fprintf(‘w = %f\n’,w);

fprintf(‘t = \n %f\n’,t);

CI = (t-n)/(n-1);

RI = [0 0 .58 .90 1.12 1.24 1.32 1.41 1.45 1.49 1.51];

CR = CI/RI(n);

if CR < 0.1;

disp(‘CI = ‘).

disp(CI).

disp(‘RI = ‘).

disp(RI(n)).

disp(‘CR = ‘).

disp(CR).

fprintf(‘\n CR < 0.1\n\n’);

disp(‘Success’).

else disp(‘Fail’).

end

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