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Krishna_MCC.m
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%% MATLAB Code for Cam-Clay Model
clear all;
%% Input Parameters
out3=fprintf('\nINPUT PARAMETERS FOR MODIFIED CAMCLAY\n\n');
cp=input('Enter the inital Consolidation pressure (kPa) (eg., 150 kPa) = ');%cp=150;
p0=input('Enter the initial Confining pressure (kPa) (eg., 150 kPa) = ');%p0=150;
M=input('Enter the value of Critical Friction Anlge M (eg., 0.95) = ');%M=0.95;
l=input('Enter the value of Lamda (eg., 0.2) = ');%l=0.2;
k=input('Enter the value of Kappa (eg., 0.04) = ');%k=0.04;
N=input('Enter the value of N (eg., 2.5) = ');%N=2.5;
v=input('Enter the value of poissons ratio (eg., 0.15) = ');%v=0.15;
%% Computation of Other Parameters (V,e0 and OCR)
pc=cp;V=N-(l*log(pc));e0=V-1;OCR=cp/p0;%Initalizing confining pressure
%% Strain Increament and Strain Matrix Definition
out4=fprintf('\nSTRAIN INCREAMENT AND ITERATION\n\n');
iteration=input('Enter number of iterations to perform (eg., 5000) = ');
if (iteration <=2000 || iteration == ' ')
iter=2000;
out5=fprintf('\nThe iterations entered is too low using defaults %f\n',iter);
else iter=iteration;
end
strsteps=input('Enter the strain increament (in decimal) (eg., 0.01) = ');
if (strsteps > 0.01|| strsteps == ' ' || strsteps <= 0.)
ide=0.01;
out6=fprintf('\nThe strain step entered is too low using defaults %f\n',ide);
else ide=strsteps;
end
de=ide/100;
es=0:ide:(iter-1)*ide; %strain
dstrain=[de;-de/2;-de/2;0;0;0];%strain increament
%% Block Memory allocation
De=zeros(1,6);
dfds=zeros(6,1);
dfdep=zeros(6,1);
u=zeros(1,iter);
p=zeros(1,iter);
q=zeros(1,iter);
%% Yield Surface and Conditions
p1=(0:pc);% CSL in p-q space
q1 = M*p1;
qy=(M^2*(pc*p1-p1.^2)).^0.5;%Plot the initial yield locus
%% Initialize
a=1;
S=[p0;p0;p0;0;0;0];
strain=[0;0;0;0;0;0];
p(a)=(S(1)+2*S(3))/3;
q(a)=(S(1)-S(3));
yield=(q(a)^2/M^2+p(a)^2)-p(a)*pc; %Defining the yield surface
%% CamClay Iteration Uni-Loop Iteration for OC/NC & Inside/Outside Yield
while a<iter
K=V*p(a)/k;G=(3*K*(1-2*v))/(2*(1+v));
if yield==0, pc=(q(a)^2/M^2+p(a)^2)/p(a);
else pc=cp;
end
%Elastic Stiffness and other Matrix
for m=1:6
for n=1:6
if m<=3
if yield <0, dfds(m,1)=0;dfdep(m,1)=0;
else
dfds(m,1)=(2*p(a)-pc)/3 + 3*(S(m)-p(a))/M^2;
dfdep(m,1)=(-p(a))*pc*(1+e0)/(l-k)*1;
end
if m==n
De(m,n)= K+4/3*G; %Elastic Stiffness
else if n<=3, De(m,n)=K-2/3*G;
end
end
end
if m>3, dfds(m,1)=0; dfdep(m,1)=0;%df/ds' and %df/dep
if m==n, De(m,n)= G; %Elastic Stiffness
else De(m,n)=0;
end
end
end
end
%Stiffness Matrix
if yield<0, D=De;
else D=De-((De*dfds*(dfds')*De)/((-(dfdep')*dfds+(dfds')*De*dfds)));
end
%Stress and Strain Updates
dS=D*dstrain;
S=S+dS;
strain=strain+dstrain;
%Subsequent cycle update
a=a+1;
p(a)=(S(1)+S(2)+S(3))/3;
q(a)=S(1)-S(3);
u(a)=p0+q(a)/3-p(a);
if yield<0, yield=q(a)^2+M^2*p(a)^2-M^2*p(a)*pc;
else yield=0;
end
end
%% Results and Plots
if OCR<=1
out7=fprintf('\n Soil is Normally Consolidated with a OCR of = %d \n',OCR);
else
out8=fprintf('\n Soil is Over Consolidated with a OCR of = %d \n',OCR);
end
disp('Choose your Plot Options, Enter number in bracket');
f=input('Plot Request: (1) Single Page; (2)Multiple Page =');
if f==1, r=2;c=2;
else if f==2, r=1;c=1;
else out9=fprintf('\nEnter either 1 or 2 \n');
f=input('Plot Request: (1) Single Page; (2)Multiple Page =');
end
end
disp('The Stress Path and other plots are being generated...');
if OCR<=1
figure1 = figure('Name','Soil is Normally Consolidated','Color',[1 1 1]);
else
figure1 = figure('Name','Soil is Over Consolidated','Color',[1 1 1]);
end
if f==2
figure1 = figure(1);
else
subplot(r,c,1,'parent',figure1)%Deviatoric Stress Vs. Axial Strain
end
plot(es,q)
xlabel('Axial strain, \epsilon_a (%)')
ylabel('Deviatoric Stress, q (kPa)')
title('Deviatoric Stress Vs. Axial Strain')
if f==2%Deviatoric Stress Vs. Axial Strain
if OCR<=1
figure2=figure(2);
plot(p,q,p1,q1);
else
figure2=figure(2);
plot(p,q,p1,q1,p1,qy);
end
axis equal
xlabel('Mean Stress, p (kPa)')
ylabel('Deviatoric Stress, q (kPa)')
title('Stress Path')
else subplot(r,c,2,'parent',figure1),
if OCR<=1
plot(p,q,p1,q1);
else
plot(p,q,p1,q1,p1,qy);
end
axis equal
xlabel('Mean Stress, p (kPa)')
ylabel('Deviatoric Stress, q (kPa)')
title('Stress Path')
end
if f==2%Excess Pore water Pressure;
figure3=figure(3);
plot(es,u);
else
subplot(r,c,3,'parent',figure1), plot(es,u)
end
xlabel('Axial strain, \epsilon_a (%)')
ylabel('Excess Pore Water Pressure, u (kPa)')
title('Excess Pore Water Pressure Vs. Axial Strain')
% Create an output folder
status = mkdir('Output');
cd('Output');
if f==2
saveas(figure1,'DeviatoricStress_vs_AxialStrain','fig')
print(figure1,'-depsc2','DeviatoricStress_vs_AxialStrain.eps')
print(figure1,'-dtiff','-r600','DeviatoricStress_vs_AxialStrain.tiff')
saveas(figure2,'StressPath','fig')
print(figure2,'-depsc2','StressPath.eps')
print(figure2,'-dtiff','-r600','StressPath.tiff')
saveas(figure3,'ExcessPWP_vs_AxialStrain','fig')
print(figure3,'-depsc2','ExcessPWP_vs_AxialStrain.eps')
print(figure3,'-dtiff','-r600','ExcessPWP_vs_AxialStrain.tiff')
else
saveas(figure1,'MCC','fig')
print(figure1,'-depsc2','MCC.eps')
print(figure1,'-dtiff','-r600','MCC.tiff')
end
cd ../