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seepage_concrete_dam_isotropic_soil.m
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seepage_concrete_dam_isotropic_soil.m
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%=========================================================================
% MATLAB script file to draw the flownets of a flat-bottomed concrete
% dam without any sheet pile using the conformal mapping technique
% For further details, go to the link below:
% https://github.com/SubhadipN/Conformal_Mapping#seepage-analysis
%=========================================================================
% Prepared by SUBHADIP NASKAR, RESEARCH SCHOLAR, IIT GUWAHATI
%=========================================================================
clear all; clc; warning('off','all')
%=========================================================================
% INPUTS::
a1 = 20;
a2 = 18;
a3 = 4.5;
b1 = 9;
b2 = 1.5;
h1 = -15;
h2 = -2;
k = 3.5*10^(-8); % Coefficient of permeability (m/s)
fl = 17; % Numbers of flow lines (odd number)
yf = 2.00; % Depth factor: controls the y-axis limit of the plot
xf = 5.75; % Width factor: controls the x-axis limit of the plot
f = 0.65; % Ratio between minimum psi and minimum varphi values
%=========================================================================
% DERIVED PARAMETERS::
A = -2*b1;
B = -b1;
C = b1;
D = 2*b1;
h = h1-h2;
%=========================================================================
% PLOT OF THE GIVEN EMBANKMENT DAM IN Z-PLANE::
for i = 1:8
if i == 1
x1 = A;
y1 = 0;
x2 = D;
y2 = 0;
elseif i == 2
x1 = B;
y1 = 0;
x2 = B;
y2 = a1;
elseif i == 3
x1 = B;
y1 = a1;
x2 = B+b2;
y2 = a1;
elseif i == 4
x1 = B+b2;
y1 = a1;
x2 = B+b2;
y2 = a2;
elseif i == 5
x1 = B+b2;
y1 = a2;
x2 = C;
y2 = a3;
elseif i == 6
x1 = C;
y1 = a3;
x2 = C;
y2 = 0;
elseif i == 7
x1 = B;
y1 = -h1;
x2 = A;
y2 = -h1;
else
x1 = C;
y1 = -h2;
x2 = D;
y2 = -h2;
end
if x1 ~= x2
xx = linspace(x1,x2,200);
m = (y2-y1)/(x2-x1);
yy = m.*xx-m*x1+y1;
else
yy = linspace(y1,y2,200);
xx = x1*diag(eye(length(yy)))';
end
figure (1);
xlim([-xf*b1 xf*b1]);
ylim([-yf*a1 1.5*a1]);
set(gca,'FontSize',20);
hold on;
box on
if i <= 6
if i == 1
leg1 = plot(xx,yy,'b','linewidth',1.5);
end
plot(xx,yy,'b','linewidth',1.5);
else
if i == 7
leg2 = plot(xx,yy,'b-.','linewidth',1.5);
end
plot(xx,yy,'b-.','linewidth',1.5);
end
end
%=========================================================================
% FLOW LINES IN W-PLANE::
x = linspace(-k*h,0,fl);
y = linspace(0,-f*k*h,fl);
for i = 1:fl
xx = linspace(0,-k*h,100);
yx = y(i)*diag(eye(100)); % '||' to x-axis
xy = x(i)*diag(eye(100));
yy = linspace(0,-f*k*h,100); % '||' to y-axis
wx(i,1:100) = complex(xx,yx');
wy(i,1:100) = complex(xy',yy);
end
%=========================================================================
% FLOW LINES IN Z-PLANE::
zx = b1*cos(pi.*wx/(k*h));
zy = b1*cos(pi.*wy/(k*h));
sz = size(zx);
for jj = 1:sz(1)
for kk = 1:sz(2)
if imag(zx(jj,kk)) >= 0
zx(jj,kk) = complex(real(zx(jj,kk)),0);
end
end
end
%=========================================================================
% PLOT OF THE FLOWNETS IN Z-PLANE::
for i = 1:fl
leg3 = plot(real(zx(i,:)),imag(zx(i,:)),'k--','linewidth',1.5);
leg4 = plot(real(zy(i,:)),imag(zy(i,:)),'r','linewidth',1.5);
end
xlabel('Width (m)','fontsize',20);
ylabel('Height (m)','fontsize',20)
% title('Flownets underneath a flat-buttoned hydraulic structure (z-plane)',...
% 'fontsize',20)
legend([leg1 leg2 leg3 leg4],{'Dam outline','Water level',...
'Flow lines','Equipotential lines'},'fontsize',20)
for i = 1:2:fl
if i == fl
t1 = ['\phi_{',num2str(i),'} = ',num2str(x(i))];
else
t1 = ['\phi_{',num2str(i),'} = ',num2str(x(i),'%10.1e')];
end
if i == 1
t2 = ['\psi_{',num2str(i),'} = ',num2str(y(i))];
else
t2 = ['\psi_{',num2str(i),'} = ',num2str(y(i),'%10.1e')];
end
if i <= (fl+1)/2
xc1 = min(real(zy(i,:)));
yc1 = min(imag(zy(i,:)));
text(xc1,yc1,t1,'HorizontalAlignment','right',...
'VerticalAlignment','top','Color','r','fontsize',20)
else
xc1 = max(real(zy(i,:)));
yc1 = min(imag(zy(i,:)));
text(xc1+1.5,yc1,t1,'HorizontalAlignment','left',...
'Color','r','fontsize',20)
end
if i == 1
text(0,0,t2,'HorizontalAlignment','left','VerticalAlignment',...
'bottom','Color','k','fontsize',20)
elseif mod(i-1,4) == 0
xc2 = min(real(zx(i,:)));
ht = text(xc2,0.5,t2,'HorizontalAlignment','left',...
'Color','k','fontsize',20);
set(ht,'Rotation',90);
end
end
t = ['z = f(w) = b_1cos(\piw/kh)'];
text(-0.65*b1,1.2*a1,t,'HorizontalAlignment','left',...
'Color','k','fontsize',20);
axis equal; grid on; grid minor;
%=========================================================================