%% Initiating valuablesm=1;%% no. of construction stagen=30; %% no. of layerst=2.5; %% Thickness of layerCu_mob_active=zeros(m,n); %% Mobilizable shear strength of active zoneCu_mob_passive=zeros(m,n); %% Mobilizable shear strength of passive zoneCu=zeros(1,n); %% Undrained shear strengthg_mob_active=zeros(m,n); %% Mobilizable shear strain of active zoneg_mob_passive=zeros(m,n); %% Mobilizable shear strain of passive zonebeta_active=zeros(m,n); %% Mobilizable strength ratio of active zonebeta_passive=zeros(m,n); %% Mobilizable strength ratio of passive zoneH=zeros(m,1); %% Excavation DepthA=zeros(m,n); %% Area of shearing zone in active sideAp=zeros(m,n);%% Total area of shearing zone in passive sideAp1=zeros(m,n); %% Area of shearing zone 1 in passive sideAp2=zeros(m,n); %% Area of shearing zone 2 in passive sidel=zeros(m,1); %% Wavelength of deformationwall_energy=zeros(m,1); %% Elastic energy stored in the wallwtemp=0; %% Assumed max. dispgsat=zeros(1,n);%% Saturated unit weightlower=zeros(1,n); %% Lower bound of layerupper=zeros(1,n); %% Upper bound of layerupper2=zeros(m,n); %% Integration upper bound of zone 2 in construction stage mlower2=zeros(m,n); %% integration lower bound of zone 2 in construction stage mactive_zone=zeros(m,n); %% Active zone indexpassive_zone=zeros(m,n); %% Passive zone indexD=zeros(m,1); %% Depth of mechanismdga=zeros(m,n); %% Averaged shear strain increment in active zonedgp1=zeros(m,n); %% Averaged shear strain increment in passive zone (Sector above)dgp2=zeros(m,n); %% Averaged shear strain increment in passive zone (Triangle)dgp3=zeros(m,n); %% Averaged shear strain increment in passive zone (Sector below)dgp=zeros(m,n);%% Averaged shear strain increment in passive zonedpw=zeros(m,n); %% Plastic work in layer n at excavation stage m tpw=zeros(m,1); %% Total plastic workdpep1=zeros(m,n);dpep2=zeros(m,n);dpep3=zeros(m,n);dpea=zeros(m,n);dpe=zeros(m,n); %% Change in PE in layer n at excavation stage mtpe=zeros(m,1); %% Total change in PE% User defined parametersEI=2.3*10^6*0.9^3/12; % bending stiffness of walls=2.5; %% Support spacingL=24; %% Length of the wallB=70; %% width of excavation%% g/gmaxX=[0,0.015585734,0.032343117,0.050409424,0.06994425,0.091134233,0.114199036,0.139398994,0.167044978,0.197511287,0.231252696,0.268827305,0.310927661,0.358423827,0.412424165,0.474362904,0.546129411,0.630264282,0.730266386,0.851091702,1];%% C_mob/CuY=[0,0.05,0.1,0.15,0.2,0.25,0.3,0.35,0.4,0.45,0.5,0.55,0.6,0.65,0.7,0.75,0.8,0.85,0.9,0.95,1];%X=[0,0.000316228,0.001,0.003162278,0.01,0.031622777,0.1,0.316227766,1]; %% g/gmax%Y=[0,0.010638298,0.042553191,0.095744681,0.20212766,0.382978723,0.638297872,0.893617021,1]; %% C_mob/Cugmax=4.9748; %% Max. shear strainw=zeros(m,1); %% Maximum deformation of staged constructionerror=zeros(m,1); %% Error of calculationfor y=1:n %% assigning bounds of n layersupper(1,y)=(y-1)*t;lower(1,y)=y*t;gsat(1,y)=18;end;upper(1,1)=0.0000000000001;for y=1:n %% assigning bounds of n layers if t*ylimit) l(x,1) = 1.5*(L-H(x,1)); % l(x,1) = B*sqrt(2)/2+s+10; %l(x,1)=50; for y=1:n %% layers n %% Calculate depth of mechanism D(x,1)=H(x,1)-s+l(x,1); %% Zone checking for each layer for active side if D(x,1)l(x,1) %% Integration lower bound for zone 2 lower2(x,y)=l(x,1); else lower2(x,y)=lower(1,y)-H(x,1)+s; end; if (D(x,1)-(H(x,1)-s))>=lower2(x,y) b=lower2(x,y); a=upper2(x,y); A(x,y)=b/2*sqrt(l(x,1)^2-b^2)-a/2*sqrt(l(x,1)^2-a^2)+l(x,1)^2/2*asin(b/l(x,1))-l(x,1)^2/2*asin(a/l(x,1));%% Shearing Area of Zone 2 else b=(D(x,1)-(H(x,1)-s)); a=upper2(x,y); A(x,y)=b/2*sqrt(l(x,1)^2-b^2)-a/2*sqrt(l(x,1)^2-a^2)+l(x,1)^2/2*asin(b/l(x,1))-l(x,1)^2/2*asin(a/l(x,1));%% Shearing Area of Zone 2 end end; %% Calculating Area of shearing in passive side if passive_zone(x,y)==0 Ap(x,y)=0; elseif passive_zone(x,y)==3 %% Shearing Area of Zone 3 Ap(x,y)=t*B/2; elseif passive_zone(x,y)==4%% Shearing Area of Zone 4 Ap(x,y)=(D(x,1)-upper(1,y))*B/2; end;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Calculating averaged mobilizable shear strain and potential energy loss for active zone%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if active_zone(x,y)==0 dga(x,y)=0; dpea(x,y)=0; elseif active_zone(x,y)==1 dga(x,y)=2*wtemp*(lower(1,y)-upper(1,y))./A(x,y); %% average shear strain in zone 1 %wy=-wtemp/2*(1-cos(2*pi*x1/L)); dpea(x,y)=gsat(1,y)*wtemp*l(x,1)/2*(lower(1,y)-upper(1,y)); %% PE loss in zone 1 %%dg(x,y)=int(int( abs(wtemp*pi/l(x,1)*sin(2*pi*x1/l(x,1))) ,x1,0,l(x,1) ) ,y1,lower(1,y),upper(1,y) )/A(x,y); elseif active_zone(x,y)==2 %%syms x1 y1; %%wy=wtemp./2.*(1-cos(2.*pi./l(x,1).*sqrt(x1.^2+y1.^2))).*(-x1./sqrt(x1.^2+y1.^2)); %%wx=wtemp./2.*(1-cos(2*pi/l(x,1)*sqrt(x1^2+y1^2)))*(y1/sqrt(x1^2+y1^2)); %% PE loss in zone 2 Q = @(x1,y1) (gsat(1,y)*wtemp./2.*(1-cos(2.*pi./l(x,1).*sqrt(x1.^2+y1.^2))).*(-x1./sqrt(x1.^2+y1.^2))).*(x1.^2+y1.^2A(x-1,y) g_mob_active(x,y) = ( dga(x,y)*(A(x,y)-A(x-1,y))+(dga(x,y)+g_mob_active(x-1,y))*A(x-1,y) )/(A(x,y));% g_mob_active(x,y) = ( dga(x,y)*(A(x,y)-A(x-1,y))+(dga(x,y)+g_mob_active(x-1,y))*A(x-1,y) )/(A(x,y)); else g_mob_active(x,y) =( dga(x,y)*(A(x-1,y)-A(x,y))+(dga(x,y)+g_mob_active(x-1,y))*A(x,y) )/(A(x-1,y));% g_mob_active(x,y) =( dga(x,y)*(A(x-1,y)-A(x,y))+(dga(x,y)+g_mob_active(x-1,y))*A(x,y) )/(A(x,y)); end; end; else g_mob_active(x,y) = dga (x,y); end %% Calculating beta values and mobilized strength beta_active(x,y)= interp1(X,Y,g_mob_active(x,y)/gmax*100,'pchip'); %% Getting mobilizable strength ratio Cu_mob_active(x,y)=Cu(1,y)*beta_active(x,y);%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Calculating averaged mobilizable shear strain and potential energy loss for passive zone%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if passive_zone(x,y)==0 dgp(x,y)=0; dpep1(x,y)=0; dpep2(x,y)=0; dpep3(x,y)=0; elseif passive_zone(x,y)==3 %% PE loss in passive zone Q_Ap1=@(x1,y1)(gsat(1,y).*l(x,1).*wtemp./4./B.* (sin(2*pi.*y1./l(x,1))+2*pi.*y1./l(x,1)+pi) .*sin(pi.*x1./B) .*(y1+l(x,1)/2>0).*(y1-l(x,1)/2=0).*(x1-B/20).*(y1-l(x,1)/2=0).*(x1-B/20).*(y1-l(x,1)/2=0).*(x1-B/20).*(y1-l(x,1)/2=0).*(x1-B/21 if passive_zone(x,y)>0 g_mob_passive(x,y) = ( dgp(x,y)*(Ap(x,y)-Ap(x-1,y))+(dgp(x,y)+g_mob_passive(x-1,y))*Ap(x-1,y) )/(Ap(x-1,y)+Ap(x,y)); end; else g_mob_passive(x,y) = dgp (x,y); end %% Calculating beta values and mobilized strength beta_passive(x,y)= interp1(X,Y,g_mob_passive(x,y)/gmax*100,'pchip'); %% Getting mobilizable strength ratio Cu_mob_passive(x,y)=Cu(1,y)*beta_passive(x,y); end; %% Virtual work principal tpw(x,1)=0; tpe(x,1)=0; for j=1:n %% layers n for second excavation and onwards dpw(x,j)=Cu_mob_active(x,j)*(dga(x,j)) *A(x,j) + Cu_mob_passive(x,j)*(dgp(x,j))*Ap(x,j); tpw(x,1)=tpw(x,1)+dpw(x,j); tpe(x,1)=tpe(x,1)+dpea(x,j)-dpep1(x,j)-dpep2(x,j)-dpep3(x,j); end; %Calculating elastic energy of the wall if L-H(x,1)+sH(x,1)-s) && (depth(y,1)