// STATE BOUNDARY SURFACE (SBS) OF THE MODIFIED CAM CLAY MODEL 
// Project: Animating Soil Models https://soilmodels.com/soilanim
// by: Gertraud Medicus, University of Innbruck, 08/2021

import graph3;

//view
currentprojection=orthographic(60,120,120);

// fill in M and p0:
real M=1; // M=6*sin(phi)/(3-sin(phi))
real p0=100; // preconsolidation pressure to define size of yield locus


// The sbs is formulated as parametric surface by x(p,theta), y(p,theta), z(p,theta)
triple f(pair l) {
real theta=l.x; // Lode angle theta
real p=l.y; // mean effective stress p
real q=sqrt(M^2*p*(p0-p)); //q: deviatoric stess; equation for ellipse 
// Drucker-Prager: deviatoric plane; formulation e.g. in Griffiths (1990): doi: 10.1061/(ASCE)0733-9410(1990)116:6(986)
return (
(p+2/3*q*sin(theta-2*pi/3)), //x(p,theta)
(p+2/3*q*sin(theta)), //y(p,theta)
(p+2/3*q*sin(theta+2*pi/3)) //z(p,theta)
);}
surface s=surface(f,(-180*pi/180,.01),(180*pi/180,100),10,100,Spline);
draw(s,orange+opacity(0.9),meshpen=black,render(merge=true));

// axes
xaxis3("$\sigma_1'$",0,p0);
yaxis3("$\sigma_2'$",0,p0);
zaxis3("$\sigma_3'$",0,p0);