A method includes obtaining total stresses and pore pressures of each porous medium of a formation, determining a first and second set of effective stresses for the formation, determining an individual collapse and fracturing mud weight for each porous medium of the formation using a first set of associated failure criteria, wherein the first set of associated failure criteria are based on the first set of effective stresses, determining an overall collapse and fracturing mud weight for the formation using a second set of associated failure criteria, wherein the second set of associated failure criteria is based on the second set of effective stresses, determining a mud weight window for the formation using the individual collapse mud weight, the individual fracturing mud weight, the overall collapse mud weight, and the overall fracturing mud weight, and transmitting a command to a drilling system based on the mud weight window.