A state of stress that is necessary to produce rock failure in an element can be described by the three principal stresses σ1, σ2, and σ3. In this book, compressive stress is taken positive and σ1 >σ2 >σ3, that is, σ1 is the maximum principal stress, σ2 is the intermediate principal stress, and σ3 is the minimum principal stress. In principal coordinates, the points (σ1, σ2, σ3) representing different states of stress necessary to produce failure might form a surface

σ1 = f (σ2, σ3) (2.1) for a given material. The most fundamental problem of rock mechanics is the study of the shape of this surface for various rocks. In the next chapter, this is fully discussed.