## Failure states in soil

As stated in Section 1.11, and illustrated in Figure 1.23, the total stress across any interface through particle contact points in a soil mass is made up of the pore water pressure in the soil voids and the effective stress, equal to the summation of interparticle forces over a unit area. This leads to the effective stress equation given by equation 1.32. As the pore water pressure acts with equal intensity in all directions, it follows from equation 1.32 that

where σ1, σ3 are the major and minor total principal stresses; σ ′1, σ ′3 are the major and minor effective principal stresses. From equations 2.1a and 2.1b,

It follows from equations 2.2a and 2.2b that the total stress and effective stress Mohr circles have the same radius, but are separated along the σ axis by an amount equal to the pore pressure. This is shown for positive (compression) pore pressure +u in Figure 2.1(a) and for negative (tension) pore pressure –u in Figure 2.1(b).