Specifically, the ordering of Principal Stresses is such that
(including signs). In geotechnical applications the dominant principal stresses will usually be compressive, so the third principal stress will the be the one which you may consider as “largest”.
The convention used in Ref. 1 refers to the hydrostatic pressure (trace of the stress Cauchy tensor) with a positive sign. The use of the first invariant of Cauchy stress tensor
I1(
σ) is preferred in this document where there is a risk of confusion. The pressure in COMSOL Multiphysics is always defined as positive under compression, or equivalently, it has the opposite sign of the Cauchy stress tensor’s trace.