Module 09
Stress paths, drainage and loading
Following the stress state as a load is applied: the Mohr circle and its invariants, total and effective stress paths, and why drained and undrained loading trace different routes to failure.
What this module covers
- Represent a stress state with the Mohr circle and its centre/radius invariants
- Compute the s–t and p–q invariants and relate them to total and effective stress
- Show that pore pressure shifts the mean stress but not the deviatoric stress
- Draw total and effective stress paths for a loading
- Explain how drained and undrained paths differ and reach the failure line differently
Lessons
The Mohr circle, the s–t and p–q invariants, and the total–effective split.
Start lesson →- 9.2
Stress paths
Tracking the stress point through a loading; total and effective paths.
Start lesson → The same soil, two loadings, two routes to failure.
Start lesson →
Module checkpoint
Check what you have taken in
3 questions
Question 1
A stress state has total principal stresses σ1 = 300 kPa and σ3 = 120 kPa with pore pressure u = 50 kPa. What is the effective mean-stress invariant s′, in kPa?
Question 2
On a plot of shear (t) against mean stress (s), increasing the pore pressure at constant total stress moves the effective stress point:
Question 3
For total stresses σ1 = 180 kPa and σ3 = 60 kPa, what is the deviatoric invariant t (the Mohr-circle radius), in kPa? (It is the same in total and effective stress.)