Soil Mechanics / Stress paths, drainage and loading

Stress paths

Tracking the stress point through a loading; total and effective paths.

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A geotechnical reviewer must check laboratory interpretation, classification conventions and the limits of drained, undrained and one-dimensional idealisations.
Stress-path and critical-state illustrations simplify stress anisotropy, total vs excess pressure, loading history, drainage, structured soils, strain softening and cyclic behaviour. Full specialist review remains necessary; selected corrections do not certify the models.

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Why this matters

Two soil elements can end at the same failure stress yet behave completely differently on the way, because they travelled different paths. The stress path records that journey, and — crucially — the effective stress path is what the soil actually feels. Reading it tells you how close a loading is driving the soil towards failure.

From first principles

Pore pressure shifts the path sideways, not up

We want to show: Show that changing pore pressure moves the stress point horizontally (mean stress) but not vertically (deviatoric stress).

Pore pressure is a hydrostatic (all-round) stress. It pushes equally on every face, so it cannot create any shear — it can only change the mean stress. On a plot of shear against mean stress, that means a purely sideways move.

Now the two loading cases fall out:

Drained loading — the soil drains as it is loaded, so no excess pore pressure develops ( $u$ stays at its static value). The ESP runs parallel to and a fixed distance left of the TSP; both climb as the load adds shear.
Undrained loading — the water cannot escape, so shearing generates excess pore pressure that changes with the load. The ESP peels away from the TSP: it bends left if the soil wants to contract (loose or normally consolidated, positive excess $u$ ), or right if it wants to dilate (dense or heavily overconsolidated, negative excess $u$ ).

When using an effective-stress failure envelope, assess the effective stress path. A total-stress path requires a compatible total-stress strength model, such as an appropriate undrained-strength representation.

Practice

During undrained loading a clay element reaches total stresses σ1 = 250 kPa, σ3 = 130 kPa with a total porewater pressure u = 70 kPa. What is the effective mean-stress invariant s′, in kPa?

Summary

A stress path is the track of the stress point through a loading.
ESP = TSP shifted left by the pore pressure u; the two are the same height (t, q).
Drained: no excess u, ESP parallel to TSP. Undrained: excess u develops, ESP peels left (contractive) or right (dilative).
Compare the effective stress path with an effective-stress envelope; use a compatible undrained-strength model for total-stress analysis.