Chapter 7 — Effective Stress & Pore Pressure¶

7.1 The principle of effective stress¶

Terzaghi's principle is the foundation of soil mechanics:

\[\sigma' = \sigma - u\]

where \(\sigma\) is the total stress at a point, \(u\) is the pore-water pressure, and \(\sigma'\) is the effective stress carried by the solid skeleton. Every aspect of soil behaviour — strength, stiffness, and volume change — depends on effective stress, not total stress.

7.2 Computing total stress¶

Total stress at depth is the sum of the weights of everything above:

\[\sigma_v = \sum \gamma_i h_i\]

using the appropriate unit weight for each layer — bulk above the water table, saturated below it.

7.3 Pore pressure¶

Pore pressure is measured with piezometers (see the Dunnicliff and FHWA references). Two states matter:

Hydrostatic (steady) — \(u = \gamma_w z\), increasing with depth below the water table.
Excess pore pressure — generated by loading or unloading faster than the water can drain; it dissipates over time (consolidation).

7.4 Effective stress profiles¶

Combining the two gives the effective stress profile. Key observations:

Below the water table, effective stress increases with the submerged unit weight, not the saturated one.
An upward seepage gradient reduces effective stress; a downward gradient increases it.
Where effective stress reaches zero, the soil loses all strength (liquefaction, heave, boiling).

7.5 Why it matters¶

Effective stress explains:

Consolidation — settlement from dissipation of excess pore pressure (Chapter 9);
Shear strength — governed by \(\sigma'\) (Chapter 10);
Liquefaction — loss of effective stress under cyclic loading; and
Seepage stability — uplift and piping (Chapter 6).

7.6 Key takeaways¶

\(\sigma' = \sigma - u\) — the central principle of soil mechanics.
Total stress is the sum of layer weights; pore pressure comes from piezometers.
Below the water table use submerged unit weight for effective stress.
Seepage changes effective stress — upward flow reduces it.
Effective stress drives consolidation, strength, and liquefaction.