Consolidation & Settlement

What consolidation is

When load is applied to a saturated clay, water cannot escape quickly because permeability is very low. The load is first carried by excess pore water pressure; as water slowly drains, the load transfers to the soil skeleton, effective stress increases and the soil compresses. This time-dependent volume reduction due to expulsion of pore water is consolidation.

Total settlement of a foundation on clay:

• $S_i$ = immediate (elastic) settlement — distortion at constant volume.
• $S_c$ = primary consolidation settlement — expulsion of pore water (this chapter).
• $S_s$ = secondary compression — creep of the skeleton after excess pore pressure has dissipated.

Spring–piston analogy (Terzaghi)

A cylinder full of water with a spring (soil skeleton) and a piston with a small valve (low permeability):

1. Instant of loading ($t=0$): water carries the whole load; excess pore pressure $\Delta u=\Delta \sigma$; spring stress unchanged.
2. During drainage: water escapes through the valve; load gradually shifts to the spring; $\Delta u$ falls, $\Delta {\sigma }^{\prime }$ rises.
3. End of consolidation: $\Delta u=0$; the spring carries the full load; $\Delta {\sigma }^{\prime }=\Delta \sigma$.

Oedometer (consolidation) test

An undisturbed specimen (typically 60–75 mm diameter, 20–25 mm thick) is confined laterally in a ring between porous stones (one-dimensional compression, drainage top and bottom). Loads are applied in stages (each usually doubled, held about 24 hours) and dial readings recorded with time. Results give void ratio $e$ at the end of each stage.

Compressibility parameters

Normally consolidated and over-consolidated clays

• Preconsolidation pressure ${\sigma }_p^{\prime }$ (or ${\sigma }_c^{\prime }$) — the maximum effective stress the soil has experienced in its history. Found from the $e$–log σ′ curve by Casagrande's graphical construction (point of maximum curvature, horizontal line, tangent, bisector, intersection with the extended virgin line).
• Normally consolidated (NC): present effective stress ${\sigma }_0^{\prime }={\sigma }_p^{\prime }$ — soil is on the virgin line; highly compressible.
• Over-consolidated (OC): ${\sigma }_0^{\prime }<{\sigma }_p^{\prime }$ (past erosion, desiccation, lowered water table, glacial load); much less compressible for stresses below ${\sigma }_p^{\prime }$.
• Under-consolidated: still consolidating under its own recent weight (${\sigma }_0^{\prime }$ less than the final value).

Consolidation settlement

Settlement and why it matters

Settlement is the vertical downward movement of a foundation. Every foundation settles; the design objective is to keep the total and especially the differential settlement within limits that the structure can tolerate without damage to structure, finishes or services.

Components

Immediate (elastic) settlement

Based on the theory of elasticity for a flexible or rigid footing on a semi-infinite elastic medium:

Typical influence factors (surface footing, semi-infinite medium):

A rigid footing settles uniformly, at roughly the average settlement of a flexible one (about 0.8 of the flexible centre value).

Settlement of footings on sand

Undisturbed sampling of sand is difficult, so settlement is estimated from field tests:

• Plate load test — relates settlement of a test plate to that of the footing (Terzaghi–Peck for sand):

For clay (settlement proportional to width): $S_f=S_p\frac{B_f}{B_p}$.

• Standard penetration test (SPT) — IS 8009 and IS 6403 provide charts relating corrected $N$, footing width and settlement (e.g. pressure causing 25 mm settlement).
• Static cone penetration test — De Beer / Schmertmann methods using cone resistance.