Primary Consolidation Settlement (Over-Consolidated Clay)
Settlement of an OVER-consolidated clay, which most natural clays are.
Example
You enter
- Compression index Cc (virgin) 0.25
- Recompression index Cr (~0.1 to 0.2 Cc) 0.05
- Clay layer thickness H (ft) 10
- Initial void ratio e0 0.9
- Initial effective stress at mid-layer (psf) 2000
- Preconsolidation pressure sigma'p (psf) 3000
- Stress increase from load (psf) 2000
You get
- Sc (in) 2.529
- Sc (ft) 0.2107
- Over-consolidation ratio / load path 1.5
Checked against published worked examples from: Terzaghi primary consolidation, OC clay (Das / NAVFAC).
Details, formula, and sources
Scopeit settles on the flat recompression index Cr until the load pushes the stress past the preconsolidation pressure sigma'p, then on the steep virgin Cc. Sc = (Cr H/(1+e0)) log10(sigma'p/sigma'0) + (Cc H/(1+e0)) log10((sigma'0+d_sigma)/sigma'p) when the load crosses sigma'p, else the recompression term alone. The same 10 ft clay (Cc 0.25, Cr 0.05, e0 0.90) at sigma'0 2,000 psf with sigma'p 3,000 psf: a 2,000 psf load crosses into virgin compression and settles 2.53 in, but a 500 psf load stays below sigma'p and settles only 0.31 in - the whole reason OCR matters. Reduces to the normally-consolidated case at OCR 1. A design aid; the oedometer data and the geotechnical engineer of record govern.
Formula or tablefinal = sigma'0 + d_sigma. If final <= sigma'p: Sc = (Cr H/(1+e0)) log10(final/sigma'0). Else: Sc = (Cr H/(1+e0)) log10(sigma'p/sigma'0) + (Cc H/(1+e0)) log10(final/sigma'p). OCR = sigma'p/sigma'0.
Source and editionTerzaghi primary consolidation of an over-consolidated clay with the recompression index Cr and the preconsolidation pressure sigma'p, as compiled in the Das and NAVFAC references, by name; reduces to the NC-clay tile at OCR = 1.
Free accessThe over-consolidated consolidation equations are standard soil-mechanics theory in every geotechnical text; no proprietary table is used, and Cc, Cr, and sigma'p are the user's own oedometer results.
What governsEstimate. AHJ and licensed professional govern.
API field namescc, cr, h_ft, e0, sig0_psf, sigp_psf, dsig_psf, sc_in, sc_ft, ocr
- Recompression branch Sc = (Cr H/(1+e0)) log10(final/sigma'0) while final <= sigma'pTerzaghi / Das
- Virgin branch add (Cc H/(1+e0)) log10(final/sigma'p) once the load crosses sigma'pTerzaghi / Das
- Indices Cr about 0.1 to 0.2 of Cc; sigma'p from an oedometer test (Casagrande)NAVFAC / soil-mechanics practice
- Reduction reduces to the NC-clay tile at OCR = sigma'p/sigma'0 = 1consistency check