Primary Consolidation Settlement (Over-Consolidated Clay)
What the NC-clay tile leaves out and most natural clays actually are: an OVER-consolidated clay 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 NC tile at OCR 1. A design aid; the oedometer data and the geotechnical engineer of record govern.
Formula and source
final = 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.
Terzaghi 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.
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