Allowable Load for a Settlement Limit (NC Clay)
The inverse of the primary-consolidation tile: the maximum load-induced stress increase that keeps a clay's settlement within an allowable limit - d_sigma = sigma'0 (10^(Sc(1 + e0)/(Cc H)) - 1). To hold a 10 ft NC clay (Cc 0.25, e0 0.90, sigma'0 2,000 psf) to a 2 in settlement, the added stress can be at most 677 psf; tighten the limit to 1 in and only 314 psf is allowed - because settlement grows with the log of the stress ratio, a tighter limit allows disproportionately less load. Single NC layer, no time rate. A design aid; the geotechnical engineer of record governs.
Formula and source
d_sigma = sigma'0 (10^(Sc_ft (1 + e0) / (Cc H)) - 1), Sc_ft = Sc_in / 12; final_stress = sigma'0 + d_sigma.
The Terzaghi primary consolidation relation solved for the allowable load increment, the inverse of the settlement tile, as compiled in the Das and NAVFAC references, by name.
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