Calculation of the compression index and precompression stress from soil compression test data

AS Gregory*, WR Whalley, CW Watts, NRA Bird, PD Hallett, AP Whitmore

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

121 Citations (Scopus)


When compressing soil, there is a characteristic relationship between compressive stress and volume change that can be used to define important soil mechanical properties. Two defining features can be determined - the compression index (C-c - the modulus of the slope of the linear virgin compression curve) and the precompression stress (sigma'(p) - the transition point between the elastic rebound curve and the virgin compression curve). These are indicators of compressibility and stress history respectively. The purpose of this paper is to evaluate different ways of estimating these indicators based on laboratory test data.

Repacked soils with a range of textures were subjected to sequential compressions of 50, 100 and 200 kPa, which provided two compression characteristics with "known" sigma'(p) of 50 and 100 kPa. Three functions were fitted to the measured test data (fourth-order polynomial, symmetrical logistic sigmoidal and asyntmetrical Gompertz sigmoidal). Values of C, were estimated by linear regression (for the data later fitted with a polynomial function) or by the tangent at the inflection point derived from model parameters (logistic and Gompertz functions). Three estimates of sigma'(p) were calculated for each of the three functions: the standard Casagrande method (C), the intercept of the virgin compression curve and the initial (no stress) horizontal line (V-1), and the point of maximum curvature (MC) derived from the curvature function (K).

The accuracy of estimating sigma'(p) and the magnitude of C. generally increased with clay content. Estimates of C, based on sigmoidal curves did not differ greatly from the linear regression estimate. Sigmoidal curves yielded sigma'(p) estimates with lower absolute deviations from known values than polynomial-based estimates. The MC calculation based on the Gompertz function gave the most accurate estimate of sigma'(p). The lower asymptote of sigmoidal curves may also correspond to the water-P filled pore space. Thus, despite the fact that all three functions fitted the measured data equally well, characteristics based on the sigmoidal curves were deemed to be most appropriate. The greater accuracy of the prediction of sigma'(p) favoured the Gumpertz function. Wider applicability of this was further checked with data selected from an independent database on subsoil compaction.

We recommend fitting the Gompertz function to measured soil compression characteristic test data, and to define C-c objectively as the modulus of the slope of the tangent at the inflection point, providing this lies within the measured data range, and sigma'(p) as the point of maximum curvature as defined by K. (c) 2005 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)45-57
Number of pages13
JournalSoil & Tillage Research
Issue number1
Early online date2 Aug 2005
Publication statusPublished - Aug 2006


  • precompression stress (sigma(')(p))
  • compaction
  • compression index (C-c)
  • arable soils
  • mechanical-properties
  • sigmoidal
  • precompaction stress
  • clays
  • compression characteristic
  • load
  • curvature function (kappa)
  • polynomial


Dive into the research topics of 'Calculation of the compression index and precompression stress from soil compression test data'. Together they form a unique fingerprint.

Cite this