We found a recent paper by the Laboratoire d’essais, d’études et d’expertises (L3E) to be particularly interesting. Here’s a quick summary on this novel work and how we see its potential practical implications for geotechnical engineering applications.
The standard model of one-dimensional consolidation has been largely settled since Terzaghi formalised it in 1923. Load is applied, excess pore pressure develops, water drains, effective stress increases, settlement accumulates. Primary consolidation ends when excess pore pressure dissipates; secondary compression — creep — then takes over, driven by time-dependent rearrangement of the soil skeleton under constant effective stress. This two-phase framework underpins virtually every settlement calculation in routine geotechnical practice. A paper by Ayeb et al. (2017), published in the Revue Française de Géotechnique, takes direct aim at several of its core assumptions — and makes a case that is harder to dismiss than it might first appear.
The hydraulic hypothesis
The central proposition of the paper is that the consolidation process is, from start to finish, hydraulic in character. Settlement occurs because water leaves the soil; the rate of settlement at any time reflects the rate of water flow, governed by the prevailing hydraulic gradient. In the standard framework, the transition from primary to secondary compression at t₁₀₀ is interpreted as the moment when pore pressure has fully dissipated and a different physical mechanism — viscous or structural creep of the soil skeleton — takes over. Ayeb et al. challenge this directly.
Using an oedometer instrumented with a pore pressure sensor at its base, they show that at the moment defined as t₁₀₀ by the Casagrande construction, the pore pressure is not zero. For the two soils tested — a low-plasticity canal silt (vase, liquid limit 48%) and a highly active Moroccan clay mineral called ghassoul (liquid limit 137%, plasticity index 83%) — residual pore pressures at t₁₀₀ were 32 kPa and 60 kPa respectively, under a 200 kPa applied stress. The hydraulic gradient between the base and the drainage face had not reached zero; water was still flowing. What the Casagrande construction identifies as the end of primary consolidation is, on this interpretation, merely a change in flow regime — from fast flow, where hydraulic gradients are large and settlement rates are rapid, to slow flow, where gradients are small and settlement rates are slow. The so-called secondary phase is still hydraulic drainage, just under a much reduced driving force.
This interpretation is corroborated by a further observation: when drainage is interrupted during the slow phase, settlement ceases immediately. If creep were a time-dependent skeletal process independent of drainage, it would continue regardless of boundary conditions. That it stops when drainage stops is, the authors argue, strong evidence that even late-stage consolidation remains hydraulically driven. The dependence of Cα on drainage path length — longer drainage paths yielding higher apparent creep coefficients — further supports this view, since a purely skeletal mechanism would be insensitive to specimen geometry.
A two-parameter hyperbolic law
Rather than treating primary and secondary as distinct phases requiring separate characterisation, Ayeb et al. propose fitting the entire settlement-time curve with a single rectangular hyperbolic function:
εₜ = t / (1/ε̇₀ + t/ε∞)
where ε∞ is the asymptotic final strain and ε̇₀ is the initial strain rate. In the linearised form t/ε = (1/ε∞)·t + 1/ε̇₀, the parameters are recovered from the slope and intercept of a straight line fitted to (t, t/ε) data — a procedure familiar from the hyperbolic pile load-settlement method and used previously for consolidation by Sridharan and Sreepada Rao (1981) and Tan et al. (1991).
Applied to oedometer data from both the vase and the ghassoul under three successive load increments (200, 400 and 600 kPa), the hyperbolic fit achieves excellent coefficients of determination — R² values consistently above 0.99 — using only the first 24 hours of data to predict the full final deformation. The predicted ε∞ values match those obtained by the Asaoka (1978) observational method closely, and when applied to field settlement data from the Rabat–Salé urban bypass preloading project and the well-documented Cubzac-les-Ponts embankment, the method extrapolates measured settlement histories accurately where a previously published approximate method diverged progressively from observations.
The stabilised compressibility curve and preconsolidation stress
The most theoretically provocative contribution of the paper concerns the nature and location of the preconsolidation stress. In the Bjerrum (1967) timeline framework, creep under constant effective stress progressively increases the apparent preconsolidation pressure — this is the mechanism by which geological ageing generates quasi-preconsolidation, and it is a cornerstone of the interpretation of OCR profiles in soft clays worldwide.
Ayeb et al. reject this directly. The preconsolidation stress, they argue, is by definition the maximum stress under which a soil has reached hydraulic equilibrium — that is, a state where excess pore pressure has fully dissipated and no further settlement occurs under that load. This equilibrium state corresponds to the asymptotic final strain ε∞. The locus of points (log σ, ε∞) across different load levels defines what the authors call the Stabilised Compressibility Curve (SCC), which forms the lower envelope of all time-limited compressibility curves. Preconsolidation stresses belong on the SCC and nowhere else. A soil that has crept for a finite time under a given stress has not reached the SCC — it remains on a dynamic compressibility curve — and therefore the apparent preconsolidation stress inferred from a conventional oedometer test on such a soil does not reflect a true equilibrium state. Creep under constant stress moves the soil toward the SCC but cannot move it beyond it; no increase in true preconsolidation stress is generated by time alone, whatever the duration of loading.
This is a direct challenge to the Bjerrum (1967) framework and its widespread application in the interpretation of soft clay behaviour. It is a challenge that the experimental evidence in the paper — pore pressure measurements, drainage-interruption tests, and the geometry of the SCC — supports with some force.
Whether the mainstream view needs wholesale revision is another question, and one that will require engagement from a wider body of experimental evidence. But as a stimulus to examine assumptions that are often applied without scrutiny, this paper does its job.
References
Asaoka, A. (1978) Observational procedure of settlement prediction. Soils and Foundations, 18(4), pp. 87–100.
Ayeb, M., Benechebli, M. and Ayeb, Y. (2017) Nouvelle approche d’analyse de la consolidation unidimensionnelle des sols argileux. Revue Française de Géotechnique, 153, article 2.
Bjerrum, L. (1967) Engineering geology of Norwegian normally consolidated marine clays as related to settlements of buildings. Géotechnique, 17(2), pp. 83–118.
Sridharan, A. and Sreepada Rao, A. (1981) Rectangular hyperbola fitting method for one-dimensional consolidation. Geotechnical Testing Journal, 4, pp. 161–168.
Tan, T.S., Inoue, T. and Lee, S.L. (1991) Hyperbolic method for consolidation analysis. Journal of Geotechnical Engineering, ASCE, 117(11), pp. 1723–1737.
Terzaghi, K. (1923) Die Berechnung der Durchlässigkeit des Tones aus dem Verlauf der hydrodynamischen Spannungserscheinungen. Akademie der Wissenschaften, Wien, 132(3/4), pp. 125–138.
