We found a recent paper by Kobe University, Chuo University and the Yokosuka Port & Airport Research Insitute and the Japan Agency for Marine Science & Technology 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.
Most practising geotechnical engineers default to saturated soil mechanics. It is the framework we are trained in, the framework embedded in most design codes, and — for the soft clays and granular soils that dominate infrastructure work — a reasonable approximation for much of what we encounter. But the ground is rarely fully saturated above the water table, and many of the most interesting and challenging problems in geotechnics occur precisely in that partially saturated zone. A paper by Iizuka et al. (2019), published in Geotechnical Research, makes a compelling case for a more general framework — and demonstrates its reach through four diverse application examples that span differential settlement caused by trees, salt damage in arid soils, specimen disturbance in deep-sea sampling, and the liquefaction resistance of partially saturated sand.
The theoretical structure
The starting point is three-phase mixture theory, treating soil as a continuum composed of solid, liquid and gas phases, each governed by mass conservation and momentum equations. The governing equations are derived from first principles, with Darcy’s law introduced a priori for both pore water and pore air flow by analogy with Hagen–Poiseuille pipe flow. Effective stress is expressed in the Bishop form as σ’ = σN + χ(Sr)s·1, where σN is net stress, s is suction (= pa − pw) and χ is a parameter dependent on degree of saturation. The soil-water retention characteristic (SWRC) — the relationship between degree of saturation and suction — acts as a mediator connecting the deformation problem with the two seepage problems for pore water and pore air.
What the authors do particularly well is to make this theoretical structure explicit and modular. By isolating the deformation problem, the incompressible seepage problem (soil–water) and the compressible seepage problem (soil–gas) as distinct but coupled subproblems linked through the SWRC, the framework becomes straightforwardly extensible: to incorporate a new physical phenomenon, one replaces or augments the relevant governing equation rather than rebuilding the whole system. The constitutive model employed is the Se-hardening elasto-plastic model of Ohno et al. (2007), an extension of the Cam-Clay framework in which the pre-consolidation stress is modified by a function of the effective degree of saturation Se = (Sr − Sr0)/(1 − Sr0), allowing seamless transition between unsaturated and fully saturated behaviour.
Four applications
The first application concerns differential settlement induced by tree root absorption, following a documented case from Poland where progressive cracking in a residential building was attributed to moisture extraction by adjacent aspens, willows and maples over a 30-year period (Wojtasik and Jez, 2000). The numerical simulation, developed by Kawai et al. (2008), models annual root growth by extending the finite-element domain, with transpiration estimated from climate data using the Penman (1948) evaporation model. The computed settlement and degree of saturation histories are consistent with the observed cracking pattern, and the simulation reproduces the cessation of cracking after the trees were felled in 1993. Crucially, the modification to the governing equations is minimal: vegetation effects enter as hydraulic boundary conditions rather than requiring changes to the theoretical framework itself.
The second application addresses salt damage in the unsaturated zone above a saline water table, motivated by land degradation problems in northeast Thailand. The seepage equation for pore water is extended by incorporating Fick’s law for solute diffusion and an advection term, yielding a coupled solid–fluid–solute formulation developed by Nomura et al. (2011). The simulation shows saline groundwater migrating upward by capillary action during dry seasons, with net upward flux dominating over seasonal rainfall recharge, resulting in salt crystallisation at the ground surface within three years. The paper also examines the effectiveness of gravel mulching as a capillary barrier — a practically useful result for engineers working in arid and semi-arid regions.
The third application is perhaps the most conceptually striking. When sediment cores are retrieved from the deep ocean floor, dissolved gas in the pore water vaporises as confining pressure decreases during ascent — a process governed by Henry’s law. The authors incorporate this into the air-seepage equation and simulate the sampling process in two stages: uplifting the core barrel (drained boundaries, lateral confinement) and extrusion of the specimen (undrained, stress release to atmosphere). For sampling from 200 m below the seafloor, the computed suction increase from desaturation substantially exceeds the loss of effective stress from unloading, leaving the specimen in a heavily overconsolidated state that bears little resemblance to its in situ condition. This has direct implications for the interpretation of laboratory strength data from deep marine investigations, and echoes — in a very different context — the sample disturbance concerns familiar to practitioners working with soft sensitive clays on land.
The fourth application examines liquefaction resistance. Post-earthquake surveys following the 1964 Niigata and 1995 Kobe earthquakes identified zones of reduced liquefaction correlated with lower degrees of saturation, a phenomenon also noted experimentally by Yoshimi et al. (1989). The extended Se-hardening model, incorporating subloading surface and rotational hardening concepts, is used to simulate cyclic loading at the element level. For saturated soil, mean effective stress approaches zero by the fourth loading cycle. For soil at Sr = 0.9, suction persists throughout cyclic loading, preventing full effective stress collapse even after ten cycles. The paper also examines the liquefaction criterion proposed by Okamura and Soga (2006) — that liquefaction occurs when pore air pressure equals initial effective stress — and finds that it underestimates liquefaction resistance, since the effective mean stress converges to a non-zero value before this condition is met.
The broader point
What unifies these four examples is the modular character of the theoretical framework. In each case, a targeted modification — an extended continuity equation, an added diffusion term, a revised gas-seepage law, a dynamic constitutive extension — is sufficient to address a qualitatively different physical problem. The soil-water retention characteristic, often treated as a mere soil property, emerges as the central organising quantity that connects deformation and flow. For engineers working with compacted fills, unsaturated slopes, or any ground above the water table, this framework offers a more honest description of soil behaviour than classical saturated theory — and, as Iizuka et al. (2019) demonstrate, a more useful one.
References
Iizuka, A., Tachibana, S., Takeyama, T. et al. (2019) Extension of unsaturated soil mechanics and its applications. Geotechnical Research, 6(3), pp. 156–176.
Kawai, K., Yamada, R., Iizuka, A., Tachibana, S. and Ohno, S. (2008) Influence of vegetation uptake on the deformation of ground. Journal of Applied Mechanics, 11, pp. 443–450.
Nomura, S., Kawai, K., Kakui, S. et al. (2011) Transfer model of water-soluble material in saturated/unsaturated ground. Journal of Applied Mechanics, 14, pp. 231–240.
Ohno, S., Kawai, K. and Tachibana, S. (2007) Elasto-plastic constitutive model for unsaturated soil applied effective degree of saturation as a parameter expressing stiffness. Proceedings of the Japan Society of Civil Engineers, Division C (Geotechnical Engineering), 63(4), pp. 1132–1141.
Okamura, M. and Soga, Y. (2006) Effects of pore fluid compressibility on liquefaction resistance of partially saturated sand. Soils and Foundations, 46(5), pp. 695–700.
Penman, H.L. (1948) Natural evaporation from open water, bare soil and grass. Proceedings of the Royal Society of London, Series A, 193(1032), pp. 454–465.
Wojtasik, A.T. and Jez, J. (2000) Multistory apartment building on Poznań clay — case history. Proceedings of the 1st Asian Conference on Unsaturated Soils, Singapore, pp. 757–762.
Yoshimi, Y., Tanaka, K. and Tokimatsu, K. (1989) Liquefaction resistance of partially saturated sand. Soils and Foundations, 29(3), pp. 157–162.
