We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Department of Engineering

Staff Profile

Publication details for Professor David Toll

Toll, D. G. & Ong, B. H. (2003). Critical-state parameters for an unsaturated residual sandy clay. Geotechnique 53(1): 93-103.

Author(s) from Durham


This paper presents experimental data from constant water content triaxial tests on a residual soil from Singapore, tested under unsaturated conditions with measurements of matric suctions. The data for critical-state conditions from these tests are presented within a framework previously proposed by the first author. The unsaturated critical state requires five parameters: Ma, Mb, Γab, λa and λb. At high degrees of saturation (in a nonaggregated condition) Ma = Mb = Ms (the saturated critical-state stress ratio). At lower degrees of saturation, the value of Mb drops considerably and reaches values near to zero at degrees of saturation below 60%. Conversely, the value of Ma appears to increase as the degree of saturation reduces. A similar pattern is observed for λa and λb. The functions relating the critical-state parameters to degree of saturation (or volumetric water content) can be expressed in normalised form by referencing them to the saturated state. The same normalised functions for Ma/Ms, Mb/Ms, λa/λs and λb/λs fit the experimental data for the residual sandy clay from Singapore and a lateritic gravel from Kenya previously tested. This suggests that the form of these functions may be common to a range of soil types.

Cet exposé présente les résultats expérimentaux d'essais triaxiaux á teneur en eau constante sur un sol ré siduel de Singapour, testé dans des conditions non saturées avec prises de mesures des succions matricielles. Dans le cadre de travail proposé par Toll (1990), nous présentons les données provenant de ces tests et relatives aux conditions d'état critique. L'état critique non saturé demande cinq paramètres Ma, Mb, Γab, λa et λb. À de hauts degrés de saturation (dans une condition non agrégée) M a = Mb = Ms (le taux de contrainte d'état critique saturé. À des degrés moindres de saturation, la valeur de Mb baisse considérablement et atteint des valeurs proches de zéro avec des degrés de saturation en dessous de 60%. De même, la valeur de Ma semble augmenter á mesure que le degré de saturation baisse. Un comportement similaire est observé pour λa et λb. Les fonctions mettant en rapport paramètres d'état critique et degré de saturation (ou teneur en eau volumétrique) peuvent être exprimées dans une forme normalisée en les référençant á l'état saturé. Les mêmes fonctions normalisées pour Ma/Ms, Mb/Ms, λa/λs et λb/λs correspondent aux données expérimentales pour l'argile sableuse résiduelle de Singapour et pour un gravier latéritique du Kenya testé par Toll (1990). Ceci suggère que la forme de ces fonctions peut être commune á toute une gamme de types de sols.


Alonso, E. E., Gens, A. & Josa, A. (1990). A constitutive model for partially saturated soils. Géotechnique 40, No. 3, 405–430.
Bishop, A. W. (1959). The principle of effective stress. Teknisk Ukeblad 106, No. 39, 859–863.
Cui, Y. J. & Delage, P. (1996). Yielding and plastic behaviour of an unsaturated compacted silt. Géotechnique 46, No. 2, 291–311.
Delage, P., Suraj de Silva, G. P. R. & de Laure, E. (1987). Un nouvel appareil triaxial pour les sols non saturés. Proc. 9th Eur. Conf. Soil Mech. Found. Engng, Dublin1, 25–28.
Escario, V. & Saez, J. (1986). The shear strength of partly saturated soils. Géotechnique 36, No. 3, 453–456.
Fredlund, D. G. & Morgenstern, N. R. (1977). Stress state variables for unsaturated soils. Can. Geotech. J. 16, 121–139.
Fredlund, D. G. & Rahardjo, H. (1993). Soil mechanics for unsaturated soils. New York: Wiley.
Fredlund, D.G., Morgenstern, N. R. & Widger, R. A. (1978). The shear strength of unsaturated soils. Can. Geotech. J. 31, 533–546.
Fredlund, D. G., Rahardjo, H. & Gan, J. K.-M. (1987). Nonlinearity of strength envelope for unsaturated soils. Proc. 6th Int. Conf. Expansive Soils, New Delhi, 49–54.
Fredlund, D. G., Xing, A., Fredlund, M. D. & Barbour, S. L. (1995). The relationship of the unsaturated soil shear strength to the soil-water characteristic curve. Can. Geotech. J. 32, 440–448.
Maâtouk, A., Leroueil, S. & La Rochelle, P. (1995). Yielding and critical state of a collapsible unsaturated silty soil. Géotechnique 45, No. 3, 465–477.
Matyas, E. L. & Radhakrishnan, H. S. (1968). Volume change characteristics of partially saturated soils. Géotechnique 18, No. 4, 432–448.
Ng, C. W. W., Chiu, C. F. & Rahardjo, H. (2000). Laboratory study of loosely compacted unsaturated volcanic fill. In Unsaturated soils for Asia (eds H. Rahardjo, D. G. Toll and E. C. Leong), pp. 551–556. Rotterdam: Balkema.
Ong, B. H. (1999). Shear strength and volume change of unsaturated residual soil. MEng Thesis, School of Civil and Structural Engineering, Nanyang Technological University, Singapore.
Schofield, A. W. & Wroth, C. P. (1968). Critical state soil mechanics. London: McGraw-Hill.
Toll, D. G. (1990). A framework for unsaturated soil behaviour. Géotechnique 40, No. 1, 31–44.
Toll, D. G. (2000). The influence of fabric on the shear behavior of unsaturated compacted soils. In Advances in unsaturated soils (eds C. Shackelford, S. L. Houston and N.-Y. Chang), pp. 222–234. Reston: American Society of Civil Engineers, Geotechnical Special Publication No. 99.
Vanapalli, S. K., Fredlund, D. G., Pufahl, D. E. & Clifton, A. W. (1996). Model for the prediction of shear strength with respect to soil suction. Can. Geotech. J. 33, 379–392.
Wheeler, S. J. & Sivakumar, V. (1995). An elasto-plastic critical state model for unsaturated soil. Géotechnique 45, No. 1, 35–53.
Zakaria, I., Wheeler, S. J. & Anderson, W. F. (1995). Yielding of unsaturated compacted kaolin. Proc. 1st Int. Conf. on Unsaturated Soils, Paris, Rotterdam: Balkema (eds E. E. Alonso and P. Delage), 1, 223–228.