, Volume 16, Issue 3, pp 136–148 | Cite as

An engineering theory of soil behaviour in unloading and reloading

  • Roberto Nova
  • Tomasz Hueckel


A constitutive law is proposed for describing the stress-strain characteristic of soils in unloading-reloading. The constitutive equations are valid piecewisely between subsequent, appropriately formulated, stress reversal loci. The stress-strain relationships are formulated in terms of generalized stress and strain differences referred to the last stress reversal point and connected through a variable compliance tensor. The shear compaction effect is modelled by a suitable formulation of the compliance tensor.

Specialization to conventional triaxial condition is given. As well as fitting available experimental data in unloading-reloading of normally consolidated and overconsolidated clays, the proposed constitutive relation can model the dependence on OCR of the shape of the undrained effective stress paths, the phenomenon of cyclic mobility of clay in undrained compression and the unloading-reloading stress paths in the oedometer. The theory requires the identification of only three material constants in addition to those pertinent to the usual elastoplastic theory of soil with which it may be easily combined.


Stress Path Soil Behaviour Reversal Locus Compliance Tensor Stress Reversal 
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Si propone una legge costitutiva per descrivere il legame sforzi-deformazioni dei terreni sottoposti a processi di scarico e ricarico. Le equazioni costitutive sono formulate a tratti e definite su un dominio limitato dai luoghi di inversione di carico. Nella formulazione della legge costituitiva verranno introdotte delle variabili generalizzate di sforzo riferite all'ultimo punto di inversione di carico. Queste variabili sono legate alle deformazioni, riferite anche esse allo stato relativo all'ultimo punto di inversione di carico, da un tensore di cedevolezza variabile. Un'adeguata formulazione di questo tensore permette di modellare l'efferio di densificazione sotto carico deviatorico ciclico.

Questa legge costitutiva interpreta bene i risultati sperimentali su argille normalmente consolidate e sovraconsolidate. La teoria permette anche di descrivere la dipendenza del percorso degli sforzi efficaci in condizioni non drenate dal grado di sovraconsolidazione, la mobilità ciclica dell'argilla in condizioni non drenate e il percorso degli sforzi efficaci in un processo di scarico e ricarico in un edometro.

Per identificare il modello sono necessari solo tre parametri oltre a quelli necessari per identificare il comportamento del terreno vergine.


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  1. [1]
    Boisserie J. M., Guelin P.,Remarks on the Tensorial Formulation of Constitutive Law Describing Mechanical Hysteresis, Proc. SMiRT IV, S. Francisco, L 1/9, 1977.Google Scholar
  2. [2]
    Dafalias Y. F., Popov E. P.,A Model of Nonlinearly Hardening Materials for Complex Loadings, Acta Mech., 21, pp. 173–192, 1975.Google Scholar
  3. [3]
    Hardin B. O., Drnevich V. P.,Shear Modulus and Damping in Soils. Measurements and Parameters Effects, Proc. ASCE, 98, SM6, pp. 603–624, 1972.Google Scholar
  4. [4]
    Holubec I.,The Yielding of Cohesionless Soils, Ph. D. Thesis Univ. of Waterloo, 1976.Google Scholar
  5. [5]
    Hueckel T.,On Plastic Flow of Granular and Rocklike Materials with Variable Elasticity Moduli, Bull. Polish Academy of Sciences, Sec. Sci. Techn., 23, 8, pp. 405–414, 1975.Google Scholar
  6. [6]
    Hueckel T., Nova R.,On Paraelastic Hysteresis of Soils and Rocks, Bull. Polish Academy Sci., Sec. Sc. Tech., 27, 1, pp. 49–55, 1979a.Google Scholar
  7. [7]
    Hueckel T., Nova R.,Some Hysteresis Effects of the Behaviour of Geologic Media, Int. J. of Solids and Structures, 15, 625–642, 1979b Google Scholar
  8. [8]
    Maier G., Hueckel T.,Non Associated and Coupled Flow Rules of Elastoplasticity for Geotechnical Media, Proc. IX ICSMFE, Tokyo, Session 9, pp. 129–142, 1977.Google Scholar
  9. [9]
    Mróz Z.,On the Description of Anisotropic Workhardening, Int. J. of Mech. and Phys. of Solids, vol. 15, pp. 163–175, 1967.Google Scholar
  10. [10]
    Mróz Z.,A Description of Workhardening of Metals with Application to Variable Loading, Proc. Int. Symp. on Foundations of Plasticity ed. by A. Sawczuk, 1972.Google Scholar
  11. [11]
    Mróz Z., Lind N. L.,Simplified Theories of Cyclic Plasticity, Acta Mech., 22, pp. 131–152, 1975.Google Scholar
  12. [12]
    Mróz Z., Norris V. A., Zienkiewicz O. C.,An Anisotropic Hardeing Model for Soils and its Application to Cyclic Loading, Int. J. Nume. Anal. Methods in Geomech., vol. 2, pp. 203–221, 1978.Google Scholar
  13. [13]
    Nova R.,Theoretical Studies of Constitutive Relations for Sands, M. Sc. Thesis, Univ. of Cambridge, 1977.Google Scholar
  14. [14]
    Nova R.,Un modello costitutivo per l'argilla, Rivista Italiana di Geotecnica, 13, 1, 37–54, 1979.Google Scholar
  15. [15]
    Nova R., Wood D.,A Mathematical Model for Sands, Int. J. of Num. and Anal. Methods in Geom., 3, 3, 255–278, 1979.Google Scholar
  16. [16]
    Parry R. H. G.,Strength and Deformation of Clay, Ph. D. Thesis, Imperial College, London, 1956.Google Scholar
  17. [17]
    Prévost J. H.,Mathematical Modelling of Monotonic and Cyclic Undrained Clay Behaviour, Int. J. Num. Anal. Meth. in Geom., vol. 1, pp. 195–201, 1977.Google Scholar
  18. [18]
    Schofield A. N., Wroth C. P.,Critical State Soil Mechanics, Wiley, 1968.Google Scholar
  19. [19]
    Som N. N.,The Effect of Stress Path on the Deformation and Consolidation of London Clay. Ph. D. Thesis, Imperial College, London, 1968.Google Scholar
  20. [20]
    Wroth C. P.,The Prediction of Shear Strains in Triaxial Tests on Normally Consolidate Clays, 6th ICSMFE, Montreal, 2, pp. 417–420, 1965.Google Scholar
  21. [21]
    Wroth C. P., Loudon P. A.,The Correlations of Strains Within a Family of Triaxial Tests on Overconsolidated Samples of kaolin, Proc. Geotechn. Conf., Oslo, 1, pp. 159–163, 1967.Google Scholar

Copyright information

© Pitagora Editrice Bologna 1981

Authors and Affiliations

  • Roberto Nova
    • 1
  • Tomasz Hueckel
    • 2
  1. 1.Department of Structural EngineeringTechnical University of Milan, (Politecnico)MilanItaly
  2. 2.Institute of Fundamental Technological ResearchPolish Academy of SciencesWarsawPoland

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