RESEARCH PAPER Impact of constitutive models on the numerical analysis of underground constructions Yousef Hejazi Æ Daniel Dias Æ Richard Kastner Received: 22 October 2007 / Accepted: 28 January 2008 / Published online: 18 March 2008 Ó Springer-Verlag 2008 Abstract The constitutive model frequently used in numerical calculations of tunnel excavation is linear-elastic perfectly plastic with a Mohr–Coulomb (MC) failure cri- terion. Generally, this leads to shallower and wider surface settlement troughs than those observed experimentally. It is therefore necessary to use adapted constitutive models for the design of underground works. In this paper, three constitutive models are implemented in a two-dimensional simulation of an underground excavation in plane strain: a linear-elastic perfectly plastic model (the MC model), an elastoplastic model with isotropic hardening [the hardening soil (HS) model, Schanz et al., Beyond 2000 in computa- tional geotechnics, Balkema, Rotterdam, pp. 281–290, 1999] and an extension of this model which implies an evolution of the stiffness modulus in the small-strain range according to the strain level (the HS model with small- strain stiffness ‘‘HS-Small’’, Benz, Small-strain stiffness of soils and its numerical consequences. Ph.D. thesis, Uni- versitat Stuttgart, 189 pp., 2007). The study is based on the results of drained triaxial compression tests representing an overconsolidated clay (Gasparre, Advanced laboratory characterisation of London clay. Ph.D. thesis, Imperial College London, 598 pp., 2005); and is then applied to a shallow tunnel. The impact of the constitutive model is highlighted as well as the limits of the simplest constitutive model. Keywords Constitutive models  Modeling  Underground constructions List of symbols c unit weight c 0.7 level of strains where the shear modulus reaches 70% of its initial value e p plastic strain tensor e v p plastic volumetric strain j hardening parameter k relaxation ratio in the k-method m Poisson’s ratio r i principal stresses u angle of friction w angle of dilatancy c cohesion D tunnel diameter E drained Young’s modulus E 50 ref triaxial loading Young’s modulus E oed ref oedometric loading Young’s modulus E ur ref unloading–reloading Young’s modulus G 0 shear stiffness modulus i the distance from tunnel centerline to point of inflection K 0 ratio of initial (Benz [7]) horizontal to vertical effective stress m a Janbu-type parameter p mean pressure p ref reference mean pressure p p preconsolidation pressure q deviatoric triaxial stress S settlement of point y from the axis of the tunnel S max the maximum settlement Y. Hejazi (&)  D. Dias  R. Kastner LGCIE Laboratory, INSA Lyon, Villeurbanne, France e-mail: yousef.hejazi@insa-lyon.fr 123 Acta Geotechnica (2008) 3:251–258 DOI 10.1007/s11440-008-0056-1