r7.01.23 Cyclic behavior law of HUJEUX for soils

Summary:

The so-called « Hujeux » behavior model, designed in laboratory MSSMat of ECP [bib5] _, is one of the cyclic elastoplastic models of soil mechanics (granular geomaterials: sandy clays, normally consolidated or over-consolidated, normally consolidated or over-consolidated, serious…) most suitable for simulations of geotechnical structures in earthquakes. In addition, it has been used for many years, its configuration being therefore well controlled.

This multi-mechanism model (spherical —for a consolidation path— and deviatory) with memory variables is characterized by eight load surfaces with hardening, defined for monotonic paths and for cyclic paths. The mechanisms are defined by fixed planes, which induces an orthotropy of soil behavior. Within these reversibility surfaces, the material is non-linear elastic. Work hardening is governed by several variables and the normal flow rule is adopted for consolidation mechanisms, while the flow rule for deviatory mechanisms is not associated, following the Roscoe dilatance rule. Like other soil behavior models, work hardening is positive in the pre-peak phase and negative in the post-peak phase, which corresponds to the effect of expansion; these effects induce the « liquefaction » behavior of the soil. The plastic deformation tensor results from the accumulation of the contributions of various active mechanisms. Volume plastic deformation couples the mechanisms.

The equations of the model, its parameterization, and then its numerical integration are described according to an implicit general Newton diagram. Users can access four implicit integration schemes for the Hujeux model: “NEWTON”, “NEWTON_PERT”, “NEWTON_RELI” and “SPECIFIQUE”.

• 1. Theoretical formulation
  • 1.1. Behavioral relationship of Hujeux
  • 1.2. Identification of the characteristic parameters of the material
• 2. Numerical integration of the behavioral relationship
  • 2.1. Problem reminder
  • 2.2. General local integration scheme
  • 2.3. Tangent operator in speed: option RIGI_MECA_TANG
  • 2.4. Incremental tangent operator: option FULL_MECA
• 3. Implementation in Code_Aster
  • 3.1. Internal variables
• 4. Features and verification
• 5. Bibliography
• 6. Appendix 1: Analytical calculation of the tangent local integration matrix
  • 6.1. Derivatives of the equation of state
  • 6.2. Derivatives of the plastic deformation evolution equation
  • 6.3. Derivatives of the evolution equation for deviatory work hardening
  • 6.4. Derivatives of the equation for the evolution of spherical work hardening
  • 6.5. Derivatives of the criteria of deviatory mechanisms
  • 6.6. Derived from the criteria for spherical consolidation mechanisms
• 7. Appendix 2: Notation of tensors, their invariants and expressions of various derivatives
• 8. Appendix 3: Validity of the multi-mechanism formulation of Hujeux’s law
  • 8.1. Representation of a state of constraint by Mohr circles
  • 8.2. Mohr-Coulomb plasticity criterion
  • 8.3. Expression of the Hujeux plasticity criterion
  • 8.4. Validity of the Hujeux criterion
  • 8.5. Conclusions
• 9. Appendix 4: Internal redistricting strategy for the Hujeux Act