Evaluation of constitutive models for crushed salt Page: 3 of 14
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and dislocation creep. The Spiers model was formulated for wet crushed-salt aggregates
and is based on grain boundary diffusional pressure solution processes.
CANDIDATE CONSTITUTIVE MODELS
This section presents the general form of the crushed-salt constitutive model and
development of the three-dimensional generalization for the candidate constitutive
models. An empirical function containing the effects of moisture, particle size, and
temperature is included, which modifies the equivalent inelastic strain rates defined by
the candidate models.
General Constitutive Model Form
The total strain rate for the crushed-salt constitutive model is assumed to consist
of three components. The components include nonlinear elastic (siK), consolidation (i .),
and creep (El) contributions, and the total strain rate is written as the sum of these
rates:
ejj = 8iJ+Si.J+Eij (1)
Both the nonlinear elastic and consolidation portions of the model describe the material
behavior in bulk (volumetric) and in shear (deviatoric). However, the creep portion of
the model only describes deviatoric material behavior and is, in fact, the creep
deformation model used for intact salt. The nonlinear elastic model adopted is that
given by Sjaardema and Krieg [1987]. The creep portion of the model is described by
Munson et al. [1989].
Consolidation Model
The consolidation model is of primary concern in this study, and thus, this section
is divided into subsections that address important issues regarding the consolidation
portion of the crushed-salt model. Typically, equations proposed to describe the behavior
of a particular material are written in one-dimensional form or as scalar relationships.
To be useful in numerical analyses and applicable to a variety of laboratory experiments
with different load paths, any constitutive model must be generalized to include three-
dimensional states of stress. The first subsection presents the generalization of the
candidate constitutive model forms. The next subsection presents considerations for
moisture, particle size, and temperature effects on the deformation of crushed salt.
Since no single model includes all of these state variables, an empirical function is
proposed to include their influence in the models. The last subsection presents the
candidate constitutive model forms as modified to capture the phenomena associated
with the crushed-salt creep component of the constitutive model.
Consolidation Model Generalization
Following the approach of Fossum et al. [1988], the three-dimensional generalization
of the kinetic equation for the consolidation inelastic flow is:
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Callahan, G. D.; Loken, M. C.; Hurtado, L. D. & Hansen, F. D. Evaluation of constitutive models for crushed salt, article, May 1, 1996; Albuquerque, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc668857/m1/3/: accessed March 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.