Comparison and Tensorial Formulation of Inelastic Constitutive Models of Salt Rock Behaviour and Efficient Numerical Implementatio
Abstract:The design process of geotechnical installations includes the application of numerical simulation tools for safety assessment, dimensioning and long term effectiveness estimations. Underground salt caverns can be used for the storage of natural gas, hydrogen, oil, waste or compressed air. For their design one has to take into account fluctuating internal pressures due to different levels of filling, the stresses imposed by the surrounding rock mass, irregular geometries and possibly heterogeneous material properties  in order to estimate long term cavern convergence as well as locally critical wall stresses.
Constitutive models applied to rock salt are usually viscoplastic in nature and most often based on a Burgers-type rheological model extended by non-linear viscosity functions and/or plastic friction elements. Besides plastic dilatation, healing and damage are sometimes accounted for as well .
The scales of the geotechnical system to be simulated and the laboratory tests from which material parameters are determined are vastly different. The most common material testing modalities to determine material parameters in geoengineering are the uniaxial and the triaxial compression tests. Some constitutive formulations in widespread use are formulated based on equivalent rather than tensorial quantities valid under these specific test conditions and are subsequently applied to heterogeneous underground systems and complex 3D load cases. We show here that this procedure is inappropriate and can lead to erroneous results. We further propose alternative formulations of the constitutive models in question that restore their validity under arbitrary loading conditions.
For an efficient numerical simulation, the discussed constitutive models are integrated locally with a Newton-Raphson algorithm that directly provides the algorithmically consistent tangent matrix for the global Newton iteration of the displacement based finite element formulation.
Finally, the finite element implementations of the proposed constitutive formulations are employed to simulate an underground salt cavern used for compressed air energy storage with OpenGeoSys . Transient convergence and stress fields are evaluated for typical fluctuating operation pressure regimes.