Constitutive model with time-dependent deformations

In many geological and engineering problems it is necessary to transform information from one scale to another. Data collected at laboratory scale are often used to evaluate field problems on a much larger scale. This is certainly true for geological problems where extreme scale differences are common in time as well as size. This problem is addressed by means of a new constitutive model for soils. It is able to describe the behavior of soils at different deformation rates. The model defines time-dependent and stress-related deformations separately. They are related to each other and they occur simultaneously. The model is based on concepts from elasticity and viscoplasticity theories. In addition to Hookeʹs law for the elastic behavior, the framework for the viscoplastic behavior consists, in the general case (two-dimensional or three-dimensional), of a yield surface, an associated flow rule and a hardening law. The model is formulated in incremental terms and is therefore suitable for computational modeling and it has been implemented in a computer program used for analyzing the depositional history of an oil field in the Danish part of the North Sea. An important part of the problem in this case was the difference in time scale between the geological process of deposition (millions of years) and the laboratory measurements of mechanical properties (minutes or hours). In addition, the time scale relevant to the production history of the oil field was interesting (days or years).