Abstract
This paper presents a constitutive modelling approach for the viscoplastic-damage behaviour of geomaterials. This approach is based on the hyperelasticity framework, where the entire constitutive behaviour is derived from only two scalar potentials: a free-energy potential and a dissipation function. The novelty of the new proposed model, in addition to being thermodynamically consistent, is that it requires only a few parameters that can be derived from conventional laboratory testing. The model has been specifically tested for its ability to reproduce a series of triaxial compression tests on core rock samples. The comparison between the viscoplastic-damage model predictions and experimental results shows that the model is remarkably successful in capturing the stress–strain response both at peak stress and in the region of material softening and the time to reach failure.
Highlights
Creep may be defined as continued deformation without a stress change
The new model has only a few parameters that have physical meanings and is capable of capturing the tertiary creep observed in soft rocks
A novel coupled viscoplastic-damage constitutive model has been derived from two scalar potentials: a free-energy potential that provides the elasticity law and a dissipation potential that provides the yield function, the direction of plastic flow and the evolution of a damage variable
Summary
Creep may be defined as continued deformation without a stress change. Creep has been studied since about 1905, such behaviour was documented as early as 1833 (Griggs, 1939). Laboratory data from creep tests are mostly depicted in the form of strain–time curves of which the general form is displayed in Figure 1 (Goodman, 1989; Jaeger et al, 2007; Jeremic, 1994). Secondary creep (region 2) follows if the constant stress overcomes a given limit and is characterised by a constant strain rate. For higher constant stress levels, tertiary creep (region 3) is observed, which is characterised by a strain rate increase with time and leads eventually to failure. The tertiary stage of creep behaviour (region 3) appears due to progressive microcracking of the material and would result in a loss of strength and stiffness, which may eventually lead to failure and a complete loss of the load-carrying capacity of the material.
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