Formulation of a three‐dimensional rate‐dependent constitutive model for chalk and porous rocks

Abstract

SUMMARYRate-dependent behaviour of chalk and other porous rocks has undergone widespread study in geomechanics due to its implications on the performance of engineering structures. We present a ratedependent constitutive model for chalk and other porous rocks with several new features. The model formulation is based on a viscoplastic rate-lines approach in which the axial strain rate depends on the proximity of the stress point to an elliptical reference surface. A non-associated viscoplastic potential surface and an axial scaling algorithm are used to determine the viscoplastic strain components. The model predicts that axial yields stress varies as a power function of applied axial strain rate, as shown by published laboratory data. Comparisons with published experimental data indicate that the model is capable of reproducing observed rate-dependent behaviour of chalk under a variety of loading conditions.

A model for pore‐fluid‐sensitive rock behavior using a weathering state parameter

“…The rate-dependent model for porous rocks presented by Hickman and Gutierrez [56] was modified as described here to include effects of weathering and used to simulate several of these results for offshore and outcrop chalks. For the waterflooding simulation on offshore chalk, the values for parameters bulk modulus K , critical state slope M, ellipticity parameter R, and compression coefficient for oil-saturated chalk were all obtained using appropriate values from Hickman [58] for a representative porosity value.…”

“…Several parameters of the model of [56] described in the previous section change their values as a result of weathering or change in pore fluid. These parameters include the bulk modulus K , reference void ratio N , cohesion c (or adhesion a = c/tan where is Mohr-Coulomb friction angle), failure shear stress ratio f = 6 sin/(3−sin ) (and critical state slope M), creep parameter , and tensile strength t [58].…”

“…Typical rate-dependent inelastic behavior is described in the constitutive model of Hickman and Gutierrez [56] using the following equation:…”

Cnoidal waves in solids

“…In addition, we emphasize that in this approach the non-associativity of the plastic evolution is introduced through the viscous (rate-dependent) part of the flow law. The additive use of both rate independent (in this case near-yield) and viscoplastic (in this case far-from-yield) flow laws has been discussed in the literature to be mutually equivalent (Hickman and Gutierez, 2007). Indeed the essential physics can be captured without the use of the rate-independent component, since when the rate component approaches the rate-independent case, n ϵ̇→ ∞, then the only possibility of obtaining finite plastic strain rate would be to have 0 ij σ → , or the stresses to be incrementally close to the yield surface.…”

An elasto-viscoplastic model for chalk including suction effects

“…Various viscoplastic models have been formulated adopting the Bjerrum's notion of equivalent (or reference) time (e.g. Bjerrum, 1967;Borja & Kavazanjian, 1985;Hickman & Gutierrez, 2007). Other models have used the concept of the Non Stationary Flow Surface (NSFS) theory (e.g.…”