Theoretical analysis of strain response envelopes using incrementally non-linear constitutive equations

Abstract

SUMMARYThis paper reviews some incrementally non-linear constitutive equations of interpolation type, and proposes a new approach to illustrate the discrepancies between different interpolation models. This approach uses the strain response envelopes, based on experimental data when restricted to triaxial plane, and the Jacobian of the constitutive equations to examine the loss of uniqueness. A new family of interpolation functions is proposed to meet the three requirements: C-continuity of strain response envelope, correct description of experimental data, and respect of the one-to-one property.

Instabilities in granular materials and application to landslides

“…The generalization of the interpolation procedure between incremental stress directions can be formalized as follows [19,20]:…”

“…The signi"cant di!erence between all these interpolations of the incremental stress direction d lies in the existence of the subsidiary term in Royis' formulation [20]. This relation was essentially established under mathematical considerations.…”

“…More recently [20], tests on an axisymmetric triaxial apparatus have been carried out on a dense Hostun sand (density"1.56) in order to determine experimentally the strain response envelope (see Figures 2}4). This has been performed for three stress}strain states (isotropic, intermediate and near failure).…”

“…The comparison between the experimental strain increment (rate) envelopes and those obtained by the interpolation function shows that the Darve's octolinear and non-linear interpolations accurately describe such experimental strain response envelopes. The numerical and experimental results are shown in Figures 2}4 for di!erent axial ( "100, 200, 400 kPa) and lateral ( "100 kPa) stresses (from Doanh's experiments [20]). In the following, only Darve's non-linear and Darve's octolinear interpolations will be used.…”

“…Experimental and numerical strain envelope responses on dense Hostun sand ( "400 kPa, "100 kPa) (after[20]). …”