A new gradient-dependent plasticity model for compaction banding in sedimentary rocks

Inelastic compaction of sedimentary rocks can occur in the form of localized bands of intense damage. Understanding the formation these compaction bands is of significant importance since they drastically affect the performance of geosystems. In order to model the formation of these bands, constitutive laws accounting for the microstructure and including internal lengths are required. Unlike the standard Cauchy continuum, higher-order continua are able to model the deformation bands with a finite thickness. However, a major difficulty with these models is to give a physical significance to the additional parameters, such as the internal length, in relation with the material microstructure, and a reliable method to measure them in experiments. In this study, we develop a gradient-dependent plasticity model by considering a yield function which depends on the porosity and its second gradient. To calibrate the model, a Saint-Maximin limestone sample is tested in axisymmetric triaxial loading under relatively high confining pressure. The sample is imaged with X-Ray Computed Tomography before and after several loading stages. An image processing method is developed to build porosity maps averaged at the mesoscopic scale. The Fast Fourier Transformation is applied on several porosity profiles to identify the dominant wavelength of porosity heterogeneity, which is interpreted as the internal length of the constitutive model. In addition, a method is developed to evaluate the second gradient of porosity over cubic domains selected inside the porosity maps. On the other hand, the Digital Volume Correlation technique is applied to build 3D strain maps. These maps are used to calibrate the model.