On the Determination of Softening Parameters for Nonlocal Constitutive Models

Several regularized formulations exist in the literature, such as nonlocal constitutive models, for the objective simulation of localized deformations in quasibrittle materials that prevent the well-known pathological dependence on the employed mesh. Although they usually require a significant discretization to represent the localization zone of a given material, characterized by some length scale linked to its microstructure, scaling techniques exist to derive representative parameters for full-scale simulation of geotechnical problems. However, the softening response observed in conventional triaxial or uniaxial compression tests is not solely a constitutive feature but also the result of a complex boundary value problem (BVP), where the specific localization pattern formed affects the global response of the experiment. Therefore, constitutive softening parameters should be backcalculated through the simulation of a given laboratory test as a BVP. However, as demonstrated in this paper, the cylindrical geometry of the samples in conventional tests hinders the onset of localization, resulting in a stiffer response that underestimates the resulting nominal softening rate. Within this context, the paper aimed to demonstrate the complexity and difficulty in the determination of a softening rate for nonlocal constitutive models from data of conventional triaxial tests performed on cylindrical specimens and to provide relevant insights toward a practical procedure for the determination of parameters in regularized simulations of quasibrittle geomaterials for practical applications.