Homogeneous equilibrium model for geomechanical multi-material flow with compressible constituents

Abstract

Multi-material flow generally describes a situation where several distinct materials separated by sharp material interfaces undergo large deformations.In order to model such flow situations in the context of geomechanics and geotechnical engineering, a theoretical framework is presented which introduces a possible two-phase coupled saturated granular material behavior among the different materials. This is achieved by extending the technique of local volume averaging to a hierarchy of three spatial scales, based on a product of two indicator functions. A homogeneous equilibrium mixture model is subsequently derived for an example flow consisting of bulk solid, bulk fluid, and undrained granular material with compressible constituents.The closure relations are provided at the macroscale, including those describing granular behavior covering the full frictional-collisional flow regime and bulk material volume fraction evolution. The paper discusses the advantages and restrictions of the proposed mixture model and addresses its application and full-scale numerical implementation. *

Contribution to the Non-Lagrangian Formulation of Geotechnical and Geomechanical Processes

“…In particular, the complexity in the behavior of the soil is attributable to its granular nature and internal structure, and to the presence of multiple phases (solid, liquid and gas). The grain-fluid mixture is generally subject to different flow regimes and undergoes changes in phase composition and internal structure depending on the dynamics of the geotechnical process [17,22] The mechanisms and phenomena associated with geotechnical installation processes, except perhaps for the significance of soil-structure-interaction, are similar to those of geomechanical or geomorphological flows, for example, avalanches and debris flows [87,90,92,130,133], submarine landslides [103,114], and soil liquefaction [97,145]. Although the objectives of geomorphologists and geotechnical engineers in studying these phenomena may be somewhat different, both need reliable continuum mechanical models and validated numerical methods for prediction.…”

“…From the previous discussion it can be concluded that adequate non-Lagrangian models for geotechnical or geomechanical processes must account for the dynamical interaction of multiple materials on at least three different length scales [17,21,22]: the scale l micro defined by a typical grain diameter of the granular material (microscale), the scale l meso at which the granular material can be represented as a continuum interacting with other bulk materials (mesoscale), and the scale l macro at which the immiscible mixture of mesoscale continua can be represented as an effective single-phase material (macroscale). The mesoscale is the scale commonly used in soil mechanics, and at which continuum mechanical material models operate, e.g.…”

“…homogeneous bulk material. In the section that follows, we summarize a rigorous theoretical framework we have developed [17,21,22] to construct macroscopic mixture models for the dynamical interaction of grain-fluid mixtures with multiple other, physically distinct bulk materials, e.g. pure fluids or pure solids.…”

“…After combining the mixture balance principles (41) and (42) with the particularizations made for saturated granular material in Sect. 2, and doing some algebraic manipulation, the following Lagrangian model for geotechnical or geomechanical multi-material flow is obtained [17,21]:…”

Explicitly coupled consolidation analysis using piecewise constant pressure

“…Fully coupled solution procedures often require enormous software development and can be computationally expensive. This is particularly true for multi-physics and multi-material problems where consolidation might be only one physical aspect of the problem, and only locally, in small regions of the computational domain [1,3]. In such situations, and others, less rigorous coupling procedures can be more efficient [15,12,10].…”