Micromechanical approach to effective viscoelastic properties of micro‐fractured geomaterials

The aim of this paper is to formulate a micromechanics‐based approach to non‐aging viscoelastic behavior of materials with randomly distributed micro‐fractures. Unlike cracks, fractures are discontinuities that are able to transfer stresses and can therefore be regarded from a mechanical viewpoint as interfaces endowed with a specific behavior under normal and shear loading. Making use of the elastic‐viscoelastic correspondence principle together with a Mori‐Tanka homogenization scheme, the effective viscoelastic behavior is assessed from properties of the material constituents and damage parameters related to density and size of fractures. It is notably shown that the homogenized behavior thus formulated can be described in most cases by means of a generalized Maxwell rheological model. For practical implementation in structural analyses, an approximate model for the isotropic homogenized fractured medium is formulated within the class of Burger models. Although the approximation is basically developed for short‐term and long‐term behaviors, numerical applications indicate that the approximate Burger model accurately reproduce the homogenized viscoelastic behavior also in the transient conditions.     

A micromechanical finite element model for linear and damage‐coupled viscoelastic behaviour of asphalt mixture

This study presents a finite element (FE) micromechanical modelling approach for the simulation of linear and damage‐coupled viscoelastic behaviour of asphalt mixture. Asphalt mixture is a composite material of graded aggregates bound with mastic (asphalt and fine aggregates). The microstructural model of asphalt mixture incorporates an equivalent lattice network structure whereby intergranular load transfer is simulated through an effective asphalt mastic zone. The finite element model integrates the ABAQUS user material subroutine with continuum elements for the effective asphalt mastic and rigid body elements for each aggregate. A unified approach is proposed using Schapery non‐linear viscoelastic model for the rate‐independent and rate‐dependent damage behaviour. A finite element incremental algorithm with a recursive relationship for three‐dimensional (3D) linear and damage‐coupled viscoelastic behaviour is developed. This algorithm is used in a 3D user‐defined material model for the asphalt mastic to predict global linear and damage‐coupled viscoelastic behaviour of asphalt mixture. For linear viscoelastic study, the creep stiffnesses of mastic and asphalt mixture at different temperatures are measured in laboratory. A regression‐fitting method is employed to calibrate generalized Maxwell models with Prony series and generate master stiffness curves for mastic and asphalt mixture. A computational model is developed with image analysis of sectioned surface of a test specimen. The viscoelastic prediction of mixture creep stiffness with the calibrated mastic material parameters is compared with mixture master stiffness curve over a reduced time period. In regard to damage‐coupled viscoelastic behaviour, cyclic loading responses of linear and rate‐independent damage‐coupled viscoelastic materials are compared. Effects of particular microstructure parameters on the rate‐independent damage‐coupled viscoelastic behaviour are also investigated with finite element simulations of asphalt numerical samples. Further study describes loading rate effects on the asphalt viscoelastic properties and rate‐dependent damage behaviour. Copyright © 2006 John Wiley & Sons, Ltd.     

Post-seismic relaxation following the great 2004 Sumatra-Andaman earthquake on a compressible self-gravitating Earth

The   M _w γ 9.0  2004 December 26 Sumatra-Andaman and   M _w = 8.7  2005 March 28 Nias earthquakes, which collectively ruptured approximately 1800 km of the Andaman and Sunda subduction zones, are expected to be followed by vigorous viscoelastic relaxation involving both the upper and lower mantle. Because of these large spatial dimensions it is desirable to fully account for gravitational coupling effects in the relaxation process. We present a stable method of computing relaxation of a spherically-stratified, compressible and self-gravitating viscoelastic Earth following an impulsive moment release event. The solution is cast in terms of a spherical harmonic expansion of viscoelastic normal modes. For simple layered viscoelastic models, which include a low-viscosity oceanic asthenosphere, we predict substantial post-seismic effects over a region several 100s of km wide surrounding the eastern Indian Ocean. We compare observed GPS time-series from ten regional sites (mostly in Thailand and Indonesia), beginning in 2004 December, with synthetic time-series that include the coseismic and post-seismic effects of the 2004 December 26 and 2005 March 28 earthquakes. A viscosity structure involving a biviscous (Burgers body) rheology in the asthenosphere explains the pattern and amplitude of post-seismic offsets remarkably well.     

Semi-Analytic Modelling of Subsidence

This paper presents a forward model for subsidence prediction caused by extraction of hydrocarbons. The model uses combinations of analytic solutions to the visco-elastic equations, which approximate the boundary conditions. There are only a few unknown parameters to be estimated, and, consequently, calculations are very fast. The semi-analytic model is applicable to a uniform and layer-cake stratigraphy, with visco-elastic parameters changing per layer, and an arbitrary depletion pattern. By its capabilities to handle a multi-layered visco-elastic subsurface, the semi-analytic model fills the gap between the analytic single-layered elastic models available to date and the more elaborate numerical, e.g. finite element, models.     

2-D viscoelastic FEM simulation on stress state in the deep part of a subducted slab

Introduction It is found that there are some relationships between the thermal structures of subduction zones and the deep seismicity, while the mechanism relates the thermal structure and the deep seismicity is still unsure (Helffrich, Brodholt, 1991; Furukawa, 1994; Kirby, et al, 1996). From 1980s, geoscientists have constituted a series of numerical simulations on the stress states of subduction slabs. Based on the kinetic computation of Sung and Burns (1976a, b), Goto, et al (1983, 1987…     

The onset of Pleistocene glaciation in the Barents Sea: implications for glacial isostatic adjustment

In this paper the effect of a delayed onset of glaciation in the Barents Sea on glacial isostatic adjustment is investigated. The model calculations solve the sea-level equation governing the total mass redistributions associated with the last glaciation cycle on a spherically symmetric, linear, Maxwell viscoelastic earth for two different scenarios for the growth phase of the Barents Sea ice sheet. In the first ice model a linear growing history is used for the Barents Sea ice sheet, which closely relates its development to the build-up of other major Late Pleistocene ice sheets. In the second ice model the accumulation of the Barents Sea ice sheet is restricted to the last 6 ka prior to the last glacial maximum.
The calculations predict relative sea levels, present-day radial velocities, and gravity anomalies for the area formerly covered by the Weichselian ice sheet. The results show that observed relative sea levels in the Barents Sea are appropriate for distinguishing between the different glaciation histories. In particular, present-day observables such as the free-air gravity anomaly over the Barents Sea, and the present-day radial velocities are sensitive to changes in the glaciation history on this scale.
A palaeobathymetry derived from relative sea-level predictions before the last glacial maximum based on the second ice model essentially agrees with a palaeobathymetry derived by Lambeck (1995). The additional emerged areas provide centres for the build-up of an ice sheet and thus support the theory of Hald, Danielsen & Lorentzen (1990) and Mangerud et al. (1992) that the Barents Sea was an essentially marine environment shortly before the last glacial maximum.