HR: 1340h
AN: MR33A-0144    [Abstracts]
TI: Modeling Elastic Properties of Unconsolidated Sands
AU: * Dutta, T
EM: tanima@pangea.stanford.edu
AF: Stanford Rock Physics Laboratory, Geophysics Department, 397 Panama Mall, Mitchell Building 360, Stanford University, Stanford, CA 94305 United States
AU: Mukerji, T
EM: mukerji@pangea.stanford.edu
AF: Stanford Rock Physics Laboratory, Geophysics Department, 397 Panama Mall, Mitchell Building 360, Stanford University, Stanford, CA 94305 United States
AU: Mavko, G
EM: mavko@stanford.edu
AF: Stanford Rock Physics Laboratory, Geophysics Department, 397 Panama Mall, Mitchell Building 360, Stanford University, Stanford, CA 94305 United States
AB: Laboratory and well log measurements as well as results from numerical simulations in unconsolidated sands demonstrate lower velocities than predicted from Hertz-Mindlin contact theory for random packing of identical grains. The Vp/Vs ratios are significantly higher than predicted from Hertz-Mindlin model. This discrepancy can severely affect AVO modeling of unconsolidated sands. In this poster we explore two aspects of granular media models: one related to the type of the contact between spheres, and the other related to the evolution of coordination number (C) with pressure and porosity. We use the Jenkins et al (2005) model and augment it to include friction between spheres. The Jenkins et al. model considers the centers of a typical pair of contacting particles to be able to translate in order to equilibrate forces. The incorporation of additional degrees of freedom in the displacement of a typical pair relaxes the system, leading to a decrease in the effective moduli of the aggregate. We confirm that Jenkins model follows different trend of moduli-vs-porosity than Hertz-Mindlin model; and predicts decrease in bulk modulus and huge drop in shear modulus compared to Hertz-Mindlin model. However, the spheres are assumed frictionless in Jenkins model. We incorporate the frictional term as given by Walton (1987) to compute the effective moduli of isotropic, random aggregate of identical frictional spheres. Incorporating the frictional terms increases the effective shear modulus as compared to the original Jenkins et al. model but it is still significantly lower than the Hertz-Mindlin model predictions. In the existing granular media models one of the critical assumptions is that the average strain provides a good approximation for their interaction with the neighbors. Numerical simulations using molecular dynamics approach have been used as one way of overcoming the average strain approximation. The simulation results of Garcia et al. (2004) indicate drastically different trends of C-vs porosity from the empirical relationship given by Murphy. The simulation also considers evolution of C as the porosity changes due to compaction. In this poster we have compared Hertz-Mindlin model in two ways: (a) using C-porosity relationship as given by Murphy (b) using C-porosity relationship obtained from molecular dynamics simulations by Garcia et al. (2004). We find that the effective moduli predicted using Garcia's relationship follow similar moduli-porosity trend as that using Murphy's relationship but the moduli are lower in magnitude. We conclude that we can improve upon existing models for unconsolidated sands two different ways: (a) by considering additional degree of freedom like translation which helps to relax the system and lower the effective moduli, and (b) by using C-porosity relationship obtained from molecular dynamics simulation which helps to overcome the average-strain assumption. Molecular dynamics simulation demands significant computational resources and may not always be possible. However, we can still benefit from the results of such simulations by borrowing the C-porosity relationship obtained from numerical simulation to augment granular media models like Hertz-Mindlin model or Jenkins model. The augmented granular media models explain better the elastic behavior of unconsolidated sands.
DE: 1859 Rocks: physical properties
DE: 1865 Soils (0486)
DE: 5100 PHYSICAL PROPERTIES OF ROCKS
DE: 5102 Acoustic properties
DE: 5112 Microstructure
SC: Mineral and Rock Physics [MR]
MN: Fall Meeting 2005