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Application of viscoelastic, viscopl...

Hagin, Paul N.

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Application of viscoelastic, viscoplastic, and rate-and-state friction constitutive laws to the deformation of unconsolidated sands.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Application of viscoelastic, viscoplastic, and rate-and-state friction constitutive laws to the deformation of unconsolidated sands./
Author:	Hagin, Paul N.
Description:	126 p.
Notes:	Source: Dissertation Abstracts International, Volume: 64-11, Section: B, page: 5412.
Contained By:	Dissertation Abstracts International64-11B.
Subject:	Geophysics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3111723
ISBN:	049659253X

Application of viscoelastic, viscoplastic, and rate-and-state friction constitutive laws to the deformation of unconsolidated sands.
Hagin, Paul N.

Application of viscoelastic, viscoplastic, and rate-and-state friction constitutive laws to the deformation of unconsolidated sands. - 126 p.

Source: Dissertation Abstracts International, Volume: 64-11, Section: B, page: 5412.

Thesis (Ph.D.)--Stanford University, 2004.

Laboratory experiments on dry, unconsolidated sands from the Wilmington field, CA, reveal significant viscous creep strain under a variety of loading conditions. In hydrostatic compression tests between 10 and 50 MPa of pressure, the creep strain exceeds the magnitude of the instantaneous strain and follows a power law function of time. Interestingly, the viscous effects only appear when loading a sample beyond its preconsolidation pressure. Cyclic loading tests (at quasi-static frequencies of 10-6 to 10 -2 Hz) show that the bulk modulus increases by a factor of two with increasing frequency while attenuation remains constant. I attempt to fit these observations using three classes of models: linear viscoelastic, viscoplastic, and rate-and-state friction models. For the linear viscoelastic modeling, I investigated two types of models; spring-dashpot (exponential) and power law models. I find that a combined power law-Maxwell solid creep model adequately fits all of the data. Extrapolating the power law-Maxwell creep model out to 30 years (to simulate the lifetime of a reservoir) predicts that the static bulk modulus is 25% of the dynamic modulus, in good agreement with field observations. Laboratory studies also reveal that a large portion of the deformation is permanent, suggesting that an elastic-plastic model is appropriate. However, because the viscous component of deformation is significant, an elastic-viscoplastic model is necessary. An appropriate model for unconsolidated sands is developed by incorporating Perzyna (power law) viscoplasticity theory into the modified Cambridge clay cap model. Hydrostatic compression tests conducted as a function of volumetric strain rate produced values for the required model parameters. As a result, by using an end cap model combined with power law viscoplasticity theory, changes in porosity in both the elastic and viscoplastic regimes can be predicted as a function of both stress path and strain rate. To test whether rate-and-state friction laws can be used to model creep strain, I expand the rate-and-state formulation to include deformation under hydrostatic stress boundary conditions. Results show that the expanded rate-and-state formulation successfully describes the creep strain of unconsolidated sand. Finally, I show that the viscoplastic end cap and rate-and-state models are mathematically similar.

ISBN: 049659253XSubjects--Topical Terms:

535228
Geophysics.

Application of viscoelastic, viscoplastic, and rate-and-state friction constitutive laws to the deformation of unconsolidated sands.
LDR:03297nmm 2200265 4500 001 1813892
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008 130610s2004 eng d
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035 $a AAI3111723
040 $a UnM $c UnM
100 1 $a Hagin, Paul N. $3 1903381
245 1 0 $a Application of viscoelastic, viscoplastic, and rate-and-state friction constitutive laws to the deformation of unconsolidated sands.
300 $a 126 p.
500 $a Source: Dissertation Abstracts International, Volume: 64-11, Section: B, page: 5412.
500 $a Adviser: Mark Zoback.
502 $a Thesis (Ph.D.)--Stanford University, 2004.
520 $a Laboratory experiments on dry, unconsolidated sands from the Wilmington field, CA, reveal significant viscous creep strain under a variety of loading conditions. In hydrostatic compression tests between 10 and 50 MPa of pressure, the creep strain exceeds the magnitude of the instantaneous strain and follows a power law function of time. Interestingly, the viscous effects only appear when loading a sample beyond its preconsolidation pressure. Cyclic loading tests (at quasi-static frequencies of 10-6 to 10 -2 Hz) show that the bulk modulus increases by a factor of two with increasing frequency while attenuation remains constant. I attempt to fit these observations using three classes of models: linear viscoelastic, viscoplastic, and rate-and-state friction models. For the linear viscoelastic modeling, I investigated two types of models; spring-dashpot (exponential) and power law models. I find that a combined power law-Maxwell solid creep model adequately fits all of the data. Extrapolating the power law-Maxwell creep model out to 30 years (to simulate the lifetime of a reservoir) predicts that the static bulk modulus is 25% of the dynamic modulus, in good agreement with field observations. Laboratory studies also reveal that a large portion of the deformation is permanent, suggesting that an elastic-plastic model is appropriate. However, because the viscous component of deformation is significant, an elastic-viscoplastic model is necessary. An appropriate model for unconsolidated sands is developed by incorporating Perzyna (power law) viscoplasticity theory into the modified Cambridge clay cap model. Hydrostatic compression tests conducted as a function of volumetric strain rate produced values for the required model parameters. As a result, by using an end cap model combined with power law viscoplasticity theory, changes in porosity in both the elastic and viscoplastic regimes can be predicted as a function of both stress path and strain rate. To test whether rate-and-state friction laws can be used to model creep strain, I expand the rate-and-state formulation to include deformation under hydrostatic stress boundary conditions. Results show that the expanded rate-and-state formulation successfully describes the creep strain of unconsolidated sand. Finally, I show that the viscoplastic end cap and rate-and-state models are mathematically similar.
590 $a School code: 0212.
650 4 $a Geophysics. $3 535228
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710 2 0 $a Stanford University. $3 754827
773 0 $t Dissertation Abstracts International $g 64-11B.
790 1 0 $a Zoback, Mark, $e advisor
790 $a 0212
791 $a Ph.D.
792 $a 2004
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3111723