Uniform asymptotic Green's functions for efficient modeling of cracks in elastic layers with relative shear deformation controlled by linear springs |
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| Authors: | Anthony P Peirce Hongren Gu Eduard Siebrits |
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| Institution: | 1. Department of Mathematics, University of British Columbia, Vancouver, BC, Canada;2. Schlumberger IPC, Sugar Land, TX, U.S.A.;3. Schlumberger Moscow Research, Moscow, Russia |
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| Abstract: | We present a uniform asymptotic solution (UAS) for a displacement discontinuity (DD) that lies within the middle layer of a three‐layer elastic medium in which relative shear deformation between parallel interfaces is controlled by linear springs. The DD is assumed to be normal to the two interfaces between the elastic media. Using the Fourier transform method we construct a leading term in the asymptotic expansion for the spectral coefficient functions for a DD in a three‐layer‐spring medium. Although a closed‐form solution will require a solution in terms of an infinite series, we demonstrate how this UAS can be used to construct highly efficient and accurate solutions even in the case in which the DD actually touches the interface. We compare the results using the Green's function UAS solution for a crack crossing a soft interface with results obtained using a multi‐layer boundary element method. We also present results from an implementation of the UAS Green's function approach in a pseudo‐3D hydraulic fracturing simulator to analyze the effect of interface shear deformation on the fracture propagation process. These results are compared with field measurements. Copyright © 2008 John Wiley & Sons, Ltd. |
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| Keywords: | uniform asymptotic solutions interfaces with relative shear deformation cracks in layered elastic media Fourier transforms |
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