Abstract

Transient response of a permeable cylindrical borehole arises from dynamic loadings applied to the borehole internal surface. Biot's theory of poroelastodynamics is used in this work to study the dynamic response of a circular borehole in a fluid-saturated medium under a non-hydrostatic initial stress state. Using the Helmholtz decomposition for the displacement fields, analytical solutions for the stresses, displacements, pore pressure are derived in the Laplace-Fourier transform domain; and the superposed solution of the axisymmetric mode and the asymmetric mode is inverted numerically to the real time domain using a reliable numerical scheme. Influences of the dimensionless poroelastic parameters on the dynamic response of the borehole are analyzed in a detailed parametric study. Radial variations of the pore pressure and stresses in the two different modes are examined; and the dynamic evolution of the superposed solution is analyzed. A direct comparison between the classical quasi-static poroelastic theory and current poroelastodynamic theory shows that inertial effect is important in early times; and the poroelastodynamic response resembles a damped oscillator, exhibiting wave-diffusion behavior. At longer times, diffusion dominates and the poroelastodynamic solution approaches the quasi-static poroelastic solution. The presented solution can be applied to study borehole stability under dynamic loadings.

Original languageEnglish (US)
Pages (from-to)82-93
Number of pages12
JournalInternational Journal of Rock Mechanics and Mining Sciences
Volume93
DOIs
StatePublished - Mar 1 2017

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Boreholes
stress field
borehole
dynamic response
pore pressure
Pore pressure
Dynamic response
borehole stability
saturated medium
Biot theory
Laplace transform
Fourier transform
Laplace transforms
Transient analysis
decomposition
Fourier transforms
fluid
Decomposition
Fluids

Keywords

  • Analytical solution
  • Laplace-Fourier transform
  • Non-hydrostatic stress field
  • Poroelastodynamic response

ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology

Cite this

Poroelastodynamic response of a borehole in a non-hydrostatic stress field. / Xia, Yang; Jin, Yan; Chen, Mian; Chen, Kangping.

In: International Journal of Rock Mechanics and Mining Sciences, Vol. 93, 01.03.2017, p. 82-93.

Research output: Contribution to journalArticle

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N2 - Transient response of a permeable cylindrical borehole arises from dynamic loadings applied to the borehole internal surface. Biot's theory of poroelastodynamics is used in this work to study the dynamic response of a circular borehole in a fluid-saturated medium under a non-hydrostatic initial stress state. Using the Helmholtz decomposition for the displacement fields, analytical solutions for the stresses, displacements, pore pressure are derived in the Laplace-Fourier transform domain; and the superposed solution of the axisymmetric mode and the asymmetric mode is inverted numerically to the real time domain using a reliable numerical scheme. Influences of the dimensionless poroelastic parameters on the dynamic response of the borehole are analyzed in a detailed parametric study. Radial variations of the pore pressure and stresses in the two different modes are examined; and the dynamic evolution of the superposed solution is analyzed. A direct comparison between the classical quasi-static poroelastic theory and current poroelastodynamic theory shows that inertial effect is important in early times; and the poroelastodynamic response resembles a damped oscillator, exhibiting wave-diffusion behavior. At longer times, diffusion dominates and the poroelastodynamic solution approaches the quasi-static poroelastic solution. The presented solution can be applied to study borehole stability under dynamic loadings.

AB - Transient response of a permeable cylindrical borehole arises from dynamic loadings applied to the borehole internal surface. Biot's theory of poroelastodynamics is used in this work to study the dynamic response of a circular borehole in a fluid-saturated medium under a non-hydrostatic initial stress state. Using the Helmholtz decomposition for the displacement fields, analytical solutions for the stresses, displacements, pore pressure are derived in the Laplace-Fourier transform domain; and the superposed solution of the axisymmetric mode and the asymmetric mode is inverted numerically to the real time domain using a reliable numerical scheme. Influences of the dimensionless poroelastic parameters on the dynamic response of the borehole are analyzed in a detailed parametric study. Radial variations of the pore pressure and stresses in the two different modes are examined; and the dynamic evolution of the superposed solution is analyzed. A direct comparison between the classical quasi-static poroelastic theory and current poroelastodynamic theory shows that inertial effect is important in early times; and the poroelastodynamic response resembles a damped oscillator, exhibiting wave-diffusion behavior. At longer times, diffusion dominates and the poroelastodynamic solution approaches the quasi-static poroelastic solution. The presented solution can be applied to study borehole stability under dynamic loadings.

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