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 language | English (US) |
|---|---|
| Pages (from-to) | 82-93 |
| Number of pages | 12 |
| Journal | International Journal of Rock Mechanics and Mining Sciences |
| Volume | 93 |
| DOIs | |
| State | Published - Mar 1 2017 |
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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 journal › Article
}
TY - JOUR
T1 - Poroelastodynamic response of a borehole in a non-hydrostatic stress field
AU - Xia, Yang
AU - Jin, Yan
AU - Chen, Mian
AU - Chen, Kangping
PY - 2017/3/1
Y1 - 2017/3/1
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.
KW - Analytical solution
KW - Laplace-Fourier transform
KW - Non-hydrostatic stress field
KW - Poroelastodynamic response
UR - http://www.scopus.com/inward/record.url?scp=85010910662&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85010910662&partnerID=8YFLogxK
U2 - 10.1016/j.ijrmms.2017.01.008
DO - 10.1016/j.ijrmms.2017.01.008
M3 - Article
AN - SCOPUS:85010910662
VL - 93
SP - 82
EP - 93
JO - International Journal of Rock Mechanics and Minings Sciences
JF - International Journal of Rock Mechanics and Minings Sciences
SN - 1365-1609
ER -