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
N1 - Publisher Copyright:
© 2017 Elsevier Ltd
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
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U2 - 10.1016/j.ijrmms.2017.01.008
DO - 10.1016/j.ijrmms.2017.01.008
M3 - Article
AN - SCOPUS:85010910662
SN - 1365-1609
VL - 93
SP - 82
EP - 93
JO - International Journal of Rock Mechanics and Mining Sciences
JF - International Journal of Rock Mechanics and Mining Sciences
ER -