Open AccessA new gradient elasticity model for the elastic boreholes
Author(s) -
G. Efremidis,
Ioannis Tsagrakis
Publication year - 2021
Publication title -
iop conference series. earth and environmental science
Language(s) - English
Resource type - Journals
eISSN - 1755-1307
pISSN - 1755-1315
DOI - 10.1088/1755-1315/833/1/012188
Subject(s) - elasticity (physics) , isotropy , borehole , mechanics , hydrostatic equilibrium , constitutive equation , infinitesimal strain theory , linear elasticity , cauchy stress tensor , rock mass classification , laplace operator , mathematical analysis , geology , materials science , geotechnical engineering , mathematics , physics , thermodynamics , finite element method , composite material , quantum mechanics
A new gradient elasticity model is employed to discuss strain gradient effects and its ability in predicting size effects on an elastic rock mass with microstructure, around an axisymmetric borehole under internal pressure and remote isotropic compressive stress. The constitutive equation of the model involves the Laplacian of the strain tensor multiplied by the gradient coefficient. The formulated boundary value problem is solved analytically to derive stress, strain, and displacement distributions and discuss respective gradient effects on the mechanical behavior of the rock mass and the corresponding borehole stability. The paper concludes with the employment of the Rankine failure criterion to investigate size effects on the stress concentration factor at the perimeter of the borehole, and the comparison with another gradient elasticity model which involves the Laplacian of the hydrostatic part of the strain tensor.