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The authors of this book have already provided the correct approach for solving the hole problem in Sect.  3.3.4 . The outer regions of the hole in z1- and z2-planes are mapped onto the outer regions of the unit circle in \(\zeta_{1}\) - and \(\zeta_{2}\) - planes by utilizing the mapping functions \(z_{1} \, = \omega_{1} (\zeta_{1} )\) and \(z_{2} \, = \omega_{2} (\zeta_{2} ),\) respectively, where \(\zeta_{1} = \rho_{1} e^{{i\theta_{1} }}\) and \(\zeta_{2} = \rho_{2} e^{{i\theta_{2} }} .\) In the unit circle, which corresponds to the hole boundary, we have \(\rho_{1} = \rho_{2} = 1.\)

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Analytical Solutions for Mechanical Analysis of Hole/Tunnel Problems in Anisotropic Elastic Plane/Rock Mass

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  • 发表日期：

    2025年

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  • Aizhong Lu,
  • Huaning Wang,
  • Luqing Zhang

摘要

The authors of this book have already provided the correct approach for solving the hole problem in Sect.  3.3.4 . The outer regions of the hole in z1- and z2-planes are mapped onto the outer regions of the unit circle in \(\zeta_{1}\) - and \(\zeta_{2}\) - planes by utilizing the mapping functions \(z_{1} \, = \omega_{1} (\zeta_{1} )\) and \(z_{2} \, = \omega_{2} (\zeta_{2} ),\) respectively, where \(\zeta_{1} = \rho_{1} e^{{i\theta_{1} }}\) and \(\zeta_{2} = \rho_{2} e^{{i\theta_{2} }} .\) In the unit circle, which corresponds to the hole boundary, we have \(\rho_{1} = \rho_{2} = 1.\)