Table 2 Traction coefficients obtained under boundary conditions.

From: Analytical prediction of groundwater loss in deep coal mines induced by ground vibration

Equation (17)

Equation (18)

\(a_{k} = - 0.5A_{k} ,\) k = 2, 3, 4, …,

\(a_{k} = - 0.5B_{k} /k\); k = 2, 3, 4, …,

\(a_{1} = - 0.26\,u_{\varepsilon } \;A_{1}\)

\(a_{1} = - 0.5u_{\varepsilon } \mu \left( {kB_{1} + \overline{B}_{1} } \right)/\left( {k^{2} - 1} \right)\)

\(b_{k} = 1.99\overline{A}_{ - k} - \left( {u_{\varepsilon } .\nabla } \right)u_{\varepsilon } \left( {k + 2} \right)a_{k + 2}\), k = 0, 1, 2, …

\(b_{k} = - \mu \nabla^{2} u_{\varepsilon } \left( {\overline{B}_{ - k} + \left( {k + 2} \right)a_{k + 2} } \right)\), k = 0, 1, 2, …