Table 4 Compliance factors for surface...

Table 4

Compliance factors for surface displacements

Factor	Description	FILE material	TILE material
Factor	Description	FILE material	General	Constant volume
C_zz	Vertical displacement due to vertical force	1 − μ	$- \frac{m_{1} λ_{2} + m_{2} λ_{1}}{2}$	$\frac{1}{u_{1}^{u} + u_{2}^{u}}$
C_zx	Vertical displacement due to horizontal force	$\frac{1 - 2 μ}{2}$	$\frac{λ_{1} + λ_{2}}{2}$	0
C_rz	Radial displacement due to vertical force	$\frac{2 μ - 1}{2}$	$- \frac{λ_{1} + λ_{2}}{2}$	0
C_rx	Radial displacement due to horizontal force	1	$\sqrt{\frac{G_{vh}}{G_{hh}}}$	$\sqrt{\frac{G_{vh}}{G_{hh}}}$
C_θz	Circumferential displacement due to vertical force	0	0	0
C_θx	Circumferential displacement due to horizontal force	μ − 1	$\frac{m_{1} λ_{2} + m_{2} λ_{1}}{2 m_{1} m_{2}}$	$\frac{- 1}{u_{1}^{u} + u_{2}^{u}}$

Factor	Description	FILE material	TILE material
Factor	Description	FILE material	General	Constant volume
C_zz	Vertical displacement due to vertical force	1 − μ	$- \frac{m_{1} λ_{2} + m_{2} λ_{1}}{2}$	$\frac{1}{u_{1}^{u} + u_{2}^{u}}$
C_zx	Vertical displacement due to horizontal force	$\frac{1 - 2 μ}{2}$	$\frac{λ_{1} + λ_{2}}{2}$	0
C_rz	Radial displacement due to vertical force	$\frac{2 μ - 1}{2}$	$- \frac{λ_{1} + λ_{2}}{2}$	0
C_rx	Radial displacement due to horizontal force	1	$\sqrt{\frac{G_{vh}}{G_{hh}}}$	$\sqrt{\frac{G_{vh}}{G_{hh}}}$
C_θz	Circumferential displacement due to vertical force	0	0	0
C_θx	Circumferential displacement due to horizontal force	μ − 1	$\frac{m_{1} λ_{2} + m_{2} λ_{1}}{2 m_{1} m_{2}}$	$\frac{- 1}{u_{1}^{u} + u_{2}^{u}}$