Symbols and Greek Letters	Nomenclature
${\mathrm{F}}_1$(${\mathrm{F}}_2$)	the foundation reaction forces before the existing tunnel deformation
${\mathrm{F}}_{11}$(${\mathrm{F}}_{22}$)	the foundation reaction forces after the existing tunnel deformation
$k_1$($k_2$)	the subgrade modulus coefficients of strata above and below the tunnel
$\sigma$	the vertical unloading stress on the existing shield tunnel
$w$	the vertical deformation of the existing shield tunnel
$M$	the bending moment
$Q$	the shear force
$mg$	the gravity of the tunnel microunit
$b$	the width of the excavation area
$P$	the upward unloading pressure
$\mathsf{\mu }$	the Poisson’s ratio
$z_1$	the distance from the axis of the shield tunnel to the surface
$z_0$	the distance from the floor of the excavation area to the surface
$L_1$	the distance from the start of the excavation area to the intersection of the axes
$L_2$	the distance from the intersection of the axes to the end of the excavation area
$\left\{W\right\}$	the elemental nodal vertical displacement vector
$\left\{\sigma \right\}$	the elemental nodal vertical unloading stress vector
$\left[A\right]$	the deformation stiffness matrix of the shield tunnel
$\left[B\right]$	the upper foundation spring stiffness matrix
$\left[C\right]$	the lower foundation spring stiffness matrix
$E$	the Young’s modulus
$I$	the moment of inertia of the tunnel section
$E_c$	the Young’s modulus of the shield tunnel segments
$D$	the outer diameter of the shield tunnel
$d$	the inner diameter of the shield tunnel
$E_s$	the Young’s modulus of soils
$B$	the width of the beam
$E{I}_{eq}$	the longitudinal equivalent bending stiffness
$C_u$	the undrained shear strength