Rigid sliding blocks are used to construct twofailure modes of the tunnel's circumferential excavation surface of circulartunnel. The compiled nonlinear programming program is used to solve the optimalupper bound solution of the support force coefficient / ( is uniformly distributed support load and is the effective cohesion) and thestratum failure mode so as to reveal the influences ofstratum parameters on tunnel stability. A simple and practical simplifiedformula for the ultimate support force of the tunnel's circumferentialexcavation surface is proposed. For undrained condition

the failure region ismainly concentrated in the upper part of the tunnel when the tunnel depth ratio / ( is the buried depth and is the tunnel diameter) and thegravity coefficient / (is unit weight) aresmall. With the increase of / and /

the starting position of the slip linegradually expands to the bottom of the tunnel along the tunnel contour

and thefailure region expands to the horizontal direction. For drainage conditions

there are three main stratum failure modes. When the internal friction angle and / are large

with the decrease of thedilatancy coefficient

the ultimate supporting force increases significantly

and the range of failure region varies greatly

which may even cause a changein the failure mode. The ultimate supporting force of the tunnelcircumferential excavation surface can be quickly obtained through the proposedsimplified formulas.