Abstract: The aim of this paper is to improve the control theory for the rheological behavior of the surrounding rock around roadway. Based on the theory of viscoelasticity and nonlinear optimization principle, a time-dependent viscoelastic model of coupling action between the surrounding rock mass and the anchorage body is developed considering the space effect of tunnel face advancement; and then an optimization model of roadway support is established. The influences of the support time, the thickness of anchor, the original rock stress and the road radius on the deformation of surrounding rock mass are analyzed; and then the optimal design parameters of the roadway support are discussed in detail by a case study. The results show that the support time, the thickness of anchorage body, the original rock stress and the road radius have certain impacts on the stability of tunnel. With the increases of the roadway support time, the original rock stress and the road radius, and the decrease of the thickness of the anchor body, the displacement increases. The optimal design parameters of the roadway support are obtained; when the force acted on the support body reaches a critical state, the thickness of anchorage body decreases with the support time elapsing, and when the thickness of anchorage body is smaller, they show an approximately linear relationship with time.

Key words: surrounding rock mass, viscoelasticity, coupling, optimization