确定围岩-支护结构体系动态协同变形关系是地下工程支护需要解决的关键问题之一。运用Mohr-Coulomb准则推导隧道开挖支护后围岩径向变形与支护结构径向变形的协同方程，探讨Ⅳ级围岩塑性半径、围岩位移及支护刚度随支护强度的变化关系；并运用FLAC^3D数值模拟验证协同变形方程的合理性和有效性。结果表明，围岩-支护结构体系协同变形方程能很好地反映围岩位移和塑性区半径随支护强度变化的关系，且相互关系是非线性的。支护强度为0.75 MPa时，理论计算拱顶沉降为18.9 mm，数值模拟拱顶沉降为21.6 mm；支护强度为1.5 MPa时，理论计算拱顶沉降为11.2 mm，数值模拟拱顶沉降为11.1 mm，表明围岩-支护结构动态协同变形方程的有效性。针对Ⅳ级围岩在采用超前支护和交叉中隔壁法（cross diaphragm, CRD）施工时，建议支护强度设计为0.75 ~ 1.5 MPa，支护刚度设计为59.8 ~ 375.0 kN/mm。

Determining the dynamic synergistic deformation relationship of surrounding rock-support structure system is one of the key problems to be solved in underground engineering support. The synergistic equation of radial deformation of surrounding rock and radial deformation of supporting structure after tunnel excavation and support was derived by using Mohr-Coulomb criterion. The relationship between the plastic radius, displacement of surrounding rock and supporting stiffness of grade Ⅳ surrounding rock with supporting strength was discussed. FLAC^3D numerical simulation was used to verify the rationality and effectiveness of the synergistic deformation equation. The results show that the collaborative deformation equation of surrounding rock-supporting structure system can well reflect the relationship between surrounding rock displacement and plastic zone radius with the change of supporting strength, and the relationship is nonlinear. When the supporting strength is 0.75 MPa, the theoretical calculation of vault settlement is 18.9 mm, the numerical simulation of vault settlement is 21.6 mm. When the supporting strength is 1.5 MPa, the theoretical calculation of vault settlement is 11.2 mm, and the numerical simulation of vault settlement is 11.1 mm, which shows the effectiveness of the dynamic synergistic deformation equation of surrounding rock-supporting structure. In view of the Ⅳ surrounding rock in the use of advanced support and cross diaphragm (CRD) construction method, it is recommended that the support strength design is 0.75 ~ 1.5 MPa, the support stiffness design is 59.8 ~ 375.0 kN/mm.