A broken zone usually exists in the deeply buried tunnels after excavation, and the rock mass in the broken zone is in the state of unloading failure and exhibiting a nonlinear dilatancy effect. In order to study the deformation of isotropic rock mass in an initial hydrostatic stress field, a method is proposed to calculate the radius of the broken zone of the surrounding rock in a circular tunnel. Based on the unloading experiment of rock samples, a layer-wise summation method is established to calculate the displacement of the circular tunnel after excavation. The results reflect the impact of the nonlinear dilatancy effect on the displacement of the tunnel wall along the radial direction. Moreover, the method does not include complex integral calculation. Comparing with the Kastner’s (Houska 1981) method and Y K Lee’s (Lee and Pietruszczak 2008) method. This article reveals that the residual strength parameters c_r, φ_r and dilation angle ψ, that are essential in Y K Lee’s method, are highly sensitive to displacement calculation, which makes the Y K Lee’s method difficult to apply. In contrast, the method proposed in this study provides accurate prediction and has access to obtain its parameters more easily, making it easy to popularize.

开挖后的深埋隧道通常存在破碎带，破碎带内的岩体处于卸荷破坏状态，呈现非线性剪胀效应。为研究初始静水应力场下各向同性岩体的变形，提出了一种计算圆形隧道围岩破碎带半径的方法。在岩样卸荷试验的基础上，建立了逐层求和法计算圆形隧道开挖后位移。结果反映了非线性剪胀效应对隧道壁沿径向位移的影响。而且，该方法不包括复杂的积分计算。与 Kastner 的 (Houska 1981) 方法和 YK Lee 的 (Lee 和 Pietruszczak 2008) 方法进行比较。这篇文章揭示了残余强度参数c _r、φ _r和膨胀角ψ是YK Lee 方法中必不可少的，它们对位移计算高度敏感，这使得YK Lee 方法难以应用。相比之下，本研究提出的方法提供了准确的预测，并且更容易获得其参数，易于推广。