考虑围岩软化特性和应力释放的圆形隧道黏弹塑性解

将围岩的塑性应变软化特性引入到考虑应力释放的圆形隧道黏弹塑性解中，并且在围岩的软化和残余强度阶段考虑围岩的塑性体积膨胀特性，提出了考虑塑性软化以及塑性体积膨胀和围岩应力释放的圆形隧道弹塑性解。当软化系数k = ∞、膨胀系数h = s时，该解转化为黏弹-脆塑性解；当k = 0、h = s时，则转化为黏弹-理想塑性解，进一步令h = s = 1，则转化为不考虑塑性体积膨胀的黏弹-理想塑性解。通过具体实例计算，分析了掌子面与研究断面间距x、围岩的软化系数k、膨胀系数h和s、支护结构等对围岩塑性区、破碎区半径和变形的影响。当开挖面与研究断面间距x在(0~4)D（D为隧道直径）范围内，随着时间增加塑性圈和破碎区迅速增大；超过4D，塑性区和破碎区半径增量逐渐变小，趋于稳定值；围岩中包含塑性区和破碎区时，二者半径的比值只取决于围岩的性质，与支护结构无关，但支护结构可以限制塑性区及破碎区的范围；考虑应变软化和塑性体积膨胀时，围岩径向位移和塑性区及破碎区半径均大于不考虑应变软化和塑性体积膨胀时的结果；软化系数k增大，围岩位移、塑性区和破碎区半径增加、塑性区半径和破碎区半径之间的比值变小。得到的结果对于隧道工程设计和施工具有一定的指导性和参考价值。

Visco-elastoplastic solutions for circular tunnel considering stress release and softening behaviour of rocks

The softening behaviour of rocks is introduced into the visco-elastoplastic solutions for the circular tunnel considering the stress release. During the softening process and residential strength stage, the plastic voluminal expansion is taken into account. When the softening coefficient k = 0 and swelling coefficient h = s, the solutions could be transformed into viscoealsto-brittle plastic solutions. Otherwise, k = 0 and h = s, the solutions could be transformed into viscoealsto-perfectly plastic solutions; furthermore, when h = s = 1, the solutions would be the viscoelasto-perfectly plastic solution without considering the plastic swelling. By the case study, the effects of distance x between the face and the setting section, softening coefficient k, plastic swelling coefficient h and s, supporting system on the radii of the plastic zone and broken zone, and displacements of surrounding rock have been analyzed in detail. When x is smaller than 4D, where D is the diameter of tunnel, with time increase, the plastic zone and broken zone enlarge rapidly. When x >4D, the increments of plastic zone and broken zone will diminish. The support system has no effects on the ratio between radii of plastic zone and broken zone; but it could limit the development of the plastic and broken zones. The calculating results of the paper are larger than the results without considering the softening behaviour and swelling behaviour of the rock mass. With softening coefficient k increases, displacements, plastic zone and broken zone will enlarge; but the ratio between the radii of plastic and broken zones will diminish. The results could be taken as reference and guide for the tunnel design and construction.