预应力锚杆-围岩耦合模型时变效应分析

为了揭示预应力锚杆-围岩耦合时变效应机理，利用分布力模型获取耦合模型的弹性解，结合材料性质和维度效应选用符合锚杆和围岩的流变模型（锚杆选用一维Kelvin模型，围岩选用三维Burgers模型），求解预应力锚杆-围岩耦合模型在Laplace空间的解析解，通过Laplace逆变化便得到耦合模型的黏弹性解。探究锚杆预应力和流变模型的黏性参数对围岩应力、位移场和锚杆轴力的影响，并基于理论模型和数值模拟软件FLAC^3D的二次开发，开展相应数值模拟，对比分析解析解和数值解，验证解析解的正确性。研究结果表明：解析解与数值解吻合程度良好，在隧道内壁处，锚杆支护力随着时间的增大逐渐减小，且锚杆预应力和围岩的黏性参数与支护效果密切相关，其中围岩的支护效果与锚杆预应力大小呈现明显的正相关关系；围岩的位移变化表现出明显的时间相关性，并且与锚杆预应力大小呈现负相关关系；当锚杆的预应力过大时，围岩位移不再随之显著减小，由此可见，施加于锚杆的预应力不应过大；围岩Burgers模型中第Ⅰ蠕变阶段黏性系数影响锚杆的初期支护效果，而后期支护效果主要受围岩Burgers模型中第Ⅱ蠕变阶段黏性系数影响，并且随着黏性系数的增大锚杆后期支护效果越好；锚杆的流变状态不受围岩黏性系数的影响。

Time-dependent Behavior for Coupling Model of Pre-stressed Bolt and Rock Mass

To reveal the time-dependent behavior of pre-stressed bolt and rock mass, the elastic solutions of the coupling model under a distributed force model were acquired. The rheological model of the bolt and rock mass were selected based on the material properties and scale effect. A one-dimensional Kelvin model was selected for the bolt, and a three-dimensional Burgers model was used for the rock mass to solve the analytic solutions in the Laplace space. Then, the viscoelastic solutions of the coupling model can be acquired by the inverse variation of the Laplace space. The influences of pre-stress and viscous parameters on the stress or displacement fields of the rock mass and the axial force were discussed. The numerical simulation was performed based on the theoretical model and the secondary development of numerical simulation software FLAC^3D. The comparison and analysis show that the analytical solutions are in good agreement with numerical solutions, which verifies the correctness of the analytical solutions. The results show that with the increase in time, the support force gradually decreases at the excavation surface in the tunnel. In addition, the pre-stress and rock mass viscosity parameters strongly affect the bolt support effect. There is a significant positive correlation between support effect and bolt pre-stress. The change in rock mass displacement shows a significant time correlation. In addition, there is a negative correlation between the rock mass displacement and bolt pre-stress. The research shows that when the bolt pre-stress is too large, the rock mass displacement is no longer significantly reduced. Thus, it can be seen that the pre-stress applied to the bolt should not be too large. In addition, the early support effect is mainly affected by the viscosity coefficient of the first creep stage in the Burgers model of rock mass. However, the later support effect is mainly affected by the viscosity coefficient of the second creep stage. The greater the viscosity coefficient, the better the later support effect. Furthermore, the rheological state of the bolt is independent of the viscosity coefficient of the rock mass.