大变形锚杆-围岩耦合模型及其计算方法

在矿山、水利、交通等工程领域中大变形锚杆已经获得了广泛的认可和应用，而相应理论水平落后于工程实践的现状则限制了大变形锚杆支护技术的进一步发展。针对大变形锚杆的力学及变形特性，提出了一种锚杆-围岩耦合作用结构模型，并基于塑性增量理论，从锚杆-围岩相互作用的角度，提出了大变形锚杆加固岩体的求解方法，推导了加锚岩体的平衡方程、位移协调方程和锚杆响应方程。在Visual Basic开发环境中编制有限差分计算程序，利用龙格库塔法求得了大变形锚杆-围岩耦合模型的半解析解，并通过数值模拟验证了理论模型的有效性。基于上述理论模型和计算方法，不仅可以计算得到大变形锚杆轴力和剪应力分布情况，定量分析其支护效应，还可以系统地求得加锚岩体的地层响应曲线及锚杆自身的响应曲线，对于地下工程中大变形锚杆的支护设计有基础性指导意义。

Coupling model and calculation method of yielding bolt and rockmass

Yielding bolt has been widely used for rock reinforcement in mining and civil engineering in high stress conditions. However, the interaction mechanism of the yielding bolt and the rockmass is still not clear at present; and no model is available to predict its reinforcement effect quantitatively. According to the mechanical and deformation characteristics of yielding bolt, an interaction model is proposed to account for the coupling action between the bolt and rockmass. Based on the plane strain axial symmetry assumption and the incremental theory of plasticity, equilibrium equations and compatibility equations of rockmass, and also the response of yielding rock bolt are deduced theoretically. The proposed method has been programmed in the Visual Basic development environment; and a semi-analytical solution for the coupling model is achieved using Runge-Kutta method. The reinforcement mechanism of yielding bolt is demonstrated through an illustrative case study. The distribution of shear stress and axial force along the bolt are presented; and the reinforcement effect of yielding bolt is estimated quantitatively. In addition, the validity of the proposed method is verified by numerical simulations. The reinforced ground reaction curve and the yielding bolt reaction curve can also be constructed systematically by the proposed method, which could help the support system design in conventional tunnelling.