非局部摩擦模型的核函数研究及其在锚杆中应用

Studies of Kernel Function in the Nonlocal Friction Model and Its Application on Bolt

为研究非局部摩擦理论中核函数的性质及其选取原则,在Oden等提出的非局部摩擦模型的基础上,分别采用指数型、三角函数型、负指数型和幂函数型等4种函数作为非局部摩擦模型中的核函数,并利用Mindlin问题的位移解导出的全长黏结式锚杆沿杆体表面所受剪应力的弹性解,对全长黏结式锚杆进行非局部摩擦分析.研究表明,基于这几种核函数的非局部摩擦模型以及局部摩擦模型所得到的剪应力分布大致相似.通过与实验数据对比可知,采用负指数函数的核函数形式计算所得锚杆侧剪应力分布比其他形式更接近于实验值.

To investigate the characteristics together with optimum selection of kernel functions in the nonlocal friction model, the nonlocal friction model proposed by Oden et al is modified. The kernel function in model is replaced by exponential function, trigonometric function, negative exponential function and power function. Based on the elastic solution of shear stress on bolt surface of the wholly grouted anchor derived with Mindlin＇s solution of displacement, wholly grouted anchor is analyzed by the modified nonlocal friction models which have four different kernel functions. The shear stress distributions on bolt surface given by the modified nonlocal friction models and the local friction models are similar. The nonlocal friction effect is also discussed. The results obtained by the modified nonlocal friction model with different kernel functions and local friction model are compared with experimental results. It is found that the calculating results obtained by modified nonlocal friction model with the negative exponential kernel functions agree better with experimental results.