基于改进指–幂混合函数模型的锚杆承载力预测方法研究

A REVISED MODEL FOR PREDICTING THE BEARING CAPACITY OF ROCK BOLTS BASED ON MIXED EXPONENTIAL AND POWER UNCTION

针对不能准确地区分弹性与弹塑性阶段数据,以及难以测量较多破坏阶段数据的实际情况,一个受破坏阶段和弹性阶段数据影响较小、模拟锚杆荷载P–位移S曲线效果较好、预测锚杆极限承载力破坏值准确度较高的模型是非常重要的。分析双曲线、指数和幂函数3种模型,对3种模型的结构共性进行总结,提出一种可以用来模拟锚杆P-S曲线的通用函数模型框架,并从实际的锚杆P-S曲线的特点出发,构建基于通用函数模型框架的锚杆P-S曲线的数学函数模型。针对指数函数模型精度差的缺点,使用函数模型框架对指数函数模型进行改进,改进后的模型精度得到很大提高;分析调整双曲线和修正双曲线模型,使用通用函数模型框架构建一种由改进指数和幂函数组和而成的混合函数模型。通过实际的工程案例验证,改进指–幂混合函数模型不仅是模拟锚杆P-S曲线精度较高的模型,而且是预测锚杆极限承载力破坏值误差较小的模型,受弹性阶段和破坏阶段数据影响较小。

The elastic and elasto-plastic stages of rock are very difficult to be separated precisely and few of data in failure stage has been measured. To establish a model,fitting the P-S curve of rock bolts at large and affected little by the data at failure and the elastic stages,is therefore very important for the prediction of the ultimate bearing capacity of rock bolts with higher accuracy. After analysis of the hyperbolic,index and the power function,a general model was put forward to simulate the load and displacement curve of rock bolts(shorted for P-S curve). According to the actual P-S curve(through the origin,non-negative bounded,monotone increasing,infinite convergence and convex),a mathematical function for P-S curve of rock bolts based on the general model was established. The exponential function model was revised and the hyperbola model were adjusted so that,a mixed function model was established. The application of the mixed function model simulated the P-S curve and the ultimate bearing capacity of rock bolts with higher accuracy.