用矩阵权函数分析基层底部混合型裂缝的应力强度因子

Analysis on the stress intensity factor(SIF) for mixed-mode crack at bottom base layer with weight functions expressed with matrix

由于基层材料的变异性、基层干缩 (尤其是水泥基基层 )、温度应力、土基压实不够、施工和养护不当 ,以及混合型荷载等都会在基层形成混合型裂缝 ,这些裂缝很容易形成反射裂缝 ,因而分析基层混合型裂缝应力强度因子就非常有必要。根据能量准则、叠加原理、贝蒂互换定理等推导出用矩阵权函数计算混合型应力强度因子的方法。并分析了待定权函数系数的求法 ,即结合有限元计算混合型裂缝应力强度因子方法求出待定的权函数系数 ,继而得到了矩阵型权函数。并利用有限元检验得到的权函数 ,两种不同方法在不同荷载作用下的计算结果吻合得很好 ,表明该方法可行。并编制了相应的程序来实现上述理论 。

Due the variations of materials,shrinkage of base layer(especially the cementitious binder is used),temperature stresses,poorly compacted soil,poor constraction and poor maintenance and the mixed mode loads subjected to the pavement,mixed mode cracks are easy to occur at the bottom of the base layer of pavements,so it is necessary to analyze the stress intensity factors for the mixed mode cracks at the bottom of base layer.The method to calculate the mixed mode stress intensity factors is derived with the matrix weight functions according to the energy rule,superpostition theory and Betti's reciprocity theory.The method to get the constant coefficients of weight functions is also analyzed, which is based on the SIFs by finite element method.The weight functions are checked by the finite element method,and the agreement appears to be fairly good for the whole results by the two methods,which reveals the weight function method is very efficient.The corresponding programs are also made,and it will be useful for analysis on the reflecting cracks in pavements and the engineering applications.