基于概率论求二维钢纤维混凝土方向有效系数

Study on Orientation Effective Factor of Two-dimensional Steel Fiber Reinforced Concrete Based on the Probability Theory

钢纤维混凝土是一种多相非均质复合材料,其本构关系非常复杂,需要考虑纤维方向、长度以及与基体的界面粘结性状等因素对材料强度的影响。因钢纤维随机乱向分布且难以测量其方向,文章结合复合力学本构模型,从随机变量的角度推导二维钢纤维方向有效系数。假设钢纤维分布服从二维均匀分布,运用概率论的相关知识,计算出钢纤维与受力方向夹角的分布函数,并计算出夹角余弦值的期望,即方向有效系数。结果表明,研究区域内钢纤维和截面相交的概率为1/π,理论上方向有效系数为0.25;实际工程中由于边壁效应和重力效应的存在,方向有效系数应比该数值略小。

Steel fiber reinforced concrete is a kind of multiphase heterogeneous composite material,therefore its constitutive relations are very complex and the effects of orientation,length of fibers and bonding behavior of the interface between fibers and matrix on material strength should be considered.Due to the random distribution of steel fibers,it is difficult to measure its orientation;the orientation effective coefficient of steel fibers in 2-dimension was deduced in a perspective of random variable on the basis of a composite mechanical constitutive model.Assuming the distribution of steel fibers obeys the two-dimensional uniform distribution,the distribution function of the angleθbetween steel fibers and force direction was calculated using probability theory,and the expectation of cosθ,i.e.orientation effective coefficient,was calculated.The results show that the probability of steel fiber intersecting with section is 1/πwithin the studied area and theoretically the orientation effective coefficient is 0.25,while the actual orientation effective coefficient should be slightly smaller than 0.25 due to the boundary effect and gravitation effect.