类岩石材料内置不规则裂纹形状因子分析

脆性岩体中内置裂纹的萌生、扩展和贯通将导致岩体失稳破裂。为研究脆性岩体中内置裂纹的断裂特性,首先,利用室内相似材料模拟试验,验证了1/4节点奇异单元建立的含圆形水平内置裂纹的圆柱体有限元数值模型的正确性与可靠性。其次,为了分析裂纹尖端弯曲程度和裂纹相对试件尺寸对内置裂纹断裂特性的影响作用,定义了相对曲率半径比t和相对尺寸比n,用于描述不规则水平内置裂纹的几何形态。然后,利用圆型和椭圆型内置裂纹数值模型,分别研究了t值与n值对裂纹形状因子的影响规律。在此基础上,综合考虑二者的影响作用,得出了一种适用于计算任意凸曲线型水平内置裂纹形状因子的简易表达式。同时,对该表达式可靠性进行了验证,结果表明,对于圆型、椭圆型、不规则型裂纹,该式计算结果与数值计算结果的误差均小于2%。同时得出,在与极轴夹角约为60°和300°处,文中所述不规则裂纹尖端的应力强度因子值最大,裂纹将率先由此处扩展。研究结果可以为工程或实验中估算内置裂纹岩体的应力强度因子提供参考。

Shape factor of irregular internal cracks in rock-like materials

The initiation, propagation and coalescence of internal cracks will lead to the failure of rock mass. To study the fracture characteristics of the internal cracks in brittle rock mass, the validity and reliability of a cylinder FEM numerical model containing a horizontal circular crack with 1/4-point singular elements are verified by the similar material simulation tests. Then, to analyze the effects of the size and curvature on the fracture characteristics of internal cracks, the relative-size-ratio (n) and relative-curvature-radius-ratio (t) of crack are defined to describe the geometrical feature of the internal cracks. Furthermore, the influences of n and t on the shape factors of crack (Y) are examined by the numerical model with circular and elliptical internal horizontal cracks. In addition, based on the above research results, a simple formula is proposed to calculate the shape factor of arbitrary convex-curve-type internal horizontal crack. Moreover, the comparisons of the calculated results and the numerical simulations of circular, elliptical and irregular crack show that all the deviations are within 2%. Meanwhile, SIF of the irregular crack in this research approaches its maximum at positions of 60° and 300° from X-axis positive direction approximately, where the crack will develop firstly. The results can be applied to the estimation of SIF value of internal cracks in laboratory tests or practical engineering.