混凝土K_R阻力曲线的实用解析方法

A practical analytical approach to determine K_R-curves of concrete

根据混凝土Ⅰ型裂缝扩展准则,提出了新的KR阻力曲线及计算新方法。该KR阻力曲线认为,裂缝的扩展阻力由混凝土材料起裂断裂韧度KiniIc和黏聚力提供的阻力组成并等于裂缝扩展的驱动力。采用该方法,只需给出混凝土的起裂断裂韧度KiniIc,弹性模量E,抗拉强度ft和断裂能GF便可计算混凝土的KR阻力曲线,而无需测定试件的荷载-裂缝口张开位移(P-CMOD)全曲线。在此基础上,研究了混凝土三点弯曲梁试件强度等级从C20到C120的KR阻力曲线,计算了强度相同初始缝高比不同以及初始缝高比相同而试件高度不同的混凝土KR阻力曲线,并探讨了各种情况下的断裂过程区长度以及黏聚力分布。研究结果表明:混凝土强度等级提高,KR阻力曲线上升,但其上升幅值逐渐减小,强度等级在C60以后,其上升幅值趋于稳定;混凝土的KR阻力曲线存在一定的尺寸效应,当韧带长度足够大时,KR阻力先增大,而后趋于稳定;混凝土强度等级提高,最大完整断裂过程区长度减小;试件的尺寸对断裂过程区长度也有着较大影响。

Based on the crack propagation criterion for the mode I crack, a practical analytical method is developed for determining the crack extension resistance curves of concrete. In this method, the crack extension resistance is composed of the initial fracture toughnessK-ini/Ic and the resistance caused by the cohesive force, equaling the driving force of the crack extension. It is concluded that as long as the initial fracture toughnessK-ini/Ic, the elastic modulus E, the tensile strength ft and the fracture energy GF of concrete are obtained, the KR extension resistance curves can be calculated by using this method without testing the load-crack mouth opening displacement curves. Further, the practical analytical method is applied to calculate the KR extension resistance curves, the fracture process zone lengths and the cohesive stress distribution for concrete with varied strength grades from C20 to C120, different initial crack length/depth ratios and different depths under the three-point bending conditions. Based on the numerical analysis results, it is found that the Kn extension resistance curves increase with the increase of the strength grades, but the growth amplitude decreases, and when the strength grades is larger than C60, the growth amplitude will tend to be stable; the Kn extension resistance curves are dependent of the initial crack length and specimen depth, and when the ligament is long enough, the crack extension resistance increases and then tends to be stable ; the maximum lengths of the complete fracture process zone decrease with the increase of concrete strength grades; and the specimen size has remarkable impacts upon the fracture process zone length.