基于PFC2D岩石颗粒破碎强度和能量的分形模型

摘要

颗粒的破碎强度随着粒径的增大而减小，即颗粒破碎的尺寸效应，分形模型为解释固体颗粒破碎的尺寸效应提供了可行的方法。根据岩石颗粒破碎时的分形特征，采用Sammis破碎准则，通过模拟分析得出岩石颗粒破碎能量和强度的分形模型，建立和验证用分维D来表示岩石颗粒破碎的能量和强度准则，得出并验证了岩石颗粒破碎分维的确定方法。利用离散元软件PFC2D的黏结颗粒模型BPM（Bonded Particle Model）模拟了小孔隙率n＝0．12和大孔隙率n＝0．3，即密实和松散两种情况。其中小孔隙率采用在模型上添加小颗粒的新方法，分别做了400组粒径不等的数值模拟试验，从粒径与破碎强度、破碎能量之间的关系和应力-应变曲线3个方面进行了统计，验证了岩石颗粒破碎强度与分维D的理论关系为σf∝dD－3，并得出颗粒破碎时的能量和与分维D之间的关系为Ef∝dD－1。验证了分形理论在分析颗粒破碎的尺寸效应中的较好应用，为确定岩石颗粒的破碎强度和岩石堆砌体剪切强度提供新的方法和参考意见。%The tensile strength is not independent of fragment size,but decreases with increasing size known as“size effect”.Recent developments in fractal theory suggest that fractal model may provide a more realistic representation of solid particle crushing.A fractal model for crushing of rock particle is constructed using the Sammis model.The relationship between crushing strength and diameter and the relationship between crushing power and diameter of rock particle are simulated respectively.The porosity equals to 0. 1 2 and 0. 3 of rock particles,which are simulated using the bonded particle model (BPM)in particle flow code (PFC2D ).The relationship between crushing strength and diameter of particle is verified and can be expressed by σf∝dD-3 .A relationship between crushing power and diameter of rock particle is expressed by Ef∝ dD-1 .The good application of fractal theory in the analysis of particle size effect in fractured rock is verified and the results provide a reference for determination of crushing strength.