基于分形理论的北京地区砂砾石地层细观建模

A mesoscopic model of sand-gravel stratum in Beijing based on fractal theory

土石混合体材料及相应地层中地下结构的力学行为及变形规律受到颗粒粒度组成与分布规律的影响。采用分形几何学对土石混合体的粒度分布进行描述,进一步明确了质量–粒径级配曲线与粒度分形维数之间的关系。在双对数坐标系Tlg(M(r<R)M)-lg R下对34组砂砾石土进行粒度分形,结果表明:北京地区砂砾石土粒度分布满足分形结构,其粒度分维区间值为2.4~2.6。根据统计的粒度分维区间,分析了颗粒级配随分形维数及最大粒径的变化规律,对土石混合体的力学性质及稳定性给出了新的认识。并将分形理论与室内试验颗粒级配分布结合,反演出土石混合体完整的颗粒级配分布。基于Monte-Carlo原理,结合分形理论,采用圆形或球体表征块石的形状,编写砂砾石地层模型生成程序,建立砂砾石地层模型,并针对隧道的开挖问题展开了数值分析。

The mechanical properties and deformation behavior of soil-rock mixture and underground structure in soil-rock mixture stratum are influenced by the particle size distribution. The mesoscopic structural characteristics of soil-rock mixture were analyzed based on the fractal geometry theory and the relationship between the quality-particle size grading curve and the fractal dimension was determined. The fractal analysis on grain-size of 34 groups of sand-gravel soil in coordinate system Tlg（M（r 〈R）/M）-lg R was conducted and the results indicated that the sand-gravel in Beijing has the characteristics of self-similarity. The range of the fractal dimension of sand-gravel in Beijing is 2.4–2.6. The variation of the quality-particle size grading curve with the fractal dimension and maximum grain size were analyzed,yielding some new findings regarding the mechanical behavior of soil-rock mixture. It is clear that the whole grading curve can be obtained by combining the fractal geometry theory and the laboratory test on grain size distribution. A program generating the model of sand-gravel stratum is compiled based on the Monte Carlo method using the sphere to represent the shape of stone. Then,3D numerical analysis on tunnel excavation were carried out.