在微觀顆粒力學中，顆粒間之接觸點數目為一重要的參數，一般認為其值與整體孔隙率有關，但鑑於對同一孔隙率的顆粒性土壤可能有多種不同的排列方式，接觸點數目將為之不同，僅以孔隙率此一平均值恐無法完全反映這一事實。本文引用碎形理論中的方格維度及叢集維度，分別來描述圓形土粒之大小級配分佈與叢聚的程度，並探討其與孔隙率之關聯性，進而瞭解土粒間之接觸行為。研究結果顯示：均勻級配土壤之顆粒填充較疏鬆，均勻係數較小，反應級配分佈的方格維度亦較小(0~1.5)；而兼具大中小粒徑之優良級配時，均勻係數較大方格維度亦趨近於3。具相同孔隙率之土壤可能有不同之排列方式，故叢集維度亦不同，但孔隙率並不能描述此一現象，而叢集維度確能反映此一事實。顆粒越多即n越小，叢集維度未必愈大，接觸點也未必愈多。土壤孔隙率n低於0.4時，才有較大量的接觸點。 In the field of micro-mechanics, the total number of particle contacts is a key factor. There is a relation between the co-ordination number and its corresponding porosity. However, a soil mass with a specified porosity could have several packing styles of particles and thus the contact number is different. This paper employs the box dimension and cluster dimension of the fractal theory to correlate the fractal-packing characteristic and soil porosity. These two parameters will be helpful to understand the contact behavior between soil particles. It is found that the box dimension of the uniform-graded soil is smaller than the well-graded soil. The particle packing may be different for the soils with the same porosity. The porosity cannot response this characteristic. However, the cluster dimension is capable of describing this difference. The group of soil grains will occur a great number of point contacts at the porosity being smaller than 0.4.
