本文研究砂土顆粒形狀對摩擦角之影響，並引入顆粒形狀於砂土剪力強度函數中。依據碎形理論之碎形維度D 來量化砂土顆粒之形狀特徵，建立良好圓球狀至角狀所對應之碎形維度。試驗之四種砂土皆為均一級配，顆粒尺寸範圍介於75 ~ 2000 mm，碎形維度介於1.023 ~ 1.052。由直剪試驗於三種不同相對密度下求得砂土剪力強度，並經分析顯示於試驗範圍內砂土摩擦角與碎形維度呈上凹之雙曲線函數關係。 This paper aims to verify a relationship between the shape of sand grains and the friction angle. In fractal theory, the fractal dimension (D) can provide a measure of particle surface shape. The boxcovering method used squared grids of various sizes to cover the particles to calculate a fractal dimension. From the well rounded to angular sand grains were analyzed to obtain the fractal dimension D = 1.023 ~ 1.052 in this study. The samples are poorly graded sand within the granulometric band ranging from 75 to 2000 mm. The shear strength of sand was carried using direct shear tests to determine the values of the shear strength parameters with three relative densities. A hyperbolic relationship was found between the friction angle and fractal dimension in this study range.
