中文摘要：

根据分形理论建立了岩土体在二维和三维空间分维数之间的联系,从而可以通过二维数字图像技术估算岩土体在三维空间的分维数.证明了岩土体的颗粒分布分维数与孔隙分布分维数在有限尺度范围内能同时存在,并给出了两者之间的关系式.黏性土的微观结构实验数据表明：通过此关系式可有效估算孔隙分布分维数.最后提出了一种基于孔隙面积分布的颗粒分布分维数的计算方法,以Sierpinski地毯模型为实例证明了该方法是合理的.

英文摘要：

Based on the fractal theory, a new method is presented to estimate the fractal dimensions in 3D space from the 2D structures of rocks and soils, thus the technique of digital image in 2D can be easily applied to obtain the fraetal dimensions in 3D space. This study shows that the fractal dimension of grain area distribution and the fractal dimension of pore area distribution can exist simultaneously on a finite scale. The expression for the relationship between the two fractal dimensions was established. The experimental results of the microstrueture of clay indicate that the expression is valid for estimating the fractal dimension of pore area distribution. At last, a new means was developed to calculate the fractal dimension of grain area distribution through the pore area distribution of rocks and soils, and its rationality has been verified by Sierpinski carpet model.