岩石断面分形插值稳定性的实验研究

岩石断裂表面是粗糙的 ,而断裂表面的粗糙度 ,对研究裂纹的萌发、扩展以及最后导致岩石断裂破坏过程中的本质规律起着十分重要的作用 因此 ,根据断裂表面上有限的数据点生成或拟合具有一定精度和适当粗糙度的曲线或曲面是研究断裂表面的一个重要课题 应用分形插值的方法能够得到预先给定的粗糙度 (分形维数 )的曲线 对线性分形插值在拟合岩石断面过程中的稳定性问题进行了讨论 ,所得到的结论说明当数据点 (插值结点 )存在微小误差时 ,得到的分形插值曲线也均只有相应的微小误差 从而得到了应用分形插值方法生成和预测断裂表面的可靠性保证

Experimental Research on Stability of Fractal Interpolationof Rock Fracture Surface

Rock fracture surface is rough. While roughness plays an important role in the study of the process of crack germination, crack development and the final rocks breakdown, it is an important research topic to produce or simulate fractal curves with certain precisions and appropriate roughness by finite data on fracture surface. By applying the method of fractal interpolation, the curves with a given roughness (fractal dimension) are obtained. The problem of linear fractal interpolation stability in the process of rock fracture surface simulation is further discussed. The obtained results reveal that if the datum (interpolation knots) has a small error, so does the corresponding fractal interpolation curve. Thus the reliability of producing or simulating fracture surface by applying the method of fractal interpolation is ensured.