Vol 56, Núm. 1, 2003, p. 1-9

Estimación de densidades, distribuciones de longitud y longitud total de fracturas; un caso de estudio en la Falla de Los Planes, La Paz, B.C.S.

Ángel Francisco Nieto-Samaniego1,*, Susana A. Alaniz-Álvarez1, Gustavo Tolson2, Shunshan Xu1 y J. Antonio Pérez-Venzor3

1 Centro de Geociencias, Universidad Nacional Autónoma de México, Campus Juriquilla, Apdo. Postal 1-742, 76001 Querétaro, Qro., México.
2 Instituto de Geología, Universidad Nacional Autónoma de México, Apdo. Postal 70-296, 04510 México, D. F., México.
3 Departamento de Geología Marina, Universidad Autónoma de Baja California Sur, Apdo. Postal 19-B, La Paz, B.C.S., 23080, México.

* This email address is being protected from spambots. You need JavaScript enabled to view it.


In order to know if there is an upper limit for the amount of fractures contained in a rock mass, we studied fracture arrays in the Las Cruces Granite using photographs covering horizontal lengths of ca. 10, 1 y 0.1 m. We analyzed the following parameters: total length (L=ΣLi), intensity (I=ΣLi/A), density [D=(1/A)Σ(Li/2)2], the exponent of cumulative length (C), and the Box dimension (Cb).

Parameters L and I show a variation with exponent ca. 0.6 and ca. -0.4 respectively, indicating that scales 1 and 0.1 m were preferred for fracture formation. In addition, within each scale interval there is a large dispersion of I indicating different degrees of fracturing in the sampling sites.

The parameter D eliminates the effect of area; and its value is consistently below 3 over three orders of magnitude in fracture length. We interpret this behavior as indicative of the existence of an upper limit for fracture density. Cumulative length C and Box dimensions Cb show values below 1.87, also suggesting that there is a limiting value. We used our data for calculating the total fracture length in an image of ca. 10 m scale. The analysis shows that we need a multi-scalar treatment; using a single scale the result was underestimated by a factor of 31.

Keywords: fractals, fractures, fracture density, fracture length.