Predicting Fracture Characteristics Using Three-Dimensional Modelling

Judy Ehlen
U.S.A. Topographic Engineering Center, CETEC-TD-TI, 7701 Telegraph Road, Alexandria, VA 22315-3864

Abstract
This paper describes a method for quantitatively predicting fracture spacing, orientation, density, and length in the subsurface or other inaccessible areas using a variety of computer-based procedures to analyse a combination of field data and data derived from remotely-sensed imagery. The study uses fracture data collected at five potential analogue sites in deeply weathered granites. Lineations were delineated on remotely sensed imagery over each study area and over the areas for which predictions were to be made. The procedure involves statistical comparisons among these data sets as well as with simulated results from three-dimensional modelling. Procedures used for data analysis include (1) georectifying (or rubber sheeting) and digitizing lineations using a GIS; (2) three-dimensional discrete feature modelling of the field and lineation data; (3) fractal analysis of fracture spacings measured in the field; and (4) regression analysis of field and simulated data to make the predictions.

The field data, which consisted of measurements of joint spacing, joint orientation and joint length, acted as controls on the simulated data from three-dimensional modeling, the selection of analogue areas, and, ultimately, the predictions. Rose diagrams showing joint strikes and frequency histograms of joint length and joint spacing were plotted for each of the five study areas. Statistical analysis of these data played an important role in selecting a reasonable analogue for the unknown areas.

The lineations were delineated manually on aerial photography and then digitised or were digitised directly from digital orthographic SPOT imagery. Digitising was done using ARC/INFO so that the data would be spatially correct and the results would be real measurements. Output from ARC/INFO consisted of the xy co-ordinates for each lineation, its length and its strike. Strikes were corrected for magnetic declination and rounded to the nearest 5o so that they would compare directly with the field data. Rose diagrams showing lineation strikes and frequency histograms of lineation length were plotted and compared to each other and to the field data. Possible analogues were identified at this stage by comparing lineation strikes from the imagery of the study sites with those from imagery of the unknown areas. Analogue selection was also highly dependent on visual comparison and statistical analysis of lineation patterns from area to area.

Three-dimensional (3-D) modeling of the field data and lineations was accomplished using FracMan (a software package for discrete feature 3-D modelling developed by Golder Associates). Fracture plunge and trend, mean radius and standard deviation, fracture intensity and fracture termination percent comprised the input. For the field data, these values were all calculated directly, but for the two-dimensional lineation overlays, they were obtained from statistical models. Sampling of the three-dimensional patterns generated by FracMan was done using simulated boreholes and trace planes. Construction of vertical trace planes through the models allowed joint lengths to be determined and also allowed the simulated data to be matched to the data from vertical outcrop faces. Horizontal trace planes through models of the field data allowed matching to the lineation data. Simulated joint spacings were determined from the boreholes. The simulated data were compared to the field data, and the modeling process was repeated until the match between field data and the simulations was reasonably close. Block size analysis was also done.

Fractal analysis of some of the joint spacings measured in the field was also done. identical. This was done manually using the box counting method. It was expected that fractal dimension would provide a useful way to compare and discriminate between the image and field data, as well as assisting in analogue selection, but the fractal dimensions for the lineation patterns and the horizontal trace planes were virtually identical, and could thus not perform this function.

Finally, using regression analysis of the field and image data from the analogue site and both small and large-scale image data over the unknown areas, predictions of the means, standard deviations and distributions were made for joint length, joint spacing, joint intensity, and rock block sizes.

Although this combination of procedures has been applied as described, the results of the predictions have not as yet been verified in the field. Comparisons with the field data indicate that all predictions are within the standard deviations of the field data, although the results are not as close to field measurements as they could be. However, in situations where it is impossible to gain access to areas where detailed fracture data are required, and these procedures allow realistic predictions to be made.