This study focuses on estimating fracture size and aspect ratio of subsurface fractures in sedimentary rocks. Fractures in sedimentary rock are typically elongated in one direction and their shapes can be considered rectangles. The study shows how information about sizes and aspect ratios of rectangular fractures can be discerned from study of borehole-fracture (or core-fracture) intersections. Based on the possible geometric relations between a fracture and a sampling cylinder, six types of intersection: complete, long-edge, short-edge, corner, end, and pierced, are defined. The probabilities of occurrence of these different intersection types are related to the sizes and aspect ratios of fractures. The sizes and aspect ratios of fractures are then estimated directly from the observed counts of different types of intersection in a borehole or rock core.


Fracture information is essential in rock engineering and engineering geology as well as in hydrogeology. Tunnels and boreholes often provide the main sources of data from which fractures are characterized. However, those data are still underutilized [1, 2, 3, 4, 5, 6, 7, 8, and 9]. Recently researchers and engineers have been working on developing new techniques to obtain more information about fractures through borehole and tunnel data [3, 4, 6, 7, and 10]. In this paper we give a method to estimate the size and shape of fractures in sedimentary rocks using borehole data.

Since fractures in sedimentary rock are commonly elongated in one direction, rectangles are considered to be good assumptions for their shape. For this study we assume a single set of parallel rectangular fractures with constant width W and length L = W, and with long axes aligned in the same direction. This fracture set is intersected by a borehole of diameter D, oriented normal to the fractures (Fig. 1).

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Based on geometric relations (Fig. 2) between a rectangular fracture and a sampling cylinder, six types of intersection are defined. They are:

  • Type A Complete intersection

  • Type B1 Long-edge intersection

  • Type B2 Short-edge intersection

  • Type B3 Corner intersection

  • Type B4 End intersection

  • Type C Pierced.

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Because fracture locations at depth are unknown, the boring locations can be assumed independent of specific fracture locations [3, 4]. Independence holds regardless of any grid or other pattern used to choose locations for borings. Probabilities of occurrence of the different intersection types, assuming independence between the borehole and the fracture population and assuming, in this case, boreholes perpendicular to fractures, depend only on the sizes and aspect ratios of fractures and the size of the borehole.

We consider two cases, W>D and W<D, L>D, which we discuss below.

2.1 Case 1: W > D

Fig. 3 shows the locus of the center of borehole corresponding to each intersection type (in the case of W>D).

Let ¿B1, ¿B2, ¿B3, ¿B4, ¿A, ¿C denote the areas of possible regions for the borehole center corresponding to each intersection type. The equations below relate these areas to the length and width of the fracture and diameter of the borehole.

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