The basic idea early stated in the Swedish building codes (AMA) is that the boreholes should be directed as perpendicular to the water bearing fractures as possible.
In general, the grouting design with respect to the fan layout results in a fan having a certain length, inclination outside the tunnel contour, a predetermined spacing between boreholes and specified number of rounds per fan. Knowing the fracture orientation and the flow dimensionality one can optimize the layout of the fan to have a best “hit-rate” of the fractures at hand.
The “hit-rate” in this article is defined as the ratio between the area that if formed at the intersection between the borehole and a fracture and the borehole area itself.
This paper brings up a theoretical approach how to assess the best “hit-rate” together with a practical case-scenarios where boreholes has been added in the areas where the systematic fan layout has a very low “hit-rate”.
If the borehole is perpendicular the shape of the intersection will be circular, equivalent to the cross section of the bore hole. This would be referred to as the best “hit-rate” giving that the ratio between the borehole area and the circular area of intersection 1, a “hit-rate” of 100 %. If the borehole is not perpendicular to the fracture, the boundary of intersection would instead be elliptic, resulting in a larger area of intersection. The worst “hit-rate” would occur when the borehole is parallel to the fracture and the “hit-rate” would asymptote towards 0 %.
In the practical case showcases a scenario where a minor change of drill direction or borehole layout can be carried out to improve the “hit-rate” without compromising the simplicity of the grouting fan this is an option that should be considered, especially for areas of the tunnel where the prognosed “hit-rate” is low.