Sjotroll
Geotechnical
- Jan 2, 2018
- 29
Hello, since there is no forum for rock mechanics I'm posting this question here, hopefully it's the right place.
The question is theoretical. So there is one thing bothering me with the block theory analysed through the stereographic projection method. For reference, I've been reading the book "Block Theory and its Application to Rock Engineering" (Goodman, R.E., Shi, G., 1985). My question is regarding joint blocks in three dimensions when more than two joint sets are repeated. As a reminder, when there is one repeated joint set then the stereographic projection of a joint pyramid is a circular arc segment of the plane's great circle. When two joint sets are repeated the projection of the joint pyramid must lie on the arc segment of both planes, meaning that it is the point of intersection of those 2 planes. Then, if 3 or more joint sets are repeated the joint pyramid will be the intersection of all 3 or more planes. Here it says that the only possible intersection is the origin of the reference sphere, which doesn't plot on the stereographic projection, since in the stereographic projection all planes pass through the origin. By this logic it says that all joint pyramids are empty, which means that they are all finite block which after an excavation will all become tapered and are thus unremovable from the rock mass (stable). But shouldn't it be theoretically possible for 3 or more nonparallel planes to share the same intersection? In that case the intersection would in fact be a point on the stereographic projection indicating a non-empty joint pyramid, which could very well become a potential key block after some excavation is carried out.
The question is theoretical. So there is one thing bothering me with the block theory analysed through the stereographic projection method. For reference, I've been reading the book "Block Theory and its Application to Rock Engineering" (Goodman, R.E., Shi, G., 1985). My question is regarding joint blocks in three dimensions when more than two joint sets are repeated. As a reminder, when there is one repeated joint set then the stereographic projection of a joint pyramid is a circular arc segment of the plane's great circle. When two joint sets are repeated the projection of the joint pyramid must lie on the arc segment of both planes, meaning that it is the point of intersection of those 2 planes. Then, if 3 or more joint sets are repeated the joint pyramid will be the intersection of all 3 or more planes. Here it says that the only possible intersection is the origin of the reference sphere, which doesn't plot on the stereographic projection, since in the stereographic projection all planes pass through the origin. By this logic it says that all joint pyramids are empty, which means that they are all finite block which after an excavation will all become tapered and are thus unremovable from the rock mass (stable). But shouldn't it be theoretically possible for 3 or more nonparallel planes to share the same intersection? In that case the intersection would in fact be a point on the stereographic projection indicating a non-empty joint pyramid, which could very well become a potential key block after some excavation is carried out.
