In order to calculate the volume of an in situ block intersected by three joint sets, besides spacings between joints, we also need the intersection angle between joint sets. How can we calculate the intersection angle between joint sets using dip and dip direction data? Can you recommend any methods, software, or papers related to this subject?
Dear Mehmet,
You can indicate three point as pols of the three joint planes on the countor diagram of the joint sets in the Dips software environment. Then, you can determine the angles between the three pols. These three angles are intersection angles between the joint sets.
Best wishes
Hello,
details for graphical procedure are available in Chapter 3: Graphical presentation of geological data of textbook Rock Slope Engineering, by Hoek and Bray, IMM1981, or Ch.2.5 Stereographic analysis of structural geology in the revised 4th edition, SponPress 2005. Otherwise in other textbooks (e.g. Priest, Hemispherical Projection Methods in Rock Mechanics).
Hope this can help
Best Regards
Dear Davood and Claudio,
The procedure you suggested is to calculate the line of intersection between two joints. We can define a line of intersection between two joints with a trend (dip direction) and plunge (dip angle). However, I am asking about the intersection angles between joint sets, not the line of intersection angle.
Dear Mehmet,
But you can determine the angle between two joint sets from this method. You can also determine dip and dip direction of the intersection plane.
Best
Teta is the angle between the two joint set. You can determine teta, and dip and dip direction of the intersection plane. Please see the attach shematic paint.
Best wishes
Hello,
in the mentioned chapters and in the above answer there are the procedures well described. The angles between two crossing planes representing joint sets are determined by referring to the normals of the planes. Angles are measured on the great circle containing the pole to the line of intersection and the poles of the two joint planes.
Regards
Dear Mehmet,
There are several ways to calculate the intersection angle between joint sets, of course, hand-calculation of them. you can use a spreadsheet program, convex optimization, or Heliot algorithm.
Please kindly see these papers:
Article A new algorithm for contact detection between convex polygon...
Article Numerical modeling of discontinuous rock slopes utilizing th...
Article Spacing and block volume estimation in discontinuous rock ma...
Best regards,
Dear Mohammad, if you have, can you share the spreadsheet program to calculate intersection angle with me?
Best regards,
Dear Followers of the Question,
I asked my question to ChatGPT. Here is the answer:
To calculate the intersection angle between two joint sets using dip and dip direction data, we can use the following formula:
cos(θ) = cos(α1)*cos(α2) + sin(α1)*sin(α2)*cos(δ1-δ2)
where:
- θ is the intersection angle between the two joint sets
- α1 and α2 are the dips of the two joint sets
- δ1 and δ2 are the dip directions of the two joint sets
Once we have calculated the value of cos(θ), we can use the inverse cosine function (usually denoted as cos^-1 or acos) to obtain the value of θ.
Note that dip direction data is typically given in degrees clockwise from north, so we may need to convert this to azimuth (degrees clockwise from east) before using the formula. This can be done using the following formula:
azimuth = (450 - δ) mod 360
where:
- δ is the dip direction in degrees clockwise from north
- the "mod 360" ensures that the value of azimuth is always between 0 and 360 degrees.
The intersection angle between two joint sets can be calculated using the following steps:
The angle between the line and the strike of the first joint set is the intersection angle between the two joint sets.
Here are some additional details about each step:
Strike = 90 - dip direction Dip = dip
2. A stereonet is a two-dimensional representation of a three-dimensional sphere. It is used to plot poles to planes.
3. To plot the poles to each joint set on the stereonet, use the following steps: Find the strike and dip of the joint set. Convert the strike and dip to a spherical coordinate system. Plot the point on the stereo net corresponding to the spherical coordinate.
4. To draw a line between the poles of the two joint sets, use the following steps: Find the poles of the two joint sets. Draw a line between the two poles.
5. To measure the angle between the line and the strike of the first joint set, use the following steps: Find the strike of the first joint set. Measure the angle between the line and the strike of the first joint set.
The angle between the line and the strike of the first joint set is the intersection angle between the two joint sets.
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