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Calculation of Rock Joint Spacing

Calculation of Rock Joint Spacing

Calculation of Rock Joint Spacing

(OP)
Hi. This is my first post. It's a bit long but please have a read if you know about the geometry of rock joints.

I am trying to calculate 'true' rock joint spacing based on apparent dip angles along a scanline. I have used the following equations to calculate the apparent dip of a joint on a scanline:
AD = ARCTAN(SIN(B)*TAN(D))
where: AD = Apparent Dip; B = angle between strike of joint and strike of scan line; D = True Dip

I have then tried to use the following equation to calculate true joint spacing:
S = AS*SIN(AD)
where: S = True Spacing; AS = Apparent Spacing; AD = Apparent Dip

This seems to work fine for some cases (e.g. scanline orientated perpendicular to strike of joint) but i have found it does not work for many cases, as shown by the following example:

Scanline orientated 0 deg (North).
2 parallel joints located 2 m apart on the scanline, both striking at 90 deg (dip direction 180 deg), both dipping 45 deg.


Based on this scenario and the above equations, the Apparent Dip is 45 deg and the True Spacing is 1.414 m, which is correct.

Now rotate the scanline so it is striking at 45 deg. The dip and dip direction of the 2 joints remain exactly the same.

The measured distance between the 2 joints along the new scanline should now be 2.828 m (2m/COS(45)). But using the above equations the apparent dip is now 35.26 deg which gives a true spacing of 1.633 m, different to the previous true spacing. Shouldn't the true spacing remain constant no matter how you orientate your scanline??

Sorry for the long-winded question, but can someone please explain what I have done wrong here? I'm sure there is probably a simple answer but this is really confusing me.

Thanks in advance,
Andrew

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