Kinematic Wedge Intersection Calculator
Calculates the trend and plunge of the line of intersection of two discontinuity planes — the key geometry for a wedge-failure kinematic check in rock slopes. For engineering geologists and geotechnical engineers assessing pit and cut-slope stability.
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Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter plane 1's dip and dip direction, then plane 2's dip and dip direction (decimal degrees; dip directions 0–360° clockwise from north).
- Read the intersection line's plunge (angle below horizontal) and trend (azimuth).
- Compare that line against your slope face for daylighting and against the joint friction angle to judge wedge feasibility.
How it works
Each plane is written as its downward pole (unit normal) on East–North–Up axes: N = (−sinδ·sinα, −sinδ·cosα, −cosδ), where δ is dip and α is dip direction (the pole trends opposite the dip and plunges 90°−δ).
The line common to both planes is the vector cross product L = N1 × N2. It is flipped if needed so it points downward, then its plunge = asin(|Lz|/|L|) and its trend = atan2(Lx, Ly) as an azimuth. Parallel or coincident planes give a zero-length cross product and no unique intersection, which the tool flags.
Worked example
Two joints each dipping 45°, toward 090° and 180°. The downward poles cross to a line pointing south-east and down: plunge 35.3° toward trend 135°. If the slope faces south-east and is steeper than 35°, this wedge can daylight and slide.
Common mistakes
- Entering strike instead of dip direction — this tool expects dip direction (the down-dip azimuth), 90° clockwise from strike.
- Forgetting the kinematic test: the intersection must daylight and plunge between the friction angle and the face angle for sliding to be feasible.
- Assuming the intersection trend equals the average of the two dip directions — it does not in general.
Frequently asked questions
What is the line of intersection used for?
In wedge (two-plane) rock-slope failure, the wedge slides along the line where the two discontinuities meet. Its trend and plunge decide whether the wedge can daylight and slide.
How do I know if the wedge can fail?
The intersection must plunge out of (daylight in) the face, plunge more steeply than the joint friction angle, and less steeply than the slope face angle. Combine this with a kinematic screen.
Dip direction or strike?
Dip direction — the compass azimuth the plane dips toward, 0–360° clockwise from north. It is 90° clockwise from the strike.
Why do parallel planes give an error?
Two parallel (or identical) planes never meet in a unique line, so their normals are colinear and the cross product is zero — there is no wedge intersection.
Related tools
- Wedge Failure Kinematic Screen
- Plane Failure Kinematic Screen
- Berm Width Calculator
- RQD Calculator
- Dip & Dip Direction to Trend & Plunge Converter
- Discontinuity Spacing Calculator
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Tip: Enter any known values to calculate the remaining results.
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