Engineering Theory

Orientation Measurements

Dip is the maximum angle a plane makes below horizontal. Dip direction is the azimuth of that maximum downward slope, measured clockwise from north. JStereonet expects dip in degrees from 0 to 90 and dip direction in degrees from 0 to 360.

A plane can be represented by:

• its great circle, which is the trace of the plane on the stereonet sphere
• its pole, which is the vector normal to the plane
• its dip vector, which points down the line of maximum dip

The app uses poles and dip vectors for different operations. Pole plots are compact and useful for set recognition. Great circles make plane geometry and intersections easier to inspect.

Lower-Hemisphere Equal-Angle Stereonet

The stereonet uses a lower-hemisphere equal-angle projection. Orientations are projected onto a circular net so angular relationships are preserved. This is useful for kinematic checks because sliding and toppling criteria depend strongly on angular relationships between discontinuities, slope or face orientation, and friction angle.

Equal-angle projection preserves angles but not areas. Density contours should therefore be interpreted as visual concentration estimates rather than direct area-weighted probabilities.

Plane Intersections

The intersection of two discontinuity planes defines a line. Wedge and direct-toppling checks use those intersection lines to test whether a block can move relative to a slope face.

When intersections are enabled, the app plots sampled intersection points. Very large datasets may cap the number of displayed intersections for rendering performance while still reporting total counts.

Joint Sets and Fisher Statistics

A joint set is a group of similarly oriented discontinuities. The app can use set labels entered by the user, manual stereonet assignment, drawn assignment windows, or fuzzy auto-clustering.

Set summaries include:

• n: number of planes in the set
• mean dip and mean dip direction
• Fisher K, a concentration indicator for grouped orientation vectors

Higher Fisher K generally means tighter clustering. Low values indicate a broader scatter of orientations.

Ordinary sets use a lower-hemisphere vector sum. For a set assigned with a cross-equator window, opposite-side poles in the window are reversed into its common hemisphere before summation. Fisher K uses this same corrected resultant, so a steep cluster split across the perimeter is not mistaken for a widely scattered set. The resulting mean is reported on the lower hemisphere. Global means and proposed automatic-cluster summaries retain their own ordinary vector convention.

Density Contours

Density contours estimate orientation concentration using Fisher kernel density over selected vectors. The vector source can be pole vectors or dip vectors.

The Fisher kappa value controls smoothing:

• lower kappa gives broader, smoother density regions
• higher kappa gives tighter, more localized density regions
• auto mode estimates a representative value from the current data

Density contours help identify orientation clusters, but they do not by themselves define engineering design domains.

Kinematic Feasibility

Kinematic analysis tests whether discontinuity orientations satisfy geometric conditions for potential movement. The app reports counts and percentages of planes or plane intersections that satisfy those geometric criteria.

These outputs do not include:

• shear strength variability
• persistence, roughness, water pressure, or infill strength
• block size or driving/resisting forces
• reinforcement or support
• stress redistribution
• probability of occurrence

Use the results as screening indicators and confirm critical cases with appropriate engineering analysis.