Slope Stability (Kinematic Analysis)

Slope Stability tests where the geometry of a slope and of its discontinuities lets a block slide or topple. It checks four failure modes against the discontinuity sets you have measured — planar sliding, wedge sliding, flexural toppling and direct toppling — and reports each as the percentage of a set's planes, or of the lines where two sets' planes meet, that are critical.

It works two ways, with the same tests:

• On a mesh or point cloud, it fits the slope face around every point at a scale you choose and writes a map for each mode, plus Kinematic Mode, the dominant mode at every point. Use it to find where along an outcrop or a cutting each set becomes a hazard.
• On the stereonet, it analyses one slope face you set, draws its construction and critical zones over your, and lists the percentages group by group.

Kinematic screening, not a factor of safety

The analysis says where the geometry permits failure. It knows nothing of cohesion, water pressure, block size or persistence, and a critical percentage is not a probability of failure. Use it to decide where to look, then assess those places properly.

The tests, with the formulas, are in Slope Stability — Method.

The four failure modes

Mode	Tested on	Critical when
Planar sliding	Each plane of a set	The plane dips out of the face more steeply than the friction angle but less steeply than the face, so it daylights, and its dip direction is within the lateral limit of the face's (default 20°).
Wedge sliding	The lines where planes of two sets meet	The line plunges out of the face more steeply than the friction angle and daylights (Markland's test). The block may then slide along the line or, by Hocking's test, down one of its planes; either way it counts. No lateral limit.
Flexural toppling	Each plane of a set	The plane dips steeply into the face — its pole lies below the slip-limit plane, which dips at the face dip minus the friction angle — within the lateral limit of straight in (default 30°).
Direct toppling	The lines where planes of two sets meet	The line plunges into the slope within the lateral limit of straight in (default 20°), and is no further from vertical than the face dip, so the columns it bounds lean out of the face.

Wedge sliding and direct toppling need planes in at least two sets. Lines are only formed between planes of different sets, and two planes within 10° of parallel form no line.

Before you start: discontinuity sets

Both ways of running the analysis treat one folder as one set. Put the measured planes of each set in a folder of its own under Orientations in the Interpretation tree — by hand, or with Auto-cluster Selected Orientations on the Orientation branch, which sorts the selected measurements into set folders.

• Lineations are left out: they have no plane.
• The map analysis takes the planes directly in each folder you tick; planes in a subfolder belong to the subfolder, which is listed as a set of its own. Every orientation folder counts, including one made with the stereonet's Group Selected.
• The stereonet takes the plane interpretations it plots, one set per folder, as the maps do: two folders with the same name are two sets, and the key tells them apart by their paths. Planes that sit directly under Orientations form one set, Ungrouped.
• Auto-cluster copies. Auto-cluster copies the planes into its cluster folders and leaves the originals where they were. A folder that holds every plane of a folder below it — the one Auto-cluster read from — is not a set unless you choose it: the dialog leaves it unticked the first time, and the stereonet leaves its poles out and says how many in the key. As a set, its planes would meet copies of their own set's in lines that no two sets form, inflating wedge sliding and direct toppling.

Mapping a mesh or point cloud

Typical workflow

1. Sort the measured planes into one folder per set (above).
2. In the Data Tree, select one or more loaded meshes or point clouds, right-click, and choose Attributes & Analysis → Slope Stability (Kinematic)….
3. In the dialog, tick the folders to use as sets, check the Radius, the Friction angle and the modes to test, and press OK.
4. When the run finishes the object is coloured by Kinematic Mode, and the messages panel gives the share of the surface in each mode.
5. Look at the percentage layer of each mode to see how strongly a place is affected, and at Face Dip and Face Dip Direction to check the faces were fitted at a sensible scale.

Prerequisites

• A loaded triangulated mesh or point cloud. A tile of a tiled model cannot be analysed.
• At least one folder under Orientations with plane measurements in it. Without one the command stops with a warning telling you to make the set folders first.
• To tell a face from its back — an overhang from a slope facing the other way — the analysis needs to know which side of the surface is out of the rock. A mesh has this from its triangle winding. A point cloud has it only if it carries camera-oriented normals, the Nx, Ny and Nz layers of an SfM dense cloud; without them every face is taken to look upward.

The dialog

The line at the top names the object, its number of points and where the outward side of each face comes from. With several objects selected, one dialog is filled from the first and its options apply to all of them.

Discontinuity sets lists every folder under Orientations that holds planes, with its path and its number of planes. Each ticked folder is one set. The first time on an object every folder is ticked — which errs towards more hazard, not less — except one Auto-cluster copied its planes out of (above); after that, the folders you ticked last time. When a plane is in more than one ticked folder, the messages panel warns how many.

Slope face

Field	Description
Radius (model units)	The scale of the failures being assessed: the slope face at a point is fitted over the surface within this radius. The note beside it gives the point spacing and a suggestion, 2% of the model's diagonal but no less than twenty point spacings. A radius under four point spacings is raised to four.
Its normals point into the rock (flip them)	Reverse the outward side taken from the mesh winding or the point normals. Tick it for a mesh wound inside out — the messages panel warns when more than half of a mesh's faces look downward. Greyed when the object has no oriented normals.

Kinematic tests

Field	Description
Friction angle (deg)	Friction angle of the discontinuities, 0–89. The first time, it is the angle whose tangent is the project's Friction Coefficient (Project Properties): about 31° (30.96°) for the default 0.6.
Classify at (% critical)	A point is given a mode in Kinematic Mode only when that mode's percentage reaches this. Default 10.
Planar sliding · Lateral limit (deg)	Test planar sliding, with how far a sliding plane's dip direction may swing from the face's. Default 20.
Wedge sliding	Test wedge sliding on the lines where planes of two different sets meet.
Flexural toppling · Lateral limit (deg)	Test flexural toppling, with how far a toppling plane may swing from dipping straight into the face. Default 30.
Direct toppling · Lateral limit (deg)	Test direct toppling on the lines of two sets, with how far a line may swing from plunging straight into the slope. Default 20.

The lateral limits run from 0 to 90. At least one folder and one mode must be ticked.

Running and cancelling

The run shows as a slopestability progress bar: sampling the surface, fitting the slope faces, forming the intersections, then the kinematic tests. Stop it with the bar's terminate button or the tree's Cancel Operation on the object; with several objects selected, cancelling stops the rest too. A run fits the faces once and then evaluates each face orientation once, so its time depends on the model's area and the radius far more than on its number of points.

What it writes

Every run replaces these point (vertex) layers on the object:

Layer	Values
Face Dip	Dip of the fitted slope face, 0–180°. Above 90 the face overhangs.
Face Dip Direction	The direction the face looks, 0–360°, on a cyclic colour map so 359 and 1 look alike.
Planar Sliding	Percentage critical, 0–100, of the most critical set.
Wedge Sliding	Percentage of the lines of the most critical pair of sets that pass Markland's test, whether the block slides along the line or down one of its planes.
Flexural Toppling	Percentage critical of the most critical set.
Direct Toppling	Percentage critical of the lines of the most critical pair of sets.
Kinematic Mode	The dominant mode: 0 none (grey), 1 planar sliding (red), 2 wedge sliding (orange), 3 flexural toppling (purple), 4 direct toppling (blue).

• A percentage layer holds the highest percentage over the sets, or pairs of sets, so one critical set is not diluted by others that are not. The stereonet reports each set separately.
• Kinematic Mode takes the tested mode with the highest percentage (on a tie: planar, wedge, flexural, then direct), or none when that is below Classify at.
• A mode you did not tick has no layer: one left by an earlier run is removed.
• Points with too few neighbours within the radius for a face get no value in any layer.
• The percentage layers have a fixed 0–100 range, so colours compare between runs and objects.
• Kinematic Mode uses the Kinematic Failure Mode colour map, kept with the project's colour maps; change its colours there. A layer made before direct toppling existed keeps the older, four-colour Kinematic Mode map, which is left as it was, and the five-colour map starts from its colours, so any you chose carry over.

The messages panel ends the run with the share of the surface in each mode, the radius, the friction angle and the numbers of sets and planes. It adds a notice when points got no face, when faces could not be told from their backs, and when wedge sliding and direct toppling found no pair of sets to form lines from.

Remembered settings

The settings of the last run — radius, flip, friction angle, limits, modes, threshold and the folders used — are kept on the object and saved with the project, so the dialog reopens with them.

On the stereonet

The stereonet analyses one slope face: it draws the construction for the chosen failure mode, shades the critical zones, and lists the percentage of each set's planes — or of the lines where two sets' planes meet — that are critical.

Typical workflow

1. Open a Stereonet window on your orientation data.
2. In its property sheet, under Analysis Display Properties, tick Kinematic Analysis.
3. Pick the Failure Mode, and enter the Slope Dip and Slope Dip Direction of the face.
4. Check the Friction Angle — the first time it is taken from the project's friction coefficient — and the Lateral Limit.
5. Read the zones on the net and the percentages in the key.

Properties

Stereonet window only. These settings belong to the window and are not saved with the project.

Property	Description
Kinematic Analysis	Draw the analysis.
Failure Mode	Planar Sliding, Wedge Sliding, Flexural Toppling or Direct Toppling. The rows below follow the mode.
Slope Dip	Dip of the slope face, 0–180°; above 90 it overhangs. Default 60.
Slope Dip Direction	The direction the face looks, in degrees clockwise from north. Default 180.
Friction Angle	Friction angle of the discontinuities. It starts from the project's Friction Coefficient the first time the analysis is shown in the window, as the mesh analysis does (about 31° for 0.6).
Lateral Limit	Degrees either side of straight out (planar sliding) or straight in (toppling) that a plane or line may swing and still count: 20 for planar sliding, 30 for flexural toppling, 20 for direct toppling, each kept separately. Wedge sliding has none, and the row is not shown.

What is drawn

Mode	The net shows	Curves	Zones
Planar Sliding	Poles	Slope face, friction cone, daylight envelope, lateral limits	Red: poles of the planes critical for planar sliding.
Wedge Sliding	Lines of intersection	Slope face, friction cone, friction plane	Red: lines that slide (Markland's test). Yellow: lines that daylight between the slope face and the friction plane, where a wedge can slide only on one of its planes.
Flexural Toppling	Poles	Slope face, slip limit plane, lateral limits	Red: poles of the planes critical for flexural toppling.
Direct Toppling	Lines, and the poles of base planes	Slope face, friction cone, slope angle cone, lateral limits	Red: direct toppling (Dips' zones 1 and 2). Yellow: oblique toppling (zone 3).

The zones sit over the density contours and under the poles and planes; the curves are drawn over the planes, under the interpretation poles. Both work in equal-angle and equal-area.

Lines of intersection

In wedge sliding and direct toppling the zones apply to lines of intersection, but the net plots poles. Turn on Show Planes and read the zones where the great circles cross; the percentages in the key count the lines themselves.

The key

The kinematic key sits in the top-right strip, below the stereonet key when that is shown, and a long key continues in further columns to the right rather than off the bottom of the view. It names the mode, the slope face, the friction angle and the lateral limits, gives a swatch for every curve and zone drawn, and then a table:

Mode	Table
Planar Sliding, Flexural Toppling	Planes: the percentage Critical and the number of planes N, for All planes together and for each set.
Wedge Sliding	Lines: Wedge (passing Markland's test, as the map counts), 1 plane (blocks that slide on one of their planes rather than along the line: Hocking's cases among the Wedge lines, and lines in the secondary zone) and N, the number of pairs of planes that meet in a line, for All and for each pair of sets, A × B.
Direct Toppling	Lines: Direct and Oblique, and N; then Planes: Base, the share of each set's planes that can be the base of a toppling column.

A set's percentage is what the map layers hold for a face of this orientation when that set is the most critical one. All counts every plane, or every line between two sets, together. Long set names are shortened with an ellipsis in the middle, so they stay clear of the columns and names that start alike stay apart. When a folder's poles were left out as Auto-cluster's originals, the key ends with how many.

Exporting

Export → SVG writes the zones, the curves and the key with the rest of the net. The canvas widens to make room for the key and lengthens when the keys run below the net, so nothing is cropped; a stereonet figure in an analysis report is drawn the same way.

Choosing the parameters

• Radius. Match it to the failures you are assessing: a few metres for bench-scale blocks, tens of metres for a whole cutting. Too small a radius follows rubble and noise, and leaves points on sparse parts of the surface without a face; too large a radius smooths benches and gullies into the overall slope. Check Face Dip on the model before trusting the percentages.
• Friction angle. The friction angle of the discontinuities themselves. The default follows the project's friction coefficient, so the slip-tendency tools and this analysis start from the same value.
• Lateral limits. 20° for planar sliding and 30° for flexural toppling are the usual values (Hoek & Bray; Goodman & Bray). Widening a limit is the conservative choice.
• Classify at. Raise it to show only places where a large share of a set is critical.

Tips and troubleshooting

• "Slope stability needs discontinuity sets". No folder under Orientations holds planes. Put each set's planes in a folder of its own and run it again.
• Wedge Sliding and Direct Toppling are 0 everywhere. They need planes in two sets that are not parallel; the messages panel says so when there are none. On the stereonet the key says Lines need planes in two folders.
• A folder is unticked the first time, or the key says poles were left out. The folder holds every plane of a folder below it, as the one Auto-cluster read from does, so its planes are already in the clusters. Tick it only if it is a set in its own right.
• Overhangs read as slopes facing the other way. The faces could not be told from their backs. On a point cloud without Nx, Ny, Nz layers this is always so; analyse a mesh of the same surface instead. On a mesh, a surface that faces both ways within the radius does the same: use a smaller radius.
• More than half of a mesh's faces look downward. Its normals probably point into the rock. Run it again with Its normals point into the rock ticked.
• Many points have no value. The radius is too small for the point spacing or the gaps in the surface. Raise it.
• No zones are drawn on the stereonet. Remove Regional Dip is on: the zones are drawn for the orientations as measured, and the key asks you to turn it off.
• Part of the key is off the right of the window. A long key continues in further columns to the right. Widen the window or pan the view; the SVG export always holds the whole key.
• The 3D stereosphere shows no zones. The kinematic overlay is drawn on the 2D stereonet only.

See also

• Slope Stability — Method — the tests, the percentages, the face fitting and the construction, with the formulas and references.
• Stereonet User Guide — plotting, grouping and contouring the orientations the analysis reads.
• Orientation — the set folders and Auto-cluster Selected Orientations.
• Attributes — displaying, filtering and colouring the layers the analysis writes.