Kinematic Analysis of Rock Slopes — Planar, Wedge and Toppling Failure

The four modes, and what each one is looking for

Planar sliding is a block sliding out on a single plane. It needs three things at once, and the figure draws all three: the plane must daylight in the face — its dip vector has to emerge from the cut, which means it dips out of the face and more gently than the face does; it must be steeper than the friction angle, or it will not move; and it must strike close enough to parallel with the face, conventionally within 20°, that the block is not held at its ends. Tested against poles, and the critical zone is the crescent inside the daylight envelope, outside the friction cone, between the lateral limits.

Wedge sliding is a block sliding out along the line of intersection of two planes. This is the mode that catches people out, because both joint sets can pass the planar screen individually and their intersection still walk out of the face. It also has no lateral limits: the second plane gives the wedge an extra degree of freedom, so it can slide obliquely across the whole face. The critical zone is the crescent between the slope great circle and the friction cone, and every pairwise intersection in your table is computed, not only those between named sets.

Flexural toppling is a stack of steep, thin layers dipping into the face and bending forward like a row of books. It cannot happen unless the layers can shear past one another, which is the Goodman and Bray interlayer-slip condition: the layers must dip more steeply than 90° + φ − ψf. On the net that boundary is the slip limit, a great circle at (slope dip − friction angle) in the slope dip direction, and critical poles sit beyond it, out towards the primitive, within the lateral limits. Note that no friction cone appears in this mode at all — the friction angle enters only through where the slip limit sits.

Direct toppling is columns bounded by two steep sets, tipping forward over a shallow base plane. It is tested on intersections, like wedge sliding, but looking for the opposite thing: intersections that lean into the slope steeply enough to form columns. It also reports the shallow planes that could act as base or release surfaces — the poles falling inside the friction cone on the out-of-slope half of the net.

The friction angle is the assumption to argue about

Everything else on the figure is a measurement. The friction angle is a judgement, and it moves every boundary on the sheet, which is why it is printed in the footer rather than buried in a settings panel.

It is the friction angle of the discontinuity surface — not of the intact rock, and not a Mohr-Coulomb φ from a triaxial test. For a clean, planar, unweathered joint in a strong rock, 30–35° is the usual screening value. A rough, undulating surface can mobilise considerably more once the dilation implied by its roughness is counted, which is what the Barton JRC–JCS relation is for. A clay-infilled, chlorite-coated or slickensided surface can be under 20°, and if you have one of those in a set that daylights, it is the whole answer.

Screening at one value across all sets is standard practice and it is also the method’s loosest joint. If your sets genuinely differ — a smooth bedding parting and a rough tectonic joint are not the same surface — run the screen twice and quote both. It costs one number here, and it is a far more honest figure than a single run at an averaged value.

What the percentages do and do not mean

The counts under each net are the deliverable: how many of your poles, or of your intersections, fall in the critical zone, as a fraction of the total and broken down by set — or, for the intersection modes, by set pair, which is what tells you *which two sets* are the problem. In the sample below, J2 and J3 are individually blameless and every one of their nine intersections is critical. That line is the figure.

What the percentage is not is a probability of failure. It is a proportion of your sample, and your sample is a scanline or a window on one face on one day. It says nothing about persistence — a critical joint 300 mm long does not release a bench — nothing about spacing or block size, nothing about water, and nothing about whether the measured population is representative of the ground behind the face. Two sites with identical percentages can be in entirely different trouble.

It also cannot see the modes it is not looking for. Circular failure through a weak or heavily fractured rock mass has no controlling discontinuity and therefore no kinematic signature; a slope can score zero here and still be at risk. The screen is a filter, not a verdict.

Who this is for

Engineering geologists and geotechnical engineers designing or reviewing rock cuts — highway and rail cuttings, quarry and open-pit benches, portal faces, spillway and penstock excavations, dam abutments. Mining geotechnical staff running bench-scale stability from face mapping or televiewer data. And anyone reviewing somebody else’s design who wants to reproduce their Dips output from the same table and see whether it comes out the same.

It is not a slope-design suite and does not pretend to be one. There is no limit-equilibrium calculation, no factor of safety, no support design, no probabilistic analysis, no bench-berm optimisation. What it does is the part everybody needs first: take the orientations you measured and produce one correct, printable, properly cited screening sheet, with no installation, no licence server and nothing uploaded.

Honest limits

One planar cut face per figure, given as a dip direction and a dip — no benched profiles, no curved highwalls, no per-bench face angles. One friction angle for every discontinuity in the table. Every pairwise intersection is computed, up to 220 planes; past that the pairing is capped and the figure says so on its face. Only plane rows are analysed; lineation rows in the same table are noted and ignored rather than rejected.

The constructions follow Goodman (1989), Wyllie and Mah (2004) and the drawing conventions Rocscience document for Dips, with direct toppling after Hudson and Harrison (1997). Two things about direct toppling are worth stating plainly, because the source states them plainly: its friction cone is not a stability criterion for the intersections but a capture area for the oblique zone, which Rocscience themselves describe as somewhat arbitrary; and the base-plane count here covers the non-sliding release planes only, since anything outside the friction cone is already reported by the planar-sliding panel.

Everything runs in this browser tab. No face mapping is uploaded anywhere, which for pre-tender pit data is usually the whole question.

Common questions

The page says Pro — what can I actually do for free?

Everything except enter your own data. The figure below is the finished tool running live on a real 19-plane face mapping: change the slope orientation, the friction angle and the lateral limits and watch every zone and every count move, switch between the 2 × 2 panel and a single large net, swap the projection, turn the construction lines off, add a title, and export as SVG or PNG (watermarked, like every free export on this site). What Pro buys is the right to replace the sample measurements with yours. There is no trial timer and no account, and the demo does not expire.

Which projection should I use?

Either — the answer does not change. Every construction is defined on the reference sphere and every classification is made there, so a measurement is critical or not regardless of which flat net it is drawn on, and the test suite asserts exactly that. The default here is equal-angle (Wulff), which is also what Rocscience recommend for kinematic work, because a cone about any axis stays a true circle on it and the friction cones therefore keep their shape wherever they sit. Equal-area (Schmidt) is one click away and is the right choice if you are also contouring pole density on the same dataset. Just never mix the two in one figure.

Do you accept dip direction instead of strike?

Yes, and it is the same toggle the stereonet uses. A column actually named "dip direction" is always read as one, whatever the setting says. That is deliberate: a table which plots on the stereonet drops onto this page unchanged — same columns, same keys, same parser — so a face mapping does not have to be retyped to be screened.

Why does wedge sliding have no lateral limits when planar sliding does?

Because a wedge has somewhere else to go. A single sliding plane is held at its lateral edges unless it strikes nearly parallel to the face, which is what the ±20° limits express. A wedge is bounded by two planes and slides along their line of intersection, in whatever direction that line happens to point, so restricting it to a narrow sector would discard real failures. This is Rocscience’s stated reasoning too, and it is the single most common thing to get wrong when implementing the screen by hand.

What is the secondary zone on the wedge plot?

Intersections lying between the slope great circle and a great circle dipping at the friction angle. They plunge less steeply than φ, so the wedge cannot slide on both of its planes at once — but one of those two planes may still be able to slide on its own. They are counted and shaded separately rather than folded into the critical total, because they are a different mechanism and usually a different remedy.

Does a zero count mean the slope is safe?

No. It means no measured discontinuity is oriented so that one of these four modes could occur. It says nothing about circular failure through a weak rock mass, ravelling, rockfall from small blocks, weathering-driven degradation, water pressure in a tension crack, or a discontinuity that exists in the face and did not make it into your table. Kinematic screening is a necessary check and never a sufficient one, which is what the note on the figure means by verifying against project standards.

Can I map at the face on a phone and finish the figure in the office?

Yes. Enter the readings on whichever device is with you, then use "Send to device" to turn the table into a QR code and a plain link; scan it from the desktop and the same mapping opens there with your slope orientation and friction angle already applied. The orientations ride in the fragment of the URL — the part after the "#", which browsers never transmit to any server — so a face mapping over a client’s licence area does not pass through anybody else’s system on the way to your report. Creating the link needs Pro; opening one does not.