Kinematic screening
Planar, wedge and toppling screens compare discontinuity orientations with the slope face, friction angle and the selected directional limits. Wedge intersections are derived from plane normals. A critical orientation identifies a geometrically possible mechanism; it does not establish a connected or persistent block, available shear resistance, or a probability of failure.
Orientation percentages describe the included observations or intersections. Pair selection, filters and joint-set means change that population. Use a common north reference before comparing directions.
All included measurements and all hypothetical pairs are the opening default; no set assignments are required. Same-outcrop pairing is an optional restriction. Same recorded survey additionally requires matching explicit project, outcrop and survey IDs. Same geological domain and slope reach requires matching explicit project and domain IDs and a matching nonempty reach. Unknown assignments do not qualify for these stricter scopes. All-pairs and different-set pairing are explicit hypothetical combinations. Scope exclusions, parallel pairs and tested intersections remain separate; context agreement is not evidence of a physical connection.
Stereonet conventions
Field, desktop and kinematic plots open on a lower-hemisphere equal-angle (Wulff) stereonet with a 10° graticule. Equal area (Schmidt) remains an explicit display option. A pole is perpendicular to its plane: shallow planes plot near the center, steep planes near the rim. The pole trend points opposite the plane’s dip direction. Great circles represent planes; points can also represent specified lines or plane intersections.
For a line with trend T and downward plunge P, normalized radius is tan((90°−P)/2) for equal angle and √2 sin((90°−P)/2) for equal area. East/north screen coordinates are r sin T and r cos T. Equal angle preserves local angular relationships; equal area preserves spherical area for displaying populations. Changing the projection changes the drawing and its inverse cursor query, not the underlying directions, axial means, clustering or kinematic classifications. Saved views and exported figures identify the selected projection; old views without a projection retain their original equal-area convention when explicitly loaded. Density is computed on the sphere, with its counting or smoothing method and settings shown beside the plot.
Orientation statistics and interpreted sets
Plane normals are axial: opposite normals describe the same plane. Mean planes use this symmetry, avoiding ordinary arithmetic averaging of azimuths. Clustering is an orientation-based aid to interpretation; it does not establish geologic continuity.
Fisher concentration and approximate confidence/variability cones are withheld for small, broad, elongated, ambiguous or mixed-reference populations. The approximate mean cone uses Fisher’s finite-sample concentrated-population expression: cos(α95) = 1 − (n − R)/R × (20^(1/(n − 1)) − 1), where R is the sign-aligned resultant. The variability cone uses estimated concentration K and describes individual scatter. Neither is a site-specific guarantee of coverage. Repeated measurements of one surface are not independent samples. Confidence in a mean direction and the spread of individual readings describe different quantities.
Fisher, R. (1953). Dispersion on a Sphere. Proceedings of the Royal Society A, 217(1130), 295–305.
Survey sampling and line RQD
Outcrop survey records distinguish reconnaissance, selected critical joints, scanlines and windows. Record dimensions in feet, orientation and north reference, completeness, minimum observable trace and visibility limits. Complete scanlines require length and line direction/plunge; complete windows require width, height and exposure orientation. These records describe collection conditions; they do not automatically apply sampling corrections or calculate RQD.
Record visible trace length separately from hidden persistence, including both endpoint descriptions and whether the length is measured, estimated or a lower bound. A trace hidden by cover or continuing beyond the exposure must retain a lower-bound basis. Geological domains are explicit interpretations; preserve their boundary and correlation basis.
A traverse intersects different joint orientations at different rates. Reciprocal intersection-angle weighting can compensate for this directional bias, but becomes unstable near parallel orientations. Record the actual traverse geometry and review the minimum-angle cap. Weights do not create additional independent observations.
Geometric line RQD sums intact segments longer than the stated threshold and divides by interval length. Exact-threshold segments are excluded. This requires a complete interval and appropriate natural-break interpretation; it is not measured core RQD when recovery or break origin is unknown.
Terzaghi, R.D. (1965). Sources of Error in Joint Surveys. Géotechnique, 15(3), 287–304.
Rock mass rating and observed GSI
RMR combines ratings for intact strength, RQD, discontinuity spacing, discontinuity condition and groundwater, with an orientation adjustment where applicable. Preserve the individual observations and rating selections; a total alone loses the evidence behind the classification. Missing selections remain unassessed.
GSI is an observed description of rock-mass structure and discontinuity surface condition. The app retains the selected field value and chart guidance; it does not calculate an observed GSI from the other inputs.
Bieniawski, Z.T. (1989). Engineering Rock Mass Classifications. Wiley. Marinos, P. & Hoek, E. (2000). GSI: A geologically friendly tool for rock mass strength estimation. GeoEng2000 / ISRM International Symposium, Melbourne, paper ISRM-IS-2000-035. The in-app UCS, intact-constant and GSI charts retain their author attribution.
Barton–Bandis field characterization
Record joint roughness, joint-wall compressive strength, residual friction, scale, weathering, infill and the applicable stress range. Joint-wall strength is distinct from the intact rock specimen’s UCS. Roughness and strength must represent the joint surface and scale being analyzed.
The shear envelope uses effective normal stress: τ = σ′n tan[JRC log10(JCS / σ′n) + φr]. JCS and normal stress must use the same units. The displayed domain checks and scaling assumptions remain part of the calculation.
Barton, N. & Choubey, V. (1977). The shear strength of rock joints in theory and practice. Rock Mechanics, 10, 1–54. Scale effects follow the Barton–Bandis framework described in the app’s field guidance.
Discontinuity shear strength
Select the contact law from the available evidence. Mohr–Coulomb uses τ = c + σ′n tan φ, normally with a defensible linear fit to joint shear data over the expected stress range. Barton–Bandis uses field-scale JRC, joint-wall JCS and residual friction for an applicable unfilled rough joint; infill-controlled shear requires a separate strength assessment. The power curve is an empirical fit whose coefficients and stress range must be documented. Neither mathematical input bounds nor an outcrop average establish a validated material law.
The recommended default is no additional waviness (0°). This does not mean the joint is physically smooth. Keep zero when the test envelope or selected JRC already represents the roughness at the relevant scale and shear direction. Record the source, scale, direction, effective normal stress range and peak/residual basis in the case evidence notes.
The advanced waviness option preserves the app’s existing additive convention: Δτ = σ′n tan(w), added to the selected base law. It is not the Patton-style angle addition tan(φ + w). The USBR discussion of large-scale undulations uses angle addition; it does not validate the app’s separate additive term. A mapped undulation angle alone does not establish additional shear resistance. Nonzero values require a separate documented basis and a comparison with 0°. Existing saved or imported values are retained; choosing “No additional waviness” explicitly removes the term.
Only retained compressive contacts contribute contact friction and cohesion. A rock-mass strength interpretation or intact UCS must not be substituted for discontinuity friction and cohesion.
USBR Engineering Geology Field Manual, Chapter 5, pp. 108–109: roughness, waviness and angle addition. Barton & Choubey (1977), The shear strength of rock joints in theory and practice: joint shear-strength evidence and scale effects. Barton–Bandis equations and domain limits.
Generalized Hoek–Brown rock-mass interpretation
Inputs are intact UCS, intact-rock constant mi, observed GSI and disturbance factor D, with a stated applicable rock-mass domain. Selected outcrop parameters use the explicitly reported aggregation; manual overrides retain their stated basis.
mb = mi exp[(GSI − 100)/(28 − 14D)]; s = exp[(GSI − 100)/(9 − 3D)]; a = 0.5 + [exp(−GSI/15) − exp(−20/3)]/6. The effective principal-stress envelope is σ′1 = σ′3 + σci(mbσ′3/σci + s)a.
Rock-mass stresses retain explicitly labeled MPa. The interpretation is attached separately to slope cases; it does not replace the selected joint strength law.
Hoek, E., Carranza-Torres, C. & Corkum, B. (2002). Hoek–Brown failure criterion—2002 edition. NARMS-TAC 2002, 267–273.
Finite-block slope equilibrium
Planar and finite-wedge calculations construct the stated block geometry, resolve applied forces and contact reactions, and compare available sliding resistance with driving force for the selected mechanism. Weight is unit weight × volume. The isolated-block model also compares resisting and driving moments about the downslope toe.
Lengths are feet; forces lbf; unit weight lbf/ft³; moments lbf·ft; contact stresses psi. Pressure × area includes 144 in²/ft². A released contact contributes no contact friction or cohesion. No finite block, lost contact, unsupported motion, unresolved force paths and search limits do not establish safety.
The calculation package records the actual input snapshot, geometry, equations, force branches, numerical status and result audit. A ratio above one alone is not a project design acceptance criterion.
The planar setup uses one shared section dip direction. Slope, failure plane and inclined upper ground must describe the same vertical section. Their dips are section inclinations. Imported directions that disagree are retained until explicitly reconciled; aligning bearings does not calculate apparent dip or establish that a measured plane lies in the section. Use the diagrams beside the inputs and the linked setup-issue list to review dimensions and corrections.
Wedge geometry, persistence and cracks
The block is bounded by the specified planes and offsets. For the through-toe two-joint wedge, slope height H1 is measured vertically where Joint 1 intersects the slope crest. With an explicit basal plane, H1 is the vertical crest height at the slope dip-direction reference section, and joint locations use explicit signed plane offsets. Neither is necessarily the final clipped block’s full vertical span. Explicit basal planes and rear tension cracks add geometric constraints; they are not automatically placed to search for an unknown worst-case block.
Joint persistence and size limits constrain finite geometry. Check the plotted block and surface labels against the surveyed exposure. Translational force equilibrium does not solve progressive fracture, rotation or complete moment equilibrium of a general rock mass.
Water pressures and resultants
Uniform mean contact pressure produces a normal force equal to pressure × wetted area. Hydrostatic models integrate the prescribed head over the selected wetted surfaces. Distinguish joint pressure, rear-crack water and external ponding; their forces act on different surfaces.
Elevations share the case’s model origin. Water distributions are prescribed inputs, not a groundwater-flow solution. Review head limits, surface clipping, resultant locations and the selected drainage assumptions. Toppling water loads require explicit joint/base selections.
Reinforcement and force conventions
Active support is a prescribed retained force after lock-off and losses. Passive support contributes resistance only through its selected engagement and capacity rules. For a tension anchor, enter the direction from the head toward anchorage in stable ground: this is the pull direction on the block. Positive plunge is downward from horizontal; negative is upward. Axial, shear, bond and anchorage limits are distinct checks.
Starting orientation and load context
New checked bolts on ordinary planar/wedge faces start at the inward face normal: bearing = slope dip direction + 180° (wrapped to 0–360°); plunge = 90° − face dip. A 70° face therefore starts at 20° downward. Existing bolts retain their directions when geometry changes. This editable construction starting point follows FHWA FP-24 §260.08(a), printed p196; it is not an optimized stabilization angle. Unknown or overhanging face geometry does not receive a plunge default. An isolated-block force instead starts horizontally toward the uphill side of its base and needs a reviewed moment arm.
FHWA GEC 4, §§5.3.6, 5.3.8 and 7.5 describes ground-anchor inclinations commonly 15–30° below horizontal and anchored-wall lock-off commonly 75–100% of design load. These are scoped examples, not universal rock-bolt requirements or a typical force in lbf. FP-24 §260.09(b) specifies a 1.33 × design-load proof test followed by lock-off at design load after acceptance. Select a load from the actual design and testing specification; do not use proof-test load as service pretension.
Guided bolt selection and editable defaults
The reinforcement editor follows five decisions: choose the system, select the bar, place and aim the bolts, establish anchorage, and set loading/review. New passive entries are a 20 ft fully grouted trial dowel, one head at the face center, inward face-normal orientation and zero credited plate resistance. FHWA rock-slope guidance describes 20 ft as a typical length; it is not a proof of sufficient embedment. Select required embedment and bond resistance from the design. Existing cases retain their values. Explicit full-grout mode follows a changed total length; specified partial bond is kept independent.
The angle menu distinguishes horizontal plunge from an offset below the inward face normal. For a 70° face, the inward normal is 20° down from horizontal and 15° below that normal is 35° down. These options copy an angle for review; they do not optimize it or automatically rotate an existing bolt after geometry edits. The diagrams distinguish total length, actual joint crossing, geometric embedment and bonded segment.
Published Williams Grade 75 threaded rebar (#8/#10) and Grade 150 prestressing bar (1/1¼ inch product designations) are material presets. A saved selection retains its source table, version, original properties, manual overrides and design basis. Net steel area is tabulated rather than inferred from nominal diameter. Material loads are Ty = A Fy and Tu = A Fu. The FP-24 rock-bar steel option uses the 60% ultimate design ceiling and 80% ultimate test ceiling; WillItMap adds a conservative minimum-yield ceiling at each stage. Selecting a product begins with the editable FP-24 test/design ratio m = 1.33. The resulting steel design limit is min(0.60Tu, Ty, 0.80Tu/m, Ty/m). If no multiplier is selected, the test-governed term is absent and the report says so.
Example: the published Grade 75 #8 area is 0.79 in², Fy = 75,000 psi and Fu = 100,000 psi. Ty = 59,250 lbf and Tu = 79,000 lbf. At m = 1.33 the added yield ceiling gives 59,250/1.33 = 44,548.872 lbf, below the 47,400 lbf design-stage ceiling. This is a steel component value; plate, bond, rock failure, corrosion and installation can govern lower. The separate GEC 4 prestressing-bar option also reports a lock-off ceiling. Product selection never supplies ground/plate capacity or applied pretension. Product edits must be applied or discarded before calculation, and the source snapshot travels into reports. See the manufacturer rebar table and prestressing-bar table.
Live bolts and patterns in the model
The 3D view regenerates bolt shafts from the current heads, directions and lengths before and after calculation. Pattern members use the same finite-face grid as the analysis. Show bolts, Transparent block and Bolt labels control the view. Head circles, true-length shafts and joint-crossing rings help check the layout. Green means geometric engagement, red means a known shaft does not meet that check, and dashed amber means the embedment criterion is missing. These are geometric checks only; they do not qualify capacity or establish stability.
The view fits the displayed heads and tips. Invalid or off-face locations are omitted with explanations, and changing or clearing inputs removes stale shafts. A single location with an equivalent count remains one drawn shaft; choose a generated pattern for actual separate locations. At most 200 shafts, 12 optional labels and 30 text details are displayed, with counts and omissions disclosed. A prescribed force without head and length does not create an imagined bolt.
Independent capacity and steel checks
Available tensile-capacity diagrams describe capacity along a bolt, not a calculated stress distribution. Component models check the entered qualified steel, plate, anchorage or bond resistances at the joint crossing. The local linear orientation convention uses the plane containing the bolt and movement direction. Pattern inputs create explicit bolts checked against the modeled block and joint geometry.
An independent service limit can further restrict a group's resistance. Active pretension and specified passive force above that limit reject the calculation; geometric passive resistance uses the smaller of intersection capacity and service limit before orientation efficiency. A legacy force without independent capacity evidence remains visibly unchecked and retains historical arithmetic until edited. It is not automatically certified by copying the requested force into a capacity field.
The optional saved FHWA prestressing-steel check uses certified minimum ultimate tensile load Tu = specified minimum tensile strength × certified steel area. An actual measured break-test load is not this input. Design force ≤ 0.60Tu, lock-off ≤ 0.70Tu, and maximum test force ≤ 0.80Tu. For a test multiplier m, the governing design steel ceiling is min(0.60Tu, 0.80Tu/m). For the illustrative Tu = 100,000 lbf and m = 1.33, the design, lock-off and test ceilings are 60,000, 70,000 and 80,000 lbf. Saved active pretension above the lock-off steel limit rejects calculation. These steel ceilings do not calculate the complete anchor's service resistance, ground breakout, corrosion allowance or installation performance. Nothing automatically copies them into an applied force or qualified capacity. The original physical support is qualified before optional scenario factors are applied.
The beneficial-support convention retains the greatest admissible evaluated active-only, supported or lift candidate; the report records the branches separately. A supported sliding candidate requires compressive contact and no unresolved force transverse to its stated movement. A passive force that would change the contact or movement mode requires a coupled solution and receives no factor in this model. Shotcrete uses the chosen trace lengths, thickness and material inputs under the displayed force model. Document capacity qualification, anchorage and deformation assumptions.
Interacting blocks and diagnostic flexure
Interacting toppling uses a column-by-column force recurrence with the specified basal and intercolumn strength, force-transfer heights, water and applied loads. The reported strength-reduction threshold is distinct from an isolated block’s resisting/driving moment ratio. Each critical contact must satisfy the applicable force, shear and moment conditions.
Block-flexure provides a diagnostic recurrence and elastic-section force/stress audit. It does not report an accepted whole-slope factor of safety. Tensile intercolumn transfer and compatible displacement/contact evolution are not solved; the local bending check does not resolve those missing conditions.
Goodman, R.E. & Bray, J.W. (1976). Toppling of rock slopes. ASCE Specialty Conference on Rock Engineering for Foundations and Slopes, Boulder, Colorado, vol. 2, 201–234.
Parameter sampling and scenario statistics
Sampling uses the stated distributions, truncation, correlations, seed and sample count. Orientation sampling follows the specified spherical distribution. Factor statistics, fits, percentiles and charts use accepted factors only. Support-only lift ratios retain their raw values and a separate count, but are excluded from the sliding-factor population; sensitivity lines break at those samples. Other omitted, unresolved or invalid states remain visible in the result counts. The conditional fraction uses the accepted-factor count as its denominator, not the total sample count.
These results depend on the chosen population and uncertain inputs. They are not a measured site failure frequency. Fisher orientation statistics and source.
Bench scenario comparison
The comparison reruns explicitly selected finite wedge, planar-prism and generated dry block-toppling cases for each candidate face angle, within their displayed geometry restrictions. Cases share one bench height and one factor basis. Required width combines the stated backbreak and spill quantiles for cases below the chosen design factor, with swelling, repose and usable-width assumptions. Wedges use their cone/pyramidal accumulation model. Planar and toppling scenarios use a uniform triangular-prism resting deposit: S = √[2KV(cot φr − cot β)/L], where K is swelling, V the potential debris volume, φr repose angle, β face angle and L release width. Deposit height S/(cot φr − cot β) must fit below the bench crest. Toppling volume uses the identified critical sliding/toppling columns. This is an accumulation scenario, not a prediction of progressive collapse or rockfall runout.
Scenario counts are not probabilities of failure. Strength-cell resampling is not included. Unresolved or inadmissible outcomes withhold a recommendation. Retain the complete scenario table and assumptions alongside any selected bench geometry.
Langford, J.C., Corkum, B. & Curran, J.H. (2014). Preliminary selection of optimum bench face angle using uniformly distributed wedges. First International Conference on Discrete Fracture Network Engineering, Canadian Rock Mechanics Association, Vancouver, DFNE 2014–260.
Explicit project design factors
An optional named set records the governing reference, numerical factors and each applied load's permanent/variable category. Characteristic inputs are preserved. For Mohr–Coulomb contacts, φd = atan[tan(φk)/(γφ γR)] and cd = ck/(γc γR); tensile strength follows the cohesion divisor. Self-weight, water pressures and categorized loads use their explicit multipliers. Support capacities use a separate divisor. Heads, dimensions and seismic coefficients stay unchanged; inertia follows factored weight.
The result is a design-value equilibrium ratio, not an unfactored FS or an automatically certified design-standard check. Favorable/unfavorable actions and combinations require engineering judgment. Non-unit material factors for nonlinear contact laws are rejected. A physical rock-weight wedge-size limit must first be expressed as a volume at characteristic unit weight before self-weight can be factored. Reports list every transformed value and retain original inputs.
European Commission JRC: EN 1990 and EN 1997-1 general rules. This background does not select a design approach or National Annex for the project.
Discrete bolt-spacing search
The reinforcement editor can enumerate horizontal and along-face spacing ranges for one qualified geometric pattern across selected planar/wedge cases. Every grid is analyzed explicitly. A grid qualifies only when every case returns an accepted finite factor or ratio meeting the common target under the same factor basis. The objective is the largest tested grid-cell area, not a global minimum-cost installation.
The study replaces existing geometric patterns in analysis copies with the selected template while retaining other supports. A no-pattern baseline is shown. Geometry, engagement, capacities and scenario coverage still require review. Applying a recommendation changes only the current draft; calculate and save it explicitly. Cancelled, stale or unresolved studies withhold recommendations. Full inputs and result rows can be exported.
Named result views
Saved AND/OR filters can combine accepted FS/design ratio, volume, status, mode and outcome class in study tables and charts. They select a view without deleting results or rerunning calculations. Missing values are not zero. Original study counts, exclusion counts and the accepted-factor denominator remain visible and unchanged. Full exports preserve all rows; filtered CSV exports state the view and original counts. Named views are local workspace settings and can be exported separately.
What the reported factors mean
Sliding resistance / driving force, isolated-block restoring / overturning moments, and interacting-column strength reduction are different definitions. They cannot be interchanged merely because each is labeled as a factor.
For a simple joint with compression N, outward driving force D, friction φ, and support adding compression C and opposing tangential force T: an active preload gives (N + C) tan φ / (D − T); passive capacity gives [(N + C) tan φ + T] / D. These expressions share equilibrium at one but generally differ away from one. Cohesive resistance, where applicable, is added to the numerator.
A support-only release ratio requires the support and factored active load to balance in every vector component. An opposing projection with an unbalanced transverse force is diagnostic only and does not receive a numerical factor. The wedge's beneficial-support selection remains a declared capacity convention; it is not a general displacement-compatible reinforcement solution.
Nonlinear joint resistance is evaluated at the mean effective normal stress on each retained face. This does not integrate a solved nonuniform contact-stress distribution. Optional waviness adds σ′ tan(w) to the selected law; it does not replace φ by φ + w. Zero compression releases the contact and credits no cohesion.
The interacting-column solver searches a finite factor range of 0.01–100 and audits the critical contacts. Whole-slope flexure remains diagnostic with no accepted factor. None of these ratios alone establishes a project design acceptance criterion.