Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
TerraLapsus
Limit equilibrium slope stability with layered ground, pore water pressure, computed seepage, surface loads and tension cracks. Bishop, Janbu, Morgenstern-Price, Spencer and Sarma on one model definition and one slice builder, so a difference between two answers is a difference in method and nothing else. Circular and non-circular searches, a map of every surface below a chosen factor of safety, and the line of thrust.
Getting started
One Needs, a help summary, the worked examples and the manual.
— lists the five bundled examples as clickable rows: click one to OPEN it
— lists the five bundled examples as clickable rows: click one to OPEN it
— returns every documented function in the paclet as a Dataset - name, context and the first line of its usage - which is the searchable index the Documentation Center pages do not yet provide.
— prints a summary of the whole package: how to define the ground, the five methods, the two non-circular searches, seepage, the tension crack, and the checks worth running every time.
— OPENS the quick-start manual, Limitas-QuickStart.pdf, and returns its path
The model
The ground, the materials, the water and the slices - defined once and shared by every method.
— returns the Bishop simplified factor of safety of the single trial circle centred at {xc,yc} with radius R, or Infinity if the circle is kinematically inadmissible.
— sweeps CircleSearchGrid[model, opts] and returns <|"FoS"->..., "Center"->{xc,yc}, "Radius"->R, "Trials"->n|>, the circle with the lowest factor of safety.
— is the convenience wrapper: it builds the model and returns the critical circle in one call.
— returns the list of trial circles {xc,yc,R} that the default search sweeps
— integrates the unit weight of the ground down the column at x between the two elevations, splitting each region at the water table where a saturated unit weight has been supplied.
— returns the graphics primitives for a tension crack on that surface - the open face, the water standing in it, the triangular pressure distribution and its resultant - or {} when the model has no crack.
— scans tension crack depths on one surface and returns {Fworst, depth}, where f[model, surface, opts] gives the factor of safety.
— returns the slice forces and BOTH equilibrium residuals for a given factor of safety
— plots the interslice normal and shear forces along the slip surface, labelled with both residuals.
— maps f[model, circle, opts] over a list of trial circles, serially or across subkernels according to "Parallel" in opts
— runs the SAME circle sweep serially and in parallel and compares the factor of safety, the critical circle and the elapsed time.
— launches subkernels if none are running and loads Limitas onto each
— returns the pore water pressure at a point, using the water table of the material region containing it where that region defines one, and the model-wide "PorePressure" field otherwise.
— returns a pure function u[x, yBase, sigmaV] giving the pore water pressure on a slice base
— returns the material region containing the point {x, y}
— discretises one trial circle and returns <|"Slices"->{...}, "Entry"->xa, "Exit"->xb, "Width"->b, "Circle"->..., "N"->n|>, or Missing["Grazing"|"ShortChord"|"BelowBase"] if the circle is inadmissible.
— returns the per-slice quantities for one circle as a Dataset: x, base elevation, height, weight, pore pressure, base angle and the c' and phi' actually used.
— draws SlopeModelPlot with the critical circle, its centre and the arc of the slip surface superimposed.
— assembles a complete analysis model: it resolves the profile, the material regions, the water table, the pore pressure field and the surface tractions into a single association that BishopCircleFoS consumes.
— draws the ground profile, the material regions as shaded bands, the phreatic surface and any surface loads
— turns a geometry specification into an association describing the ground surface
— normalises one material region
— builds the surface load exerted by free water standing against the slope up to the given level
— returns a pure function of x giving the elevation of the phreatic surface, or None if the specification does not define one.
Janbu and non-circular surfaces
Force equilibrium on any shape, and the local optimiser that bends a surface into a weak layer.
— sweeps the standard circular search grid with Janbu's method and returns the weakest circle
— returns <|"FoS", "Uncorrected", "f0", "b1", "dOverL", "Kind", "Converged"|> for one slip surface
— is the whole job in one call: a circular Janbu search to locate the mechanism, then OptimiseSurface to relax it into a non-circular shape.
— searches for a non-circular slip surface of lower factor of safety, starting from a circle or a polyline
— draws the model with a non-circular slip surface, its nodes, and - where the result came from an optimisation - the starting circle in grey for comparison.
— discretises a circular slip surface into an n-node polyline running from entry to exit, ready to be optimised into a non-circular shape.
Morgenstern-Price
The general limit equilibrium form: both equilibria, solved for lambda.
— returns the normalised interslice force function f(t) for t running 0 to 1 from the entry point to the exit point
— sweeps the same CircleSearchGrid the Bishop search uses and returns the circle with the lowest Morgenstern-Price factor of safety, as <|"FoS", "Center", "Radius", "Lambda", "Fm", "Ff", "Trials", "Converged"|>.
— solves one trial circle and returns <|"FoS", "Lambda", "Fm", "Ff", "Converged", "Bracketed", "MinMAlpha", "E", "X"|>, or a result with "FoS"->Infinity if the circle is inadmissible.
— builds the model and runs the full Morgenstern-Price search in one call.
— returns <|"Bishop", "MPMoment0", "Difference"|>
— runs the Bishop search, then solves the same critical circle by Morgenstern-Price, and tabulates the two answers side by side with the percentage difference.
— draws the classic GLE diagnostic: the moment factor of safety and the force factor of safety against lambda
Spencer
Morgenstern-Price with a constant interslice inclination.
— sweeps the standard circle grid on Spencer's method and returns the weakest circle
— returns Spencer's factor of safety for one slip surface: force and moment equilibrium with the interslice resultant at a constant inclination.
— plots the force and moment factors of safety against the interslice inclination theta
Sarma
Full equilibrium, solved for the critical horizontal acceleration as well as the factor of safety.
— returns the horizontal acceleration coefficient k required to bring the surface to limiting equilibrium when the strength has been factored by F.
— plots the required acceleration k against the strength factor F
— re-runs the three closed-form verifications of the D expression - friction only, cohesion only, and the horizontal base with pore pressure - and returns the residuals.
— sweeps the standard circle grid and returns the weakest circle on Sarma's method
— applies Sarma's method to one slip surface and returns <|"FoS", "CriticalAcceleration", "Lambda", "Converged", ...|>.
— verifies lambda and k from equations (5.51) and (5.52) against a reference obtained by solving the full 3n equilibrium system directly, on a NON-UNIFORM surface with a phi' = 0 band.
Global search and strata
Global non-circular search, the layer boundaries, and systematic two-wedge block mechanisms.
— plots best-so-far factor of safety against generation, with the seed and the final polish marked
— searches globally for the critical non-circular slip surface by cuckoo search and returns the JanbuFoS association for the winner, extended with "Surface", "History", "SeedFoS", "CircularFoS", "LayerUsage" and "Evaluations".
— returns the initial population as a list of polylines, without searching
— returns the modelled stratum boundaries that lie inside the soil body, each as <|"Points", "Fn", "XRange", "Region", "Name", "Elevation", "Above", "Below", "Thickness"|>.
— is LayerInterfaces[model] as a readable Dataset: the elevation of each boundary, the material above and below it, the thickness of the material below, and the x-range over which the boundary exists.
— reports what fraction of the slip surface length sits in each material, as a Dataset
— builds explicit two-wedge block mechanisms on every stratum boundary - active wedge down from the ground, a base running along the boundary, passive wedge up to the ground - over a grid of start points, end points and wedge angles, and returns them sorted by Janbu factor of safety as {<|"FoS", "Surface", ...|>, ...}.
Seepage
The bridge to TerraPercolatio, so one description of the ground serves both stability and seepage.
— returns the counterclockwise boundary polygon of the model - ground surface over rigid base - which is what TerraPercolatio wants as "Profile".
— returns just the layer polygons, one per material region, each with "Polygon", "kx", "ky" and "Name"
— returns the bare pore pressure function u[x, y] in kPa from a TerraPercolatio solution.
— turns a TerraPercolatio solution into the association <|"Field" -> u|> that Limitas accepts as "PorePressure"
— builds the whole TerraPercolatio unconfined-seepage specification from a Limitas slope model: the boundary profile, the two water levels, and one layer polygon per material region carrying its kx and ky.
Criticality map
Every trial surface below a stated factor of safety, mapped on the section rather than in centre space.
— rasterises the sub-critical population onto the section
— runs the sweep, rasterises it and draws the map over SlopeModelPlot
— returns the numbers behind the picture: how many trials fell below the threshold, the lowest F found, and the horizontal and vertical extent of the envelope of sub-critical failure masses.
— normalises an already-evaluated population of NON-CIRCULAR surfaces - anything shaped like the output of WeakLayerSurfaces, {<|"FoS"->F, "Surface"->polyline, ...|>, ...} - into the form CriticalityField expects, keeping those below fcrit.
— sweeps CircleSearchGrid[model, opts] and returns <|"Surfaces"->{...}, "Trials"->n, "Admissible"->n, "Threshold"->F*|>, where each entry of "Surfaces" is <|"Circle"->{xc,yc,R}, "FoS"->F, "Entry"->xa, "Exit"->xb|> for every trial circle with F below "Threshold" (default 1.3).
Line of thrust
Where the interslice resultant acts, and whether it stays inside the sliding mass.
— returns the line of thrust for a Spencer or Morgenstern-Price result as <|"X", "Y", "HeightRatio", "Inside", "MeanHeightRatio", "InsideFraction", "CheckResidual", ...|>.
— draws the slip surface of the result with the line of thrust on it, labelled with F, the interslice angle and the mean height ratio.
— returns the per-boundary numbers behind the line as a Dataset: x, the base and ground elevations there, E, X, the thrust elevation and its height ratio.
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