Two modules give the factor of safety of a slope: one finds the critical slip circle by the method of slices, the other takes a plane parallel to the ground. This page helps you choose the module that matches your slope and links to the manual of each.
The Slope Stability family has two modules. Both give a factor of safety against sliding. They differ in the slip surface. Pick the one that matches the slope you are checking.
Your slope
Module
A section with layers, groundwater, loads or reinforcement, where the critical slip circle has to be found by the method of slices
Each manual follows the same plan: what the module calculates, what you need before you start, a quick start, the screen, every input section by section, the choices that decide the margin, the results, the report, a worked example you can reproduce, a table of how each input changes the answer, the messages the module gives, and answers to common questions.
What the two modules share
The workspace. The drawing, the tabs, Analyze and the input lock, units and the report follow the same layout as the other GeoTerva modules. See the workspace guide.
The factor of safety. Both give a factor of safety against sliding, to compare with the value you require.
Groundwater. Both take the water in the slope into account.
An earthquake. Both can add a pseudo-static earthquake, with the horizontal and vertical coefficients you enter.
What each module takes, side by side
Slope stability
Infinite slope
Slip surface
Circle, found by a search
Plane parallel to the ground
Ground
Layers
One uniform soil
Also takes
Loads, nails, anchors, geogrids
Seepage or a pore pressure ratio
A typical slope check in order
Choose the module
Pick the one that matches the slope and open its manual for the fields.
Describe the slope
Draw the ground, or give the slope angle and the depth of the plane.
Describe the soil and the water
Enter the strength and the unit weights, and the water.
Add the loads and the earthquake
Enter any surface loads, reinforcement and seismic coefficients.
Analyze and read the factor of safety
Press Analyze. Read the factor of safety, then save a report with the cover filled in.
Frequently asked questions
How do I check the stability of a slope with GeoTerva?
Open Slope stability for a section with layers, or Infinite slope for a long uniform slope. Describe the slope, the soil and the water, press Analyze, and read the factor of safety.
Which methods of slices does the Slope stability module use?
The ordinary method, Bishop’s simplified method and Spencer’s method.
Can I add soil nails or anchors?
Yes. The Slope stability module takes soil nails, ground anchors and geogrids.
Which module do I use for a long slope with seepage?
Infinite slope. It takes the water table with seepage parallel to the slope, or a pore pressure ratio.
Can I include an earthquake?
Yes. Both modules take a pseudo-static earthquake with horizontal and vertical coefficients that you enter.
Find the factor of safety of a layered slope by the method of slices, with a search for the critical circle, groundwater, loads, reinforcement and a pseudo-static earthquake. This manual walks through the screen, every input section, the methods, the results and the report, with a worked example you can follow.
Slope stability gives the factor of safety of a slope by the limit-equilibrium method of slices. You draw a section (the ground surface, layers of soil or rock, groundwater, loads, reinforcement), choose a method, and the module cuts many slip surfaces out of the slope, analyses every one and keeps the lowest factor of safety: the critical surface. The section is two-dimensional: every force is per metre of its length.
Ground: layers bounded by lines of points, each layer with a material that is drained (c′, φ′), undrained (cu, which may grow with depth) or a rock mass (Hoek–Brown criterion).
Water: a water line of any shape, ponded water, a pore pressure ratio ru per material, and a rapid drawdown.
Loads: strip loads and point (line) loads on the ground surface, vertical, normal or at an angle.
Reinforcement: soil nails, ground anchors and geogrids.
Earthquake: a pseudo-static analysis with kh and kv that you give.
Methods: the ordinary method of slices (Fellenius), Bishop simplified, and Spencer (forces and moments). Circular slip surfaces come from a grid of centres; a non-circular surface is searched as a polyline and analysed by Spencer.
Input aids: a DXF drawing can be imported, and the Measure tools put dimensions on the drawing.
For a plane failure surface parallel to the ground use Infinite slope.
Before you start: what you need
What
Notes
The section
The ground surface as points x, z in metres, left to right, and the level zbase below which no slip surface passes (it must lie below the lowest ground point).
The layers
The lines between the layers and a material for each layer.
The strength of each material
Unit weights γ and γsat and c′, φ′ (or cu, or the rock parameters).
Water, loads, reinforcement
Only if they exist on your site.
kh, kv
Only for a pseudo-static case; the module takes them as inputs.
Quick start in seven steps
Draw the ground surface
In Ground surface type the points or drag them on the drawing; set the base zbase.
Add layer boundaries and materials
Add boundaries in Layer boundaries, create materials in Materials and give each layer one in Assign materials.
Add water, loads, reinforcement, earthquake
Use Groundwater, Loads, Soil nails, Ground anchors, Geogrids and Earthquake as the site requires.
Set the search
In Slip surfaces place the rectangle of centres (the Suggest a rectangle button gives a start). In Analysis choose the method and the slicing.
Check the model
Press Model check to see errors, warnings and notes.
Press Analyze
The module analyses every circle of the grid, switches to the Results tab and shows the factor of safety. The model is locked until you press Edit inputs.
Read and report
Press a slice for its working, read the Calculations tab, and take the Report as PDF or Word.
The screen: tools, chips and dragging
The layout is the shared one described in the workspace guide: the drawing on the left and five tabs on the right: Model, Results, Calculations, Report and Theory. When you press Analyze the module moves to Results by itself.
The workspace after Analyze on the example.
The tools
Select: press a point, a boundary, the water line, a layer, a load or a reinforcement element to select it and open its row on the Model tab; drag a point to move it.
Add point: press a line (ground, boundary, water line, slip surface) to insert a point there.
Pan: drag the drawing; the wheel zooms in any tool; Fit, + and − also zoom.
Centres: drag a rectangle; the centres of the slip circles are the points of a grid inside it. The tool returns to Select when the rectangle is drawn.
The four Measure buttons: a horizontal, a vertical and an aligned dimension (two points each) and an angle (the vertex, then a point on each line). A measure lands on a point of the section when one is within ten pixels; Esc drops it. A distance reads like 20.000 m and an angle like 153.4°. Press a dimension to select it and press Delete to remove it. The dimensions are shown with the Dimensions chip, which switches itself on when you make one.
Grid shows the grid lines; Snap 0.5 m makes dragged points land on 0.5 m (switched off, they land on 0.01 m).
Undo and redo (Ctrl+Z, Ctrl+Y) keep the last 60 changes. Delete removes the selected point, load, reinforcement element or dimension.
The drawing before Analyze: points are drawn with their names and coordinates, and the rectangle of centres is on the drawing.
The bulb: what the drawing shows
The bulb opens Show on the drawing, with All and None. Points: names and coordinates of the ground, boundaries and groundwater, and the Drag points handles. Labels: Material names, Material values, Loads, Dimensions, Reinforcement, Slip circle. Result: Slices and Colours of the centres. The choice is kept by the browser. After Analyze the point labels are hidden for a clear drawing; press a chip to bring them back.
The bulb menu.
Dragging
Points of the ground, a boundary, the water line or a polyline slip surface move with the pointer; a point stays between its neighbours in x, so a line remains a function of x. Double-click a point to remove it (a line keeps at least two points).
A strip load has two ends and a point load one, dragged along the surface; a load keeps its place on the surface when the ground is edited.
A reinforcement element has two handles: the head moves along the surface; the tip turns and lengthens it (a geogrid stays horizontal).
The rectangle of centres moves when dragged and is resized by its corners.
After Analyze the model is locked: nothing is dragged, but pan, zoom and selecting a slice still work. Edit inputs unlocks it.
A model with groundwater, a load, nails, an anchor and geogrids.
Entering the model, section by section
The Model tab starts with Model data, which stands apart; then twelve sections walked one at a time (the one open carries Back and Next): Ground surface, Layer boundaries, Materials, Assign materials, Groundwater, Loads, Soil nails, Ground anchors, Geogrids, Earthquake, Slip surfaces, Analysis. A box takes its value when you press Enter or leave it.
Model data: keeping the model
Every change is kept by the browser, so the page opens on the model you last worked on; the line under the buttons says so and gives the time it was kept. The analysed state is not kept: you press Analyze again. Buttons: Save to file… (a .json file named after the model name, with the report cover details inside; a browser without a save window puts it in its downloads folder), Open file…, Quick Save… (asks for a name; a name already in use asks whether to replace it; the saved versions are in the list, with Load and Delete), Reset to the example (asks first, and clears the model name) and Import DXF…. While the model is locked after an analysis, Open file…, Load, Delete and Reset to the example are off, and the DXF button is off too (its tooltip says to press Edit inputs first): press Edit inputs first.
DXF import. The layers read are EXTERNAL (one closed line: the ground surface, the two sides and the base), MATERIAL (the lines between soils), WATER TABLE (a space, a hyphen or an underscore between the words is accepted), NAIL, ANCHOR (three points: head, end of the free length, tip) and GEOGRID; LINE, LWPOLYLINE and POLYLINE entities are read. A window then lists what was read, for example: the ground surface with 4 points, 1 layer boundary (2 layers), the water table with 3 points, the base of the model at z = −6 m; the reinforcement found (1 soil nail, 1 ground anchor, 1 geogrid, whose place and direction come from the drawing and whose capacities are starting values); and the layers of the drawing that were not read. Every region gets a soil of its own (γ 18 / 20 kN/m³, c′ 5 kPa, φ′ 30°) for you to rename and edit. The import replaces the whole model, loads and earthquake included, and Undo brings the old one back. Without an EXTERNAL layer the module says so and lists the layers in the file.
Model data.
Ground surface
A line of points from left to right. A vertical face (two points with the same x) is allowed; an overhang is not.
+ Add a point at the end adds a point 5 m on; × removes a point (two remain at least). The line under the points gives the width and the rise.
Ground surface.
Field unit
Default
Point x, zm
G1 (0, 0), G2 (10, 0), G3 (30, 10), G4 (50, 10)
zbase base of the modelm
−6
Layer boundaries and Assign materials
Boundary k is the bottom of layer k; the lowest layer rests on the base. + Add a boundary below puts a level boundary half-way between the lowest ground and the base (z = −3 m on the example); the new layer takes the material of the layer above it. Press a boundary to edit its points; × removes it (the layer above extends down). Where a boundary rises above the ground, that layer is absent there: the example has this, and the module notes it as INFO. Assign materials has one row per layer with a material list.
Boundaries.
Assign materials has one row per layer: the layer, the two boundaries it lies between (the lowest rests on the base of the model) and its material. Press a layer on the drawing to find its row.
Assign materials.
Materials
Choose the Strength: Drained — c′ and φ′, Undrained — cu, φ = 0 or Rock — Hoek–Brown, fill the form and press + Add material; press a row of the table to change it (changes apply as they are entered); × deletes a material not used by a layer.
Drains freely in a rapid drawdown is a switch per material. A name is automatic when left empty; the colour is chosen on the form. The example holds Fill (18 / 20, c′ 5, φ′ 30) and Clay (17.5 / 19.5, c′ 20, φ′ 18).
Materials.
Field unit
Default of a new material
γ moist unit weightkN/m³
18
γsat saturatedkN/m³
20
c′kPa
5
φ′°, 0 to 60
30
cu (undrained)kPa
50
k: growth of cu per metre below level zkPa/m
0
z level at and above which cu is as givenm
10
σci (rock)MPa
20
GSI (rock)5 to 100
45
mi (rock)
10
D (rock)0 to 1
0
ru pore pressure ratio0 to 0.95; 0 = not used
0
Groundwater
Switch Present on for a water line (points left to right, any shape, level beyond its ends); Level line makes a level line a little over a third of the way up the surface. γw is an input (9.81 kN/m³). Where the line stands above the ground is either “Held at the ground surface — no water on the slope” or “Ponded water on the slope — its weight and pressure act”. Below the line the pressure is hydrostatic and the soil weighs γsat; with ponded water the water standing on the slope adds its weight as a vertical load and its pressure against the rising ground as a horizontal one, and the pore pressure at the base is measured up to the line. Rapid drawdown (on/off, level zdd) takes the line as the state before the water falls.
Groundwater.
Loads
+ Strip load (q in kPa between two points x₁, x₂ of the surface) and + Point load (P in kN/m at one point). New loads sit on the crest (strip 20 kPa across the middle half; point 100 kN/m at its middle). The direction is “Global vertical”, “Normal to the surface” or “At an angle from the vertical” (θ, positive toward +x; a value outside −89° to 89° is an error in the model check). A strip load acts on the horizontal projection of the loaded surface; a normal one on its length.
Loads.
Soil nails, ground anchors, geogrids
+ Soil nail, + Row of nails (n nails down the face at vertical spacing Sv; defaults 3 and 1.5 m), + Anchor, + Geogrid, + Row of geogrids; Apply to all copies the angle, length, free length, load, capacities, bond, hole diameter and spacing of the selected element to the others of its kind (not the head position or the direction). A new nail is put on the face 1.5 m under the crest and each row continues down the face: a row of 3 on the example with no nails yet gives heads at x = 27, 24 and 21 m.
Each element also has its head x on the ground and a direction (toward +x or −x). A nail carries the least of the bar tension, the pull-out behind the circle and the pull-out in front plus the head; an anchor the least of P, Tt and the root pull-out, taken from the driving side; a geogrid the least of Td and the two pull-outs. The force is per metre of section: T / Sh (a geogrid is already per metre). An element whose tip lies inside the sliding mass, or whose head lies outside it, carries nothing on that circle.
Soil nails.
Element
Defaults
Soil nail
α 15°, L 8 m, Tt 200 kN, qu 100 kPa, Dh 100 mm, Th no limit, Sh 1.5 m
Anchor
α 20°, L 12 m and free length 5.5 m on the example slope (about 1.2 times the height, 45 % free), P 300 kN, Tt 500 kN, qu 150 kPa, Dh 150 mm, Sh 2.5 m
Geogrid
L 8 m, Td 40 kN/m, Ci 0.8, Tc no limit
A ground anchor has the length, the free length, the lock-off load P and the capacity of the tendon; the section shows the head, the tip, the root and its bond, and the pull-out of the whole root (459.5 kN for the default anchor on the example). A geogrid has its end at the face, the length, the design strength Td, the interaction coefficient Ci and the strength of the connection Tc; it is horizontal.
Ground anchors.
Geogrids.
Earthquake
Switch Pseudo-static analysis on. kh (0 to 1, default 0.15), kv (−0.5 to 0.5, positive downward, default 0), the direction of the horizontal force (Critical — the lower factor of the two directions, toward −x, toward +x) and of the vertical force (critical, downward, upward). The static and the pseudo-static factors are both given. You choose kh and kv yourself; the module applies no code.
Earthquake.
Slip surfaces
Circular (default): the rectangle x₁, x₂, z₁, z₂ and the numbers of centres across (nx) and up (nz), 2 to 81 (default 15 × 15), and the radii at every centre nr, 3 to 40 (default 12). Drag it with Centres, or Suggest a rectangle. The example rectangle is x 5 to 35, z 11.5 to 40. The grid widens by itself when the lowest centre stands on an edge. Not circular: a polyline of points (ends on the ground), analysed by Spencer; Search for the lowest surface is on by default, Convex only — no reversal of curvature too; n = 3 to 30 pieces (10); From the critical circle, Along the boundary (with a boundary list) and Clear the surface give starts.
Slip surfaces, circular.
Slip surfaces, not circular.
Tension crack at the crest: depth zcr (default 2 m) and the part full of water in percent (default 0, 0 to 100); Suggest a depth gives 2c′/γ · tan(45° + φ′/2) of the soil at the crest, or 2cu/γ undrained (1.0 m for the Fill of the example, 4.4 m if the Fill were undrained with cu 40 kPa). The slip surface of every circle ends where the mass is as deep as the crack; the arc inside the crack carries no strength.
The tension crack.
Analysis
method: Fellenius (default), Bishop simplified, Spencer. slicing: by number (5 to 200, default 30) or by a largest width (default 1 m). Slice sides at the breaks of the geometry (on by default): vertices of the surface, crossings of the arc with boundaries and the water line, ends of strip loads become slice sides. A non-circular surface is always analysed by Spencer, and the method list is disabled.
Analysis.
Choosing the method
Method what it satisfies
Factor on the example circle
Fellenius (ordinary)Moments of the whole mass; the forces between slices are neglected
1.569
Bishop simplifiedVertical equilibrium of each slice and moments; the shear between slices neglected; found by iteration
1.740
SpencerForces and moments, with one angle θ for the forces between slices (18.54° here)
1.717
The three values are for the same circle, the critical circle of the Fellenius run (centre 16.52, 16.08, r 17.35 m): the Results tab lists the other two methods for it. When you choose Bishop or Spencer the grid is searched with that method, so the critical circle and its factor change: the example gives 1.720 (Bishop) and 1.699 (Spencer). A pseudo-static case uses the governing (lower) factor in the search. Where Spencer has no solution on a circle, or a tension between slices above the tolerance, the circle is left out and the Results tab says how many.
Analyze and read the results
Press Analyze. The bar reads Analysing… while the circles run (about a second for the example; a model with geogrids took about 15 s). The module switches to Results, a short message appears at the bottom of the window (for the example “FS = 1.569 — the critical of 3487 circles”), the bar reads the factor and the circle, and the model is locked; Edit inputs in the bar unlocks it. The bar turns warm when a factor is below 1 or when slice bases lost effective normal compression.
Factor of safety cards: static (and pseudo-static), the grid and how many of its circles hold (3487 of 4650 on the example), the refinement (1.583 → 1.569), the method, the other two methods on the same circle, Σ resisting, Σ driving (and the part of the resistance that is nails and geogrids, or the anchors taken off the driving side), the critical circle and the slices. Under the cards: Model check, The model (areas), Loads, Slices, and Soil at a point (type x and z, press Probe).
Press a slice, in the table or on the drawing, for its complete working: weight by soil, α, L, the strength at the base, pore pressure, N, N′, R and D, and for Spencer the forces between slices.
The Results tab on the example.
The drawing shows the critical circle, its slices with their numbers, and the colours of the centres: every centre of the grid coloured by its lowest factor (a legend gives the scale). A line joins the critical centre to the circle.
After Analyze.
The slice table; the selected slice is highlighted.
A non-circular surface by Spencer: 1.698 on the example.
The Calculations tab, the report and the Theory tab
Calculations has five numbered sections: 1 · The grid of centres (the rectangle, circles tried and held, the lowest centres, the refinement; for a polyline 1 · The search for the slip surface), 2 · The critical circle (The critical surface for a polyline), 3 · The method, 4 · The slices, one by one and 5 · The factor of safety (all slices with the sums, the static and pseudo-static factors, the other methods on the same circle). When the model has reinforcement a section The reinforcement comes after the critical circle and the later ones move down by one, so the factor of safety is section 6.
The Calculations tab, section 1.
The Report tab has the cover (Project, Location, Client, Report no., Date, Prepared by, Title / qualification, Checked by, Notes), a preview, Save as PDF and Download Word (.docx). Without an analysis it is the model report; after it, a calculation report. For the example the parts are: Analysis summary, The model, Materials, Layers, Groundwater, Loads on the surface, Critical slip circle and slices, Factor of safety by the ordinary method of slices, Checks of the model. With reinforcement the parts Reinforcement and (for nails) Soil nails on the critical circle are added, and with an earthquake Pseudo-static earthquake; the part on the factor of safety is named after the method you chose. The analysis warnings are listed under the checks.
The Report tab: the cover.
The Theory tab explains the method in 24 sections: the section and the strength of the soil, the factor of safety and the slices, water and loads, the three methods and how they compare, the earthquake, the tension crack, the search for the critical circle and for non-circular surfaces, the reinforcement (nails, anchors, geogrids), the rock criterion, the DXF section, a worked model, what the module assumes and its references.
Worked example: the module’s own example
Open the module and press Analyze: 10 m slope at 2H:1V, Fill (γ 18, c′ 5, φ′ 30) 4 m thick over Clay (γ 17.5, c′ 20, φ′ 18), no water, Fellenius, 30 slices target. The critical circle has its centre at (16.518, 16.080) and radius 17.352 m; the arc enters the ground at x = 9.999 m and leaves at 32.769 m. The module cuts 33 slices (four sides forced by the geometry at x = 10, 18, 28.973 and 30 m).
One slice by hand (slice 2, x from 10.000 to 10.758 m). The middle is x = 10.379 m: the ground is at z = 0.189 m and the arc at z = −0.149 m, so h = 0.338 m of Clay and W = 0.758 × 0.338 × 17.5 = 4.49 kN/m. sin α = (10.379 − 16.518) / 17.352 = −0.3538 (α = −20.72°), L = 0.758 / cos α = 0.810 m, N = W cos α = 4.20 kN/m, R = c′L + N tan φ′ = 20 × 0.810 + 4.20 × tan 18° = 17.57 kN/m, D = W sin α = −1.59 kN/m (this slice resists).
FS = Σ R / Σ D = 1006.25 / 641.34 = 1.569
The same slices recomputed independently, outside the module, give 1.5690 (ordinary), 1.7401 (Bishop) and 1.7170 (Spencer, θ = 18.54°). With an earthquake (kh = 0.15 toward −x, kv = 0.05 downward) on the critical circle of that run (centre 16.719, 17.448, r 18.698 m) the independent values are 1.5756 / 1.7345 / 1.7139 static and 1.1379 / 1.2650 / 1.2502 pseudo-static, as the module gives.
Reinforcement by hand. A nail of the default row has bond qu π Dh = 100 × π × 0.1 = 31.42 kN/m. Nail N1 on the critical circle of its run has Lb = 2.03 m behind the surface, so pull-out behind = 31.42 × 2.03 ≈ 63.8 kN (the module works with Lb = 2.028 m and gives 63.7 kN, governing, below the bar tension 200 kN and the pull-out in front plus head); per metre 63.7 / 1.5 = 42.48 kN/m. The anchor A1 (bond 150 π 0.15 = 70.69 kN/m) has Lb = 2.89 m: 70.69 × 2.89 = 204 kN, less than P = 300 and Tt = 500, so the root pull-out governs: 204.0 kN, 81.59 kN/m.
How each input changes the answer
Each row changes one thing in the example (Fellenius, 15 × 15 × 12 grid, no water) and re-runs the module. The factor is that of the critical circle found for that model. Unless a row says otherwise the soils are Fill (γ 18 / 20 kN/m³, c′ 5 kPa, φ′ 30°) and Clay (γ 17.5 / 19.5 kN/m³, c′ 20 kPa, φ′ 18°), and a water line is level across the whole width.
Change what it replaces
FS static circle: centre (x, z), r
The examplereference
1.569(16.52, 16.08) 17.35
Bishopmethod
1.720(15.50, 19.64) 20.40
Spencermethod
1.699(15.51, 18.88) 19.67
Clay c′ 10 kPawas 20
1.241(15.88, 15.59) 16.67
Clay c′ 30 kPathe circle moves into the Fill
1.774(19.06, 19.52) 15.51
Clay φ′ 12°was 18°
1.296(17.54, 14.63) 16.70
Clay φ′ 24°again within the Fill
1.774(19.06, 19.52) 15.51
Clay γ 20.5 / 22.5was 17.5 / 19.5
1.579(16.20, 16.08) 17.23
Fill c′ 0, φ′ 25°weaker fill
0.944(15.63, 22.70) 18.23
Slope 3H:1V (G3 at x = 40)flatter
1.995(21.37, 21.38) 24.84
Slope 1H:1V (G3 at x = 20)steeper
1.087(10.46, 12.26) 12.27
Water at z = 5 m, level (clamped on the lower ground)
1.144(17.05, 11.28) 15.64
Water at z = 10 m (the crest), clamped
0.894(21.56, 14.55) 10.55
Water at z = 5 m, ponded on the slopeits weight and pressure act on the face
1.474(18.54, 12.82) 15.41
Water at z = 10 m (the crest), ponded
1.715(22.16, 13.54) 9.53
Clay ru 0.3
1.272(17.66, 13.15) 15.97
Clay undrained cu 50 kPa
1.533(20.03, 15.57) 21.57
Strip load 20 kPa on the crestbeyond the mass: no effect
1.569(16.52, 16.08) 17.35
Strip load 50 kPa on the crest
1.511(18.46, 20.55) 22.40
Tension crack 2 m, dry
1.584(16.70, 15.59) 16.97
Nails: row of 3 (defaults)
1.601(17.42, 15.71) 17.67
One anchor (defaults)
1.668(17.59, 14.54) 17.44
Geogrids: row of 3 (defaults)about 15 s to run
1.597(17.09, 15.68) 17.26
Base at z = −3 m, or −12 m
1.569the circle does not reach it
Slices 10 / 30 / 100
1.558 / 1.569 / 1.571
Strength of the Clay stops mattering once the critical circle can stay in the Fill: c′ 30 kPa and φ′ 24° give the same 1.774.
Ponded water presses on the ground it stands on and its weight acts there, so the same line at z = 5 m gives 1.474 ponded against 1.144 held at the ground surface; on the ponded circle 4 slice bases lose effective normal compression and the module says so. The same two cases by Bishop give 1.827 and 1.429, by Spencer 1.811 and 1.425.
Earthquake (kh 0.15, critical direction): 1.579 static and 1.147 pseudo-static; with kv 0.075: 1.575 and 1.134.
Reinforcement raises the factor only where a circle crosses it and its tip lies behind the surface: in the nail run, N3 carries nothing on that circle.
The result depends on the search: the factor is the lowest of the circles tried, so a coarser grid or fewer slices moves it slightly.
Messages
Model check (button, and on the Results tab) lists ERROR, WARNING and INFO lines. A model with an ERROR is not analysed; pressing Analyze opens a window Analysis. Examples, quoted:
“The model has 1 error — see Model check on the Results tab.” with “The base of the model must lie below the lowest point of the ground surface (now 2.00 m against 0.00 m).” (base z = 2).
“Soil "Clay" has no strength: c′ = 0 and φ′ = 0.”
“No slip circle of the grid of centres cuts a sliding mass out of the slope: move the rectangle of centres over the face of the slope.”
“Boundary 1 lies above the ground surface over part of the width: layer 1 is absent there.” (INFO, in the example.)
(a level water line at z = 12 m) “The water line stands above the ground surface between x = 0.00 and 50.00 m (300.00 m²); it is held at the ground surface there and no water stands on the slope — the choice "Where the line stands above the ground" in the Groundwater section decides.” (WARNING.)
“Static: Loss of effective normal compression on 6 slice bases: the pore force exceeds the normal force there and N′ has been taken as zero, the usual practice of the ordinary method of slices.” followed by a request to review the groundwater and the slip surface; the slices are marked orange.
“N3 carries nothing — tip inside the mass” in the reinforcement table.
Files: “Not a model file: no ground surface found in the file”; with no quick save chosen: “Choose a saved model first.”; a DXF without lines: “No lines were found in the DXF file (LWPOLYLINE, POLYLINE or LINE in the ENTITIES section).”
Spencer. On a circle where the forces and the moments do not balance at any angle of the forces between the slices, or where the forces between the slices come out as a tension above 2 % of the largest one, the circle is not a candidate. The Calculations tab counts them in the grid line: on a steep face (the ground rising 15.2 m over 5 m, c′ 43 kPa, φ′ 7° in both soils, a 12 × 12 grid) it reads “circles tried: 2550, circles that cut a sliding mass: 583, passed over because their equations have no solution: 215, left out because the Spencer solution is not admissible (a tension between the slices above the tolerance): 945”. With the ordinary method the same line reads “circles not evaluated: N” for a circle that could not be evaluated. Warnings of a Spencer solution look like these (each is followed by a request to review the groundwater and the slip surface, and the slices concerned are marked orange): “The normal force between the slices is negative — a tension — at 1 of the sides (the lowest -13.4 kN/m, 2.1% of the largest interslice force, above the tolerance of 2%): the solution is not admissible there.”, “On 10 slice bases the denominator of ΔE falls under 0.2 FS / cos θ and has been held there: the base is steeply inclined against the sliding.”, “The angle of the forces between the slices is 56.2°, outside the range of an ordinary solution.” and “Loss of effective normal compression on 1 slice base: the equilibrium gives a negative N′ there and the friction has been left out, the cohesion kept.” When every circle that cuts a mass is left out for this reason the module asks you to change the model or the rectangle of centres.
Good practice
Look at the colours of the centres: the lowest centre should lie inside the rectangle, not on its edge (the Results tab warns when it still does after the grid widened).
Start with the ordinary method for a quick look and use Bishop or Spencer for the factor you report; compare the three on the same circle.
Give γsat and the water line for a slope below the water table, and choose what happens where the line stands above the ground.
Use Model check before Analyze, and read every WARNING after it.
Choose kh and kv yourself for the earthquake and keep the critical direction unless you know the direction.
Save the model to a file as well: the browser keeps only the last model.
Frequently asked questions
How is the factor of safety of a slope calculated?
By the method of slices: the mass above a slip surface is cut into vertical slices, and the factor is the resisting moment divided by the driving moment (ordinary and Bishop) or the value at which forces and moments both balance (Spencer). The module does this for every circle of a grid and keeps the lowest.
Which method should I use?
On the example the same circle gives 1.569 (ordinary), 1.740 (Bishop) and 1.717 (Spencer). Spencer satisfies forces and moments and is the one used for non-circular surfaces.
Why is the critical circle on the edge of the rectangle?
The module widens the grid on that side by itself; if the lowest centre still stands on the edge the Results tab says so and you enlarge the rectangle.
Does the module keep my model?
Yes. Every change is kept by the browser and the page opens on it; the analysed state is not kept. Save to a file or Quick Save to keep versions.
Can I work in US units?
No: the module works in m, kN/m³, kPa and degrees and holds the unit selector on SI · kN.
How do I add an earthquake?
Switch on Pseudo-static analysis in Earthquake and give kh and kv; both factors are then shown.
Why does an anchor reduce the driving side?
An anchor is stressed before the mass moves, so its force is taken from the driving moment; nails and geogrids work as the mass moves and add to the resistance.
What does a nail "carry nothing" mean?
On that circle its tip lies inside the sliding mass or its head outside it, so it does not cross the slip surface.
Can I analyse a non-circular surface?
Yes: choose Not circular in Slip surfaces. The search starts from the surface drawn, the critical circle and each boundary, and Spencer analyses the result.
Can I import a drawing?
Yes, a DXF with the layers EXTERNAL, MATERIAL, WATER TABLE (a space or an underscore between the words), NAIL, ANCHOR and GEOGRID, with Import DXF… in Model data.
Why can I not edit after Analyze?
The model is locked while results are shown; press Edit inputs.
How can I check a result by hand?
Open the Calculations tab and the section The slices, one by one: each slice has its working. On slice 2 of the example, W = 0.758 × 0.338 × 17.5 = 4.49 kN/m and R = 20 × 0.810 + 4.20 × tan 18° = 17.57 kN/m.
Find the factor of safety of a long slope against sliding on a plane parallel to the ground, dry, with seepage, with a pore pressure ratio or with an earthquake, with the depth and angle at the required value. This manual walks through the screen, every input, the results and the report with an example you can reproduce.
Infinite slope gives the factor of safety of a long, uniform slope against sliding on a plane parallel to the ground, at the vertical depth H below it. The slope is taken as so long that its ends play no part, so every point of the plane is in the same state and one strip of the sliding mass stands for all of it. The factor of safety is the shear strength of the soil on the plane over the shear stress that the weight of the strip puts on it:
FS = τf / τ, σ = σv cos²β, τ = σv sin β cos β, τf = c′ + σ′ tan φ′
σv is the total vertical stress at the plane, σ′ = σ − u is the effective normal stress and u the pore water pressure on the plane. For an undrained clay the strength is cu alone (φu = 0, total stress).
What you can describe
A slope angle β and the depth H of the failure plane, measured vertically.
One soil above the plane: Drained — c′, φ′ (effective strength, long term) or Undrained — cᵤ, φᵤ = 0 (a clay in the short term).
Pore water on the plane, in a drained analysis: None, a Water table, seepage parallel to the slope at the depth zw, or a Pore pressure ratio ru.
A pseudo-static earthquake with kh and kv that you give.
The required factor of safety, which decides the verdict.
What you get
The factor of safety with its verdict (OK, OK, near the limit or NOT OK), and the stresses behind it: σ, u, σ′, τ and τf.
The depth Hreq at which the factor of safety falls to the required value, the steepest slope angle βreq that keeps it, and the critical depth Hcr where it falls to 1.
With water, the same slope without pore pressure and with the water at the ground surface.
With an earthquake, the earthquake factor of safety, the yield coefficientky (the kh at which the factor of safety falls to 1) and its own Hreq and βreq.
Three views (the section, the stresses on the plane, charts), a step-by-step working and a PDF or Word report.
What belongs to the other module
A slope of finite length, with layers, a groundwater line, loads, reinforcement and a search for the critical slip circle belongs to Slope stability. This module is for the shallow sheet that slides on a plane parallel to the ground.
Before you start: what you need
What and where from
Notes
The slope angle β Survey or design
From 0.1° to 70°. The failure plane has the same angle.
The depth H of the plane Borehole logs, observed slips
Measured vertically, from the ground down to the plane. The thickness at right angles to the slope is H cos β.
The unit weight γ Tests
Of the soil as it lies. With a water table it is the unit weight above the table.
The strength: c′ and φ′, or cu Tests or correlations
Effective strength for the long term; cu for a clay in the short term.
The saturated unit weight γsat Tests
Only with a water table; it must be above 9.81 kN/m³.
The water Piezometers, design assumption
A water table parallel to the slope, or a ratio ru.
kh and kv Your design criteria
The module takes them as you enter them.
The required factor of safety Your design criteria
Default 1.50 (static) and 1.10 (earthquake).
Quick start in eight steps
Open the module and choose the units
Open Infinite slope from the Slope Stability family and pick SI · kN, SI · tf or US in the header.
Enter the slope
In Slope, type the slope angle β and the depth H of the failure plane, then press Next.
Describe the soil
In Soil, choose the strength (drained or undrained) and enter γ with c′ and φ′, or cu.
Give the pore water
In Pore water, choose None, a water table or ru. With a table the soil section also asks for γsat.
Add an earthquake if you need one
In Earthquake, choose Pseudo-static and enter kh and kv.
Set the required factor of safety
In Analysis Settings, enter FSreq (and FSreq,eq with an earthquake).
Press Analyze
Press Analyze. The inputs lock and the bar reads Analysed — the factor of safety calculated. Open Results; the Stresses and Charts views fill in.
Take the working and the report
Calculations shows the steps with your numbers; Report saves a PDF or a Word file.
The screen: three views of the slope
The layout is the one every GeoTerva module shares, described in the workspace guide. The drawing has three views, chosen with the buttons above it:
Section is the slope in section: the ground surface at the angle β, the failure plane parallel to it, the depth H, the water table with zw and hw when there is one, the soil box (γ, c′, φ′, the pore water, the earthquake) and, after Analyze, the factor of safety in a box at the top right (two boxes with an earthquake).
Stresses draws a strip of the mass with the failure plane horizontal: its weight W/A, the normal stress σ and the shear stress τ it puts on the plane and what the plane gives back, σ′, u and τf. A panel lists the values. With an earthquake the picture shows the earthquake case, with the horizontal force and the resultant.
Charts plots the factor of safety against the slope angle, the depth of the plane and the water (its depth, ru, or cu), and the strength line against the stresses. With an earthquake the earthquake case is a second line and a fifth chart gives the factor of safety against kh with the yield coefficient.
Section before Analyze: the drawing follows the inputs.
Section after Analyze.
Stresses after Analyze.
Charts after Analyze.
The Show chips
Section: Dimensions shows or hides the dimension lines (H, and zw, hw with a water table).
Stresses: Loads on the plane and Reaction of the plane show or hide the two sets of arrows.
Charts: FSreq shows or hides the required-value lines and No pore pressure the dry curve.
Before Analyze the Stresses and Charts views are empty: the Stresses bar reads “The pressures and the resultant appear after Analyze” and the drawing says “The strip and its stresses appear after Analyze”.
Stresses before Analyze.
Zoom, and nothing to drag
Each view has −, + and a fit button at its lower right corner; each click of + raises the zoom by about a third (100 %, 135 %, 182 %, 246 % and on to 800 %) and each click of − lowers it again to 100 %. Nothing on the drawing can be dragged: the slope, the plane and the water are set in the Model tab, and the drawing follows the inputs.
Entering the model, section by section
The Model tab has six sections: Model data, Slope, Soil, Pore water, Earthquake and Analysis Settings. Model data opens and closes on its own; the other five work as an accordion: opening one closes the previous one. Next and Back walk you through them and Analyze waits below. Defaults are shown in SI; units follow the system chosen in the header (m · ft, kN/m³ · pcf, kPa · psf).
Model data
The model name, Save to file…, Open file…, Quick Save… with its list, Load, Delete and Reset to defaults, as in the workspace guide. The section says every change is kept in this browser. After Analyze all inputs are locked until Edit inputs.
Model data.
Slope
The ground is a plane at the angle β; the failure plane is parallel to it at the vertical depth H.
Slope: the angle and the depth.
Field and unit
Default
Accepted
Slope angle β °
15
0.1 to 70
Depth of the failure plane H m · ft
6
0.05 or more
Soil
Two buttons choose the strength. The fields that apply to the choice appear under them.
Soil, drained.
Field and unit
Default
Shown when
Unit weight γ kN/m³ · pcf (1 or more)
17.8
always
Saturated unit weight γsat kN/m³ · pcf (1 or more)
19.5
water table
Effective cohesion c′ kPa · psf (0 or more)
10
drained
Effective friction angle φ′ ° (0 to 50)
20
drained
Undrained shear strength cu kPa · psf (0.1 or more)
40
undrained
The unit weight γ is that of the soil above the water table; below it the saturated unit weight γsat is used. Choosing Undrained — cᵤ, φᵤ = 0 hides c′, φ′ and the Pore water choices: an undrained analysis is in total stress.
Soil, undrained.
Pore water
Three buttons give the pore pressure on the plane (drained analyses only).
Pore water: the water table.
Option, field, default
None no field; no pore pressure
Water table, seepage parallel to the slope Depth zw of the table below the ground, m · ft default 2; 0 or more
Pore pressure ratio ru Ratio ru default 0.25; 0 to 0.9
Water table. A line parallel to the slope, the water flowing down the slope parallel to it, so the pore pressure on the plane is that of the water column vertically over it: u = γwhw cos²β, with hw = H − zw and γw = 9.81 kN/m³. zw = 0 is the water at the ground surface. A table at or below the plane puts no water on it.
Pore pressure ratio.u = ruγH, the way slope charts take the water; it uses γ for the whole column.
Earthquake
None gives the static analysis alone. Pseudo-static gives the static and the earthquake factors of safety side by side.
Earthquake: the two coefficients.
Field and unit
Default
Accepted
Horizontal coefficient kh
0.15
0 to 1
Vertical coefficient kv
0
0 to 0.5
The weight of the strip over the plane is given the horizontal force khW down the slope and the vertical force kvW, upward or downward, whichever gives the lower factor of safety. The coefficients are the ones you enter; the shaking adds no pore pressure.
Analysis Settings
Field
Default
Accepted
Required factor of safety FSreq
1.5
1 to 5
Required factor of safety, earthquake FSreq,eq (with an earthquake)
1.1
1 to 5
FSreq decides the verdict, and the depth and the angle that just reach it are given. With an earthquake the earthquake case has its own required value.
Choosing the strength, the water and the earthquake
Choice use it for
The strength is
Drained — c′, φ′ The long term, or any soil where the water can drain.
τf = c′ + σ′ tan φ′
Undrained — cᵤ, φᵤ = 0 A clay in the short term, in total stress.
τf = cu, so FS = cu / (γH sin β cos β)
The three ways of giving the water are compared on the example (drained, γsat = 19.5 kN/m³): no pore pressure gives FS = 1.733; a table 2 m below the ground gives 1.241; the table at the ground surface gives 1.017; and ru = 0.25 gives 1.369. A table 6 m deep, at the plane, gives 1.733 again.
Use the water table when you know where the water stands and that it flows parallel to the slope; the module takes the pressure from the column of water over the plane.
Use ru when you work from a ratio, as slope charts do. Set ru = γw cos²β / γ to reproduce a water table at the surface when γ = γsat.
Use None only for dry soil or for water far below the plane.
The earthquake
With Pseudo-static the module evaluates both directions of the vertical force and keeps the lower factor of safety; the line “kv upward” or “downward” in the Calculations tab says which governed. In an undrained analysis the larger shear stress governs.
Analyze and read the results
Press Analyze. The bar reads Analysed — the factor of safety calculated with Notes (1) (or Warnings (n)) and Edit inputs; the inputs are locked, the Model tab stays on screen, and the answer is in the Results tab. Edit inputs unlocks the model and clears the results.
The bar after Analyze.
Below the cards the module lists σ = 99.65 kPa, u = 0, σ′ = 99.65 kPa, τ = 26.70 kPa and τf = 46.27 kPa, and a table Values, step by step.
The Results tab of the example.
Card
The example
Factor of safety FS
1.733 OK (FSreq = 1.50)
Depth of the plane at which FS = FSreq Hreq
15.86 m
Steepest slope angle with FS ≥ FSreq βreq
17.28 °
Critical depth, FS = 1 Hcr
none
The verdict words
The factor of safety reads OK at or above FSreq, OK, near the limit within 10 % above it (1.583 at H = 10 m) and NOT OK below it. With an earthquake a second card carries the same words against FSreq,eq.
With water, with an earthquake
With water two cards are added: the factor of safety without pore pressureFSdry and, with a water table, with the water at the ground surfaceFSsat, and the list gains the equivalent ratio u / σv.
With an earthquake the cards add FSeq and the yield coefficientky, and the list adds σeq, σ′eq, τeq, τf,eq, Hreq,eq and βreq,eq.
Results with a water table and the earthquake.
When a card has no number
Hreq reads no limit when FS stays at or above the required value at every depth (the slope at 10°), and none when it is below it already at the shallowest depth (a dry soil with c′ = 0).
βreq reads above 70° or none in the same way.
Hcr reads none when FS stays at or above 1 at every depth, and every depth when it is below 1 everywhere.
ky reads above 3 when FS stays above 1 up to kh = 3.
Using the numbers
Hreq and βreq are found with the other inputs as entered; they are the depth and the angle to design to for the required value.
ky is the horizontal coefficient the plane can take before FS reaches 1, with kv as given.
Changing the unit system after Analyze re-states the cards, tables, working and report without a new run.
The Calculations tab, the report and the Theory tab
The Calculations tab opens with Given and what is sought and writes out the working in numbered steps, each with its equation, the equation with your numbers and the result:
Stresses on the failure plane — σv, σ, τ, u and σ′.
Shear strength of the soil on the plane — τf.
Factor of safety — FS = τf / τ, and for a dry slope the same written in closed form.
The same slope with other water (with water) — FSdry and FSsat.
Pseudo-static earthquake (with an earthquake) — the forces, σ and τ of the earthquake case, FSeq and ky.
Depth and slope angle at the required factor of safety — Hreq, βreq, Hcr (and the earthquake values).
The tab ends with Notes and assumptions. Before Analyze it says “Press Analyze on the Model tab to calculate the factor of safety.”
The Calculations tab: the first step with the example’s numbers.
Notes and warnings
Notes (n) opens the assumptions of the run: the slope is a plane so long that its ends are not part of the analysis, and, as the case may be, that the water flows parallel to the ground, that ru gives the pore pressure, that the analysis is undrained in total stress, or that the shaking adds no pore pressure. A Warnings window opens by itself after Analyze when the run has a warning, with the warnings first; the Results tab then carries a brown banner “1 warning”.
Notes for the example.
The report
In Report fill in the cover (project, location, client, report number, date, prepared by, title / qualification, checked by, notes). The details are kept in this browser and saved with the model file. After Analyze, Save as PDF and Download Word (.docx) produce the report.
Its parts: 1 Introduction and scope, 2 Input data (with the section, stresses and charts drawings), 3 Calculation (3.1 to 3.4, one per step), 4 Results, 5 Assumptions and notes, 6 Summary and 7 References.
The Report tab.
The Theory tab has eleven sections: Infinite slope, and this module; The idea: one strip of the mass; Strength, and the factor of safety; Undrained clay; Water in the slope; The earthquake, pseudo-static; The charts; Depth and angle at the required factor of safety; A worked example; What the module assumes, and what it does not do; and References.
Worked example: the module’s own example
The module opens on this example: β = 15°, H = 6 m, γ = 17.8 kN/m³, c′ = 10 kPa, φ′ = 20°, dry, FSreq = 1.50.
FS = 46.27 / 26.70 = 1.733, above 1.50: OK. In closed form 10 / (17.8 × 6 × cos²15° × tan 15°) + tan 20° / tan 15° = 0.375 + 1.358 = 1.733.
Step 4: depth and angle
Hreq = 10 / (17.8 × cos²15° × tan 15° × (1.50 − 1.358)) = 15.86 m; the steepest angle with FS ≥ 1.50 is 17.28°; FS never falls to 1 at any depth, so there is no critical depth.
The same slope with a water table
Choose Water table, seepage parallel to the slope with zw = 2 m (γsat = 19.5): hw = 4 m, σv = 17.8 × 2 + 19.5 × 4 = 113.6 kPa, σ = 105.99 kPa, u = 9.81 × 4 × cos²15° = 36.61 kPa, σ′ = 69.38 kPa, τ = 28.40 kPa, τf = 10 + 69.38 × tan 20° = 35.25 kPa and FS = 1.241, NOT OK. The same slope with no pore pressure gives 1.733 and with the water at the surface 1.017; Hreq falls to 4.173 m.
The same slope with an earthquake
With Pseudo-static, kh = 0.15 and kv = 0: σ = 103.16 × (cos 15° − 0.15 sin 15°) = 95.64 kPa, τ = 103.16 × (sin 15° + 0.15 cos 15°) = 41.65 kPa, τf = 10 + 95.64 × tan 20° = 44.81 kPa and FSeq = 1.076, against 1.10: NOT OK. The yield coefficient is 0.1789.
In the other unit systems
In SI · tf the example gives σ = 10.16 t/m², τ = 2.723 t/m² and τf = 4.718 t/m² (99.65 / 9.80665, 26.70 / 9.80665, 46.27 / 9.80665). In US the boxes show H = 19.685 ft, γ = 113.313 pcf and c′ = 208.854 psf, and the results σ = 2.081 ksf, τ = 0.5576 ksf, τf = 0.9663 ksf and Hreq = 52.05 ft; the factor of safety is 1.733 in all three.
The example with a water table and the earthquake.
The stresses of that case.
The charts of that case.
How each input changes the answer
Each row changes one thing in the example (β = 15°, H = 6 m, γ = 17.8 kN/m³, c′ = 10 kPa, φ′ = 20°, dry, FSreq = 1.50) and runs the module again. Rows with water use γsat = 19.5 kN/m³ and γ = 17.8 kN/m³. The undrained rows have γ = 17.8 kN/m³ and no c′, φ′. The numbers are the ones the module gives.
The example with one change at a time
Change
FS
Hreq βreq
The example
1.733
15.86 m 17.28°
β = 10°
2.612
no limit 17.28°
β = 20°
1.291
3.496 m 17.28°
β = 25°
1.025
2.039 m 17.28°
H = 3 m
2.107
15.86 m 21.11°
H = 10 m
1.583
15.86 m 15.81°
c′ = 0
1.358
none 13.64°
c′ = 20 kPa
2.107
31.73 m 21.11°
φ′ = 15°
1.375
4.494 m 13.76°
φ′ = 30°
2.529
no limit 24.73°
γ = 20 kN/m³
1.692
14.12 m 16.87°
Water table zw = 4 m
1.479
5.860 m 14.80°
Water table zw = 2 m
1.241
4.173 m 12.43°
Water table zw = 0
1.017
2.486 m 10.17°
ru = 0.1
1.587
7.824 m 15.85°
ru = 0.25
1.369
4.444 m 13.74°
ru = 0.5
1.005
2.584 m 10.30°
ru = 0.9
0.4226
1.548 m 4.889°
Undrained, cu = 40 kPa
1.498
5.993 m 14.98°
Undrained, cu = 80 kPa
2.996
11.99 m 43.57°
FSreq = 1.3
1.733
no limit 19.87°
FSreq = 2
1.733
3.502 m 13.02°
The slope angle: from 10° to 25° the factor of safety falls from 2.612 to 1.025, and the critical depth appears (6.683 m at 25°).
The depth matters when there is cohesion: c′ shares the load over a thicker mass, so FS falls from 2.107 at 3 m to 1.583 at 10 m. A dry cohesionless soil gives the same FS at every depth.
Cohesion acts through c′ / (γH cos²β tan β): 0.375 in the example, so c′ = 0 lowers FS from 1.733 to 1.358.
The water reduces σ′: a table 4 m below the ground costs 0.25, at the surface 0.72. A table at or below the plane (6 m) changes nothing.
ru = 0.9 takes FS to 0.4226 and opens a warning.
FSreq does not change FS, only the verdict and the depth and angle: 1.3 gives OK with no limit on the depth; 2 gives NOT OK and 3.502 m.
The earthquake
Earthquake case on the example (kh and kv as shown)
kh, kv
FSeq
ky
0.05, 0
1.445
0.1789
0.15, 0
1.076
0.1789
0.30, 0
0.7660
0.1789
0.15, 0.1
1.057
0.1702
0.15, 0.3
1.009
0.1527
The yield coefficient does not depend on the kh you enter: it is the kh at which FS falls to 1, with kv as given. With kh = 0 and kv = 0 the earthquake case equals the static one (1.733) and the module notes it.
Messages: when the module stops or warns
A value outside its range is checked when you press Analyze: a window Cannot analyse — 1 input error names the field and the limit, and nothing is calculated. The Results tab then says “Press Analyze on the Model tab to calculate the factor of safety.” and the bar stays Not analysed.
The window Analyze opens for a slope angle of 80°.
Message
When
“Slope angle (β) must be at least 0.1°.” / “… at most 70°.”
β outside 0.1° to 70°
“Depth of the failure plane (H) must be at least 0.05 m.”
H below 0.05 m
“Unit weight of the soil (γ) must be at least 1 kN/m³.”
γ below 1
“Effective friction angle (φ′) must be at most 50°.”
φ′ above 50°
“Effective cohesion (c′) must be at least 0 kPa.”
c′ negative
“Undrained shear strength (cu) must be at least 0.1 kPa.”
cu below 0.1
“Depth of the water table below the ground (zw) must be at least 0 m.”
zw negative
“Pore pressure ratio (ru) must be at most 0.9.”
ru above 0.9
“Horizontal seismic coefficient (kh) must be at most 1.” / “Vertical seismic coefficient (kv) must be at most 0.5.”
kh above 1, kv above 0.5
“Required factor of safety (FSreq) must be at least 1.” / “… earthquake (FSreq,eq) must be at least 1.”
a required value below 1
“Slope angle (β) is missing.” / “Depth of the failure plane (H) is missing.”
an empty box
One more stop, a window Cannot analyse — a condition of the solution is not met, comes from the saturated unit weight: “The saturated unit weight 9.00 kN/m³ is not above that of water. Below the water table the effective unit weight (saturated minus that of water) would be zero or negative. Enter the saturated unit weight of the soil.” It ends with “Nothing was calculated. Change the inputs marked in red, then press Analyze again.”
Warnings
Warnings are given after a run that is calculated; the window opens by itself. Two of them:
“The factor of safety is below 1: FS = 0.423.” with the text “The shear stress on the plane is larger than the strength of the soil there: the mass is not in equilibrium on this plane. Flatten the slope, lower the pore pressure, or check the strength and the unit weights entered.” (here ru = 0.9)
“The factor of safety with the earthquake is below 1: FS = 0.766.” with the text “… in a pseudo-static analysis the mass would move on this plane during the shaking. Flatten the slope, lower the pore pressure, or check the coefficients and the strength entered.” (here kh = 0.3)
The Warnings window.
A third warning, that the effective normal stress on the plane is not positive, is written when the pore pressure carries more than the normal force, so that friction cannot act and the strength is the cohesion alone; check ru or the table and the unit weights then.
A result below the required value is not a stop: the card reads NOT OK and the numbers are given.
Good practice and common mistakes
Check that the model fits. The module treats a long slope with a plane parallel to the ground; for a slope of limited length or a deep circular surface use Slope stability.
Measure H vertically, as a borehole meets the plane, not at right angles to the slope.
Enter γ as the unit weight above the water table and γsat below it; the module stops if γsat is not above 9.81 kN/m³.
Run the water two ways when you are unsure: with the table at the surface and with the ratio. They agree when ru = γw cos²β / γ and γ = γsat.
Read FSdry and FSsat to see how much the water costs.
Choose the coefficients knowingly.kh and kv are the ones you enter; the vertical force is applied in the less favourable direction.
Use ky to judge the margin of the earthquake case: the horizontal coefficient the plane can take before FS reaches 1.
Set FSreq for your project before reading the verdict and the depth and angle.
Note your model. It is kept in this browser; Save to file… keeps it with the project and the report is the record.
Frequently asked questions
How is the factor of safety of an infinite slope calculated?
It is the shear strength of the soil on the plane over the shear stress the weight puts on it: FS = τf / τ with σ = σv cos²β and τ = σv sin β cos β. For the example σ = 99.65 kPa, τ = 26.70 kPa, τf = 46.27 kPa and FS = 1.733.
Why does the depth matter for a cohesive soil but not for a sand?
The friction term, tan φ′ / tan β, does not depend on H; the cohesion term c′ / (γH cos²β tan β) falls as H grows. A dry cohesionless slope has FS = tan φ′ / tan β at every depth (1.340 for 32° and 25°).
What do the depth and angle cards mean?
Hreq is the depth at which FS falls to the required value, βreq the steepest slope angle that keeps it at the depth you gave, and Hcr the depth where FS falls to 1. They are found with the other inputs as entered.
How is the water taken?
A water table parallel to the slope gives u = γwhw cos²β with hw = H − zw, and γsat below the table; zw = 0 is the water at the ground surface. A ratio gives u = ruγH.
What is the yield coefficient?
The horizontal coefficient kh at which the earthquake factor of safety falls to 1, with kv as given. For the example it is 0.1789; for a dry cohesionless soil it is tan (φ′ − β).
Which direction does the vertical force take?
The one that gives the lower factor of safety, upward or downward; the Calculations tab shows both factors and the one kept. In an undrained analysis the larger shear stress governs.
Can I use an undrained strength with water?
No. An undrained analysis is in total stress, so the Pore water choices are not offered; the factor of safety is cu / (γH sin β cos β).
What values does the module accept?
β from 0.1° to 70°, H from 0.05 m, γ from 1 kN/m³, φ′ from 0° to 50°, ru from 0 to 0.9, kh from 0 to 1, kv from 0 to 0.5 and the required values from 1 to 5. Others stop the analysis with a message that names the field.
Can I drag the slope or the plane?
No. Set β, H and zw in the Model tab; the drawing follows. The zoom buttons enlarge each view.
Does the module remember my inputs?
Yes. Every change is kept in this browser, with the analysed state, and the page opens on the model you last worked on. Reset to defaults restores the example; Save to file… keeps the model outside the browser.
Which units does it use?
SI · kN, SI · tf or US, switchable at any time. The stresses are in kPa, t/m² or ksf, the depths in m or ft and the unit weights in kN/m³, tf/m³ or pcf; the factor of safety and the coefficients have no unit.
What does the report contain?
A cover with your project details, then Introduction and scope, Input data with the drawings, the Calculation step by step, Results, Assumptions and notes, Summary and References, as a PDF or a Word file after Analyze.
Two modules give the factor of safety against liquefaction with depth for a site with several boreholes or soundings, from SPT blow counts or from CPT cone resistance. This page helps you choose the module that matches your test and links to the manual of each.
The Liquefaction family has two modules. Both work out the factor of safety against liquefaction with depth for a site with several boreholes or soundings, and mark the triggered and marginal zones. They differ in the test you have. Pick the one that matches your site investigation.
Your test
Module
Standard penetration test blow counts in boreholes
Each manual follows the same plan: what the module calculates, what you need before you start, a quick start, the screen, every input section by section, the choices that decide the answer, the results, the report, a worked example you can reproduce, a table of how each input changes the answer, the messages the module gives, and answers to common questions.
What the two modules share
The workspace. The drawing, the tabs, Analyze and the input lock, units and the report follow the same layout as the other GeoTerva modules. See the workspace guide.
A project of many tests. Several boreholes or soundings in one project, entered one by one or filled in from an Excel template.
The earthquake. You give the magnitude and the peak ground acceleration of the site.
The factor of safety with depth. The cyclic stress ratio, the cyclic resistance ratio and their ratio at every reading.
Colour-band sections. The factor of safety is drawn as a colour-band section between the boreholes or soundings, with the triggered and marginal zones marked.
The report. A project summary and a Word report close the work.
What each module takes, side by side
SPT triggering
CPT triggering
Test
SPT blow counts
CPT cone resistance
Method
Idriss and Boulanger (2014)
Boulanger and Idriss (2014) or Robertson and Wride (1998)
Also takes
Fines content, unit weights
Soil behaviour index, cone data
A typical liquefaction check in order
Choose the module
Pick the one that matches your test and open its manual for the fields.
Enter the tests
Type the boreholes or soundings, or fill in the Excel template and load it.
Enter the water and the earthquake
Give the water table, the magnitude and the peak ground acceleration.
Analyze and read the profile
Press Analyze. Read the factor of safety with depth and the colour-band section, then save the report.
Frequently asked questions
How do I check liquefaction with GeoTerva?
Open SPT triggering for blow counts or CPT triggering for cone readings. Enter the boreholes or soundings, the water table, the magnitude and the peak ground acceleration, press Analyze, and read the factor of safety with depth.
Can I enter several boreholes?
Yes. Both modules take several boreholes or soundings in one project, entered one by one or loaded from an Excel template.
Which methods do the modules use?
SPT triggering uses the procedure of Idriss and Boulanger (2014). CPT triggering uses the procedure of Boulanger and Idriss (2014) or of Robertson and Wride (1998).
What does the colour-band section show?
The factor of safety against liquefaction between the boreholes or soundings, with the triggered and marginal zones marked.
Do the modules give a report?
Yes. A project summary and a Word report close the work.
Check liquefaction triggering from SPT blow counts at every test of every borehole of a site: the corrected blow count, the cyclic stress and resistance ratios, the factor of safety with depth, the triggered and marginal zones, colour-band sections and a report. This manual walks through every input, the Excel template, the results and a worked example you can reproduce.
SPT triggering checks whether liquefaction is triggered in a site with several boreholes. For every standard penetration test below the groundwater table it corrects the blow count, works out the cyclic stress ratio CSR (the demand of the earthquake) and the cyclic resistance ratio CRR (what the soil can carry), and gives the factor of safety:
FS = CRR / CSR
FS below 1.0 is triggered; FS from 1.0 up to the required value FSreq is marginal; above it the result is OK. The method is Idriss & Boulanger (2014); the magnitude Mw and the peak ground acceleration amax are your inputs.
What you get
The corrected blow counts, CSR, CRR and FS of every test, with a step-by-step calculation of each one.
The triggered and marginal zones of every borehole, their thickness, and the minimum FS with its depth.
Colour-band sections between the boreholes, or colour columns when no section is defined, and a project summary with every borehole side by side.
An Excel template (one sheet per borehole) to fill in and import, model files, and a Word or PDF summary report.
What belongs elsewhere
Tests in clay-like soil are listed but not evaluated; the module reminds you to check those layers for cyclic softening separately. Consequences of liquefaction (settlement, lateral spreading, loss of bearing capacity) are outside this module.
Cone penetration data have their own module: CPT triggering.
Before you start: what you need
What
Source
Notes
Each borehole: name, groundwater depth, ground elevation
Boring logs, site survey
The groundwater depth is measured from the ground surface of that borehole.
Soil layers of each borehole
Boring logs, laboratory tests
USCS symbol, description, unit weight γ and saturated unit weight γsat, plasticity index PI (blank for non-plastic) and fines content FC. The first layer starts at the ground surface and each layer starts where the one above ends.
The SPT tests
Field blow counts
Depth and the raw field blow count N30 (last 30 cm, no correction); a laboratory fines content for a test is optional.
The design earthquake
Your design
Peak ground acceleration amax in g (site effects included) and moment magnitude Mw.
The test equipment
Boring report
Hammer energy ratio ER, borehole diameter, sampler type, rod stick-up above the ground.
For sections: distances along the line
Site plan
The distance of each borehole along each section line, in metres (or the unit of the page).
Quick start in eight steps
Open the module and choose the units
Open SPT triggering from the Liquefaction family. Pick SI · kN, SI · tf or US in the header.
Enter the boreholes
In Boreholes, Soil layers and SPT tests, enter each borehole, or fill the Excel template and use Import Excel….
Define the sections
In Sections, name a line through some of the boreholes and give the distance of each along it. Without a section the Contours view shows colour columns.
Enter the earthquake
In Earthquake, type amax and Mw.
Set the corrections and the settings
In SPT corrections give the hammer energy ratio, borehole diameter, sampler and stick-up; in Analysis Settings the required factor of safety, the clay-like limit and the deepest test.
Press Analyze
Press Analyze. The bar reads Analysed, the inputs lock and the Contours view opens. A Warnings window opens when the run carries warnings.
Read the answer
Look at the colour bands, the Borehole and Project summary views and the Results tab; open Calculations for any test.
Take the report
In Report fill in the cover, then save a PDF or download a Word file.
The screen: three views, five tabs
The layout is the shared GeoTerva one, described in the workspace guide. The drawing has three views, chosen above it; the right-hand panel has the tabs Model, Results, Calculations, Report and Theory.
Borehole shows one borehole: its soil log with the groundwater level, the N30 and (N1)60cs points, the CSR curve against the CRR points, and the factor of safety against depth with the triggered and marginal zones tinted. Grey hatched bands are not evaluated (above the groundwater, clay-like, or deeper than the limit). Choose the borehole with the buttons above the drawing. Layers chips (N₃₀ field, (N₁)₆₀cs, Result zones, FS values) hide or show parts of the drawing; the analysis always uses every test.
Contours draws colour bands of a chosen Field over the section between the boreholes. It is the view that opens after Analyze.
Project summary plots FS against depth for all boreholes, and a fence of every borehole side by side (soil on the left half, result on the right half) with its minimum FS. One chip per borehole switches its curve.
Borehole view before Analyze: the log and the field blow counts.
Borehole view after Analyze.
Project summary view.
The Contours controls
Field: FS (the factor of safety), Result (triggered, marginal, OK as three colours), CSR, CRR, (N₁)₆₀cs, N₆₀ and σ′v0 (the initial effective vertical stress). One legend serves all panels.
Layout: Columns (every borehole as its own colour column against its own depth, no interpolation), one button per section, and All when there are two or three sections (one panel under the other).
Show: Logs (the soil strip of each borehole), Tests (a dot at every test, coloured by result) and Labels.
Between two boreholes the field is interpolated linearly at equal elevation; beyond the outer boreholes the nearest one is used. Grey is not evaluated. The title line states the vertical exaggeration of the section.
Contours of the factor of safety on Section 1.
The Result field.
Columns layout.
What stays after a reload
Unlike some other modules, this one keeps your work. Every change is stored in the browser, and the page opens with the project you last worked on (also when it was analysed: it opens analysed). The store message names the time. Save to file… writes the model to a .json file you can send or move, Open file… reads one, Quick Save… keeps named versions in the browser list with Load and Delete, and Reset to defaults returns to the example. The model name box names the file and the Excel template.
Entering the model, section by section
The Model tab is a column of sections. Model data stays open on its own; the others form an accordion: opening one closes the previous one, and Next and Back walk through them. The inputs lock after Analyze (Edit inputs unlocks them and clears the results). A box you leave empty goes back to its last value; a value the module cannot use is reported when you press Analyze.
Model data and Excel input
Model data: files and quick saves.
The Excel input section has Download template (.xlsx) (the template filled with the current model, named after the model), Import Excel… and Preview the template. The template has a Project sheet (earthquake, corrections, settings), a Sections sheet (which borehole lies on which section, and where) and one sheet per borehole, whose name is the borehole name, with the soil layers on the left and the SPT tests on the right. It always holds metres, kN/m³, % and g, whatever the unit system of the page.
Excel input.
Boreholes
A project holds any number of boreholes. Choose one with the buttons (each shows its number of tests and, after Analyze, its result); + Add borehole, Duplicate and Delete borehole (the project keeps at least one) change the list.
A new borehole starts with zw = 2 m, EL = 0, one layer of silty sand to 10 m and tests at 1.5, 3 and 4.5 m (N30 10, 12, 14).
The Boreholes section.
Fields of a borehole
Field
Default
Notes
Borehole name ID
BH-1
Up to 24 characters; a name already used is not accepted.
Groundwater depth zw
1.80 m
Below the ground surface of this borehole. Also 2.40 m (BH-2) and 3.10 m (BH-3).
Ground elevation EL
4.20 m
Used to place the borehole in a section. 4.05 m and 5.10 m for BH-2 and BH-3.
Sections
A section is a line through some of the boreholes; the Contours view draws the colour bands between them. + Add section adds one, named “Section n”. In each section the boreholes are listed from the left end to the right end with their distance along the line. ↑ ↓ exchange a borehole with its neighbour (they take each other’s distance), the distance box accepts a new value, × takes the borehole out, and the list under the table adds one. A borehole may belong to several sections. The example has one section: BH-1 at 0 m, BH-2 at 32 m, BH-3 at 70 m.
The Sections section.
Soil layers
From the ground surface down; To is the only depth you type, the next layer starts there. The PI box decides the screening and FC is the fines content used for the tests of the layer that have no laboratory value. + Add layer adds a 2 m layer of silty sand (γ 18, γsat 19.5, FC 20) below the last one; × deletes a layer (the last layer cannot be deleted).
The Soil layers section.
Fields of a layer
Field
Default
Notes
From, To
0.00 – 1.50 …
m; the profile of BH-1 ends at 20 m.
Soil (USCS), Description
GM, Fill, silty gravel …
A symbol from the list or your own; when PI is blank, CL, CH, OL, OH and PT mean clay-like.
γ, γsat
18.5 / 19.5 kN/m³ …
γ is used above the groundwater table and γsat below it.
PI
blank = NP
Percent; PI at or above the clay-like limit: not evaluated.
FC
20 %
Percent.
SPT tests
Depth, the raw field blow count N30, and an optional laboratory FC lab that replaces the layer value for that test. The Layer column names the layer found at the depth, and the Result column shows the FS after Analyze (a pill: triggered, marginal, OK) or N/E for not evaluated. + Add test adds a test 1.5 m below the deepest with N30 = 10. Columns can be pasted straight from Excel.
The SPT tests section.
Earthquake
The earthquake is one for the whole project.
Earthquake.
Earthquake fields
Field
Default
Notes
Peak ground acceleration amax
0.35 g
At the ground surface, site effects included. Must be above zero.
Moment magnitude Mw
7.5
The box is set for 4 to 9.5. Must be above zero.
SPT corrections
N60 = N30 · CE · CB · CS · CR. The rod length of a test is its depth plus the stick-up.
Read-only boxes show the CE, CB and CS in use.
SPT corrections.
Correction fields
Field
Default
Notes
Hammer energy ratio ER
60 %
CE = ER / 60.
Borehole diameter CB
65–115 mm
Buttons: 65–115 mm (1.00), 150 mm (1.05), 200 mm (1.15).
Sampler CS
Standard sampler
Standard sampler (1.00) or Without liners (1.20).
Rod stick-up L0
1.50 m
Above the ground; CR follows the rod length: 0.75 below 3 m, 0.80 below 4 m, 0.85 below 6 m, 0.95 below 10 m, 1.00 beyond.
Analysis Settings
The method button shows Idriss & Boulanger (2014); it is the one method.
Analysis Settings.
Analysis settings
Field
Default
Notes
Required factor of safety FSreq
1.20
Below it (and from 1.0) a test is marginal.
Clay-like screening PIlim
7 %
Not evaluated when PI is at or above it.
Deepest test zmax
20 m
Deeper tests are listed but not evaluated.
The Excel template, step by step
Use Preview the template to see the sheets in a window, or download it. Yellow cells are inputs. On import the module shows a window, Import Excel — check before replacing, listing each sheet (borehole name, layers, tests, groundwater), the sections found and any problems; Replace the boreholes replaces the boreholes and the sections of the model (and the project settings the Project sheet carries). Import is not offered while results are shown: Edit inputs first.
The template preview.
The import check window.
The method and its options
There is one method, Idriss & Boulanger (2014). What you can choose is how the tests are corrected and screened:
Equipment corrections — ER, borehole diameter, sampler and stick-up. They scale N60: a higher energy ratio or a larger factor raises N60 and the resistance.
Fines — the fines content of the layer (or the laboratory value of the test) adds Δ(N1)60 to the corrected count, so a silty sand is stronger than a clean one at the same blow count.
Screening — tests above the groundwater table, deeper than zmax or in clay-like soil (PI at or above PIlim; CL, CH, OL, OH, PT when PI is blank) are listed but not evaluated.
Required factor of safety — it only separates marginal from OK; the triggered limit is always 1.0.
Each evaluated test stands for its layer from halfway to the neighbouring test above to halfway to the one below; neighbouring intervals with the same result merge into zones.
Analyze and read the results
Press Analyze. The bar counts the boreholes (“Analysing… BH-1 (1 / 3)”) and then reads Analysed — 3 boreholes, 39 tests, adding the number of warnings. The view switches to Contours, a short message says the colour bands show the selected field, and, when there are warnings, the Warnings window opens by itself. The module stays on the Model tab: open Results.
The bar after Analyze.
Results tab
At the top a line says Liquefaction is triggered in 3 of 3 boreholes (or “not triggered in any borehole”), with amax, Mw and FSreq. One row per borehole follows: its result chip, the groundwater depth, how many tests were evaluated, the minimum FS with its depth, the triggered thickness with the zones, and the marginal thickness with the zones. Clicking a row selects the borehole.
The example, as the module gives it
Borehole
Triggered
Marginal
BH-1 minimum FS 0.46 at 4.00 m
5.45 m 1.80–6.00, 12.25–13.50 m
3.00 m 6.00–9.00 m
BH-2 minimum FS 0.70 at 3.00 m
2.85 m 2.40–5.25 m
3.50 m 5.25–7.50, 9.75–11.00 m
BH-3 minimum FS 0.84 at 6.00 m
3.25 m 5.00–8.25 m
1.75 m 8.25–10.00 m
The Results tab.
Test by test
Below, a table lists every test of the chosen borehole: depth, soil, N30, N60, σ′v, (N1)60cs, CSR, CRR, FS and the result chip. All columns adds CR, σv, CN, (N1)60, FC, Δ(N1)60, rd, CRR7.5, MSF and Kσ. A test that is not evaluated shows N/E with the reason (above groundwater, clay-like (PI ≥ 7), deeper than zmax). Click a row for its calculation.
The test table with all columns.
Warnings
The Warnings window lists the warnings and the assumptions of the analysis. The warnings the module writes are:
“Tests in clay-like soil (PI ≥ 7) are not evaluated: BH-1 — 2 tests, BH-2 — 2 tests, BH-3 — 4 tests. Check these layers for cyclic softening separately.” (the example)
“(N₁)₆₀cs ≥ 37, taken at the upper limit of the CRR curve: BH-1 at 10.00, 11.50, 17.50, 19.00 m; BH-2 at 7.50, 9.00, 15.00, 16.50, 18.00, 19.50 m; BH-3 at 10.50, 12.00, 13.50 m.” (the example with ER = 80 %: it appears when a corrected count reaches the end of the CRR curve)
“No fines content given for BH-1 layer 2 — FC = 0 % is used.”
“No test evaluated in BH-1 (all above the water table, clay-like or deeper than the deepest test).” (the module writes the last words with a z and a subscript max)
The bar turns amber and the Results and Report tabs carry the same warning bar.
The Calculations tab, the report and the Theory tab
The Calculations tab writes out one test. Choose the borehole and the test in the two lists (or click a row or a mark), and six steps follow with your numbers: 1 vertical stresses, 2 corrected blow count N60, 3 clean-sand equivalent (N1)60cs (with CN iterated on its exponent), 4 seismic demand CSR, 5 cyclic resistance CRR (with MSF and Kσ), 6 factor of safety. A test that is not evaluated stops after step 3 with the reason. Each step opens and closes.
The Calculations tab (steps 2 to 5).
The report
In Report fill in the cover (project, location, client, report number, date, prepared by, title / qualification, checked by, optional notes); it is kept in the browser and saved with the model file. After Analyze Save as PDF (opens a print window: choose “Save as PDF” as the printer) and Download Word (.docx) are available, and the preview shows the report. Its parts: 1 Introduction and scope, 2 Boreholes and soil profiles (borehole table, sections, layers of every borehole), 3 Earthquake, SPT corrections and settings, 4 Results by borehole (with the contour figure and the project figure), 5 Test by test (a table and a figure for every borehole), 6 Warnings (only when the run has warnings) and 7 Summary.
The Report tab: warning bar and cover.
The Theory tab has fourteen sections: Scope, Screening of the tests, Stresses, SPT corrections, Overburden correction, Fines content, Cyclic stress ratio, Cyclic resistance ratio, Magnitude scaling factor, Overburden factor, Factor of safety, Zones and thickness, References, Colour-band section. Its Scope section names the same method as Boulanger & Idriss (2014).
Worked example: BH-1 at 4.00 m
The default example, test at 4.00 m in BH-1 (SP-SM, FC 8 %, N30 = 10, groundwater at 1.80 m, amax = 0.35 g, Mw = 7.5, ER 60 %, stick-up 1.50 m). A separate Python calculation from the formulas the module states gives the same numbers.
Stresses: σv = 18.5·1.5 + 18.0·0.3 + 19.5·2.2 = 76.05 kPa; the pore pressure below the groundwater table u = 9.81 × (4.00 − 1.80) = 21.58 kPa, so σ′v = 76.05 − 21.58 = 54.47 kPa.
Rod length 4.00 + 1.50 = 5.50 m, CR = 0.85; N60 = 10 × 0.85 = 8.50.
For the test at 2.50 m the module gives CSR = 0.263, CRR = 0.130 and FS = 0.49.
The same project in US units
Switch to US after Analyze: nothing is run again. BH-1 now reads groundwater 5.91 ft, the minimum FS 0.46 at 13.12 ft, the triggered zones 5.91–19.69 and 40.19–44.29 ft (17.88 ft) and the test table σ′v in ksf; the calculation shows σ′v = 1.14 ksf at 13.12 ft with CN = (2.12 / 1.14)0.517 = 1.378. The stick-up box shows 4.92 ft. FS is the same 0.46.
The same project in SI · tf
In SI · tf the stresses are in t/m²: σv = 7.75 and σ′v = 5.55 t/m² at 4.00 m, with CN = (10.33 / 5.55)0.517 = 1.378 (54.47 kPa ÷ 9.80665 = 5.55). Depths and zones stay in metres.
How each input changes the answer
Each row changes one thing in the example and runs the module again (typing into the boxes). The first table gives the test at 2.50 m of BH-1 (SP-SM, FC 8 %, N30 = 7, γsat = 19.5 kN/m³); the example gives CSR 0.263, CRR 0.130, FS 0.49.
BH-1 at 2.50 m with one change at a time
Change
CSR / CRR
FS
The example
0.263 / 0.130
0.49
amax = 0.25 g Lower demand; BH-1 triggered thickness 4.20 m
0.188 / 0.130
0.69
amax = 0.45 g Higher demand; thickness 8.45 m
0.338 / 0.130
0.38
Mw = 6.5 Smaller earthquake: CRR rises through the magnitude factor
0.260 / 0.139
0.54
Mw = 8.0 Larger earthquake: CRR falls
0.265 / 0.126
0.48
ER = 80 % N60 7.93; this run adds the warning for (N1)60cs ≥ 37
0.263 / 0.154
0.59
ER = 45 % N60 4.46; thickness 15.20 m
0.263 / 0.112
0.43
Borehole 200 mm (CB 1.15)
0.263 / 0.141
0.53
Sampler without liners (CS 1.20)
0.263 / 0.144
0.55
Stick-up 0 CR 0.75 instead of 0.85
0.263 / 0.122
0.46
Stick-up 3.0 m Same CR 0.85 here: no change at this test
0.263 / 0.130
0.49
BH-1 groundwater 1.0 m The test becomes the minimum of BH-1
BH-1 groundwater 3.0 m The test lies above the groundwater: not evaluated
—
N/E
The pattern: amax acts on CSR only; the magnitude, the corrections and the fines act on CRR only (the magnitude also on CSR through rd, slightly); the groundwater depth and the unit weight act on both through the stresses, and the blow count on CRR.
Settings change which tests count and how they are classed, not the FS of a test. Effect on the project (BH-1 triggered thickness, boreholes triggered / marginal-only of 3; the BH-1 minimum FS stays 0.46 in all five runs):
Change
Triggered BH-1
Boreholes
The example
5.45 m
3 / 0
FSreq = 1.0
5.45 m
3 / 0
FSreq = 1.5
5.45 m
3 / 0
zmax = 10 m
4.20 m
3 / 0
PIlim = 4 %
5.45 m
3 / 0
PIlim = 20 %
8.45 m
3 / 0
In the second table the last column reads “triggered / marginal-only”. PIlim decides which layers count as clay-like (a larger limit evaluates more of them: BH-1 triggered thickness 8.45 m at 20 %), and zmax cuts the deep tests (4.20 m at 10 m).
Messages: when the module stops, and what it warns about
Before it calculates, the module checks the inputs. If one cannot be used, a window Cannot analyse — n input error(s) lists the messages, nothing is calculated, and the bar stays Not analysed. Fix the values and press Analyze again.
The stop window.
When
Message
amax is zero
“Peak ground acceleration is missing.”
Mw is zero
“Moment magnitude is missing.”
ER is zero
“Hammer energy ratio is missing.”
FSreq is zero
“Required factor of safety is missing.”
A test lies below the profile
“BH-1 test 13 at 25 m lies below the profile (20 m).”
A unit weight is zero
“BH-1 layer 2: unit weight is missing.” / “… saturated unit weight is missing.”
Several problems appear together in one window. A box left empty is not an error: it returns to its last value. The warnings that do not stop the run are in the Results section above.
Messages of the files and the template
Import: “Edit inputs first — the import replaces the boreholes.” while results are shown.
Import window problems: “BH-1: groundwater depth is missing.”, “BH-1!E8: unit weight γ is missing.”, “BH-1!K8: SPT N30 is missing.” (the row is skipped), “Sections!B7: "BH-9" is not a borehole of this file.”, “BH-1: the header row "From (m) · To (m) · USCS …" was not found — the sheet is skipped.” and, without a Project sheet, “No "Project" sheet — the earthquake, corrections and settings of the model are kept.” Replace the boreholes is offered unless an input error remains.
A file that is not a workbook: “Not a GeoTerva template: not a zip (.xlsx) file”.
Open file: “Not a model file: no boreholes found in the file”.
“The project keeps at least one borehole.”
Good practice and common mistakes
Give the groundwater depth of each borehole. Tests above it are not evaluated; the depth sets σ′v and so both CSR and CRR.
Enter the raw N30. The module applies the corrections; correcting twice lowers the answer.
Give ER from the hammer record (60 % when unknown is the example default), and the real borehole diameter and sampler.
Check the screening. Layers of PI at or above the limit are not evaluated: look at the Warnings and check them for cyclic softening separately.
Use laboratory fines (FC lab) for tests that have them; the layer value is the fallback.
Make one section per line and give the true distances; use Columns to look at the boreholes alone.
Check amax and Mw — they are your inputs and the answer is sensitive to them (table above).
Save to a file for the project record: the browser store is only in this browser.
Frequently asked questions
How is the factor of safety against liquefaction calculated here?
FS = CRR / CSR at every test below the groundwater table, with CSR = 0.65 · (σv/σ′v) · amax · rd and CRR from the clean-sand equivalent corrected blow count, scaled for magnitude and overburden. For BH-1 at 4.00 m: CSR 0.3087, CRR 0.1413, FS 0.46.
When is a test triggered, marginal or OK?
Below 1.0 it is triggered; from 1.0 up to the required factor of safety (1.20 by default) it is marginal; at or above it, OK.
Why are some tests “not evaluated”?
They lie above the groundwater table, deeper than the deepest test (20 m by default) or in clay-like soil (PI at or above the limit, 7 by default; CL, CH, OL, OH, PT when PI is blank). They stay in every table with the reason.
Which method does it use?
Idriss & Boulanger (2014) for SPT: corrected blow count with energy, diameter, sampler and rod-length factors, overburden and fines corrections, and the magnitude and overburden scaling of the same reference.
Can I analyse several boreholes at once?
Yes. Any number of boreholes in one project; the results table, the project summary and the sections show them together.
How do I draw a section between boreholes?
In Sections press Add section, add the boreholes and give each its distance along the line. The Contours view then draws colour bands between them; without a section it draws one colour column per borehole.
Does the module keep my project?
Yes. Every change is kept in the browser and the page opens with the project you last worked on, analysed or not. Save to file, Quick Save and Reset to defaults are in Model data.
How do I use the Excel template?
Download it (filled with your model), edit the Project, Sections and borehole sheets, and import it. A window lists what was found and the problems before anything is replaced.
Which units can I use?
SI · kN, SI · tf or US, switchable in the header even after Analyze. The drawings stay in SI; the cards, tables, boxes and calculations convert. The Excel template is always metres, kN/m³, % and g.
Where do I enter the magnitude and the acceleration?
In Earthquake: the peak ground acceleration in g and the moment magnitude. They are your inputs for the whole project.
What does the report contain?
A cover, then introduction and scope, boreholes and soil profiles, earthquake and settings, results by borehole with figures, test by test tables, warnings when there are any, and a summary. Save it as PDF or download it as Word after Analyze.
Does it check settlement or lateral spreading?
No: the module gives triggering. Settlement, lateral spreading and loss of bearing capacity are separate checks that use the zones it finds.
Check liquefaction triggering from cone penetration tests: enter or import several soundings, set the earthquake, choose Boulanger & Idriss (2014) or Robertson & Wride (1998), and read the factor of safety with depth, the triggered and marginal zones and the colour-band sections. This manual walks through the screen, every input, the Excel template, the results and the report, with a worked example you can reproduce.
CPT triggering checks whether liquefaction is triggered at every reading of a cone penetration test below the groundwater table. You enter one or several CPT soundings (or fill in the Excel template), the design earthquake (a peak ground acceleration and a moment magnitude) and a method. For each reading the module finds the cyclic stress ratio CSR (what the earthquake asks of the soil), the cyclic resistance ratio CRR (what the soil can give), and the factor of safety:
FS below 1.0 is a triggered reading; FS from 1.0 up to the required value FSreq is marginal; at or above FSreq it is OK. Readings the procedure does not apply to (above the design water table, clay-like, deeper than a limit you set) are listed as not evaluated.
What you can describe
Several soundings in one project, each with its own groundwater depth, ground elevation and readings (depth, cone resistance qc, sleeve friction fs, and the pore pressure u2 when recorded).
Two methods, each a complete package: Boulanger & Idriss (2014) and Robertson & Wride (1998).
Sections: lines through some of the soundings, with the distance of each along the line, for the colour-band drawings.
Excel in and out: a template with a Project sheet, a Sections sheet and one sheet per sounding.
The module gives, for every sounding, the soil behaviour log, the profile of qc1Ncs, CSR, CRR and FS against depth, the triggered and marginal zones with their thickness, colour-band sections between the soundings, a project summary, a step-by-step calculation of any reading, and a PDF or Word report.
Which module for which job
This module starts from cone data. The soil type, the unit weight and the fines content are estimated from qc, fs and u2, so no samples are needed to run it.
For SPT blow counts, boreholes with fines content and unit weights, use the SPT triggering manual.
Before you start: what you need
Have these ready:
What
Notes
The CPT readings
Depth, cone resistance qc and sleeve friction fs for every reading. The pore pressure u2 behind the cone is used when you have it. If the file holds the corrected cone resistance qt or a friction ratio instead, the import and the paste dialog convert them.
The groundwater depth of each sounding
The depth at the time of the test. A different design depth can be entered for each sounding.
The ground elevation of each sounding
Needed for the sections: the soundings are placed at their elevations.
The design earthquake
The peak ground acceleration amax at the ground surface, in g, and the moment magnitude Mw. Both are your inputs.
Where the soundings lie
For a colour-band section: the distance of each sounding along a line.
Quick start in eight steps
Open the module and choose the units
Open CPT triggering from the Liquefaction family. Pick SI · kN, SI · tf or US in the header; you can change it at any time.
Bring the soundings in
Either download the template from Excel input, fill one sheet per sounding and press Import Excel…, or choose a sounding under Soundings and use Paste readings… in Cone readings.
Set the groundwater and the sections
For each sounding enter the groundwater depth (and the elevation). In Sections give each sounding its distance along a section.
Enter the earthquake
In Earthquake type amax and Mw.
Choose the method
In Analysis Settings pick Boulanger & Idriss (2014) or Robertson & Wride (1998) and review the unit weight, FSreq and the screening limits.
Press Analyze
Press Analyze at the foot of the Model tab. The inputs lock, the drawing changes to Contours, and a Warnings window opens if the run has warnings.
Read the answer
The Results tab gives the result of each sounding and a table reading by reading; the Sounding and Project summary views show the same against depth. Click a depth to open its calculation.
Take the report
The Report tab saves a PDF or a Word file.
The screen: three views of the project
The layout is the one every GeoTerva module shares, described in the workspace guide: drawings on the left, the Model, Results, Calculations, Report and Theory tabs on the right, and the Analyze bar at the foot of the Model tab. This module has three views, chosen with the buttons above the drawing.
Before Analyze: the Sounding view follows what you enter; the result panels say “Press Analyze”.
Sounding
One sounding at a time, chosen with the buttons beside Sounding. From the left: the soil behaviour log with the result strip beside it, then five panels against depth: the cone resistance qt, the soil behaviour index Ic with the clay-like limit, the clean-sand cone resistance qc1Ncs, CSR and CRR, and FS with the lines at FS = 1.0 and at FSreq. The groundwater depth is the dashed blue line; ranges that are not evaluated are hatched and named (above groundwater, clay-like), and the lowest FS is marked with its value and depth.
The Show chips switch qt, qc1Ncs, Soil log, Result zones and Minimum FS. They change the drawing only; the analysis always uses every reading. Before Analyze the cone resistance is drawn and the other panels say “Press Analyze”. Click any depth in the panels after Analyze and the Calculations tab opens at the nearest reading.
Sounding view of CPT-1 after Analyze.
Contours
The colour-band section between the soundings of the chosen section. Each sounding gives the field against depth; between two soundings the field is interpolated linearly at equal elevation, and beyond the outer ones the nearest sounding is used. Grey is not evaluated. Three groups of chips sit above it:
Field: FS, Result (triggered, marginal, OK, not evaluated), CSR, CRR, qc1Ncs, Ic, qt and σ′v0. FS runs on a fixed scale from 0 to 2 (2 and above at the top of the legend).
Layout: Columns (one colour column per sounding against its own depth, no interpolation) or one chip per section; All appears when the project has two or three sections and draws them one under the other.
Show: Logs (the soil log of each sounding), Results (the result strip) and Labels (name, elevation and distance).
Contours, field Result.
Contours, layout Columns: no interpolation.
The chips of the Contours view.
Project summary
The factor of safety of every sounding on one plot, with the lines at 1.0 and FSreq (values above 2.0 are drawn at the edge), and on the right one column per sounding with its soil log and its result strip, the groundwater mark and the minimum FS written under it. The chips switch each sounding on or off.
Project summary.
Entering the model, section by section
The Model tab walks you through its sections: Model data stands on its own, and the others open one at a time with Back and Next at their foot: Excel input, Soundings, Sections, Cone readings, Earthquake and Analysis Settings. Opening one closes the previous one. After Analyze the inputs are locked until you press Edit inputs; the unit system can still be changed.
Model data
The box where the work is kept. Every change is kept in this browser: after a reload the module opens on the project you last worked on, analysed or not, and says so (“Opened with the project you last worked on …”). Model name is a label that goes into file names.
Save to file… writes the model as a JSON file (in SI, whatever the page shows; the report cover is included). Where the browser offers it you choose the folder; otherwise the file goes to the download folder.
Open file… reads such a file back and reports what it ignored.
Quick Save… asks for a name and keeps this version in the list under it; choose it and press Load, or Delete it (after a confirmation). A name already used asks whether to replace it.
Reset to defaults goes back to the example project: “The inputs are back at the module defaults, and this is now the model kept in the browser.”
Model data.
Excel input
A CPT sounding has hundreds or thousands of readings, so the module works with a template. Download template (.xlsx) gives a workbook filled with the current model; Preview the template shows its first rows on the screen. The strip of tabs shows the sheets: Project, Sections and one sheet for each sounding.
Project: amax, Mw, the method, CFC, f, a, the unit weight option and values, FSreq, Ic,lim, zmax and hmin.
Sections: one row for every sounding of a section: the section name, the sounding and its distance along the line (m).
One sheet per sounding: the sheet name is the sounding name; on top the groundwater depth during the test, the design groundwater depth (blank: the same) and the ground elevation; below the heading row the readings depth · qc · fs · u2.
Excel input.
The template preview: the Project sheet.
The template is always written in metres, MPa (cone resistance), kPa (sleeve friction and pore pressure), kN/m³ and g. On import the unit of a column may be written in its heading, in brackets: (m), (cm), (mm), (ft) for the depth and (MPa), (kPa), (kg/cm2), (bar), (tsf), (psi), (atm) and others for the stresses. A corrected cone resistance column qt is turned back into qc with the net area ratio, and a friction ratio column Rf into fs.
Press Import Excel… and choose the file. The module does not import at once: a window Import Excel — check before importing lists each sheet with its sounding, the number of readings, the groundwater depth and the units it read, and then either “No problems found.” or a numbered list of Problems. Without problems you choose:
Add the soundings of the file to the project: a sounding of the same name is replaced, the others stay, and the earthquake, method and settings of the model are kept. The module then says, for example, “Added 2 soundings from …; the project has 5 soundings now.”
Replace the soundings and the sections of the model by those of the file; the Project sheet then also sets its parameters (“Imported 2 soundings and 1 section from …”).
With problems the window offers only Cancel and the message under the buttons reads “The file could not be imported — see the problems.” A problem is, for example, a sounding sheet with no groundwater depth, no sleeve friction column, or a section row naming a sounding that is not in the file. Import is not possible while the model is analysed: press Edit inputs first.
The import window: the units read from the headings are listed.
The import window with problems: nothing is imported.
Soundings
A project holds any number of soundings. The buttons list them with their number of readings (and, after Analyze, their result); the one you choose is the one in the drawing and in the readings table. + Add sounding adds an empty one: its groundwater depth is blank and it has no readings (its elevation is copied from the sounding you were on), so the analysis asks for both. Duplicate copies the chosen sounding; Delete sounding removes it (the project keeps at least one).
Soundings.
Field
Notes
Sounding name (ID)
First sounding: CPT-1. Up to 24 characters. A name already used by another sounding is not accepted: the box goes back to the old name and a message says the name is already used. The name is also the sheet name in Excel.
Groundwater depth at the time of the testzw m · ft
First sounding: 1.80 (CPT-2 2.40, CPT-3 3.10). Used for the pore pressure at the time of the test, that is for the normalisation of the cone resistance. The box accepts 0 or more; a blank is not accepted.
Design groundwater depthzw,D m · ft
First sounding: blank (“same”). Used for CSR and Kσ. Blank means the same as zw. Also the depth above which readings are not evaluated.
Ground elevation EL m · ft
First sounding: 4.20 (CPT-2 4.05, CPT-3 5.10). Places the soundings in the Contours view.
The default values of the three example soundings are listed in the table; a sounding you add has no groundwater depth until you enter one.
Sections
A section is a line through some of the soundings, and the Contours view draws one section at a time (or all, when there are two or three). + Add section makes a new, empty one, named “Section 2” and so on. In each section card: its name (editable), the list of its soundings from the left end to the right with the distance x of each along the line, ↑ ↓ to exchange a sounding with its neighbour (the two take each other’s distance), × to take a sounding out of the section, and a list at the foot to add a sounding that is not yet in it. A sounding may belong to more than one section. Typing a new distance puts the sounding in its place along the line. The default section is “Section 1”: CPT-1 at 0 m, CPT-2 at 32 m, CPT-3 at 70 m.
Sections.
Cone readings
The readings of the sounding you chose (the buttons under Readings of change it). A summary line gives the number of readings, the depth range, the usual interval, the range of qc, whether u2 is given, and the number of gaps in the record. The table is paged (40 rows); go to depth jumps to a depth. Once analysed, each row shows its result, and clicking it opens its calculation.
Type in the table. Enter and the arrow keys go along a column, Tab goes along the row. A depth typed out of order is put in its place.
Paste into the table. Select a cell and paste columns from Excel: the values go down and to the right from that cell, rows are added at the end, and a heading row is skipped. The values are read in the units the table shows.
Paste readings… opens the paste window (below). + Add reading adds a copy of the last reading one step deeper, to be edited. Delete a range… takes out the readings between two depths.
The × on a row deletes it (not below three readings).
Cone readings.
The paste window
Paste readings reads the text you paste: columns depth · qc · fs · u2 (u2 may be missing), separated by tabs, semicolons, commas or blanks, with a decimal point or comma. A heading row sets the order of the columns and the unit in its brackets; the four unit boxes below show what was understood, and you can change them. A line under the boxes checks the paste (a unit in brackets that the module does not know, such as “(furlong)”, is named there with “check it”, and the box below is used): the number of readings, the depth and qc range, whether u2 is given and the columns found. Replace the readings of the sounding (at least three rows) or Add to them (a reading at the same depth is replaced, the others stay). A paste with no sleeve friction, or a qc above 150 MPa, or a depth beyond 150 m cannot be accepted: its button stays greyed, and the line says why.
The paste window: the units are taken from the heading.
Delete a range: it says how many readings go.
Earthquake
The design earthquake of the whole project. Both values are yours; the module does not derive them.
Earthquake.
Field
Default
Range
Peak ground acceleration (PGA)amax g
0.35
Above 0 and up to 2 g, at the ground surface, site effects included.
Moment magnitudeMw
7.5
4 to 9.5.
Analysis Settings
The method, the unit weight, and the limits of the screening. A box that does not apply is hidden: CFC shows only with Boulanger & Idriss, f only with Robertson & Wride, and the two unit weights only with Constant values.
Analysis Settings.
Field
Default
Range and effect
CFC
0
Fines content fitting parameter of Boulanger & Idriss: FC = 80·(Ic + CFC) − 137, kept between 0 and 100 %. From −1 to 1; the correlation scatter is ±0.29.
f
0.7
Exponent of Kσ for Robertson & Wride, 0.5 to 1.
a
0.8
Net area ratio of the cone, above 0 up to 1: qt = qc + (1 − a)·u2.
γ, γsat kN/m³ · t/m³ · pcf
18.0, 19.0
Only with Constant values: above and below the groundwater level, 10 to 30 kN/m³.
FSreq
1.20
The limit between marginal and OK. Above 0, up to 5 (the box accepts from 0.01 to 5).
Ic,lim
2.6
Readings with Ic above it are clay-like and not evaluated. 1.5 to 3.6 (the box has the same limits).
zmax m · ft
20.0
The deepest reading evaluated. Above 0, at most 150 m (a larger value typed is taken as 150 m, one below 1 m as 1 m).
hmin m · ft
0.10
The thinnest zone listed: a run of one result thinner than this joins its longer neighbour. 0 to 5 m.
Where a box needs a number and you clear it, the module keeps the previous value; a number outside the range the procedures were built for is not clipped silently but stops the analysis with a message (see Messages). The unit weights are only accepted in kN/m³ terms (10 to 30): a value of 1.9 typed in t/m³ in the SI · kN system is refused.
Choosing the method and the options
The two methods are two complete packages: each has its own stress reduction factor rd, its normalisation of the cone resistance, its clean-sand adjustment, its magnitude scaling factor and its Kσ. Do not mix their steps; choose one and read the result with it.
Normalisation. Boulanger & Idriss: CN = (Pa/σ′v) raised to an exponent m that is found from qc1Ncs by iteration, at most 1.7. Robertson & Wride: CQ = (Pa/σ′v) raised to the exponent n of Ic, at most 1.7.
Clean-sand value. Boulanger & Idriss: qc1Ncs = qc1N + Δqc1N, with the fines content FC from Ic and CFC. Robertson & Wride: (qc1N)cs = Kc · qc1N, with Kc from Ic.
Stress reduction rd. Boulanger & Idriss: depends on depth and Mw. Robertson & Wride: depends on depth only.
Magnitude scaling MSF. Boulanger & Idriss: depends on qc1Ncs and Mw. Robertson & Wride: 102.24 / Mw2.56.
Overburden factor Kσ. Boulanger & Idriss: from qc1Ncs and σ′v, at most 1.1. Robertson & Wride: (σ′v/Pa)f−1 above one atmosphere, otherwise 1.
With the default example the two methods give, at the same reading, FS = 0.52 (Boulanger & Idriss) and 0.49 (Robertson & Wride); see the worked example. Over the whole example the lowest factor of safety of CPT-1, CPT-2 and CPT-3 is 0.45, 0.60, 0.65 with Boulanger & Idriss and 0.42, 0.64, 0.68 with Robertson & Wride.
Unit weight
Estimated from the CPT (the default): the unit weight of every reading is found from Rf and qt (kept between 1.5 and 2.5 times the unit weight of water) and integrated down to the stresses. No sample data needed.
Constant values: γ above and γsat below the groundwater level. Use it when you have measured unit weights you trust more. With 18 and 19 kN/m³ the example changes little: the lowest FS is 0.45, 0.61, 0.66.
The screening limits
Ic,lim decides what counts as clay-like. The default 2.6 leaves out the silt mixtures and clays of the example. Raising it to 3.0 brings readings of silty soil into the evaluation, and the lowest FS of CPT-1 and CPT-2 falls to 0.32 (triggered thickness of CPT-1: 7.20 m instead of 4.20 m). Where evaluated readings have Ic between 2.4 and the limit, a warning lists them.
zmax limits the depth of the evaluation.
FSreq moves the border between marginal and OK; it changes no FS.
hmin only tidies the zones: thin runs join their neighbours in the zones and in the thicknesses, not in the readings.
Analyze and read the results
Press Analyze. The bar counts through the soundings (“Analysing… CPT-1 (1 / 3)”) and then reads Analysed — 3 soundings, 1200 readings, with the number of warnings when there are some, and “The inputs are locked. Edit inputs clears the results; the unit system can still be changed.” The module stays on the Model tab; the drawing changes to Contours, a short message says “Analysed — the colour bands show the selected field; see also the Sounding view and the Results tab.”, and when the run has warnings the Warnings window opens by itself. Open the Results tab for the answer.
After Analyze: Contours on the left, the Analyze bar with its Warnings and Edit inputs buttons at the foot of the Model tab.
The Results tab
At the top a banner gives the verdict of the project in words: “Liquefaction is triggered in 3 of 3 soundings”, “Not triggered, but marginal (FS below 1.20) in 1 of 3 soundings”, “Liquefaction is not triggered in any sounding”, or “No reading could be evaluated — no factor of safety”, with amax, Mw and FSreq. Under it, one row for each sounding (click it to show the sounding in the drawing and in the table below):
The Results tab of the example.
Cell
What it is
Name and chip
The sounding, its groundwater depth and how many readings were evaluated. The chip is TRIGGERED (any reading with FS below 1.0), MARGINAL (none triggered, some below FSreq) or OK.
Minimum FS
The lowest FS of the sounding and its depth.
Triggered · FS < 1.0
The total thickness of the triggered zones and the zones themselves (the first four, then “+ n more”).
Marginal · FS < 1.20
The same for the marginal zones (the limit is your FSreq).
Each reading stands for the depth halfway to its neighbours (at most a quarter of a metre either side, or three quarters of the usual interval where that is larger), so a gap in the record is not filled with results. Neighbouring runs with the same result are merged into zones.
Reading by reading
Below the rows, the readings of the chosen sounding in a table. The buttons choose the sounding and the depth step (0.25 m, 0.50 m, 1.00 m or every reading; the labels follow the unit system). The default columns are the depth, the soil type, qt, σ′v, Ic, FC, qc1Ncs, CSR, CRR, FS and the result; All columns adds fs, Rf, γ, σv, n, the normalisation factor, qc1N, the clean-sand adjustment, rd, CRR7.5, MSF and Kσ. A reading that is not evaluated shows N/E and the reason under the chip. Click a row to open its calculation.
The reading-by-reading table of CPT-1.
The Warnings window
Warnings (n) (on the Analyze bar and on the warning banner) opens a window with the numbered warnings of the run and, below them, the assumptions of this analysis: the method and its formulas, how the unit weight was found, which groundwater depth each step uses, the screening and the zone rule. The default example has two warnings:
“Readings with Ic above 2.6 are clay-like and are not evaluated: CPT-1 — 6 m, CPT-2 — 4 m, CPT-3 — 6 m. Check these layers for cyclic softening separately.”
“q₁Ncs ≥ 211, taken at the upper limit of the CRR curve (thickness of the readings concerned): CPT-1 — 1.9 m; CPT-2 — 0.05 m.”
The Warnings window.
A warning does not stop anything: the numbers are there. Read it as a note on what the result rests on. Press Edit inputs to unlock the model and clear the results; the view returns to Sounding.
The Calculations tab, the report and the Theory tab
Calculations
The Calculations tab writes out the working for one reading with your numbers. Choose the sounding and the depth at the top (the nearest reading is used), press Minimum FS to jump to the lowest FS of the sounding, or arrive by clicking a depth in the Sounding view or a row of a table. The tab opens on the minimum reading. Seven steps, each with its equation, the equation with your numbers, and the result:
Cone data: qt = qc + (1 − a)·u2 and Rf.
Vertical stresses: the unit weight, σv, the pore pressure u and σ′v0, at the test and for the design water level.
Soil behaviour type index Ic: the iteration on the exponent n and the soil type.
Clean-sand equivalent cone resistance: FC, the exponent, the normalisation and the adjustment (or CQ and Kc for Robertson & Wride).
Seismic demand CSR: rd and CSR.
Cyclic resistance CRR: CRR7.5, MSF and Kσ (with the limits applied shown in the line).
Factor of safety: FS = CRR / CSR and the word (triggered, marginal, OK). A reading that is not evaluated stops after the normalisation and says why.
The Calculations tab: the top and the first step.
Steps 4 to 6 of the same reading.
Before Analyze the tab says “Press Analyze on the Model tab first.” Each step folds and unfolds with its heading.
The report
In the Report tab fill in the cover: project, location, client, report number, date (today’s date at the start), prepared by, title or qualification, checked by, and optional notes. The details are kept in the browser and saved with the model file. After Analyze, Save as PDF (it opens a print window; allow pop-ups and choose “Save as PDF” as the printer) and Download Word (.docx) are available; before it they are greyed out and the preview says “Open this tab after the analysis to build the preview.” or asks you to press Analyze. The preview is the report itself.
The report has a cover with the key results and a one-sentence conclusion, then the parts 1 Introduction and scope, 2 Soundings (the table of soundings and the table of sections), 3 Earthquake, method and settings, 4 Results by sounding (the table of results with the colour-band drawing of each section and the project drawing), 5 Reading by reading (for each sounding a table of readings every 0.50 m and its drawing), 6 Warnings (only when the run has warnings) and Summary. It states the units of the unit system you had chosen.
The Report tab: the cover and the two buttons.
The Theory tab
The Theory tab has sixteen sections: the scope, the cone data, unit weight and stresses, the soil behaviour index, the screening, the two methods, the cyclic stress ratio, the factor of safety, the zones, the colour-band section, a comparison of the two methods, a worked reading computed from the example, the limits of the module and the references. The first three are open; the others open with their headings or from the contents list.
Worked example: the module’s own example
The module opens on this project: three soundings of 400 readings each (every 0.05 m to 20 m), amax = 0.35 g, Mw = 7.5, Boulanger & Idriss, the unit weight from the CPT, FSreq = 1.20. The results are those in the Results tab: CPT-1 minimum FS 0.45 at 6.00 m; CPT-2 minimum FS 0.60 at 7.10 m; CPT-3 minimum FS 0.65 at 8.50 m (all three triggered; triggered thickness 4.20, 4.90 and 5.00 m).
One reading by hand: CPT-1 at 4.00 m
Open the Calculations tab on CPT-1 at 4.00 m: qc = 4.956 MPa, fs = 46.2 kPa, u2 = 21.6 kPa, groundwater at 1.80 m. The numbers below are the module’s, and each was re-computed by hand.
The Results table gives FS = 0.52 for 4.00 m, and the lowest value of CPT-1, 0.45, is at 6.00 m (the Calculations tab opens there).
The same reading with Robertson & Wride
Choose Robertson & Wride (1998) and press Analyze again (after Edit inputs). At 4.00 m: Ic = 2.031 as before, CQ = (101.3/52.05)0.5 = 1.395, qc1N = 68.30, Kc = 1.343 (the quartic of Ic), (qc1N)cs = 91.73, CRR7.5 = 93 × 0.09173³ + 0.08 = 0.1518, rd = 1 − 0.00765 × 4.00 = 0.9694, MSF = 102.24 / 7.52.56 = 1.000, Kσ = 1.0 (the effective stress is below one atmosphere), CSR = 0.65 × (73.64/52.05) × 0.35 × 0.9694 = 0.3120, so FS = 0.1518 × 1.000 / 0.3120 = 0.49. The lowest FS of the three soundings is 0.42, 0.64, 0.68.
Checking the units
Switch to US after Analyze: the cards re-state without a new run. The groundwater depth of CPT-1 reads 5.91 ft, the lowest FS is the same 0.45 at 19.69 ft, the triggered thickness 13.78 ft (4.20 m) and hmin 0.33 ft. In the Calculations tab at 6.00 m (19.685 ft): qt = 58.210 tsf (5.574 MPa), σ′v0 = 1.434 ksf (68.64 kPa) and Pa = 2.116 ksf, and the factor of safety is again 0.45. In SI · tf the same step reads qt = 56.841 kg/cm² and σ′v0 = 6.999 t/m², the unit weight 1.84 t/m³, and again FS = 0.45. Only the units change; the drawings stay in SI.
How each input changes the answer
Each row changes one thing (two where the label says so) in the example: Boulanger & Idriss, amax = 0.35 g, Mw = 7.5, CFC = 0, a = 0.8, the unit weight from the CPT, FSreq = 1.20, Ic,lim = 2.6, groundwater as in the example (1.80, 2.40 and 3.10 m), and runs the module again. The numbers are the minimum FS of each sounding, as the Results tab gives them.
The lowest factor of safety of each sounding (CPT-1 · CPT-2 · CPT-3)
Change
Lowest FS
Result
The example Boulanger & Idriss, 0.35 g, Mw 7.5
0.45 · 0.60 · 0.65
triggered in 3 of 3
amax = 0.15 g CPT-1 is marginal at the lowest point
1.04 · 1.41 · 1.53
marginal in 1 of 3
amax = 0.25 g
0.62 · 0.85 · 0.92
triggered in 3 of 3
amax = 0.45 g
0.35 · 0.47 · 0.51
triggered in 3 of 3
Mw = 6.5
0.52 · 0.74 · 0.82
triggered in 3 of 3
Mw = 8.0
0.42 · 0.55 · 0.59
triggered in 3 of 3
Mw = 6.5 and 0.25 g
0.72 · 1.04 · 1.15
triggered in 1 of 3
Robertson & Wride, f = 0.7
0.42 · 0.64 · 0.68
triggered in 3 of 3
Robertson & Wride, f = 0.9 Only CPT-3 changes at two decimals
0.42 · 0.64 · 0.70
triggered in 3 of 3
0.20 g, Boulanger & Idriss
0.78 · 1.06 · 1.15
triggered in 1 of 3
0.20 g, Robertson & Wride
0.73 · 1.12 · 1.19
triggered in 1 of 3
CFC = +0.29 More fines in the correlation
0.58 · 0.87 · 0.91
triggered in 3 of 3
CFC = −0.29 Fewer fines
0.32 · 0.37 · 0.38
triggered in 3 of 3
CPT-1 water at 0.50 m (test and design) Only CPT-1 changes
0.38 · 0.60 · 0.65
triggered in 3 of 3
CPT-1 water at 4.00 m (test and design) Only CPT-1 changes
0.55 · 0.60 · 0.65
triggered in 3 of 3
CPT-1 design water at 0.50 m, test 1.80 m Only CPT-1 changes
0.37 · 0.60 · 0.65
triggered in 3 of 3
γ = 18, γsat = 19 kN/m³
0.45 · 0.61 · 0.66
triggered in 3 of 3
a = 0.6
0.45 · 0.61 · 0.66
triggered in 3 of 3
Ic,lim = 3.0 Silty readings are evaluated
0.32 · 0.32 · 0.65
triggered in 3 of 3
Reading the table:
The earthquake moves everything. Raising amax from 0.35 to 0.45 g lowers the lowest FS of CPT-1 from 0.45 to 0.35; at 0.15 g no sounding is triggered. A smaller magnitude raises FS through MSF: Mw 6.5 gives 0.52, 0.74, 0.82.
The two methods agree to a few hundredths at the lowest points (0.42, 0.64, 0.68 against 0.45, 0.60, 0.65), and differ more in the zones: the marginal thickness of CPT-2 is 0.85 m with Boulanger & Idriss and 0.25 m with Robertson & Wride. At 0.20 g CPT-1 is triggered with both and CPT-2 and CPT-3 are marginal.
CFC is a strong lever on silty sand. The ±0.29 range of the correlation scatter moves the lowest FS of CPT-2 from 0.37 to 0.87.
A groundwater change moves only its own sounding, and both the level at the test and the design level matter: water at 0.50 m for CPT-1 gives 0.38, at 4.00 m 0.55.
The unit weight option and the net area ratio shift the lowest FS by a hundredth or so in this example: 0.45, 0.61, 0.66 with constant weights, 0.45, 0.61, 0.66 with a = 0.6.
Some inputs change the zones and not the factor of safety:
CPT-2: thickness in metres of the zones, with the same factors of safety
Change
Triggered
Marginal
The example
4.90
0.85
FSreq = 1.0
4.90
0.00
FSreq = 1.5
5.00
1.75
hmin = 0
4.95
0.75
hmin = 0.5 m
5.10
0.00
zmax = 10 m
4.90
0.75
The minimum FS of CPT-2 stays 0.60 in all of these rows.
Messages: when the module stops, and what it warns about
When a value cannot be used, Analyze stops: a window titled Cannot analyse — 1 input error (or “2 input errors”) lists the messages, nothing is calculated, and the Analyze bar stays on “Not analysed”. Correct the value and press Analyze again.
A stop: the PGA typed as 3 g.
Kind
When
Message
Stop
amax above 2 (or 0)
“Peak ground acceleration 3 g is out of range (it is entered in g, up to 2).” (0: “Peak ground acceleration is missing.”)
Stop
Mw outside 4 to 9.5
“Moment magnitude 10 is out of range: the magnitude scaling factors are defined for 4 to 9.5.”
Stop
FSreq above 5
“Required factor of safety 6 is out of range (up to 5).”
Stop
a outside 0 to 1
“The net area ratio of the cone must be between 0 and 1.”
Stop
CFC beyond ±1
“The fines content parameter CFC 2 is out of range (the correlation scatter is ±0.29; keep it between −1 and 1).”
Stop
f outside 0.5 to 1 (Robertson & Wride)
“The Kσ exponent f 2 is out of range (0.5 to 1; 0.7–0.8 for DR 40–60 %).”
Stop
Constant unit weight outside 10 to 30
“The unit weight above the water table 1.9 kN/m³ is out of range (10 to 30 kN/m³ — t/m³ values such as 1.9 are not accepted).”
Stop
Ic,lim outside 1.5 to 3.6
“The clay-like limit Ic,lim = 4 is out of range (1.5 to 3.6).”
Stop
hmin above 5 m
“The thinnest zone listed, hmin = 9 m, must be between 0 and 5 m.”
Stop
zmax 0 (from a file)
“The deepest reading evaluated, zmax = 0 m, must be above 0 and at most 150 m.”
Stop
Groundwater depth outside −30 to 300 m
“CPT-1: groundwater depth 400 m is out of range (−30 to 300 m; a negative depth is water above the ground surface).”
Stop
A new sounding left empty
“CPT-4: groundwater depth is missing.” and “CPT-4: fewer than three readings of depth and cone resistance.”
Stop
A cone resistance above 150 MPa
“CPT-1: a cone resistance of 200 MPa is not possible (more than 150 MPa) — check the unit of the cone resistance column.”
Stop
No sleeve friction in any reading
The message says the soil behaviour index and the fines content cannot be found without it.
Stop
Two soundings of the same name (from a file)
“Two soundings are named "cpt-1" (names are compared without regard to case): rename one.”
A reading deeper than 150 m or a sleeve friction above 3000 kPa stops in the same way, with a hint to check the unit of the column. Several wrong values are listed together.
Warnings: the run goes on
A warning appears in the banner of the Results and Report tabs and in the Warnings window; it never blocks the result. The ones you may meet:
Clay-like readings. “Readings with Ic above 2.6 are clay-like and are not evaluated: … Check these layers for cyclic softening separately.”
Sand-silt transition. “Evaluated readings with Ic between 2.4 and 3 (sand-silt transition, where samples should be taken to confirm the soil type): …” (when Ic,lim is above 2.4).
Beyond the curve. Boulanger & Idriss: “q₁Ncs ≥ 211, taken at the upper limit of the CRR curve …”; Robertson & Wride: “(q₁N)cs ≥ 160, beyond the end of the chart of CRR7.5 (the cubic is continued to 250) …”.
No pore pressure. “No pore pressure u₂ given for CPT-1 — qt = qc is used (an unequal-area correction is not made).” and, when only some readings lack it, “The pore pressure u₂ is missing in some readings of CPT-1 (100 of 400) — qt = qc is used for those readings.”
No sleeve friction in some readings. “Evaluated readings with no sleeve friction (fs = 0): CPT-1 (20) — F is taken as 0.1 %, which makes the soil look cleaner and more granular; check the record.”
A gap in the record. “No readings between the depths listed — they are not evaluated and the zones do not extend into them: CPT-1 — 8.2–9.3 m.”
A coarse record. “The usual reading interval is larger than 0.1 m in CPT-2 (0.2 m) — thin layers are not resolved and the zones are coarse.”
A short record. “The sounding ends less than 0.5 m below the design groundwater level in CPT-3.” and “No reading evaluated in CPT-1 (all above the water table, clay-like or deeper than zmax).”
Unusable readings. “Readings with qt ≤ σv are not evaluated: CPT-1 — 1 reading.” and “Rows without a depth or a cone resistance were ignored: CPT-1 — 1.”
Other messages sit next to the action: in the paste window (“Fewer than three rows with a depth and a cone resistance were found.”, “no sleeve friction — the soil behaviour index cannot be found without fs”), under Excel input (“The file could not be imported — see the problems.”), and as short toasts (“CPT-4 added — it is empty: enter its groundwater depth and paste its readings.”, “Results cleared — the inputs can be edited.”, “The project keeps at least one sounding.”).
Good practice and common mistakes
Check the units of a pasted or imported column. The heading unit is read, but a column with no unit in its heading is taken as m, MPa and kPa, and an unknown unit word is reported in the check line (or, for an Excel file, in the import window) with the unit used: confirm before you accept. A cone resistance of 150 MPa or more is refused as impossible.
Enter both groundwater depths. The level at the test governs the normalisation; the design level governs CSR, Kσ and where the evaluation starts. Give the design depth when it differs from the test.
Give the readings at their real interval. The zones follow the record: a coarse interval (above 0.1 m) gives coarse zones, and a gap is left as a gap.
Keep u2 when you have it. Without it qt = qc; the warning says so.
Pick one method and keep to it for a whole assessment. The two packages are not meant to be mixed; if you run both, compare results, not steps.
Read the clay-like warning. Readings above Ic,lim are not evaluated; the module asks you to check those layers separately.
Use sections for what they are: a line through the soundings you want drawn together. A section needs the distance of each sounding along it; the elevation of each sounding sets its place vertically.
Name the soundings as the sheets are named. The sounding name is the Excel sheet name; names are compared without regard to case.
Save the model to a file when the project matters: the browser memory belongs to one browser. Quick Save is a list of versions in the same browser.
Note the earthquake you used.amax and Mw are inputs: the report states them, and the cover carries your project details.
Frequently asked questions
How does the module decide that liquefaction is triggered?
At every evaluated reading it divides the cyclic resistance ratio CRR by the cyclic stress ratio CSR. FS below 1.0 is triggered; from 1.0 up to FSreq (1.20 by default) is marginal; at or above FSreq it is OK. A sounding is TRIGGERED when any of its readings is below 1.0.
Which methods are available?
Boulanger & Idriss (2014) and Robertson & Wride (1998), each a complete package with its own stress reduction factor, normalisation, clean-sand adjustment, magnitude scaling and overburden factor. You choose one in Analysis Settings; the report states which.
Why are some readings not evaluated?
A reading is evaluated when it lies below the design groundwater level, is not deeper than zmax and is not clay-like (Ic not above Ic,lim). Readings that fail are listed with N/E and the reason, and shown hatched in the drawings.
Do I need a unit weight?
No. By default the unit weight of every reading is estimated from Rf and qt, and integrated for the stresses. Choose Constant values if you prefer your own γ and γsat (10 to 30 kN/m³).
What if my cone data has no pore pressure?
Leave u2 blank. The module takes qt = qc and says so in a warning. With u2 given, qt = qc + (1 − a)·u2 with the net area ratio a (0.8 by default).
How do I bring in a long sounding?
Download the template from Excel input, copy your readings into a sounding sheet (the unit may be written in the heading), and press Import Excel…. Or open Paste readings… for one sounding and paste the columns. Either way the module checks the data and tells you what it read before anything is changed.
Does the import replace my project?
You choose in the check window: Add the soundings of the file (a sounding of the same name is replaced, the others stay, and your earthquake and settings are kept) or Replace the soundings and sections by those of the file, which also takes the parameters of the Project sheet.
What is a section, and do I need one?
A section is a line through some of the soundings, with the distance of each along it. The Contours view interpolates a colour band between its soundings at equal elevation. Without a section the Contours view draws one colour column per sounding.
Can I drag or zoom the drawings?
No. You choose what they show with the chips and the inputs. The only click on a drawing is on a depth of the Sounding view, which opens the calculation of the nearest reading.
Does the module keep my project?
Yes, in this browser: every change is kept, and after a reload the module opens on your last project, analysed or not. For another computer or for the file of a project, use Save to file… and Open file…. Reset to defaults brings back the example.
Which units does it use, and what does the template use?
SI · kN, SI · tf or US, switchable in the header at any time, even after Analyze: cards, tables, calculations and the report follow, while the drawings stay in SI. The Excel template and the model file are always in m, MPa, kPa, kN/m³ and g.
What does the report contain?
A cover with your project details and the key results, then the introduction, the soundings and sections, the earthquake and settings, the results by sounding with the colour-band section and the project drawing, the readings of each sounding with its drawing, the warnings when there are some, and the summary. It is saved as PDF or Word after Analyze.
Slope stabilityLimit equilibrium by slices, with a search for the critical circle.
Infinite slopeA plane failure surface parallel to the ground, with seepage, a pore pressure ratio and an earthquake.
