Tailings Flow Slide Calculator - HELP (Draft)
(last updated 7 Dec 2022)
Contents:
This calculator determines the extent of a flow slide of liquefied mill tailings. Such liquefaction can be caused from an earthquake occuring near a tailings dam, and/or from inadequate tailings management procedures.
The calculator is adapted from the program TFLOW [Jeyapalan 1980] and uses a two-dimensional approach described in [Jeyapalan 1982]. For the purpose of the flow slide analysis, the tailings deposit is represented as a body of fluid material with a vertical face as shown in the following figure:
The calculator uses a Bingham plastic model to represent the flow behaviour of the liquefied tailings material: motion of the fluid only commences when a threshold shear stress is exceeded.
The calculator is applicable to laminar flow, as observed with most liquefied tailings materials.
Note: It is not applicable to phosphate tailings: their strength and viscosity parameters are orders of magnitude lower than for other tailings, thus causing turbulent rather than laminar flow.
The properties of the dam and the tailings are defined in the Input Data table. The output format can be set in the Output Options table.
The Result field repeats the input data and shows the numerical calculation results.
The contents of the Result field can be highlighted and copied for further use.
If the browser is HTML 5-capable, a drawing of the results is produced. It shows the initial dam contour and the extent of the flow slide for each time step.
The Animate button produces a computed sequential animation of the flow slide.
See special instructions for offline use of this calculator.
See also:
- For a stability analysis of tailings dams under seismic loads, see the Slope Stability Calculator .
- For background information, see also Properties of Tailings Dams and Safety of Tailings Dams.
The Units can be selected for the whole calculator as Imperial or Metric. This selection must be made before any other entry, since it resets the complete calculator.
| Imperial | Metric |
Length | ft. | feet | m | meters |
Velocity | ft./sec | feet per second | m/s | meters per second |
Pressure, Cohesion | p.s.f. | pounds per square foot (lb/ft^{2}) | kPa | kilo Pascal |
Viscosity | lb·sec/ft^{2} | pounds-seconds per square foot | kPa·s | kilo Pascal-seconds |
Unit Weight | p.c.f. | pounds per cubic foot (lb/ft^{3}) | kN/m^{3} | kilo Newton per cubic meter |
Unit Weight of Water | 62.4 p.s.f. | 9.81 kN/m^{3} |
(all pounds are pounds force)
1 ft. = 0.3048 m | 1 m = 3.281 ft. |
1 ft./sec = 0.3048 m/s | 1 m/s = 3.6 km/h = 3.281 ft./sec |
1 lb = 4.448 N | 1 kN = 224.8 lb |
1 p.s.f. = 47.88 Pa | 1 kPa = 1 kN/m^{2} = 20.89 p.s.f. |
1 lb·sec/ft^{2} = 47.88 Pa·s | 1 kPa·s = 10^{6} cP = 20.89 lb·sec/ft^{2} |
1 p.c.f. = 157.1 N/m^{3} | 1 kN/m^{3} = 6.366 p.c.f. |
(all pounds are pounds force)
See also Unit Converter .
Input Data
Some Sample Data Sets can be selected from a pick list. These sets include several tailings dams of various heights and bed slopes.
The (real) Gypsum tailings and Aberfan coal tip examples are taken from [Jeyapalan 1980], the (hypothetical) Bunker Hill examples from [Bryant 1983].
- Initial height of dam at dam axis [ft.] · [m]
- height of tailings material above ground before liquefaction
- Initial fetch of dam [ft.] · [m]
- surface length of impounded tailings material before liquefaction
- Bed slope [%V:H] (optional)
- slope of the ground surface downstream from the tailings dam, expressed as percent vertical vs. horizontal.
If no value is entered, 0 is assumed.
> See also: Unit Converter (Slope angle <-> ratio)
- Prismatic valley cross section shape
- select appropriate shape and enter side slopes (expressed as percent vertical vs. horizontal) or width ([ft.] · [m])
- Total unit weight [p.c.f.] · [kN/m^{3}]
- Unit weight of the tailings material.
Typical values for mill tailings range between 90 and 110 p.c.f. (lb/ft^{3}) (14.1 - 17.3 kN/m^{3}).
> See also: Unit Converter (Density/Unit Weight)
- Bingham yield strength [p.s.f.] · [kPa]
- also known as residual shear strength: threshold shear stress required for flow to occur.
Typical values for mill tailings range between 20 and 150 p.s.f. (lb/ft^{2}) (0.96 - 7.2 kPa)
> See also: Unit Converter (Pressure)
- Bingham plastic viscosity [lb·sec/ft^{2}] · [kPa·s]
- If the value is not known, it can be estimated from the water content of the tailings [%].
Typical values for mill tailings range between 2 and 100 lb·sec/ft^{2} (0.096 - 4.8 kPa·s).
> See also: Unit Converter (Dynamic Viscosity)
Output Options
- Show free surface listing every ... time steps (optional)
- Determines, how often the complete free surface profile during flow is shown in the Results field in addition to Tip displacement and Tip velocity.
If no value or 0 is entered, no intermediate free surface profiles are shown
- Last time of calculation
- Time, after which the calculation aborts, if no freezing is detected.
- Max. Y/X ratio (optional)
- max. ratio of vertical vs. horizontal scale to be used for the drawing.
If no value, or 0, is entered, the highest possible ratio is used.
- Show bed slope
- check, in case the bed slope is to be shown in the drawing. Otherwise, the x-axis is drawn horizontally even for non-zero slopes. It is advisable to uncheck this box in cases when the visible flow slide depth becomes very small (for example for steep slopes and long run-out distances).
The computation of the flow slide is not affected by this selection.
Note that the actual y/x-ratio affects the visible slope angle.
- Show intermediate contours
- check, in case the contours for all time steps are to be shown in the drawing. Otherwise, only the final contour is shown.
- Animation: Time step [sec] - or - Time-lapse factor
- Enter either Time step or Time-lapse factor.
...
Bingham plastic fluids are time-independent viscous fluids for which the apparent viscosity decreases with shear rate, and motion only commences when the yield stress is exceeded.
The equation for the Bingham fluid is:
SS = SS_{o} + eta_{p} * SN for values of SS>SS_{o}
where:
SS = shear stress
SS_{o} = threshold stress (yield strength)
eta_{p} = plastic viscosity
SN = shear strain
The criterion used for detection of freezing of the flow slide is a tip velocity less than 0.1 ft/s or m/s.
⚠ Investigations by [Bryant 1983] "showed that the program TFLOW produces peculiar results for some conditions", and "These pecularities make it difficult, to assess the reliability of TFLOW for dynamic wave theory analysis for cases where [slope angle] β > 0."
- [Jeyapalan 1980] Analyses of Flow Failures of Mine Tailings Impoundments, Dissertation by K.Jeyapalan, University of California, Berkeley 1980
- [Jeyapalan 1982] Dam-break studies for mine tailings impoundments by Jey K.Jeyapalan. In: Geotechnical Engineering Program, Civil Engineering Department, Colorado State University (Ed.), Uranium Mill Tailings Management. Proceedings of the Fifth Symposium, December 9-10, 1982, Fort Collins, Colorado 1982, p.39-53
- [Bryant 1983] Application of Tailings Flow Analyses to Field Conditions, Dissertation by Samuel Morris Bryant, University of California, Berkeley 1983