Tailings Flow Slide Calculator - HELP (Draft)
(last updated 11 Dec 2014)
Contents:
This calculator determines the extent of a flow slide of liquefied mill tailings. Such liquefaction is typically caused from an earthquake occuring near a tailings dam (for a stability analysis of tailings dams under seismic loads, see also the Slope Stability Calculator)
The calculator 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. It is, however, 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 calculator does not take into account the frictional resistance from the flow channel sides and may, therefore, overestimate the inundation distance for situations where the flow slide runs through narrow valley channels.
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, including the flow depth h* and the max. velocity u* for each horizontal distance x* from the dam toe and for each time t*.
If the SUMMARY section reports any warnings, change the time step and/or X step parameters accordingly.
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 extent of the flow slide for each time step. The Animation button produces a computed sequential animation of the flow slide.
See special instructions for offline use of this 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 |
Line Load | lbs/ft. | pounds per foot | kN/m | kilo Newton per meter |
Pressure, Cohesion | p.s.f. | pounds per square foot | 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 | 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 lb/ft. = 14.59 N/m | 1 kN/m = 68.52 lb/ft. |
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.
- Initial height of dam [ft.] · [m]
- height of tailings material above ground before liquefaction
- Bed slope [%V:H] (optional)
- slope of the ground surface downstream from the tailings dam, expressed as percent vertical vs. horizontal. Positive values indicate falling slopes; negative values for rising slopes are also possible.
If no value is entered, 0 is assumed.
- 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. (14.1 - 17.3 kN/m^{3}).
- 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. (0.96 - 7.2 kPa)
- Bingham plastic viscosity [lb·sec/ft^{2}] · [kPa·s]
Typical values for mill tailings range between 2 and 100 lb·sec/ft^{2} (0.096 - 4.8 kPa·s).
Output Options
- Time step width [sec] (optional)
- Entry only required, if the time step width used by the calculator is inappropriate.
Value should be low enough to obtain the desired time resolution, and high enough to avoid computing resource problems and time-related warnings (see SUMMARY section in the Results field).
If no value, or 0, is entered, then a reasonable time step width is determined automatically. If the value entered violates computing resources constraints, a higher value is used.
- Max. no. of time steps (optional)
- Entry only required, if computing resource problems occur.
If no value, or 0, is entered, then the number of time steps is determined automatically to cover the complete run-out until final freeze.
- X step width [ft.] · [m] (optional)
- Entry only required, if the X step width used by the calculator is inappropriate.
Value should be low enough to obtain the desired distance resolution, and high enough to avoid computing resource problems and distance-related warnings (see SUMMARY section in the Results field).
If no value, or 0, is entered, then a reasonable X step width is determined automatically. If the value entered violates computing resources constraints, a higher value is used.
- Min no. of X steps (optional)
- Entry only required, if a fixed X-axis length is desired for easier comparison of drawings from different cases.
If no value, or 0, is entered, then the number of X steps is determined automatically to cover the max. run-out distance.
- 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).
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 (optional)
- Enter either Time step or Time-lapse factor.
If neither value is entered, a default time step is used.
Note that the Time step value overrides any Time-lapse factor entered
...
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
}
SS = shear stress
SS_{o} = threshold stress (yield strength)
eta_{p} = plastic viscosity
SN = shear strain
- [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