Tailings Flow Slide Calculator - HELP (Draft)

(last updated 11 Dec 2014)

Contents:

• Introduction · Input Data · Calculation Details · Bibliography

Introduction

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/ft2	pounds-seconds per square foot	kPa·s	kilo Pascal-seconds
Unit Weight	p.c.f.	pounds per cubic foot	kN/m3	kilo Newton per cubic meter
Unit Weight of Water	62.4 p.s.f.		9.81 kN/m3

(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/m2 = 20.89 p.s.f.
1 lb·sec/ft2 = 47.88 Pa·s	1 kPa·s = 106 cP = 20.89 lb·sec/ft2
1 p.c.f. = 157.1 N/m3	1 kN/m3 = 6.366 p.c.f.

(all pounds are pounds force)
See also Unit Converter.

Input Data

Geometry

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.

Tailings Properties

Total unit weight [p.c.f.] · [kN/m³]

Unit weight of the tailings material.
Typical values for mill tailings range between 90 and 110 p.c.f. (14.1 - 17.3 kN/m³).

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/ft²] · [kPa·s]

Typical values for mill tailings range between 2 and 100 lb·sec/ft² (0.096 - 4.8 kPa·s).

Output Options

General 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.

Drawing Options

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

Calculation Details

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

Bibliography

• [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

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