2018 Tailings and Mine Waste Conference
Gordan Gjerapic, Golder Associates, Inc.
Dobroslav Znidarcic, University of Colorado at Boulder
October 1, 2018
Improved Methodology for TSF
Capacity Prediction
___Outline
2
▪ Three-dimensional considerations of seepage and
compression
▪ Large strain deformation during deposition and closure
▪ Variable production rate and complex geometries
▪ Robust numerical approach
▪ Mass balance and water balance errors
___Numerical Models
3
H I S T O R I C A L P E R S P E C T I V E
Gibson et al. (1967) – large strain consolidation theory
One-dimensional models
Schiffman et al. (1992) – ACCUMV
Yao and Znidarcic (1997) – CONDES
Fox and Berles (1997) – CS2
GWP Software (1999) – FSConsol
___Numerical Models – 2D and 3D
4
C O M M E R C I A L M O D E L S U S E D F O R T S F C O N S O L I D AT I O N
Programs supporting large strain consolidation
approach
• FLAC® and FLAC3DTM- ITASCA Consulting Group
• PLAXIS, PLAXIS3D – Plaxis BV => Bentley
Systems, Inc.
• SVOFFICETM5 – SVFLUX – SVSOLID, SoilVision
=> Bentley Systems, Inc.
___Simplified Consolidation Approach – 3D
5
D O M I N A N T S E E PA G E A N D C O M P R E S S I O N M E C H A N I S M S
TSF modelling using a series of one –dimensional columns
(Gjerapic et al. 2008)
• Consolidation dominated by seepage in vertical
direction
• Applicable to most TSF geometries and boundary
conditions
SoilVision => Pseudo 3D large-strain consolidation (under
development as of May 2018)
___Improved Methodology
6
P R A C T I C A L I M P L I C AT I O N S
Develop solutions for rapid assessment of TSF capacity
• Negligible vertical strains during the filling process
• Fully consolidated tailings (apply analytical solutions)
• TSF filling starting with the deepest column and
continuing by filling horizontal layers at higher elevation
(e.g. FSConsol approach)
• TSF filling using a series of one-dimensional vertical
columns (Gjerapic et al. 2008) => computationally
efficient and relatively easy to implement
___Upper and Lower Bound
7
N U M E R I C A L M O D E L S
Horizontal Layers: Vtotal = i=1
n
Hi − Hi−1 Ai
___Upper and Lower Bound
8
N U M E R I C A L M O D E L S
Vertical Columns: Vtotal =i=1
n
ALBi HLBi
___Does it Matter ?
9
TA I L I N G S V S . F O U N D AT I O N C O M P R E S S I B I L I T Y
___How to Determine Calculation Errors ?
10
M A S S C O N S E R VAT I O N
න0
t
Qs τ dτ = Gsρwi=1
n
ALBi Hi𝑠𝑜𝑙𝑖𝑑𝑠
Total Mass of Solids =
Mass Density of Solids x Volume of Solids in
Individual Columns
Total Mass of Solids = Avg. Dry Density of Tails x TSF Volume
න0
𝑡
𝑄𝑠 τ 𝑑τ = ρ𝑑𝑟𝑦,𝑎𝑣𝑔 × 𝑉𝑇𝑆𝐹 𝑡
___Example
11
F I L L I N G S C E N A R I O
0
20
40
60
80
100
120
0 5 10 15 20
Mass (
Mt)
Time (year)
Case 1
Case 1 => 30,000 t/day for 10 years
Case 2 => On-off filling (1yr + 1yr) – see paper
___Case 1 Results – Time Settlement
12
M A S S C O N S E R VAT I O N
0
20
40
60
80
100
0 5 10 15 20
Heig
ht
(m)
Time (year)
FSConsol
FILLCON - Tallest Column
Incompressible Tailings (U=0%)
Instantaneous Consolidation (U=100%)
___Case 1 – Void Ratio Profiles at 10 years
13
0
15
30
45
60
75
90
0 1 2 3 4
Heig
ht
(m)
Void Ratio (-)
FSConsol
Column 1
Column 2
Column 3
Column 4
Column 5
___Case 1 – Avg. Void Ratio Profiles at 10 years
14
0
15
30
45
60
75
90
0 1 2 3 4
Heig
ht
(m)
Void Ratio (-)
FSConsol
Column 1
Layer FillingModel
ColumnFilling Model
___Case 1 – Void Ratio Profiles at 16 years
15
0
15
30
45
60
75
90
0 1 2 3 4
Heig
ht
(m)
Void Ratio (-)
FSConsol
Column 1
Column 2
Column 3
Column 4
Column 5
___Case 1 – Avg. Void Ratio Profiles at 16 years
16
0
10
20
30
40
50
60
70
80
90
0 1 2 3 4
Heig
ht
(m)
Void Ratio (-)
FSConsol
Column 1
Layer FillingModel
ColumnFilling Model
___Mass Balance Errors – Horizontal Layer Approach
17
-70%
-60%
-50%
-40%
-30%
-20%
-10%
0%
Year 10 Year 16 Year 20 Year 30
Mass B
ala
nce E
rror
Error - Using Average Solids Content/ Density
Error - Integrated Void Ratio Profile
___Mass Balance Errors – Vertical Column Model
18
-0.70%
-0.60%
-0.50%
-0.40%
-0.30%
-0.20%
-0.10%
0.00%
Year 10 Year 16
Mass B
ala
nce E
rror
Error - Using Average Solids Content/ DensityError - Integrated Void Ratio Profile
More things should not be
used than are necessaryWilliam of Ockham
19
Everything should be made
as simple as possible, but
not simplerAlbert Einstein
