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