Department of Mining Engineering

Geotechnical considerations to reduce adverse impacts

of mine waste rock dumps on the environment

Rennie B. Kaunda

Department of Mining Engineering

What gets measured gets managed

Peter Drucker(?)

(slideshare.net)

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Department of Mining Engineering

Outline

• Problem statement and motivation

• Principal component analysis (PCA)

• Results

• Summary and conclusions

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Acknowledgements

• Tailings and Mine Waste ‘18 Conference Organizers and Session Chair

• Colorado School of Mines

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Problem statement: How should the slope stability analysis be assessed??

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Strength envelopes

t – s coordinates

(normal and shear stresses acting on the failure

plane)

s

t

s3 s1s3scis3 s1

t = c + s tanf

c

f

Highly nonlinear especially here

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Factors affecting shear strength and stability analysis

• Dump Height

• Density

• Moisture

• Weathering

• Transport

• Construction method

• Ore type

• Foundation/topography

• Mineralogy

• Clay content

• Mechanical properties

• Geochemistry

• Particle shape

• Porosity

• Petrology

• Other 7

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Empirical correlations to establish shear strength

(Dorador et al., 2017, Material characterization, In: Hawley, M., & Cunning, J. (eds.), Guidelines for Mine Waste Dump and Stockpile Design: 13-27. The

Netherlands: CSIRO PUBLISHING/Balkema)

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Large-scale triaxial testing

(Linero et al., 2008) 9

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Gradation analysis

(Dorador et al., 2017, Material characterization, In: Hawley, M., & Cunning, J. (eds.), Guidelines for Mine Waste Dump and Stockpile Design: 13-27. The

Netherlands: CSIRO PUBLISHING/Balkema)10

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Data Dimension Reduction: Principal Component Analysis (PCA)

• A statistical technique used to reduce the dimensionality of a data set

• Useful technique to discover patterns in high-dimensional data

• Basic idea is to capture as much of the variation in the data as possible, using covariances and eigen vectors

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• Calculate the covariance between all possible axes (i.e. dimensions)

• Example for three axes expressed in covariance matrix C:

),cov(),cov(),cov(

),cov(),cov(),cov(

),cov(),cov(),cov(

zzyzxz

zyyyxy

zxyxxx

C

)1(

))((

),cov( 121

n

yyxx

AA

n

i

ii

Data Dimension Reduction: Principal Component Analysis (PCA)

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Department of Mining Engineering

Data Dimension Reduction: Principal Component Analysis (PCA)

• Calculate the eigen vector and eigen value of the covariance matrix of adjusted original data (transformed using the mean of the data)

• The eigen values with the largest absolute values capture most of the variability in the dataset (principal components)

Ce = λe

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0

5

10

15

20

25

PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10

Var

ian

ce (

%)

Data Dimension Reduction: Principal Component Analysis (PCA)

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Department of Mining Engineering

Global Database:120 test data

*D10, D30, D60, and D90 = 10%, 30%, 60% and 90% percent passing sieve sizes respectively; cu = coefficients of uniformity; cc = curvature; GM = gradationmodulus; FM = fineness modulus; R = ISRM hardness rating; “min UCS” = minimum uniaxial compression strength of group; “max UCS” = maximumuniaxial compression strength of group; “dry unit wt” = dry unit weight at corresponding confining stress.

GM=∑(Cumulative percentage passing sizes through specified sieves)/100

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{ 1 ½ in. (37.5 mm), ¾ in. (19 mm), 3/8 in. (9.5 mm), #4(4.75 mm), #8(2.36 mm), #16(1.18 mm), #30(600 µm),

#50(300 µm), #100(150 µm), and #200 (75 µm)}

Parameter*D10

(mm)

D30

(mm)

D60

(mm)

D90

(mm)Cc Cu GM FM

Hardness

(R.)

Min UCS

(Mpa)

Max UCS

(Mpa)

Dry unit

wt

(kN/m3)

Confining

Stress

(Mpa)

Shear

Stress

(Mpa)

Min 0.02 0.92 3.2 10 0.42 1.36 0.2 3.94 1 1 5 9.32 0.002 0.0065

Max 33.9 42.4 80.1 100 22.3 220 5 8.8 6 250 400 38.9 4.21 3.92

Mean 5.49 9.25 20.4 42.7 2.27 33.7 2.72 6.35 4 73.4 166.6 20.6 0.67 0.63

STDEV 10.05 11.56 15.92 24.1 3.6 46.73 1.26 1.27 1 41.84 92.17 5.44 0.76 0.66

(N = 120)

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*Parameter A=D10, B=D30, C=D60, D=D90, E=coefficient of uniformity, F=coefficient of curvature, G=gradation modulus, H= finenessmodulus, I= ISRM hardness rating, J= minimum uniaxial compression strength, K= maximum uniaxial compression, L= dry unit weight,M=confining stress, N=shear stress.

Data Dimension Reduction: Principal Component Analysis (PCA)

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A B C D E F G H I J K L M N VarianceCum.

Proportion

PC(1) 0.305 0.344 0.359 0.264 -0.2 -0.13 -0.366 0.362 0.284 0.287 0.284 -0.141 0.037 0.06 6.09 43.50%

PC(2) 0.28 0.205 -0.063 -0.282 0.086 0.017 -0.019 0.042 -0.055 -0.076 0.014 -0.216 -0.6 -0.608 2.45 61.00%

PC(3) 0.207 0.237 0.207 0.274 0.344 0.172 -0.238 0.212 -0.428 -0.334 -0.365 0.321 0.042 0.018 2.07 75.70%

PC(4) -0.041 -0.02 0.116 0.063 0.474 0.592 0.091 -0.123 0.18 0.372 0.35 0.276 -0.096 -0.053 1.4 85.80%

PC(5) 0.014 -0.031 -0.091 0.104 -0.035 0.613 -0.028 0.115 0.115 -0.193 -0.187 -0.69 0.127 0.107 0.76 91.10%

PC(6) 0.46 0.284 -0.162 -0.588 0.277 -0.05 0.061 -0.052 -0.058 0.017 0.124 -0.074 0.371 0.296 0.47 94.50%

PC(7) -0.295 -0.115 0.199 0.081 0.601 -0.388 0.014 0.111 -0.246 0.177 0.076 -0.48 -0.012 0.033 0.34 96.90%

PC(8) 0.151 0.236 0.476 0.104 -0.255 0.065 0.435 -0.461 -0.337 0.23 -0.131 -0.16 -0.023 0.05 0.18 98.20%

PC(9) -0.348 -0.082 0.417 -0.603 -0.188 0.201 -0.169 0.331 -0.127 0.209 -0.212 0.082 0.069 -0.061 0.12 99.10%

PC(10) -0.065 0.177 0.234 -0.076 0.258 -0.158 0.019 -0.231 0.677 -0.069 -0.536 0.027 -0.065 0.045 0.05 99.40%

PC(11) -0.119 0.082 0 0.022 0.006 0.005 -0.476 -0.476 -0.049 0.01 0.058 -0.074 0.498 -0.516 0.04 99.70%

PC(12) -0.103 -0.003 0.077 -0.135 -0.04 0.05 -0.533 -0.411 -0.107 -0.157 0.167 -0.059 -0.45 0.488 0.03 99.90%

PC(13) 0.27 -0.232 -0.343 0.08 0.005 -0.006 -0.258 -0.049 -0.118 0.656 -0.472 -0.012 -0.096 0.067 0.01 100.00%

PC(14) -0.489 0.73 -0.397 0.053 -0.043 0.039 0.039 0.066 -0.088 0.191 -0.061 0.013 -0.063 0.076 0.01 100.00%

*Principal

Component

Parameter

Department of Mining Engineering

Summary and Conclusions

• Many previous studies have recognized the correlation between rock

particle size distribution and shear strength in waste rock dumps

• This study has identified and ranked key geotechnical parameters in

terms of their influence on the shear strength of waste rock, based on

a compiled global database (120) and principal component analysis

• These include GM, FM, D60% passing size; for a given confining

stress, rock particle hardness, UCS, and density.

• However, when possible site specific tests and data should be

acquired

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