D12 WP4 Demonstration Final

8/12/2019 D12 WP4 Demonstration Final

1/85

IRIS FP7-NMP-2007-LARGE-1

IRIS WP4 Demonstration Report page 1 of 85

D12DELIVERABLE

PROJECT INFORMATION:

Project Title: INTEGRATED EUROPEAN INDUSTRIAL RISK

REDUCTION SYSTEM

Acronym: IRISContract N: CP-IP 213968-2 Project N: FP7-NMP-2007-LARGE-1Project Start: 01 October 2008 Project End: 31 March 2012

REPORT INFORMATION:

Report Title: WP4DEMONSTRATION,CASE 1AND IMPROVEDTECHNOLOGY

Date of Issue: 31 March 2010

Rep. Period: 01 October 2008 31 March 2009

Prepared by: KGHM Cuprum

Author: Witold Pytel

coordinating person:

organisation:

e-mail:

fax:

telephone:

Dr. Helmut Wenzel

VCE Holding GmbH

[email protected]

+43-1-893 86 71

+43-1-897 53 39


2/85



Table of Contents

Table of Contents...........................................................................................................................21 TAILINGS STRUCTURES INCIDENTS....................................................................................4

1.1 Examples of Historical Incidents and Failures...................................................................41.2 Variability of Incidents Causes..........................................................................................8

2 DEFINITION OF INHERENT AND EMERGING RISKS.........................................................103 COMPUTATIONAL TOOLS OF RISK ASSESSMENT...........................................................14

3.1 Reliability Concepts (Bauer and Pula, 2000) ...................................................................143.2 Response Surface Method..............................................................................................173.3 Simulation Methods.........................................................................................................173.4 Random Finite Element Method (RFEM) ........................................................................183.5 Mining Related Seismic Events Occurrence Model.........................................................21

4 RELIABILITY OF SYSTEMS...................................................................................................245 RANDOM VARIABLES DESCRIPTION..................................................................................27

5.1 Soil and Tailings..............................................................................................................275.2 Water Table (Phreatic Surface).......................................................................................325.3

Mining Induced Seismicity (also Earthquakes Events) ....................................................33

5.4 Soil/Tailings Liquefaction.................................................................................................355.5 Rain Falls.........................................................................................................................38

6 ACCURACY OF SAMPLING AND AUTOCORRELATION PROBLEMS................................396.1 Minimum Number of Samples Necessary for Reliable Database....................................396.2 Variation of the Soil/Tailings Parameters in Space.........................................................40

7 ENVIRONMENTAL RISK ASSESSMENT PROCEDURES....................................................457.1 Risk Assessment for Potentially Contaminated Soils and Ground water........................457.2 Risk to Human Health......................................................................................................47

8 RISK ASSESSMENT FOR POTENTIAL MECHANISMS OF DAMS STRUCTURAL FAILURE498.1 Dams Stability Analysis..................................................................................................498.2 Limit Equilibrium Methods General Assumptions. ........................................................538.3 Numerical Examples Using SLIDE 5.0............................................................................60

9 FLOODS FROM TAILINGS DAM FAILURES.........................................................................6710VARIABILITY OF CONSEQUENCES (FREQUENTLY TRANSBOUNDARY EFFECT) ........70


3/85



11EVENT PROBABILITIES ........................................................................................................7111.1General............................................................................................................................7111.2Event Trees.....................................................................................................................76

12WHAT SHOULD BE DONE IN THE NEAR FUTURE (rough estimate) .................................79

13MEASUREMENTS AND MONITORING PERFORMED AT ELAZNY MOST TAILINGS POND

.........................................................................................................................................81


4/85



1 TAILINGS STRUCTURES INCIDENTS

1.1 Examples of Historical Incidents and Failures

Presently the available data on vulnerability of property/people due to tailings ponds/storageyards damage is rather not scarce since at least 221 serious tailing dams accidents reportedby UNEP (http://www.mineralresourcesforum.org/docs/pdfs/Bulletin121.PDF) (see Fig. 1.1and Table 1.1).

Fig. 1.1 Tailings dams incident history summary (number of incidents per 5 year period) after ICOLDBulletin 121

Rico et al. (2008)1 also reviewed 147 cases of tailings dam incidents occurred over the

world. In Fig. 1.2 a distribution of causes of failure are presented since Fig. 1.3 shows adependence between dam height and the number of incidents.

1Rico M., Benito G., Salgueiro A.R., Dfez-Herrero, H.G. Pereira. Reported tailings dam failures. A review of the

European incidents in the worldwide context. J. of Hazardous Materials 152 (2008): 846-852


5/85



97

9

3

36

2

10

21

13

22

15

0

5

10

15

20

25

30

35

40

F

S

O

/O

M

U

S

P

/S

S

S

U

M

Fig.. 1.2 Number of incidents related to causes

10

15

16 16

9

6

4

6

3

2

1

0

1 1

0 0

1

0 0 0 0

2

0

2

4

6

8

10

12

14

16

18

15

1

015

2

025

3

035

4

045

5

055

6

065

7

075

8

885

9

095

100

105

Fig. 1.3 Number of incidents related to dam height

Examples of well known tailings dams failures are shown in Table 1.1.


6/85



TABLE 1.1 SELECTED MAJOR ACCIDENTS OF TAILINGS DAMS

LOCATION DATE IMPACT

Baia Mare(Romania)

30.01.2000 100,000 m3

cyanide

contaminatedwater withsome tailingsreleased

Baia Borsa(Romania)

10.03.2000 22,000 t oftailingscontaminatedby heavy

metalsreleased

Stava, Italy 19.07.1985 269 deaths,tailingsflowed up to8 km

Merriespruit,(SouthAfrica)

22.02.1994 17 deaths,500,000 m3

slurry flowed2 km

BuffaloCreek, USA

26.02.1972 125 deaths,more than500 homesdestroyedcoal slurrydam burst.

The resultingfloodunleashedapproximately

132 milliongallons


7/85



(500,000,000L) of blackwaste water,cresting over30ft high.

Mufilira,Zambia

25.09.1970 89 deaths,68,000 m

3

into mineworkings

Omai,Guyana

19.08.1995 4.2 million m3

cyanide slurryreleased

Los Frailes,Spain

24.04.1998 released 4-5million cubicmeters oftoxic tailingsslurries


8/85



Aitik mine,Sweden

09.08.2000 1.8 million m3

waterreleased

1.2 Variability of Incidents Causes

Due to unique conditions concerning geology, mineralogical properties of extracted ore,topography of surface as well as due to different technological mining systems andprocedures, different mines produce unique tailings materials which are stored in surfacestorage structures of different technical and safety characteristics. All these objects areconstructed according to laws and codes applicable to tailings storage facilities, neverthelessmany failures of tailings dams occurred in European countries each year. Among the mainreasons of such events occurrences one may indicate (see also Fig. ):

insufficient knowledge of material characteristics, improper calculation models and theories describing the physical behavior of structures, operational departure from the prior accepted design criteria, lack of appropriate structure monitoring including the water level measurements, inadequate management, insufficient understanding of connections between the instability manifestation and the

causes, lack of control of hydrological system, error in site selection and investigation, unsatisfactory foundation, lack of stability of downstream slope, seepage, overtopping, earthquake (also mining related seismicity).

Among the factors directly affecting dam stability are: Active environment (e.g rain, snow, freeze, etc.); Earthquake and mining related seismicity; Difficult geological/geotechnical conditions.

Indirectly dam stability is mostly influenced by:

Wrong design conception; Construction failure; Material failure; Bad maintenance; Lack of control;

Human error.


9/85



The most important consekwence of dam failure/damage are:

Water and sludge movement;

Mechanical contamination by solid particles;

Chemical toxicity/ecotoxicity;

Radioactivity.

Sources:

Tailings Dam Incidents, U.S. Committee on Large Dams - USCOLD, Denver,

Colorado, ISBN 1-884575-03-X, 1994, 82 pages [compilation and analysis of 185tailings dam incidents]

Environmental and Safety Incidents concerning Tailings Dams at Mines:Results of a Survey for the years 1980-1996 by Mining Journal Research Services; areport prepared for United Nations Environment Programme, Industry andEnvironment . Paris, 1996, 129 pages [compilation of 37 tailings dam incidents]

Tailings Dams - Risk of Dangerous Occurrences, Lessons learnt from practicalexperiences, Bulletin 121, Published by United Nations Environmental Programme(UNEP) Division of Technology, Industry and Economics (DTIE) and InternationalCommission on Large Dams (ICOLD), Paris 2001, 144 p. [compilation of 221 tailings

dam incidents mainly from the above two publications, and examples of effectiveremedial measures]> Read review Download full text: UNEP (1.2M PDF) , or: ICOLD (947k PDF)

http://www.wise-uranium.org/mdefhtml


10/85


11/85



From Fig. 2.1 one may determine an approximate ranges of annual probabilities of failure aswell as the consequences of such events also in reference to tailings ponds where the failureevent is usually associated with dams breakage. The accepted and marginally acceptedprobability of failure may be estimated as:

4.0, )1(5.0

+= (accepted), and

3.0, )1(

+= (marginally accepted)

where CF consequence of failure [USD]. These equations are presented also in Fig. 2.2.

1,E-05

1,E-04

1,E-03

1,E-02

1,E-01

1,E+00

1,E+00 1,E+02 1,E+04 1,E+06 1,E+08 1,E+10

Consequences of failure [USD]

Probability

off

ailure

Accepted probability Marginally accepted probability

Fig. 2.2 Accepted aqnd marginally accepted probability of failure based on Fig. 2.1


12/85



With moderate consequences from 1 m$ to 100 m$, the respective acceptable probability offailure is ranging from 0.0003 to 0.002 while the marginally accepted probability of failure isestimated between 0.004 and 0.016. All the estimated probabilities are considerably small.

The problem of risk created by tailings ponds, landfills and waste stockpiles is known widelyfor many years, particularly as an issue of earth dams stability. These structures work instatistically non-homogeneous natural and man-made environment subjected to variousrandomly defined external natural inter-correlated influences such as floods, rainfalls,earthquakes, tectonic movement of surface geological deposits (rocks and soil). Theseeffects in conjunction with possible mining-related static and dynamic influences areextremely complex and therefore their analytical (numerical) solutions are unavailable inliterature in a complete form.

One may agree that the risk model will consist of product of different risks described byappropriate probabilities and associated consequences (Fig. 2.3), some mutually correlated.This is one of the most important feature of the project since previously applied methods oftailings facilities risk assessment have been based on a qualitative concluding rather than atruly probabilistic-quantitative approach.

Fig. 2.3 Risk described qualitatively vs. quantitatively


13/85



The project integrates two basic paths of tailings ponds safety estimation, each of them ofextreme internal complexity, and immersed in statistically non-homogeneous environment:

the path embracing analytical methods and measurement techniques addressed to a

general problem of risk estimation in a case of possible structural instability due tonatural and man-made hazards, and the path grouping analytical methods and measurement techniques useful for

environmental risk assessment, for a case of soil/water possible pollution.

Each of the mentioned groups will utilize its own characteristic analytical and measurementmethods as well as the specific methods of concluding.

Although the true risk assessment analysis for tailings ponds has been not required by theexisting law in the past, the present knowledge of the subject is already sufficient for itspartial development. This may be done using the principles of probabilistic risk assessment(PRA) theory addressed to earth/tailings surface structures.


14/85



3 COMPUTATIONAL TOOLS OF RISK ASSESSMENT

3.1 Reliability Concepts (Bauer and Pula, 2000)3

Structural reliability problems of earth dams are usually described by the so-called limitstate function F = g(x), stability factor. The argument x of the function g is a randomvector X = (X1, X2, ..., Xn) consisting of basic random variables defining loads, materialproperties, geometrical quantities, etc. The function g(x) may be defined in the followingway:

>=

1

1)( (3.1)

The hyper surface g(x) = 0 is called the limit equilibrium surface.

As a reliability measure the probability of failure is used:

{= 1),) )( (3.2)

Here xf represents a multidimensional joint probability density function (p.d.f.) of the random

vector X. In the special case if Xis a Gaussian random vector with uncorrelated componentsXi, I = 1,2,,n, a linear transformation of the coordinate system, known as thestandardization, is convenient to use:

.,...,1,)(

=

=

(3.3)

where E(Xi) and xi. are expected value and standard deviation of the random variable Xi,respectively. The corresponding mapping of the limit state surface g(x) = 1is as follows:

G(y) = g(x(y)) = 0. (3.4)

If the limit state function g is a linear one, G will remain linear. It could be also proved that:

),()(1)( 00

==


15/85



the linear transformation another type of mapping of the coordinate system has to beutilized. In this mapping random vector X is transformed into the standard normal randomvector Ywith independent components: Y= Y(X).

Fig. 3.I. Schematic presentation of the failure probability assessment in the case of Gaussiandistribution and a linear limit state function.

Such a transformation is known as a probability transformation. Most common types ofprobability transformations are Rosenblatt, Nataf and Hermite ones. The limit state surfaceg(x) = 1is mapped onto G (y) = 1, which is a hyper-surface of the standard normal space.

Hence the probability of failure is as before equal to:


16/85



In the SORM approximation, the limit stale surface is fitted with a quadratic surface in thevicinity of the design point y

*and the right-hand side of the above equation is multiplied by a

certain correction factor, affected by curvatures of the hyper-surface G(y) = 1at the point y*.

This gives the value of FSORMp . Next the reliability index SORM can be computed by inverting

the above relationship:

)(1

0 = (3.8)

Fig. 3.2 Schematic presentation of the FORM approximation

The most important problem in the FORM and the SORM lies in finding the minimum-distance point y*, i.e. the design point. Hence the problem can be formulated in terms of aconstrained optimization as follows:

1)(, = (3.9)

where denotes the Euclidean norm. Several sophisticated algorithms for this problem

were developed with the most effective utilizing the gradient vector Gy of the limit state

function G.

An important feature of the FORM and SORM methods is that the complete probabilityinformation about random vector Xin the form of probability density function (or cumulativedistribution function) must be known. Furthermore an explicit formulation of the limit statefunction g(x)in a closed analytical form makes a reliability computations more efficient andmore accurate.


17/85



3.2 Response Surface Method

The response surface method applied to numerous fields of knowledge is exhaustively

described in a number of monographs. In general, this method consists in approximating anunknown function by the known function chosen appropriately. This approximation can bebased on the results of experiments and also on the results of numerical computations, e.g.results obtained by means of the finite element method. In the case of numericalcomputations, a relationship between the model parameters ,...,, 21 , which are introduced

as input data, and the values obtained as output data ),...,,( 21 = is defined. Roughly

establishing such a relationship allows us to replace a troublesome numerical procedure witha simple analytical relationship, which helps to forecast a response of the model beinganalyzed in the input set.

3.3 Simulation Methods

Reliability measures may be also assessed using one of simulation approaches, e.g. MonteCarlo method or Latin Cube technique. These methods are based on numerical samplingof vectors from the probability function of random vector X using the random numbersgenerator, and afterwards the approximate value of failure probability may be assessed as:

=

=

1

1]1),([1

(3.10)

with the variance:

)1(1

1)([1

221

=


18/85



3.4 Random Finite Element Method (RFEM)

A powerful and general method of accounting for spatially random shear strength

parameters and spatial correlation, is the Random Finite Element Method (RFEM)whichcombines elasto-plastic finite element analysis with random field theory generated using theLocal Average Subdivision Method (Fenton and Vanmarcke 1990).

The RFEM offers many advantages over traditional probabilistic slope stability techniquesbecause it enables slope failure to develop naturally by seeking out the most criticalmechanism. It has been proved, that simplified probabilistic analysis, in which spatialvariability is ignored by assuming perfect correlation, can lead to unconservative estimates ofthe probability of failure. This contradicts the findings of other investigators using classicalslope stability analysis tools.

A typical finite element mesh for the test problem considered in this paper is shown below.


19/85



Fig. 3.3

The code enables a random field of soil parameters (e.g. cohesion) to be generated andmapped onto the finite element mesh, taking full account of element size in the local

averaging process. In a random field, the value assigned to each cell (or finite element in thiscase) is itself a random variable. Thus the mesh of Figure 3.3 which has 910 finite elements,contains 910 random variables.

The random variables can be correlated to one another by controlling the spatial correlation

length c , hence the single random variable approach where the spatial correlation length

is implicitly set to infinity, can now be viewed as a special case of a much more powerfulanalytical tool. Figures below show typical meshes corresponding to different spatialcorrelation lengths. Figure 3.4 shows a relatively low spatial correlation length of 2.0= and

Figure shows a relatively high spatial correlation length of 0.2= . Dark and light regions

depict "weak" and "strong" soil respectively. It should be emphasized that both these shear

strength distributions come from the same lognormal distribution, and it is only the spatialcorrelation length that is different.

In brief, the analyses involve the application of gravity loading, and the monitoring ofstresses at all the Gauss points. The slope stability analyses use an elastic-perfectly plasticstress-strain law with a Tresca failure criterion which is appropriate for "undrained clays". Ifthe Tresca criterion is violated, the program attempts to redistribute excess stresses toneighboring elements that still have reserves of strength. This is an iterative process whichcontinues until the Tresca criterion and global equilibrium are satisfied at all points within themesh under quite strict tolerances.

Plastic stress redistribution is accomplished using a visco-plastic algorithm with 8-node

quadrilateral elements and reduced integration in both the stiffness and stress redistributionparts of the algorithm. The theoretical basis of the method is described more fully in Chapter


20/85



6 of the text by Smith and Griffiths (1998), and for a detailed discussion of the methodapplied to slope stability analysis, the reader is referred to Griffiths and Lane (1999).

For a given set of input shear strength parameters (mean, standard deviation and spatialcorrelation length), Monte-Carlo simulations are performed. This means that the slope

stability analysis is repeated many times until the statistics of the output quantities of interestbecome stable. Each "realization" of the Monte-Carlo process differs in the locations atwhich the strong and weak zones are situated.

Fig. 3.4

(vc coefficient of variation for cohesion)


21/85



3.5 Mining Related Seismic Events Occurrence Model4

The following model is an analytical tool used for risk assessment from the mining relatedseismicity, with the following assumptions

(a) seismic events are mutually independent phenomena,

(b) the time of occurrence and the seismic energy are the two parameters sufficientlydescribing the particular event,

(c) seismic activity and the energy of tremors are independent quantities,

(d) time-dependency of the seismicity process is described by the process p.d.f. parameterstime-dependency only,

(e) the seismicity process is represented by the Poissons process with the followingprobability of the nevents occurrence within the time period t

)(

!

)]([;

== (3.13)

where )( - time-dependent seismic activity.

(f) within a reasonable time-window the mining-related seismicity is a stationary process.

Seismic risk (i.e. the conditional probability of the seismic event ,if any, of the energy greaterthan Ep, occurrence) may be described by the following formula:

],[)(,...,)(,)(

],[)],(),...,(;[1)1()0,();,(

1

1)(

===

=+=

(3.14)

where: )(),...,(; 1 - the seismic energy marginal distribution function, )(),...,(1 are

the time-dependent parameters, is the time-window length.

From the number of the available mathematical models of the seismic eventsmagnitude/energy distribution functions, the following two models are broadly applied in themining seismology:

(a) the right-hand unlimited model with the Pareto distribution function for energy and the

left-hand truncated exponential distribution function for the event magnitude Model I,

(b) the right-hand limited model with the truncated Pareto distribution function for energy andthe both-sides truncated exponential distribution function for the events magnitude.

4 S. Lasocki. 1996. Ocena i prognoza lokalnego ryzyka sejsmicznego poprzez analiz danych

sejsmologicznych. Seria Wykady nr 12 Szkoy Eksploatacji Podziemnej 96, s. 49-67


22/85


23/85



Model II

Model II is generally derived from the Model I by introduction the upper bound for energy.The energy distribution function is then as follows (band Emaxare time-dependent):

632.1

923.20)'(002.0)(848.0)(177.7)850.01()001.0()110.0(0.1

1,045.11,


38/85



Fig. 5.6

5.5 Rain Falls

The probability of future rain falls based on the data recorded in the past may be assessedusing Bayesian distribution. Particularly, we would like to know what is the probability that inthe next myears, rain falls grater than a given number (mm) will occur ytimes, since fromthe available data one may notice that in the period of the last nyears ssuch events haveoccur.

Assuming bi-nomial p.d.f B(m,p)for Yvariable (sum of the yearly events) and assuming ptobe known random parameter characterized by beta distribution:

10)1()!()!(

)!1()(

+=

, (5.10)

Bayesian distribution of Yis as follows:

.1

1

1

1)(

1

++

++

++

+=

(5.11)


39/85



The above presented expression may be used for the dams overtopping probabilityassessment.

6 ACCURACY OF SAMPLING AND AUTOCORRELATION

PROBLEMS

6.1 Minimum Number of Samples Necessary for Reliable Database

The required number of samples which may be treated as the sufficient database for anystatistical analyses depends on a number of factors, among them the following factors seemto be the most important:

(a) the importance (also the value) of the planned earth structure and the respective demand

for the extend of soil tests;

(b) the required accuracy of design;

(c) the degree of the heterogeneity of the structural materials in 3D space (the naturalstratification, different sources of material supply etc.);

(d) the homogeneity of the deposits of the different kinds of (sub)soil, rocks, ground tailingsetc.

(e) the available archival database, the allowable cost and time horizon limits of theexploration, monitoring and the laboratory/field tests, access to the appropriate laboratoryfacilities etc.;

(f) the expected reliability of the work results.

Nevertheless, based on the principles of the mathematical statistics5 it is known that the

required number of independent estimates should fulfill the following relation:

=

(6.1)

where is the maximum relative error in mean value estimation (assumed a priori), is the

empirical coefficient of variability, and tis the value of the Student distribution function for n-1 degree of freedom with a chosen probability level . For instance, assuming

,95.0,2.0%),5(05.0 === at least 60 samples must be taken to maintain the required

accuracy. The applied values of nand were found in table .

5Rethati L. Probabilistic Solutions in Geotechnics. Elsevier 1988


40/85



Tab. 6.1 nand t values pairs for different (Rethati, 1988)

n 9.0 95.0 99.0 n 9.0 95.0 99.0

1 - - - 18 0.410 0.497 0.683

2 4.465 8.985 45.013 19 0.398 0.482 0.660

3 1.686 2.484 5.730 2 0.387 0.468 0.640

4 1.177 1.591 2.920 21 0.376 0.455 0.621

5 0.953 1.241 2.059 22 0.367 0.443 0.604

6 0.823 1.050 1.646 23 0.358 0.432 0.558

7 0.734 0.925 1.401 24 0.350 0.422 0.573

8 0.670 0.836 1.237 25 0.342 0.413 0.559

9 0.620 0.769 1.118 26 0.335 0.404 0.547

10 0.580 0.715 1.028 27 0.328 0.396 0.535

11 0.546 0.672 0.955 28 0.322 0.388 0.524

12 0.518 0.635 0.897 29 0.316 0.380 0.513

13 0.494 0.604 0.847 30 0.310 0.373 0.503

14 0.473 0.577 0.805 40 0.266 0.315 0.412

15 0.455 0.554 0.769 60 0.216 0.256 0.344

16 0.438 0.533 0.737 120 0.151 0.180 0.239

17 0.423 0.514 0.708 0 0 0

6.2 Variation of the Soil/Tailings Parameters in Space

The properties of embankments and fillings materials always vary in space, horizontally andvertically, and depend on the underground excavation site geology (e.g artificial groundmaterials from processing/enrichment plants) as well as on the entire structures naturalsubsoil geological features.

If the tested variable is plotted vs. the distance, one may decompose the general data onthree components as follows:

++= )()()( (6.2)


41/85



where: t(x) the trend component, p(x) the periodic component, stochasticcomponent. The trend function is usually described by a straight line, however a parabola oran exponential curve may be also used. The trend function may be built-in into thedeterministic model of the structure as a set of parameters sufficiently describing itstechnical characteristics. The periodicity may be in turn verified using so called

autocorrelationanalysis, which enables to specify numbers describing the memory of theprocess and the mutual (in)dependence of the elements.

Having two corresponding empirical vectors of correlated variables (e.g. distance andcohesion, d1and c1), numerical spacing(s) kimay be chosen and the new correlated pairs ofvectors di and ci can be created for which coefficients of correlation ri can be found.Furnishing the obtained data in the form of a diagram )(= (see Fig. 6.1 ), the so called

autocorrelogrammay be obtained.

As a criterion for determining if the particular value rk differs significantly from zero, theAndersons formula may be used:

1

11

=

(6.3)

where: n number of elements in the series, k step spacing, t value of the Students

function with the chosen probability (if 1.0

reliability of estimation rapidly decreases).

Selected cases of autocorrelogramsdependent on the general case of series may be foundin Table 6.2 .

Table 6.2

General case description

0)()( == All elements in the series areuncorrelated.

white noise

0)(,0)( = Every element depends only on thedirectly preceding element.

The accelerogram may be written up as

follows: =

first-order Markov process

0)(,0)( The autocorrelation functions distortionmay be compensated by the constant c

and then:

= .

first-order Markov process

Series contain alsoperiodic elements ])([ 0

0

0

+=

where: /20 = , T the length of the

step, index of the memory.

second-order Markovprocess


42/85



Fig. 6.1 Field determined correlation function = )( for CPT resistance (Bolotin, 1968)6

It is also generally accepted that any soil/material property Xmay be modeled as a randomfield formulated in ndimensions (Fenton and Griffiths, 2009). The spatial variability of thegiven parameters value will be described as a random process characterized by the infinite-dimensional probability density function (p.d.f):

,...),( 21...21 (6.4)

In practice the infinite number of considered positions is replaced by the (possibly very large)finite number k.

To simplify the problem the following assumptions are often introduced:1. The joint p.d.f. is a k-variate normally distributed random process (Gaussian process)

specified by the mean vector and the covariance matrix.2. The joint p.d.f. is independent on spatial position, depending just on relative positions

of the points all moments (mean, covariance and higher) are constant in space(stationary field).

3. The joint p.d.f. is invariant under rotation the correlation between two pointsdepends only on the distance between them.

Under the above mentioned assumption, the necessary data which knowledge is needed forthe field characterization, may be confined to the following parameters:

1. The field mean - .

2. The field variance - 2 .

3. The parameter which is the measure of how rapidly the field varies in space.

For stationary random fields the covariance (auto-correlation) function is as follows:

6 .. . 1966


43/85



)()( 2 = (6.5)

where: - distance between two points, - correlation function.

Homogeneous, normalized (zero mean) normal/lognormal scalar random fields arecompletely characterized by their auto-correlation functions )( or their two-side or one-side

spectral density functions )( and )( respectively:

2

)()()(

2

1)(

==

. (6.6)

Selected auto-correlation functions and the respective spectral density functions for one-dimensional models are presented in the Table 6.3.

The (auto)correlation functions of different soil/water parameters belong to the mostimportant. These functions describe spatial relationship of parameters value depending on adistance between two points where the parameter have been determined.

The example of a such function determined for CPT in fine sand is shown in Fig. 6.1.

A convenient measure of the autocorrelation within the random field is the correlation length(also known as correlation radius, scale of fluctuation or correlation distance) which may beassessed arbitrarily or from the following equation

2

)0(

= (6.7)

however usually it is difficult to estimate. Correlation length is utilized in RFEM on the routinebasis.


44/85



Table 6.3 One-dimensional models for auto-correlation and spectral (one-sided) density functions7,8

Type of auto-correlationfunction

Autocorrelation function )(C Spectral density function )(G

I 2 222 2

+

II 2

++

++ 2222

2

)(

1

)(

1

2

222222

22

4)(

+

+

2

222222

222

4)(

)(4

+

+

III )()(2 2

0

22)()()(2

IV2

2 )4(

22

2

2

+

+

2

2

2

22

4

)(

4

)(

2

V)(2

)()(

1

2

2/1

2

2

2

1

)/1(2)(

)2/1(+

+

+

VI

>

=

0

1)(

2 2

2

2

2

Jo the Bessel function of first kind and order 0, Iv the modified Bessel function of secondkind and order v

7R. Rackwitz / Computers and Geotechnics 26 (2000) 199-223

8B. Skalmierski, A. Tylikowski. Stochastic Processes in Dynamics (in Polish), Mae Monografie PWN, 1972


45/85


46/85



Fig. 7.1 Scheme of measurement grid for contaminants of concern detection

The risk generated by the contaminant of concern k in the area of influence may be

calculated from the following relationship:

(7.1)

where: jK unit cost of soil rehabilitation using the remedial technology j, Sil area of the

cell il, ]),([ , - probability of contaminant klevel will be greater than the ultimate level

accepted by authorities. Each considered cell should be characterized by p.d.f for thecontaminants levels data gathered during the long-term surveying.

The total risk created by all considered contaminants of concern may be assessed using thefollowing sum:

=

1

. (7.2)

The total cost of soil remediation will be then:

(7.3)

where - the area where ultil FF .

Contaminated Zone W

y

x

]),([ ,1 1

=

= =

=


47/85



In Fig. 7.2 ground water flow contour measured at elazny Most is shown. This kind of thedata may be used for water/soil contamination probability assessment.

Fig. 7.2 Example of ground water flow-out investigation at elazny Most tailings pond

7.2 Risk to Human Health

The overall risk assessment has to include the evaluation of both the risks to theenvironment and the risks to human health posed by the release of chemical agents from thetailings/wastes storage facilities. The latter one relates quantitatively the concentration of acontaminant in an exposure medium (air, water and soils) to its toxicological effect in abiological organism through multiple exposure pathways. The determined value may be usedfurther to estimate an acceptable exposure level, if a such information has not beenavailable in being in force regulations yet.

This may be done using so called risk-based action levels (RBALs)11which are the ultimatelimits for human and environment exposure to contaminants of concern requiring theappropriate remedial action to be undertaken. This type of parameters (ultimateconcentrations) may be assessed using available sources complemented with appropriateanalytical methods:

11 Robinson S., Pavlou S., R. Kadeg. Applications of risk assessment techniques in RCRA clean closure of

surface impoundments with trace metal contamination. Risk Assessment/Management Issues in theEnvironmental Planning of Mines (Dirk Van Zyl, Marschall Koval, Ta M. Li eds.), Chapter 22,: 171-175,Society fo Mining, Metallurgy, and Exploration, Inc., Littleton, Colorado 1992


48/85



(A) Concentrations limits may be assessed from relevant standards following otherenvironmental regulations (e.g. the chemical-specific Maximum Contaminant Levels(MCLs) promulgated under the Safe Drinking Water Act).

(B) For soils, relevant standards are typically lacking, and therefore risk-basedconcentration limits are mostly used.

A general approach to computing risk-based soil concentrations requires:

(a) the identification of appropriate site (also its use, restricted/free access etc.), and

(b) commensurate exposure parameters for use with the generic exposure pathwaymodels; for exposures to soil borne contaminants the direct soil contact pathways:ingestion, inhalation and dermal contact, are the major routes through whichindividuals may be potentially exposed.

Each of the three RBALs representing three soil exposure pathways actually are the kinds ofthresholds which values should not be less than the actual concentration Ck of the

contaminant of concern k. They may be calculated as follows:

Soil Ingestion

]/[,

= (7.4)

where: BW body weight [kg], AT averaging time appropriate to carcinogenic or systemictoxicants [days], CF conversion factor [10

6 mg/kg], CTV critical toxicity value for

carcinogenic or systemic toxicants [mg/kg-day], SIR soil rate [mg soil/day], EF exposurefrequency [days/year], ED exposure duration [years], RAF relative absorption factor

[dimensionless].

Dermal Contact

= (7.5)

where: SA skin surface area exposed [cm2], SC soil covering on skin [mg/cm

2-day].

Particulate Inhalation

= (7.6)

where: BR breathing rate [m3/hour], RPF respirable particulate fraction PM10 [mg/m

3],

ET exposure time [hours/day].

Since exposure to contaminants in a soil medium may occur through more than oneexposure pathways, a cumulative risk-based criterion should be used

12:

12 Rosenblatt D.H., Dacre J.C., and D.R. Cogley. 1982. An environmental fate model leading to preliminary

pollutant limit values for human health effects. In: Environmental Risk Analysis for Chemicals (ed. R.A.Conway), Van Nostrand Reinhold Company, New York


49/85



111

1

++

= (7.7)

Knowing the p.d.f. for the actual concentrations Ckwithin particular cellsil, the risk posed by

contaminated soil for human health, may be assessed from:

(7.8)

where: Kh cost of hospitalization or death, Ck concentration of k toxic substance in soil.

8 RISK ASSESSMENT FOR POTENTIAL MECHANISMS OF

DAMS STRUCTURAL FAILURE

8.1 Dams Stability Analysis

Tailings dams of different methods of raising and of a different technical designation revealdifferent resistibility against any instabilities resulted in failure event. Typicaladvantages/disadvantages of different embankment dams are presented in Table 8.1 (basedon Vicks, 1990) while typical modes of embankment dams failure are shown in Table 8.2.

Most of the modern analysis of the dam failure potential is based on a conventional

approach involving slope stability assesment..

Conventional slope stability analyses investigate the equilibrium of a mass of soil boundedbelow by an assumed potential slip surface and above by the surface of the slope. Forcesand moments tending to cause instability of the mass are compared to those tending toresist instability. Most procedures assume a two-dimensional (2-D) cross section and planestrain conditions for analysis. Successive assumptions are made regarding the potential slipsurface until the most critical surface (lowest factor of safety) is found. Figure shows apotential slide mass defined by a candidate slip surface. If the shear resistance of the soilalong the slip surface exceeds that necessary to provide equilibrium, the mass is stable.

If the shear resistance is insufficient, the mass is unstable. The stability or instability of the

mass depends on its weight, the external forces acting on it (such as surcharges oraccelerations caused by dynamic loads), the shear strengths and pore-water pressuresalong the slip surface, and the strength of any internal reinforcement crossing potential slipsurfaces.

)],([1 1

=

= =


50/85

IRIS

IRIS WP4 Demonstration Report

Table 8.1 Comparison of Embankment Dams Types

Embankment Type

source: Design And

Evaluation ofTailings Dams, EPA530-R-94-038,1994

Water retention Upstream Downstream

Mill Tailings Requirements Suitable for any type oftailings

At least 60% sand inwhole tailings. Low pulpdensity for grain-sizesegregation.

Suitable for any tytailings

Discharge Requirements Any discharge proceduresuitable

Peripheral discharge, wellcontrolled beach

necessary

Varies according to details

Water Storage Suitability Good Not suitable for significantwater storage

Good

Seismic Resistance Good Poor in high seismic areas Good

Raising Rate Restrictions Entire embankmentconstructed initially

Less than 5-10 m/yearmost desirable. Over 15m/year can be hazardous.

None

Embankment Fill

Requirement

Natural soil borrow Native soil, sand tailings,

waste rocks

Sand tailings, waste

native soilsRelative EmbankmentCost

High Low High

Use Of Low PermeabilityCores

Possible Not possible Possible (inclined co


51/85



Table 8.2 Basic failure modes for embankment dams and the most important parameters governingthe failure processes (red stochastic, green deterministic parameters)

Kinds of failure event Failure causes Parameters governing the failure

1. Foundation instabilityFAILURE OF EMBANKMENT DAM FOUNDATION

IN NORMAL CONDITIONS

UPSTREAMDAMS

SLIP LINE

WATER TABLE

FOUNDATION

SOLIDTAILINGS FILLING

1. Geometry (structural dimensions)

2. Weight of materials.

3. Dams, fillings and subsoil strengthcharacteristics:

(a) cohesion,

(b) angle of internal friction,

3. Phreatic surface location.

Method of solution: Limit EquilibriumMethod

2. Slope instability

FAILURE OF DOWNSTREAM SLOPE OF EMBANKMENT DAM


UPSTREAM DAMS

SLIP LINE

WATER TABLE

FOUNDATION

SOLID TAILINGS FILLING

As (1) above

3. Horizontal slide ofembankment dam

HORIZONTAL SLIDE OF EMBANKMENT DAM


UPSTREAM DAMS

WATER TABLE

FOUNDATION


As (1) above

Method of solution: LEM involvingfillings active and/or passive pressure

4. Piping through/underembankment

FAILURE OF DOWNSTREAM SLOPE DUE TO PIPING THROUGH/UNDER

EMBANKMENT DAM IN NORMAL CONDITIONS

UPSTREAM DAMS

WATER TABLE

FOUNDATION


As (1) above and

1. Coefficients of water permeabilityof materials.

Method of solution: FEM

5. Overtopping in normalconditions

FAILURE OF DOWNSTREAM SLOPE DUE TO OVERTOPPING OF

EMBANKMENT DAM IN NORMAL CONDITIONS

UPSTREAM DAMS

WATER TABLE

FOUNDATION


1. Geometry (structural dimensions)

2. Rain fall.

Method of solution: Volumetricbalance condition


52/85



6. Horizontal slide androtation of embankmentdam in tailings

liquefaction conditions(seismicity)

HORIZONTAL SLIDE AND ROTATION OF EMBANKMENT DAM

IN TAILINGS LIQUEFACTION CONDITIONS

UPSTREAM DAMS

WATER TABLE

FOUNDATION

LIQUEFIED TAILINGS

FILLING

As (1) above and

1. Pressure from liquefied filling

2. Seismic action (acceleration)

3. Particle distribution.

Method of solution: LEM involvingfillings active and/or passive pressure

7. Horizontalslide/rotation and waterovertopping ofembankment dam intailings liquefactionconditions (seismicity)

HORIZONTAL SLIDE/ROTATION AND WATER OVERTOPPING

OF EMBANKMENT DAM IN TAILINGS LIQUEFACTION CONDITIONS

UPSTREAM DAMSWATER TABLE

FOUNDATION

LIQUEFIED TAILINGS

FILLING

OVERTOPPING WATER FLOWAs (6) above and

1. Rain fall.

Method of solution: LEM involvingfillings active and/or passive pressureand volumetric balance condition


53/85



8.2 Limit Equilibrium Methods General Assumptions.

All of the methods presented in this manual for computing slope stability are termed limit

equilibrium methods. In these methods, the factor of safety is calculated using one ormore of the equations of static equilibrium applied to the soil mass bounded by anassumed, potential slip surface and the surface of the slope.

For example, the Ordinary Method of Slices, the Simplified Bishop Method, and the U.S.Army Corps of Engineers Modified Swedish Methods do not satisfy all the conditions ofstatic equilibrium. Methods such as the Morgenstern and Prices and Spencers do satisfyall static equilibrium conditions. Methods that satisfy static equilibrium fully are referred toas complete equilibrium methods.

Complete equilibrium methods have generally been more accurate than those procedureswhich do not satisfy complete static equilibrium and are therefore preferable to incomplete

methods. However, the incomplete methods are often sufficiently accurate and useful formany practical applications, including hand checks and preliminary analyses. In all of theprocedures described in this manual, the factor of safety is applied to both cohesion andfriction.

The factor of safety is also assumed to be constant along the shear surface. Although thefactor of safety may not in fact be the same at all points on the slip surface, the averagevalue computed by assuming that F is constant provides a valid measure of stability forslopes in ductile (nonbrittle) soils. For slopes in brittle soils, the factor of safety computedassuming F is the same at all points on the slip surface may be higher than the actualfactor of safety.

All of the limit equilibrium methods require that a potential slip surface be assumed in orderto calculate the factor of safety. Calculations are repeated for a sufficient number of trialslip surfaces to ensure that the minimum factor of safety has been calculated. Forcomputational simplicity the candidate slip surface is often assumed to be circular orcomposed of a few straight lines.

Most of limit equilibrium methods utilize a kinf of slicing of the rotating/moving soil/rockconfined between the slip surface and the external surface.

The Ordinary Method of Slices (OMS) was developed by Fellenius (1936) and is sometimesreferred to as Fellenius Method.. In this method, the forces on the sides of the slice areneglected (Figure 8.1). The normal force on the base of the slice is calculated by summingforces in a direction perpendicular to the bottom of the slice. Once the normal force iscalculated, moments are summed about the center of the circle to compute the factor ofsafety. For a slice and the forces shown in Figure 8.2.

the factor of safety may be computed from the equation,

+

==

]')('[ 2

(8.1)


54/85



where: c, shear strength parameters for the center of the base of the slice, G weightof the slice, a inclination of the bottom of the slice, u pore water pressure at the centerof the base of the slice, Dl length of the bottom of the slice.

Fig. 8.1


55/85



Fig. 8.2

Different limit equilibrium methods are based on the similar assumptions, however theydiffer in loading assumptions and methods of solution.

In some instances, e.g. when: slopes are curved or discontinuous in plan: ends and corners of embankments, narrow

excavations, earth dam abutments and spillways, bridge approach fills, conical heaps,shafts, pits, ridges and re-entrants,

anticipated failure surfaces are narrow: spoon-shaped slides, failures situated betweenlateral constraints,

slopes are of significant lateral variation in steepness, failure surface geometry,stratigraphy, strength properties, piezometric conditions, loads, or all of the above,

slopes exhibit complex wedge geometries with or without anchor support, slope failures under concentrated loading situated on the slope face or at the crest may

be expected,

the 3D configuration is recommended for the slope stability assessment (see Fig. 8.3).


56/85



Fig. 8.3 Coordinate system and column assembly (mesh) CLARA/W Users Manual, 2001

Unfortunately, computer programs based on the limit equilibrium methods involvingprobabilistic analyses formulated in 3D are not available yet on the market.

Therefore if 3D effects seem to be important , the best available method is to consider anumber of parallel (or almost parallel) cross-sections through the slope/dam (Fig. 8.4) withtheir factors of safety. A weighted safety factor may be then calculated using e.g. the totalweight above the failure surface in each cross-section as a weighting factor:

321

332211

++

++= (8.2)

Based on the above relationship and assuming uniform distribution of tailings pond damscross-sections (see Fig. 8.5) for which safety factors Fihave been assessed (with similarsurfaces Ai of determined slipping blocks), the weighted safety factor for a dam of thelength of L may be formulated by the following expression:


57/85



Fig. 8.4 Approximate treatment of three-dimensional effects (a) plan view of landslide, (b) safetyfactors for different cross-sections (Lambe & Whitman, 1979)

Fig. 8.5 Schematic of elazny Most tailings pond


58/85



=

1

(8.3)

where: nL number of cross-sections (also F-s) confined in the distance L.

If safety factors are random variables, then safety factor FLis the random variable either,with the probability density function (p.d.f.) characterized by mean value E{FL}and standarddeviation FL. If the number of cross-sections is large one may assume that the weightedsafety factor has distribution function in almost the normal form (the central boundarytheorem). Therefore probability of failure of the dam of length Lmay be approximated as:

),(

= (8.4)

where: 0

denotes the one-dimensional standard normal cumulative distribution function,and mFand Fare mean value and standard deviation of stability factor FL:

=

1

(8.5a)

=

2

2 1 (8.5b)

where: mi, i mean value and standard deviation of safety factor Fi, rij spatial correlationlength expressed in a form of exponentially decaying correlation function

=)( (8.6)

where distance between points iandj.

Mean values miand standard deviations imay be assessed using appropriate computersoftware e.g. SLIDE 5.0 which one may consider to be one of the most comprehensiveslope stability analysis software available, complete with sensitivity, probabilistic and backanalysis capabilities. Using Slide 5.0, you may determine the probability of failure andreliability index for either the deterministic failure surface with the smallest factor of safety,or for the entire slope.SLIDE can perform the probabilistic analysis using two different methods:

1. Assume that the failure surface is the deterministic global minimum surface and do thesampling and safety factor calculations only on this surface. The probability of failure andreliability index is then calculated for this surface.

Note that we are using the default Probabilistic Analysis options:

Sampling Method = Monte Carlo

Number of Samples = 1000

Analysis Type = Global Minimum


59/85


60/85



8.3 Numerical Examples Using SLIDE 5.0

EXAMPLE 1

EXAMPLE 2


61/85



EXAMPLE 3

Fig. 8.6

Table 8.3 Input data and obtained results

Example 1 Example 2 Example 3

Analysis Methods

Analysis Methods used:Bishop simplified

Number of slices: 25

Tolerance: 0.005

Maximum number ofiterations: 50

Surface Options

Surface Type: Circular

Search Method: Grid Search

Radius increment: 10

Composite Surfaces: Disabled

Reverse Curvature: CreateTension Crack

Minimum Elevation: NotDefined

Minimum Depth: Not Defined

Analysis Methods



Tolerance: 0.005


Surface Options








Analysis Methods



Tolerance: 0.005


Surface Options









62/85



Material Properties

Material: dam

Strength Type: Mohr-Coulomb

Unit Weight: 20 kN/m3

Cohesion: 1 kPa

Friction Angle: 30 degrees

Water Surface: None

Material: tailings



Cohesion: 10 kPa


Water Surface: None

Material: foundation



Cohesion: 10 kPa


Water Surface: None

Global Minimums

Method: bishop simplified

FS: 1.445030

Loading

Seismic Load Coefficient(Horizontal): 0.1

Seismic Load Coefficient(Vertical): 0.1

Material Properties

Material: dam



Cohesion: 1 kPa


Water Surface: None

Material: tailings



Cohesion: 10 kPa


Water Surface: None




Cohesion: 10 kPa


Water Surface: None

Global Minimums


FS: 1.164400

Loading

Seismic Load Coefficient(Horizontal): 0.1

Seismic Load Coefficient(Vertical): 0.1

Material Properties

Material: dam



Cohesion: 1 kPa


Water Surface: Water Table

Custom Hu value: 1

Material: tailings



Cohesion: 10 kPa



Custom Hu value: 1




Cohesion: 10 kPa



Custom Hu value: 1

Global Minimums


FS: 0.833836


63/85



Center: 24.706, 20.600

Radius: 14.898

Left Slip Surface Endpoint:

12.769, 11.687

Right Slip Surface Endpoint:25.108, 5.708

Resisting Moment=2701.45kN-m

Driving Moment=1869.48 kN-m

Probabilistic Analysis Input

Project Settings

Sensitivity Analysis: Off

Probabilistic Analysis: On

Sampling Method: Monte-Carlo

Number of Samples: 1000

Analysis Type: Global

Minimum

Material: dam

Property: Cohesion

Distribution: Lognormal

Minimum: 1 (relativeminimum: 0)

Mean: 1

Maximum: 3 (relativemaximum: 2)

Standard Deviation: 0.1

Material: dam

Property: Phi



Center: 24.494, 20.600

Radius: 14.378


13.501, 11.332





Project Settings






Minimum

Material: dam

Property: Cohesion



Mean: 1



Material: dam

Property: Phi



Center: 23.856, 20.600

Radius: 16.386


9.249, 13.174





Project Settings






Minimum

Material: dam

Property: Cohesion



Mean: 1



Material: dam

Property: Phi




64/85



Mean: 30


Standard Deviation: 12

Material: tailings

Property: Cohesion



Mean: 10



Material: tailings

Property: Phi


Minimum: 7 (relative

minimum: 8)

Mean: 15




Property: Cohesion



Mean: 10




Mean: 30



Material: tailings

Property: Cohesion



Mean: 10



Material: tailings

Property: Phi



minimum: 8)

Mean: 15




Property: Cohesion



Mean: 10




Mean: 30



Material: tailings

Property: Cohesion



Mean: 10



Material: tailings

Property: Phi



minimum: 8)

Mean: 15




Property: Cohesion



Mean: 10





65/85



Property: Phi



minimum: 10)

Mean: 20



Correlation Coefficients

Material: dam: Correlation: -0.5

Material: tailings: Correlation: -0.5

Material: foundation:Correlation: -0.5

Property: Phi



minimum: 10)

Mean: 20



Horizontal Seismic Coefficient


Minimum: 0.1 (relativeminimum: 0)

Mean: 0.1

Maximum: 0.32 (relativemaximum: 0.22)


Vertical Seismic Coefficient



Mean: 0.1







Property: Phi



minimum: 10)

Mean: 20



Horizontal Seismic Coefficient



Mean: 0.1



Vertical Seismic Coefficient



Mean: 0.1








66/85



Probabilistic Analysis Results(Global Minimum)

Factor of Safety, mean:1.254260

Factor of Safety, standarddeviation: 0.536401

Factor of Safety, minimum:0.496386

Factor of Safety, maximum:5.090920

Probability of Failure: 33.400%(= 334 failed surfaces / 1000valid surfaces)

Reliablity index: 0.47401(assuming normal distribution)

Reliablity index: 0.34785(assuming lognormaldistribution) * best fit =Lognormal







Reliablity index: -0.14767(assuming normal distribution)

Reliablity index: -0.34867(assuming lognormaldistribution) * best fit =Lognormal







Reliablity index: -1.06743(assuming normal distribution)

Reliablity index: -1.12626(assuming lognormaldistribution) * best fit =Lognormal


67/85


68/85



In the model, planes on which sliding or separation of moving slurry can occur, so calledinterfaces, are introduced. They are characterized by Coulomb sliding and/or tensile andshear bonding represented by the following properties: friction, cohesion, dilation, normal

and shear stiffness, tensile and shear bond strength(see Fig. 9.1).

Fig. 9.1 Components of the bonded interface constitutive model13

13FLAC3D Fast Lagrangian Analysis of Continua In 3 Dimensions. Theory and Background. Itasca Consulting

Group, Inc., 2003


69/85



WAVE OF SLURRY

SUBSOIL

INTERFACES

Fig. 9.2 Schematic for the liquefied tailings run-out due to dam-break occurrence

The most important expected results obtained from the performed computational analysisbased on FDM are:

1. The velocity of tailings movement.

2. The final range of the movement.

3. The intermediate and the final area of terrain surface covered by the liquefied tailings

slurry.


70/85



However, these data is quantitatively strongly affected by:

1. The accepted slurry physical-mechanical parameters.

2. The accepted parameters characterized the interfaces.

3. The width of the dam-break.

4. The topography of the terrain.

Due to lack of knowledge on the problem parameters statistics as well as lack of closedanalytical solution, presently it is difficult to analyze the problem as a stochastic process.For a time being the problem of liquefied tailings run-out due to dam-break occurrence willbe treated deterministically within a probabilistic space, as a consequence of dam breakdue to tailings liquefaction due to seismic event occurrence.

The risk of the event will be therefore assessed using the following formula:

)]([)( = (9.1)

where: A dam break, B tailings liquefaction, C appropriate seismic action.

10 VARIABILITY OF CONSEQUENCES (FREQUENTLY

TRANSBOUNDARY EFFECT)

Flooding, wave of slurry Contamination of surface water, living organisms (biota), intoxication Drinking and irrigation water contamination (surface) Drinking and irrigation water (underground) contamination Soil contamination Living organisms Injuries for the population around tailings dam Malfunctions in the functioning of enterprises (including indirect losses) Production stopping.


71/85



11 EVENT PROBABILITIES

11.1 General

The problem of risk created by tailings ponds, landfills and waste stockpiles is knownwidely for many years, particularly as an issue of earth dams stability. These structureswork in statistically non-homogeneous natural and man-made environment subjected tovarious randomly defined external natural inter-correlated influences such as floods,rainfalls, earthquakes, tectonic movement of surface geological deposits (rocks and soil).These effects in conjunction with possible mining-related static and dynamic influences areextremely complex and therefore their analytical (numerical) solutions are unavailable inliterature in a complete form.

Although the true risk assessment analysis for tailings ponds has been not required bythe existing law in the past, the present knowledge of the subject is already sufficient for itspartial development. This may be done using the principles of probabilistic riskassessment (PRA) theory addressed to earth/tailings surface structures. The presentedflowchart indicate all recommended steps of such analysis (Fig. 11.1).

PRA is generally used for LOW PROBABILITY AND HIGH-CONSEQUENCE events forwhich unsufficient statistical data exist. Tailings ponds are a such category of engineeringstructures.

At the present moment however, only selected parts of PRA analysis are sufficientlyrecognized and theoretically developed to be ready for instant application. Neverthelesscurrent practice in risk analyses of tailings ponds/storages is already able to consider in

deep the following aspects of the problem :

A. Object description and hazard identification:

(a) mechanical/functional model of the object (e.g. geometry (Fig. 11.2), material withinembankments, filling and foundation, drainage, water flow etc., methods ofparameters description and determining);

(b) identification of direct and indirect (complex) hazards and associated phenomena,e.g. dam failure modes with relevant parameters and methods of

measurement/estimation, moving mass volume, velocity and distance of movement,soil liquefaction, seismicity, forced displacement etc.;

(c) analytical methods and computer programs selection for appropriate modeling ofany deterministic phenomena associated with the object behavior (stress/straindistribution FEM,FDM, water flow and seepage, filling flow, debris movement etc);

(d) soil and surface water contamination (chemistry, range of pollution etc.);

(e) laboratory and field investigation, measurements and tests following internationallyrecommended procedures.


72/85



B. Frequency/probability of failure events assessment:

(a) analytical methods selection: first-order, second-moment approach (FOSM), first-and second-order reliability methods (FORM and SORM), Monte-Carlo simulationtechniques, event tree and fault tree analyses, Bayesian updating approach etc.

(b) random variables and their distribution functions and estimators.


73/85


74/85



Fig. 11.2 Example of tailings dam geometry

C. Consequence analysis and vulnerability:

(a) property,

(b) people,

(c) roads,

(d) vehicles

D. Quantitative risk estimation (wherever possible should be based on a quantitativeanalysis).

E. Risk evaluation: acceptable and tolerable risk.

F. Risk treatment:

(a) treatment options (methods for reducing of probability or consequences,monitoring and warning systems, transfer the risk);

(b) treatment plan how the options will be implemented;

(c) surveillance, monitoring and inspections.

However, mathematical complexity of full solution as well as a lack of law enforcing strictrequirements in this matter discourage owners to perform such analysis in a truly extendedformulation. Therefore currently practiced so called risk analyses/assessment areconfined rather to the basic deterministic considerations/solutions and field activities.


75/85



It must be however emphasized that the A-F list of topics mentioned above, applied for therare and very important objects, has also a large number of shortcomings concerned withlack of advanced solutions and procedures.

IRIS focuses on the fact that natural materials are spatially variable and that representation

of this variability appears crucial to getting a realistic understanding of certain geotechnicaland hydro-geological problems. The project looks specifically at the stability of tailingsdams and possibly contaminated water flow within ground mass.

The risk model consists of a product/sum of different risks described by appropriateprobabilities and associated consequences, some mutually correlated

PRA is generally used for LOW PROBABILITY AND HIGH-CONSEQUENCE events forwhich insufficient statistical data exist. Large tailings ponds are a such category ofengineering structures.

PRA is an analysis of the probability of event and the magnitude of its consequence. It is

an analytical tool which permits expressing quantitavely the risk of failure in a frame of ourknowledge. It assesses also the efectiveness of risk reduction options. The basic analyticaltools offered by PRA (Fig. 11.3):

Fig. 11.3 PRA analytical tools14

14 Stamatelatos M. Probabilistic Risk Assessment Procedures Guide for NASA Managers and Practitioners.

Office of Safety and Mission Assurance, NASA Headquarters, Washington , DC, 2002


76/85



MASTER LOGIC DIAGRAM (MLD) hierarchical, top-down display of IEs (initial events),showing general types of undesired events at the top, proceeding to increasingly detailedevent descriptions at lower tiers, and displaying initiating events at the bottom.

EVENT SEQUENCE DIAGRAM (ESD) a flowchart, with paths leading to different end

states (each path through this flowchart is a scenario). Along each path, pivotal events areidentified as either occuring ot not occuring.

EVENT TREE (ET) distills the pivotal event scenario definitions from the ESD andpresents this information in a tree structure that is used to help classify scenarios accordingto their consequences. The headings of the ET are the IE, pivotal events, and the endstate. The tree structure below these headings shows the possible scenarios ensuing fromthe IE, in terms of occurrence or non-occurrence of the pivotal events. Each distinct paththrough the tree is a distinct scenario.

FAULT TREE (FT) deductive logic model whereby a system failure is postulated (topevent) and reverse parhs are developed to gradually link this consequence with all

subsystems, components or human actions.

Generally, scenarios are developed through a combination of ETs and FTs. It is howeverpossible for simple risk models to use only FTs or ETs. Each scenario has its own Booleanequation with appropriate probabilities of all events.

11.2 Event Trees

The main typical failure modes of tailings storage facilities are associated with the

following, independent events (see Tables 8.2 and 11.4): Static slope/foundation instability (Event A); Overtopping due to the overloading with precipitation water (Event B); Internal erosion/piping (Event C); (Sub)soil and water contamination due to seepage (Event D).

All the mentioned above modes of failure are usually confined within large volumes ofmaterials moving in 3D coordinates, and some of them are additionally related to timeprogress. They also lead to dam(s) break and following uncontroled release of the facilitycontent, or contamination of environment with no structural failures.

The scale of failure increases due to the following additional effects: Seismicity (natural and mining-related), loading the structure with the additional load

due to the acceleration acting in 3D from the external source (Event S); this suggests todistinguisch a new event - dynamic slope/foundation instability (Event AS);

Possible liquefaction of the structures material resulting from the seismic action anscausing extremely difficult conditions of maintaining of dams stability; this may cause anew event dynamic slope/foundation instability due to liquefaction Event ASL.;

Intensive precipitation affecting positively the potential of overtopping and piping thispotential is represented in the water level data;

Foundation static movement due to external influences (e.g. mining, tectonicprocesses, etc.).


77/85



The event tree for the potentially possible failure events are presented in Fig. 11.4 below.

The different modes propabilities (see above) assessment constitutes the essentialproblem of tailings/waste storage facilities risk assessment. There are introduced thefollowing assumptions concerned with particular, mentioned above events:

1. Events A, ASand ASLexclude each other (mutually exclusive).

2. Events Band BSalso exlude each other.

3. Events of groups: A(S,SL), B(S),Cand Dmay occurr independently.

4. The total risk may be calculated as a sum of particular risks created by different events.

5. Probabilities of the group AS, ASL and BS (related to seismic action) should becalculated for a number of different magnitudes of seismic event (with different probabilitiesof occurrence assigned). This may affects severity of expected consequences of possible

failure modes or may influence different probabilities of soil/tailings liquefaction.

6. Probabilities P(AS) and P(BS) may be assesed using different approaches:

(a) using the model including seismic action (e.g. acceleration) treated as a randomforce/variable characterized by its own p.d.f simulation methods, or

(b) using the model with seismic action represented by a single number(s) (e.g.acceleration) associated with approproate probability of occurrence P(S) then

)()()( =

where: - event of the model failure involving seismic action represented by asingle number(s).


78/85

IRIS

IRIS WP4 Demonstration Report

Fig. 11.4 Example of event tree applied to tailings ponds risk assessment


79/85


IRIS Current Practice Report page 79 of 85

7. Probability P(ASL) may be calculated similarly as above using the following equation:

)()()( =

where: )( - event of the model failure involving both seismic action and liquefaction

characterized by probability of occurrence (L) Eq. 5.9 may be used.

More investigations on this subject should be done further.

12 WHAT SHOULD BE DONE IN THE NEAR FUTURE (rough

estimate)

PARTNER WHAT SHOULD BE DONE

1. ICEMENERG Romanian partner is asked to deliver the following data on the (Rovinari)site(s):

1. Geometry of dams, foundation, filling (drawings, maps, dimension,etc..).

2. Geology and geotechnical data (crossections, geotechnical features,

etc.).3. Procedures used for measurements (detailed description).

4. CPT data for the tailings dam, and also drained and undrained triaxialtest data for the tailings. Different test data is also very welcome.

5. All information on technical characteristics, functions and locationwithin the technological processes of the power plant/mine.

6. Data on the water level, air and soil (ground water)chemistry/contamination.

7. All the measurement data (both the archival and presently obtained)should be gathered in the manner which will enable us to use them instatistics/probability analyses (largr number of measurements, theirlocations in 3D space, etc.).

For the required sites parameters identification you may use also Table8.2 (column 3).

Site stabilisation will be included in the chapter concerned with the riskreduction measures (risk management) chowever this problem is notcritical now.


80/85


WP4 Demonstration Report page 80 of 85

2. LULEA Swedish partner is asked to deliver the following data on the (Aitic?)site(s):

As above (Partner 1) but research should be more focussed on dams

internal time-dependent corrosion.3.CARTAGENA

Spanish partner is asked to deliver the following data on the(Cartagena?) site(s):

As above (Partner 1) but research should be more focussed on groundwater flow and its chemistry (3D space location, time of measurements,etc.).

4. DELFT Dutch partner will focus on computational issues concerned with

1. The statistical interpretation of cone penetration test (CPT) data.

2. The calibration of the Monot double-hardening constitutive model.

3. The 2D and 3D finite modelling of the tailings dam, using random fieldtheory to generate the spatial property distributions and Monte Carlosimulation to account for parameter uncertainty. This should includemodelling of the construction sequence.

4. The probabilistic evaluation of the results in terms of reliability andprobability of failure. Risk will be quantified in terms of the volumes ofmaterial associated with potential slides.

(from Summary of Proposed Work as of December 2008 (M .A. HICKS)

5. KGHM and

CSM

Polish partner in cooperation with Colorado School of Mines (D.V.Griffiths) will focus on the delivery of:

1. Data mentioned in p. 1-7 (partner 1 above) from elazny Most tailingspond.

2. The probabilistic general system coupling all relevant phenomenaaffecting risk level.

3. Conventional/deterministic design methods used for safety/riskassessment applied to the tailings/waste storage facilities.

4. Failure consequence and its severity assessment.


81/85


WP4 Demonstration Report page 81 of 85

13 MEASUREMENTS AND MONITORING PERFORMED AT

ELAZNY MOST TAILINGS POND

Monitoring of elazny Most tailings pond include the following elements:1) environment quality,2) emission from the pond,3) Technical conditions and

D12 WP4 Demonstration Final

Documents

Transcript of D12 WP4 Demonstration Final