Relleno Minas Diseño

8/11/2019 Relleno Minas Diseo

1/28

ORIGINAL PAPER

Design and Application of Underground Mine Paste Backll

TechnologyTikov Belem Mostafa Benzaazoua

Received: 15 September 2005 / Accepted: 22 August 2007 / Published online: 13 October 2007 Springer Science+Business Media B.V. 2007

Abstract This paper reviews the design and appli-cation of paste backll in underground hard rock mines used as ground support for pillars and walls, tohelp prevent caving and roof falls, and to enhancepillar recovery for improved productivity. Archingafter stope lling reduces vertical stress and increaseshorizontal stress distribution within the ll mass. It istherefore important to determine horizontal stress onstope sidewalls using various predictive models in thedesign of paste backll. Required uniaxial compres-sive strength (UCS) for paste backll depends on theintended function, such as vertical roof support,development opening within the backll, pillarrecovery, ground or pillar support, and workingplatform. UCS design models for these functionsare given. Laboratory and backll plant scale designsfor paste backll mix design and optimization arepresented, with emphasis on initial tailings densitycontrol to prevent under-proportioning of bindercontent. Once prepared, paste backll is transported(or pumped) and placed underground by pipeline

reticulation. The governing elements of paste backlltransport are rheological factors such as shear yieldstress, viscosity, and slump height (consistency).Different models (analytical, semi-empirical, andempirical) are given to predict the rheological factorsof paste backll (shear yield stress and viscosity).Following backll placement underground, self-weight consolidation settlement, internal pressurebuild-up, the arching effect, shrinkage, stope volume,and wall convergence against backll affect mechan-ical integrity.

Keywords Paste backll Mix design Arching effect Backll strength Backll rheology

1 Introduction

Underground cemented paste backll (CPB) is animportant component of underground stope extrac-tion, and is commonly used in many cut-and-llmines in Canada (e.g., Landriault et al. 1997; Nayloret al. 1997; Nantel 1998). As mining operationsprogress, paste backll is placed into previouslymined stopes to provide a stable platform for minersto work on and ground support for the walls of theadjacent adits by reducing the amount of open spacethat could potentially be lled by a collapse of thesurrounding pillars (Barret et al. 1978). Undergroundpaste backll provides not only ground support to

T. Belem ( & ) M. BenzaazouaDepartment of Applied Sciences, Universite du Quebec enAbitibi-Te miscamingue (UQAT), 445, boul. delUniversite , Rouyn-Noranda, QC, Canada J9X 5E4e-mail: [email protected]

M. BenzaazouaDepartment of Applied Sciences, CRC on IntegratedManagement of Sulphidic Mine Tailings by Backlling,UQAT, Rouyn-Noranda, Canada

1 3

Geotech Geol Eng (2008) 26:147174DOI 10.1007/s10706-007-9154-3


2/28

pillars and walls, but also helps prevent caving androof falls and enhances pillar recovery, therebyimproving productivity (Mitchell 1989a, b; Coates1981). Thus, the placement of paste backll providesan extremely exible system for coping with changesin ore body geometry that result in changes in stope

width, dip, and length (Wayment 1978). The lldelivery method depends on the amount of energyrequired to deliver the backll material underground,which in turn depends on the distribution cone(Arioglu 1983). Paste backll is usually transportedunderground through reticulated pipelines.

Paste backll is composed of mill tailings gener-ated during mineral processing, mixed with additivessuch as Portland cements, lime, pulverized y ash,and smelter blast furnace slag, which react as bindingagents. Binding agents develop cohesive strengthwithin CPB so that exposed ll faces become self-supporting when adjacent stopes are extracted. Withthe current uctuations in metal prices, the survival of many mines depends on their ability to maximizeproductivity while minimizing costs. Backllingcosts in underground mining operations must becritically examined to identify potential cost savings(Stone 1993). Although paste backlling is somewhatexpensive, it is indispensable for most undergroundmines as it provides crucial ground support for minesafety and mining operations. Therefore, the llshould be cost-effective and capable of achieving thedesired ground support and stability.

An analysis of ll stability must consider thegeometric boundaries of the ll in terms of optimaleconomic use of CPB. Mine openings and exposedll faces in large underground mines vary in shapefrom high and narrow to low and wide. Additionally,wall rock next to the backll may be either steeplydipping or relatively at-lying. The extractionsequence can be modied to reduce the number of CPB-lled stopes, or the stope geometries could bemodied to reduce the required strength for CPBexposure (Mitchell 1989a, b; Stone 1993).

This paper reviews the design and application of paste backll for underground ground support inmining operations, from preparation to placementunderground. First, arching effects and their impor-tance in lled stopes stability analysis is brieyintroduced. This is followed by an overview of thedesign of required ll strength, from a review of current design methods. Next, optimal CPB-mix

design (to reduce costs and improve ll strength) isdiscussed, followed by a discussion on the rheolog-ical properties of CPB. Finally, CPB delivery systemsand underground placement are discussed.

2 Design of Horizontal Pressure on Filled StopeSidewalls

In general, since self-weight stresses govern backlldesign, the traditional design has been a free-standing wall requiring a uniaxial compressivestrength (UCS) equal to the overburden stress atthe bottom of the lled stope. In many cases,however, the adjacent rock walls actually helpsupport the ll through boundary shear and archingeffects. Therefore, backll and rock walls may bemutually supporting (Mitchell 1989a). In backlledstopes, when arching occurs (which is the case inmany mines, depending on stope dimensions), thevertical pressure at the bottom of the lled stope isless than the weight of the overlying ll (overburdenweight) due to horizontal pressure transfer, some-what like a trap door (Martson 1930; Terzaghi1943). This pressure transfer is due to frictional and/ or cohesive interaction between ll and wall rock.When the pillars or stope walls begin to deform intothe lled opening, the ll mass provides lateralpassive resistance. Passive resistance is dened asthe state of maximum resistance mobilized whenforce pushes against a ll mass and the mass exertsresistance to the force (Hunt 1986).

The pressure transferred horizontally to the side-walls should be included in the required ll strengthdesign. Horizontal pressures affected by ll archingare determined by ve analytical or semi-analyticalsolutions that account for cohesion at the ll-sidewallinterface and/or frictional sliding along the sidewalls.These solutions are Martsons model and its modiedversion, Terzaghis model, Van Horns model andour proposed model.

2.1 Martsons Cohesionless Model

Martson ( 1930) developed a two-dimensional archsolution to predict horizontal pressure ( r h) at thebottom of an excavated trench (in kPa) along theexcavation sidewalls, as follows:

148 Geotech Geol Eng (2008) 26:147174

1 3


3/28

r h c B2l 0

1 exp 2K al 0 H

B 1The corresponding vertical pressure r v at the

bottom of the excavation and the parameter K a aregiven as follows:

r v r h=K a 2K a tan2 45 / =2 3where c = ll bulk unit weight (kN/m 3); B = stopewidth (m); H = ll mass height(m); l 0 = tan d = sliding friction coefcient betweenll and sidewalls ( d is the wall friction angle,generally assumed at between / /3 and 2/ /3, andranging from 0 to 22 ); / = ll internal frictionangle (degree); and K a = active earth pressure.

2.2 Modied Martsons Cohesionless Model

Aubertin et al. ( 2003) proposed a modied version of Martsons two-dimensional arch solution, originallydened using active earth pressure ( K a) and wallsliding friction ( l 0). The modied version to predicteffective horizontal pressure ( r 0hH ) along pillarsidewalls at a depth H corresponding to the stopebottom is given as follows:

r 0hH c B

2tan / 0 f 1 exp

2KH tan / 0 f B 4

Corresponding effective vertical pressure r 0vH atthe stope bottom is given as follows:

r 0vH r 0hH =K 5where c = ll bulk unit weight (kN/m 3); B = stopewidth (m); H = ll height (m); / 0f filleffective internal friction angle (degree) ; and K =earth pressure coefcient.

Earth pressure coefcient K corresponds to threedifferent states: K a (active), K 0 (at rest), and K p(passive), given by the following relationships:

K K 0 1 sin / 0 f K K a tan2 45 / 0 f =2 K K p tan2 45 / 0 f =2 8


4/28

2.4 Three-dimensional Predictive Models

Van Horn ( 1963) proposed a theoretical 3D solutionfor vertical stress at a depth h below the surface in abox of width B and breath L , in which the interfacefriction angle between backll and walls d is

estimated by following equation:

r v c

2k r tan d BL

B L 1 exp 2k r tan d2h B L

BL 11

where c = ll bulk unit weight (kN/m 3); h = llheight in the stope below the surface (m); B = stopewidth; L = stope strike length (m); and k r = r h / r v;d = interface friction angle ( ) between backll andstope wall.

Belem et al. ( 2004) proposed a three-dimensionalmodel that implicitly takes into account archingeffects to predict horizontal pressures at the stopeoor (r h): both longitudinal pressure r x (across orebody) and transverse pressures r y (along ore body).The model is given as follows:

r h xc H H B L 1 exp

2 H B 12

Corresponding vertical pressure r v(= r z) at thestope bottom is given as follows:

r v 0:185c H H B L 1 exp 2 H B r z13

where c = ll bulk unit weight (kN/m 3); H = llheight in the stope (m); B = stope width; L = strikelength of stope (m); and x = directional constant,which is 1 for pressure across ore body ( r h = r x) and0.185 for pressure along ore body ( r h = r y).

3 Paste Backll Required Strength Design

The required strength for paste backll depends onthe intended function. To provide adequate groundsupport, the required uniaxial/unconned compres-sive strength (UCS) of the ll should be at least5 MPa, whereas for free-standing ll applications,UCS is commonly lower than 1 MPa (Stone 1993; Liet al. 2002). A typical vertical exposure measures46 m wide by 3045 m high. A UCS of 100 kPa is

commonly adopted as the liquefaction potential limit(Grice 2001; le Roux et al. 2002). Required staticstrength for paste without exposures may be arbi-trarily selected at 200 kPa (e.g., Li et al. 2002).Previous work indicates that ll mass UCS variesfrom 0.2 MPa to 4 MPa, while surrounding rock

mass UCS varies from 5 MPa to 240 MPa (e.g.,Grice 1998; Revell 2000).

3.1 Vertical Backll Support

The mechanical effects of ll differ from those of primary ore pillars. Research and in situ testing haveshown that ll is incapable of supporting the totalweight of overburden ( r v = cH), and acts as asecondary support system only (Cai 1983). The llmodulus of elasticity varies from 0.1 GPa to 1.2 GPa,while the surrounding rock mass elasticity variesfrom 20 GPa to 100 GPa. As discussed by Donavan(1999), we may assume that any vertical loading is aresult of roof deformation (Fig. 1), and that designUCS can be estimated by the following relationship:

UCS design E pepFS E pD H p H p FS 14

where E p = rock mass or pillar elastic modulus;ep = pillar axial strain; D H p

strata deformation

v

Openstope

Openstope

P i l l a r

Fillmass

Fillmass

Fillmass

H (pillar)

H (fill)

v

Openstope

Openstope

P i l l a r

Fillmass

Fillmass

Fillmass

H (pillar)

H (fill)

Fig. 1 Schematic showing vertical loading on the backllblock next to a pillar

150 Geotech Geol Eng (2008) 26:147174

1 3


5/28

m; H p = strata initial height (m); and FS = factor of safety.

When stope walls deform before backlling,maximum load probably never approaches totalweight of the deformed overlying strata (Donavan1999), and design UCS can be estimated by the

following relationship:

UCS design k cp H p FS 15where k = scaling constant, which must vary from0.25 to 0.5; cp = strata unit weight (kN/m 3); H p =strata height below surface (m); and FS = factor of

safety.Numerical modeling is also used to determine

the required stiffness or strength of CPB to preventsubsidence due to roof deformation. Results arevery useful to indicate the required paste backllamount. Modeling is performed with either theFLAC (2D and 3D) or Phase 2 D code. Physicalmodeling, such as using a centrifuge, offers analternative to numerical modeling, but its applica-tion is usually limited to simple gravitationalmodels without high tectonic or in situ horizontalstresses (Stone 1993).

3.2 Development Opening Through BackllMass

When a gallery has to be opened through the pastebackll to access a new ore body (Fig. 2), safe designcriteria must be applied. A conservative designconsiders a ll mass as more than two contiguouslyexposed faces after blasting adjacent pillars or stopes.Consequently, the walls conning the ll areremoved and the ll mass is subjected to gravityloading similar to a laboratory sample subjected tothe uniaxial compression test (Yu 1992). Design UCSis estimated by the following relationship:

UCS design cf H f FS 16where cf = ll bulk unit weight (kN/m 3); H f = llheight (m); and FS = factor of safety.

3.3 Pillar Recovery

To maximize ore recovery, it is very common torecycle mine pillar ore after primary ore recovery.

During the process, large vertical heights of pastebackll mass may be exposed. For delayed paste

backll, as in open stoping operations, the ll must bestable when free-standing wall faces are exposedduring pillar recovery (Fig. 3). In addition the llmust have sufcient strength to remain free-standingduring and after the pillar extraction process byresisting blast effects. Figure 3 illustrates a failuremechanism that could potentially occur after a stopeblast. Depending on the mining schedule, moderateCPB strength (UCS \ 1 MPa) may be required in theshort term (Hassani and Archibald 1998).

In the absence of numerical modeling, many mine

engineers rely on two-dimensional limit equilibriumanalyses along with a calculated factor of safety ( FS )to determine ll exposure stability. The typical resultis an over-conservative estimate of limiting or criticalstrength (Stone 1993), which increases backll

F i l l d e s t o p e

F i l l e d s t o p e s

s a m

l l i F

N e w g a l l e r y

F i l l d e s t o p e

F i l l e d s t o p e s

s a m

l l i F

N e w g a l l e r y

Fig. 2 Development opening through a backll mass

ore

F i l l m a s s

PillarF r

e e f a c e

Possible failure plane

Secondarystoping

ore

Pillar

Fig. 3 Fill mass failure mechanism during secondary stopeextraction

Geotech Geol Eng (2008) 26:147174 151

1 3


6/28

operational costs. In recent years, however, 2D- andpseudo-3D empirical models have been developed toaccount for arching effects, cohesion, and frictionalong sidewalls (Mitchell et al. 1982; Smith et al.1983 ; Arioglu 1984; Mitchell 1989a, b; Mitchell andRoettger 1989; Chen and Jiao 1991; Yu 1992). These

design methods use the concept of a conned llblock surrounded by wall rock.

3.3.1 Case of More than Two Exposed Faces

Equation 16 should be used if there are more thantwo contiguously exposed faces after blasting adja-cent pillars or stopes (Fig. 4).

3.3.2 Case of Narrowly Exposed Fill Face

This design method accounts for arching effects onconned ll by adjacent stope walls (Fig. 5) usingTerzaghis arching model (Eq. 9). Based on 2D niteelement modeling, Askew et al. ( 1978) proposed thefollowing formula to determine design ll compres-sive strength:

UCS design 1:25 B2K tan /

c 2c B

1 exp 2 HK tan / B FS 17

where B = stope width; K = ll pressure coefcient(see Eq. 10); c = ll cohesive strength (kPa); / = llinternal friction angle (degree); c = ll bulk unit

weight (kN/m 3); H = ll height (m); and FS = factorof safety.

Fill cohesion ( c) and its angle of internal friction(/ ) are obtained from triaxial tests performed onlaboratory or in situ backll samples.

3.3.3 Case of Exposed Frictional Fill Face

This design addresses an exposed ll where the twoopposite sides of the ll are against stope walls(Fig. 6). Assuming shear resistance between ll andstope walls due to ll cohesion, design UCS is[estimated] by the following relationship (Mitchellet al. 1982):

E x p o s e d f a c e E x p o s e

d f a c e H

vv

E x p o s e d f a c e E x p o s e

d f a c e H

v v

Fig. 4 Schematic of a ll mass showing three exposed verticalfaces

H

L

v < H

P i l l a rh

0

H

Fill

h h

B

E x p o s e d

f a c e

A r c h n i g

e f f e c t

Fill

Fig. 5 Schematic illustration of a stability analysis of anarrowly exposed ll face

L

B

H

H e

Wall shear resistance= cBH e (kN)

Direction of sliding alongfailureplane

tan2

B H H H H

e

( H e)LB = block weight

245 = +

=

Fig. 6 Conned block with shear resistance mechanism (fromMitchell et al. 1982)

152 Geotech Geol Eng (2008) 26:147174

1 3
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


7/28

UCS design c L 2c

L H

B2

tan 45 /2

sin 45 /2 FS

18

where c = ll bulk unit weight (kN/m 3); c = llcohesive strength (kPa); L = stope strike length (m); B = stope width (m); H = total ll height (m); /= ll internal friction angle (degree); and FS = factorof safety.

Again, ll cohesion ( c) and its angle of internalfriction ( / ) are obtained from triaxial tests performedon laboratory or in situ backll samples.

3.3.4 Case of Exposed Frictionless Fill Face

The compressive strength of paste backll is mainlydue to binding agents, and any strength contributedby friction is considered negligible in the long term(i.e., / & 0). For a frictionless material (Fig. 7),cohesion is assumed at half the UCS ( c = UCS /2).Thus, design UCS is determined by the followingrelationship, proposed by Mitchell et al. ( 1982):

UCS design c L H B2 L FS sin45

H B2

c L H B2 FS ffiffiffi2p 2 L

H B2

FS

ffiffiffi2p 19

where c = ll bulk unit weight (kN/m 3); c = llcohesive strength (kPa); B = stope width (m); L =stope strike length (m); H = ll height (m); andFS = factor of safety (ca. 1.5).

The stability of free-standing backll (Fig. 7) canalso be determined from physical model tests such ascentrifugal modeling tests. Mitchell ( 1983) proposeda formula derived from Eq. 19, where B = 0 and FS =H2, and which is used to determine design UCS asfollows:

UCS design c LH L H

c H 1 H L

20and for a factor of safety other than 1, Eq. 20 is givenas follows:

UCS design c LH FS L H

c H FS 1 H L

21where c = ll bulk unit weight (kN/m 3); L = stopestrike length (m); H = ll height (m); and FS = factorof safety.

3.4 Ground Support

After passive resistance has been mobilized by thell, the strength increase in the surrounding pillars isequal to the passive ll pressure. Thus, the mainstabilizing effect of the ll is to provide increasedlateral conning pressure to the pillars (Fig. 8).Compressive strength of the pillar increases accord-ing to the following formula (Guang-Xu and Mao-Yuan 1983):

UCS cp UCS up cf H f K a f K p p 22and

L

B

H

H e

Direction of sliding alongfailure plane

tan2

B H e

245

No wall shearresistance( H e)LB

= block weight

245

= +

= H

Fig. 7 Conned block with no shear resistance mechanism of frictionless ll (adapted from Mitchell et al. 1982)

F i l l m a s s pillar

h_fill

h_ p i l la r

F i l l m a s s

Fig. 8 Schematic diagram of a pillar conned by the ll mass

Geotech Geol Eng (2008) 26:147174 153

1 3
http://-/?-http://-/?-http://-/?-http://-/?-


8/28

K a f tan2 45 / f =2 23aK p p tan2 45 / p=2 23bwhere UCS cp = conned pillar compressive strength(kPa); UCS up = unconned pillar strength before

stope lling (kPa); cf = ll bulk unit weight (kN/ m3); H f = paste backll (m); / f = ll internal frictionangle (degree); / p = pillar internal friction angle(degree); K a-f = ll active pressure coefcient; andK p-p = passive pressure coefcient of the pillar.

3.5 Working Platform

For cyclic backll operations, as in cut-and-llstoping, each ll must serve as a platform for bothmining equipment and personnel, and typicallyrequires high strength development in the short-term.A standard bearing capacity relationship, developedwith civil engineering methods for shallow founda-tion design, would be suitable for this type of backll.Fill top surface bearing capacity Qf (kPa) is deter-mined using Terzaghis expression, modied byCraig (1995), as follows:

Q f 0:4c BN c 1:2cN c 24Bearing factors N c (developed by Hansen 1968) and N c are given by the following relationships:

N c 1:8 N q 1 tan / 25a N c

N q 1 tan / 25band

N q tan2 45 / =2 exp p tan / 25cwhere N c = unit weight bearing capacity factor; N c = cohesion bearing capacity factor; N q = sur-charge bearing capacity factor; c = ll bulk unitweight (kN/m 3); c = ll cohesive strength (kPa); B = width of square footing at surface contactposition (m); and / = ll internal friction angle(degree).

Equation 24 assumes that the backll bearing issupported by a square footing, which is reasonablerepresented by the footprint of a mine vehicle tire(Hassani and Bois 1992; Hassani and Archibald1998). For mine vehicles (Fig. 9), contact width B

corresponds to tire contact width, and is determinedby the following relationship (Hassani and Bois1992):

B ffiffiffiffiffiF t ps 26where F t = tire loading force (kN); and p = tire airpressure (kN/m 2).

4 Optimizing Paste Backll Mix Designs

Once required strength has been determined, mixvariables are optimized to provide the desired mixthat achieves target strength and minimum cementi-tious usage. Mix variables considered include bindercontent Bw% (by dry mass of tailings) and bindertype, tailings particle size distribution (PSD) andmineralogy, mix solids concentration by mass ( C w% )or volume ( C V% ), and mixing water geochemistry. Todesign a certain uniaxial compressive strength(UCS design ), variables are adjusted to produce anoptimal mix design (Stone 1993; Benzaazoua et al.1999, 2000, 2003; Benzaazoua et al. 1999, 2000;Benzaazoua and Belem 2000; Fall and Benzaazoua2003; Kesimal et al. 2003; Yilmaz et al. 2004).

The other essential requirement is that the backllmust be economical. Typical backll costs vary from$2 CDN/m 3 to $20 CDN/m 3 for paste backll,depending on the service required. These costs wielda signicant impact on the mines operating costs.Paste backll costs alone are typically between 10%and 20% of total mine operating costs, with binderagents accounting for up to 75% of backll costs(Grice 1998; Fall and Benzaazoua 2003).

B B

Fill mass

Fig. 9 Schematic diagram of a working platform (adaptedfrom Hassani and Bois 1992)

154 Geotech Geol Eng (2008) 26:147174

1 3
http://-/?-http://-/?-


9/28

4.1 Laboratory Optimization of CPB MixDesigns

Optimizing CPB mix designs reduces binder usageand offers signicant cost savings (e.g., Benzaazouaand Belem 2000; Benzaazoua et al. 2002; Fall and

Benzaazoua 2003). Figure 10 shows the main com-ponents affecting the nal quality of paste backllsuch as binding agents, tailings characteristics (spe-cic gravity, mineralogy, particle size distribution),and nally, mixing water chemistry and geochemistry(sulphate concentration, pH, Eh, Electrical conduc-tivity). Each component plays an important role inbackll transportation and delivery, placement, andlong-term hardening (Benzaazoua et al. 2002).

4.1.1 Binder Types and Content

Hardening of CPB occurs as bonds are formedbetween ll particles at grain contact points. Severaltypes of binding agents are used, but the mostcommon is ordinary Portland cement (CEM I, OPC,Type 10, or Type I). Sulphate resistant Portlandcement (SRPC, Type 50, or Type V) is sometimesused, although it is much more expensive than OPC.Admixtures with pozzolanic materials are often usedto curb costs by reducing the amount of Portlandcement needed for hardening. Pulverized y ash(PFA) and smelter ground granulated blast furnaceslags (GGBFS) are the most popular pozzolans usedas admixtures (e.g., Douglas and Malhotra 1989).They can be used alone or blended with OPC(binding agent = x*OPC + (1 x)* Admixture ) toactivate reactivity.

Typical binder content Bw% 100 M binder = M dry tailings varies from 3 wt.% to 7 wt.% (by drymass of tailings). Solids mass concentrationC w% (wt.%) is given as follows:

C w%

100 M solid M

water M

solid

100 M dry tailings M dry binder M water M dry tailings M dry binder

27

where M = mass of the substance (in g, kg, or tonne).Corresponding volumetric binder content Bv% (v/

v%) and solids concentration C v% (v/v%) are given asfollows:

Bv% V binderV tailings

100 Bw%q s tq s b 28

andC v%

V solidV bulk

100 qd f q s f

100 29where V binder = volume of binder; V tailings = volumeof dry tailings; V solid = volume of dry tailings andbinder; V bulk = volume of pastell; Bw% = bindercontent (wt.%); qs-t = specic density of tailinggrains; qs-b = specic density of binder grains; qd-f = dry density of pastell; and q s-f = specic densityof pastell grains. Volumes are in cm 3 or m3;

densities are in g/cm3

, kg/m3

or tonne/m3

.From the known solids concentration by mass of paste backll ( C w% ), the corresponding anhydrousbinder concentration (%binder) and tailings grainsconcentration (%tailings) are calculated using thefollowing formulae:

%binder C w% Bw%

100 Bw% 30aand

%tailings C w%100 Bw% 100 C

w% %binder30b

where C w% = solids concentration by mass of CPB(%); and Bw% = binder content by dry mass of tailings (wt.%).

Numerous laboratory test results have reportedthat, for a given curing time, paste backll strength isproportional to binder content Bw% (Fig. 11).However, this relationship is specic to each mine

Tailings

Binding agents Sulphides contentGrain size distributionDensity, specific gravity

Paste backfill(70% Cw% 85%)

SO4

2-, pH, Ehsoluble lime

Mixing water

Additives

(SiO2+Al2O3)/

(CaO+MgO)

(3 wt.% 7 wt.%)Water content

(expected slump 6" 10")

Solid mass concentration

(78% Cw% 85%)

Tailings

Sulphides contentGrain size distribution

Density, specific gravity

Paste backfill(70% Cw% 85%)

2 3)/

(3 wt.% 7 wt.%)Water content

(expected slump 6" 10")

Solid mass concentration

(78% Cw% 85%)Binder %

Fig. 10 Schematic diagram of various paste backll compo-nents (adapted from Benzaazoua et al. 2002)

Geotech Geol Eng (2008) 26:147174 155

1 3


10/28

(e.g., Benzaazoua et al. 1999, 2000; Belem et al.2000 ; Benzaazoua and Belem 2000; Benzaazouaet al. 2002, 2004). Recent results have shown that the

hardening process within paste backll material isdue not only to binder hydration but also precipitationof hydrated phases from the paste pore water(Benzaazoua et al. 2004).

4.1.2 Mixing Water and its Quality

Water is required to ensure proper hydration of thebinding agents. Without adequate binder hydration,the ll cannot meet required strength and stiffness.

Moreover, since additional water is usually requiredto pump the paste backll underground, the volu-metric water content of paste backll is always farin excess of the OPC hydration requirements (as isthe case for blends of OPC with SRPC, PFA orGGBFS). The main concern is therefore the waterspH and sulphate salts content. Acidic water andsulphate salts attack cementitious bonds within thell, leading to loss of strength, durability, andstability (e.g., Mitchell et al. 1982; Lawrence 1992;Wang and Villaescusa 2001; Benzaazoua et al.

2002 , 2004).Figure 12 illustrates that, when using blended

Portland cement/GBFS binder with the same tailingssample mixed with three different waters, CPBhardening is slow for all three waters at 14-daycuring. Beyond that curing time and at 28-day curing,UCS reaches a maximum value for sulphate-freewaters (tap and lake water), or 600 kPa higher than amix with sulphate-rich Mine A process water(Benzaazoua et al. 2002).

4.1.3 Binder Hydration Process

According to dissolution test data performed on thegeneral use Portland cement (OPC or Type I) andblast furnace slag binders (Benzaazoua et al. 2004), alinear regression equation was derived for the calcu-lation of percentage (by weight, wt.%) of dissolvedbinder Db as a function of water-to-cement ratio(w / c): Db(wt.%) = 3.125 (w / c) + 3.3125 (Belemet al. 2007). Figure 13 is a schematic illustration of the hydration process in cemented paste backllmaterials. This gure illustrates that paste backllhardening occurs in two main stages: dissolution/ hydration , dominated by the dissolution andhydration processes, and hydration/precipitation ,characterized by the precipitation process and directhydration of binding agents (Benzaazoua et al. 2004).

Figure 14 presents a diagram of all possible stagesin the hydration process of a paste backll withtailings containing sulphide minerals (pyrite, pyrrho-tite) and the mix solution containing sulphates. Itreveals that, immediately after paste mixing with thebinding agent, OH anions are released, which bufferthe solution at a pH varying between 12 and 13.Consequently, the dissolution / hydration and hydra-tion / precipitation phases take place successively.This hardening process rst involves the formationof primary ettringite, followed by portlandite forma-tion. At mid- and long-term hydration, CSH phasesare formed, which largely contribute to paste backllstrength development. Depending on initial sulphatecontent, the formed portlandite could possibly reactto gypsum.

1.5 3 4.5 6 7.50

5001000

1500200025003000350040004500

Binder content B w% (wt.%)

) a P k ( S C U

14day

28day

56day91day

118 dayBinder type:20% cement + 80% slag

Fig. 11 Typical variation of UCS with binder content atdifferent curing times (from Benzaazoua et al. 2000)

0

200

400600

800

1000

1200

1400

1600

1800

0 7 14 21 28Curing time (days)

) a

P k ( S C U

Binder type:5 wt.% (30:70 of OPC-Slag)

Tap waterLake waterMine-A process water

Key

Fig. 12 Effect of mixing water on strength developmentwithin paste backll mixtures with mine A tailings (fromBenzaazoua et al. 2002)

156 Geotech Geol Eng (2008) 26:147174

1 3


11/28

Bellmann et al. ( 2006) demonstrated that portlan-dite reacts to gypsum at a minimal sulphateconcentration of approximately 1,400 mg/l (pH =12.45). Their results suggest that, at common

moderate concentrations of up to 1,5003,000 mg/lof sulphate, gypsum formation is either not possibleor cannot lead to damage, since supersaturation andswelling pressure are very low. At low sulphateconcentrations, minor amounts of alkali ions alreadypresent in the pore solution act to protect themicrostructure from the destructive process of gyp-sum formation.

Sulphide mineral (pyrite, pyrrhotite, arsenopyrite)oxidation has been shown to produce increased acidity(pH drops), metal remobilisation, sulphate ionsrelease, and dissolution of formed hydrates. Forexample, when pH \ 12 (stability limit of portlan-dite), potential outcomes are partial or total dissolutionof portlandite (Ca(OH) 2), release of calcium from theformed hydrates (decalcication of CSH phases),and increased micro and mesoporosity.

The presence of sulphates in the mixture playsvarious other roles, depending on concentration(Benzaazoua et al. 2004). When sulphate content isbetween 200 and 8,000 mg/l, an inhibition stage of

paste backll hydration is likely. For sulphateconcentrations ranging between 8,000 and10,000 mg/l, precipitation of secondary gypsum isprobable, and contributes to develop paste backllstrength. For sulphate content higher than10,000 mg/l, sulphate attack, characterized by mas-sive and harmful precipitation of secondary gypsumand ettringite (swelling phases), is expected. Thisexcess volume is unable to ll capillary pores, asgypsum and ettringite crystals become much largerthan the pores, which leads to expansion andmicrocracking of cured paste backll. The outcomeis loss of initially developed strength.

4.1.4 Paste Backll Mixing Procedure

As mentioned above, a quantity of water is added tothe tailings and binding agent and mixed for approx-imately 57 min in a concrete mixer. Due to the widevariety of tailings types, the resultant paste backllmixture typically contains between 63 wt.% and85 wt.% solids concentration by mass C w% , depend-ing on initial tailings solid particles density

2:8 q s t 4:7; binder content ( Bw% ), and

Unhydrated binder

Water Capillary Water Capillary water

Hydrates

PrecipitatesDissolved binder

Unhydrated binder

Stage 1(after few hours)

Stage 2(after many days)

Stage 0(before hydration)

Unhydrated binderHydratesUnhydrated binder

Fig. 13 Schematic diagramof volumetric proportions inhardening process of pastebackll having w / c = 7(adapted from Benzaazouaet al. 2004)

OH ions release12 pH 13

PortlanditeCa(OH) 2

Ettringite3CaSO 4.3CaO.Al 2O3.32H2O

GypsumCaSO 4.2H2O

Silica gels formation(C-S-H decalcification)

If pH < 12

Dissolution / hydration Hydration / precipitation

If sulphides oxide

PortlanditeCa(OH) 2

secondar y

s e c o n d a r ypr ima r y

C-S-H phases

Fresh mixture of sulphide-richand sulphate-rich

cemented paste backfill

OH

PortlanditeCa(OH) 2

Ettringite3CaSO 4.3CaO.Al 2O3.32H2O

GypsumCaSO 4.2H2O

(C-S-H decalcification)

If pH < 12

Dissolution / hydration Hydration / precipitation

If sulphides oxide

PortlanditeCa(OH) 2

secondar y

s e c o n d a r y

C-S-H phases

Fresh mixture of sulphide-richand sulphate-rich

cemented paste backfill

Fig. 14 Schematic diagramof paste backll hydrationprocess

Geotech Geol Eng (2008) 26:147174 157

1 3


12/28

water-to-cement ratio ( W / C ), given by the followingrelationships:

C w% 100 100 Bw% 100 Bw% 1 W C

31aand

W C

w%100

100 Bw% 1 100 C w%C w% 100 Bw% 1

31bwhere C w% = solids concentration by mass of CPB(%); Bw% = binder content by mass (wt.%); W / C = water-to-cement ratio; w(%) = water content of the nal backll mix (in percent), given by:

w% 100 M water

M dry solid 32Considering the range of variation in C w% (from63 wt.% to 85 wt.%) and Bw% (from 3 wt.% to7 wt.%) encountered in the mining industry, W / C varies from 2.7 to 20.2 (compared to the approxi-mately 0.5 W / C used in the concrete industry).Figure 15 presents a typical variation of water-to-cement ratio W / C for four different binder contentscommonly used in the mining industry. The equiv-alent volumetric solids concentration C v% iscalculated by the following formula:

C v% 1001 n 1001 e 33a

and for backll solids concentration by mass ( C w% )as follows:

C v% C w%qbulk f

q s f 1001 100C w% 1 Gs f S r33b

where qbulk-f = pastell bulk density (kg/m 3); qs-f = pastell solid particles (tailings + binder) specicdensity (kg/m 3); n = CPB porosity ( V void / V bulk ); e =CPB voids ratio ( V void / V solid ); G s-f = pastell specicgravity; S r = pastell degree of saturation (varyingfrom 0 to 1).

Figure 16 shows a typical variation of volumetricsolids concentration ( C v% ) with solids concentrationby mass (C w% ) for ve CPB mixes using ve differenttailings and one binding agent (0.3 OPC + 0.7 GGBFS ) at 4.5 wt.%. The resultant paste backllmixtures were poured into plastic moulds 10.125 cm(4 inches) in diameter and20.5 cm(8 inches) in heightor 7.62 cm (3 inches) in diameter and 15.24 cm(6 inches) in height, sealed, and cured in a humidity-controlled chamber at approximately 90100% RHand 25 C (similar to underground mine workingconditions). CPB samples were then subjected tocompression tests at different curing periods.

4.2 CPB Preparation at a Backll Plant

Figure 17 shows a typical ow chart for a backllplant (Cayouette 2003). Final mill tailings are rst fedinto a high-capacity thickener to increase solidsconcentration from 35 wt.% to approximately

2

4

6

8

10

1214

16

18

20

22

63 65 67 69 71 73 75 77 79 81 83 85

Solid mass concentration C w% (wt.%)

( o i t a r t n e m e c - o t - r e t a

W

w / c )

B w% = 3 wt.%

B w% = 4.5 wt.%

B w% = 5 wt.%

B w% = 7 wt.%

Paste backfill systems

Fig. 15 Typical variationof water-to-cement ratio w/ c with paste backll nalmix solids concentration bymass (C w% ) for fourdifferent binder contents( B

w%) commonly used in

the mining industry

158 Geotech Geol Eng (2008) 26:147174

1 3


13/28

5560 wt.% by mass. Flocculent is added to aidltration. The thickened tailings are then pumpedfrom the thickener to a high-capacity holding tank (after cyanide destruction). From the surge tank, thethickened tailings are gravity-fed to disc ltersoperating alone or in parallel to produce lter cakewith a solids concentration of approximately 7082 wt.%. The lter cake is then discharged onto a belt(or reversible) conveyor and fed to a screw feeder for

weighing. Finally, lter cake batches are mixed in aspiral (or screw) mixer with binder and water addedfor about 45 s to produce a paste with a speciedconsistency or slump height value S .

4.3 Importance of Controlling Tailings Density

Since binder proportion Bw% in the mix is calculatedfrom tailings dry mass, the slightest variation in

tailings grain density qs-t produces an excess or loss-of-prot in binder proportioning. This variation of qs-tmay be due to mineralogical changes in the ore bodyduring stope extraction. Using a regression analysison data taken from Benzaazoua and Bussie `re (1999)and Benzaazoua et al. ( 2000), and knowing totalsulphur content % S (in percent), tailings grainsspecic density qs-t (in g/cm3) is estimated usingthe following regression equation:

q s t 19:5674

1 6:0094 exp 0:0072 %S R 0:9999

34where qs-t is in g/cm

3; %S = tailings total sulphurcontent (wt.%).

For a given constant binder content Bw% (wt.%),increase in qs-t produces an increase in volumetricbinder content Bv% (v/v%), and a reduction in qs-tproduces a reduction in Bv% , as described by Eq. 28.

25

30

35

40

45

50

55

60

65

70

63 65 67 69 71 73 75 77 79 81 83 85

Solid mass concentration C w% (wt.%)

n o i t a r t n e c n o c

d i l o s c i r t e m u l o

V

C % v

) % v / v (

Gs-bkf = 2.805

Gs-bkf = 3.282

Gs-bkf = 3.752

Gs-bkf = 4.123

Gs-bkf = 4.672

B w% = 4.5 wt%

x = 0.3 and 1-x = 0.7Binder = x*OPC + (1-x)*GGBFS

S r = 1

Gs-tailings = 2.8Gs-tailings = 3.3Gs-tailings = 3.8Gs-tailings = 4.2Gs-tailings = 4.8

Paste backfill systems

/ v

Fig. 16 Typical variationin volumetric solidsconcentration ( C V% ) withsolids concentration byweight ( C w% ) for ve CPBmixes using ve differenttailings and one bindingagent (OPC-GGBFS) at4.5 wt.% and 100% watersaturation

Fig. 17 Paste backll plant

ow sheet at the Louvicourtmine, Canada (fromCayouette 2003)

Geotech Geol Eng (2008) 26:147174 159

1 3
http://-/?-http://-/?-


14/28

4.3.1 Calculation of Adjusted Binder Content

To take into account the variation in tailings solidgrains specic density q s-t in the mix design, adjustedbinder content Bw%-adj (i.e., actual binder proportionused, not constant binder content, Bw% init) must be

calculated using the following formula:

Bw% adj Bv% initq s bq s t Bw% init qs t initq s t

35where Bv% init initial constant volumetric bindercontent (v/v%), corresponding to initial constantbinder content by dry mass of tailings Bw% init; Bw% init initial constant binder content by drymass (wt.%) ; qs-t = current tailings solid particles

density; q

s-b = anhydrous binder particles density;and q s tinit initial tailings solid particles density.Densities are in g/cm 3 , kg/m3 or tonne/m 3 .

Figure 18 presents a typical variation in adjustedbinder content Bw%-adj with tailings grains density q s-t ,varying from the initial assumed value (( q s-t )init =3.85 g/cm 3). It shows that a decrease in tailings solidgrains initial density qs-t produces a lack of bindercontent (loss-of-prot) with respect to adjusted bindercontent ( Bw%-adj ), which leads in turn to under-propor-tioning of the binding agent in the nal paste backll

mix. In contrast, an increase in qs-t produces excessbinder content with respect to the adjusted bindercontent, which leadsto over-proportioningof thebindingagent, and therefore cost inefciencies. However, under-proportioning of the binding agent causes the greater

damageof reducingpaste backll strength development,while over-proportioning affects prots alone.

4.3.2 Calculation of Differential Binder Contentsand Economic Implications

If adjusted binder content Bw%-adj is not considered,the result may be erroneous interpretation of thehypothetical inuence of tailings solid grains densityq s-t on paste backll compressive strength develop-ment (e.g., Fall et al. 2004, 2005). Differential bindercontent D Bw% due to variations in tailings grainsinitial density q s-t (increase or decrease) is calculatedwith the following formula:

D Bw% Bw% init Bw% adj Bw% init

q s t

qs t

init

q s t 36

where Bw%-init = initial binder content (wt.%);q s-t = current tailings solid particles density; and(q s-t )init = initial tailings solid particles density.Densities are in g/cm 3 , kg/m3 or tonne/m 3 .

From Eq. 35, note that D Bw% may be positive

D Bw% [ 0 or negative D Bw% \ 0; depending oncurrent tailings grains density qs-t :

D Bw%[ 0 Bw% excess if qs t [ q s tinitD

Bw%\

0 Bw% lack if qs t\

q s tinit( 37where Bw%-excess = excess binder content (wt.%); Bw%-lack = lack of binder or loss-of-prot binder

0

1

2

3

4

5

6

7

8

9

10

2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0Tailings solid grains density s-t (g/cm 3)

B

j d a -

% w

) % . t w (

B w% = 3 wt.%

B w% = 4.5 w t.%

B w% = 7 wt.%

Increase in s-t(overproportionning)

Decrease in s-t(underproportionning)

3.85

Excess

Excess

Excess

Lack

Lack

Lack

Excess binder usage(money to save)

Lack binder usage(stability concerns)

3

7

Excess

Excess

Excess

Lack

Lack

Excess binder usage(money to save)

Lack binder usage(stability concerns)

Fig. 18 Typical variationin adjusted binder content Bw% adj(wt%) with tailingsgrains density qs t; varyingfrom the initial assumedvalue of 3.85 g/cm 3 and for

three different bindercontents (3, 4.5, and7 wt.%)

160 Geotech Geol Eng (2008) 26:147174

1 3
http://-/?-http://-/?-


15/28

content, i.e., under-proportioned binding agent in thenal mix.

Figure 19 presents typical variations in differentialbinder content D Bw% with tailings grains density(q s-t ), varying from the initial assumed value of 3.85 g/cm 3 . As shown, increased q s-t produces excess

binder proportioning, while reduced qs-t producesunder-proportioned (loss-of-prot) binder in the pastebackll mix.

Excess binder content ( Bw%-excess ) may be con-verted into savings (if Bw%-adj is considered in themix design) or loss (if Bw%-adj is not considered in themix design), and annual savings or loss may becalculated as follows:

$=year saved=lost

M dry tailings tonne=year Bw% excess

100 $binder =tonne

38

where ($/year) saved/lost = money saved or lost per yearif initial binder content is lower than the excessbinder proportion; M dry-tailings = total mass of drytailings used per year (tonne/year); Bw%-excess =excess binder content (wt.%); and ($binder/

tonne) = current cost of the binding agent.To illustrate, consider an underground hard rock

mine that uses 6 105 tonnes/year of total dry

tailings having an initial solid grains density ( q s-t )initof 3,800 kg/m 3 (3.8 tonnes/m 3). Fixed constantbinder content Bw%-init is 4.5 wt.% and solidsconcentration of the nal mixes C w% is 78%. Thebinder type used is a blended OPC-GGBFS at a ratioof 70:30 at a cost of 126.5 $/tonne. Assuming a 7%increase in tailings solid density over the initial value

(i.e., qs-t = 4,050 kg/m 3), savings would amount toabout $211k/year. With an approximately 16%increase (i.e., qs-t = 4,400 kg/m 3), savings wouldamount to about $466k/year (Fig. 20).

5 Paste Backll Transportation

As dened above, paste backll consists of the fullsize fraction of the tailings stream prepared as a highslurry density. The slurry behaves as a non-Newto-nian uid, meaning that it requires an applied force tocommence owing (Fig. 21). For example, tooth-paste, a commonly used non-Newtonian uid, mustbe squeezed (yield stress or applied load) to get thetoothpaste out of the tube (Clark et al. 1995). Sincebackll paste has higher viscosity, it exhibits plugow when transported through a pipe. The outerportions of the slurry shear against the sidewall of thepipe while the central core travels as a plug (Grice1998). Paste backll ow in pipelines is entirelygoverned by its rheological properties. Rheology isthe science of the ow and deformation of matter.

5.1 Rheological Models for Paste Backll

The main method to achieve paste backll ow in

pipelines is the full-fall. Full-pipe occurs when theowing paste forms a continuum with no air-lledgaps or discontinuities (vacuum holes) in thepipeline segment under consideration (Li and Moer-man 2002). The most fundamental relationship in therheology of a non-Newtonian uid is between shearrate, _c s 1 and pipe wall shear stress, sw (Pa). Once

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0

Tailings solid grains density s-t (g/cm 3)

r e d n i b l a i t n e r e f f i D

B

% w

Bw% = 3 wt.%

Bw% = 4.5 wt.%

Bw% = 7 wt.%

B w% = 3 wt.%

B w% = 4.5 wt.%

B w% = 7 wt.%

B w% > 0 [ s-t > ( s-t)init = 3.85 g/cm 3]

B w% < 0 [ s-t < ( s-t)init = 3.85 g/cm 3]

Excessbinder usage(money to save)

Lack binder usage(stabilityconcerns)

B w% = B w%-init B w%-adj

%

B w% > 0 [ s-t > ( s-t)init = 3.85 g/cm 3]

B w% < 0 [ s-t < ( s-t)init = 3.85 g/cm 3]

Fig. 19 Typical variationin differential bindercontent D Bw% with tailingsgrains density qs t;varyingfrom the initial assumedvalue of 3.85 g/cm 3 and forthree binder contents (3, 4.5and 7 wt.%)

Geotech Geol Eng (2008) 26:147174 161

1 3


16/28

this relationship is known, uid behaviour in all ow

situations can be deduced (e.g., viscosity and yieldstress). The most frequently used fundamental non-Newtonain models to describe simple ow behaviourare the power law model, the Bingham model, andthe HerschelBulkley model.

5.1.1 Power-law or Ostvald-de Waele Model

Many non-Newtonian materials undergo a simpleincrease or decrease in viscosity as shear rateincreases. One of the most widely used forms of thegeneral non-Newtonian constitutive law is a power-law (or Ostvald-de Waele) model, or two-parametermodel, expressed as:

sw gappdV dr

a

gapp _c a

39where sw = wall shear stress (Pa); sy = shear yieldstress (Pa); gapp = non-Newtonian apparent viscosity

dening uid consistency (Pa s); dV =dr _c shear rate s

1

or velocity ratio V (m/s); a pointon the velocity prole r (m); and a = power-lawmodel constant indicating the degree of non-Newto-nian behaviour (the greater the departure from unitythe more pronounced the non-Newtonian propertiesof the uid). This model does not account for yieldstress. If a \ 1, a shear-thinning (or pseudoplastic)uid is obtained, characterized by a progressivelydecreasing apparent viscosity with increasing shearrate. If a [ 1, a shear-thickening (or dilatant) uid inwhich apparent viscosity increases progressively with

increasing shear rate is obtained. When a = 1, aNewtonian uid is obtained.

5.1.2 Bingham Plastic Model

Some materials exhibit innite viscosity until asufciently high stress is applied to initiate ow(yield stress). Above this stress, the material showssimple Newtonian ow. One of the simplest modelscovering viscoplastic uids exhibiting such yieldresponse is the ideal Bingham model (Fig. 22),expressed by the following two-parameter model:

sw sy gBdV dr sy gB _c 40

where sy = shear yield stress (Pa); gB = Binghamplastic viscosity (Pa s); and _c shear rate s 1:Basically, the Bingham model describes the viscositycharacteristics of a uid with yield stress whenviscosity is independent of shear rate (constant).Therefore, the Bingham plastic model cannot account

$-

$100

$200

$300

$400

$500

$600$700

$800

$900

$1,000

$1,100

$1,200

$1,300

3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0Increase in tailing grains solid density s-t (g/cm 3)

) r a e y / k $ ( s s o l

/ g n i v a s y e n o

M

B w%_init = 4.5 wt.%

B w%_init = 7 wt.%

B w%_init = 3 wt.%

3.8

Fig. 20 Example of moneysaved or lost according toincrease in tailings solidsdensity q s t for threedifferent binder contents (3,4.5 and 7 wt.%)

(a) No flow(Vertical head= yield stress)

Hopper

openstope

Pressure(2 MPa)400200 600

8000

Hopper

400

2 00 6 00

8000

Pressure(3 MPa)

Stope

(b) Flow(Vertical head> yield stress)

openstope

400

200 600

8000

400

200 600

8000

400

2 00 6 00

8000

400

2 00 6 00

8000

Stope

Fig. 21 Schematic diagram of yield stress in paste backllowing through a pipeline (from Revell 2000)

162 Geotech Geol Eng (2008) 26:147174

1 3


17/28

for the shear-thinning characteristics of general non-Newtonian uids. Many concentrated particle sus-

pensions and colloidal systems, such as mortar,concrete and possibly pastell, show Binghambehaviour at low shear rates.

5.1.3 HerschelBulkley Model

The HerschelBulkley model is a three-parametermodel used to describe viscoplastic materials exhib-iting yield response with a shear-thinning relationshipabove yield stress (Fig. 22). This generalized model

is a combination of the power law (Eq. 39) andBingham models (Eq. 40), and is expressed by thefollowing relationship:

sw sapp gappdV dr

n

sapp gapp _c n

41where sapp = constant, interpreted as apparent shearyield stress (Pa); gapp = consistency index or appar-ent viscosity (Pa s); _c shear rate s 1; andn = ow parameter indicating the degree of non-Newtonian behaviour (the greater the departure from

unity the more pronounced the non-Newtonian prop-erties of the uid). When n = 1, the HerschelBulkley model is reduced to the Bingham model(Eq. 39). If n \ 1, a pseudoplastic (or shear-thinning)uid is obtained. If n [ 1, a dilatant (or shear-thickening) uid is obtained. The Herschel-Bulkleymodel is better tted for many biological uids, foodproducts, and cosmetic products. Since this modeltends to more realistically predict ow over a widerrange of conditions than the Bingham model, it is

often applied to industrial uids to specify designconditions for processing plants.

Since paste backlls are considered non-Newto-nian uids, their rheology is time-independent duringpipeline transport. Most paste backlls show appre-ciable yield stress, and are therefore treated as

HerschelBulkley uids (Eq. 41). Some paste back-lls are Bingham plastic in limited shear rate ranges.Others are yield pseudoplastic or yield dilatant, withthe former more common than the latter (Li andMoerman 2002). Shear or apparent yield stress sy orsapp , apparent viscosity gapp , and ow parameters aand n are obtained by tting Eqs. 39, 40 and 41 to agiven ow curve or rheogram (shear rate-shear stresscurve) obtained from rheometer tests (capillary,extrusion or rotational rheometer) using differenttool geometries (vane, concentric cylinder, cone andplate, parallel plate, etc.).

5.1.4 Model for Plastic Fluid Flow Through a Pipe

For a Bingham plastic uid such as pastell, therelationship between pseudo shear rate 8 V / D andshear stress at the pipe wall sw is given by:

sw D PD

4 L

gB 8V D 1 43 sy 4 L D PD 13 sy 4 L D PD 4

" #1

42where sy = shear yield stress (Pa); gB = Binghamplastic viscosity (Pa s); D P = pressure drop through asection of circular pipe of length L (Pa); D = pipeinner diameter (m); L = pipe length (m); and V =paste laminar velocity (m/s). Effective pipe innerdiameter ( D) for paste backll transport rangesbetween 10 cm and 20 cm (4 and 8 inches). Paste

ow velocity varies from 0.1 m/s to 1 m/s. Thepractical pumping distance of paste can reach 1,000 mlongitudinally ( L h) and is unlimited vertically.

5.2 Standard Measurements of CPB RheologicalFactors

In practice, it is not easy to obtain the true rheologicalproperties of pastes, due to the complexity of the

s s e r t s r a e h s l l a

W

w

) a P (

y

Shear rate (1/s)

B

app

app

Bingham plastic

Pseudoplastic fluid

Fig. 22 Rheograms for time-independent uids

Geotech Geol Eng (2008) 26:147174 163

1 3
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


18/28

experimental devices (rheometer tests). This makes itdifcult or even impossible to determine or predictpaste viscosity, which depends on several factors.Due to its simplicity, the standard slump test (used inthe concrete industry) is widely used to determinepaste backll consistency. Slump is a measure of the

drop in height of a material when released from atruncated metal cone that is open at both ends andsitting on a horizontal surface (Fig. 23). Slumpdetermination allows characterizing the materialsconsistency in terms of transportability (Clark et al.1995). According to Landriault et al. ( 1997), theoptimum paste backll slump to facilitate under-ground pumping is between 150 mm (6 inches) and250 mm (10 inches).

Solids concentration C w% is often used to comparemix compositions, particularly batches. To achievemix consistency across batches, consistency can bemeasured by monitoring the electrical power used bythe motor that turns the mixer paddles. The mixer isstarted and water is added until the power required bythe motor reaches target for the mix consistencydesired (Brackebusch 1994; Landriault and Lidkea1993). The only requirement is that slump must becorrelated to consistency and consistency correlatedto power. Once the correlation between slump andpressure loss has been established, produced pressuregradient can be predicted.

5.3 Alternate Methods for MeasuringRheological Factors

To accurately dene the rheology of paste backll,both shear yield stress ( sy) and viscosity ( l ) must bemeasured. Most current tests measure only onerheological factor (i.e., slump height). The relation-ship between the factor measured and either of the

two fundamental rheological parameters is notobvious (Ferraris 1999). In most cases, sy and lcannot be calculated from the measured factor, andare only assumed to be related. According toFerraris ( 1999), slump, penetrating rod, and K -slumptests are related to shear yield stress ( sy), since they

measure the pastes ability to start owing. Theremoulding test, LCL apparatus, vibrating testingapparatus, ow cone, turning tube viscometer, llingability, and Orimet apparatus are related to viscositybecause they measure the pastes ability to owonce applied stress (vibration or gravity) exceedsyield stress.

Slump height, an empirical measure of consis-tency, is dependent on both material yield stressand density, which are in turn dependent onchemical composition, particle specic gravity,and particle size. In the minerals industry, thesefactors may vary with changes in ore origin andprocessing. As a result, using slump height as thesingle parameter of consistency for paste backlldistribution systems potentially leads to problems(Clayton et al. 2003). Therefore, yield stress, aunique material property, is the preferred indicatorof consistency. If slump height can be related toyield stress, the slump test offers a simple and idealtechnique for on-site yield stress measurement(Clayton et al. 2003).

5.3.1 Direct Measurement of Yield Stress

Nguyen and Boger ( 1983 , 1985) have suggestedadapting the laboratory vane shear test to measurematerial yield stress ( sy). Test results allow obtaininga torque-angular deformation curve of material,where peak corresponds to maximum torque ( M 0).Using the peak torque value and vane geometry

H 0

S (mm)= slump

Before

After

H 0

After

(b)

H 0

After

H 0

After

(a)

Fig. 23 Paste backllconsistency measurementby slump tests: ( a ) slumpcone mould; ( b) schematicview of the slump test(adapted from Ferraris andde Larrard 1998)

164 Geotech Geol Eng (2008) 26:147174

1 3


19/28

parameters, yield stress is calculated by the followingrelationship (Nguyen and Boger 1983, 1985):

sy M 0

p D32

H D 1m3

43

where sy = paste yield stress (Pa); M 0 = maximumpeak torque (N m); D = vane diameter (m); H = vaneheight (m); and m = constant describing stressdistribution over the cylinder (end effect): uniformdistribution ( m = 0) and non-uniform distribution ( m[ 0). Nguyen and Boger ( 1985) veried that theassumption of uniform stress distribution ( m = 0) isvalid.

Coussot and Boyer ( 1995) proposed a method todetermine yield stress from the inclined plane test.The inclined plane used was a 1-m-long ( D) channel

with width L varying between 5 cm and 25 cm andslope ( i) varying between 10 and 30 . The bottomsurface was plywood. The authors demonstrated thatwall slip is negligible for mud ows on this surfacetype, and they successfully compared measureduniform ow depths ( h) with theoretical predictions(based on rheometrical tests). They also observed noow depth change when using surfaces with differentroughness. Asymptotic depth ( h0), corresponding toat rest state (nal position or equilibrium), leads tothe determination of yield stress:

sy qgh 0 sin i 44where q = material bulk density (kg/m 3); g = grav-itational acceleration (m/s 2); h0 = nal height of material (m); and i = inclined plane slope angle.

Ulherr et al. ( 2002) developed a novel and simplemethod for measuring yield stress using a cylindricalpenetrometer. Basically, static equilibrium of afalling penetrometer in a yield stress uid (partialimmersion) is measured, and uniform shear stressacting on the entire penetrometer surface is assumed.

Yield stress is simply determined by a balance of forces acting on the penetrometer, as follows:

sy g mp qp d 2 l4 d 12 pd l pd 8

45where g = gravitational acceleration (m/s 2); mp =total mass of the penetrometer (kg); q = uid bulk

density (kg/m 3); and d and l are the diameter (m) andimmersed length (m) of the cylindrical section of thepenetrometer.

Equation 45 indicates that yield stress is afunction of the weight and dimensions of theimmersed penetrometer. Thus, yield stress is readilydetermined by measuring equilibrium depth in theuid for a penetrometer with known weight anddiameter.

5.3.2 Analytical Models of Yield Stress and Slump

A number of analytical models have been devel-oped to relate slump to a corresponding yield stressin order to predict slumping behaviour. The rstanalysis was made by Murata ( 1984), followed byChristensen ( 1991), who corrected a simple inte-gration error made by Murata. Rajani andMorgenstern ( 1991) and Schowalter and Christen-sen (1998) further investigated the conical test. Theslump test was rst adapted to a cylindricalgeometry by Chandler ( 1986) for application tothe aluminium industry. Chandler realised there wasa relationship between slump height and owbehaviour of the bauxite residue he was testing,but did not analytically relate the two. Pashias et al.(1996) developed a model for cylindrical geometry,for a favourable comparison of model and staticvane test results. They also investigated slumpheight sensitivity to sample structure, material,aspect ratio, lift rate, and measurement time, andfound slump measurement to be essentially inde-pendent of these factors.

These results were successfully validated byClayton et al. ( 2003), Iveson and Franks ( 2003),Gawu and Fourie ( 2004), and Saak et al. ( 2004) forcylindrical moulds. Recently, Roussel and Coussot(2005) proposed an analytical correlation betweenspread and yield stress of cement pastes for theASTM mini cone test, based on the work of Coussotet al. (1996). Roussel et al. ( 2005) correlated yieldstress to slump or spread over a large range of yieldstresses for any conical geometry. In addition, theyquantied the inuence of secondary phenomenasuch as surface forces, ow inertia, and initial coneshape on test meaningfulness.

Rajani and Morgenstern ( 1991) proposed a modelto predict plastic yield stress sy from the ASTM C-143 slump cone height, based on both 2D (Trescacriterion) and 3D (von Mises criterion) yield criteria,as follows:

Geotech Geol Eng (2008) 26:147174 165

1 3
http://-/?-http://-/?-


20/28

s y qg H h0 S b ln 7 H

3

H h0 3 H 3

46where q = material bulk density (kg/m 3); g = gravi-tational acceleration (m/s 2); h0 = height of unyielded

material (m or mm); H = height of the ASTM C-143slump cone ( H = 300 mm); S = slump height (mm orm); and b = constant depending on the yield criterion.b = H3 (von Mises) or 2 (Tresca). It should also bementioned that h1 = H h0 S and h0 = H h1 S .

Helmuth et al. ( 2006) developed a slump modelbased on geometric constraints for the standardASTM C-143 concrete slump cone. Yield stresswas calculated based on Muratas ( 1984) forcebalance approach, as follows:

sy qgV c2pr 2s 47a

and

r s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi33612 S 3s ! 1 47bwhere q = material bulk density (kg/m 3); g = grav-itational acceleration (m/s 2); V c = cone or mouldvolume (m 3); r s = the radius of the slumped materialbase (m); and S = slump height (m).

Pashias et al. ( 1996) adopted the slump test as asimple means to determine yield stress ( sy). Theyshowed that slump height ( s) measured by themodied slump test using an open-ended cylinderwith an aspect ratio of 1 (diameter =height = 200 mm) could be directly related to yieldstress, using the theory originally suggested byMurata ( 1984) and corrected by Christensen ( 1991).The relationship between slump height s and yieldstress is given by (Pashias et al. 1996):

s H 1

2syqgH 1 ln

2syqgH 48aor

s0 1 2s0y 1 ln2s0yh i 48bwhere q = pastell bulk density (kg/m 3); g = gravi-tational acceleration (m/s 2); s0 = s / H = dimensionlessslump; s = cylindrical slump height (m); sy = shearyield stress obtained by the vane method (Pa);

H = cylinder height (m); and s0y sy=qgH dimensionless shear yield stress.

Iveson and Franks ( 2003) demonstrated that shearyield stress ( sy) of a paste-like suspension can bepredicted by the modied slump method (Pashiaset al. 1996), using the following analytical

relationship:

sy qgH

2 1 ffiffiffiffis H r 49

where q = paste-like suspension bulk density (kg/ m3); g = gravitational acceleration (m/s 2); H = slumpcylinder height (m); and s = cylinder slump height(m).

Clayton et al. ( 2003) proposed a general modelrelating slump height ( S ) and yield stress ( sy) to conegeometry. Thus, cylinder and cone geometries forslump measurement of the same material werecompared. Predicted yield stress for the relatedcylinder model (Eq. 45) and cone model werecompared to yield stress, determined using the well-established vane method (Nguyen and Boger 1983,1985). The general cone model is given by:

s0 1 h00 2s0y ln1 1a

3 1

1 h00

a

31

0B@

1CA

50a

with

s0y a6

1 h00a 11 h00a

2264375

50b

and

a R0

RH R0 50c

where a = dimensionless quantity relating the top( R0) and base ( RH ) radii of the cone (when RH = 2 R0 , a = 1, which is the case for theASTM C-143 cone); h00 dimensionless heightof unyielded material ;s0 y s y=qgH dimensionlessshear yield stress ; q = material bulk density (kg/ m3); and g = gravitational acceleration (m/s 2).

Saak et al. ( 2004) proposed a generalized model todetermine yield stress by slump height from eithercylindrical or conical geometries. This model may be

166 Geotech Geol Eng (2008) 26:147174

1 3
http://-/?-http://-/?-


21/28

thought of as a combination of the Pashias et al.(Eq. 48) and Clayton et al. models (Eq. 50).

s H 1 h0 H h1 H or s0 1 h00 h01

8

Relleno Minas Diseño

Documents

Transcript of Relleno Minas Diseño