Experimental Study andNumerical Reproduction of Self-WeightConsolidation Behavior of Thickened Tailings

Michaël Demers Bonin1; Mathieu Nuth, Ph.D.2; Anne-Marie Dagenais, Ph.D., P.Eng.3; andAlexandre R. Cabral, Ph.D., P.Eng.4

Abstract: Thickened tailings, defined as mineral wastes that behave as a non-Newtonian fluid, show a small yield stress and release a smallamount of water following deposition. Thickening has become an increasingly used option in tailings management. This paper presents a de-tailed examination of gold mine thickened tailings undergoing self-weight consolidation, which is an important mechanism affecting soft soilsimmediately after deposition. Self-weight consolidation was evaluated using a column equipped with water pressure transmitters whereasa slurry consolidometer was employed to obtain the compressibility relationship under low vertical effective stresses. The piecewise-linearmodel CS2 was used to model the experimental self-weight consolidation test. This model proved very accurate in reproducing the observedbehavior. Both the test results and themodel results also confirmed the absence of sedimentation in the thickened tailings, which is in agreementwith values reported in the literature related to similar materials.DOI: 10.1061/(ASCE)GT.1943-5606.0001179. © 2014 American Society ofCivil Engineers.

Author keywords: Thickened tailings; Self-weight consolidation; Piecewise-linear model CS2; Tailings disposal.

Introduction

The technology of thickened tailings (TT) has gained the attention ofthe mining industry in the last 30 years, as several mines adopted aTT approach to tailings management (Barbour et al. 1993; Williamsand Ennis 1996; McPhail et al. 2004; Oxenford and Lord 2006).Many advantages have been reported since the development of thistechnology by Robinsky in 1973 (Robinsky 1975), such as lesswater released following deposition and the possibility of stackingtailings with a greater beach angle than non-TT (Robinsky 1999).However, Fourie (2012) questions whether the attributed benefits toTT have in fact been realized. Thickened or not, a key considerationin tailings management is the storage capacity of tailings disposalareas (TDA). This aspect is in fact largely affected by how tailingssettle. Understanding the settlement behavior of TT is paramount tofurthering the use of TT technology.

In this context, extensive research has been undertaken in the recentpast to define the most important mechanisms causing settlementin soft deposits such as marine sediments, dredging residues, andmine tailings. Gibson et al. (1967) published a theory on large-strain

consolidation of soft clays. Further studies were published on the issueof large-strain consolidation of soft deposits; Imai (1981), Been andSills (1981), and Schiffman et al. (1988) made fundamental con-tributions by including flocculation, sedimentation, and self-weightconsolidation. These physical mechanisms were found to be the firstprocesses influencing settlement of soft deposits after deposition.

The removal of process water affects the settlement processesimmediately after deposition, insofar as it can inhibit (or at leastreduce) the flocculation and sedimentation phases that precede oroverlap self-weight consolidation. In other words, depending on thesolids content, self-weight consolidationmay be the solemechanismresponsible for TT settlement and dissipation of excess pore-waterpressure (ue) after deposition.

The work reported in this paper analyzed self-weight consoli-dation of TT samples in a unique way by combining slurry de-position in settling columns, consolidation tests in a consolidometer,and the use of a numerical model to reproduce the observed results.The evolution of pore-water pressure values during the tests per-formed in the settling columns and the accuracy with which theseresults were reproduced by the piecewise-linear model CS2 havemade it possible to clearly document an important element of thephenomena of self-weight consolidation. This element relates to thefact that the settlement of the tailings-water interface generated bythe region undergoing self-weight consolidation affects excess pore-water pressures in the region immediately above, which itself isabout to undergo self-weight consolidation.

Reviewof Self-Weight Consolidation and ItsModeling

Different behaviors may be observed in soft deposits or hydraulicfills, such as flocculation, sedimentation and self-weight consoli-dation (Fig. 1). Initially, the particles are in suspension in a densefluid medium. Self-weight consolidation begins as soon as the solidparticles build a skeletonwhereby soil particles transmit their weightto the bottom (following time t1 in Fig. 1) (Been and Sills 1981),whereas dissipation of ue occurs simultaneously with settlement.The driving mechanism is the dissipation of ue, which is caused by

1Junior Engineer, Golder Associés Ltée., 1001 Boulevard de Maison-neuve O., 7th Floor, Montréal, QC, Canada H3A 3C8; formerly, GraduateStudent, Dept. of Civil Engineering, Univ. de Sherbrooke, Sherbrooke, QC,Canada J1K 2R1.

2Assistant Professor, Dept. of Civil Engineering, Univ. de Sherbrooke,Sherbrooke, QC, Canada J1K 2R1.

3Engineer, Golder Associés Ltée., 1001 Boulevard de Maisonneuve O.,7th Floor, Montréal, QC, Canada H3A 3C8.

4Professor, Dept. of Civil Engineering, Univ. de Sherbrooke, Sher-brooke, QC, Canada J1K 2R1 (corresponding author). E-mail: alexandre.cabral@usherbrooke.ca

Note. This manuscript was submitted on December 12, 2013; approvedon July 17, 2014; published online on August 13, 2014. Discussion periodopen until January 13, 2015; separate discussions must be submitted forindividual papers. This paper is part of the Journal of Geotechnical andGeoenvironmental Engineering, © ASCE, ISSN 1090-0241/04014068(10)/$25.00.

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the buoyant unit weight of the soil particles. When self-weightconsolidation starts, the effective stress builds up and the slurry startsto behave as a soil. Self-weight consolidation is over when the soilstratum is in equilibrium under its own weight (time tf in Fig. 1).

Settling columns are commonly used to evaluate self-weightconsolidation of soft deposits. In column tests, the initial void ratiois uniform. In addition, effective stress and self-weight consolidationstart simultaneously. Alexis et al. (2004) provide further details onsettling column experiments, in which the transition from a settlingsuspension regime (sedimentation) to a soil formation regime (self-weight consolidation) can be observed. Been and Sills (1981) ob-served the development of effective stress together with structuraldensity that seemed to indicate the transition from a settling sus-pension to a soil formation. This transitionwas also described in termsof critical water content (Imai 1980), of void ratio (Carrier et al. 1983;Pane and Schiffman 1985; de Oliveira-Filho and van Zyl 2006;Jeeravipoolvarn et al. 2009a), or in terms of volumetric solid con-centration (Li and Williams 1995; Bürger and Concha 1998). In silt-like materials, de Oliveira-Filho and van Zyl (2006) proposed thatsedimentation starts to be negligible at a void ratio of 2.20, whereasBartholomeeusen et al. (2002) studied the self-weight consolidationof silt-like river sediment at initial void ratios between 2.09 and 4.48.

Several authors attempted to use numerical codes to predict theresults of experimental self-weight consolidation tests performed onvarious types of soils, dredging residues, and mine tailings. Been andSills (1981) used an analytical solution to the Gibson’s finite-strainconsolidation theory.McVay et al. (1986),Hawlader et al. (2008), andJeeravipoolvarn et al. (2009b) used a numerical solution of theGibson’s equation. Berïlgen et al. (2006) preferred to use a piecewise-linear model. Townsend andMcVay (1990) showed that a numericalsolution of the finite-strain theory and a piecewise-linear modelyielded similar predictions of self-weight consolidation. In turn, theuse of analytical solutions to the finite-strain consolidation theoryappears too limiting to predict consolidation behavior of soft depositsbecause of restrictive assumptions that simplify the solution.

The selection of a characteristic e-sv9 relationship is a key factorin modeling self-weight consolidation settlement of soft deposits insettling columns. A major difficulty is measuring low effectivestresses occurring during the self-weight consolidation. Been andSills (1981), Alexis et al. (2004), and Pedroni (2011) overcame thisdifficulty by measuring the evolution of density using accurate

nondestructive apparatuses (g-rays). With density and pore water itis possible to evaluate the vertical effective stress within the settlingcolumn at any time, thus estimating a e-sv9 relationship (Been andSills 1981; Sills 1998). Toorman (1999) suggested nonetheless thatthe measurements of the lower effective stresses, especially in thetop 10 cm, may not be reliable because of the imprecision of thedensity and the pore-water pressure measurements.

Materials and Methods

Materials

The tailings samples were taken from a gold mine tailings facility(location to remain undisclosed). At their arrival at the Soil Me-chanics Laboratory of the Université de Sherbrooke in Sherbrooke,Canada, the tailings within the pails had settled, as evidenced bythe presence of supernatant water. The average gravimetric watercontent (w) of the settled material was approximately 34.7%. Thegravimetric water content was approximately 50.7% after beinghomogenized with the supernatant water, corresponding to a tailingssolids content of 66.4% (mass of dry solids divided by the total massof solids). For this study, thematerial was brought to a solids contentof 68% (e0 5 1:3, for a degree of saturation of 100% and specificgravity, Gs, of 2.76) by drying and rehomogenizing with distilledwater. This is generally considered to be in the range of reportedsolids content (50–70%) for hard rockmine TT (McPhail et al. 2004;Oxenford and Lord 2006; Fourie 2012; Bussière 2007). As as-sessment tests confirmed (results not presented herein), the use ofdistilled water instead of process water did not lead to any significantvariation in the ue dissipation during self-weight consolidation.The mine tailings studied in this project correspond to a silt-sizedmaterial of low plasticity, a classification often reported for goldmine tailings (de Oliveira-Filho and van Zyl 2006; Bussière 2007).Table 1 summarizes the geotechnical characteristics of the studiedtailings. In addition, hydraulic conductivities of 4:203 1028, 4:993 1028, 5:663 1028, and 6:223 1028 m=s for void ratios of 0.61,0.65, 0.67, and 0.69, respectively, were obtained from falling headpermeability tests performed in a one-dimensional (1D) consoli-dation cell. The 1D consolidation tests started at void ratios between0.88 and 0.89 and were performed according to ASTM D2435-11

Fig. 1. (a) Sedimentation and self-weight consolidation processes expressed in terms of the settlement-time response (adapted from Imai 1981);(b) dissipation of pore-water pressure with elevation when self-weight consolidation dominates

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(ASTM 2011) in a 101.6-mm-interior-diameter cell. Compressionindexes (Cc) ranged between 0.052 and 0.070 and the recompressionindex (Cr) was 0.011. Compression indexes between 0.050 and0.150, for initial void ratios between 0.5 to 1.0, have often beenreported (e.g., McPhail et al. 2004; Bussière 2007; Mittal andMorgenstern 1976; Qiu and Sego 2001; Fahey et al. 2010).

Laboratory Equipment and Experimental Procedure

Settling ColumnSelf-weight consolidation experiments were conducted in a settlingcolumn represented in Fig. 2. The settling column is made of clearacrylicwith an internal diameter of 101.6mm.Total pore-water pressurewasmonitoredat threeelevations (bottom,0.1m,and0.2m)viapressuretransmitters (LMP 331, BD Sensors, Thierstein, Germany; range of0 to 10 kPa, accuracy of60:01 kPa) attached to the column wall. Thesaturation chambers helped to establish saturation in the lines betweenthe pressure transmitters and the embedded porous stones. The outputsignal from the pressure transmitters was monitored with a measuringinstrument (HandyscopeHS4, TiePie Engineering, Sneek,Netherlands)coupled with the software Tie-Pie Multi Channel 1.0.23.0. The trans-mitters are excited by a 20-V external power supply. It was assumed thatthe column wall friction was negligible because of the use of a columndiameter greater than 100mm (Elder 1985;Migniot 1989). Because thephenomenonof self-weight consolidationwasprimarily studied in termsofue dissipation, noactual direct densitymeasurementwas performed inthis study. As detailed later, the e-sv9 and the k-e relationships were notobtained directly from the settling column experiments.

Once the porous stones had been saturated, the column wasemptied and each transducer reading was set to zero on the data-logging system. Tailings were then poured to an initial height (H0)of 300 mm, and the sample was mixed to ensure homogeneity inwater content and void ratio. The column allowed single drainage(upward). Total pore-water pressure (u) data started being recordedafter the mixer was removed from the sample. Self-weight con-solidation caused a reduction of the tailings height (H), while waterexpelled from tailings formed a supernatant layer in the column.After completion of self-weight consolidation (i.e., once ue had beencompletely dissipated), the final tailings height (Hf ) was recorded,the supernatant water was weighed, and samples were taken at thetop and bottomof the column to determinewater content. Void ratioswere calculated fromwater content measurements, and by assumingcomplete saturation. The authors calculated ue by subtracting thehydrostatic pressure (uh) from the total pore-water pressure.

ConsolidometerThe consolidometer shown in Fig. 3 was used for self-weight andprimary consolidation. The apparatus is similar to slurry consolido-meters used elsewhere to obtain a e-sv9 relationships for samplessubmitted to large strains (Qiu and Sego 2001; Wong et al. 2008). Itconsists of a 100-mm-high acrylic column equipped with a water-pressure transmitter installed at the base. A counterweight-swivelsystem was developed to support the mass of the loading piston.Because the latter does not apply any additional stress to the sample,initial low-stress increments can be applied.

For the self-weight consolidation phase, the testing procedure isthe same as in the 300-mm-high settling column. Once the samplehad consolidated under its own weight from the initial height (H0),the final height (Hf ) of the sample and the thickness of supernatantwater were recorded. The loading piston was then gently lowereduntil it came into contact with the tailings surface. Loadings cor-responding to stresses (Ds) of 0.06, 0.12, 0.3, 0.61, 1.1, 2.2, 4.4, and8.8 kPa were applied to the tailings surface. The strain was recordedbefore applying a new load. The dry mass of solids was measured atthe end of the experiment. The height of the sample after each loadstep (Hp2c) and the height of solids (Hs) were used to calculate theaverage void ratio throughout the column as the following ratio:ðHp2c 2HsÞ=Hs. The vertical effective stress was considered to beequal to the load increment stress (Ds5s9) because the self-weightstress of the sample and the hydrostatic pressurewere neglected, as isoften reported in the technical literature (e.g., Qiu and Sego 2001;Wong et al. 2008).

Demers Bonin et al. (2013) reported the dissipation of ue withtime during self-weight consolidation of TT samples (e0 5 1:3) withinitial heights (H0) of 100 and 300 mm. These results showed thatthe trend of dissipation of ue measured at the bottom of samples ofboth heights was nearly the same. Subsequently, the e-sv9 relation-ship obtained from the consolidometer is assumed to represent thecompressibility behavior of the 300-mm-high TT samples at loweffective stresses. Complementary data were obtained from standardconsolidation tests carried out with a 101.6-mm-internal-diameter

Fig. 2. 300-mm-high settling column

Table 1. Characteristics of the Studied Gold Mine Tailings

Characteristics ASTM standardGold minetailings

Specific gravity, Gs D854-10 (ASTM 2010b) 2.76Liquid limit, WL (percentage) D4318-10 (ASTM 2010a) 29a

Plastic limit, WP (percentage) 25b

Plasticity index, IP (percentage) 4Sand .75mm (percentage) D422-63 (ASTM 1963) 8Silt (percentage) 81Clay-sized particles ,2mm(percentage)

11

D10 (mm) 0.0018D60 (mm) 0.021Uniformity coefficient, CU 12Unified Soil ClassificationSystem (USCS) classification

ML

aDetermined with the Swedish cone method.bBased on one sample.

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oedometer cell placed in a 1D consolidation apparatus, using dead-weight loading.

CS2 Numerical Model

This study used the CS2 numerical model (Fox and Berles 1997)to reproduce the behavior of the fine-grained tailings during self-weight consolidation. The CS2 model was developed to predict

large-strain consolidation. It is based on a 1D piecewise-linearmethod that includes a Lagrangian approach, which follows themotion of the solid phase during the consolidation process (Fox andPu 2012). The initial geometry is discretized in vertical elements thathave constant properties during each time increment. The numberof vertical elements (Rj) defined by the user affects the accuracy ofthe results. The CS2 model accounts for large strain, self-weighteffects, relative velocity of fluid and solid phases, and nonlinearity ofhydraulic conductivity and compressibility. The code was imple-mented in MATLAB R2011B 7.13.0.564 and its capability was veri-fied with the four verification problems presented by Fox and Berles(1997).The input includes twoconstitutive relationships in the formofdiscrete point functions.One function represents compressibility as aneffective stress-dependent function and the other represents hydraulicconductivities as a void ratio–dependent function. Additional inputsneeded for a CS2 simulation are specific gravity, water head at thebottom and at the top, the duration of the analysis, and the initialeffective stress associated with the initial void ratio (e0). The CS2model does not account for sedimentation of solid particles (Fox2000).

A third time-step criterion was added to the code to ensure nu-merical stability. It was observed that self-weight effects were respon-sible for high hydraulic gradients in the beginning of the simulationnear the bottom of the column. By implementing the time-step criteriaprovided by Fox (2000), the code ensures that the change in elementheight for any time step is no greater than 0.5%. Moreover, the codewas modified to consider a uniform void ratio distribution in thebeginning of self-weight consolidation. The user specifies the initialvoid ratio, and CS2 refers to the compressibility constitutive re-lationship to find the initial effective stress. In theory, the effectivestress equals zero in the beginning of self-weight consolidation buta value different from zero is required to run CS2.

Results and Discussion

Self-Weight Consolidation: Settling Column

From a total of 16 tests performed in the 300-mm-high settlingcolumn, four had the same initial conditions, i.e., H0 and e0 weresimilar (see Table 2). At the end of self-weight consolidation, therewas a supernatant water layer at the top of the column, resulting froman average vertical strain of 11.7%and an average increase in density(rf 2 r0) of 111 kg=m

3. Final void ratio values ranged between 1.11and 1.16 at the top (eft) and between 1.00 and 1.01 at the bottom (efb).The greater density at the bottom of the column is caused by theincreasing weight of slurry with depth.

Fig. 4 presents the evolution of average dissipation of ue withtime and the corresponding SDs. The greatest SDs for the four testsare noticeable between 500 and 1,100 min, i.e., approximatelyhalfway through the self-weight consolidation process. Nonetheless,they show the consistency within the four tests. The intercepts withthe y-axis in Fig. 4 are 2.24 kPa (at the bottom), 1.52 kPa (0.1 m

Fig. 3. Consolidometer apparatus

Table 2. Summary of Self-Weight Consolidation Tests in the 300-mm-High Settling Column

Testnumber

H0

(m)Initial voidratio, e0

r0(kg=m3)

Mass of tailingsdeposited (g)

Hf

(m)Final void

ratio (top), eft

Final void ratio(bottom), efb

rf average(kg=m3)

Dr(kg=m3)

Mass of supernatantwater on top (g)

Verticalstrain (%)

6 0.302 1.28 1,769.8 4,330.4 0.266 1.12 1.00 1,880.6 110.8 270.79 11.87 0.300 1.29 1,787.8 4,345.4 0.265 1.16 1.01 1,897.6 109.8 264.48 11.514 0.301 1.28 1,786.9 4,357.6 0.267 1.13 1.01 1,897.2 110.3 254.45 11.316 0.298 1.29 1,772.2 4,285.3 0.262 1.11 1.00 1,886.9 114.7 281.06 12.2Average 0.300 1.29 1,779.2 4,329.7 0.265 1.13 1.00 1,890.6 111.4 267.7 11.7

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above the bottom), and 0.72 kPa (0.2 m above the bottom). From theaverage initial density (r0) and the mean initial height (H0), thetheoretical intercepts with the y-axis are, respectively, 2.29, 1.53,and 0.76 kPa. Dissipation of ue at the base (0 m) began immediatelyafter homogenization of the sample in the column, whereas dissi-pation of ue at 0.1 and 0.2 m was slower (dissipation curves aresmoother). The results in Fig. 4 indicate that self-weight consoli-dation started at approximately 300 min at an elevation of 0.1 mabove the bottom, and at 600 min at 0.2 m above the bottom. Thosetimes were determined graphically by locating the change in slope.Before self-weight consolidation reached 0.1m and then 0.2m, therewas still a slow decrease in ue. Apparently, this slow dissipation wascaused by self-weight consolidation at the bottom. Indeed, thetailings-water interface moving down by self-weight consolidationgenerated a decrease in the height of tailings (H), which, in turn,reduced the excess pore-water pressure at 0.1 m [ue 5 g9ðH2 0:1Þ]and 0.2 m [ue 5 g9ðH2 0:2Þ]. Theoretically, the part of the columnundergoing self-weight consolidation causes a change in the voidratio distribution, whereas the part of the column that has not begunself-weight consolidation remains at its initial void ratio. Conse-quently, in the present case, the ue in the uppermost part that had notbegun to consolidate was affected by the tailings-water interfacesettlement (H is decreasing), while the buoyant unit weight (g9)remained constant. Self-weight consolidation was complete after1,440 min (24 h) for all four tests.

Variations above and below the average dissipation curves inFig. 4 may be due to slight differences in initial experimentalconditions, such as initial height or initial water content, or slightvariations in grain size or mineralogy. Those may have influenceddissipation of ue because they can affect the hydraulic conductivityor the specific gravity of the samples.

Fig. 5 presents the elevation versus average ue at the sameelevations (bottom, 0.1 m, and 0.2 m). The theoretical maximumue developed in the beginning of self-weight consolidation (2.29kPa) is represented by an arrow and was calculated using the meaninitial density (r0) and the mean initial height, both presented inTable 2. This estimated value is quite close to the highest average ue

at 0 m (∼2:24 kPa shown in Fig. 4). At the beginning of the test(1-min reading), dissipation of ue was only observed at the bottom.As the test progressed, dissipation of ue moved from the initial tri-angular ue distribution, particularly near the bottom of the sample.As long as the self-weight consolidation had not reached a specificelevation, dissipation curves above this elevation were nearlyparallel to the initial ue distribution curve, which is represented bythe Due portions at 0.1 and 0.2 m in Fig. 4. This typical pattern isassociated with self-weight consolidation in settling columns withan impervious base, and shows that the process started from thebottom up (Sills 1997; Masutti 2001). For instance, the 600-minprofile shows that the process of self-weight consolidation already

Fig. 4. Evolution of average dissipation of excess pore-water pressure with time and SDs for the four tests performed in the 300-mm-high settlingcolumn; Due is the diminution in excess pore-water pressure caused by the reduction in tailings height above the measuring points at 0.1 and 0.2 m

Fig. 5.Elevation versus average excess pore-water pressure for the fourtests performed in the 300-mm-high settling column

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reached 0.2 m because the profile comprised between 0.1 and 0.2 mfollowed a steeper slope than the initial distribution.

Self-Weight and Primary Consolidation Tests

The authors performed five tests using the consolidometer to eval-uate the e-sv9 relationship under a low effective stress range. Table 3summarizes the main characteristics of samples C1–C5. In the be-ginning of each test, the samples had a similar initial height (H0),therefore the same water-pressure conditions. The initial void ratios(e0) of the five experiments were approximately 1.3, whereas initialdensities (r0)were similar to those of the settling column experiments.

Fig. 6 presents the compressibility curves in terms of averagevoid ratio versus vertical effective stress obtained in the con-solidometer (lower stress range) and in the 1D consolidation ap-paratus (higher stress range). The load range of the consolidometerwas between 0.06 and 8.80 kPa. The results followed a rather similartrend for all tests with a slight scatter in void ratios, which decreasedwith the increase in vertical effective stress. Furthermore, the 1Dconsolidation cell was used for loads between 1.5 and 1,500kPa. Theprimary consolidation in the consolidometer experiments started atinitial void ratios varying between 1.11 and 1.19, whereas the initialvoid ratios in the 1D consolidation cell varied between 0.78 and 0.83to avoid self-weight consolidation prior to load application. The 1Dconsolidation results have shown that lower initial void ratios resultin lower final void ratios for the same effective stress (Aubertin et al.1996;Aydilek et al. 2000). Finally, the overlap zone between 1.5 and

8.8 kPamade possible two explanations related to the slight variationin compression indexes (Cc) obtained from both tests. First, lowerinitial void ratios imply a stiffening of the material, hence lower Cc.Secondly, in most soft soils such as TT, the e-sv9 relationship at loweffective stresses greatly depends on the initial void ratio and is notunique (Imai 1981; Been and Sills 1981).

Fig. 6 shows more scattering in the results from the consol-idometer than those from the 1D consolidation tests and there is oneorder of magnitude between the SDs obtained in the two types oftests. The slight variation inCc observed in thefive tests performed inthe consolidometer possibly relates to the accuracy of the adoptedexperimental method. Moreover, the void ratio during self-weightconsolidation was nonuniform over the entire depth. As Liu (1990)reported, the use of an average value over the whole sample (aswas the case with the 1D consolidation tests) can raise concerns. Toovercome these limitations, other apparatuses or methods might berecommended to obtain the e-sv9 relationship at low effective stresses,i.e., the hydraulic consolidation test (Abu-Hejleh et al. 1996; Foxand Baxter 1997) or actual densitymeasurements with nondestructivereadings using X-ray or g-ray, during self-weight consolidation (Beenand Sills 1981; Alexis et al. 2004; Bartholomeeusen et al. 2002;Pedroni 2011; Masutti 2001).

Fig. 7 shows that a compressibility relationship (e-sv9) for lowvertical effective stresseswas found from the consolidometer results.The latter is comprised between the estimated vertical effectivestress at a void ratio of 1.3 and the theoretical vertical effective stressreached in the 300-mm-high settling column. The e-sv9 relationship

Table 3. Summary of Experimental Results from the Consolidometer

Test H0 (m)Initial

void ratio, e0 r0 (kg=m3)

Mass of tailingsdeposited (g) Hf (m)

Verticalstrain (%)

Height ofsupernatant water (m)

Dry solidsmass (g)

Void ratioat 0.06 kPa

C1 0.094 1.28 1,711.2 1,295.63 0.085 9.7 0.009 862.40 1.13C2 0.097 1.27 1,702.7 1,330.58 0.087 10.4 0.01 900.53 1.14C3 0.096 1.30 1,715.8 1,326.85 0.087 9.4 0.009 899.94 1.13C4 0.086 1.29 1,704.4 1,180.07 0.077 10.5 0.009 800.61 1.11C5 0.085 1.30 1,684.8 1,152.85 0.078 8.3 0.01 782.72 1.20

Fig. 6. Compressibility (average void ratio versus vertical effective stress) of experiments in consolidometer apparatus and one-dimensional (1D)consolidation cell

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was estimated bymeans of a power lawof the form e5As9B (Carrieret al. 1983; McVay et al. 1986; Aydilek et al. 2000; Somogyi 1980;Huerta and Rodriguez 1992; Stone et al. 1994). The power law wasfitted by regression analysis using the average void ratio at each stress.The authors used this relationship as a preliminary fit to reproduce theself-weight consolidation behavior in a CS2 simulation.

Reproduction of Experimental Self-WeightConsolidation

In addition to the best-fit compressibility relationship obtained inFig. 7, a hydraulic conductivity versus void ratio relationship wasobtained from falling head permeability tests performed in the 1Dconsolidation cell (Fig. 8). To prevent seepage-induced consoli-dation, hydraulic conductivity measurements were not performed atvoid ratios greater than e5 0:7. The available experimental valueshad to be used as a preliminary fit of the k-e relationship despite thefact that the range of void ratios observed in the 300-mm-highsettling column was 1.0 to 1.3. Best-fit regression of the experimen-tal results by means of a power law (k5CeD) is generally reportedto represent the k-e relationship for soft soils (Jeeravipoolvarn et al.2009a; Pane and Schiffman 1997; Gjerapic and Znidarcic 2007).Thus, the following hydraulic conductivity relationshipwas estimatedfrom a best-fit regression analysis: [kðm=sÞ5 2:13 1027e3:29].

Both best-fit relationships obtained by regression analysis (e-sv9and k-e) were used in thefirst CS2 preliminary fit, which showed thatin terms of final void ratio distribution, CS2 reproduced the ex-perimental results quite well. However, the reproduction over-estimated the time of dissipation of ue. The dissipation of ue at 0 mthat was obtained from the preliminary fit is represented by a grayline in Fig. 9. Subsequently, the constitutive parameters (A,B,C, andD) were optimized to determine the relationships giving the bestreproduction of the experimental ue response, the tailings-waterinterface settlement, and the final void ratio distribution.

Suthaker and Scott (1994) and Bharat and Sharma (2011) notedthat parameters A and B seem to have little influence on the tailings-water interface response, but their influence on the final void ratiodistribution is important. On the other hand, parameter D consid-erably affects both the settlement response and the final void ratiodistribution. Suthaker and Scott (1994) also reported that the changein the compressibility characteristics (A and B) does not affect the

short-term prediction of ue, whereas the long-term prediction isslightly affected. They also reported that the variation of parameterDhas considerable effects on the ue response.

The parameters retained from this optimization process includingthe constitutive relationships are presented in Figs. 7, 8, and 10. Theretained C parameter implies a higher hydraulic conductivity thusa faster dissipation of ue. This could be a consequence of channeling.Indeed,Namet al. (2008) denoted that channeling enhancesdissipationof ue during sedimentation and self-weight consolidation. Both re-tained constitutive relationships used 51 discrete data points in CS2.The self-weight consolidation was modeled with a 0.3-m-high samplesubdivided in 50 vertical elements (Rj 5 50). An initial vertical ef-fective stress (q0) of 0.0083 kPa and an initial hydraulic conductivity(kqo) of 8:113 1027 m=s were derived from the retained constitutiverelationships for the homogeneous initial void ratio of 1.29. The topboundary was considered drained whereas the bottom boundary wasconsidered undrained. The water was maintained at a constant ele-vation, which was equal to the initial height (0.3 m).

Fig. 9 presents the evolution of uewith time at the three elevationscorresponding to the positions of the pressure transmitters. TheCS2 model accurately reproduces the immediate startup of the ue

Fig. 7. Compressibility (average void ratio versus vertical effective stress) from the five experiments in the consolidometer apparatus

Fig. 8. Hydraulic conductivity relationships

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dissipation at the bottom. At 0.1 and 0.2 m above the bottom, CS2quite accurately reproduces the pseudolinear decrease in ue beforethe start of the self-weight consolidation (change in slope). Forinstance, at 0.1 m, CS2 predicts the start of the self-weight con-solidation after approximately 200 min. The slope of the pseudo-linear portions of the experimental curves is slightly steeper, whichmay be attributed to several factors: superficial sedimentation,channeling effects, a nonunique experimental compressibility rela-tionship (Been and Sills 1981; Hawlader et al. 2008), or discrepancybetween constitutive relationships and the self-weight consolidationbehavior. The end of self-weight consolidation at 1,440 min is alsoclosely reproduced by CS2.

The reproduction of the experimental results proved to be suc-cessful, as confirmed by the evolution of the ue with elevation(Fig. 10). The theoretical experimental maximum ue is indicatedby an arrow (max ue 5 2:29 kPa). The ue profiles are calculated byCS2 using the density, pore-water pressure conditions, and elevationat each element of the discretized geometry. The 1-min profiledetermined by CS2 indicates that the model had not begun to

consolidate under its own weight at this time given that the cal-culated ue is 2.24 kPa at 0 m (the experimental value was 2.21 kPa)and the ue profile was linear throughout the column. The reproducedintercept with the y-axis after 1 min is 0.3 m, which was the averageinitial height of the samples. From50min onward, the curved ends ofthe ue profiles indicated the portion of the column that had begun toconsolidate under its own weight. Based on the profiles determinedby CS2, self-weight consolidation had been initiated for a height ofapproximately 0.06 m at 100 min, and after 300 min it had reached0.12 m above the bottom. Moreover, the intercept with the y-axiswent down as the tailings-water interface settled because of self-weight consolidation at lower depths. It is alsoworth noting that CS2has the capacity to reflect the fact that dissipation of ue by self-weightconsolidation at the bottom affects the ue at the top as observed byexperimental results.

Fig. 11 shows the profiles of void ratio fromCS2 at several times.The CS2 profiles were obtained from the retained relationships,whereas the 3,000-min profile (in gray) was obtained from thepreliminary fit. At 1,440 min, the CS2 profile reproduces closely the

Fig. 9. Evolution of average dissipation of ue with time in the 300-mm-high column; experimental results and values reproduced by CS2 with theretained relationship (black lines) and the preliminary fit at 0 m (gray line)

Fig. 10. Profile of elevation versus ue in the 300-mm-high settlingcolumn; experimental results and values reproduced by CS2 withretained relationships

Fig. 11. Profile of elevation versus void ratio from CS2 and experi-mental void ratios at top (eft) and bottom (efb) from the 300-mm-highsettling column at the end of self-weight consolidation

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experimental values at the top (eft) and bottom (efb). The predictedvertical strain of the tailings-water interface was 11.0%, whereas theexperimental value was 11.7% in the 300-mm-high settling column.Moreover, as with the excess pore-water pressure profiles, it ispossible to identify which part of the column undergoes self-weightconsolidation from the void ratio profiles. The 1-min profile indi-cates that self-weight consolidation had not yet begun and the wholecolumn remained at its initial void ratio of 1.29. The latter is lowerthan critical void ratios reported in the technical literature for siltymaterials (de Oliveira-Filho and van Zyl 2006; Bartholomeeusenet al. 2002). Furthermore, at 200 min, the CS2 profile moved fromthe initial void ratio between the bottom and 0.1 m, which indicatesthat the self-weight consolidation had reached this elevation.

Conclusion

The study used a 300-mm-high settling column to assess the self-weight consolidation behavior of TT deposited to 68% of solids.An accurate monitoring of total pore-water pressure showed thatself-weight consolidation finishes after 24 h at 68% solids andconfirmed that a TT sample would undergo mainly self-weightconsolidation. The void ratio corresponding to this initial solidscontent is well below the critical void ratios reported by de Oliveira-Filho and van Zyl (2006) and Bartholomeeusen et al. (2002) forsilty materials. The sedimentation phase seems to be inhibited bythe proximity of solid particles that can rapidly transmit their ownweight to a soil structure supported at the bottom of the column anddissipate ue. The main ue decrease occurs by self-weight consoli-dation from the bottom and proceeds upward, whereas a minor uediminution is observed in the uppermost part of the column. TheCS2simulations support that this minor dissipation seems to resultmainly from settlement of the slurry height caused by self-weightconsolidation and not because of potential sedimentation.

TheCS2model proved quite capable of reproducing the behaviorof TT under self-weight consolidation, be it the ue dissipation, thefinal settlement, or the final void ratio distribution. This tends toconfirm that the sole mechanism (or the main one) influencingsettlement of TT initially deposited at 68% solids is probably self-weight consolidation. It is believed that CS2 would not have ade-quately reproduced the experimental behavior of the same materialdeposited at an initial void ratio higher than its critical void ratio. Infact, the prediction of the sedimentation combined with self-weightconsolidation should lead to different profiles of ue, as shown byBürger and Concha (1998). Sills (1998) and Masutti (2001) pre-sented such experimental ue profiles of soils deposited below theirstructural density.

The reproduction of the self-weight consolidation behavior in the300-mm-high settling columnproved to be reliable using the 1DmodelCS2 and the calibrated constitutive relationships. The transposition ofthis model to a larger scale should be conducted with caution given thenature of the constitutive relationships, which might not represent thebehavior at higher effective stresses (Carrier et al. 1983) and the 1Dformulation. A better understanding of self-weight consolidation helpsto identify processes involved in TT settlement. This is relevant to themining industry to estimate the storage capacity of tailings disposalareas, to evaluate the freeboard of confining structures, and to analyzethe density distribution throughout the tailings deposit.

Acknowledgments

The authors thank geotechnical technicians Jean-Guy Lemelin andValérie Dumoulin for their technical support. Funding for thisresearch was provided by the National Sciences and Engineering

Research Council (NSERC), the Fond Québécois pour la RechercheNature et Technologies (FQRNT), and Golder Associés Ltée., througha BMP-Innovation Scholarship.

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