Settlement prediction model of slurry suspension based on sedimentation rate attenuation

Water Science and Engineering, 2012. 5(1): 79-92doi:0882./.issn.1674-2370.2012.01.008http://www. waterjournal.cne-mail: wse2008@vip.163.comSettlement prediction model of slurry suspension based onsedimentation rate attenuationShuai-jie GUO*1l,2, Fu-hai ZHANG, Bao-tian WANGI',, Chao ZHANGI. Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering,Hohai University, Nanjing 210098, P. R. China2. Institute of Geotechnical Engineering, Hohai University, Nanjing 210098, P R. China3. Bureau of Hydrology, Changjiang Water Resources Commission, Wuhan 430012, P. R. ChinaAbstract: This paper introduces a slury suspension sttlement prediction model for cohesivesediment in a still water environment. With no sediment input and a still water environmentcondition, control forces between settling particles are significantly different in the process ofsedimentation rate attenuation, and the settlement process includes the free sedimentation stage,the log-linear attenuation stage, and the stable consolidation stage according to sedimentation rateattenuation. Setlement equations for sedimentation height and time were established based onsedimentation rate attenuation properties of different sedimentation stages. Finally, a slurrysuspension setlement prediction model based on slurry parameters was set up with a foundationbeing that the model parameters were determined by the basic parameters of slurry. The results ofhe settlement prediction model show good agreement with those of the settlement columnexperiment and reflect the main characteristics of cohesive sediment. The model can be applied tothe prediction of cohesive soil settlement in still water environments.Key words: cohesive sediment; sedimentation rate attenuation; slurry suspension; sttlementprediction model; settlement column experiment1 IntroductionSolid particles of slurry suspension in still water environments settle freely under gravity,forming a high-void ratio, high-water content, and high- compressibility soil (Yang and Zhang1997). The existence of a large amount of soil will cause serious bydraulic problems, such asriver and port deposition and dredging problems. The estuary and bay areas can be regarded asthe natural still water environment, which is favorable for the deposition of silt soil (Shi2004; Tsuneo et al. 2009). Pollutant enrichment in silt soil will also lead to seriousenvironmental problems. Therefore, research on the hydrostatic settlement process of solidparticles is urgently needed in bydraulic projects for flood control, dredging, andenvironmental protection.中国煤化工This work was supported by the Research Funds for the Cent.MHC N M H G9B13514) and theDoctoral Fund of the Ministry of Education of China (Grant No. 20100094110002).*Corresponding author (e-mail: 8sj@hhu.edu.cn)Received Feb.14, 2011; accepted Dec.28, 2011Sediment deposition in still water is classified as non-cohesive and cobesive settlementsaccording to the content of fine particles (Fei 1992). Interactions between particles are ignoredin non-cohesive settlement, and the settlement of particle obeys Stokes' law (Winterwerp 1998;Yang et al. 2003a). Due to the development of flocculation and influence of particle weight,different sedimentation stages can be defined in cohesive settlement, and the settlementprocess can be found by investigating the variation of interface. For the first stage, interactionscan be ignored as the particle settlement following Stokes' law due to the large distancebetween particles. When the particle distance reaches a certain limit, Stokes' law will not beapplicable due to the development of electrostatic forces and flocculation, which means thatflocculation needs to be introduced (Zhu et al. 2009; Yang et al. 2003b; Lin et al. 2007).Microstructure formation of flocs is subject to the law of fractal growth (Zhu et al. 2009; Maand Pierre 1998; Pierre and Ma 1999), and the attenuation of the interface sedimentation rateis log-linear. With the particle distance decreasing and effective stress coming into being, theconsolidation of soil begins (Xie and Leo 2004) and the sedimentation rate finally attenuatesto zero. .Numerous scholars have studied the sedimentation rate formula. Li et al. (2006)summarized current research on the interface sedimentation rate formula and concluded thatthe modified sedimentation rate formula for single particles and infiltration theory formula aretwo most meaningful ways. Li and Yang (2006) obtained fractal dimension values of flocsfrom microstructure pictures through laser scanning. Zhang and Xiong (1991) studied thesettlement and resistance characteristics of single particles with plastic sands of standard size.Yang et al. (2003a, 2003b) studied the influences of fine particle flocculation on the interfacesedimentation rate and provided a modified formula. Han (1997) conducted research on thedistribution of dry bulk density of soil along the sedimentation direction to predict the finalsedimentation height. Cook et al. (2004) developed a direct simulation equipment to test thesettlement characteristics of partial-fluid systems. Fox et al. (2005) and Fox (2007) researchedthe characteristics of mud soil based on the large strain consolidation theory and carried outmany experiments with a centrifuge.The research mentioned above mainly focuses on the initial free sedimentation stage orsome indicators of consolidation rather than the entire settlement process. Slurry settlement,from non-Newtonian fluid status to steady consolidation status, is a complete process.Therefore, it is necessary to determine the sedimentation rate attenuation of the wholesettlement process. Different sedimentation rate attenuation equations were established for thecorresponding sedimentation stages in this study. The time-integrated sedimentation rateequations are the control equations for the sedimentation stages, and the equation parametersare determined by the sedimentation rate attenuation parameters and the physical properties ofslurry. The study of Merckelbach (2000) shows that there are some. relationships between中国煤化工，sedimentation rate attenuation parameters and the inilnent predictionTYHCNMHG8Shuaijie GUO et al. Water Science and Engineeing, Mar. 2012, Vol. 5, No.1, 79-92model was built up based on basic soil parameters and the attenuation parameters of thesettlement process of slurry with a reference concentration.2 Settlement column experimentThe main experimental device was a 1 000 mm-high and 130 mm-inner diameterplexiglass (PMMA) settlement column (Merckelbach 2000; Liu and Wang 2006). Two rulerswere set outside to record the sedimentation height. The settlement column is shown in Fig. 1.-Paper ruler. SlurySlury(a) Plexiglass stlement column(b) Slury sttement processFig. 1 Settlement column experiment2.1 Sedimentation soil materialsThe sedimentation soil came from the deposited soil, which is 20 cm under the waterbottom, in the Shenzhen River and Bay, and the mixing water was from the upper river or sea.There were 40 soil groups in all, and three types of slurry with initial concentrations of100g/L, 50 g/L, and 20 g/L，respectively, were prepared for each group in settlementexperiments. The slury concentration was defined as the soil particle weight per unit slurryvolume. One group of soil was chosen as the reference soil, and the rest were used as fitteddata to determine the equation parameters. The soil specific gravity (G,), liquid limit (a),plastic limit ( ap ), plasticity index (Ip ), and water specific gravity (Gw ) of the reference soilwere, respectively, 2.73, 50.5%, 21.7%, 28, and 1.024, and the contents of the reference soilwith grain sizes of less than 0.001 mm, 0.002 mm, 0.004 mm, 0.01 mm, and 0.02 mm were14.2%, 28.7%, 49.2%, 79.8%, and 100%, respectively. According to the physical propertiesand the classification in the plasticity chart of soil, the reference soil can be defined as the highliquid-limit clay.2.2 Sedimentation curves of reference soilThe initial sedimentation height was defined as the slurry height at the beginning of thesettlement experiment. According to the settlement column experiment, relationships betweensedimentation height and time can be expressed in na中国煤化Ile logarithmiccoordinates (Fig. 2).MYHCNMHGShuai-jie GUO et al. Water Science and Engineering, Mar. 2012, Vol.5, No.1, 79-9281The reference soil sedimentation curves in natural coordinates (Fig. 2(a)) have linearrelationships in the beginning. But because of the limitations of the natural coordinate scale,the log -linear attenuation and consolidation stage cannot be expressed properly. In doublelogarithmic coordinates, sedimentation curves can be expressed as in Fig. 2(b), ftom whichthree sedimentation stages can be defined, and the sedimentation attenuation stage is shown tohave significant linear characteristics.一20g/L --- 50 g/L---- 100gL1.0 [10宜101“0.4102 ，0~40210306 101(10+5)1(5)(a) Natural coordinates(b) Double loganihmic codinatesFig. 2 Slurry sedimentation curves of reference soil with different concentrations in different coordinates2.3 Sedimentation rate attenuation curvesAccording to the relationship between sedimentation height and time, settlementequations of different stages can be determined, and sedimentation rate attenuation curves canbe obtained through the time differential method. The sedimentation rate is witten as (Liu andWang 2006)Shh-h，(1)4-1-1where v; is the sedimentation rate at time 1，Nh is the difference of sedimentation heightat different times, Ot is the time interval, and h is the sedimentation height at time t.，The sedimentation rates at different times can be evaluated and determined by Eq. (1), sothe sedimentation rate attenuation curves responding to sedimentation height and time can beobtained in different coordinate systems (Fig. 3).2.4 Discussion of sedimentation rate attenuation curves(1) Sedimentation rate curve characteristics: Figs. 3(a) and (b) are the sedimentation rateattenuation curves responding to sedimentation height and time. The initial section in Fig. 3(b)is almost horizontal, which means that the sedimentation rate remains constant in the freesedimentation stage, and the constant values are associated with the initial concentration ofslurry. When the sedimentation height reaches a certa中国煤化工rate atenuatessignificantly. Fig. 3(c) shows that the sedimentat:TYTHCNMHGe lgnithmic82Shuai-jie GUO et al. Water Science and Engineering, Mar. 2012, Vol. 5, No. 1, 79-92coordinates are two attached lines including the initial horizontal part and the subsequentlog-linear part. The connection of the two parts is the tuming limit.一20g/L---- 50gL---- 100 g/L1.5 [1.0rh.0.50.0.6 0.8 1.0()Atenuation curves with height10-2 r1.60.2.10-10-* t.8 t号10*1021010+0203104105106(s)!(s)(b) Attcouation curves with logrihmic time(C) Logarithmic ateuationo curves wit logarithmic timeFig. 3 Sedimentation rate atenuation curves with sedimentation height and time(2) Relationships between sedimentation curves and control forces: Particle gravity is thecontrol force in the free sedimentation stage, and the sedimentation rate remains constantwhen gravity equals the resistance effect. When the sedimentation height reaches a certainlimit, flocculation will be fully developed. Therefore, equilibrium will be destroyed, and theresistance effect grows more significant, so the sedimentation rate continues to attenuate.Flocs are three -dimensional in microstructure and subject to fractal structure in micro-growth,so sedimentation rate attenuation relationships are double log-linear. Effective stresses beginto develop with the contact of particles, which means that the deposited soil reaches a finalstable consolidation stage under gravity, and the sedimentation rate is almost zero.(3) Fitting of sedimentation rate curves: Sedimentation rate curves in Fig. 3(c) areobviously piecewise linear. The settlement equation and equation parameters can be obtainedby the ftting of the initial linear and subsequent log-linear parts.3 Process of establishing settlement equation3.1 Definition of sedimentation stagesFrom the sedimentation curves in Fig. 2 and中国煤化工tion curves inYHCNMHGShuai-jie GUO et al. Water Science and Engineeing. Mar. 2012, Vol. 5, No. 1, 79-9283Fig. 3, it can be seen that there are different sedimentation stages throughout the process ofcohesive sedimentation. Therefore, the key is to determine the time limits. Three differentsedimentation stages, the free sedimentation stage, the sedimentation rate log-linearattenuation stage, and the consolidation stage, can be determined according to thesedimentation curves in Fig. 2.(1) Free sedimentation stage: The sedimentation curves of the free sedimentation stageare shown in Fig. 2(a). The main settlement materials of the stage are sandy particles and basicflocculation units. Particle states and structures are shown in Fig. 4(a). The sedimentation rateof large-size sandy particles is larger than others and follows Stokes' law of sedimentation rate,that is, the sedimentation rate remains proportional to the particle size. Sandy particles havelitle flocculation and concentrate at the bottom due to greater sedimentation rates. Thesedimentation rate in Fig. 3 is the settlement rate of the slurry interface formed by fineparticles except sandy particles. It is mainly determined by the sizes of fine particles and basicflocculation units and remains constant in the initial free sedimentation stage. Distancesbetween particles are greater than the interaction distance, so there are no significant forcesbetween particles. Flocculation occurs in the initial development state, and basic flocculationwith a simple structure is formed, as shown in Fig. 4(a). Sedimentation rates of fine sandyparticles and basic flocculation units determine the interface settlement rate. The end of thefree sedimentation stage is defined as the first time limit to. For the case t<1q, itis in thefree sedimentation stage and the sedimentation rate remains constant.8Basic foato 9c8。&Seand@ fine-OparucleS 0280Water888好(8s particle(a) Free sedimentation stage(b) Log-linear ateouation stage(C) Consohdation stageFig. 4 Particle state and stucture in dfferent sedimentation stages(2) Log-linear attenuation stage: With ongoing settlement, distances between singleparticles and basic flocculation units get smaller, leading to full flocculation development.Flocs with a large size are formed at this time, and connections between flocs appear, asshown in Fig. 4(b). With the formation and connections of large amounts of flocs, integratedflocs with loose structures come into being: this is the second log-linear stage. Many studies(Yang et al. 2003b) have sbown that cohesive sediment aggregates or flocs exhibit fractalproperties and form greater flocs with a constant fractal dimension. This is why thesedimentation rate maintains log-linear attenuation. Due to the loose structure of the formedflocs, there is no effective stress. When the distances between particles come to a limit, theeffective stress begins to appear, and this time bound中国煤化工ation stage is ,fYHCNMHGShuaijile GUO et al. Water Science and Engineering. Mar. 2012, Vol. 5, No.1, 79-92definedas 1.(3) Consolidation stage: With the slurry interface decreasing, the average void ratio of thecohesive sediment decreases to about 12.0, the effective stress passing in the network forms,and the slurry develops into consolidation, as shown in Fig. 4(c). In the consolidation process,the excessive pore water pressure is dissipated and the effective stress begins to work, and theapplicable stlement theory applied here is the consolidation theory. The consolidation stageis very slow, and the sedimentation rate is almost zero. When the excessive pore pressure istotally dissipated, the consolidation stage is over. The sedimentation curves of theconsolidation stage are shown in Fig. 5.0.5. 20 g/L.4---- 50 gL100 g/)3 t)2 t.1 A1(10°s)Fig. 5 Sedimentation curves of consolidation stage3.2 Settlement equations of different stages(1) Free sedimentation equation: The sedimentation rate remains constant in the initialfree sedimentation stage, and the relationship between the sedimentation rate v and thesedimentation height h is as follows:v= - dh/dt(2)The initial free sedimentation governing equation (Eq. (3)) can be obtained by integration oftin Eq. (2) from 0 to I as follows: .h= [xd=h-vt(3)where h is the initial sedimentation height, and v。 is the constant free sedimentation rate.(2) Log-linear sedimentation equation: There are apparent log-linear parts on thesedimentation rate attenuation curves in Fig. 3(c). The log-linear equation of the sedimentationrate can be established by ftting the linear parts. The log-linear equation isIgv= Rlgt+b(4)where R and b are the log-linear parameters.The log linear governing equation can be found by integration oftfrom 1o to t:10*h()=p ;(5*-rR+)+C(5)中国煤化工Substituting Eq. (3) into Eq. (5) yields the constant (-cal derivation:FHCNMHGShualjie GUO et al. Water Science and Engineering, Mar. 2012, Vol. 5, No.1, 79-9285c=万-v。o :(6)Subtuting Eq. (6) into Eq. (5) yields the final log-linear sedimentation equation:h=-10°(t8+-1t*t)+h% -v%(7)R+1(3) Consolidation sedimentation equation: The sedimentation rate is almost zero, so it isnot accurate by integrating the sedimentation rate to establish the sedimentation equation. Theconsolidation sedimentation equation can be built according to the characteristics ofconsolidation curves. Consolidation curves can be modified by hyperbolas, and the twovariables are the sedimentation height and the time increment. The consolidationsedimentation equation ish-h=-(8)p(t-4)+qwhere h is the solid height; and p and q are the hyperbolic parameters, which can be givenand determined from the consolidation sedimentation curves in Fig. 5.After the sedimentation equations of the three stages are determined, the subsequent keyis the determination of the equation parameters. Sedimentation equation parameters includethe sedimentation rate of the initial free stage v。 , the fluid-limit time to , the solid-limit time4, the log-linear parameters R and b, and the hyperbolic parameters p and q. These sevenindependent parameters can be determined by the stlement column test, physical propertiesof soil, and initial concentration. After the determination of these parameters, a wholesettlement prediction model will be set up based on soil properties.3.3 Determination of sedimentation equation parameters(1) Determination of fuid height and solid height: The interaction force between particleskeeps developing with the decrease of particle distance, so there are certain relationshipsbetween the sedimentation height, interaction degree, and void ratio. Monte and Krizek (1976)first introduced the concept of fluid limit, which means that the shear stress is zero. In thissituation, it is reasonable to define the fluid moisture content and fluid void ratio. With theconcept of the fluid void ratio, the corresponding fluid height can be defined, i.e., theconnection point of the free sedimentation stage and log-linear attenuation stage. Carrier (1983)proposed that there are constant multiple relationships between the initial void ratio andliquid-limit void ratio. The initial void ratio of different soil has been shown to be from 9 to 30through many different experiments, and the relationship between the initial void ratio andliquid limit void ratio ise,=7e_ =7G,a(9)where e is the initial void ratio, and e is the liquid-limit void ratio.Similarly, the solid void ratio concept can also be proposed for the log- linear atenuationstage and consolidation stage. If e(t)>e, where e(i中国煤化工t, there are nocontacts between particles, and the electrostatic force:YHCN M H G e(1)qwhere the fluid-limit time 6, solid-limit time 4, fluid height ha, and solid height ha areexpressed as[r6=(h-ha)/v。J4 =[&H -(ha -ha )(R。+1)10 ]研(22)ha = (ea +1)nh/(G,pw)ha =(ea +1)n0/(G,pw)The log-linear attenuation parameters of the sedimentation rate can be determined byEqs. (16) and (17). The goveming equation parameters can be obtained by soil properties,which means that the settlement process can be predicted beforehand.4.2 Prediction model performanceIn order to verify the reliability and accuracy of the prediction model, reference soilproperties were taken as the model input, and the settlement process was verified withdifferent concentrations. The model parameters with different concentrations are listed inTable 1, where C' is the concentration.中国煤化工MHCNMHGShuaijie GUO et al. Water Science and Engineeing. Mar. 2012, Vol. 5, No. 1, 79-9289Table 1 Model parameters of objective concentrationLog-linear parameters Consolidation parametersC'(g/L) av。(mm/d) ho (m) h。 (m)to(s)1 (s)RbPala200.100600.1570.049681321 826 -1.8849 5.561 7200160978303 866.2010.07016727375196 -1.64884.731 9334887 7664025500.2410.09124027742259 -1.49954.150 10011 083 23620390.2770.11028 522830946 -1.3930 3.701 7B012 6907560 0.17800.3100.12931 045925893 -1.3117 3.33695714450166800.81 5290.3720.16732 6591 280 360-1.19292.76345021 320556101.14120.4280.20331 9291937133 -1.1082 2.320035042 2041201.213460.4810.23830124 3037233 -1.0435 1.9585360113743150121 2900.5540.290265325942000. -0.9694 1.5168 .134 499048After the determination of the model parameters and initial input in the govermingequations, slurry sedimentation prediction curves can be given based on the model output.Sedimentation curves with different concentrations are shown in Fig. 8. Prediction modeloutputs shown in Fig. 8 successfully reflect basic characteristics of the slurry suspensionsettlement process, compared with the settlement curves obtained from settlement columnexperiments described in Fig. 2. If applied to practical engineering, the sedimentation height atany time can be determined effectively. Thus, the settlement lasting time, consolidation degree,and sediment concentration can also be predicted and given reasonably.00 pE 101-20g/L十30g/L + 80g/L，←40g/L - 100g/L--- 50 g/一130 g/L60 g/L+ 150 g/1010210+061081(s)Fig. 8 Settlement prediction curves with different objective concentrationsThe reference concentration here is 100 g/L, and it is more accurate when the objectiveconcentration is close to the reference concentration, which can also be reflected in Fig. 3.Moreover, the model prediction results are sensitive to some model parameters, and there aremany limitations for the whole sedimentation stage simulation, especially for the turming point,so the determination of applicable model parameters needs to be improved in future research.Slurry suspension is fully mixed beforehand,中国煤化工e of randomYHCNMHG90Shuai-jie GUO et al. Water Science and Engineeing. Mar. 2012, Vol.5, No. 1, 79-92variability in the initial settlement process for the flocculation effect. As slurry sedimentationis very sensitive to the external disturbance factors, the prediction model developed in thisstudy merely simplifed some features rather than all the random factors.5 Conclusions(1) Three sedimentation stages, the initial free sedimentation stage, the log-linearattenuation stage, and the consolidation stage, of the whole slurry suspension settlementprocess were defined by the characteristics of sedimentation rate curves. Boundary indicatorswere expressed by the fluid void ratio and solid void ratio and the corresponding fluid heightand solid height. It was found that there are constant multiple relationships between the fluidvoid ratio, solid void ratio, and liquid-limit void ratio.(2) Stokes' law for the sedimentation rate of a single particle is applicable to sand soil butnot to cohesive sediment, and it is necessary to research the influences of flocculation on thesedimentation rate. The evaluation formula of the interface sedimentation rate also needs to bemore deeply discussed.(3) There are apparent segmentations on the double logarithmic sedimentation rate curves,and the settlement governing equations of the first two sedimentation stages were set byintegration of the sedimentation rate. Equation parameters were determined by the physicalproperties of soil, and then a settlement prediction model was built based on the physicalproperties of soil and parameters from setlement column experiments of the referenceconcentration.(4) The settlement prediction model shows a high degree of sensitivity to certain modelparameters, and some parameters need modification, which will affect the prediction results.Sensitive parameters, such as the slope and intercept of the logarithmic line, must bedetermined by a series of diferent settlement column experiments, in order to obtain the mostapplicable parameters. The settlement prediction model can give a reasonable outputof different objective concentrations, especially near the reference concentration.Improvements can be made on the selection of a reference concentration and the determinationof model parameters.ReferencesCarrier, W. D. 1983. Design capacity of slurred mineral waste ponds. Geotechnical Engineering, 109(65),1011-1019.Cook, B. K., Noble, D. R., and Williams, J. R. 2004. A direct simulation method for particle-fluid systems.Engineering Computations, 21(2-3), 151-168. [doi:10.1108/0264400410519721]Fei, X. J. 1992. Settling of particles in suspension: Two typical cases in calculation of the settling velocity ofnonuniform sediment. Journal of Sediment Research, (3), 11-19. (in Chinese)Fox, P. J., Lee, J, and Qiu, T. 2005. Model for large strain consolidation by centrifuge. Intermnational JournalofGeomechanics, 5(4), 267-275. [doi: 10.1061/(ASCE)532-3641(2005)5:4(267)1Fox, P. J. 2007. 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