A cement-based method for fixing sand in laboratory channels

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A cement-based method for fixing sand in laboratorychannelsMohsen Ebrahimi a & Ana Maria Ferreira da Silva aa Department of Civil Engineering , Queen's University , Kingston , Ontario , Canada , K7L3N6Published online: 18 Apr 2013.

To cite this article: Mohsen Ebrahimi & Ana Maria Ferreira da Silva (2013) A cement-based method for fixing sand inlaboratory channels, Journal of Hydraulic Research, 51:3, 306-316, DOI: 10.1080/00221686.2013.771129

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Journal of Hydraulic Research Vol. 51, No. 3 (2013), pp. 306316http://dx.doi.org/10.1080/00221686.2013.771129 2013 International Association for Hydro-Environment Engineering and Research

Research paper

A cement-based method for xing sand in laboratory channelsMOHSEN EBRAHIMI, PhD Candidate, Department of Civil Engineering, Queens University, Kingston, Ontario, Canada K7L 3N6.Email: [email protected]

ANA MARIA FERREIRA da SILVA (IAHR Member), Professor, Department of Civil Engineering, Queens University, Kingston,Ontario, Canada K7L 3N6.Email: [email protected] (author for correspondence)

ABSTRACTA method to x movable beds in river-related laboratory research or physical model studies is proposed and investigated. The motivation was todevelop a method that would: (1) not involve the use of harsh chemicals and (2) ensure that the granular roughness of the original movable bed wasmaintained. The method involves coating the surface with a mixture of sand and Portland cement. Laboratory tests were conducted to determine theamount of cement, and investigate the best method of application, eect on roughness, shear strength and durability. It is found that the method canbe used to x both at and deformed beds. The method is particularly eective for sands up to 1.1mm, when it is possible to ensure that the granularroughness of the xed bed is comparable to that of the movable bed by merely using in the coating mixture a coarser sand than the original one.

Keywords: Bed roughness; durability; xed bed; hardening; movable bed; sandcement mixture; shear strength

1 Introduction

To properly investigate the mechanics of formation and timedevelopment of a variety of river morphodynamics features, itis important to be able to fully characterize the structure of therelated ows at dierent instants of the process. In the labo-ratory, and given that measurements of the ow velocity eldare time-consuming, such studies require that the deformationof the movable boundary be impeded by xing the granularmaterial, i.e. require the freezing of the stream at given stagesof development. As pointed out by Kashyap et al. (2010), thisremains challenging, which explains why most studies to datewere largely restricted to the study of the equilibrium stage. Ascan be inferred from the considerations below, the problem iscompounded by the fact that few detailed reports of methods tox the bed can be found in the literature.

Almost invariably, the existing methods involve spraying dif-ferent chemical products and adhesives on the movable bed.The idea behind these methods is for the products to seep into the11.5 cm topmost layer of sediment, leading to bonding of thesediment grains in that layer, with minimal eect on grain rough-ness. Vanoni and Nomicos (1959) appear to have been the rst tobriey report such a technique. Theirmethod consists of spraying

onto the sand separate solutions of sodium aluminate and sodiumsilicate, followed by calcium chloride and nally a synthetic var-nish. Benson et al. (2001) developed and tested a simplied andmore durable version of theVanoni andNomicosmethod, involv-ing repeated spraying (up to 35 times) of separate solutions ofsodium silicate and sodium bicarbonate, and bypassing the useof varnish. The method was used to stabilize dunes formed by0.84mm sand in a straight channel, as well as the bed and banksof a meandering channel. After spraying the chemicals, the bedsurface looked similar to the original sand surface, in both appear-ance and texture, the eect on grain roughness being negligible.The xed boundaries withstood the action of continuous waterow for periods of 24 h or so. However, longer periods requiredrepairs and recoating. da Silva (1995) and da Silva et al. (2006)succeeded to x the 2.2mm sand forming the at initial bedof meandering channels by spraying a diluted varnish. Just likein Benson et al. (2001), this method led to the formation of a11.5 cm xed topmost sand layer, with the bed surface remain-ing unchanged in appearance. For this reason, da Silva (1995)assumed that the eect on granular skin roughness, if any, wouldbe minimal. Each channel was used for a period of 34 months,although not continuously, without any damage to the bed. Morerecent attempts by the second author to apply the same method

Revision received 26 March 2012/Open for discussion until 30 November 2013.

ISSN 0022-1686 print/ISSN 1814-2079 onlinehttp://www.tandfonline.com

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Journal of Hydraulic Research Vol. 51, No. 3 (2013) A cement-based method for xing sand 307

to 0.65mm sand were not successful. In this case, the varnishsolution failed to percolate deeply into the sand, adhering onlyto the grains in a top layer of 13 grain diameter thickness. Thisinvariably failed to maintain its integrity during testing, breakingat random locations because of water pressure from underneath.Khalil (1972) developed a method consisting of spraying a resin(urea-formaldehyde)-based solution followedby spraying a solu-tion of formic acid. The method was applied to a movable bedconsisting of a rippled pattern formed by 0.705mm sand. Theresulting xed bed can be viewed as permanent as it withstoodat least 2 years of hydraulic tests. By testing on at beds of 2.0and 0.7mm sands, Khalil found that the method does not changegrain roughness.

Testing over stabilized beds was also carried out by Best(1988), Whiting and Dietrich (1993), Blanckaert (2002) andTermini (2009). Best (1988) used two coats of urethane varnishspray followed by two coats of an acetone diluted epoxy resin tostabilize deformed beds of 0.49mm sand; Whiting and Dietrich(1993), followed by Termini (2009), impregnated dry sand withpaint to form the topmost (immobilized) layer of a 0.65mm atsand bed in a meandering channel; and Blanckaert (2002) usedspray paint to immobilize 1.62.2mm sand beds. Details on theapplication technique and durability of the hardened beds are notprovided in these works. To the best knowledge of the writers,the eect on granular roughness was not assessed.

Other approaches to produce a stabilized bed were adopted byTermini (2011), who coated the deformed surface of a meander-ing channelwith amixture of cement dust and paint, andKashyapet al. (2010), whose method employed a surcial layer of plasterof Paris coated by spar urethane. However, not enough details areprovided by Termini (2011) on the adopted hardening technique,while the testing presented in Kashyap et al. (2010) could notconclusively establishwhether or not themethod altered granularroughness.

The chemical products in the above methods need to beexpertly handled during application, as they carry health risksand can damage the walls of the laboratory channels. The chem-icals used in Khalils method, in particular, are highly poisonousand very acid. All methods are quite involved, and require somepreliminary work to nd the best spraying method, curing time,etc., especially as these may need to be adjusted for grain sizesdierent from those used by the original authors.

In the course of ongoing research on meandering at QueensUniversity, the need arose to measure ow velocity elds in ameandering stream with movable sand bed and banks (D50 =0.65mm), before any deformation would occur. The stream,having a trapezoidal cross-section (bank slope angle = 30; topwidth = 0.64m; bottom width = 0.48m), was formed inside anexisting meandering channel (0.8m wide; vertical side walls)that is described elsewhere (da Silva and El-Tahawy 2008). Thisproblem was used as an opportunity to explore an alternative tothe existing hardening methods that would not involve specialchemical products and also not change the grain roughness in anyappreciable way. The method proposed here consists of coating

the movable boundary with a mixture of sand and a small amountof Portland cement Type III (Type HE). This paper is intendedas a report of the results of the tests done to assess the viabilityof such a solution.

2 Granular roughness and shear strength of asandcement coat

2.1 General

As a rst step in this work, two series of experimental tests werecarried out in a small tilting ume to assess the extent to whicha coat of a sandcement mixture may alter the hydraulic condi-tions because of changes in granular roughness. The ume usedis 2m long, 0.13m wide and 0.08m deep, and has a maximumdischarge capacity of 2.5 l/s. The ume walls are made of plex-iglass, the bottom of aluminium. A tailgate is installed at thedownstream end of the ume to control the free surface slope. Inthe rst series of tests, movable sand beds were used. The resultswere then compared with those from the second series of testswhere the beds were xed.

2.2 Movable bed tests

In these tests, the bed was formed by a 2-cm-thick (compacted)layer of sand, with a at (scraped) bed surface. Four dier-ent silica sands, with D50 = 0.195, 0.65, 1.1 and 2.0mm, wereused. The sands were well sorted, with coecients of uniformityD60/D10 of 1.44, 2.07, 1.64 and 1.56, respectively. To avoiderosion at the ume entrance, the rst 10 cm of the bed at theupstream end of the ume consisted of a gravel layer. The bedslope was achieved by tilting the ume. A total of 12 tests werecarried out, with hydraulic conditions as summarized in Table 1.The test names start with a letter (A, B and C) or a number(1, 2 and 3), each designating a particular combination of owdepth h and slope S (e.g. 1 implies h = 2 cm and S = 1/567).This is followed by D0195, D065, D110 or D200, indicatingthe sand grain size, and the symbol M, denoting movablebed. Here, Q = measured ow rate, R = ow Reynolds number(= vh/, with v = Q/(Bh) being the average ow velocity and as uid kinematic viscosity), R = roughness Reynolds number(= vks/, with v = (gSRh)1/2 as shear velocity, where g andRh stand for acceleration due to gravity and hydraulic radius; ksas granular skin roughness) and Y /Ycr = relative ow intensity.In the latter, Y = mobility number (= v2/(sD), with as uiddensity, s as submerged specic weight of grains, D as typicalgrain size), and Ycr = value of Y at the critical stage of initiationof sediment transport. For the present purposes, , and s wereidentiedwith 1000 kg/m3, 106 m2/s and 16186.5N/m3, andDwith D50. As per Eq. (1.34) in Yalin and da Silva (2001), Ycr wasidentied with 0.061, 0.031, 0.038 and 0.044 for D50 = 0.195,0.65, 1.1 and 2.0mm, respectively. In this sub-section R couldbe initially evaluated by adopting ks = 2D50 (Kamphuis 1974,Yalin 1992). The length of development of the velocity prole,

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308 M. Ebrahimi and A.M. Ferreira da Silva Journal of Hydraulic Research Vol. 51, No. 3 (2013)

Table 1 Hydraulic conditions in movable bed tests (B = 0.13m)

Test D50 (mm) h (cm) S Q (l/s) R Ra Y /Ycr c ks (mm)b

A-D0195-M 0.195 1.0 1/567 0.230 1770 4.8 0.78 14.4 B-D0195-M 0.195 1.0 1/867 0.173 1330 3.9 0.51 13.4 C-D0195-M 0.195 2.0 1/867 0.537 4130 5.1 0.89 15.7 1-D065-M 0.65 2.0 1/567 0.532 4092 21.1 0.81 12.6 1.492-D065-M 0.65 3.0 1/567 0.967 7438 24.5 1.09 13.2 1.523-D065-M 0.65 2.0 1/369 0.645 4962 26.2 1.25 12.3 1.571-D110-M 1.10 2.0 1/567 0.489 3762 35.8 0.39 11.6 2.062-D110-M 1.10 3.0 1/567 0.930 7154 41.5 0.52 12.7 1.783-D110-M 1.10 2.0 1/369 0.589 4530 44.4 0.60 11.2 2.211-D200-M 2.00 2.0 1/567 0.410 3154 65.1 0.19 9.7 3.812-D200-M 2.00 3.0 1/567 0.760 5846 75.4 0.26 10.3 3.853-D200-M 2.00 2.0 1/369 0.501 3854 80.8 0.29 9.5 3.91

aCalculated by adopting ks = 2D50.bDetermined from Eq. (1).

Lent , at the upstream end of the ume was estimated fromEq. (2.95) in Yalin (1977). This yielded Lent = 0.2m for thetests with h = 1.0 cm; 0.26m Lent 0.35m for the tests withh = 2.0 cm, except for test C-D0195-M, where Lent = 0.49m;and 0.45m Lent 0.58m for the tests with h = 3.0 cm. Con-sidering this, for practical purposes the eective ume lengthwasdened as the central 1.2m of the ume. Local ow depths weremeasured with the aid of a point gauge (resolution 0.1mm)every 20 cm along the eective length. The ow rate was mea-sured volumetrically by deviating the water discharged by theume to a container, over a known period of time (usually 60 s,although time was reduced to 30 s for ow rates > 0.6 l/s).The container had a square base with an internal area of 0.36m2.The height of water in the container was measured with a pointgauge (resolution 0.1mm); time was measured with a digi-tal stopwatch (resolution 0.01 s). The estimated error in themeasurements of slope of the tilted ume (= bed slope) wasS 24%, with the smallest and largest errors corresponding tothe slopes 1/369 and 1/867, respectively. The error in the valuesof ow depth and ow rate was estimated on the basis of multiplemeasurements of these quantities. This yielded h 0.2mm, andan average absolute error of 1.8% for the measurements of Q,varying from 1% in tests 1-D065-M, 1-D110-M and 3-D200-Mto 3% in tests C-D0195-M and 2-D110-M. Further details on theexperimental set-up are given in Ebrahimi (2013).

The uniform ow was sub-critical in all tests, with the Froudenumber F = v/(gh)1/2 varying from 0.36 in tests 1- and 2-D200-M to 0.56 in tests A-D0195-M and 3-D065-M. In orderto impede the formation of bed forms, the values of ow depthand slope were selected so that, as much as possible, the result-ing values of bed shear stress would be smaller than the criticalbed shear stress. Y /Ycr < 1 was realized in all tests, except intests 2- and 3-D065-M. In these tests, but especially in test 3-D065-M, some sediment transport was noticeable. However,the bed remained at (no bed forms) throughout the tests. Toavoid any possible degradation of the bed that could aect the h-measurements, in test 3-D065-M, the sand exiting the ume was

manually re-inserted at the ume upstream end approximatelyevery 5min. This procedure was followed until the measure-ments of h had been accomplished. The amount of sand exitingthe ume in test 2-D065-M was minimal, so that feeding thissand at the entrance was deemed not necessary. It should beclear that achieving Y /Ycr < 1 restricts the values of slope andow depth that could be used and thus imposed limitations onthe ow conditions that could be produced. The condition Y /Ycrwas particularly restrictive in the case of the 0.195 and 0.65mmsands.Keeping this inmind, note that in the testswith the 0.65 and1.1mm sands the turbulent owwas invariably in the transitionalregime ( 5 R 70). In the tests with the 2.0mm sand, theconditions were rough turbulent in tests 2- and 3-D200-M, andvery nearly so in test 1-D200-M (R = 65). In the 0.195mmsand tests, the resulting values of R were rather small. In thiscase, a value of R > 2000 (where 2000 is the upper limit of thetransitional region between laminar and turbulent ows, Graf1998) was achieved only in test C-D0195-M. In the remainingtwo tests, but especially in test B-D0195-M (where R = 1330),the conditions may have been only transiently turbulent. As canbe inferred from the content of this paper, the results of these twotests nonetheless provide additional insight. Thus, they were notexcluded from the present analysis. Table 1 shows also the val-ues of the (dimensionless) Chzy resistance factor c, determinedfrom c = v/v, as well as the values of ks estimated from thefollowing relation (Schlichting 1955, Yalin 1977)

v

v= 2.5 ln

(0.368

Rhks

)+ Bs, (1)

where the roughness function Bs = (vks/) was expressedwith the aid of the following equation, due to Yalin and da Silva(2001),

Bs =[2.5 ln

(vks

)+ 5.5

]e0.0705[ln(vks/)]

2.55

+ 8.5{1 e0.0594[ln(vks/)]2.55}. (2)

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Table 2 Hydraulic conditions in xed bed tests (B = 0.13m)

Test h (cm) S Q (l/s) Q (%) c c(%) ks (mm) ks (%) R R

1-D065-F 2.0 1/567 0.619 16.4 14.6 16.4 0.74 50.2 4762 12.12-D065-F 3.0 1/567 1.170 21.0 15.9 21.0 0.60 60.7 9000 11.33-D065-F 2.0 1/369 0.826 28.1 15.7 28.1 0.48 69.7 6354 9.61-D110-F 2.0 1/567 0.564 15.3 13.3 15.3 1.17 43.3 4338 19.02-D110-F 3.0 1/567 1.089 17.1 14.8 17.1 0.89 50.0 8377 16.83-D110-F 2.0 1/369 0.724 22.9 13.8 22.9 0.97 56.2 5569 19.51-D200-F 2.0 1/567 0.518 26.3 12.2 26.3 1.66 56.5 3985 27.02-D200-F 3.0 1/567 0.984 29.5 13.4 29.5 1.41 63.3 7569 26.63-D200-F 2.0 1/369 0.676 34.9 12.9 34.9 1.30 66.8 5200 26.2A-D065-F 1.0 1/567 0.252 15.8 a 1938 a

B-D065-F 1.0 1/867 0.161 12.5 0.98 1238 9.7C-D065-F 2.0 1/867 0.509 14.9 0.66 3915 8.7A-D110-F 1.0 1/567 0.181 11.4 1.47 1392 18.0B-D110-F 1.0 1/867 0.144 11.2 1.62 1108 16.0C-D110-F 2.0 1/867 0.403 11.8 2.00 3100 26.41-D065-G 2.0 1/567 0.580 9.0 13.7 9.0 1.03 30.8 4462 16.82-D065-G 3.0 1/567 1.041 7.7 14.2 7.7 1.10 27.4 8008 20.83-D065-G 2.0 1/369 0.692 7.3 13.2 7.3 1.18 25.0 5323 23.81-D200-G 2.0 1/567 0.444 8.3 10.5 8.3 2.90 23.8 3415 47.32-D200-G 3.0 1/567 0.813 7.0 11.1 7.0 3.00 22.0 6254 56.63-D200-G 2.0 1/369 0.535 6.8 10.2 6.8 3.11 20.4 4115 62.9aNo value of ks could be found that would satisfy Eq. (1) (implying hydraulically smooth ow).

Here, v was determined from the measured ow rate, and v wasas dened earlier (= (gSRh)1/2). It follows that the values of vused to calculate ks were identical for tests carried out with thesame slope and ow depth, which, for the case of the tests inTable 1, means those tests having the same rst number 1, 2, 3.On the basis of the estimated errors in the measured values of Q,S and h, the error in values of ks was estimated as varying from12% in tests 3-D200-M to 16% in tests 3-D065-M, although intests 1-D200-M and 2-D110-M the estimated error (namely 18and 22%, respectively) was higher.

In the case of hydraulically smooth ows,Bs = 2.5 ln(vks/)+ 5.5, and Eq. (1) reduces to v/v = 2.5 ln[0.368(Rhv/)] +5.5, which does not depend on ks. Hence, ks can be revealed withthe aid of Eq. (1) only for transitional and rough turbulent ows.This explains why a value of ks could not be determined for testC-D0195-M (and also not for tests A- and B-D0195-M, even if,keeping in mind earlier comments on the values of R, these testswere to be treated as being in the hydraulically smooth regimeof the turbulent ow). For the remaining tests, the ratio of theresulting ks values to D50 was invariably close to 2 (the meanvalue of ks/D50 in Table 1 being 2.04, with a standard deviationof 0.24).

As indicated by Yalin (1977), the procedure used here toestimate ks is the simplest. However, it has the disadvantageof involving the whole cross-section, and thus the inuence ofside walls. Therefore, the procedure is associated with a certainamount of error (an intrinsic error, independent of any error inmeasurements). This error is, to some extent, mitigated throughthe use of Rh instead of h in the term h/ks in Eq. (1). The factthat the estimates of ks/D50 in the present tests were comparable

to the literature value of 2.0 suggests that the intrinsic error forthe reason mentioned above was relatively small. However, thematter is inconsequential in this paper, as the estimated values ofks are only intended for comparative purposes between movableand xed bed tests with identical side walls.

2.3 Fixed bed tests

The xed bed tests are summarized in Table 2. In the rst 15of these tests, with names ending with F, compacted and wetat sand beds were coated with sandcement mixtures. Eachmixture was prepared by mixing sand of a specic D50, cementand water in a concrete mixer: the cement/sand volume ratiowas 8%; the amount of water was 60% of the cement volume.Approximately 5mm of such mixture was then spread over theat sand bed, with the aid of a scraper. Finally, the ume wascovered with a plastic sheet and the mixture was cured for 7days, with water being sprayed once a day over the bed surface.After curing, the coating appeared as a hardened layer. In thefollowing, this coating surface will be termed hardened mortarmixture. The letters A, B and C and numbers 1, 2 and 3 in thetest names designate the same combinations of h and S as in themovable bed tests previously reported (see the rst paragraph ofSection 2.2). D065, D110 and D200 indicate the average grainsize of the sand in the sandcementmixture. Of these 15 tests, therst nine are the xed bed counterparts of the movable bed tests1-D065-M to 3-D200-M inTable 1. The next six tests (A-D065-Fto C-D110-F) are not intended as xed bed counterparts of any ofthe movable bed tests in Table 1; the reason to conduct these testswill become apparent later, in point 3. (As a side note, it should

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be mentioned that the cement/sand volume ratio was selectedafter examining sample mixtures of a 0.65mm sand and cement,prepared with cement/sand volume ratios of 4, 8 and 15%, anda water content of 60% of cement volume. After curing, the 4%samples were found to deform somewhat under the pressure ofa nger, while those with 8 and 15% not only withstood such apressure, but also resisted well dusting with a soft brush. Out ofthese two, the 8% cement/sand volume ratio was selected, as thesmaller the amount of cement, the smaller would be the eect ongrain roughness.)

The last six of the xed bed tests, with names ending with Gwere carried out merely for purposes of further comparison anddiscussion. In these tests, a layer of sand was glued to previouslyxed beds, after allowing them to dry. The adhesive Sikadure

330 two-component epoxy, with a pot life of 57min, was brushedon the surface, and sand was then sprinkled over it so as to ensurea full coverage by sand grains. Tests 1- to 3-D065-G were carriedout by gluing the 0.65mm sand; and tests 1- to 3-D200-G, bygluing the 2.0mm sand. These tests are to be viewed as xed bedcounterparts of the movable bed tests 1- to 3-D065-M and 1- to3-D200-M.

In addition to the measured values of Q, and the values of cand ks (determined as described in Section 2.2), Table 2 showsalso, as Q, c and ks, the relative dierence (in %) between Q,c and ks in the xed bed tests and the equivalent movable bedtests. No values of Q, c and ks are shown for tests A-D065-F toC-D110-F, as they do not have equivalent movable bed tests.Furthermore, given the low values of R in tests B-D065-F,A-D110-F and B-D110-F, the estimated values of ks in thesetests must be viewed with caution. The values of R in the lastcolumn of Table 2 were calculated using the values of ks shownin the same table. From Tables 1 and 2, it follows that:

(1) For the same values of ow depth and slope, the ow ratewas considerably higher when a hardened mortar mixtureof the same sand was used instead of the original sand beds(compare the results of the rst nine tests in Table 2with theirmovable bed counterparts 1- to 3-D065-M, 1- to 3-D110-M,and 1- to 3-D200-M, noting that the relative increase in owrate was between 15 and 35%, with an average of 24%).The fact that the xed beds were considerably smoother thanthe original beds, despite the small content of cement, is alsoreected in an appreciable decrease in the values of ks andR, and increase in the values of c.

(2) As expected, the values of Q and, consequently, c, ks and Rof the tests with glued sand were much closer to those of theequivalent movable bed tests (compare the last six tests inTable 2 with tests 1- to 3-D065-M and 1- to 3-D200-M inTable 1). In this case, Q remained between 6.8 and 9.0%.

(3) The values of Q, and consequently the values of c and ksin the xed bed tests 1- to 3-D200-F were close to those inthe movable tests 1- to 3-D065-M, respectively. The relativedierence between measured ow rates in these tests var-ied from 2.6 to 4.8%, with an absolute average of 3.1%.

That is, the granular roughness of a movable bed formedby the 0.65mm sand was comparable to that of a xed bedwhere the 2.0mm sand was used in the coating mortar mix-ture. In other words, in the case of the 0.65mm sand, it waspossible to preserve the granular roughness of the originalbed by using in the coating mixture a sand with an aver-age grain size approximately three times larger than that ofthe original sand. On the other hand, the values of Q and cin the xed bed tests A- to C-D065-F were close to thosein the movable bed tests A- to C-D0195-M, respectively.In this case, the relative dierence between measured owrates varied from 7.5 to 8.7%, with an absolute averageof 7.2%. Despite the limitations identied earlier associatedwith the tests involving the 0.195mmsand, the similarities inhydraulic conditions between tests A- to C-D065-F andA- toC-D0195-M suggest that in this case too, similar roughnessconditionswere present. This further suggests that, as long asD50 0.65mm, the granular roughness can be preservedif the average grain size in the coating mixture is increasedby approximately three times in comparison with that of theoriginal sand.

(4) The relative dierence inow rate between thexedbed tests1-, 2- and 3-D200-F, and the movable bed tests 1-, 2- and3-D110-M was 5.9, 5.8 and 14.8%, respectively. The condi-tions nonetheless were suciently close so that, in practice,the granular roughness of a sandcement mixture where thesand grain size is 2mm or slightly larger could be viewedas a reasonable approximation to the roughness of a1.1mmmovable sand bed.

Points 3 and 4 above indicate that the relation between theaverage grain size in the coating mixture and that of the originalsand is likely to be of a form consistent with that of the solidline in Fig. 1. Considering the present tests alone, this line wasdrawn so that for sand up to 0.6mm, the grain size of the sand inthe coating mixture is roughly three times larger than the grainsize of the original sand; while for sands from 0.6 to 1.1mm,this relation is gradually reduced to roughly two times. From

Data points resulting frompresent experiments

0.1

2.502.252.001.751.501.251.000.750.500.25

0.3 0.5 0.7D50 (mm) of movable bed

D50

(m

m) of

sand

in sa

nd-ce

ment

mixtu

re

0.9 1.1 1.3

Figure 1 Plot of D50 of sand in coating sandcement mixture versusD50 of original movable sand bed (solid line drawn so as to follow thetrend of the data-points)

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the present study, it follows that if D50 > 1.1mm, then a betterapproach is to coat the bed with a hardened mixture of (any) sandand cement, and then glue on it a layer of the original sand. Forthis reason, the solid line in Fig. 1 has not been extended beyondD50 of the movable bed equal to 1.1mm.

3 Proposed stabilizing method

3.1 General

Clearly, the method of application of the coating sandcementmixture described in the previous section can only be used whenthe bed is at. In this section, a dierent method of application isexplored, with the goal of simplifying the procedure and, even-tually, making it also applicable to the case of deformed beds a matter that is dealt with separately in Section 3.4.

In this new procedure, only dry sand and cement were mixedbeforehand in amixer (nowaterwas added at this stage; in viewofthe tests previously reported, a cement/sand volume ratio of 8%was adopted). When forming the laboratory sand bed (or sandchannel), this dry mixture was used to form its topmost layer.For this purpose, a layer 5mm thick of the mixture was spread(with the aid of a scraper) over the previously compacted andstill wet bed. The channel was then slowly lled with water so asnot to disturb this layer, until the entire surface of the layer wassubmerged in water; and subsequently slowly drained. This hadthe eect of compacting the layer, whilemaking it fully saturated.The sandcement layer was then cured in the same way that wasused for the mortar mixture in the previous section.

The tests carried out to assess the durability, shear strength andgranular roughness of beds stabilized with the method describedabove are detailed next.

3.2 Durability and shear strength of stabilized beds

As a preliminary assessment of durability, a sand bed havingan immobilized top layer of 0.65mm sand (and cement) wassubjected to a uniformow,with S = 1/44 and h = 1.8 cm (Q =1.7 l/s), resulting in a bed shear stress of 0 3N/m2(= v2).This test, which was conducted in the 0.13m wide tilting umedescribed in Section 2, lasted 6 h. The bed shear stress was 7.3times larger than the largest bed shear stress in the tests previouslyreported (namely, 0.41N/m2 in the tests with h = 2.0 cm andS = 1/369).

Since the bed did not suer any damage during the test, thestabilizing layer was then subjected to dierent ow conditionsover longer periods of time in an 11.5m long, 0.385m wide, and0.41 cmdeep tilting umewith plexiglasswalls and concrete bot-tom. For this purpose, a 27.5 cm wide, 25.5 cm long and 0.5 cmthick immobilized layer sample, formed also by 0.65mm sandand cement, was prepared in a wood box with multiple drainageholes at the bottom. The box was xed at the bottom of the ume(Fig. 2), at a location 0.95m downstream of the ume headgate.Four tests were carried out with hydraulic conditions as summa-rized in Table 3. Here, h and S are the ow depth and slope ofthe uniform ow suciently downstream of the wood box so asto be undisturbed by this (note that the box locally disturbs theow, raising the ow depth upstream of the box and leading to avarying ow over the box).

A purpose of these tests was to subject the hardened surfaceto bed shear stresses substantially larger than those in the testsreported in Section 2, and representative of a wide range of typ-ical laboratory conditions. The 0.385m wide tilting ume wasselected for these tests because this ume can be tilted to pro-duce as large a value of slope as desired, and therefore it oered

Figure 2 Stabilized layer sample in 0.385m wide tilting ume

Table 3 Hydraulic conditions in durability and shear strength assessment tests of proposed stabilizing method (tests reported in Section 3.2, B =0.385m)

Test h (cm) S Q (l/s)a R F 0 (N/m2)a Y /Ycr

1 6.6 1/94 31 77,922 1.51 2.80 14.42 10.2 1/94 60 145,455 1.52 4.92 25.43 6.7 1/64 38 93,506 1.83 4.24 21.84 10.5 1/64 75 181,818 1.84 7.95 41.0

aEstimated.

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Table 4 Hydraulic conditions in granular roughness assessment tests of proposed stabilizing layer (B = 0.13m) and comparison with equivalenttests using hardened mortar mixture

Test CSVR (%) h (cm) S Q (l/s) Q (%) c c (%) ks (mm)a ks (%) R R

A-D065-FD 8 1.0 1/567 0.247 2.0 15.5 1.9 b 1901 bB-D065-FD 8 1.0 1/867 0.166 3.1 12.9 3.2 b 1280 b

C-D065-FD 8 2.0 1/867 0.530 4.2 15.5 4.1 0.47 28.8 4079 6.21-D110-FD 8 2.0 1/567 0.559 0.9 13.2 0.8 1.21 3.4 4300 19.82-D110-FD 8 3.0 1/567 1.107 1.7 15.1 2.0 0.82 7.9 8515 15.43-D110-FD 8 2.0 1/369 0.701 3.2 13.4 2.9 1.11 14.4 5392 22.41-D200-FD 16 2.0 1/567 0.551 6.4 13.0 6.6 1.29 22.3 4238 21.02-D200-FD 16 3.0 1/567 0.967 1.7 13.2 1.5 1.52 7.8 7438 28.73-D200-FD 16 2.0 1/369 0.680 0.6 13.0 0.8 1.26 3.1 5231 25.4aDetermined from Eq. (1).bNo value of ks could be found that would satisfy Eq. (1) (implying hydraulically smooth ow).

the best conditions to ensure that the objective of the tests wasrealized. However, the ume is not equipped with a ow ratemeasuring device, from where values of ow rate Q and aver-age ow velocity v could be readily obtained. No attempt wasmade to measure these quantities through point measurementsof velocity covering a ow cross-section. Instead, the values ofQ (as well as the values of 0) for these tests were estimatedon the basis of open-channel ow relations, as described below.Even though this approach is associated with substantial uncer-tainty, it is judged sucient for the present purposes, where theintention is merely to approximately characterize the strength ofthe ows used for the benet of the readers. Accordingly, thevalues of Q in Table 3 were obtained with the aid of Manningsequation on the basis of the h and S values of the downstreamuniform ow, and by adopting n = 0.012 (value provided byCrowe et al. 2009 for trowelled concrete, in accordance withthe material forming the ume bottom; the fact that the wallswere made of a dierent material than the bottom was not con-sidered in the calculations). The bed shear stress acting in themiddle of the immobilized layer sample was used as represen-tative of the (variable in ow direction) bed shear stress actingon the sample. This was estimated from 0 = Sf h, with h andSf identied with the ow depth and friction slope in the mid-dle of the sample, the rst being directly measured (h = 10.8,15.8, 10.5 and 15.5 cm for tests 14, respectively) and the lat-ter determined from Q = (1/n)BhS1/2f R2/3h (Chaudhry 1993, Jain2001). In these calculations, n was still assigned the value 0.012.The calculations thus rest on the assumption that the material ofwhich the box is made of is not particularly relevant where theshape of the free surface over the box is concerned. To give anidea of the erosive power of the present ows, values of Y /Ycrare also shown in Table 3. Since Y /Ycr can only be calculated formovable sand beds, the values of 0 were converted to values ofY (= 0/sD) for the movable sand bed that would be immobi-lized by the mixture of 0.65mm sand and cement, namely, a sandhaving D50 0.2mm (see Fig. 1), for which Ycr = 0.060. Eachof tests 14 was continued for 4 h, in a total of 16 h of testing.No damage to the surface was observed at the end of the tests,

reecting the fact that this new method of application producesequally strong beds as the hardened mortar mixture methoddescribed in Section 2.3.

3.3 Granular roughness

A question that arises is whether the two dierent methods ofapplication of the sandcement mixture previously describedlead to dierences in granular roughness. To answer this question,new tests were carried out in the 0.13m wide tilting ume brieydescribed in Section 2.1. In these tests, like in the tests describedin Section 2, the ow was uniform; however, the bed was coatedby a sandcement mixture applied as described in Section 3.1.The hydraulic conditions of these tests were as summarized inthe rst six rows in Table 4. In the rst three of these tests, thecoating mixture consisted of 0.65mm sand and cement, and inthe next three of 1.1mm sand and cement. As in all previoustests, in both cases the cement/sand volume ratio (here denotedCSVR) was 8%. Note that tests 1- to 3-D110-FD in Table 4 arethe counterparts of tests 1- to 3-D110-F in Table 2, while testsA- to C-D065-FD are the counterparts of tests A- to C-D065-F(the ow conditions were the same, the only dierence beingthe method of the application of the sandcement mixture). Thevalues of c and ks in Table 4 were determined as described inSection 2.2; R in the last column was determined using the val-ues of ks in this table. To facilitate the comparison between thesetests and their counterparts in Table 2, Table 4 shows also, asQ, c and ks, the relative dierence (in %) between Q, c and ksof the present tests and their counterparts in Table 2. As can beinferred from these tables, the hydraulic conditions in tests 1- to3-D110-FD and A- to C-D065-FD were close to those of theircounterparts. This indicates that the granular roughness of thecoating cementsand mixtures in the present tests is comparableto that of the hardened mortar mixture used in the tests in Table 2.

However, due to the large dierence in size between sandgrains and cement particles, mixing sand with D50 2mm andcement (8%) did not produce a uniform dry mixture. As a result,the xed bed was formed by patches with dierent cement

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Figure 3 Front view of movable sand dunes versus stabilized dunes with sandcement coating, in the 0.13m wide ume: (a) sand dunes; (b) stabilizeddunes; (c) stabilized dunes after 7 h of test

Figure 4 Side view of movable sand dunes versus dunes stabilized with sandcement coating in the 0.13m wide ume: (a) sand dunes; (b) stabilizeddunes; (c) stabilized dunes after 7 h of test

contents and variable shear strengths. To overcome this prob-lem, in this case the cement content was increased from 8 to 16%.Despite the increase in cement content, the granular roughness ofthe stabilized bed was nonetheless still comparable to that of thehardened mortar mixture. This was concluded after conductingthree more tests in the 0.13m wide tilting ume, with hydraulicconditions as summarized in the last three rows of Table 4. Inthese tests, which are the counterparts of tests 1- to 3-D200-Fin Table 2, the coating mixture consisted of 2.0mm sand andcement, the cement/sand volume ratio being 16%. It should benoted that in the hardened mortar method, the mixture was com-pacted manually, which likely alters the arrangement of sandgrains, especially in larger grain sizes; while with the presentmethod of application, the coating mixture was naturally com-pacted by water, likely not changing the arrangement of sandgrains. This probably explains why a dry mixture of sand andcement with large sand grain size and higher cement contentthat is compacted by water has a granular roughness compara-ble to that of a mortar mixture of the same sand grain size andlower cement content that is compacted manually. Consideringthe aforementioned, a practical rule-of-thumb would be to adopta cement/sand ratio of 8% for sands up to 0.65mm, and thengradually (linearly) increase this ratio up to 16% for 2mmsands.

3.4 Application of the present method to deformed beds

To test the applicability of the present method to the case ofdeformed beds, the method was used to stabilize dunes in the

0.13m wide tilting ume (Figs. 3 and 4). Three consecutivedunes (dune length = 30 cm; dune height = 2 cm) formed by0.65mm sand were built for the present purposes as shown inFig. 3a, and subsequently evenly covered by a layer of a drymixture of 0.65mm sand and cement (the cementsand vol-ume ratio being 8%). The ume was then very slowly lledwith water from downstream, so as not to disturb the deformedbed, until the dunes were completely drowned. Finally, the waterwas very slowly drained, and the sandcement layer was curedfor 7 days as described in Section 2.3 (see Fig. 3b). The duneswere then subjected to a ow having average ow depth hav =2.95 cm (ume slope S = 1/44), and yielding Q = 1.29 l/s,v = 33.6 cm/s. After 7 h of running the ow (in 30-min-longtimespans), no erosion occurred, with the stabilizing layer fullymaintaining its integrity (Fig. 3c).

However, in the process of stabilizing the dunes, the follow-ing was noticed. When lling the ume with water, howeverslowly, as thewater overtopped a dune crest, it ran down the duneslope on the stoss side, causing some deformations on the sandcementmixture. Although thesewere negligible in this case, theyare likely to be more prominent in the case of deformed bedsexhibiting steeper slopes between shoals and deeps. To preventthis problem, an alternative procedure is to spread the dry mix-ture of sand and cement over the bed, and then abundantly sprayit with water, before slowly lling and emptying the channel.

As an additional test, themethodwas also used to successfullystabilize the deformed, equilibrium bed of a 0.30m wide mean-dering channel, with walls made of ABS (acrylonitrile butadienestyrene) plastic.

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Figure 5 Side view of sand dune (dune length = 70 cm; duneheight = 5 cm) in the 0.385m wide ume, showing coating mixture(grey layer) applied with the aid of a basket manually conveyeddownstream

It should be noted that the areas that were stabilized in the testsreported in this paper were relatively small. Hence, it was possi-ble to manually spread the dry mixture of sand and cement overthe deformed beds. In the case of the dunes in the 0.13m wideume (Figs. 3 and 4), the sandcement coatingmixture wasman-ually applied by following lines drawn on the plexiglass walls.In the case of the meandering channel mentioned in the previ-ous paragraph, the coating mixture was applied by repeatedlypulverizing the bed with the aid of a sieve. Both methods areimpractical for application to large areas. Furthermore, althoughthe bed topography in the meandering channel was not surveyedbefore and after the application of the mixture, it is very dicultto ensure a coating layer of uniform thickness if a sieve is usedto spread it.

After concluding the tests, it was determined that the bestapplication method of the (dry) coating mixture is by adopt-ing the hourglass principle. For this purpose, a basket withtriangular cross-section (or triangular base) ending with a slot,and containing the sandcement mixture, is moved at a constantspeed along the railings of the umeor channel,while themixturecontinuously falls over the deformed bed. In the case in which aume is equipped with an automated carriage, the process is verysimple, as the carriage can be used to convey the basket at a uni-form speed along the ume. This method has recently been usedby the second author in an independent study to x a train of 10periodic dunes (dune length = 1.30m; dune height = 8 cm; owdepth 15 cm), in the sediment transport ume (B = 0.76m,length = 21m) of Queens University. However, even if the bas-ket is manually conveyed downstream, it is nonetheless possibleto achieve a coating layer of almost equal thickness all over. Thiscan be inferred from Fig. 5, showing a close-up photo of a duneafter applying the coating mixture with the aid of a basket manu-ally conveyed downstream. This dune was part of a set of dunesinstalled in the present 0.385m wide tilting ume for the solepurpose of testing this application method. (Note that a few sandgrains were spread over the coating layer after this was appliedto make it more clearly visible in the photo.)

To conclude this section, it should be pointed out that, in thecase of a deformed bed, the present method may have some eecton the surface topography due to the thickness of the hardenedlayer. The eect can be substantial, for example, in the case ofscour holes, or sequences of throughs and shoals, if their size iscomparable to the thickness of the hardened layer. Dependingon the goals of the intended research, thismay result in the presentmethod being unsuitable for some applications.

3.5 Other aspects

The purpose of this subsection is to briey mention a few aspectsrelated to the application and removal of the hardened layer notmentioned earlier, and yet that may be of interest.

(1) In the tests reported in this paper (straight umes with plex-iglass walls and the 0.30m meandering channel with plasticwalls), no wall protection was used. The sandcement mix-ture has aweak bond to plexiglass and some residualmaterialwas left on the channel walls after removal of the hardenedbed. This could be easily removed, although care had to betaken not to get the walls scratched in the cleaning process.As a preventive measure of any possible damage to the plex-iglass, either as a result of the method itself or the cleaningprocess after removal, it is recommended that some form ofwall protection be used, for the part of the wall that will be incontact with the sandcement mixture. In the authors view,the simplest way is to insert along the walls a stripe of thinplastic (or a series of plastic stripes). This can be done justbefore the mixture of sand and cement is applied, and left inplace until the mixture is cured. Since the mixture has a weakbond to plastic, the stripes can be removed (pulled out) aftercuring is accomplished. However, it is preferable to leavethem in place, to avoid the potential creation of weak spotsof the hardened layer near the walls. In the case of a paintedwall, like in our 0.8m meandering channel mentioned in theIntroduction, then wall protection should always be used.

(2) Cracking of the hardened layer, or even just a tendency forcracking, was not observed in any of the tests. In all tests, theume or channel entrances were formed by a layer of gravel,thus allowing the water to ow under the layer. Tests wereoften resumed several days after a previous test had beencompleted. However, as a preventive measure, the channelswere lled relatively slowly, before starting a test.

(3) The hardened layer can be easily removed from the bed. Byhitting it with a tool (e.g. a hammer), the layer can be madeto break into relatively large pieces (we aimed at 1015 cm),which then need to be picked up and properly disposed of.The process in not physically tiring, as the layer breaks easilyon impact.

4 Conclusions

The main ndings of the present work can be summarized asfollows.

(1) A coating consisting of a mixture of sand and a small amountof Portland cement Type III (type HE) can be used as aneective means to stabilize movable beds. However, if themixture comprises the same sand as the original bed, its gran-ular roughness will be appreciably smaller than that of theoriginal bed. For sands up to 1.1mm, it is nonetheless pos-sible to achieve a granular roughness comparable to that of

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the original bed by increasing the size of the sand in thesandcement mixture (see also point 2. below). For sandswith D50 > 1.1mm, then a better approach is to coat thebed with a mixture of (any) sand and cement, and then glueon it a layer of the original sand.

(2) For practical purposes, the grain size D50 to be used in thecoating sandcement mixture is perhaps best expressed as afunction of D50 of the original sand, i.e. D50 of sandcementmixture = f (D50 of movable bed). The present tests yieldedthree values (points) of this function. The solid line inFig. 1, which was drawn so as to capture the trend of thesepoints, is thus to be viewed as a rst representation of thisfunction. Clearly, considerable uncertainty remains regard-ing the exact form of the function f . Thus, in the absenceof further work to more precisely dene it, and especially if0.195mm < D50 < 0.65mm, it is recommended that Fig. 1is used to approximately estimate the grain size of the sandfor the coating mixture, and that this be then rened asneeded through preliminary testing comparing ow condi-tions before and after hardening. It should also be noted thatthe sands used in this work were well sorted. The sand grainsizes (and the cement content) of the coating mixture result-ing from this work may need to be somewhat modied forless uniform sands than those used in the present tests.

(3) The simplest method of application, valid for both at anddeformed beds, is to evenly spread over the bed a 5mmlayer of a dry mixture of sand and cement. After slowlylling the channel so as to fully submerge it in water andslowly emptying the channel, the coating mixture should becured for 7 days. In the case of strongly deformed beds, itis recommended that the dry mixture of sand and cementbe fully saturated with water before lling and emptyingthe channel with water. The cement/sand volume ratio ofthe dry mixture should be 8% for sands up to 0.65mm, andthen gradually increased up to 16% for sands having D50 =2.0mm.

(4) As an alternative to themethodof application above, amortarmixture of sand, cement and water can be prepared before-hand in a concrete mixer and then spread on the bed. In thiscase, a cement/sand volume ratio of 8% and a water contentof 60% of the cement volume are recommended. The con-siderations in point 1 above regarding the sand grain size tobe used in the sandcement coating mixture are still valid.This alternative method of application, however, can be usedonly when the beds are at.

(5) On the basis of the appearance of the hardened coating mix-ture and the tests carried out as part of this work, as well asthe recent experience of the writers in using the proposedstabilizing method in the meandering research mentioned atthe end of the Introduction and the larger scale dune studymentioned at the end of Section 3.4, the authors believe thatthe resulting stabilized beds can best be dened as semi-permanent, in the sense that they are able to withstand the

action of typical laboratory ows over long periods of time,and yet can be easily removed from a ume.

Acknowledgements

This research was supported by funds from the Natural Sciencesand Engineering Research Council of Canada through a Discov-ery Grant to the second author. The authors are grateful to threeanonymous reviewers, the Associate Editor and the Editor, fortheir valuable comments and suggestions, which were of greathelp to develop this paper to its present form.

Notation

B = ow width (m)Bs = roughness function ()c = Chzy resistance factor (= v/v) ()c = relative dierence between c in xed bed

and equivalent movable bed tests (%)c = relative dierence between c in bed

xed by proposed stabilizing method (asdescribed in Section 3.1) and bed xed byhardened mortar mixture (as described inSection 2.3) (%)

CSVR = cement/sand volume ratio in thesandcement mixture (%)

D = typical grain size (usually identied withD50, as done in this paper) (m)

D50 = average grain size (m)f = function determining D50 of the

sandcement mixtureF = Froude number (= v/(gh)1/2) ()g = acceleration due to gravity (m/s2)h = ow depth (m)ks = granular roughness of bed surface (m)ks = relative dierence between ks in xed bed

and equivalent movable bed tests (%)ks = relative dierence between ks in bed xed

by the proposed stabilizing method (asdescribed in Section 3.1) and bed xed bythe hardened mortar mixture (as describedin Section 2.3) (%)

Lent = development length of velocity prole (m)n = Mannings roughness coecient ()Q = ow rate (m3/s)Q = relative dierence between Q in xed bed

and equivalent movable bed tests (%)Q = relative dierence between Q in bed xed

by the proposed stabilizing method (asdescribed in Section 3.1) and bed xed bythe hardened mortar mixture (as describedin Section 2.3) (%)

Rh = hydraulic radius (m)

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R = ow Reynolds number (= vh/) ()R = roughness Reynolds number (= vks/)

()S = bed slope ()Sf = local friction slope ()v = average ow velocity (= Q/(Bh)) (m/s)v = shear velocity (= (gSRh)1/2) (m/s)Y = mobility number (= v2/(sD)) ()Ycr = value of Y at the critical stage of initiation

of sediment transport ()s = submerged specic weight of grains

(N/m3) = uid kinematic viscosity (m2/s) = uid density (kg/m3)0 = bed shear stress (= v2) (N/m2)

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Documents

A cement-based method for fixing sand in laboratory channels