The Marsh Cone as a viscometer: theoretical analysis and practical limits

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1 Available online at Materials and Structures 8 (January-February 25) 25- The Marsh Cone as a viscometer: theoretical analysis and practical limits R. Le Roy and N. Roussel Laboratoire Central des Ponts et Chaussées, Paris, France Received: 5 September 2; accepted: 2 May 24 ABSTRACT In this study, we have investigated the possibility of using the Marsh cone as a viscometer. Rheological measurements along with digital image recording of Marsh cone flow on glycerol-water mixes were carried out. The equations needed to solve the flow problem are written in the case of a purely Newtonian viscous fluid. We show that flow time can be directly linked to the Newtonian viscosity. Flow time is proportional to viscosity. The Marsh cone is then used to test several cement pastes and measured flow time is compared to predicted flow time. The correlation between flow time and cement pastes apparent viscosity stays valid only for no yield stress cement pastes and for flow time higher than about 5 s RILEM. All rights reserved. RÉSUMÉ Dans cette étude, on a évalué la possibilité d utiliser le cône de Marsh en t que viscosimètre. Des mesures rhéologiques, couplées avec des enregistrements d images numériques d écoulements au cône de Marsh, de mélanges de glycérol et d eau ont été effectués. Les équations nécessaires pour résoudre le problème ont été écrites dans le cas d un fluide purement visqueux. On montre alors que le temps d écoulement est proportionnel à la viscosité. Le cône de Marsh est ensuite essayé sur des pâtes de ciment pour lesquelles le temps d écoulement mesuré est comparé à celui calculé. La corrélation entre le temps d écoulement et la viscosité apparente reste valide uniquement pour les pâtes de ciment n ayant pas de seuil d écoulement et pour des temps d écoulement supérieurs à environ 5 s.. INTRODUCTION The Marsh cone test is a simple approach to get some data about cement pastes rheological behaviour. It has already been used in cement based materials mix design [-] in order to define the super-plasticizer saturation point, i.e. the dosage beyond which the flow time does not decrease appreciably. It is also widely used in grout control, especially those used in geotechnical reinforcement, prestressed cable protection, petroleum cementation. The test geometry depends on grout application and on sdard [4, 5], but its principle is always the same. The time needed for a certain amount of material to flow out of the cone is recorded. This flow time is linked with the material fluidity. The longer the flow time is, the lower the fluidity is. By modelling analytically the flow in the Marsh cone, it is possible to estimate the viscosity. Such a calculation is of great interest, since one is then able to calculate a physical parameter (viscosity [Pa.s]) instead of an empirical one (fluidity [s]). Before proposing that simple viscometer, it appears necessary to assess its accuracy. Moreover, this accuracy is affected by the often pseudo-plastic behaviour of some new grout mixes. It then becomes import to know the validity domain of this viscosity control device. In this study, we carry out Marsh cone and rheometric measurements on glycerol-water mixes in a first part. In a second part a simple modelling is proposed linking flow time to Newtonian viscosity. This calculation is then applied to various grout mixes flow measurements. We show that the Marsh cone test and the associated proposed calculation are relevant only when the grout behaviour is close to a Newtonian behaviour. 2. EXPERIMENTAL PROCEDURES In the present study, two types of material are tested: waterglycerol mixtures and cement pastes. For water-glycerol mixtures tested on the Marsh cone, digital images were taken using a CCD camera. The test parameters are given in Table for each material testing. They will be reminded when needed. Editorial Note LCPC is a RILEM Titular Member RILEM. All rights reserved. doi:.67/45

2 26 R. Le Roy, N. Roussel / Materials and Structures 8 (25) 25- Table - Test parameters in the present study for the two tested materials Glycerol testing test sdard N Cement pastes testing test sdard N 2 h (m) r (m).5.4 initial amount.7.8 (dm ) flowing amount..4 (dm ) H (m) H f (m) The Marsh cone Tests procedure is described in EN 445 [4], ASTM 99 94a [5]. In the EN 2 75 sdard [6], smaller nozzle diameters are proposed since the fluidity of soil grout is generally higher than for post tension applications. The procedure is the following: - A Marsh cone is attached to a sd (Fig. ) ; - Closing the nozzle, a certain amount of the tested material is poured into the cone. This amount may vary from.8 L to.7 L depending on the authors. The initial filling height is noted H ; - The orifice is opened and a stop watch started ; - The material volume flowing through the nozzle as a function of time is recorded (Fig. 2). The final filling height is noted H f. By video recording the flow, any H f values may be chosen and studied. 2.2 Rheometric measurements A coaxial Haake viscotester VT55 was used for all the experiments. A MV DIN cylinders sdard equipment is used for glycerol water mixes. Since the mix is a Newtonian fluid, the viscosity is obtained by calculating the slope of the stress-speed gradient curve. The corresponding strain rate ranges from to 2 s - (Fig. ). Paste measurements were performed on special coaxial cylinders, on which sand paper is stuck, in order to avoid slipping during measurements. The procedure is the following: - pre shearing up to s - in s ; - stage speed during 2 s ; - decreasing speed from s - to.5 s - in 6 s. 5 measurements are taken during this period, each of one taken after a 2 s stabilized speed period. This branch is used to calculate the plastic viscosity and the yield stress (Fig. 4) ; - increasing speed from.5 s - to s - in 6 s. Same measurements as above. In order to obtain the best accuracy measurements as z 52 Fig. 2 - Glycerol-water mix volume versus time for various mixes. Viscosity in [mpa.s] is mentioned in caption. Nozzle diameter equal mm [experimental results and simulations]. 2 H Hf 28 shear stress [Pa] 5 5 h 2 r = or Fig. - Studied geometry and main notations (length in mm) strain rate [s-] Fig. - Shear stress in terms of strain rate during a viscometer test. Water-glycerol mixture (water : 5%, glycerol : 95% (weight ratio)) at T = 2.7 C. The strain rate is ramped from to 2 s - [experimental results].

3 R. Le Roy, N. Roussel / Materials and Structures 8 (25) then Fig. 4 - Shear stress in terms of strain rate during a viscometer test. Cement paste N 2. If the paste is considered as a Bingham fluid, the plastic yield value K i = 6 Pa and the plastic viscosity p = 2 mpa.s. The strain rate is ramped from to s - [experimental results]. possible, viscosity temperature correction were done on water glycerol mixtures so that rheometric and Marsh cone results could be compared.. FLOW EQUATIONS The Poiseuille law for a Newtonian viscous fluid with a viscosity µ writes in the conical part for small values and if the flow is considered as a succession of steady states (slow flow): p Q g r z 4 () 8 z From () comes p 8 Q z r z 4 g with ph if the atmospheric pressure is the reference pressure. The pressure then writes p z 8 Q g H z and r z r H (2) () 8 Q p gh r r H (4) In the cylindrical part, () becomes: r p r p Q 4 4 g 8 z 8 h g (5) 8 h 4 r h with r r H Q gh h (6) 2 dh Q r H (7) dt The following relation comes h r gr 8 r dt 2 H r H h H hr H (8) dh If H is the initial conical part filling height, the flow time may be integrated : t v 2 r h with H 8 h 2 (( )( gr r h rh H h H ( LN( r H H r H H H H ( h) 2 2 H h r LN( )) H h r H h ) LN( ))) r H h (9) V r () where V is the volume that has flown out of the cylinder during a time t v. The fluid level decrease rate in the conical part accelerates through the test as shown on Fig. 5. Note that the debit decreases at the same time. The volume V increases linearly during approximately the first half of the test, as noticed by Nehdi [7] and as shown on Fig. 5. During this phase, the debit through the Fig. 5 - Filling height in the conical part as a function of time for a purely viscous fluid. h =.6m; () =.25 ; H =.27; = 2 mpa.s ; = 2 kg/m ; r =.5 m [simulation].

4 28 R. Le Roy, N. Roussel / Materials and Structures 8 (25) 25- cylinder is const. Nehdi considered only the flowing of the first.7 l out of the. l he tested. He attributed this non-linear evolution to an increased effect of friction, which is in a way correct. In fact, the friction stays the same but the pressure gradient which is the engine of the flow in the cylindrical part relatively decreases through the test as the fluid level in the conical part decreases. The pressure gradient variations at the beginning of the test are small (small variations of the fluid filling height) and become stronger at the end of the test when the phenomenon accelerates. This leads to a const debit during the first part of the experiment which decreases only at the end of the total time needed to empty the cone. Last but far from the least, it should be noted that the flow time is proportional to the viscosity. 4. EXPERIMENTAL VALIDATION ON NEWTONIAN FLUID In order to validate Equation (9), tests on water-glycerol mixture are carried out. Testing different water/glycerol ratios mixtures, several viscosity levels are studied to verify (9) validity on the largest scale. An example of shear stress / strain rates measurements is given on Fig.. The Newtonian behaviour is obvious as expected and the viscosity is easily obtained through the test and its software. Knowing the mixture flow time, the viscosity may be calculated using Equation (9). The comparison between measured viscosity and calculated viscosity is plotted on Fig. 6. For the lowest values, the predicted viscosity values are higher than the measured ones. One extreme example is the case of pure water that is also plotted as a black dot on Fig. 6. The calculated viscosity is 64 [mpa.s], whereas the measured viscosity is about [mpa.s]. In these regimes, the assumption of a succession of quasi steady states is not valid any more and the flow time is not any more proportional to the viscosity. As such, the flow time value is not a meaningful measurement from a rheological point of view. This conclusion is confirmed on Fig. 2 on which the filling volume versus time is plotted for different viscosities. It is observed that the evolution is linear up to a emptying ratio of 5%-6%. The simulation accuracy increases with the viscosity. For the given geometry (initial volume equal to.7 l and nozzle diameter equal to mm), the prediction is acceptable beyond viscosity values of 2 [mpa.s], which corresponds to a flow time of 5 s according to the EN 445 test. Nevertheless, cement grout used in geotechnical applications behave like low viscous fluid. The accuracy prediction can then be preserved by diminishing the nozzle diameter, as it is shown on Fig. 7 for a glycerol-water mix of viscosity of [72 mpa.s]. 5. APPLICATION ON CEMENT PASTES 5. Pastes composition different cement pastes, studied in [8], consisting of cement, limestone filler, superplasticizer, viscosity agent and Fig. 6 - Comparison between the measured viscosity (viscometer) and the viscosity calculated upon the flow time value using (9). The x = y curve is also plotted in dash line [experimental results and simulation] flow time [s] flow time error nozzle diameter [mm] errror [%] Fig. 7 - Prediction accuracy evolution as a function of nozzle diameter. Glycerol-water mix of viscosity [72 mpa.s]. Cement pastes N Table 2 - Cement paste compositions Cement Filler Water Super (kg.m - ) (kg.m - ) (kg.m - ) Plast. Dry 2 water, were used for the validation. The water cement ratio is around.56 and the water binder ratio is.4. The chosen compositions are given in Table 2. The components are: Visc. Agent Dry (kg.m - ) (kg.m - )

5 R. Le Roy, N. Roussel / Materials and Structures 8 (25) Cement : CEM I 52,5 N CE ; - Filler : Betocarb P2 MEAC ; - Superplasticizer : Cimfluid Adagio 29 ; - Viscosity agent: Collaxim L Pastes behaviour identification The pastes behaviour parameters are identified using the viscometer test assuming that they behave as Bingham fluids with low yield stress. A test result example is plotted on Fig. 4. The results for each paste are given in Table. 5. Marsh cone test results The filling volume is.8 L and the passing volume is.4 L. For this test sdard, the initial height is H =.22 m and the final height is H =.65 m. The nozzle diameter is 8 mm. The measured flow times and rheological behaviour for each paste are given in Table with experimental comments. Using the measured viscosity and the relation (9), one may then try to predict the flow time and compare it to the experimental flow Table Experimental results of cement pastes flow time for the tested geometry. For the paste n, the flow will not occur or will stop before.4 dm has passed through the nozzle Cement pastes N Flow Time (s) Experimental comment Plastic viscosity p (mpa.s) Plastic Yield Value K i (Pa) 9.8 Normal flow 7.69 Normal flow Normal flow Normal flow Normal flow Normal flow Normal flow Normal flow Difficult flow Normal flow Normal flow 24 8 / No flow 6 6 time. This comparison is plotted on Fig. 8. It can be observed that low plastic yield is not detrimental to the viscosity prediction in most of practical marsh cone use. Nevertheless, beyond a plastic yield of 2 [Pa], the marsh cone accuracy diminishes very rapidly. In that domain, the modelling should be improved to take into account the plastic yield value. 6. CONSEQUENCES ON MARSH CONE PRACTICAL USE We have seen that the flow time is proportional to the viscosity in a certain domain. Considering the test used for post tension grouts control (EN 445) with the mm nozzle and viscosities lower than 2 [mpa.s], it can be shown, using the previous results, that the flow time is not always directly linked to the viscosity. On one hand, a % accuracy is obtained for flow times higher than 5 s. But, on the other hand, for lower flow times, the discrepancy increases rapidly. In practice, the French regulation for public markets imposes a minimum flow time of s, value which is closed to the previous one. If a low viscosity grout is controlled using this test, it then becomes difficult to spot an accidental water content modification as a non negligible water variation doesn t affect in a great proportion the flow time. The s value has then to be considered as an absolute minimum in pre-grouting control tests. If a lower value is obtained, the batch has to be rejected, and the water content decreased up to obtain a correct flow time. This point has to be emphasized since the grout sedimentation is sensible to water content. A way to avoid the test discrepancy is to change the nozzle diameter recommended by EN 445 in order to measure higher flow time than 5 s. A correct post tension grout will then be easily differentiated from an over watered one. Moreover, apparent viscosity of grouts whose behaviour may be approximated by a Bingham law is difficult to assess using Marsh cone, because flow time becomes strongly affected by plastic yield value higher than 2 [Pa]. Another test, such as Vane test may be used to evaluate the influence of the plastic yield value on the calculated viscosity. On another hand, for geotechnical applications, the viscosity is often lower than [mpa.s]. Using a sdard EN 445 Marsh cone would lead to a viscosity overestimated by about %. As mentioned previously, it is necessary to reduce the diameter nozzle (Fig. 7). In EN 2 75, the nozzle diameter recommendation of 4.75 mm has then to be followed. 7. CONCLUSIONS Fig. 8 - Comparison between the measured flow time and the predicted flow time using (9) and the measured viscosity in Table. The x = y curve is also plotted [experimental results and simulation]. This study presents an analytical modelling of the flow process in a Marsh cone. Based on this modelling, Newtonian fluid viscosity can be precisely calculated from the flow time. The authors of course recognize that more work is still needed in order to classify the Marsh cone as a on site viscometer. Repeatability and reproducibility still have to be studied. On a practical point of view, two issues

6 R. Le Roy, N. Roussel / Materials and Structures 8 (25) 25- are of high interest: effect of marginal change in water content on flow time and acceptable change in water content for a given grout. However, this is outside the scope of the present work that focused on the correlation between flow time and apparent viscosity. The limits of the approach presented in this work have two origins. On one hand, the excessive debit obtained on low viscosity grouts is responsible for the model discrepancy. This can be corrected by choosing a narrower nozzle. On another hand, plastic yield stress is not taken into account in the modelling. For yield stress values higher than 2 [Pa], it is considered that the test is no more suitable. In practice it should be emphasised that the Marsh cone has to be used within its application domain to reach its maximum efficiency as a control tool. REFERENCES [] Aïtcin, P.C. and Baalbaki, M., Concrete admixtures Key components of modern concrete, Concrete technology: New trends, Industrial Applications, (E&FN Spon, London, 994) -47. [2] De Larrard, F., Bosc, F., Catherine, C. and Deflorenne, F., The AFREM method for the mix-design of high performance concrete, Mater. Struct. (2) (997) [] Agullo, L., Toralles-Carbonari, B., Gettu, R. and Aguado, A., Fluidity of cement pastes with mineral admixtures and superplasticizer A study based on the Marsh cone test, Mater. Struct. 2 (22) (999) [4] EN 445, Grout for prestressing tendons tests methods (996). [5] ASTM C99-94a, Sdard test method of flow of grout for preplaced-aggregate concrete (flow cone method) [6] EN 2 75, Execution of special geotechnical work grouting (2). [7] Nehdi, M., Mindess, S. and Aïtcin, P.C., Statistical modelling of the microfiller effect on the rheology of composite cement pastes, Adv. in Cem. Res. 9 () (997) [8] Cordin, J., SCC segregation: mix fitting parameters influence on SSC cement paste fresh behaviour, Internal report LCPC, France, (22) [only available in French].