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J. Non-Newtonian Fluid Mech. 139 (2006) 128–134

Flow of Herschel–Bulkley fluids through the Marsh cone

V.H. Nguyen a,∗, S. Remond a, J.L. Gallias a, J.P. Bigas a, P. Muller b

a L2MGC, Universit´ e de Cergy-Pontoise, 5 Mail Gay-Lussac, Neuville sur Oise, 95031 Cergy-Pontoise Cedex, Franceb LM2S, Universit´ e Pierre et Marie Curie, Boıte 161, 4 place Jussieu, 75252 Paris Cedex 05, France

Received 4 April 2006; received in revised form 14 July 2006; accepted 14 July 2006

Abstract

Many studies on the rheology of cement grouts have shown that these materials are viscoplastic fluids presenting a yield stress. They can

present a rheological behavior of shear-thinning type or shear-thickening type. In all the cases, this behavior can be described satisfactorily by the

Herschel–Bulkley model, characterized by three parameters τ 0, K and n, which relate the shear stress to the shear rate. The present study aims atrelating the rheological parameters of cement grouts to their flow time through the Marsh cone which characterizes in a practical way the fluidity of

grouts. A semi-analytical approach has been established initially on simple assumptions and then corrected based on numerical simulation results.

It presents a deviation lower than 12% compared to numerical simulations for a wide range of rheological characteristics of the Herschel–Bulkley

fluids. It has also been validated experimentally with success on some studied cement grouts of various water/cement ratios.

© 2006 Elsevier B.V. All rights reserved.

Keywords: Rheology; Grouts; Cement; Marsh cone; Herschel–Bulkley fluids

1. Introduction

Cement grouts are very often used for weak soils stabiliza-

tion, cracked solid masses reinforcement or prestressing sheathsfilling. They must have a sufficient fluidity to ensure a good

injection. The Marsh cone is a very simple and effective tool to

characterize globally this fluidity and to verify the formulations

constancy in laboratory and on building site. It consists of a trun-

cated cone equipped at its lower end of a removable cylindrical

nozzle. Thecharacterization of thefluidity of cement groutswith

the Marsh cone consists in measuring the flow time of a given

volume of grout flowing out the Marsh cone. The shorter this

time is, the more the grout is fluid. The diameter of the nozzle

can be selected according to the rheological characteristics of

the grouts to obtain a suitable flow time. In most of the cases, it

is selected between 8 and 12 mm so that the flow time of 1 l of grout islowerthan1 min.StandardNF P 18-358 [1] recommends

a nozzle of 10 mm of diameter for the fluidity measurement of

grouts used in prestress or for the evaluation of the action of

fluidifying admixtures. On the other hand, a nozzle of 8 mm of

diameter is recommended by standard NF P 18-507 [2] f or the

determination of the water retention of mineral admixtures (sil-

∗ Corresponding author. Tel.: +33 134256935; fax: +33 134256941.

E-mail address: [email protected] (V.H. Nguyen).

ica fume, fly-ashes, . . .) used in concretes. In the present study, a

nozzle of 8 mm of diameter is used. The Marsh cone equipped of

this nozzle is schematically represented in Fig. 1. The geometri-

cal dimensions (in millimetres) defined by standard NF P 18-358[1] and their notation used in the paper are also represented in

this figure.

Many studies on the rheology of cement grouts have shown

that these materials are viscoplastic fluids presenting a yield

stress which must be reached by the shear stress so that the

flow takes place [3,4]. The rheological behavior of the grouts

can be shear-thinning type [5–7] or shear-thickening type [8,9],

depending on many parameters such as solid concentration

(water/cement ratio), interaction between particles (attractive

due to the effect of viscosity agents or repulsive due to the effect

of superplasticizers), size and shape of grains, . . . [10]. In all the

cases, it can be described satisfactorily by the Herschel–Bulkleymodel [10,11] characterized by three parameters: yield stress τ 0,

consistency K and exponent n which relate, in the case of sim-

ple shear, the shear stress τ to the shear rate γ by the following

relation:γ = 0, if τ < τ 0

τ = τ 0 +Kγ n, if τ ≥ τ 0(1)

When n = 1, the Herschel–Bulkley model is reduced to the

Bingham model which is also used in the literature to describe

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V.H. Nguyen et al. / J. Non-Newtonian Fluid Mech. 139 (2006) 128–134 129

Fig. 1. Geometry and dimensions (in millimetres) of the Marsh cone.

the rheological behavior of cement grouts [4,7]. However, the

Bingham model cannot take into account the curvature of the

flow curve which is generally significant at low shear rate [12].

It overestimates the yield stress for the shear-thinning fluids [12]

or underestimates, even gives a negative yield stress, for the

shear-thickening fluids [13].

In spite of the widespread use of the Marsh cone for the flu-

idity measurement of cement grouts on building site and the

numerous studies on the rheological behavior of the latter in

laboratory, very few studies until now have been devoted to the

relation between the flow time measured with the Marsh cone

and the rheological characteristics of the grouts. It seems that

only Roussel and Le Roy [14] treated this problem by consider-ing the cement grouts as Bingham fluids. To our knowledge, no

study related to the flow of the Herschel–Bulkley fluids through

the Marsh cone has been carried out. We propose thus a semi-

analytical approach which allows to determine the flow time

through the Marsh cone as a function of the rheological charac-

teristics of the grouts considered as Herschel–Bulkley fluids. It

is established initially on the basis of the following assumptions:

incompressible fluid, plane free surface and flow of Poiseuille

type in the nozzle. Because the last assumption is not veri-

fied for all the fluids, a corrective coefficient of the velocity

taking into account the length of establishment of Poiseuille

flow field determined based on numerical simulation results hasbeen introduced. With this correction, the proposed approach

can be applied to fluids whose rheological characteristics cover

a wide range of values. It is finally validated satisfactorily

experimentally on some cement grouts of various water/cement

ratios.

2. Semi-analytical approach

The flow in a geometry as complex as that of the Marsh cone

(Fig. 1) is impossible to calculate analytically without making

simplifying assumptions, even in the case of a Newtonian fluid.

In the present study, to determine the flow time of cement grouts

considered as Herschel–Bulkley fluids through the Marsh cone,

we assume that:

- the fluid is incompressible;

- the free surface is plane;

- the flow in the cylindrical nozzle during an infinitesimal time

step is of Poiseuille type under the cumulatedeffects of gravity

and of the difference of pressure between the entry and exit of

the nozzle.

From the assumption of Poiseuille flow type in the nozzle

(steady and laminar flow of an incompressible fluid in a cylin-

der) under theeffectsof gravity andthe difference of pressure p

between the entry and the exit of the nozzle, based on the con-

tinuity equation (mass conservation), on the dynamics equation

(momentum conservation) and on the Herschel–Bulkley equa-

tion (Eq. (1)), the following expression for the velocity profile

in the nozzle can be deduced:

⎧⎪⎨⎪⎩

V

=V max, if r

≤r0

V = V max

1− (r − r0)(n+1)/n

(R− r0)(n+1)/n

, if r > r0

(2)

where r is the radial distance and r 0 is the radius of the non-

sheared solid block, determined by:

r0 =2τ 0

ρg+ (p/H )(3)

ρ and g are, respectively, the density of the studied fluid and the

gravity acceleration and V max is the maximum velocity in the

nozzle reached by the solid block, which has the expression:

V max = nn+ 1

1

2K

ρg+ p

H

1/n

(R− r0)(n+1)/n (4)

When r 0≥ R, no flow is possible. On the contrary (r 0 < R),

we can deduce from Eqs. (2) and (4) the average velocity V at

the exit of Marsh cone:

V = nR

3n+ 1

R

2K

ρg+ p

H

1/n

f r0

R

(5)

where

f r0

R

=

1+ 2n

2n+ 1

r0

R

+ 2n2

(n+ 1)(2n+ 1)

r0

R

2

×

1− r0

R

(n+1)/n

(6)

The calculation of average velocity V by Eq. (5) requires

the knowledge of the difference of pressure p between the

entry and the exit of the nozzle. To determine this difference of

pressure p, we have assumed that the applied external force on

the fluid in the nozzle (ρg + p / H ) is proportional to that which

is exerted if the pressure of the fluid in the truncated cone is

hydrostatic. This can be expressed by the following relation:

ρg+ p

H = αρg1+ H t

H (7)



130 V.H. Nguyen et al. / J. Non-Newtonian Fluid Mech. 139 (2006) 128–134

where α is a proportionality coefficient. In the present study,

it is determined by considering two particular cases of

Herschel–Bulkley fluids. The first case relates to the fluids of

yield stress equal to zero (power-law fluids), allowing to deter-

mine the proportionality coefficient, denoted as α1, according

to consistency K and exponent n. The second case which relates

to the fluids whose exponent n is equal to 1 (Bingham fluids)

allows to determine the variation of the proportionality coeffi-

cient, denoted as α2, according to yield stress τ 0 and consistency

K . For the Herschel–Bulkley fluids presenting three parameters

τ 0, K , n, the expression of the proportionality coefficient α must

satisfy the two following conditions:

α = α1, if τ 0 = 0 (8)

α = α2, if n = 1 (9)

The proportionality coefficients α1 and α2 can be determined

analytically based on the continuity condition for an incom-

pressible fluid which can be expressed as constant flow rate in

all the sections of the Marsh cone. By considering the truncatedcone as a series of cylinders of infinitesimal length and by sup-

posing that the flow in these cylinders is also of Poiseuille type

under the effects of gravity and of the pressure gradient [14], we

can deduce from the continuity condition the following expres-

sions for the proportionality coefficients α1 and α2 which do

not depend on consistency K (the detail of the determination of

coefficients α1 and α2 can be found in [15]):

α1 =1

1+ (R/(3nH tan ϕ))(10)

α2 =1

−(1.1(τ 0/(ρgH tan ϕ)))

1+ (R/(3H tan ϕ)) (11)

Based on Eqs. (8)–(11), we propose the following expression

for the proportionality coefficient α for the Herschel–Bulkley

fluids:

α = 1− (1.1(τ 0/(ρgH tan ϕ)))

1+ (R/(3nH tan ϕ))(12)

By substituting Eq. (7) with the coefficient α determined by

Eq. (12) in Eq. (5), we can rewrite the average velocity at the

exit of the Marsh cone in the following form:

V =nR

3n+ 1

α

ρgR

2K

H

+H t

H 1/n

f r0

R

(13)

Eq. (13) allows to calculate the average velocity at the exit

of the Marsh cone provided that the flow in the nozzle is of

Poiseuille type. However, this flow type is reached only at a suf-

ficiently long distance from theentryof thenozzle. This distance,

called length of establishment, depends on the Reynolds number

and the diameter of the nozzle. It is more and more long as the

latter are large [16]. In the case of the Marsh cone, the Poiseuille

flow occurs in the nozzle only when the Reynolds number is suf-

ficiently small (lower than 10 approximately). Eq. (13) is thus

verified only for very consistent fluids of low velocity. For less

consistent fluids, Eq. (13) overestimates the velocity according

to the Reynolds number because the assumption of Poiseuille

flow type in the nozzle is not verified.

To take into account the length of establishment of the

Poiseuille flow field, we have introduced a corrective coefficient

β so that the average velocity at the exit of the Marsh cone V βis determined by:

V β = V

β(14)

The coefficient β is an increasing function of the Reynolds

number Re corresponding to the Poiseuille flow field in the

nozzle. This latter can be determined by the following rela-

tion which was originally established for the power-law fluids

[17], but which is also used for the Herschel–Bulkley fluids

[18]:

Re = ρV 2−n(2R)n

K(15)

When the Reynolds number tends towards zero, it is not nec-essary to introduce the coefficient β because the Poiseuille flow

field is established in the nozzle. This argument can be repre-

sented by the following boundary condition:

limRe→0

β = 1 (16)

When the Reynolds number tends towards infinity, the flow

velocity tends towards that of the ideal fluid which can be deter-

mined based on the Bernoulli theorem. In this case, the yield

stress is indeed very low and can be neglected. By expressing

the average velocity V (Eq. (13)) according to the Bernoulli

velocity λ√

2g(H

+H t ) and the Reynolds number Re (Eq.

(15)), we can translate this argument by the following boundarycondition:

limRe→∞

β = 1

2λ

αR

H

n

2(3n+ 1)

n/2√ Re (17)

where λ is a constant lower than 1 taking into account the energy

dissipation due to parietal friction in the Marsh cone and to

the local contraction of section. Taking into account the small

dimension of the Marsh cone as well as rounded entry section

of the nozzle, we take λ = 0.96 [19].

With only two boundary conditions Eqs. (16) and (17), it

is impossible to determine an expression for the coefficient β.

We have thus established this latter empirically based on resultsobtained by numerical simulation. Using the commercial code

Fluent 6.1, we havesimulated the flow in the Marsh cone (Fig. 1)

of Herschel–Bulkley fluids presenting various rheological char-

acteristics: the yield stress varies from 0 to 30 Pa, consistency K

varies from 0.001 to 20Pa sn and exponent n ranges between 0.3

and 1. For all the studied fluids, the density of the fluid has been

taken equal to 1000 kg/m3 to verify the numerical simulations

by comparing the velocity of the water which can be considered

as an ideal fluid to the Bernoulli velocity. This density value

used in the numerical simulations does not correspond to that of

cement grouts which is twice higher approximately. However,

this should not affect the expression of the corrective coefficient




β since the fluid density is taken into account indirectly through

the Reynolds number.

As the Marsh cone is axisymmetric, it is enough to model

the flow in a radial plane (2D) in cylindrical coordinates. In

this radial plane, the fluid flows only under the effect of gravity

and the free surface goes down during the flow. This problem

can be calculated by using the Volume of Fluid (VOF) model

integrated in the commercial code Fluent 6.1. This model is

applied to the fixed mesh for two or more immiscible phases.

In the case of the Marsh cone, two immiscible phases: air and

Herschel–Bulkley fluid are present. For each phase, the volume

fraction (ratio between the volume occupied by the phase and

the control volume) is introduced as a local variable and is cal-

culated for each cell and at each moment based on the continuity

equation and the momentum equation by taking into account the

initial and boundary conditions of the flow. As the volume frac-

tions of the phases vary as a function of the position and time,

the free surface corresponding to the iso-surface of fluid (or air)

volume fraction equal to 0.5 is moved. Indeed, it is impossi-

ble, in our numerical simulations, to obtain an ideal free surfacewhich separates clearly the two phases because there is always

an intermediate layer in which both phases are present. How-

ever, the thickness of this intermediate layer is small (from 1

to 3 cells) which ensures that the iso-surface of fluid (or air)

volume fraction equal to 0.5 satisfactorily represents the free

surface of the flow. Fig. 2 presents the Marsh cone mesh used in

our numerical simulations as well as the initials and boundary

conditions of the flow. The parameters of the mesh such as the

number of nodes, of faces (edges in 2D) and of cells are also

given in this figure.

The rheological characteristics of the studied Herschel–

Bulkley fluids are introduced into the numerical computationcode through the dynamic viscosity µ given by the following

Fig. 2. Grid of the Marsh cone, initial and boundary conditions of the flow.

expression [20]:

⎧⎪⎪⎨

⎪⎪⎩

µ = µ0, if γ ≤ γ 0 =τ 0

µ0

µ = τ 0 +K[γ n − (τ 0/µ0)n]

γ , if γ > γ 0 =

τ 0

µ0

(18)

where µ0 represents the viscosity above which the fluid behaves

like a solid. It must be sufficiently high to ensure a good regular-

ization of the Herschel–Bulkley model. In the present study, this

viscosity µ0 has been taken equal to 106 Pa s because we have

noted that, above this value, the numerical results are almost not

changed (the deviation between the maximum average velocity

at the exit of the Marsh cone obtained with µ0 = 106 Pas and

µ0 = 1012 Pa s is lower than 0.4%).

To enhance and accelerate the convergence of the problem,

the steady flow solution of a Newtonian fluid is taken as initial

condition for the transitory flow of the studied Herschel–Bulkley

fluids [20]. The viscosity of this Newtonian fluid has been takensufficiently high (5 Pa s) to ensure that the velocity at the begin-

ning of the transitory flow is low (initial average velocity at the

exit of the Marsh cone equal to 0.02 m/s). Actually, the veloc-

ity at the initial moment is zero in all the Marsh cone when

the nozzle is opened. However, we have noted that the value

of this initial velocity hardly influences the numerical results

when the flow is stabilized (the deviation between the maxi-

mum average velocities at the exit of the Marsh cone calculated

with initial conditions generated by the steady flow of Newto-

nian fluids presenting viscosities of 5 and 1 Pa s is lower than

0.3%).

In order to increase the speed of numerical calculation, theflow in the Marsh cone is considered as laminar shear. Indeed,

on the basis of results obtained by numerical simulation in this

flow regime, we have observed that most of flows (80%) are

satisfactory with this flow regime (Reynolds number lower than

3000). For the other fluids presenting higher Reynolds number,

the results obtained by numerical simulation in laminar regime

are also used to determine the corrective coefficient β because

we have observed that the difference between the two regimes

laminar and turbulent is weak (lower than 4%).

Because the computation time is long and we wish to model

the flow of numerous Herschel–Bulkley fluids presenting a wide

range of rheological characteristics, the flow of studied fluids

has been computed only for the first 0.5 s. During this period,the flow has reached its maximum velocity and the fluid height

in the Marsh cone has almost not decreased. Fig. 3 presents

some examples of evolution of the average velocity at the exit

of the Marsh cone as a function of time. Similar evolutions have

been obtained for the other fluids. In the present study, we have

reasonably considered that the maximum value of this average

velocity corresponds to the initial fluid height (maximum) and

it is used to calculate the value of corrective coefficient β deter-

mined through Eq. (14).

From the boundary conditions (Eqs. (16) and (17)) and by

using the values of the corrective coefficient β deduced from

the velocity obtained by numerical simulation, we propose the




Fig. 3. Some examples of evolution of the average velocity at the exit of the

Marsh cone as a function of time.

following empirical expression for the corrective coefficient β:

β

=1

2λ αR

H n

2(3n+ 1)

n/2

(1−

e−0.1√

Re)

×√

Re+ 1.5

n

4√

Re

+ 1 (19)

Taking into account the velocity correction by introduction

of the coefficient β (Eq. (19)), the average velocity at the exit of

the Marsh cone determined by Eq. (14) is well verified with a

deviation lower than 12% compared to that obtained by numeri-

cal simulation for numerous fluids of rheological characteristics

varying in a wide range. This is presented in Fig. 4.

From the continuity condition which can be expressed in the

following form during an infinitesimal time step dt in the case

where the free surface is plane and where the fluid is incom-pressible:

πR2V β dt = −πR2t dH t (20)

we can determine the flow time t , for a volume of fluid which

leaves the Marsh cone while causing a drop of fluid height in

Fig. 4. Comparison of average velocities at the exit of the Marsh cone corre-

sponding to the initial fluid height given by the proposed approach taking into

account the velocity correction (Eq. (14)) and by numerical simulation.

the truncated cone from H 1 to H 2, by numerical resolution of

the following integral:

t = − H 2

H 1

(R+H t tan ϕ)2

V βR2dH t (21)

As, on the one hand, the corrective coefficient β (Eq. (19))

taking into account the length of establishment of the Poiseuilleflow field is established empirically, and on the other hand, the

integral Eq. (21) can be calculated only numerically, the pro-

posed approach is thus not analytical but rather semi-analytical.

It presents significant advantages compared to the numerical

simulation. Firstly, the semi-analytical approach allows to cal-

culate instantaneously the flow time through the Marsh cone

of a Herschel–Bulkley fluid according to its three rheologi-

cal parameters with a low deviation compared to the numer-

ical simulation while this latter requires at least a few hours,

even several days for the calculation. As a consequence, the

semi-analytical approach allows to study in a fast and system-

atic way the influence of the rheological characteristics of theHerschel–Bulkley fluids as well as that of the Marsh cone geom-

etry on the flow time. Lastly, the semi-analytical approach offers

possibilities of determining the rheological characteristics of a

Herschel–Bulkley fluid from flow time measurements whereas

this seems to be unpractical with numerical simulation.

3. Experimental validation

In order to validate the established semi-analytical approach,

we have carried out experimental measurements on some cement

grouts of various water/cement ratios.

The concoction of the cement grouts was carried out usinga propeller mixer according to the following procedure: cement

(CEM I 52.5N CP2) is introduced into water during 2 min under

the rotation velocity 1200 rpm; the mixture (of volume equal to

3 l approximately) is then mixed during 5 min by respecting the

following stages: 2 min at 1800 rpm, 1 min at 1500 rpm and then

2 min at 1800 rpm.

The rheological behavior of the cement grouts is charac-

terized by coaxial cylinders rheometer Haake RS150 with an

external cylinder of type Z43 and an inner of type Z31 accord-

ing to the standard DIN 53018. To decrease the influence of

slip which occurs between the grouts and the smooth surface of

the inner cylinder, especially at low shear rate and at high solid

concentration [21,22], the surface of the inner cylinder is maderough by sanding. Then, the diameter of this sanded cylinder

is measured and introduced into the measurement software. In

order to homogenize thesample, to decrease the hysteresis effect

and to give a reproducible reference state to the grout where all

the bonds between the cement particles are broken, the grout

once placed in the rheometer is pre-sheared during 3 min (30 s

for the shear rate ascent from 0 to 500 s−1, 120 s at 500 s−1, 30 s

for the descent from500to 0 s−1) at 10 min after the introduction

of cement into water. It is then left at rest during 1 min so that

the interparticle bonds are restored. The ascent flow curve and

then the descent flow curve are finally measured in steady mode:

15 stages during 5 min for each flow curve in a range of shear




Fig.5. Someexamplesof descentflow curves, measuredexperimentally(points)

and fitted by the Herschel–Bulkley model (lines).

rate comprised between 0.1 and 100 s−1. In the present study,

the descent flow curves are used for the determination of the

rheological characteristics of the studied cement grouts consid-

ered as Herschel–Bulkley fluids. Fig. 5 presents some examples

of descent flow curves, measured experimentally (points) and

fitted by the Herschel–Bulkley model (lines).

In parallel, the flow time of 1 l of grout through the Marsh

cone equipped of a nozzle of 8 mm in diameter has been mea-

sured (at 14 min after the introduction of cement into water)

on the same batch of cement grouts and under the same envi-

ronmental conditions. The density of the grouts has also been

measured.

All experimental measurements have been carried out at a

constant temperature 23± 1 ◦C. Table 1 presents the rheologi-calcharacteristics andthe flow time of thestudied cementgrouts,

determined experimentally. On the basis of measured rheolog-

ical characteristics, we have calculated the flow time of these

cement grouts through the Marsh cone by numerical resolu-

tion of the integral Eq. (21). We have also numerically modeled

(using the code Fluent 6.1) the flow of 5 grouts (water/cement

ratio: 0.60, 0.55, 0.50, 0.45, 0.42) through the Marsh cone by

Table 1

Rheological characteristics and flow time of the studied cement grouts, deter-

mined experimentally

No. W/C Rheological characteristics Flow time (s)

ρ (kg/m3) τ 0 (Pa) K (Pasn) n

1 0.40 1931 15.7 14.28 0.390 107.7

2 0.41 1919 15.1 7.45 0.472 63.0

3 0.42 1907 13.8 9.08 0.403 42.9

4 0.43 1895 12.6 5.33 0.478 33.6

5 0.44 1884 11.6 4.99 0.478 27.9

6 0.45 1873 10.8 4.90 0.455 24.1

7 0.46 1860 9.5 4.61 0.441 21.2

8 0.48 1842 8.6 5.30 0.390 18.2

9 0.50 1816 8.1 3.87 0.408 17.0

10 0.52 1802 7.3 2.69 0.429 15.8

11 0.55 1766 5.6 1.84 0.454 14.4

12 0.60 1726 3.2 1.32 0.447 12.8

Fig. 6. Comparison of flow times of 1 l of grout through the Marsh cone given

by the semi-analytical approach (Eq. (21)) and the numerical simulation with

the flow time measured experimentally.

pursuing the numerical calculation until 1 l of grout flowing out.

The numerical computation time is very long, varying from a

few hours to several days, depending on the flow velocity of

each grout. This is due to the fact that the lower the flow veloc-

ity of grout is, the more the time step must be decreased to ensure

the solution convergence and stability while the more the flow

time of 1 l of grout increases. With a PC of processor Pentium IV

2 GHz and of memory 512 M, the numerical computation time

cumulated for these five grouts is 1 week approximately.

Fig. 6 presents the comparison of the flow times given by the

semi-analytical approach (Eq. (21)) and by numerical simula-

tion with the flow time measured experimentally. It is noted that

the calculated flow time and the flow time obtained by numer-

ical simulation are very close to the measured flow time. Thedeviation is lower than 15% for the studied cement grouts. This

allows to conclude that the numerical simulation of the flow of

Herschel–Bulkley fluids through theMarshcone is good andthat

the semi-analytical approach is validated satisfactorily exper-

imentally. However, a larger number of tests is necessary to

ensure that the semi-analytical approach is verified in a wide

range of rheological characteristics of cement grouts.

4. Conclusion

The present studyproposes a semi-analytical approach allow-

ing to determine the flow time of cement grouts considered asHerschel–Bulkley fluids through the Marsh cone. This approach

has been established initially on the basis of the following

assumptions: incompressible fluid, plane free surface and flow

of the Poiseuille type in the cylindrical nozzle. Because the

last assumption is not verified for all the fluids, a corrective

coefficient of the velocity taking into account the length of

establishment of the Poiseuille flow field determined based on

numerical simulation results has been introduced. With this cor-

rection, the proposed approach presents a deviation lower than

12% compared to numerical simulation. It has been validated

satisfactorily by the experiment on some cement grouts of vari-

ous water/cement ratios with a deviation lower than 15%.




The proposed semi-analytical approach presents several sig-

nificant advantages. Firstly, it allows the very fast determination

of the flow time through the Marsh cone according to the rhe-

ological characteristics of the grout, compared to numerical

simulation. Secondly, the semi-analytical approach allows to

understand in a systematic way the influence of the rheologi-

cal parameters of cement grouts as well as that of Marsh cone

geometry on the flow time. Lastly, it offers possibilities of deter-

mining the intrinsic rheological characteristics of cement grouts

from measurements of the flow time through the Marsh cone.

References

[1] NF P 18-358: Adjuvants pour betons, mortiers et coulis – Coulis courants

d’injection pour precontrainte – Mesure de la fluidite et de la reduction

d’eau, 1985.

[2] NF P 18-507: Additions pour beton hydraulique – Besoin en eau, controle

de la regularite – Methode par mesure de la fluidite par ecoulement “au

cone de Marsh”, 1992.

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