A performance -based method for granular based method for granular -paste mix design

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A performance-based method for granular-paste mix design

HOORNAHAD, HOOMAN

1

and KOENDERS, EDUARD A. B.

2

ABSTRACT:

In this paper a performance-based method for the design of granular-paste mixtures

will be proposed. Focus will be on the selection and proportioning of constituents to produce a mixture with a pre-defined shape holding ability. Shape holding ability of mixtures will be characterized by the shape preservation factor SPF. This SPF shows the ability of a mixture to preserve its shape after being demolded from a slump test. SPF is the ratio of the cross sectional area of a sample after and before demolding. By increasing the flowability of a mixture, the SPF decreases. In this study a mixture is first decomposed into aggregate, void paste and excess paste. Then a combination of the consistency of the paste and excess paste volume is determined for a required SPF. Finally, depending on the aggregate grading, the volumes of paste and aggregates in the system are determined.

Keywords: Performance-based mix design method; granular-paste mixture; shape preservation factor

NOTATION

A cross sectional area; N number of aggregate particles; R radius of an aggregate particle, Vt volume of the sample; Va specific volume of the aggregates; Vb bulk volume of the aggregates

in compacted state; Vp total paste volume; Vpv void paste volume; Vpex excess paste volume;

δ pex thickness of the excess paste layer.

1 INTRODUCTION

The effect of any “action” imposed to early age granular-paste mixtures during transportation, placement and compaction, depends on the rheological properties of the paste matrix. Besides, the mechanical performance and durability of this type of material can be influenced by the rheological behavior at early age as well [1]. Therefore, understanding the viscous behavior of a mixture during this particular period is a crucial requirement for the technical and economical success of professional production sites [2]. From rheological perspective fresh granular-paste materials are considered as an intermediate class that behave like somewhere in-between pastes and granular materials [3]. These materials are capable of showing rheological behavior which can be close to either a paste or granular system depending on properties and proportions of components in a mixture. As long as the volume fraction of aggregate particles is far from the maximum packing density of aggregate particles, the material can usually be considered as a paste like material [4], dominated by paste behavior. By increasing the volume fraction of aggregate particles, the behavior gradually changes into that of a cohesive granular-like material. In this study a quantified approach is proposed addressing a performance-based method for the design of granular-paste mixtures.

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A fresh mixture is considered as a discontinuous system and it is characterized as a two-phase model [4, 5]. These phases represent the aggregates and paste in a mixture (see Figure 1(a)). Paste phase consists of powder particles, water and admixtures. 0.125 mm is considered for the boundary size between the aggregates and powder particles [6]. The granular phase is characterized by a factor ς which is a relative measure for describing the packing density of the aggregates in a system. ς can be expressed as follows:

a b V 1 V    (1) .

where Va is the specific (solid) aggregate volume and Vb is the bulk aggregate volume which

represents an aggregate skeleton in a compacted state (see Figure1(b)). The bulk volume of the aggregates when they are in compacted state can be determined according to ASTM C 29[7]. The total paste volume Vp is divided into two parts: 1) void paste Vpv and 2) excess paste Vpex. The void

paste is used for filling the void space between the aggregates when they are in a compacted state (see Figure 1(b)). The excess paste, which is the remaining portion of the paste, is used to form a layer with constant thickness around each individual aggregate particle (δpex) (see Figure 1(c)). The

volume fraction of void paste (Vpv) can be calculated with Equation 2:

  _ _   pv a 1 V - 1 V ς (2) .

The volume of the excess paste (Vpex) is calculated by subtracting the volume of the void paste (Vpv)

from the total volume of the paste (Vp) as shown in Equation 3:

pex p pv

V V V _{(3) .}

In the calculation procedure for the thickness of the excess paste it is presumed that the shape of the aggregate particles is spherical and the thickness of the excess paste around the particles is the same for all particle sizes. The latter presupposes a homogeneous dispersion of the aggregate particles in the mixture leading to a constant minimum surface to surface distance between the particles. Under these considerations, the specific volume of aggregates (Va) and the excess paste

volume (Vpex) can be calculated with Equation 4 and Equation 5, where Ri and Ni represent the radius

of particles of class i and the number of particles per class i, respectively. For Va we have: 3 a i i 4 V NR 3  



(4) .

and for Vpex:







3 ₃



pex i i pex i 4 V N R R 3  



   (5) .

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With this approach, the rheological behavior of a granular-paste mixture during its fresh state can be described qualitatively according to the “excess paste theory”, which is introduced by Kennedy [8]. According to this theory, the rheological behavior (degree of workability) is controlled by the aggregate-paste-aggregate interactions that are represented by the properties of the excess paste layers. The rheological behavior of granular-paste mixture is related to the consistency (relative flowability) of the cement paste and the thickness of the excess paste layers. By increasing consistency of the cement paste and excess paste volume a higher degree of workability would be expected for a given granular-paste mixture [8]. In this study the consistency of the paste is characterized by critical (yield) stress of the paste [4].

(a) Real system

(b) Intermediate system

(c) Equivalent system

Figure 1. Two-phase aggregate-paste model for granular-paste mixture. Vt, Va, Vb, Vp, Vpv, Vpex,

and δ pex are volume of the sample, specific volume of the aggregates, bulk volume of the

aggregates in compacted state, total paste volume, void paste volume, excess paste volume and thickness of the excess paste layer, respectively.

Void δ pex Aggregate Vt Va Vp Vpex Vb Vt Void paste Aggregate particle

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MIXTURES

The rheological performance of fresh mixtures is evaluated based on the shape holding ability of mixtures. Shape holding ability of mixtures is characterized by the shape preservation factor SPF. This SPF shows the ability of a mixture to preserve its shape after the slump test is being demolded. The cone used in this study is selected according to (NEN-EN12350-5) [9]. SPF is the ratio of the cross sectional area of a 3D sample after and before demolding, i.e. Af/Ai (see Figure 2). A SPF is

about 1 for a mixture which shows almost no deformation, i.e. no-slump mixture (NSLM). For a conventional self-compacting mixture (SCM) with a spread diameter ≥~600 mm, the SPF is less than about 0.4 (see Table 1). The correlation between the relative slump Hs/Ho and the relative spread D/Do of a mixture is shown in Figure 3. In these graphs a mixture can be identified by its excess paste volume Vpex and its paste critical stress Cs. The specification of aggregates is given in Table 2.

The maximum SPF for a self-compacting mixture is about 0.7. A mixture with SPF=0.7 shows a relative spread D/Do~1.4-1.5 and a relative slump Hs/Ho~0.5 after demolding (see Figure 3). A mixture with SPF=0.7 is denoted a “self-compacting high shape preserving mixture (SCHSPM)”. For the SPF>0.7, extra energy is required for proper compaction [4].

Table 1. Shape preservation factor (SPF) for the target mixture

Shape preservation factor (SPF)

Characteristic of the target mixture

Shape holding ability External energy for

compaction

0.9 ≤ SPF ≤ 1.0 Excellent

(NSLM*) Yes

0.7 < SPF < 0.9 Very high Yes

SPF = 0.7 High (SCHSPM**) No 0.4 < SPF < 0.7 Average No SPF ≤ 0.4 Low (SCM***) No * NSLM: No-slump mixture

** SCHSPM: Self-compacting high shape preserving mixture *** SCM: Self-compacting mixture

Figure 2. The cross sectional area of a 3D sample after and before demolding. For a 3D sample

Af ≤Ai. y x z Ai Af

Before demolding (initial state)

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Table 2. Characteristics of the mix components

Component Specification

Aggregates

Aggregates with specific density between 2500-2600 kg/m3, maximum size of 8 mm and smaller and minimum size of 0.125 mm

Aggregate particles with a shape deviation of about 3% from the spherical shape. Shape deviation determines the minimum inter-particle distance at which particles become in direct contact [4,5] Fineness modulus of granular material is kept between 3.5 and 5.0 to avoid 1) the effect of the gravitational forces acting on aggregate particles [4] and 2) the effect of the very fine aggregate particles, i.e. the aggregate particles which are in the size range of the large powder particles [4], on deformability of the mixtures

1 1,3 1,6 1,9 2,2 2,5 2,8 3,1 22 27 32 37 42 47 52 57 62 D/Do C s(P a ) Cs 1 1,3 1,6 1,9 2,2 2,5 2,8 3,1 22 27 32 37 42 47 52 57 62 D/Do C s(P a ) 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 22 27 32 37 42 47 52 57 62 Hs/Ho C s( Pa ) 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 D/Do Hs/Ho 0.7 <SPF≤1.0 1.0≥SPF>0.7 ×O

Medium slump cone Medium slump cone

D

Self-compacting mixtures Self-compacting mixtures

×O

3.1 2.8 2.5 2.2 1.9 1.6 1.3 1.0

Do Ho

Hs

Figure 3. Correlation between the relative spread diameter (D/Do) and relative slump (Hs/Ho), vs.

critical stress (Cs) of the paste for various excess paste volumes (Vpex). The specification

of aggregates is given in Table 2. O represents a SCHSPM with Vpex=17 % and Cs=30

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The mix design procedure for a granular-paste mixture with a pre-defined shape preservation factor (SPF) is presented in a flow chart, see Figure 4. The characteristics of the aggregates are given in Table 2. In this paper the focus is on the mixtures with cement ratio W/C=0.36 and water-powder ratio W/P=0.24. Paste mixtures used in this study are prepared with Portland cement I 52.5 (ρs=3150 kg/m3), limestone powder (ρs= 2640 kg/m3) and Glenium 51 as a superplasticizer. The

consistency of the paste which is characterized by critical stress (yield stress) is controlled by the amount of superplasticizer.

Figure 4. Flow chart of a mix design for a mixture with W/C=0.36 and W/P=0.24.

No

Yes

Choose the shape preservation factor from Table 1

Choose the critical stress Cs of the paste fromFigure 5(b)

Determine the relative slump (Hs/Ho) from Figure 5(a)

 Determine the quantities of aggregates, powders and water fromFigure 5(d)

 Determine the proportion of superplactisizer SP from Figure 5(e)

Choose the packing density ς of granular material from Figure 5 (c)

Determine the volume fraction of the total paste Vp from Figure 5(c)

End

Determine the volume fraction of the excess paste Vpex fromFigure 5(b)

Start Is it possible to change the aggregate? No Yes

Verify the mixture with experiment

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Step 1:

The mix design starts with choosing the shape preservation factor (SPF). SPF can be chosen form Table 1.

Step 2:

Determine the relative slump Hs/Ho of the sample from Figure 5(a) for the chosen SPF. Step 3:

Choose the critical stress Cs of the paste from Figure 5(b) for the obtained value of the relative slump Hs/Ho. The corresponding relative spread diameter (D/Do) can be estimated from Figure 3.

Step 4:

Determine the volume fraction of the excess paste Vpex from Figure 5(b) for the chosen Cs.

Figure 5. Mix design chart for granular-paste mixtures with W/C=0.36 and W/P=0.24. The specific

density of aggregate particles ρs =2560 kg/m3.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10 12 14 16 18 20 22 24 Hs/Ho Vpex (%) 0.5 0.6 0.7 0.8 0.9 1.0 1.1 22 27 32 37 42 47 52 57 Vo lu m e fra ct io n o f S P in t h e p a st e (%) Cs(Pa)

Paste: Water + CEM I 52.5+Limestone +SP

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 H s/ H o SPF(-) SCC NSlC 22 27 32 37 42 47 52 10 12 14 16 18 20 22 24 Vp (% ) Vpex (%) 22 27 32 37 42 47 52 50 300 550 800 1050 1300 1550 1800 2050 Weight (kg/m3₎ W/C=0.36, W/P= 0.24

Start

22 27 32 37 42 47 52 10 12 14 16 18 20 22 24 Vp (% ) Vpex (%) (a) (b) (e) (d) (c)

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Choose the packing density ς of the granular material from Figure 5(c). The packing density ς can be calculated with Equation 1.

Step 6:

Determine the volume fraction of the total paste Vp for the chosen granular material and the volume

fraction of excess paste Vpex (see Figure 5(c)). Step 7:

Determine the quantities of aggregates, powders and water per m3 of mixture from Figure 5(d).

Step 8:

Determine the volume fraction of superplactisizer SP in the unit volume of the paste from Figure 5(e) for the chosen critical stress Cs.

Step 9:

Determine the amount of superplactisizer SP per m3 of a mixture from the information derived in steps 6 and 8.

Step 10:

Prepare a trial mixture and do the slump test. If the required performance is obtained, the mix design process ends. Otherwise go back to the step 3 or 5.

5 EXAMPLE

An example is presented in this section to illustrate of application of the mix design process. The target mixture is a self-compacting high shape preserving mixture (SCHSPM). The packing density of granular material ς=0.82. The maximum aggregate size is 8 mm. The specific density of aggregate particles ρs=2560 kg/m3. The critical stress of the paste Cs=37 Pa. Employing the sequence outlined

in section 4, the quantities of ingredients per m3 of mixture are calculated as follows:

Step 1:

From Table 1, the desired shape preservation factor SPF= 0.7. Step 2:

From Figure 5(a), the relative slump Hs/Ho=0.5. The corresponding relative spread diameter (D/Do) is about 1.45 (see Figure 3).

Step 3:

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Step 4:

From Figure 5(b), the excess paste volume Vpex needed to produce a SCHSPM with Cs=37 Pa is

found to be about 19.3 %. Step 5:

As indicated previously, the packing density of granular material ς=0.82. Step 6:

From Figure 5(c), the volume fraction of the total paste Vp for the chosen granular material and the

volume fraction of excess paste Vpex is found to be about 34 %.

Step 7:

The quantities of aggregates, powders and water per m3 of mixture are determined from Figure 5(d). The values are given in Table 3.

Step 8:

From Figure 5(e), the volume fraction of superplactisizer SP in the unit volume of the paste is found to be about 0.75 %.

Step 9:

From the information derived in steps 6 and 8 the amount of the SP per m3 of mixture is found to be about 2.5 liter.

Table 3. Calculated mix composition of a self-compacting high shape preserving mixture per m3 following the performance-based quantification approach as presented in this paper.

Aggregate (Kg/m3) Cement (Kg/m3) Limestone powder (Kg/m3) Water (Kg/m3) SP (Liter) 1695 390 190 140 2.5

6 CONCLUSIONS

In this paper a performance-based mix design method for granular-paste mixtures was proposed. Granular-paste mixtures were designed in order to achieve a pre-defined shape preservation factor (SPF). The defined shape preservation factor, 0<SPF≤1, indicates the ability of a mixture to preserve its shape directly after demolding. By increasing the flowability of a mixture, the SPF decreases. For mixtures with SPF>0.7, extra energy is required for compaction. Mixtures with SPF≤0.7 compact under their own weight. The mix design method proposed in this paper can be used for mixtures with the wide range of workability from no-slump to self-compacting mixtures. Firstly, a mixture is

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shape deviation of about 3 % from the spherical shape, specific density between 2500-2600 kg/m , maximum size of 8 mm and smaller, minimum size of 0.125 mm and had a fineness modulus between 3.5 and 5.0.

REFERENCES

[1] Abrams, D.A.: Proportioning Granular-paste Mixtures. ACI Journal, 18(1922) 2, 174-181.

[2] Li, Z.: State of Workability Design Technology for Fresh Granular-paste in Japan. Cement and

Granular-paste Research, 37(2007), 1308-1320.

[3] Coussot, P.: Rheometry of Pastes, Suspensions, and Granular Materials, John Wiley & Sons: New Jersey 2005.

[4] Hoornahad H.:Toward development of self-compacting no-slump granular-paste mixtures. PhD thesis, Delft University of Technology, 2013.

[5] Hoornahad, H. & Koenders, E.: Effect of the mix composition on rheological behavior of a fresh granular-cement paste material. In: Proc. of the 1st Int. Conf. on Rheology and Processing of

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[6] EFNARC (European Federation of National Trade Associations Representing Producers and Applicators of Specialist Building Products): Specification and guidelines for self-compacting

granular-paste. Hampshire February 2002.

[7] ASTM C29 / C29M: Standard test method for bulk density ("unit weight") and voids in

aggregate.1997.

[8] Kennedy, C.T.: The design of granular-paste mixes. J Proc. ACI, 36(1940), 373-400. [9] NEN-EN 12350-5: Testing fresh granular-paste - Part 5: Flow Table Test. 2005.