COMPARISON OF STATISTICAL MIX-DESIGN

PROPORTIONS OF

HIGH STRENGTH SELF-COMPACTING CONCRETE

Özlem AKALIN, Plustechno

Bahar SENNAROĞLU, Marmara University

Outline

Objectives Need for optimization of HS-SCC Statistical mixture experimental

design Comparison of SMD method

results with Okamura’s Rule Conclusion

Objectives

Need for HS-SCC mixture proportioning

Statistical Mixture Experimental Design Method

Optimum proportions of HS-SCC (C100/115) concrete class using SMD method

Comparing the results obtained from SMD method with Okamura’s Rule

HSC demand is increasing due to its technical and economical

benefits

•Concrete or composite column is more

economical than building with a pure

steel

•Taking full advantage of increased

compressive strength :

reducing amount of steel, reducing

column size to increase usable floor

space or allowing additional stories

without detracting from lower floors

The development of SCC was started in 1983 to find a solution for more durable concrete structures in Japan.

Self Compacting Concrete

Prof.Dr.Hajime Okamura

Kochi University of Technology

SCC is a special type of concrete that has a high resistance to

segregation

•Adequate compaction to pour

concrete

•Better concrete quality

•Shorter construction period

Concrete design is an optimization of mixture

Concrete Classes (TS EN 206-1)

C8/10C12/15C16/20C20/25C30/37C35/45C40/50C45/55C50/60C55/67C60/75C70/85C80/95

C90/105C100/115

HSC

HSC mixture proportioning

* HSC mixture proportioning is a more critical process than the normal strength concrete. Many trial batches are required to generate data that enables the researcher to identify optimum mixture proportions.*ACI Manual of Concrete Practice,1997.

Mixture Experiments

The measured response is assumed to depend only on the

proportions of ingredients present in the mixture and not on

the amount of mixture

Experiment and you’ll see! (Cole Porter)

Mixture Experiments

A q-components mixture in which represents the proportion of the i th component present in mixture,

The composition space of the q components takes the form of a regular dimensional simplex.

ix

0 1 1,2,...,ix i q 1

1q

iix

1q

Physical, theoretical, or economic considerations often impose additional constraints on individual components

0 1 1,2,..., i i iL x U i q

* Quenouille, M.H

Mixture Experiments

The purpose of mixture experiments is to build an appropriate model relating the response(s) to components .

Most commonly used mixture model forms in fitting data are the second-degree polynomials introduced by (Scheffé, 1958) of the form

1 2, ,..., qx x x

1

q q q

i i ij i ji i j

E Y x x x

D-optimal Design for HS-SCC was used to mathematically model the influence of eight mixture parameters and their 2-way

interactions on responses

8 mixture parameters

Cement (c), Silica fume(sf), fly ash(pfa), water(w), natural sand(n-s), crushed sand(c-s), aggregate(agg), chemical admixture(adm)

Responses T50 slump flow time, Slump Flow, Compressive

Strength, Appearance, RCP

Constraints on Mixture Components

(L/m3)

Component ID Mimimum Maximum

Cement c 109.65 172.28

Silica fume sf 7.95 27.58

Fly ash pfa 18.06 85.31

Natural sand n-s 108.08 175.63

Crushed sand c-s 137.33 206.06

Aggregate agg 338.68 414.77

Admixture adm 6 10

Water w 139.99 160.02

D-optimal Design Mixtures Proportions (L/m3)

Run c w sf pfa n-s c-s agg adm

1 126.37

139.99

27.58 85.31 108.08

137.33

347.04

10.0

2 121.61

139.99

7.95 18.06 131.99

137.33

414.77

10.0

3 131.16

160.02

18.29 18.06 108.08

201.41

338.68

6.0

4 131.16

160.02

7.95 18.06 175.63

138.29

340.59

10.0

5 116.82

147.17

7.95 78.38 108.08

178.61

338.68

6.0

6 156.46

140.19

7.95 18.27 108.08

206.06

338.68

6.0

7 131.16

160.02

27.58 51.92 108.08

137.33

355.61

10.0

8 172.28

158.13

7.95 53.25 108.08

137.33

338.68

6.0

9 156.24

139.99

27.58 18.06 123.33

167.82

338.68

10.0

…….46 mixtures

Experimental Test Results

RunFlow(cm)

T50(S)

U.wt.(kg/m3)

App.By

Sight

1 day(MPa)

7 days(MPa)

28 days(MPa)

RCP(C)

Cost($/m3)

1 70 9.5 2.425 5 27.5 98.0 129.2 11.9 122.6

2 57 11.4 2.463 2 4.3 57.3 80.0 40.3 75.2

3 67 4.6 2.456 4 17.4 71.9 94.1 30.2 94.2

4 71 5.5 2.453 2 2.3 45.8 64.9 61.2 77.2

5 70 8.7 2.438 5 18.8 75.0 103.0 40.2 72.4

6 65 13.7 2.469 5 31.9 97.3 123.8 40.5 77.5

……46

1

q q q

i i ij i ji i j

E Y x x x

Analysis of mixture experiment requires

1)Developing regression model relating response variable to components

2)Use of model for prediction and optimization

Second degree Scheffé Polynomials are considered since observations indicate that the interaction terms are important

Statistical Analyses Results

Responses S PRESS R-Sq (%)

R-Sq (adj)(%)

MSE ModelP-value

Lack-of-fit

P-value

Flow 7.022248

39248.2 95.40 79.32 49.32 0.003 0.076

T50 4.65219 22221.4 95.37 79.16 21.64 0.003 0.059

1 day 3.54336 6958.2 97.38 88.23 12.55 0.000 0.280

7 day 3.42324 14290.8 98.92 95.13 11.71 0.000 0.017

28 day 4.15245 12791.3 98.90 95.03 17.24 0.000 0.068

RCP 7.31498 53385.0 92.97 68.38 53.51 0.015 0.405

Appearance

0.834594

157.026 91.55 61.98 0.696 0.031 0.914

Desirability Objective Function

1 2

11

1 21

ii

n i

rnrr rr rn i

i

D d d d d

where n is the number of responses in the measure.

The numerical optimization finds a point maximizes desirability function.

In this study desired response parameters were defined as target, maximum or minimum by giving importance degree and response optimization suggested input variables by predicting responses and desirability are tabulated in table.

Optimization Targets

Parameters Goal Lower(L)

Target(T)

Upper(U)

Weight(W)

Importance

(r )

Flow in. (cm)

Target 25.59(65)

27.56(70)

29.53(75)

1 5

T50 (s) Target 4 5 6 1 5

C. Strength psi (MPa)

Target 15950(110)

16675(115)

18125(125)

1 5

Appearance Maximum

4 5 5 1 4

Cost , $/yd³($/m³)

Minimum 53.570

53.570

68.890

1 4

Optimization SolutionsComponents (L/m³) (kg/m3) (lb/yd3)

Cement 138.5 431 149.5

Water 150.7 151 52.4

Silica fume 14.2 31 10.8

Fly ash 20.8 45 15.6

Natural sand 147.0 385 133.6

Crushed sand

165.8 441 153

aggregate 338.7 914 317

admixture 6.0 6.4 2.2

Comparison of results

Predicted Results

From analysis

Confirmation test

results

Trial&Errorresults

Slump Flow 71.0 cm 69 cm 65-72 cm

T50 Flow time 5.00 s 8.00 s 4.8-9.6 s

Compressive Strength at (28 days)

116.0 MPa 106 MPa 61-121 MPa

Appearance 4.88 5 NA

Comparison of Results(L/m3) Trial & Error Statistical

Mixture

Cement 144 138.5

Silica fume 16 14.2

Fly ash 33 20.8

Natural sand 111-146 147.0

Crushed sand 138-170 165.8

Aggregate 312-370 338.7

admixture 9 6

Cost ($/m3) 97.6 87.6

Okamura’s Rules for SCC

1) The volume of cement and fine powder: 170 <Vc+Vf= 187 < 200

2) Water/(cement+fine powder) by volume:

0.85 <Vw/(Vc+Vf) = 0.96 < 1.20

3) Volume of coarse aggregate : VG ≤ 340 L/m3

4) Maximum size of coarse aggregate:

Dmax≤ 20

Okamura’s Rules SMD’s Optimum Results

0.85 <Vw/(Vc+Vf+Vsf) < 1.20 0.85 <151/(138.6+14.1+21.0) = 0.87<

1.20

170 <Vc+Vf+Vsf< 200 (L/m3) 170 <173.7< 200

VG ≤ 340 (L/m3) VG =338.5< 340

Dmax< 25 (mm) Dmax = 12 < 25

Comparison of SMDresults with Okamura’s Rules

Conclusion

Statistical experimental design provides systematic approach for concrete design,

Mixture experiments give advantage to reach optimum proportions of concrete mixture components at a minimum cost,

Results of SMD for HS-SCC (C100/115) are confirmed with Okamura’s Rules for SCC.

THANK YOU