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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
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