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Concrete optimized mix proportioning (COMP) a reply to the discussion by V.M. Malhotra
Vol. 2, No. 2
243 DISCUSSION
CONCRETEOPTIMIZEDMIX PROPORTIONING(COMP) A REPLYTO THE DISCUSSION BY V. M. MALHOTRA
By John P. Cannon Case Western Reserve University, Cleveland, Ohio and G. R. Krishna Murti Osmania University, Hyderabad, India
There were two aspects to our paper. The main idea was the provision of an alternative, rather comprehensive, approach to concrete mix design in whtch the problem is cast as a ltnear programming problem in which the objective function (cost of concrete per cubic yard) is to be minimized subJect to constraints (requlreraents) to assure adequate product performance. Thus, acceptable levels of strength and workability are "guaranteed" by the constraints Inclosed. How good ts the guarantee? I t ts as good (or bad) as the relationships which are presumed to exist between the design variables (sand, gravel, cemnt, and water, In this case) and the product behavior (strength and workability). Thts brtngs us to the secondary contribution of our paper whtch ts the provision of reasonable, but by no means f t n a l , functional relationships ltnktng the design variables (mtx ingredients) to the concrete behavior (workability and strength). We think of this matter as occupying a secondary role in this paper because we did not originate the relationships, but chose what seemed to be the best wisdom of other investigators (Abram, Walker, B1oem, Gi lkey, Cordon, Gaynor, Murdock, Popovtcs, Orchard, e t c . ) . This is neither intended to t ~ l y that we absolve ourselves from the responstbiltty of using the best possible functional relatlonshtps, nor that the authors in the above l i s t are somehow to be blamed for any shortcomings in the relationships chosen. What does seem i ~ o r t a n t ts that the lack of perfection in the chosen functional relationships (e.g., the relationship used to express strength f c ' , as a function of water/cement ratio and MSA) not be used as a measure of the validity of applying the principles of optimization to proportion concrete mixes. What of Malhotra's criticism then?
I t is valid, in the main, when
244
Vol. 2, No. 2
DISCUSSION applied to the secondary aspects of this paper, i . e . , the question of how strength and workability are affected by the mix ingredients.
The criticisms
must not, however, cloud the primary point which is that we now have a rather general computer-based method of proportioning a concrete to satisfy a given objective (least cost in this case) without violating chosen performance requirements (strength and workability), provided the relationships between the design variables (mix ingredients) and the performance requirements are known. Mr. Malhotra complains that the cost comparison between the optimized mix and the ACI mix is "highly erroneous" and "misleading". His f i r s t charge is based on his belief that the aggregate fraction of the COMPmix has too l i t t l e sand to be workable. The authors admit that the sand content is on the lean side.
But the fact remains that i t is the least expensive
mix that satisfies the constraints imposed. What are the causes of so l i t t l e sand being used? There are two causes: (a) the sand was assumed to have a higher unit cost than the coarse aggregate (sand - $4.00, gravel - $3.00) and (b) the sand contributes, more than does an equal amount of coarse aggregate, to the water requirement (to maintain a certain workability).
This in turn, increases the cement content required to
maintain a required strength.
Both causes, (a) and (b), suggest that zero
sand would be most economical. Why is this not acceptable? Becauseworkability is not independent of the aggregate grading. Hence, the limiting grading curve (in this case the coarse limit) places a constraint on how much sand can be eliminated.
Figure 3 of the paper illustrates these ideas. Mr.
Malhotra says that 31% sand is too l i t t l e for good workability.
He thinks i t
should be at least 40% (for slum~s below 3" which is applicable here). Perhaps so.
The limiting grading curve could easily be adjusted to reflect this
thinking.
This paper used Orchard's grading limits.
I f i t be determined by a
user of COMPthat Orchard's grading curves are obsolete, as implied by Mr. Malhotra, then by all means he should adopt grading curves that are more suitable. The authors generally agree that grading curves of American origin would have added more weight, i f not validity, to their argument.
I t must be
understood, however, that there is no consensus, even among mix design experts on this continent, as to the correct grading limits for acceptable workability. A final point about the cost comparison example should be made. The authors purposely avoided making rash statements about the economical advantage to be gained from use of COMP. I t is not possible at this point to know
Vol. 2, No. 2
245 DISCUSSION
what the magnitude of that advantage is.
Examples, having varying degrees of
r e a l i t y , can be concocted to show cost savings of 1%, 5%, 10% or even 20%. I t is also possible to contrive examples for which the optimized mix cost is higher than the ACI mix! This could only result from imposing constraints on the COMPdesigned mix which are more severe than the corresponding requirements implied by the ACI mix. What COMPdoes lead to is the single most desirable (least cost) mix design for the conditions and constraints which are assumed. As we become able to express these conditions and constraints more precisely, the authors believe the use of optimized mix proportioning w i l l naturally increase. That view is shared by an ACI committee whose report* has more recently appeared: " Eventually enough w i l l be known about concrete proportioning and the effects of the proportions of concrete to reduce proportioning to a set of mathematical expressions which in turn can be put into small computers. All the engineer w i l l need to do is to feed into the computer the characteristics of the materials to be used, including t h e i r known v a r i a b i l i t y , and indicate to the computer that he wants concrete with a given level of strength, durability, workability, setting time, color and any other property that is important to a particular use of the concrete. The computer will then provide the answers as to the proportions of the various ingredients that should be used"
"Concrete--Year 2000", ACl Journal, August, 1971.
243 DISCUSSION
CONCRETEOPTIMIZEDMIX PROPORTIONING(COMP) A REPLYTO THE DISCUSSION BY V. M. MALHOTRA
By John P. Cannon Case Western Reserve University, Cleveland, Ohio and G. R. Krishna Murti Osmania University, Hyderabad, India
There were two aspects to our paper. The main idea was the provision of an alternative, rather comprehensive, approach to concrete mix design in whtch the problem is cast as a ltnear programming problem in which the objective function (cost of concrete per cubic yard) is to be minimized subJect to constraints (requlreraents) to assure adequate product performance. Thus, acceptable levels of strength and workability are "guaranteed" by the constraints Inclosed. How good ts the guarantee? I t ts as good (or bad) as the relationships which are presumed to exist between the design variables (sand, gravel, cemnt, and water, In this case) and the product behavior (strength and workability). Thts brtngs us to the secondary contribution of our paper whtch ts the provision of reasonable, but by no means f t n a l , functional relationships ltnktng the design variables (mtx ingredients) to the concrete behavior (workability and strength). We think of this matter as occupying a secondary role in this paper because we did not originate the relationships, but chose what seemed to be the best wisdom of other investigators (Abram, Walker, B1oem, Gi lkey, Cordon, Gaynor, Murdock, Popovtcs, Orchard, e t c . ) . This is neither intended to t ~ l y that we absolve ourselves from the responstbiltty of using the best possible functional relatlonshtps, nor that the authors in the above l i s t are somehow to be blamed for any shortcomings in the relationships chosen. What does seem i ~ o r t a n t ts that the lack of perfection in the chosen functional relationships (e.g., the relationship used to express strength f c ' , as a function of water/cement ratio and MSA) not be used as a measure of the validity of applying the principles of optimization to proportion concrete mixes. What of Malhotra's criticism then?
I t is valid, in the main, when
244
Vol. 2, No. 2
DISCUSSION applied to the secondary aspects of this paper, i . e . , the question of how strength and workability are affected by the mix ingredients.
The criticisms
must not, however, cloud the primary point which is that we now have a rather general computer-based method of proportioning a concrete to satisfy a given objective (least cost in this case) without violating chosen performance requirements (strength and workability), provided the relationships between the design variables (mix ingredients) and the performance requirements are known. Mr. Malhotra complains that the cost comparison between the optimized mix and the ACI mix is "highly erroneous" and "misleading". His f i r s t charge is based on his belief that the aggregate fraction of the COMPmix has too l i t t l e sand to be workable. The authors admit that the sand content is on the lean side.
But the fact remains that i t is the least expensive
mix that satisfies the constraints imposed. What are the causes of so l i t t l e sand being used? There are two causes: (a) the sand was assumed to have a higher unit cost than the coarse aggregate (sand - $4.00, gravel - $3.00) and (b) the sand contributes, more than does an equal amount of coarse aggregate, to the water requirement (to maintain a certain workability).
This in turn, increases the cement content required to
maintain a required strength.
Both causes, (a) and (b), suggest that zero
sand would be most economical. Why is this not acceptable? Becauseworkability is not independent of the aggregate grading. Hence, the limiting grading curve (in this case the coarse limit) places a constraint on how much sand can be eliminated.
Figure 3 of the paper illustrates these ideas. Mr.
Malhotra says that 31% sand is too l i t t l e for good workability.
He thinks i t
should be at least 40% (for slum~s below 3" which is applicable here). Perhaps so.
The limiting grading curve could easily be adjusted to reflect this
thinking.
This paper used Orchard's grading limits.
I f i t be determined by a
user of COMPthat Orchard's grading curves are obsolete, as implied by Mr. Malhotra, then by all means he should adopt grading curves that are more suitable. The authors generally agree that grading curves of American origin would have added more weight, i f not validity, to their argument.
I t must be
understood, however, that there is no consensus, even among mix design experts on this continent, as to the correct grading limits for acceptable workability. A final point about the cost comparison example should be made. The authors purposely avoided making rash statements about the economical advantage to be gained from use of COMP. I t is not possible at this point to know
Vol. 2, No. 2
245 DISCUSSION
what the magnitude of that advantage is.
Examples, having varying degrees of
r e a l i t y , can be concocted to show cost savings of 1%, 5%, 10% or even 20%. I t is also possible to contrive examples for which the optimized mix cost is higher than the ACI mix! This could only result from imposing constraints on the COMPdesigned mix which are more severe than the corresponding requirements implied by the ACI mix. What COMPdoes lead to is the single most desirable (least cost) mix design for the conditions and constraints which are assumed. As we become able to express these conditions and constraints more precisely, the authors believe the use of optimized mix proportioning w i l l naturally increase. That view is shared by an ACI committee whose report* has more recently appeared: " Eventually enough w i l l be known about concrete proportioning and the effects of the proportions of concrete to reduce proportioning to a set of mathematical expressions which in turn can be put into small computers. All the engineer w i l l need to do is to feed into the computer the characteristics of the materials to be used, including t h e i r known v a r i a b i l i t y , and indicate to the computer that he wants concrete with a given level of strength, durability, workability, setting time, color and any other property that is important to a particular use of the concrete. The computer will then provide the answers as to the proportions of the various ingredients that should be used"
"Concrete--Year 2000", ACl Journal, August, 1971.