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The percentage error and absolute percentage error of free-water cement ratio to obtain the cement content. The cement the results of individual concrete mix proportions and variables content also will be rounded up to the nearest 5kg. This introduces obtained with the mathematical equations and computer program double approximation, which the Program corrected, as one of the compared to those of the examples in the British DOE concrete objectives of the programming is to ensure better accuracy of the mix design code were calculated separately for each example.

The time efficiency analysis of the developed program was computed by observing the time required for running the concrete mix design for all the ten application examples manually using the British DOE code and also with the use of the generated program. The results are presented in Table 1. The optimization of the concrete mix design was carried out for each of the examples by considering the minimization of the cost function while maximizing the compressive strength of concrete. The optimization package selected forty-one 41 concrete mix batches during the optimization process.

The percentage errors of the results of variables of concrete mix design calculated with the program to those of the values available in the British DOE concrete mix design code generally varied between the values of A typical result of the percentage errors for example 1 is presented in Table 2. This percentage error is within the permissible limit. The main reason for this difference between the results generated by the program and those available in the British DOE code is that some Research article www.

This is much higher because all the design application examples are unique concrete mix designs on their own and are now replica of each other. Conclusions And Recommendation Mathematical Equations for concrete mix design, adjustments and optimization in accordance with British Department of Environment DOE method have been coded into computer programs written in Java programming language using Netbins 7. The developed software, named CLETJER are presented as a replacement to the tabular data, figures and charts available in the DOE concrete mix design manual usually used for conventional concrete mix design.

The need to: minimize considerably the expended human energy and computational errors; reduce the time taken in the concrete mix design process; eliminate interpolation of data, and optimize the desirable constituents of concrete to achieve optimum compressive strength at minimum cost, necessitated this work. All these needs were met in the developed programs. European Journal of Scientific Research. Abdullahi M. A 21 , These works encouraged the replacement of the manual 4.

Amiri B. Use of AFM technique to study the nano-silica effects statistical, numerical and computer programs. This present work, in concrete mixture. Indian Journal of Sciene and Technology, as presented, is unique in that it employs the use of the British 5 1 , DOE method of concrete mix design. It is specifically limited to 5. Bentz, D. National Institute of Standards and Technology.

The programs were written in Java language using the latest 6. Chris, C. Optimizing Concrete Mix Java 7 and the latest Netbins 7. Oklahoma Environment IDE. Dewar J. W8B 2. Dias, W. Neural Networks conversion of the values of other concrete mix variables from the for Predicting Properties of Concrete with Admixtures.

Tests on Fresh Concrete

Con- Inch-lb system of units to the Standard International S. Also, the program creates automatically Microsoft Word 9. Durocrete Mix Design Manual. Western Maharashtra: documents for the results of the optimization. Emuoyibogarhe O. Dapson Prints Ventures, Lagos. Fennis, S. The Use of types of concrete such as heavy weight, light weight, pumpable Particle Packing Models to Reduce the Water Demand concrete, etc.

Also, it is desirable that a thorough research into the of Concrete. Concrete Optimization with Re- the properties and behaviour of concrete mixes and design, be gard to Packing Density and Rheology.

Optimum Study and Engineering Application of Mixing Ratio for C50 Concrete

Version 1. The developed Gary K. Works and Housing, Nigeria, with a view to incorporating it in the com. Goodarzian H, Hejazi S. Optimization of the cross section of car lift column 5. References under pressure load using genetic algorithms. Indian Journal 1. Abdul Aleem M. Optimum mix of Science and Technology, 4 6 , — Indian Journal of Science and Grasim Industries Ltd.

Harun, T. Fuzzy Logic Model for the Prediction of Marianne, T. Else- ing Artificial Neural Network. Proceedings of Durability of vier Science Ltd, 40 3 , In fact, each manufacturing plant will have its own unique K factor curve depending on the type and quality of aggregates, the type and quality of hydraulic cement used, and the type and quality of mixing apparatus. The K factor curve will typically move up or increase with increasing mixing efficiency, aggregate strength, hydraulic cement strength, and other factors that systematically contribute to concrete strength.

So long as system inputs remain essentially the same, the K factor curve for a particular manufacturing plant can, at least in theory, be determined by identifying a single K factor point along the K factor curve and then constructing a logarithmic curve that passes through that point. Once an inappropriate K factor curve has been constructed for a particular manufacturing plant, the curve can be used to design and predict concrete strengths for a wide variety of different concretes produced by that manufacturing plant.

It should also be understood that there are different K factors depending on the context in which that term is used. The term "design K factor" refers to the K factor that is utilized within the improved DOC process of the present invention in order to design and virtually "test" a large number e. The design K factor will, of course, vary depending on the design strength, or guaranteed minimum strength, of a particular concrete composition. For a given set of raw materials inputs and processing equipment, there will typically be a single design K factor curve.

The terms "optimal K factor" and "true K factor" refer to K factors found along an optimal K factor curve that represents perfectly designed and mixed concrete by a manufacturing plant utilizing a given set of raw materials available. Thus, the "optimal" or "true" K factor can vary between different manufacturing plants and is therefore not an absolute number.

Nevertheless, for a given set of raw material inputs, there exists perfectly designed and manufactured concrete for which the optimal or true K factor can theoretically be used to predict strength. Because manufacturing plants and personnel cannot produce perfect concrete every time, there will typically be some degree of overdesign, however slight, to account for such variability.

Thus, the design K factor will typically differ from e. Notwithstanding such variation, the design K factor used to make a well optimized concrete composition will much more closely correlate to the optimal or true K factor than compared to apparent design K factors corresponding to less optimized or non-optimized concrete composition ' s. The term "apparent design K factor" refers to the K factor that can be ascertained for a preexisting concrete composition that may not have itself been designed using a K factor.

How To Do Mix Design Of Concrete As Per IS Code 10262 - SSD Condition

Even if a K factor is not used to design a concrete composition, it nevertheless can be assigned an apparent design K factor based on what K factor would have been used to design such concrete using the disclosed optimization procedures. In the case of a poorly optimized or overdesigned concrete composition, the apparent design K factor will deviate significantly from the optimal or true K factor. The apparent design K factors of such compositions will deviate much more than the design K factors of well optimized concrete made using the same inputs.

The apparent design K factor is determined based on the design strength i. The term "actual K factor" shall refer to the K factor that is determined by mixing up a concrete composition according to a given mix design, allowing the concrete to cure, measuring the compressive strength of the concrete, and then calculating the actual K factor based on actual strength and quantity of components within the concrete composition.

For a properly prepared concrete composition, the actual K factor will exceed the design K factor since the design K factor typically accounts for variations in concrete strength. A graphic representation of how the K factor varies with the compressive strength of concrete is depicted in Figure 1. Figure 1 actually includes two curved lines following a logarithmic curve corresponding to two different K factors that have been determined by the inventors.

The lower K factor curve corresponds to concrete compositions made utilizing hydraulic cement, water, aggregate and other standard admixtures used in the art. The upper K factor line corresponds to hydraulic cement compositions that additionally include an amine strengthener. In order to obtain increased strength, and therefore a higher K factor, it is preferable to utilize up to about 0.

Once it has been understood that the K factor varies logarithmically with concrete compressive strength, one of skill in the art, using techniques described or readily ascertained from the current disclosure, can modify the exemplary K factor shown in Figure 1 to account for variations based on different concentrations of THEED.

Figure 1 further demonstrates that the "optimal" or "theoretical" K factors are not absolute or lie along an absolute fixed curve that is the same regardless of the inputs and mixing apparatus of the concrete composition.


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Adding an amine strengthener raises the K factor and K factor curve representing all K factors for that system based on the increased strength of the resulting concrete even though the ratio of hydraulic cement to paste remains the same. The same would be true for other admixtures or alterations in composition such that there could be a unique or representative K factor curve for every unique set of raw materials inputs.

The same would be true for different types of mixing apparatus which might cause the cement paste to behave in unique ways specific to that mixing apparatus or methodology. In general, the effect of mixing efficiency on K factor is more dramatic with increasing cement content and strength i. That means the effectiveness of the hydraulic cement, more precisely the cement paste, as a binder that holds or glues the aggregates together decreases with decreasing strengths.

It also increases with increasing strength towards a theoretical limit beyond which no further increase in binding effectiveness is possible i. This does not mean, however, that the K factor necessarily increases with increasing hydraulic cement concentration. Many manufacturers engage in the practice of overcementing in an attempt to increase or maximize strength, sometimes with disastrous results as the concrete composition, if not properly optimized to accommodate a huge cement increase e.

What the K factor curves illustrated in Figure 1 essentially depict are the optimal. K factors for a given set of raw materials inputs. The design K factor used in an optimization procedure may be the same or may deviate from the optimal K factor to guarantee a specific minimum strength and slump. Because some variability between design strength and actual strength is possible, even in the case of highly optimized concrete compositions, some amount of deviation between the design K factor used and the optimal K factor can be tolerated to account for some expected variation.

What should be understood is that there is less variation between the design strength and the actual strength of a well optimized mix design compared to a poor mix design. In other words, the actual strength of concrete compositions made using optimized mix designs will more closely corresponding to design strength than concrete compositions made from a poor mix designs.

As a result of this, an optimized mix design made according to the inventive design optimization process will have a signature design K factor that exceeds the design K factor of a poor mix design. Similarly, because the binding efficiency of cement paste in a well-designed concrete composition typically exceeds the binding efficiency of cement paste in a poorly designed concrete composition, the actual K factor of a well-designed concrete composition would also be expected to exceed the actual K factor of a poorly-designed concrete composition.

This concept becomes more understandable with reference to Figures 2 and 3. The apparent design K factor for each specific mix design shown in Figures 2 and 3 can be determined by inputting values for cement, water, air and design strength into Feret's equation and then solving for K. The actual K factors that lie along the K factor curve can be derived by properly preparing a number of concrete compositions using standard optimized mix designs used by a plurality of manufacturers according to ASTM C or other rigorous standards known in the art, measuring the actual strength of the concrete test sample, and then solving for K.

An optimal K factor curve can be prepared by plotting measured K factors based on optimally prepared concrete compositions against the corresponding compressive strengths. In many cases, the actual strength of a concrete test sample made from a preexisting concrete mix design may substantially exceed the design strength, thereby indicating that the pre-existing concrete mix design is overdesigned. However, this alone does not provide a precise way to redesign the pre-existing concrete mix design to reduce or eliminate such overdesigning.

Using a revised design K factor that more closely corresponds to the optimal K factor within an optimization procedure that utilizes Feret's equation facilitates the ability to redesign the pre-existing mix design in order for actual strength to more closely correspond to design or predicted strength. In order to demonstrate the degree by which standard concrete mix designs used in the industry are overdesigned in several existing concrete manufacturing plants and therefore have an excessively low design K factor , reference is now made to Figures 2 and 3.

The amount by which the data points deviate from the optimal K factor line shown in Figure 2 indicates the degree to which such standard mix designs are or were overdesigned relative to their design strengths. In every case, the predicted or design strength was far less than the actual strength when the compositions were properly manufactured.

The amount by which the tested compositions were found to be overdesigned represents a potential cost savings if such mix designs could be redesigned according to the inventive methods disclosed herein. Figure 3 compares the apparent design K factors for a number of pre-existing concrete mix designs of various manufacturing plants using in manufacturing concrete compositions that either include substantial entrained air or are substantially free of entrained air.


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  • Again, the deviation between the data points representing the apparent design K factors and the optimal K factor curve shown in Figure 3 graphically illustrates the potential cost savings if the pre-existing mix designs were redesigned and optimized according to the inventive methods disclosed herein. As will be readily appreciated, by comparing the apparent design K factor of an existing concrete mix design with the optimal K factor for a given compressive strength lying on the curve shown in Figures , one may readily ascertain the degree by which an existing concrete mix design and corresponding concrete composition are overdesigned.

    Thus, knowing the optimal K factor and how it varies with compressive strength can be employed as a diagnostic tool to test whether the mix designs and concrete compositions of a concrete manufacturing plant are optimized or whether they are significantly overdesigned. Once it has been determined that an existing mix design is overdesigned, the mix design can be redesigned using the improved DOC process in order to identify one or more optimized mix designs having the desired slump and strength at lower cost.

    Because the improved DOC process takes into account the actual raw material inputs available to the manufacturer, it is better able to optimize the concrete mixtures compared to standardized tables, which typically cannot account for variations in raw materials inputs among different manufacturing plants or between batches.

    The improved DOC program understands the dynamic relationship between optimal K factor and concrete strength, which allows it to more efficiently identify one or more optimized mix designs compared to the original DOC program described in the Andersen patent. Figure 4 is a schematic diagram illustrating an exemplary computing system that may be used to implement features of the present invention.

    The described computing system is only one example of such a suitable computing system and is not intended to suggest any limitation as to the scope of use or functionality of the invention. Neither should the invention be interpreted as having any dependency or requirement relating to any one or combination of components illustrated in Figure 4. Computing systems are now increasingly taking a wide variety of forms. Computing systems may, for example, be handheld devices, appliances, laptop computers, desktop computers, mainframes, distributed computing systems, or even devices that have not conventionally considered a computing system, hi this description and in the claims, the term "computing system" is defined broadly as including any device or system or combination thereof that includes at least one processor, and a memory capable of having thereon computer-executable instructions that may be executed by the processor.

    The memory may take any form and may depend on the nature and form of the computing system. A computing system may be distributed over a network environment and may include multiple constituent computing systems. Referring to Figure 4, in its most basic configuration, a computing system typically includes at least one processing unit and memory The memory may be system memory, which may be volatile, non-volatile, or some combination of the two.

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    The term "memory" may also be used herein to refer to non-volatile mass storage such as physical storage media. Such storage may be removable or non- removable, and may include, but is not limited to, PCMCIA cards, magnetic and optical disks, magnetic tape, and the like. As used herein, the term "module" or "component" can refer to software objects or routines that execute on the computing system.

    While the system and methods described herein may be implemented in software, implementations in hardware, and in combinations of software and hardware are also possible and contemplated. If such acts are implemented in software, one or more processors of the associated computing system that performs the act direct the operation of the computing system in response to having executed computer-executable instructions.

    An example of such an operation involves the manipulation of data. The computer-executable instructions and the manipulated data maybe stored or instantiated in the memory of the computing system Computing system may also contain communication channels that allow the computing system to communicate with other computing systems over, for example, network Communication channels are examples of communications media. Communications media typically embody computer-readable instructions, data structures, program modules, or other data in a modulated data signal such as a carrier wave or other transport mechanism and include any information- delivery media.

    By way of example, and not limitation, communications media include wired media, such as wired networks and direct-wired connections, and wireless media such as acoustic, radio, infrared, and other wireless media. The term computer-readable media as used herein includes both storage media and tangible communications media i. Embodiments within the scope of the present invention also include computer- readable media for carrying or having computer-executable instructions or data structures stored thereon.

    Such computer-readable media can be any available media that can be accessed by a general purpose or special purpose computer. When information is transferred or provided over a network or another communications connection either hardwired, wireless, or a combination of hardwired or wireless to a computer, the computer properly views the connection as a computer-readable medium.

    Thus, any such connection is properly termed a computer-readable medium. Combinations of the above should also be included within the scope of computer-readable media. Computer-executable instructions comprise, for example, instructions and data which cause a general purpose computer, special purpose computer, or special purpose processing device to perform a certain function or group of functions. Rather, the specific features and acts described herein are disclosed as example forms of implementing the claims. According to a currently preferred embodiment, computer-implemented design optimized processes according to the invention can utilize at least some of the features disclosed in U.

    An important difference is that the present invention accounts for the fact that the K Factor utilized in Feret's equation is not a true constant but varies logarithmically with the compressive strength of concrete. In other words, it has now been discovered that increasing the concentration of hydraulic cement in an optimized mixture as opposed to overcementing increases its effectiveness or binding efficiency.

    The concept that the K Factor varies with concrete strength was not previously known and was therefore not appreciated in the Andersen patent or incorporated in the original DOC program though the original DOC program worked as designed and intended. Feret's equation to determine design strength is selected based on the specific minimum slump and strength of concrete that must be guaranteed by the manufacturer.

    In many other respects, the improved DOC process can be implemented in a manner similar that the original DOC program disclosed in the Andersen patent. It should be understood, however, that it is within the scope of the invention to utilize any set or series of known algorithms for designing one or more concrete mix designs so long as the design K factor that is used when calculating strength according to Feret's equation varies with changes in the desired or target strength e.

    Figure 5 is a flow chart that schematically illustrates or outlines various steps that may be performed according to an embodiment of the invention. These steps are similar to those disclosed in the Andersen patent, except that the procedure illustrated in Figure 5 selects and then utilizes a design K factor based on the specific minimum strength and slump requirement when calculating the design strength of each hypothetical concrete mix design generated by the improved DOC process. Thus, notwithstanding the similarity that may exist between the process steps illustrated in Figure 5 and those disclosed in the Andersen patent, the process of Figure 5 was not known in the prior art as embodied herein.

    The twelve steps are summarized as follows:. Step 1 : Ascertaining the maximum packing density and corresponding composition of a dry concrete mixture having cement and one or more types of aggregate;. Step 2: Utilizing a K factor corresponding to the desired or design strength, determining the initial optimal concrete mixture that is closest to the maximum packing density and has a desired strength, slump, and cohesion at a specific fine-to-coarse-aggregate ratio; Step 3: Utilizing a K factor corresponding to the design strength, designing various optimal mixtures and comparing the unit cost for each optimal mixture at defined fine-to-coarse-aggregate ratios so as to determine the overall optimal mixture with respect to cost; Steps Calculating the effects of individually combining different admixtures including fly ash, silica fume, water reducers, or fillers, respectively, to identify one or more optimal concrete mixtures;.

    Step 8: Determining the best optimal mixture having desired properties and minimal cost for mixtures that include fine aggregate, cement, coarse aggregate, mixing water, and two or more admixtures selected from fly ash, silica fume, and water reducers;. Step 9: Modifying the resulting mixture to insure that it reflects the proper concentration of air-entraining agent so as to have the proper air content; Step Utilizing a correction factor to further optimize the results of the preceding steps and ensure proper slump; Step Adjusting porosity if necessary to insure that the selected mixture has sufficient durability for its intended use; and.

    Step Accurately determining the volume or weight of the various components of a mixture needed to produce a desired concrete yield. The foregoing steps outlined above and depicted in Figure 5 will now be described with more particularity. Step 1: Ascertaining Maximum Packing Density. Step 1 includes ascertaining the maximum packing density of a dry concrete mixture for a given set of raw materials i.

    A detailed description of an exemplary embodiment for determining a ratio of hydraulic cement and one or more types of aggregates that maximizes particle packing density is set forth in the Andersen patent at col. Various methods, including measuring techniques and mathematical algorithms, for determining particle size and packing density for each of the raw materials inputs are described in this section of the Andersen patent.

    The discussion at col. These values may be experimentally determined and can be used to calculate the theoretical packing density of a theoretical concrete composition. The average diameter size is determined using known methods, such as by plotting the particle size distribution of each material according to the Rosin-Rammler-Sperling-Bennett distribution described by the equation:.

    The cylinder is then tapped against a hard surface until the material is fully compacted. By reading the height of compacted material in the cylinder and the weight of material, the packing density is calculated according to the formula: WM. In this way, not only is the volume of particles quantified but it is done as a function of particle morphology, specific surface area and other specific surface characteristics. The maximum packing density of a conventional, three-component mixture including cement, one type of fine aggregate, and one type of coarse aggregate is determined by incrementally varying the volume of each component in the mixture and calculating the corresponding packing density.

    The various packing densities are then plotted on a triangular-shaped packing density chart so as to determine what composition has the maximum packing density. By way of example, Figure 6A is a packing density chart for a ternary mixture of cement, quartz sand mm , and crushed granite mm. Side A of the chart defines the volume percent of fine aggregate sand ; side B defines the volume percent of cement; and the bottom or side C defines the volume percent of coarse aggregate crushed granite. The values inside the triangle represent the packing density at various percent volume mixtures of the components.

    The chart may be read in the following manner:. Sub-step l a : Select a desired packing density from within the triangle. By way of example, point "Z" is selected on Figure 6B which represents the maximum packing density for the defined mixture. Sub-step l b : Determine the percent volume of cement used in the concrete mixture needed to obtain the packing density at point "Z" by drawing a horizontal line 20 from point "Z" to side B of the triangle.

    The value defined by where line 20 and side B of the triangle intersect is the percent volume of cement needed to obtain the desired packing density. Sub-step l c : Determine the percent volume of fine aggregate in the mixture by drawing a line 22 parallel to side B of the triangle, the line starting from point "Z" and intersecting side A of the triangle. The value defined at where line 22 and side A intersect is the percent volume of fine aggregate needed to obtain the desired packing density. This value, however, can also be determined from the packing density chart by drawing a line 24 parallel with side A , the line starting at point "Z" and intersecting side C.

    The value at the intersection of line 24 and side C corresponds to the percent volume of coarse aggregate.

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    Using this method, the composition can be ascertained for any packing density on the chart or, using the reverse operation, the packing density can be ascertained for any desired composition. The packing density values within the chart are evaluated from the Toufar, Klose, and Born model hereinafter "Toufar model" used in connection with a correction factor. The Toufar model is a formula for calculating the packing densities of binary mixtures:. Other models may also be used for calculating the packing densities of binary mixtures.

    Examples of applicable models are the Aim model and the Larrard model discussed in the article Johansen, V. Additional discussion regarding packing density, including the use of pseudo-particles to determine packing densities using the Toufar model for ternary mixtures, is set forth in the Andersen patent. The optimization program may then be carried out using the exemplary steps discussed below, with the proviso that the actual slump is likely to vary from the theoretical or predicted slump due to variations between true packing density and the assumed packing density.

    As a result, a final correction step for slump is performed at or near the end of the process e. Because slump can be measured the moment a concrete mixture is prepared, unlike strength, slump corrections are not time consuming. A slump correction curve, as exemplified by Figure 7, can be prepared by preparing two concrete mixtures having higher and lower slumps, plotting the high and low slumps e.

    The water volume correlating to any desired slump is shown on the curve e. A final mix design having a desired slump can be prepared by utilizing an amount of water shown on the slump curve corresponding to the desired slump. As part of the improved DOC program, the average particle size d' measured for each solid component and the particle packing density for each solid component, whether measured or estimated, are input into a computing system.

    These values affect the properties that are later determined for each of the plurality of mix designs that are created. The particle size and particle packing densities permit the computer system, by virtue of one or more interrelated algorithms, to hypothetically "test" the resulting properties of each virtual concrete composition based on the mix designs that are created as part of the design optimization process.

    Step 2: Property Optimization. Step 2 involves determining an initial concrete mixture that is closest to the maximum packing density determined in Step 1 and that has the desired strength, slump, and optionally cohesion at a specific fine-to-coarse aggregate ratio. A detailed description of an exemplary embodiment of a process for identifying a concrete mixture that is optimized with respect to strength, slump and optionally cohesion is set forth in the Andersen patent at col. The term "cohesion" refers to the tendency of the concrete composition to resist segregation and bleeding. Various methods including mathematical algorithms for optimizing a concrete mixture with respect to strength, slump and optionally cohesion are described in this section of the Andersen patent.

    In sub-step 2 a , an initial mixture that is sufficiently close to the maximum packing density to optimize concrete properties without segregating or bleeding is selected by first, as discussed in Step 1, locating the maximum packing density on the packing density chart and the corresponding volume composition. Next, the volume of cement is held constant while the volume of fine aggregate is increased by a quantity defined as the cohesion safety factor, and the volume of coarse aggregate is decreased by the same quantity.

    The mixture is thus moved horizontally left on the packing density chart. The corresponding mixture is defined as the initial mixture. The volume V of the components in the initial mixture are defined by the equations:. Wherein, the variable CF represents the cohesion safety factor and is typically about 0. The cohesion safety factor insures that the mixture has sufficient fine aggregate to make a cohesive mixture that will not segregate or bleed. Mixtures to the right of the initial mixture on the packing density chart will typically segregate or bleed.

    The cohesion safety factor can vary in a range between about 0 to about 0. A lower strength concrete typically requires a higher cohesion factor up to about 0. The fme-to-coarse-aggregate ratio of the initial mixture is defined by a pseudo- particle line extending from the apex of the packing density chart, through the position of the initial mixture, and to the coarse aggregate line Figure 6C; compare Figures 6A- 6B.

    The following sub-steps are presented as an example of how to ascertain the optimal concrete mixture along this defined pseudo-particle line. In sub-step 2 b , the pacldng density of the composition of the initial concrete mixture is determined as described in Step 1. In sub-step 2 c , the amount of mixing water required to provide the initial concrete mixture with a predetermined desired slump is ascertained. Determining this amount of water is a two-step process. First, the amount of water needed to provide the mixture with a 1 cm slump is determined using the following formula:.

    The value for Wi is a fraction of the volume of the solids in the mixture. Once Wi is calculated for a 1 cm slump, the amount of water needed for the desired slump is calculated using Popovic's formula as follows:. In sub-step 2 d , using the results from sub-steps 2 a -2 c , calculating the 28 day compressive strength of the resulting mixture using Feret's equation:.

    Where AIR is the estimated percent volume of air in the mixture. The volume of air in a mixture varies based on the type of mixer used, the volume of fine aggregate in the mixture, and the types of admixtures combined with the mixture. If the theoretical strength of the mixture is less than the desired strength, sub-steps 2 b -2 e are repeated by replacing the initial mixture with a new mixture and corresponding new packing density.

    The composition of the new mixture is obtained by increasing or decreasing the volume of cement in order to obtain the desired strength. An estimate of the volume of cement needed to obtain the desired strength is determined by inputting the desired strength into Feret's equation and solving for the corresponding volume of cement according to the following equation:. As the volume of cement changes for the new mixture, the volume of fine aggregate and coarse aggregate must be normalized so that the volume of fine aggregate, coarse aggregate, and cement sum up to 1.

    However, the ratio of fme-to- coarse-aggregate remains constant. Accordingly, the volume of fine aggregate and coarse aggregate in the new mixture are defined by the equations:. This new mixture corresponds to the position on the packing density chart defined by the intersection of the pseudo-particle line described in sub-step 2 a and a horizontal line extending from new volume of cement determined by equation 16 above. As the volume of cement changes, one moves up or down on the pseudo- particle line. Sub-steps 2 b -2 d are continually repeated until the theoretical strength of the mixture equals the desired strength and the resulting mixture for the defined fine- to-co arse-aggregate ratio has the desired slump and strength using a minimal amount of cement and water.

    Typically, the desired mixture is found within ten iterations. Step 3: Cost Optimization. Step 3 involves comparing the unit cost of various optimal mixtures at defined fine-to-coarse-aggregate ratios so as to determine one or more overall optimized mixture s that are also optimized in terms of low cost.

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    A detailed description of an exemplary embodiment for identifying a concrete mixture that is optimized with respect to cost, while also having the desired strength and slump, is set forth in the Andersen patent at col. According to one embodiment, this may be accomplished by first calculating the unit cost of the initial optimal mixture determined in Step 2. An optimal composition and resulting unit price is then determined for a second optimal mixture defined by a new fme-to-coarse-aggregate ratio. The unit price of the second optimal mixture is then compared with the unit price of the initial mixture.

    If the price of the initial mixture is less than the price of the second mixture, the composition of the initial mixture is the most economical and the process is over. If the second mixture is less than the price of the initial mixture, the fine-to-coarse-aggregate ratio is again varied so as to obtain a third optimal mixture. The cost comparison is then repeated until the least expensive mixture is obtained. The combination of Steps provides exemplary methods for designing a mixture of cement, water, and aggregate having a desired strength and slump.

    The amount of water added to the mixture can be minimized to maximize strength. The proportions of fine aggregate, coarse aggregate, and cement can be optimized to minimize the cost of the mixture. Furthermore, using the above process, mixtures having desired properties can be consistently and accurately produced independent of the variations in the feedstock.

    Application results show the designed concrete mixture ratio reaches the expected requirements. Song and G. Request Permissions. Mechanical Industry Press, China All Rights Reserved. Log In. Paper Titles. Article Preview. Advanced Materials Research Volumes Main Theme:. Edited by:. Lijuan Li. Online since:.