TECHNICAL FIELD

[0001] This invention relates to the field of engineering in the part of a method to find concrete mix proportions by minimum void in aggregates and sharing of cement paste.

BACKGROUND ART

[0002] In general methods for concrete mix designs were suggested by standard institutes for concrete e.g. ACI (the American Concrete Institute), BS (the British Standards) and IS (Indian Standards) etc. These methods were based on concrete mix proportioning per unit volume. The steps of calculations are mostly 1 ) determine the maximum size of aggregate based on pre-specified criteria and performance 2) select the amount of free water to meet the requirement of workability 3) determine water-cement ratio to achieve the target compressive strength of concrete 4) calculate the amount of water and cement per unit volume and 5) for the given fineness modulus of the fine aggregate the volume of coarse aggregate can be determined. Mostly the concrete mix proportions from these methods result in over cost of concrete production because of excessive cement contents in concrete which will also have great impact on environments due to the C0 ₂ release from the cement production. Furthermore in these methods the tables for determining values of fractional volume of aggregate were given at some values of Fineness modulus of fine aggregate only. Therefore the tabulated data could not be directly applied for fine aggregate with different values of fineness modulus. These might result in limitations of selecting aggregate for the concrete mix proportions.

[0003] Because of the problems mentioned above there were research projects on analyzing concrete mix proportioning for controlling quality and cost of production by importing data from standard institutes of concrete for analyses and creating systems such as patent application publication No. WO 2013/173764 A l "QUALITY CONTROL AND COST MANAGEMENT SYSTEM FOR CEMENTATIONS MIXTURES" which could be applied for big projects and credited for utilizing available data for analyses to improve properties of concrete or to obtain suitable concrete mixtures for some special purposes. Therefore there were inventions focusing on determining cement contents suitable for special products for usage in different environments such as patent No. CN 101549976 A "CONCRETE MIXING PROPORTION FOR DEPOSITION TUBE TUNNELTRON SEGMENT" which proposed for determining concrete mix proportioning of products underground tunneling to fit to working environments in underground. Besides adjusting the conventional concrete admixtures, some materials were used for partial replacement of cement such as fly ash and mineral powders. Other substitute materials were also used for substitute materials such as patent No. US7025825 B2 "PLASTIC FIBERS FOR IMPROVED CONCRETE" proposed reinforced plastic fibers for reduction of production cost and increasing strength of concrete, patent No. US7641731 B2 "ULTRAHIGH-PERFORMANCE, SELF-COMPACTING CONCRETE, PREPARATION METHOD THEREOF AND USE OF SAME" proposed the usage of silica fume for production of high strength concrete. However these both natural and synthetic substitute materials could have some drawbacks resulting in impacts on concrete such as moisture, durability adhesion and porosity.

[0004] Nowadays many countries have paid attention for suitable nature conservation and management as well as restoration for better environments. One approach is the usage of wastes or by products from industries. This approach is major trend of researches. However there are many subsequent problems e.g. the volume of wastes or by products from industries are not sufficient for the commercial scale or the quality of these materials did not meet the requirements. An alternative approach is determining new concrete mix proportioning with less cement content without any substitute material, but resulting in concrete of good or even better quality e.g. concrete might be denser and consequently more durable. The qualities of the concrete obtained should meet all pre-specified criteria and specifications. The method of concrete mix proportioning should be flexible for aggregate from any local source of different features and engineering properties.

SUMMARY OF INVENTION

[0005] The objective of this invention was to solve the problems mentioned above by developing a method to find new concrete mix proportions by using techniques of minimum void in mixed aggregates and sharing of cement paste. The method is composed of collection or testing for engineering properties of aggregate, determining the maximum nominal size of aggregate according to the conditions of products or working conditions, selection of number of nominal sizes of aggregate and nominal sizes of aggregate available, a systematic finding of the minimum void in mixed aggregates based on an adaptive scheme of experimental designs, for the selected void in mixed aggregates determining a water-cement ratio to meet the target compressive strength according to the pre-specified specifications of the products or working conditions, determining lower and upper bounds of cement paste required from the addition of the selected void in mixed aggregates, amount of the film of cement paste coating surface of each particle of aggregates and the amount of cement paste film shared at all contact surfaces, which reflect the statistical uncertainty at the level of confidence interval required, from the main concrete mix proportions determining other admixtures for other properties according to pre- specified criteria of the products or the working conditions, adjusting concrete mix proportions slightly for concrete mix proportions per unit volume, and finally casting concrete specimens for a series of tests which may result in a slight adjustment for each concrete mix proportion.

[0006] The goal of this invention was to use the new method to find concrete mix proportions for general applications without any substitute material, to reduce cement consumption, to produce denser and more durable concrete with properties satisfied with all pre- specified engineering specifications. The proposed method could be applied for concrete production with any source of aggregate.

BRIEF DESCRIPTION OF DRAWINGS

[0007] The invention and the following detailed description of certain embodiments may be understood by reference to the following figures:

[0008] Fig. 1A I B and 1 C show the models of sharing cement paste at the contact surfaces.

[0009] Fig. 2A, 2B, 2C, 2D, 2E and 2F show the models of sharing the film of cement paste coating particles of aggregate for different number of contact surfaces.

[0010] Fig. 3A, 3B, 3C, 3D, 3E and 3F show the models of sharing the film of coating cement paste between different types of aggregate.

[0011] Fig. 4A and 4B show the sharing of coating cement paste in the cross and longitudinal sections of the standard cylinder concrete.

[0012] Fig. 5 shows the sharing of coating cement paste in the cross section of the concrete pile products.

[0013] Fig. 6 shows the flow diagram for determining concrete mix proportions with the proposed method.

[0014] Fig. 7 shows the value of the sample at percentile p.

[0015] Fig. 8 shows determination of the mean value from an engineering specification.

[0017] Fig. 9 shows a distribution function fitted to a given set of data. DETAILED DESCRIPTION

[0018] In order to be properly and clearly understood for this invention, the definitions and descriptions of the compressive strength of concrete, fine aggregate, coarse aggregate, types of cement paste and formation of each type of the cement paste will be shown in the following:

1 . The compressive strength of concrete means the compressive strength of the standard cylinder specimen of 15 cm in diameter and 30 cm in height at the age of 28 days.

2. Fine aggregate (1 ) is the aggregate with the particle sizes less than 4.75 mm.

3. Coarse aggregate (2) is the aggregate with the particle sizes not less than 4.75 mm.

4. Forms of cement paste are composed of:

- Film of coating cement paste (3) is the film of cement paste coating around each particle of aggregate and other materials such as the wall of the moulds, additional materials and reinforcement etc. This film is calculated from the diameter of a cement particle coated by water around its surface. The quantity of water film has to be sufficient for complete hydration of cement.

- The film of the shared cement paste (4) is the film of coating cement paste shared between the contact surfaces of each particle of aggregate and other materials.

- Cement paste of void in mixed aggregates (5) is the cement paste in the void in coated mixed aggregates and other coated materials.

5. Formation of each type of cement paste:

In Fig. 1A the model shows the distances among particles of mixed aggregates, which effect on sharing of the films of cement paste at the contacted surfaces within concrete that is composed of fine aggregate (1 ) and coarse aggregate (2). In the case that a pair of two particles is too far from each other, there will be no sharing between the two particles (5). In the case that a pair of two particles is close enough to each other the coating film of cement paste around the two particles can be shared (3) called the film of shared cement paste (4) which could be zoomed in as shown in Fig. 1 B and 1 C.

The concrete mixture is composed of a lot of particles of mixed aggregates. Each particle of mixed aggregates can be close to a single or multiple particles. Consequently this will effect on the numbers of contact surfaces for shared films of coating cement paste (4) which are unequal as shown in Fig. 2A, 2B, 2C, 2D, 2E and 2F for one, two, three, four, five and six contact surfaces, respectively.

The films of shared cement paste (4) can be formed between a pair of particles of the same type of aggregate and a pair of particles of different types of aggregate as well as a particle of aggregate with other materials such as:

Between a particle of fine aggregate ( 1 ) and another particle of the same type (1 ) as shown in Fig. 3 A,

Between a particle of fine aggregate (1 ) and another particle of coarse aggregate (2) as shown in Fig. 3B,

Between a particle of fine aggregate (1 ) and the wall of the mould or additional material (6) as shown in Fig. 3C,

Between a particle of fine aggregate ( 1 ) and reinforcement (7) as shown in Fig. 3D,

Between a particle of coarse aggregate (2) and another particle of the same type (2) as shown in Fig. 3E,

Between a particle of coarse aggregate (2) and the wall of the mould or reinforcement (6) as shown in Fig. 3F.

The features of hardened concrete could be shown for both the cross section and the longitudinal section of a standard cylindrical specimen as well as the cross section of the concrete product in Fig. 4A, 4B and 5, respectively. These features are similar to those of the model in the following:

The film of the shared cement paste form the cylindrical specimen of concrete (8) can be compared with the film of the shared cement paste from the model (4) as shown in Fig. 1A, I B and 1 C,

The cement paste within voids in mixed aggregates from the cylinder of concrete (9) can be compared with the cement paste in mixed aggregates from the model (5) as shown in Fig. 1A,

Sharing of the coating cement paste film between a pair of particles of fine aggregate in the cylinder concrete (10) can be compared with the figure of the model Figure 3A,

Sharing of the coating cement paste film between a particle of fine aggregate and a particle of coarse aggregate (1 1) can be compared with the figure of the model Fig. 3B, Sharing of the coating cement paste film between a pair of particles of coarse aggregate (12) can be compared with the figure of the model Fig. 3E,

Sharing of the coating cement paste film between a particle of fine aggregate and the wall of the mould or additional materials (13) can be compared with the figure of the model Fig. 3C,

Sharing of the coating cement paste film between a particle of fine aggregate and the reinforcement ( 14) can be compared with the figure of the model Fig. 3D

[0019] The method to find concrete mix proportion by minimum void in mixed aggregates and sharing of cement paste is composed of the steps in form of the flow diagram as shown in Fig. 6 in the following:

1. Study, collect and test for engineering properties of each type of aggregate ( 15) required which consist of:

Gradation

- Fineness Modulus

- Natural Void

- Saturated Surface-Dry Specific Gravity

Water Absorption

Property of water: density at different temperatures

- Properties of cement such as type of cement, particle size, specific gravity and fineness modulus.

- Other properties required for pre-specified engineering specifications and working conditions.

2. Determine the maximum nominal size of aggregate (16) for concrete products or working conditions.

3. Determine number of sources or nominal sizes of aggregate for mixed aggregates (17).

4. Find minimum void in mixed aggregates (18) with the following conditions:

a. Use an adaptive scheme of experimental designs for finding minimum void in mixed aggregates for the number of nominal sizes of aggregate at least two depending upon the following conditions: i. The adaptive scheme for finding void in mixed aggregates starts from mixed proportion of each nominal size of aggregate in a wide interval and with at least one internal point.

ii. The scheme for finding void in mixed aggregates utilizes all possible values of proportion of each type of aggregate or some values. b. Find void in mixed aggregates for each pattern according to any standard test, at least one time for each pattern with the steps as described in the following:

i. Select the pattern of experiment which results in minimum void in mixed aggregates,

ii. Narrow the interval of proportion of each nominal size of aggregate, iii. Use the scheme of experimental designs,

iv. Experiment for finding void in mixed aggregates for each pattern of experiment,

v. Select the proportion of mixed aggregates with minimum void in the narrower domain.

c. Find proportion of mixed aggregates with minimum void by using any mathematical model for a single or multiple variables as the tool for this purpose based on the condition that the number of patterns of experiments should not be less than the number of unknown coefficients in the mathematical model and repeat every steps until the proportion of mixed aggregates with the minimum void is obtained at the level of target confidence under the following conditions: i. Proportion of aggregate could be by weight or by volume,

ii. The mathematical model can be of any kind which can yield the optimum value within the domain of each nominal size of aggregate e.g. polynomial of second order or higher order,

iii. Finding the unknown coefficients of the mathematical model by interpolation technique or regression analysis,

d. Independent variables in the mathematical model is the proportion of each nominal size of aggregate and the number of independent variables is always the number of nominal sizes of aggregate minus one,

e. Number of patterns of experiments for finding void in mixed aggregates within the domain considered should not be lower than the number of unknown coefficients of the mathematical model applied, f. Finding void in mixed aggregates for each pattern of experiment should be at least one time under the following condition:

i. In the case that the number of experiments for finding void in mixed aggregates for each pattern is more than one, the mean value of void in mixed aggregates for each pattern of experiments should be used.

g. Consider uncertainty of void in mixed aggregates for each pattern of experiments by using the percentile of void in mixed aggregates for each pattern of nixed aggregates not less than p as shown in Fig. 7.

i. The value of percentile of void in mixed aggregates for each pattern of experiments should not be less than 95.

Find the expectation of the amount of cement paste film coating the surfaces of mixed aggregates and the amount of cement paste film shared at the contact surfaces of mixed aggregates (19) for minimum void in mixed aggregates under the following conditions: a. The expectation of the amount of cement paste film coating for each nominal size of aggregate and the amount of cement paste film shared at the contact surfaces of particles for all nominal sizes of aggregate.

b. The expectation of the amount of cement paste film coating at the surfaces of particles of aggregate and the amount of cement paste film shared at the contact surfaces of aggregate are calculated from statistics or the mean values of the particle size of cement, thickness of cement paste film and the particle size of each nominal size of aggregate.

c. The expectation of the amount of cement paste film coating aggregate and the amount of cement paste film shared at the contact surfaces of aggregate can be improved by using the actual types of distributions for the particle size of cement, the thickness of cement paste film and the particle size of each type of aggregate.

Find the boundary of the amount of cement paste (20) under the following conditions: a. The boundary of the amount of cement paste is calculated from the expectation of the amount of cement paste film coating at the surfaces of particles of aggregate, the expectation of the amount of cement paste film shared at the contact surfaces of aggregate and the amount of cement paste within the void in mixed aggregates at percentile p as shown in Fig. 7.

b. The lower bound of the amount of cement paste is calculated from the expectation of the amount of cement paste film coating at the surfaces of aggregate plus the expectation of the amount of cement paste within the void in mixed aggregates at percentile p minus the expectation of the amount of the cement paste film shared at the contact surfaces of aggregate,

c. The upper bound of the amount of cement paste is calculated from the expectation of the amount of cement paste film coating at the surface of aggregate plus the expectation of the amount of cement paste within the void in mixed aggregates at percentile p.

7. Find suitable water-cement ratio (21 ). This ratio should yield the values of the compressive strength of concrete at different ages not lower than the corresponding values of pre-specified by engineering specifications with the failure probability lower than pf as shown in Fig. 8. The expectation of the compressive strength of concrete at different ages should be under the following conditions:

a. The value of pf should be pre-specified and normally pf is be set to 5%.

b. The mean values of the compressive strength at different ages are calculated from the normal distribution.

c. The mean values of the compressive strength at the different ages are calculated from the actual types of distributions for the cases of sufficient old data available as shown in Fig. 9.

8. Find the main concrete mix proportions (22) which may have several formulas with the expectation of the amount of cement paste for each formula not less than the lower bound.

9. Find the amount of air voids, superplasticizer and other additional admixtures for each formula for main concrete mix proportion (23) such that the concrete for each formula will satisfied other required properties.

10. Find the values of concrete mix proportion for each formula (24) under the conditions from steps 8, 9 and 10.

1 1 . Cast concrete specimens for each formula (25) and test for engineering properties of concrete for each formula according to pre-specified criteria and working conditions.

12. Adjust the concrete mix proportion for each formula slightly such that the concrete mix proportion for each formula can be cast or produced the concrete and yield the concrete with the qualities satisfied the pre-specified criteria and working conditions (26). 13. Select the formula of the concrete mix proportion with the minimum of cost of production (27) according to the method to find concrete mix proportions as described above.

[0020J Example

Data of materials for the proposed method

1. The compressive strength of a standard cylinder concrete of 15 cm in diameter and 30 cm in height at the age of 7 days = 350 ksc,

2. Maximum nominal size of aggregate = 19 mm,

3. Ordinary Portland cement Type III: Specific gravity = 3.15,

4. Coarse aggregate Source 1 : Saturated surface-dry specific gravity = 2.779,

Fineness modulus = 8.467,

5. Coarse aggregate Source 2: Saturated surface -dry specific gravity = 2.754,

Fineness modulus = 5.896,

6. Fine aggregate: Saturated surface-dry specific gravity = 2.636,

Fineness modulus = 2.025,

7. Air voids = 1.5%,

8. Cement paste: minimum void in mix aggregate = 0.17778 plus additional cement paste in the range of 7.062 - 9.444%,

9. Water-cement ratio = 0.44,

10. Cost of materials: cement 400 = THB/m ³ , water = 14 THB/m ³ , stone = 380 THB/m ³ , Sand = 380 THB/m ³ .

Data from experiments

1. Minimum void in mixed aggregate = 0.17778, the coefficient of variation = 0.02693.

2. Thickness of cement paste film from analysis, which was verified by experiments =

13.756 microns.

Results from calculations

1. Proportion of mixed aggregates by weight: Coarse Aggregate 1 :Coarse Aggregate 2:

Fine Aggregate = 1015:301 :772 kg.

2. Adjusting factors for the lower bound and the upper bound = 0.960 and 0.955,

respectively. Proportion of mixed aggregates by weight for the lower bound: Coarse Aggregate 1 :Coarse Aggregate 2:Fine Aggregate =974.4:289.0:741 .1 kg.

Proportion of mixed aggregates by weight for the upper bound: Coarse Aggregate 1 :Coarse Aggregate 2:Fine Aggregate =969.3:287.5:737.3 kg.

Increase void in mixed aggregates to achieve 95% confidence = 0.17778x0.02693 xl .645= 0.18556.

Cement paste required for coating particles of Coarse Aggregate 1 = 0.00173/Volume. Cement paste required for coating particles of Coarse Aggregate 2 = 0.0143/Volume. Cement paste required for coating particles of Fine Aggregate = 0.29644/Volume. Lower bound of Cement paste required for coating particles of aggregates:

9.1 Cement paste required for coating particles of Coarse Aggregate 1

= (0.00173x974.4/2.779)/998 = 0.00061.

9.2 Cement paste required for coating particles of Coarse Aggregate 2

= (0.0143x 289.0/2.754)/998 = 0.00156.

9.3 Cement paste required for coating particles of Fine Aggregate

= (0.29644x 741.1 /2.636)/998 = 0.08351.

9.4 Maximum cement paste for sharing = 0.1 1 188/Volume.

9.5 The amount of cement paste for effective sharing

= 0.8x0.1 1 188x 741.1/(2.636x988) = 0.02521.

9.6 The amount of cement paste required for coating mixed aggregates

= 0.00061 +0.00156+0.08351 -0.02521 = 0.06046.

.7 Volumetric adjusting factor = 1.015+0.06774 = 1.08274.

.8 Lower bound of cement paste required for coating particles of aggregates

= (0.17778+0.18556)/ 1.08274+0.06046 = 0.232.

.9 Additional amount of cement paste = 0.18556/1.08274+0.06046 = 0.068.

pper bound of cement paste required for coating particles of aggregates:

10.1 Cement paste required for coating particles of Coarse Aggregate 1

= (0.00173x969.3/2.779)/998 = 0.00060.

10.2 Cement paste required for coating particles of Coarse Aggregate 2

= (0.0143x 287.46/2.754)/998 = 0.00155.

10.3 Cement paste required for coating particles of Fine Aggregate

= (0.29644x 737.26/2.636)/998 = 0.08308.

10.4 Maximum cement paste for sharing =0.00060+0.00155+0.08308= 0.08523.

10.5 Volumetric adjusting factor = 1.015+0.09235 = 1 .01 734.

10.6 Upper bound for cement paste

= (0.17778+0.18556)/! .10734+0.08308 = 0.253.

10.7 Additional amount of cement paste = 0.18556/1.10734+0.08308 = 0.092.

1 1. Amount of water and cement for the lower bound

1 1 .1 Cement content = 0.232x(3.15/(1+0.44 x3.15)x998 = 305.6 kg,

1 1.2 Water content = 0.44x305.6 = 134.5 kg.

12. Amount of water and cement for the upper bound

12.1 Cement content = 0.253x(3.15/(1 +0.44x3.15)x998 = 333.2 kg,

12.2 Water content = 0.44x333.2 = 146.6 kg.

Table 1 Concrete mix proportions by the proposed method

[0021] Comparison of results between the proposed method and the existing methods

Data from references

1 . The compressive strength of the concrete cubes 15 cm at the age 28 days = 20 MPa (203.9 ksc),

2. Maximum nominal size of aggregate = 20 mm,

3. Ordinary Portland Cement Type 1: Specific Gravity = 3.15,

4. Coarse aggregate: Specific gravity = 2.6, Bulk density = 1600 kg/m ³ ,

Fineness modulus = 6.5, Moisture absorption = 0.5%, 5. Fine aggregate: Specific gravity = 2.6, Bulk density = 1700 kg/m ³ ,

Fineness modulus = 2.2, Moisture absorption = 2.0%,

6. Water-cement ratio = 0.55, air voids = 2%. Data of Materials for the Proposed Method with the Properties close to those from the References

1. The compressive strength of concrete cubes 15 cm. at the age 7 days = 20 MPa (203.9 ksc),

2. Nominal maximum size of aggregate = 19 mm,

3. Ordinary Portland cement Type III: Specific gravity = 3.1 5,

4. Coarse aggregate: Saturated-surface-dried specific gravity = 2.823, fineness modulus = 6.89,

5. Fineness modulus: Saturated-surface-dried specific gravity = 2.636, fineness modulus = 2.025,

6. Water-cement ratio = 0.55, air voids = 2%,

7. Total cement paste: minimum void in mixed aggregates = 0. 1998 + additional cement paste in the range of 6.925 - 9.257%.

Table 2 Comparisons of the concrete mix proportions by the proposed method and the existing methods

Publishing Company Limited, New Delhi, 1996, p. 160-165. [0022] Comparison of results from Propose Method and the ACI Method (Steps of

Calculations which required formulas, diagrams or tables)

Data of Materials for the ACI Method and the Proposed Method

1 . The nominal maximum size of aggregate = 19 mm.

2. Ordinary Portland cement Type III: Specific gravity = 3.15.

3. The compressive strength of the standard cylinder concrete with 1 5 cm in diameter and 30 cm in height at the age of 7 days = 350 ksc.

4. Coarse aggregate 1 : Saturated surface-dried specific gravity = 2.779, fineness modulus = 8.467.

5. Coarse aggregate 2: Saturated surface-dried specific gravity = 2.754, fineness modulus = 5.986.

6. Fine aggregate: Saturated surface-dried specific gravity = 2.636, fineness modulus = 2.025.

7. Water-cement ratio = 0.44, air voids =2%.

8. Total cement paste: Minimum void in mixed aggregates = 0.17778 plus additional

cement paste 7.062 - 9.444%.

Table 3 Comparison of concrete mix proportion by ACI method and the proposed method

Remarks * Calculation in S.H. osmatka, B. Kerkhoff and W.C. Panarese, Design and Control of Concrete Mixtures, 1 l ^lh Ed., 2 ^nd Printing, Portland Cement Association, Illinois, 2005, p. 151 -158. [0023] Summary of comparisons in the two examples

It was found that concrete mix proportions with the proposed method yielded the minimum contents of cement and minimum costs compared with the corresponding cement contents and costs by the other methods for equal values of compressive strength of concrete. Furthermore the matrices of hardened concrete by the proposed method tended to be denser than the corresponding ones by the other methods. Consequently the concrete obtained by the proposed method should be more durable than the compared methods.