Optimizing the Pavement Quality Concrete Mixes (PQC) using Combined Graphical Approach

Hossein Khazaei *  P. Sravana **
*-** Department of Civil Engineering, Jawaharlal Nehru Technological University College of Engineering, Hyderabad, Telangana, India.

Abstract

In the present study, an attempt has been made to create a bridge between conventional and novel methods or combination of both methods for optimization of the concrete mix design. This method has a special emphasis on the properties and characteristics of the aggregates and is termed as Combined Graphical Method (CGM). This method is well compatible with both methods, as it is easy to use and can be adopted in any working environment condition. In this study fuzzy logic triangular membership function has been used to determine the mixed components ratio. These relations had been predicted and validated by using the CGM. The coarse and fine aggregates blending ratio carried out from 75/25% to 44/55% and mix characteristic factors such as combined gradation, maximum density, retained percentage, air voids % and density factors were examined. This method is intended for concrete pavement mix to determine the C/F ratio consisting of coarse aggregates of 10, 20 and 38 mm and fine aggregates including river and mine sand. The selected mix proportion has been made, cast and cured for the 3, 7, 28, 42, and 90 days ages. The compressive and flexural strength at various curing ages were determined

Keywords :

Introduction

Mixed design is the process of selecting the appropriate ingredients for a mixture determining their relative proportions in order to produce concrete with adequate performance, cost and environmental benefit (Shetty, 2000). In general, the cement cost is several times higher than aggregates, so that the main objective of cement concrete mix design is to decrease the total cost of mixtures (Li, 2011). From a technical point of view, concrete mixtures with a high ratio of cement to aggregates content may cause the cracks and shrinkage in the concrete and liberate huge amounts of heat of hydration in mass concrete which may cause cracking (Ghoddousi et al., 2019; Li, 2011; Shetty, 2000).

In view of the above and in order to present a concrete mix design, it is essential to develop the appropriate and suitable optimization techniques for the concrete mix design with respect to the specifications, standards and code of the practice, that can ensure the desires and sustainable objective and goal of concrete mix design.

In this report, an attempt has been made to present the coincide integration of existing design methods (consist of conventional and non-conventional approaches) in order to meet the goals and needs of the design in a more convenient practice.

1. Research Objectives

The main purpose of this study is to develop an appropriate transitional method between conventional and new existing approaches. To provide a desirable design of the concrete mixes optimistically, in order to meet standard and specifications needs with emphasis on quality and cost, which mainly includes the following.

1.1 Need of Study

Aggregate characteristics and those proportioning in concrete mixtures could affect the constructability, strength, durability, pavement smoothness and economy requirements. Various models had been presented to predict the effects of aggregates gradation in concrete mixtures (Li, 2011; Mullen & Hultquist, 1970; Shetty, 2000).

Since several approaches have been developed in the best way that can contribute to a certain extend to optimize and predict the effect of aggregate gradation and enhance the properties of concrete mixer (Richardson, 2005). In spite of all the efforts made to provide a comprehensive approach that can meet all the needs of concrete design, it cannot be claimed such designs have ever been proposed. Moreover each of the proposed models has its own advantage and limitations. This could lead to time consuming, high amount of experiment of design (EOD) tests, magnitude of the approximation errors, invalid for regions other than the studied ranges of factors, and ultimately cost effectiveness.

Therefore, choosing a complementary concrete mix design requires consideration and adjustment in order of priorities for the purpose of the mix responses so that the designer can provide the optimal proposed design.

2. Literature Review

Concrete mixing design and optimization have been studied by many researchers with different statistical methods, novel techniques and software, to obtain acceptable performances, economy, and even ecology of engineering applications. Despite the compensations of these methods, they have a certain limitation as discussed.

Statistics is not suitable for the study of the qualitative phenomenon, statistical laws are not exact, statistics table may be misused and must be used only by experts. These are only one of the methods of studying a problem. Hence, the statistical study should be supplemented by other evidences (Mullen & Hultquist, 1970).

Statistics are aggregation of facts, numerically expressed, affected to a marked extent by the multiplicity of causes, enumerated or estimated according to a reasonable standard of accuracy, collected for a predetermined purpose, in a systemic manner and should be comparable to each other (Mechanics, 2016).

Response Surface Methodology (RSM) is a 'black box' approach (Cox & Baybutt, 1981). That is, estimating the accuracy of approximation, or one can say in other words the magnitude of the approximation errors, is difficult. This method is a local analysis and developed response surface is invalid for regions other than the studied ranges of factor (Kathleen et al., 2004).

Mixture Design Methodology (MDM) has the compounds which are positioned at the vertices (single factor) or sides (Binary factor) of the triangle cannot be considered as mixtures in the concrete mix design. Since feasible concrete mixes do not exist over the whole region a meaningful subregion of a full mixture must be defined by constraining the component proportions (Marica et al., 1997). Mixture design enhanced by lower bound constraint and re-parameterization of the co-ordinate system is compulsory (Hasan et al., 2018).

3. Concept of Combined Graphical Methodology

The compressive strength and durability of concrete depends on several factors such as, mix proportion, aggregate size and characteristics, coarse and fine aggregate ratio, compaction method, curing period (Mohammed & Al-Mashhadi, 2020), aggregate gradation (Quiroga, 2003), packing and optimization which have a considerable effect on the performance of fresh and hardened concrete (Antunes & Tia, 2018; Raj et al., 2014; Richardson, 2005).

The main concept of Combined Graphical Methodology (CGM) is to provide the optimal mixture design, with accurate components proportioning in order to obtain dense concrete mixtures. Such that, fine and medium size of aggregates can be placed in the voids between coarse aggregates to achieve the maximum density of the concrete as compacted mixtures where in the Job Mix curve is closer to the Maximum Density Line (MDL), Coarseness Factor (CFA) and Retained Percentage Factor (RPF) are within the accepted zone. This method has been developed by using the MS office Excel (VBA) Visual Basic for Applications.

This method had been considered for concrete pavement mix for determining the C/F ratio consisting of coarse aggregates 10, 20, and 38 mm and fine aggregates including river and mine sand. The following steps of experimental investigation is carried out.

3.1 Combined Aggregates Conformation

The main agenda of the aggregate's proportioning process with different individual sizes is to obtain the final combination that can meet the predefined specification limits (Antunes & Tia, 2018; Hasan et al., 2018; Obla & Lobo, 2015; Richardson, 2005). In this step, each fraction ratio will be selected and whole gradation area constrained between the upper and lower gradation limits were divided into three separate areas, including the upper, middle and lower zone as shown in the Figure 2, similar to MoRTH specification.

The proportioning of individual aggregates would be selected such that their combined gradation will be positioned in the middle zone. The absolute optimum blend is obtained when final gradation matches with the mid-range of the upper and lower specification limits. This method has been adopted so that if one or more sieves were out from the middle zone, it would not go beyond the predetermined specifications and be more accurate. This can be done either traditionally or by using the statistical approaches, like polynomial regression, probabilistic, fuzzy logic analysis and so on.

Step I: In this step, each individual size of coarse and fine aggregate fractions (at least three samples) will be selected with respect to the standard code of practice and particle size distribution test should be performed. The average results will be considered for further calculations and analysis.

Step II: The average of an individual gradation for each fraction will be used to predict the optimum proportion of each ingredient of coarse and fine aggregates such that the job mix gradation will be positioned in the middle zone theoretically.

Step III: At least three samples of coarse and fine aggregates in accordance with the Blending ratios had been determined in the step II either with the conventional or novel methods or mixed together method and the gradation test should be carried out. The average of the experimental test results will be compared with theoretical distribution. If the experimental data are truthful with its theory, other parameters such as maximum density methods, coarseness factor of aggregates, retained percentage factor and packing density will be estimated. This process can be done as an example by the following procedure.

3.2 Aggregate Blending for PQC by Using Linear Optimization Approach

In the recent study, fuzzy logic triangular membership function had been used as an alternative to traditional modeling approaches and has shown a good degree of success. The main idea of fuzzy logic is to represent a number of membership functions x1 , x2 ... xn to any numerical variable x. Where the opportunity of using a membership, the function is to treat the countability related to the numerical variables (Akkurt et al., 2004). Membership performance may take different forms, such as gaussian, sigmoidal, trapezoids, triangles and so on. The association between any value of x and any function of membership can be defined by the values of membership degree μx1 (x), μx2 (x)…, μxn(x) with the range values from 0 to 1.

3.3 Formulation of Aggregates Proportioning

Determine the allocated tolerances of aggregates size distribution containing specifications limit as first factor and proposed gradation as mixture tolerance or second factor, which should satisfy these two factors. The gradation of the final blend should satisfy the minimum and maximum optimum range calculated by Equation (1) and (2) respectively.

(1)
(2)

where,

X jmin =Minimum optimization value for the passing from sieve J

X jmax =Maximum optimization value for the passing from sieve J

XLLj = Specification lower limit for sieve J

Xui = Specification upper limit for sieve J

Tj= Purposed tolerance percent for sieve J

Triangular membership function is given for the percent passing, for the purposed mix, from each sieve xj to represent its uncertainty within the minimum optimum value xjmin and maximum optimum value xjmax. The degree of membership μ(xj) is equal to 0 for both xjmin and xjmax. Although, the degree of membership is equal to 1 at the middle of design range xjo as shown in Figure 1. The optimum aggregate combination is attained when all the membership degrees are maximized to be close to 1 for all sieves (Akkurt et al., 2004).

Figure 1. Illustrates the Shape of the Triangular Membership Function

3.4 Objective Function

The objective of the future model is to maximize the summation of product of membership degree and the material variability for all sieves as indicated in Equation (3). This can ensure that the final gradation is the adjoining of the mid-range, which can be achieved by considering the variability of the material (Raj et al., 2014).

(3)

where,

m = Total number of Sieves

Vj= Final blend variability for the percent passing sieve j.

M=Membership value for the percent passing sieve j.

3.5 Limitations

The limitation of this study can be expressed as in Equation (4). It is an equality limitation to confirm that the sum of the proportioning of the various aggregate types will be equal to 100%. There are two types of constraints which are equality constraints and inequality constraints. Equality limitations is related to the fixed relationship between the variables whereas the inequality limitations contract with the flexible relationship between the variables.

(4)

where,

n = Number of aggregate types

Ri = Blending ratio for aggregate type i

Equality limitations would join the aggregates proportioning by passing percentage of final gradation leading to m linear equations as given below.

(5)

where,

Gij = Actual passing percentage for aggregate size I from the sieve j

xj = Percent passing for the final combination from sieve j

Based on the triangular membership function scheme in Figure 1, the degree of membership μ can be measured j by Equation (6) which could lead to two inequality illustrated as Equations (7) and (8). These two equations can lead to Equation (4).

(6)
(7)
(8)

3.6 Boundary Conditions

  • Boundary conditions for the blending ratio R which i leads to inequality equation where n is the number of aggregate types.
  • Boundary conditions for the percent passing for the final blend in each sieve x which leads to inequality j equation where m is the total number of sieves.
  • Boundary conditions for degree of membership for the final blend in each sieve in which it leads to inequality j equation where m is the total number of sieves.

The aggregate proportioning of an individual fractions had been determined in various coarse to fine aggregates CA/FA ratio of 90:10, 80:20, 70:30, 60:40, 55:45, 50:50 as shown in Table 1 and Figure 2.

Table 1. Final Blending Ratios of Different Mixes

Figure 2. Illustration of Purposed Aggregates Gradation

3.7 Maximum Density Methods

To optimize the density of the all aggregate in concrete mixtures, the proportion of components would be selected in such a way for the voids between large particles should be filled up with medium and fine aggregates (Richardson, 2005). The higher degree of particle packing leads to minimum voids, maximum density and less cement and water requirement (Antunes & Tia, 2018; Mangulkar & Jamkar, 2013Obla & Lobo, 2015; Raj et al., 2014; Richardson, 2005). In the present study power chart, 0.45 has been used for all aggregates combination, in order to obtain a dense and stiff particle structure in concrete mixes. Regardless of its practical use, a maximum density gradation provides a convenient reference.

Fuller and Thompson (1907) developed an equation as cited in (Richardson, 2005; Tayabji et al., 2012) to describe a maximum density gradation for a given maximum aggregate size as certain in the following Equation.

(9)

where,

D = Maximum size of aggregate

P = Percentage of finer than diameter d (by weight)

d = Maximum size of fine aggregate

n = Parameter which adjusts curve for fineness or coarseness (for maximum particle density n ≈ 0.5 according to Fuller and Thompson)

This equation with n = 0.45 is convenient for determining the maximum density line and by adjusting gradation it uses the sieve size raised to the nth power as the x-axis units. Thus, a plot of maximum density equation with n = 0.45 appears as a straight diagonal line generated from zero and the maximum aggregates size gradation for the various combinations from Table 1 had been considered as shown in Figure 3.

Figure 3. MDL of Proposed Aggregates for PQC

3.8 Coarseness/Workability Factor Chart

The coarseness factor is an experimental method for aggregate gradation analysis (Richardson, 2005). This method contains an illustration of aggregate gradation that can be used in a distinct chart to estimate the fresh concrete mixture workability and the probability of segregation (Antunes & Tia, 2018; Quiroga, 2003) as shown in Figure 4. Combined aggregate with poor gradation will be disposed to segregation onsite and will not provide the adequate workability. Presented are two factors resulting from the gradation of aggregate to forecast the workability of the fresh concrete mixtures (Tayabji et al., 2012). This method involves calculating a Coarseness and Workability Factor using the following (Mamirov, 2019; Obla & Lobo, 2015; Quiroga, 2003; Richardson, 2005).

Figure 4. Coarseness and Workability Factor Relation of Mixes

(10)

where,

Cumulative retained percentage on the 9.5 mm sieve (Q)

Cumulative retained percentage on the 2.36 mm sieve (R)

The coarseness and work ability factors of the mixtures are as in Table 1 had been calculated by using the above mentioned equations and the result are presented in Figure 4.

(11)

where,

Cumulative passing percentage the 2.36 mm sieve (W) Cementitious materials content (C) Kg/m3

3.9 Percent Retained Chart

This method assessing exact spreading of each sieve size has an individual retained percentage in the chart shown in Figure 5. This diagram can easily show the excess or missing sieve sizes of a combined grading with a maximum limit of 18-22% and a minimum margin of 5-12% retained on each sieve (Mamirov, 2019; Obla & Lobo, 2015; Quiroga, 2003; Richardson, 2005). The retained percentage of the mixtures listed in Table 1 have been calculated for each combination and the corresponding graphs are presented in the Figure 5.

Figure 5. Individual Percent Retained Chart for PQC Mixes

In the current study Individual Percent Retained Chart are developed for all aggregates combination. In order to obtain limited upper and lower retained percentage in concrete mixes gradation which provides a convenient reference.

3.10 Determination of the Bulk Density and Air Voids Content of Mixtures

The void and packing density of aggregate mixtures can be expressed as Equation (12). The packing density of combined individual aggregate represents the maximum bulk density of the mixtures with respect to the overall specific gravity. The purpose of packing density is to minimize the porosity of the mixtures (Wong & Kwan, 2005) that allows using the minimum possible amount of binder.

(12)

The air voids content is the percentage volume of the aggregate or mixture of combined aggregates determined from its bulk density from the Equation (13).

(13)

where,

PD= Packing Density (kg/m3)

BD= Bulk Density (kg/m3)

GS= Specific Gravity

3.11 Reconfirming the Mix Fractions

To reconfirm the selected mix proportions of coarse aggregates in the mixes by the CGM, fine aggregate percentages have been increased in the various mixes from 25% to 55% gradually. The specific gravity, air voids, and bulk density tests were carried out according to the Indian standard IS: 2386 (Part III)-1963 (Bureau of Indian Standards, 2016) and the test results are obtained in Table 2 accordingly.

Table 2. Bulk Density, Specific Gravity and Air Voids of Proposed Mixes

4. Selection of the Desired Mixes to Perform the Experimental Investigation

Based on the results have been obtained in the Steps I to Step III, the samples that have more favorable conditions were selected for experimental investigation and taking into account the following priorities.

  • Selection of Well Graded Mixes: From the Steps I to Steps III, and Figure 1 the samples which are in full file positions in the Middle zone will be nominated.
  • Maximum Density Line: The mixes that, are very near to MDL from Figure 2, will be selected as dense and compacted mixes.
  • Coarseness and Workability Factors: From Figure 3, the mixes which are laid down on the workability box will be obtained as workable mixes.
  • Retain percentage: From Figure 4 the mixes that are within/closer to the limit will be selected.
  • Bulk and Pacing Densities: From the Table 2, the maximum density has been plotted in Figure 6 and the minimum air voids in Figure 7.

Figure 6. Maximum Loose and Compact Density of Mixes

Figure 7. Minimum Air Voids in Loose and Compacted Density of Mixes

Step IV: Adopt the Experimental Design (DOE): From Steps I, II, and III in Section 3.1, for any desired result of atleast 90 percent achievement, a numeric value 1 will be assigned, and for mixes which have not achieved, a numeric value 0 will be given.

The mixes which have the value of +1 from the average numerical value (ANV), will be nominated for the design of experiments. In this case, the mixtures III, IV, V and average (ANV) have numerical value 4/5, 5/5 and 4/5 respectively as shown in column 7 in Table 3 which will be selected for further future experiments.

Table 3. Numerical Value of Concrete Pavement Mixtures

4.1 Pavement Quality Concrete Mix Design

Concrete mixes were carried out by the Indian code of standard IRC 44-2016 (Indian Road Congress, 2017) with the recommendation of MoRTH 5th revision for mixtures III, IV, V and similarly average (ANV) sample. The fresh and hardened concrete performance has been checked and compared with the various curing ages.

4.2 Mix Proportions for Trial Mix Based on Aggregate Gradation

The selected concrete mix design proportions in dry conditions are presented in the Table 4.

Table 4. Mix Proportions for One Cum Trial Mix with SSD Condition

4.3 Workability Measurement

The workability and fluidity of fresh mix were performed by slump cone test according to the Indian standard code of practice IS 7320-1974 (Bureau of Indian Standards, 2008). The level of the slump has been measured at the initial time, 5, 10, 15, 30, 45, 60, 90 and 120 minutes. The slump measurement continued until the concrete workability reached up to 0-25 mm. The relativity of slump and time losses is presented in Figure 8 where a scatter plot of the data for slump (y-axis) during the time losses (x-axis) has been plotted.

Figure 8. Concrete Slump Losses (mm)

4.4 Mix Design Strength Summary

The compressive strength test has been performed on cubes sample 150 mm and flexural strength of beam specimens with 150 × 150 × 700 mm standard size for the desired curing period. The samples were demolded after 24 hours of casting time and were placed in a fixed temperature tank at 25±2 ºC. The specimens were removed from water at 3, 7, 28, 42 and 90 days and were tested in surface dried condition as per IS: 516 (Bureau of Indian Standards, 2004). The mix design strength summaries are presented in Table 5, Figure 9 and Figure 10.

Table 5. Compressive and Flexural Strength of Concrete Mixes

Figure 9. Compressive Strength of PQC Mixes During Curing Age

Figure 10. Flexural Strength of PQC Mixes During Curing Age

5. Procedure and Test Results

In the present study, based on the laboratory investigations and data analysis, the following conclusions can be drawn.

  • Traditional and novel optimization techniques have been proposed in order to optimize the concrete mix design with admirable accuracy. But time consumption, the high number of EOD run, cost and environmental effect are the existing problems in the present scenario.
  • In this study, an attempt has been made to bridge the gap between traditional and novel methods of concrete mixing design optimization in an effective manner.
  • •Combined Graphical Method (CGM) is the consequence of various studies resulting from many experimental investigations with different methods that have been done by the authors to optimize the concrete mixes. The CGM method is an integration of existing methods to verify data analysis to predict the optimal blending.
  • Well and continuous gradation is the most influential factor in the inherent properties of concrete mixtures. In the suggested method, the proportion of aggregate fraction can be selected in such a way that a well and dense aggregate blending is obtained, which fits the needs of the specifications, standard and design goal.
  • Any possible method either conventional or novel technique can be used and proposed the blending of individual fractions by considering the volume of the aggregates in job mixes before casting of samples and can predict the suitability of the proposed combination.
  • In respect to the mix gradation, the mixtures III, IV, V and ANV samples are positioned to the middle zone area as shown in Figure 1, wherein numerical value 1 is assigned and other samples that are out of this limit partially or entirely will be considered as zero.
  • The average of the results obtained from the proportioning ratio shows the meaningful results as these values are very close to mixture PQC-IV. Therefore, these data are predictive combinations and could be used in future evaluations.
  • From the average of individual gradation results, blending chart has been plotted in various propositions. Using the Maximum Density Line (M.D.L) determined from the max density equation and adopting grading with particle size raised to the 0.45 power and plotting on the grading chart cares the mathematical equation smoothing.
  • The mixtures III, IV, V and ANV are the samples that were very near and close to the maximum density line wherein they were selected for concrete mix design optimization. However, the mixture IV and ANV had more acquired data.
  • Using the numerical method of aggregate mix design and transforming them to the Fuller's curve, coarseness factor and cumulative retain percentage, efficiently as a criterion of packing ability of the aggregates are required to calculate aggregate mixes for a different type of concrete that might allow to predict strength and workability.
  • As illustrated in Figure 4, the mixtures IV and ANV are within the limit and mixtures III and V are near to the workability zone and coarseness factor. Wherein they were selected for concrete mix design optimization by assigning the numerical value of 1 and other mixtures which are out of limit, the numeric value of zero has been assigned.
  • In a similar way, mixture III, IV, V and ANV about 90% where, in the limit to retain percentage will be assigned with numerical value 1 and the other samples which were out of limit were nominated as 0.
  • The packing density of combined individual aggregate represents the maximum bulk density of the mixtures concerning the overall specific gravity for different mixes from 25 to 55% gradually. Specific gravity, air voids and bulk density tests were performed according to the Indian standard IS: 2386 (Part III) -1963 (Bureau of Indian Standard, 2016). The mixtures IV and ANV have a maximum density of loose and compacted density and a minimum air voids, subsequently, the numeric value 1 have been obtained for them and other mixtures that have a lower density and more air voids were assigned numeric value 0.
  • The sum of the results of the experiments of studies were intended for the various fine to coarse aggregates ratio as shown in Table 3. The numerical value of mixtures to their total acquired values from 5 experiments has been compared. The mixtures in which the value is ± 1 of the average of the results, were used for subsequent experiments.
  • The slump has been measured at the various timing to measure the concrete workability for the selected mixes slump loses during the time as shown in Figure 8.
  • The compressive strength and flexural strength of selected mixes were carried out during the desired curing period as per Indian standard IS: 516 (Bureau of Indian Standard, 2004). The compressive and flexural strength of mixes IV and ANV were more than other mixes.

Conclusion and Recommendation

In the present study, based on the field and laboratory investigation and analyzing the result, following conclusions can be drawn.

  • As mentioned before, despite of all the efforts made to provide a comprehensive approach that can meet entire needs of concrete design, it cannot be claimed that such design has been provided so far. Concrete is not only a mixture of aggregate, cement, water but also needs a little bit of awareness as well, which might be less in the existing method.
  • In the present study, an attempt has been made to provide a bridge between traditional and novel methods and using the most available software MS office Excel (VBA) Visual Basic for Applications, which can be used in a more practical way in the concrete industry with more accuracy.
  • Aggregate is commonly considered inert filler, which accounts for 60 to 80 percent of the volume and 70 to 85 percent of the weight of concrete. The aggregates' characteristics are an important factor for the selection of aggregate. The aggregates are several times stronger than the other components in concrete and therefore an attempt has been made to consider important features such as combined gradation, maximum density, coarseness and retained percentage factor, packing density and air voids had been considered.
  • CGM is a combined technique that had been used in the concrete mixing design which significantly reduce the number of design of experiments, save time and cost involved.
  • It has been observed that by using the CGM for mix design of pavement quality concrete, the values of bulk density and air voids in the concrete mixtures significantly have been changed. In which the PQC-IV with CA/FA ratio of (60:40) loose bulk density is 1.936 7 kg/m3 and compacted density is 2.013 kg/m3. Air voids are 30.089 for loose and 29.564 for compacted density.
  • The workability of concrete after one hour has been 45 mm for sample IV and 40 mm for ANV sample, which is an acceptable range for concrete paving.
  • The slump loses for the selected mixes IV and ANV provide uniform mixes without bleeding and segregation that could be fitted by the polynomial model. This regression is statistically above than the 95 % confidence level for mixes IV and ANV.
  • Slump test for ANV: y = 0.0029x - 0.9596x + 87.348 R² = 0.9946
  • The characteristic compressive strength of mix IV has been about 8% and ANV mix has been more than 5%, and the flexural strength at given ages for mix IV has been more than 7% and ANV has been 3% more than other mixes and could be fitted by the logarithmic model. This is statistically above than 95 % confidence level for mixes IV and ANV with the following equation respectively.
  • Compressive Strength: y = 23.666ln(x) + 14.782 R² = 0.9719
  • Flexural Strength: y = 1.9435ln(x) + 2.6171 R² = 0.9855

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