Compressive strength of concrete is considered as an index property of the concrete and therefore other mechanical properties of concrete such as flexural strength and modulus of elasticity are correlated with it. The standard code practices of different nations provide empirical corelations between compressive strength and mechanical properties. However, it is observed that these correlations yield deviating results. Present paper aims on developing statistical models for accurately estimating these properties based on experimental results. Plain concrete cube, cylinder, and beam specimens are cast with varying watercement ratio and aggregatecement ratio. Based on experimental results, the prediction models for compressive strength, flexural strength, and modulus of elastic are developed. Experimental results are compared with the results obtained from generated statistical models as well as with the results available from literature. It is found that the present models accurately predict the mechanical properties of concretes.
La resistencia a la compresión del hormigón se considera una propiedad índice del hormigón y, por lo tanto, otras propiedades mecánicas del hormigón, como la resistencia a la flexión y el módulo de elasticidad, están correlacionadas con ella. Las prácticas del código estándar de diferentes países proporcionan correlaciones empíricas entre la resistencia a la compresión y las propiedades mecánicas. Sin embargo, se observa que estas correlaciones arrojan resultados desviados. El presente artículo tiene como objetivo desarrollar modelos estadísticos para estimar con precisión estas propiedades en base a resultados experimentales. Las muestras de cubos, cilindros y vigas de concreto simple se moldean con una relación aguacemento y una relación agregadocemento variables. Con base en los resultados experimentales, se desarrollan los modelos de predicción de la resistencia a la compresión, la resistencia a la flexión y el módulo de elasticidad. Los resultados experimentales se comparan con los resultados obtenidos a partir de modelos estadísticos generados, así como con los resultados disponibles de la literatura. Se encuentra que los modelos actuales predicen con precisión las propiedades mecánicas de los hormigones.
Concrete, one of the most extensively used construction materials pan world, is under the lens due to the rapid pace at which construction is being undertaken. However, the present spurt of construction activity indicates that adequate care needs to be taken in order to maintain material quality which can sustain the above said growth. The quality of concrete is determined by the mechanical properties it exhibits, therefore in order to ensure product efficacy, the mechanical properties of concrete need to be evaluated with accuracy. Among these, compressive strength (), flexural strength () (modulus of rupture), and modulus of elasticity () are important properties of concrete. In the analysis and design of any type of concrete structures viz., plain, reinforced, or prestressed, these properties need to be well evaluated and incorporated.
Practical assessment of these mechanical properties with accuracy requires a prolonged duration. However, with emerging demand for rapid construction, it is the need of hour to have models for estimating these properties at early stages with accuracy. The standard guidelines of various countries give the correlation of compressive strength with the modulus of elasticity and flexural strength.
Country  Code of Reference  Modulus of Elasticity  Flexural Strength  Remarks 

American Code  ACI 318 



New Zealand code  NZS 3101 



Euro Code  EN1992 11 



British Code  BS 8110 



Canadian Code  CSA A23.304 



Turkish Code  TS 5002003 



Indian Code  IS 456 



Initially, Li (
Further, a study of elastic modulus for sprayed concrete is conducted. It has been observed that there is a significant difference between the elastic modulus of plain concrete and sprayed concrete (
Eight basic concrete mixes of varying varieties are used in the present study.
Mix  Watercement ratio  Aggregate cement ratio  Quantities 1 cu.m of concrete (kg^{#})  

Cement content  F.A. 
C.A. 10 mm (0.393 in) 
C.A. 20 mm (0.787 in) 
Water Content  
M1  0.60  6.89  300  684.0  414.0  969.0  180.0 
M2  0.55  6.72  310  688.2  418.5  976.5  170.5 
M3  0.52  6.57  320  694.4  423.0  985.6  166.4 
M4  0.50  6.34  340  707.2  431.1  1016.6  170.0 
M5  0.50  6.07  355  710.0  505.9  939.7  177.5 
M6  0.45  5.85  365  698.6  575.6  861.4  164.3 
M7  0.33  5.08  410  681.0  421.1  982.4  135.3 
M8  0.33  4.96  420  697.6  554.4  831.6  138.6 
*F.A.  Fine Aggregate, C.A.  Coarse Aggregate^{#}1kg = 2.204 lbs
The locally available ingredient materials viz., cement, fine aggregates (river sand), and coarse aggregate are used for casting of concrete specimens. Ordinary Portland Cement (OPC) 53 grade, as stipulated in IS 12269 (
Material  Parameter Assessed  I.S. Code  Test Performed  Result 

Cement  Soundness  IS 4031  LeChatelier Method  5 mm 
Standard Consistency  Vicats Plunger Test  33%  
Initial Setting Time  33 min  
Final Setting Time  10 hours  
Fine Aggregate  Fineness Modulus  IS 2386  Sieve Analysis  3.01 
Specific Gravity  Pycnometer Bottle Test  2.699  
Water Absorption  Oven Dry Method  1.20%  
Coarse Aggregate  Fineness Modulus  IS 2386  Sieve Analysis  3.62 
Specific Gravity  Wire basket Method  2.99  
Water Absorption  Oven Dry Method  2% 
The concrete specimens are prepared following IS 10086 and IS 516 (
The testing program for all the specimens is conducted as per IS 516 (
The testing surfaces are milled before tests. The specimens are tested in saturated surface dry conditions. The cube specimens used for compressive testing are subjected to load on the adjacent side of casting. However, in the case of cylinder compression testing, the cylinders are necessarily kept vertical. The load rate used is kept at 0.233 MPa/sec (140 kg/sq.cm/min [1991.27 lbs/sq. in/min]) as recommended by IS 516 (
In the flexural testing of concrete beams, the fourpoint loading mechanism is used. Two LVDT’s are used for measuring the deflection of the beams. All the contact surfaces are cleaned to remove loose materials. The supports are 600 mm [23.62 in.] apart, and loading rollers are 200 mm [7.874 in.] apart, thereby dividing the beam into three parts of 200 mm [7.874 in.] each.
Standard cylinders (300 x 150Φmm [11.811 x 5.90 in.]) are used for measuring the modulus of elasticity of concrete. The load is continuously applied at the rate of 0.233 MPa/sec (140 kg/sq.cm/mm [1991.27 lbs/sq. in/min]) as per the guidelines of IS 516 until the average stress of (C+5) kg/sq.cm is obtained, where, C is onethird of the average compressive strength. The load is maintained at this stress value for at least a minute and then gradually unloaded to reach an average stress of 1.5 kg/sq.cm [21.94 lbs/sq.in]. The load is again applied for the second time at the same rate until the average stress of (C+1.5) kg/sq.cm is reached, and unloading is carried out in the same way. The load is further applied for the third time and in ten approximately equal increments of stress reaching up to an average stress of (C+1.5) kg/sq.cm. Two extensometers are diagonally attached to the vertical surface of the specimen for measuring the deformation of specimens at every load change.
The testing of concrete specimens is conducted at the age of 28 days after curing. IS 456 (clause 6.2.1) recommends 28 days strength as the characteristic compressive strength to be used for design purposes.
Cube compressive strength (MPa)  


M1  M2  M3  M4  M5  M6  M7  M8 

28.21  35.99  40.31  48.83  51.59  58.40  61.30  63.91 

28.03  39.19  39.25  44.31  54.69  49.93  58.93  67.98 

29.52  36.67  41.95  47.54  52.60  54.83  60.68  65.24 

29.33  38.75  41.35  46.67  54.39  58.06  60.24  65.07 










3%  4%  3%  4%  3%  7%  2%  3% 


M1  M2  M3  M4  M5  M6  M7  M8  

20.43  23.83  30.76  34.51  40.18  41.25  46.47  49.02 

21.36  26.53  32.25  36.89  36.99  45.23  47.10  55.78 

21.02  25.25  31.22  35.67  38.60  42.45  44.02  51.10 

20.52  24.51  31.70  36.25  39.54  44.35  46.29  53.41 










2%  5%  2%  3%  4%  4%  3%  6% 


M1  M2  M3  M4  M5  M6  M7  M8  

3.69  4.05  4.58  4.41  5.12  5.50  5.66  6.45 

3.72  4.39  4.65  4.68  4.96  5.185  5.78  5.91 

3.76  4.55  4.71  4.77  5.09  5.21  5.68  6.31 










1%  6%  1%  4%  2%  3%  1%  5% 


M1  M2  M3  M4  M5  M6  M7  M8  

27349.37  26997.30  34814.22  35813.57  38952.44  37388.81  43701.64  45885.27 

24458.12  30964.60  32594.59  34694.70  35837.58  38952.44  42287.62  48733.77 

25889.93  28743.32  33861.41  34744.69  37043.47  38426.51  43034.65  46757.12 










6%  7%  3%  2%  4%  2%  2%  3% 
The compressive strength, flexural strength and modulus of elasticity are important parameters considered in designing the structural concrete members. It is necessary to validate the correlation proposed by various codes with experimental results.
In the present investigation, multiple linear regression analysis of experimental data is performed to develop predictive models for the estimation of compressive strength, flexural strength, and modulus of elasticity. For statistical modeling, multiple linear regression analysis was carried out using IBMSPSS Statistics (version 23). The coefficient of correlation, i.e., Pearson’s R, a parameter indicating the strength of correlation of dependent and independent variables, is also obtained for all the proposed models. Pearson’s Rvalue in the proximity of unity signifies the efficiency of the prediction model.
Further, the linear curve fit is plotted between the predicted value and the experimental value. The R^{2} value, i.e., the coefficient of determination, is obtained for this linear curve. R^{2} value approaching closer to unity is indicative of a higher efficacy of the predictive model.
In developing a model through SPSS, compressive strength is used as a dependent, and the quantity of cement, fine aggregate, coarse aggregate, and water in 1 cu.m of concrete are used as variables. The model is developed with SPSS software (version 23) using the experimental data generated during testing of cube compressive strength as presented by
where
Pearson’s R for the aboveproposed model is found as 0.98, indicating the effectiveness of the proposed model. It is worth noting here that the coefficient of water quantity is obtained to be negative, indicating that compressive strength is inversely proportional to the quantity of water added to the concrete mix. The generated predictive models from the available test data, as detailed in the previous section, are validated from the remaining test results.
Author  Experimental Values (MPa*)  Predicted Values (MPa)  Deviation (%) 

Present Study  29.33  29.48  0.51 
28.13  29.48  4.80  
36.37  34.61  4.83  
38.45  34.61  9.98  
41.35  39.62  4.17  
40.54  39.62  2.26  
47.54  48.64  2.32  
46.67  48.64  4.23  
52.60  51.64  1.82  
54.35  51.64  4.98  
54.83  52.25  4.71  
58.04  52.25  9.98  
60.68  60.08  0.99  
60.24  60.08  0.27  
59.26  60.08  1.38  
Anbuvelan (2014) ( 
62.44  68.77  10.15 
Shelke N. (2006) ( 
50.46  44.66  11.49 
52.47  46.07  12.20  
56.07  50.05  10.75 
*1MPa = 145.04 lbs/sq.in
Additionally, to assess the efficacy of the proposed model [
According to the standard code guidelines of some of the nations such as America (ACI318), New Zealand (NZS3101), and Europe (EN 199211), the compressive strength is measured on cylindrical specimens of standard size, generally 300 mm x 150 mm for the purpose of designing. Hence, a model for prediction of cylinder compressive strength is also developed on the same lines as cube compressive strength as stated in [
Where
For the above model, the correlating coefficient is obtained as 0.98, which alludes to the effectiveness of the model. The comparison of the compressive strength of the cylinder across different mixes is as shown in
Author  Experimental Values (MPa)  Predicted Values (MPa)  Deviation (%) 

Present Study  21.02  21.05  0.16 
20.52  21.05  2.60  
25.25  25.65  1.60  
24.51  25.65  4.67  
31.22  29.93  4.14  
31.49  29.93  4.96  
35.67  37.20  4.30  
36.25  37.20  2.63  
38.60  39.29  1.79  
39.54  39.29  0.63  
42.42  40.32  4.96  
44.35  40.32  9.09  
44.02  47.76  8.49  
46.29  47.76  3.17  
51.10  52.01  1.79  
53.41  52.01  2.61  
Anbuvelan (2014) ( 
49.95  53.37  6.84 
Ahmed (2016) ( 
31.80  36.42  14.15 
78.2  76.06  2.73  
Ashour (2000) ( 
48.00  43.67  9.02 
78.00  77.13  1.12 
Moreover, when plotted, the R^{2} value for predicted values against experimental values is 0.97. This indicates the higher efficacy of the prediction model. Also, as seen in
The tensile strength of concrete is most commonly attributed to flexural strength (modulus of rupture). Almost all structural components are subjected to significant flexure stresses. Several structural components viz., slabs, beams, road pavements are designed basically for the flexural loads. In the investigation of flexural strength according to standard codes, it is revealed that the process involves tedious experimentation. Therefore, the standard guidelines of different countries have given an empirical equation for estimating the flexural strength of concrete correlating to compressive strength. However, compressive strength also needs aout 28 days of experimentation. Hence, for estimating the flexural strength at an early age with accuracy, a predictive model is developed as given in [
where,
Pearson’s R, obtained after multiple regression analyses for the above mentioned model, is 0.96.
Author  Experimental Values (MPa)  Predicted Values (MPa)  Deviation (%) 

Present Study  3.72  3.63  2.20 
3.66  3.63  0.60  
4.35  4.01  7.82  
4.37  4.01  8.24  
4.60  4.31  6.25  
4.67  4.31  7.66  
4.53  4.67  3.25  
4.73  4.67  1.11  
5.09  4.75  6.67  
4.99  4.75  4.80  
5.21  4.90  5.83  
5.34  4.90  8.12  
5.68  5.66  0.32  
6.31  6.05  4.03  
Khayat (2015) ( 
5.5  6.21  12.84 
The modulus of elasticity is the valuable mechanical property used in the analysis and designing of concrete structures. The modulus of elasticity is the measure of flexibility of the material. The deflection pattern of materials is governed by its modulus of elasticity and hence defines the serviceability of the material. The existing standard guidelines give the correlation of modulus of elasticity with compressive strength. In addition to this, standard experimental procedures are also prescribed for its determination. However, this process requires a longer duration of time. Hence for prompt analysis of elastic property of the designed concrete, the predictive model is articulated. [
where, is the modulus of elasticity of concrete (MPa).
Also, after performing statistical analysis, Pearson’s Rvalue obtained is 0.976. The predicted values obtained from the proposed model [
Author  42,898 mm  Predicted Values (MPa)  Deviation (%) 

Present Study  25889.93  26114.25  0.87 
28743.32  29527.52  2.73  
30723.71  29527.52  3.89  
33861.41  32462.65  4.13  
34744.69  36300.24  4.48  
37043.47  37070.69  0.07  
37423.2  37070.69  0.94  
38426.51  37717.53  1.85  
43034.65  43086.99  0.12  
46757.12  47430.35  1.44  
48439.49  47430.35  2.08  
Vijaylaxmi (2014) ( 
25998.43  27818.96  7.00 
Ashour (2000) ( 
24612.00  27489.00  11.69 
Additionally, a curve fit with a 95% prediction band is also developed, as shown in
In this study, mechanical properties of concrete are investigated for eight commercial concrete mixes. The models are proposed for predicting compressive strength of cube and cylinder specimens, flexural strength, and modulus of elasticity. It can be concluded that
The predicted values obtained from the proposed models are closer to the experimental values. Hence, the present approach provides a practical and generalized tool that can be adopted by the industry. This tool can be used to give results at a very early stage without much delay.
The developed models shows a negative coefficient of water quantity, which indicates that the mechanical properties are inversely related to the quantity of water added to the concrete mix.
This research was financially supported by the Technical Education Quality Improvement Programme II (TEQIPII), an initiative of the Ministry of Human Resource and Development (MHRD), Government of India.