MATHEMATICAL MODEL FOR COMPRESSIVE STRENGTH PREDICTION OF RECYCLED AGGREGATE CONCRETE

Transcription

1 CHAPTER 6 MATHEMATICAL MODEL FOR COMPRESSIVE STRENGTH PREDICTION OF RECYCLED AGGREGATE CONCRETE Preamble The design of concrete mixes involves determination of the proportions of the constituents namely cement, water, coarse aggregates and fine aggregates with admixtures if any, to achieve the desired compressive strength. (Nagabhushana and Sharada-bai, 2011; Kett, 2010, and Krishna-Raju, 2002). Accordingly the strength, durability and other characteristics of concrete depend upon the properties of these ingredients, proportion of the mix, the method of compaction and other controls during placing, compacting and curing. The compressive strength is the most significant property of concrete, amongst the various other properties (Majid, 1974). In most of the structural applications, concrete is employed primarily to resist compressive stresses. The load carrying capacity of a structure is basically dependent on the compressive strength of concrete as pre-stressed concrete and high performance concrete in bridges are generally deigned for higher compressive strength. The compressive strength of concrete is generally determined by testing cubes or cylinders made in laboratory or cores drilled from hardened concrete or from the non-destructive testing. However the strength gain is a very complex phenomenon and is directly related to the hydrated cement paste, ratio of cement to mixing water, ratio of cement to aggregate, grading, surface texture, shape, and stiffness of aggregate particles and maximum size of aggregates. Various material constituents such as admixtures are added in concrete and various trials are carried out to provide concrete with the desired compressive strength. However the process could be simplified if a mechanism is developed which gives an understanding of strength prediction with accuracy. A number of prediction techniques have been proposed by researchers which are generally applicable to normal aggregate concrete. 126

2 Thus given the fact that compressive strength plays a significant role in the concrete properties, it would be essential to understand the compressive strength gain with recycled aggregates. However on the basis of the experimental programme, it is observed that for the recycled aggregates to be used in concrete, it is essential to study the characteristics, mix proportions and mechanical properties of the material. The physical and mechanical properties of ingredients give the understanding of quality, porosity and grading of the material, which also helps in the process of proportioning of the material component in the mix design process. This however is assessed by undertaking various trials. Thus the process of compressive strength assessment of concrete with recycled aggregates required a rigorous experimentation programme comprising of various trials. Nevertheless this effort can be reduced if a model is developed to provide prediction of compressive strength at 28 days. 6.1 Model for Compressive Strength Prediction The compressive strength of concrete follows the Abrams equation which states that the compressive strength of concrete primarily depends upon the strength of cement paste and water/ cement ratio, provided the mix is workable. Popovics (1990) refined the Abrams model, given by a widely accepted equation relating the water cement ratio (w/c) of concrete to its compressive strength with additional variable such as slump, and used the least square regression to determine equation coefficients. Since the compressive strength of concrete is a complex process, a number of prediction techniques including empirical or computational modelling, statistical techniques, artificial intelligence approaches and simulation models etc. are proposed by researchers (Zain et al., 2012). A number of research efforts have been concentrated on using statistical techniques (multivariable regression models) to improve the accuracy of predictions. Statistical models have the advantage that once fitted they can be used for predictions much more quickly than 127

3 other modelling techniques, and are correspondingly simpler to implement in software. Mathematical models evaluated on the basis of test data of concrete mixes i.e. the experimental results are most reliable, accurate and scientific. They allow ascertaining rapid and reliable prediction of concrete strength without the full scale testing by reducing the chances of failures. Statistical analysis can also provide insight into the key factors influencing 28 days compressive strength through correlation analysis (Zain et al., 2012). Prediction of concrete compressive strength, therefore, has been an active area of research and a considerable number of studies have been carried out. The concrete compressive strength however is an intricate non-linear problem which makes it difficult to predict it accurately. Earlier developed models followed a linear and multi-linear regression analysis for predicting compressive strength. Linear regression model is a powerful method for analysing data which is linear in relationship as shown in equation (1). Y = a 0 + a 1 w C linear regression (Abrams Law).. (1) Multi- linear regressions determine the relationship between two or more independent variables and a dependent variable by fitting a linear equation to the observed data. Every value of the independent variable is associated with a value of the dependent variable as represented in equation (2). Y = a 0 + a 1 w C + a 2 CA + a 3 FA + a 4 C Multi- linear regression.. (2) where Y= Compressive strength of concrete w c = Water cement ratio C = Quantity of cement in the mix 128

4 CA = Quantity of coarse aggregate in the mix FA = Quantity of fine aggregate in the mix Y is the dependent variable and w, CA, FA & C are independent variables. c a 0, a 1, a 2, a 3, a 4 are coefficients to be determined. From equation (2), it is seen that all the variables are related to compressive strength in a linear relationship; however this may not always be valid, since all the components in a concrete mix affecting the compressive strength are generally interrelated with each other and may not always result into an additive function. Thus it was felt that a different type of mathematical model is required to be applied to predict the compressive strength of concrete with reasonable accuracy. For situations where the multiple dependencies are curvilinear (non-linear) the logarithmic transformation can be applied to this type of regression as represented in equation (3). log Y = log (a 0 ) + a 1 log (w/c) + a 2 log (CA) + a 3 log(fa) + a 4 log (C) +.. (3) This equation when transformed back to a form that predicts the dependent variable (Y) by taking the anti- logarithm yields equation (4) as stated below Y = a 0. (w c) a1. (CA) a2. FA a3. (C) a4..(4) This equation is referred as the multivariable power equation, the functional parameter (Y) is dependent on several independent variables, and is said to give more realistic results. This form of model has been successfully used to predict the compressive strength for ordinary Portland cement concrete by Kheder et al., (2003) and for compressive strength prediction of high performance concrete by Zain et al,. (2012). Suhad (2001) used multivariable regression techniques on concrete composition data to predict 7 and 28 days compressive strength of 129

5 normal aggregate concrete with reasonable accuracy, proposing a formula readily applicable for on-site use. To derive an equation for the present study the data obtained from the experimental work is used. 6.2 Data Set Used The data derived from the experimental programme in the present work is used to develop a mathematical model that uses the density, mix proportions and w/c ratio to represent the impact of these constituents on the compressive strength of concrete. Total 36 specimens each of size mm were cast using mix design methodology developed in this work to achieve M25 grade concrete. Data of around 27 samples without adhered mortar content and 9 samples with adhered mortar content was used in formulation of the model in order to cover a wide range of water absorption percentage. Out of total 36 results of 28 days compressive strength of concrete made with 60 percent recycled aggregates as shown in Table 6.1, 80 percent i.e. 28 number of test results were used for formulation of the model. Table 6.1 Mix Proportion of Recycled Aggregate Concrete Sr. Density No. ρ (kg/m 3 ) Water Recycled Other Water W Cement Expt./Obs. Absorption Aggregates material (kg/m 3 ) C Comp. St. w abs RA S (kg/m 3 ) (%) (kg /m 3 ) (kg/m 3 ) (N/mm 2 ) Y obs 130

6 Various parameters like density of concrete, water absorption, quantity of recycled aggregates, quantity of other ingredients consisting of sand and normal aggregates, cement and water were considered for formulation of the model. However for formulation of model the relationship of individual parameters with compressive strength required to be studied is discussed in the following section. 6.3 Relationship of Parameters with Compressive Strength The properties of concrete depend on the quantity and quality of its components. The compressive strength of concrete is mainly influenced by the proportions of mix, w/c ratio, water absorption and density of concrete. i) Water/cement ratio: To illustrate the relationship of compressive strength to water cement ratio the experimental data of the agglomerated recycled aggregate sample (R p ) consisting of adhered mortar with different water cement ratios was used. Individual ten recycled aggregate samples without adhered mortar were also considered for establishing the 131

7 relationship as shown in Table 6.2. The samples 1 to 10 in the Table 6.2 are individual samples of recycled aggregates without adhered mortar. Sample 11 to 13 were agglomerated without adhered mortar (Table 5.9) and sample 14 and 15 were agglomerated with adhered mortar content (Table 5.5 and Table 5.7 respectively). Table 6.2 Test Data of 28 days Compressive Strength with Water Cement Ratio Sample No. w/c ratio 28 days Compressive Strength (N/mm 2 ) The relationship of compressive strength to water cement ratio has been studied from the plot of compressive strength values for different water cement ratios as shown in Fig

8 45 28 days Compressive Strength N/mm Compressive Strength w/c ratio Fig. 6.1 Relationship between Compressive Strength and Water Cement Ratio of Recycled Aggregate Concrete It is observed that recycled aggregate concrete also shows decrease in compressive strength with increase in w/c ratio same as that of normal concrete. Recycled aggregate concrete designed with a water cement ratio of 0.55 with adhered mortar content provided a compressive strength upto N/mm 2 at 28 days and concrete designed with a water cement ratio of 0.45 provided a compressive strength upto N/mm 2. ii) Aggregates: Recycled aggregates have large amounts of adhered mortar which results in higher water absorption and thus have detrimental effect on the compressive strength of concrete. In case of recycled aggregate concrete it is observed that water absorption has also been a parameter influencing the compressive strength of concrete. Water absorption in recycled aggregates is related to the amount of adhered mortar content present on the aggregates. Lesser the water absorption, lower is the adhered mortar content and such concrete is also able to provide higher compressive strength in comparison to those with higher water absorption. The experimental data consisting of only observed compressive 133

9 28 days Compressive Strength strength and water absorption from Table 6.1 was used in interpreting the relationship between these two properties The relationship between water absorption and compressive strength is shown in Fig N/mm compressive strength Water Absorption in % Fig. 6.2 Relationship between Compressive Strength and Water Absorption of Recycled Aggregate Concrete From Fig. 6.2 it is observed that the compressive strength of concrete decreases with the increase in water absorption. From the depiction it is observed that recycled aggregate concrete with the highest water absorption of 7.6 percent was able to provide a compressive strength in the range of N/mm 2 at 28 days however those having a least water absorption of 2.64 percent provided a compressive strength of the order of N/mm 2. Thus considering the influence of water absorption on compressive strength of recycled aggregate this variable was also incorporated in the formulation of the model. iii) Density: The experimental data consisting of only observed compressive strength and density from Table 6.1 is used in obtaining the relationship between these two parameters of recycled aggregate concrete which is represented in Fig

10 28 days Compresive strength N/mm compressive strength Density in kg/m 3 Fig. 6.3 Relationship between Compressive Strength and Density of Recycled Aggregate Concrete From Fig. 6.3, it is observed that compressive strength of recycled aggregate concrete increases with the density which is an indication of compressive strength being proportional to density of concrete. Further it is also observed that recycled aggregate concrete with a minimum density of kg/m 3 has provided a compressive strength of N/mm 2 at 28 days and concrete having highest density of kg/m 3 has provided higher compressive strength of N/mm 2. However since compressive strength depends collectively on all the properties of recycled aggregates and mix proportions, it is possible to develop an equation taking into account every ingredient that influences the strength of such concrete. It is also observed from Fig. 6.1, Fig. 6.2 and Fig. 6.3, that the individual relationship of compressive strength with either water cement ratio or water absorption or density has been linear. However since all the parameters affecting compressive strength are inter-related with each other, a multi-linear model may not be applicable to such a data set. 135

11 Accordingly in this study, the multivariable power equation using the least square estimation was found to be suitable for predicting the compressive strength of recycled aggregate concrete. Factors affecting this strength were the compositions of the concrete mix design namely density of concrete, water absorption in percent, amount of water, quantity of cement, quantity of recycled aggregate and other ingredients which includes fine aggregates and normal aggregates. Thus the data from Table 6.1 has been used in equation (4) (section 6.1) for developing the model. Thus the model form selected is Y = a 0 ρ a 1 W abs a 2 S a 3 RA a 4 W a 5 C a 6 (5) where Y= Compressive strength in N/mm 2 ρ = Density of concrete in kg/m 3. W abs = Water absorption of recycled aggregates in %. RA= Quantity of recycled aggregate in concrete in kg/m 3. S= Quantity of other ingredients in concrete in kg/m 3. W= Water in litres to produce 1 cum of concrete. C= Cement content in kg to produce 1 cum of concrete. Advanced excel software was used to develop the regression model to predict the compressive strength of recycled aggregate concrete at 28 days. The regression analysis is carried out on the data set of Table 6.1 and values of regression coefficients a 0 to a 6 obtained are as shown in Table 6.3. The values of these coefficients are reflective of the impact of various ingredients on the compressive strength of concrete. 136

12 Table 6.3 Regression Coefficients Description of parameters Coefficients Values Constant a Density (ρ) a Water absorption(w abs ) a Other ingredients (S) a Recycled aggregates (RA) a Water (W) a Cement (C) a From the coefficients displayed in Table 6.3, it is seen that cement is the major independent variable influencing the compressive strength of concrete with a regression coefficient value of This is followed by density of concrete wherein a regression coefficient value of is observed. The quantity of recycled aggregates followed by water content are the other variables influencing the compressive strength of concrete however their impact is smaller ( and respectively) in comparison to that of cement and density. Further it is noticed that in case of water absorption the regression coefficient obtained was whereas that for other ingredients it was even smaller ( ) which is a representative of the least impact of the ingredient on the compressive strength of recycled aggregate concrete. Water absorption also seems to have influence on the compressive strength wherein from Fig. 6.2 it is seen that lower the water absorption higher is the compressive strength. The impact of water absorption is seen to be higher in comparison to other ingredient which has the least impact. The regression coefficients thus obtained in the Table 6.3 were incorporated in equation (5) to get the final model for predicting the compressive strength of recycled aggregate concrete. 137

13 Observed compressive strength in N/mm 2 Thus the final model for predicting compressive strength of recycled aggregate concrete corresponding to M25 grade concrete using the data set in Table 6.2 is Y = ρ W abs S RA W C (6) The relationship between the observed values of the compressive strength obtained from the experimental work and those predicted from the model is shown in Fig R² = expt strength Predicted compressive strength in N/mm 2 Fig. 6.4 Predicted v/s Observed Values of Compressive Strength at 28 days It is seen that the model has 86.6 percent correlation with the experimental data which means that the observed and the predicted values for the compressive strength of recycled aggregate concrete are in conformity with each other. 6.4 Validation of the Model The validation of the finally developed model equation (6) is then carried out by using the remaining 20 percent of the test results. The experimental values of another 8 specimens which were not included in the formulation of the model were used for validation of the model. Table 6.4 presents the values of each of the independent variables which were 138

14 incorporated in the model equation to get the predicted values of compressive strength. The experimentally observed values are also shown in the same table for comparison. Table 6.4 Validation of the Regression Model Sr. Density No. ρ (kg/m 3 ) Water Recycled Other Water Cement Absorption Aggregates Material W C w abs Compressive strength in (N/mm 2 ) RA S (kg/m 3 ) (kg/m 3 ) Expt./Obs Predicted (%) (kg /m 3 ) (kg/m 3 ) From Table 6.4, it is observed that the predicted values of compressive strength obtained by using the proposed model equation (6) are in good agreement with the experimental results. From the validation undertaken it is observed that recycled aggregate concrete which had a compressive strength of N/mm 2 experimentally provided an estimated value of compressive strength at 28 days of N/mm 2 by the developed model which indicates an error of 0.35 percent. Similarly when the experimental compressive strength obtained was N/mm 2 the predicted value was N/mm 2 which implies an error of 7.0 percent in the test results. Since the error percentage was in the range of 0.35 to 7 percent only and since the coefficient of correlation obtained from the model formulation was 86.6 it is acknowledged that the model could be used to predict compressive strength of recycled aggregate concrete of M25 grade reasonably well even if only the mix design compositions and properties of recycled aggregates are known. 139

15 Thus the present proposed model can be effectively employed to obtain the compressive strength of recycled aggregate concrete at 28 days for 60 percent replacement of normal aggregates by 20mm size recycled aggregates having water absorption range of 2.48 to 7.60 percent. The mathematical regression model developed also reflects the influence of important ingredients namely water absorption, density, recycled aggregate, cement water, and other ingredients on compressive strength of recycled aggregate concrete at 28 days designed by using mix design procedure developed in the present work. Closure 28 days compressive strength of recycled aggregate concrete could be predicted from the developed model. However in order to study the performance of such M25 grade recycled aggregate concrete, durability properties like water permeability, rapid chloride permeability, drying shrinkage, modulus of elasticity and creep have been studied which are discussed in the next chapter. 140