Analytical model for predicting the compressive strength of recycled aggregate concrete

1. Introduction

In recent decades, the problem of disposal of construction and dismantling waste has become global. According to various studies, concrete accounts for up to 50-60 % of the total waste of the construction industry [1], [2]. In this regard, the recycling of concrete scrap to produce recycled concrete aggregate is considered as one of the key areas of sustainable construction development.

The use of recycled aggregate makes it possible to reduce the consumption of natural resources, reduce waste disposal and reduce the carbon footprint of construction. At the same time, the widespread use of concrete with recycled concrete aggregate is limited by the deterioration of its mechanical properties, primarily compressive strength [3]-[5].

The experimental results indicate that the decrease in the strength of concrete due to the use of secondary aggregate may amount to 10-40 % or more, depending upon the degree of substitution and the quality of the aggregate [3], [6], [7]. The main reasons for this are the presence of attached old cement stone, increased porosity, microcracks, and a weakened contact zone between the aggregate and the new cement stone [8], [9].

The results of numerous experimental studies confirm that the strength of concrete with secondary aggregate systematically decreases with an increase in the proportion of substitution of natural aggregate [3], [4], [10]. At the same time, for the same replacement ratio, different authors have reported significantly different strength values, indicating the important role of recycled aggregate quality.

Studies have shown that the secondary aggregate obtained from high-strength initial concrete can significantly reduce the loss of concrete strength [11], [12]. One of the most informative indicators of the quality of secondary concrete aggregate is its water absorption, reflecting porosity, the degree of micro-damage and the amount of cement stone attached [8], [13], [14].

Despite the large amount of available experimental data, analytical models that simultaneously account for the replacement ratio and key quality parameters of recycled aggregate remain limited in the literature [15], [16]. This justifies the relevance of developing a simple and physically based analytical dependency.

The aim of this study is to develop a simple physically based analytical model for estimating the compressive strength of concrete using a secondary concrete aggregate based on a minimal set of physically interpretable parameters.

To achieve this goal, the following tasks are being solved:

– Analysis of the main factors affecting the strength of recycled aggregate concrete.

– Formulation of a dimensionless analytical dependence.

– Study of the sensitivity of the model to changes in the main parameters.

– Analysis of marginal cases and physical correctness of the model.

2. Model concept and formulation

2.5. Sensitivity analysis of the model

To assess the effect of the main parameters, we consider partial derivatives of dimensionless strength:

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$S_r=\frac{\partial \left(\raisebox{1ex}{$f_c$}\!\left/ \!\raisebox{-1ex}{$f_{c0}$}\right.\right)}{\partial r}=-Q_{RCA}.$

The negative sign of the derivative indicates a monotonous decrease in strength with an increase in the proportion of secondary aggregate. The modulus of the derivative is determined by the quality index of the secondary aggregate, which means a higher sensitivity of concrete strength to substitution when using a low-quality aggregate. Thus, the proposed model makes it possible to quantify the effect of the replacement ratio while taking into account the structural characteristics of recycled concrete aggregate:

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$S_{f_{c,o}}=\frac{\partial \left(\raisebox{1ex}{$f_c$}\!\left/ \!\raisebox{-1ex}{$f_{c0}$}\right.\right)}{\partial f_{c,o}}=\frac{1-r}{f_{c,r}}\left(\frac{W_r}{W_{RCA}}\right),$

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$S_{W_{RCA}}=-\left(1-r\right)\left(\frac{f_{c,o}}{f_{c,r}}\right)\frac{W_r}{W_{RCA}^2}.$

Sensitivity analysis shows that the water absorption of the secondary aggregate has the greatest effect on the calculated strength, which is consistent with the experimental conclusions presented in [8], [9], [14].

Fig. 2 shows the dependence of the sensitivity of the relative strength of concrete to the proportion of substitution of natural aggregate on the quality index of the secondary aggregate. Sensitivity is defined as the modulus of the partial derivative of the dimensionless strength in terms of the substitution fraction.

Fig. 1Dependence of relative compressive strength on replacement ratio for different values of RCA quality index QRCA

Fig. 2Sensitivity of relative compressive strength to replacement ratio as a function of RCA quality index

3. Discussion

The proposed analytical model is focused on identifying key patterns of the influence of secondary concrete aggregate on concrete strength, rather than on the exact reproduction of individual experimental results. This approach corresponds to the tasks of preliminary design and theoretical analysis, when detailed experimental information is missing or limited [3, 6, 9, 10].

A fundamental distinction between the proposed model and most existing empirical formulations lies in the separate consideration of quantitative and qualitative factors, namely the replacement ratio of natural aggregate and the intrinsic quality of recycled concrete aggregate (RCA). In many previously reported models, strength reduction is expressed solely as a function of the replacement ratio, which does not adequately explain the significant scatter observed in experimental results at identical replacement levels.

The introduction of the dimensionless recycled aggregate quality index $Q_{RCA}$enables an integrated representation of the mechanical and structural characteristics of RCA. This index combines the strength of the original concrete and the water absorption of the recycled aggregate, both of which are closely related to the amount of adhered mortar, porosity, and microcracking. As reported in numerous experimental studies, these microstructural features play a dominant role in determining the quality of the interfacial transition zone and, consequently, the overall mechanical performance of RAC.

The parametric analysis demonstrates that, for a fixed replacement ratio, the relative compressive strength of RAC may vary significantly depending on the quality of the recycled aggregate. This result supports the hypothesis that the use of high-quality RCA can substantially extend the feasible range of aggregate replacement without causing excessive strength degradation.

In the limiting case of ideal recycled aggregate quality, the proposed formulation reduces to the classical linear dependence on replacement ratio, which is commonly adopted in engineering practice. This confirms that the present model does not contradict existing approaches, but rather generalizes them by incorporating additional physically meaningful parameters. These observations are in good agreement with experimental studies that identify water absorption and adhered mortar content as critical parameters affecting RAC performance. The proposed model thus provides a rational explanation for these experimentally observed trends within a simple analytical framework.

To provide a simple empirical illustration of the proposed analytical model, its predictions were compared with representative experimental results reported in the literature. For example, Rahal [10] reported compressive strength reductions of approximately 15-25 % for concrete with a 50 % replacement of natural coarse aggregate by recycled concrete aggregate (RCA) with moderate water absorption. Using typical parameter values corresponding to these conditions (replacement ratio $r=$ 0.5, original concrete strength $f_{c,o}\approx$ 35-40 MPa, and $W_{RCA}\approx$ 4-5 %), the proposed model predicts a strength reduction of about 18-22 %. The difference between predicted and experimental values therefore remains within approximately 5-8 %, which can be considered acceptable for a simplified analytical formulation intended for preliminary engineering assessments. This comparison demonstrates that the proposed model is capable of reproducing not only qualitative trends but also realistic quantitative estimates of strength reduction.

4. Conclusions

Based on the conducted analytical and theoretical analysis, the following conclusions can be drawn:

1) It is shown that the strength of recycled aggregate concrete (RAC) is determined not only by the proportion of substitution of natural aggregate, but also by the integral quality of the secondary aggregate, characterized by the strength of the initial concrete and its water absorption.

2) The introduced dimensionless index of the quality of secondary concrete aggregate makes it possible to compactly and visually take into account the influence of key structural factors without complicating the analytical model.

3) The theoretical substantiation of the effect of water absorption through effective porosity confirms the physical correctness of the proposed dependence and is consistent with experimental observations presented in the scientific literature.

4) The sensitivity analysis of the model showed that the water absorption of the secondary aggregate has the greatest effect on the calculated strength, which emphasizes the importance of its structural condition and the quality of the contact zone.

5) The analysis of marginal cases demonstrates that the proposed model correctly transforms into well-known particular dependencies widely used to describe the strength of concrete, which confirms its universality.

6) The developed analytical dependence can be used as a tool for preliminary assessment of the strength of concrete with secondary aggregate, as well as a basis for further development of semi-empirical and numerical models.