Comments on “Prediction on CO₂ uptake of recycled aggregate concrete”, Frontiers of Structural and Civil Engineering, 14, 746−759 (2020)

Abstract

A methodology to compute the CO₂ uptake of recycled aggregate concrete is proposed in the commented paper. Besides some typos in several formulas, it is found that the approach to estimate the specific surface area of the recycled aggregates is not correct. This issue has some impact in the conclusions of the commented paper. Therefore, aiming to improve the understanding, accuracy and findings of the commented paper, an alternative approach to estimate the specific surface area of the recycled aggregates, as well as an erratum of the formulas and revised conclusions are suggested.

1 Comments

The investigation published on Frontiers of Structures and Civil Engineering, by Huang et al. [1], addresses a very important topic toward comprehensive Life Cycle Analysis of recycled aggregate concretes. This has stimulated a thorough reading of the paper that resulted in the present Comment.

Upon reading of the paper, some inconsistencies were found in equations, which are judged to be writing lapses. In this manner it is proposed:

for Eq. (8) of Ref. [1],

\begin{array}{rl}{v}_{\text{s}}^i=& {\displaystyle \frac{1}{6}}\text{π}\left[d_{\text{g}}^{i3}-{\left(d_{\text{g}}^i-2d_{\text{c}}\right)}^3\right]\approx {\displaystyle \frac{1}{6}}\text{π}{d}_{\text{g}}^{i3}\left[1-\left(1-6{\displaystyle \frac{d_{\text{c}}}{d_{\text{g}}^i}}\right)\right]\\ =& \text{π}{d}_{\text{c}}{d}_{\text{g}}^{i2}=d_{\text{c}}{a}_{\text{g}}^i,\end{array}

where d_{\text{g}}^i is the diameter of the RCA (m), for Eq. (9) of Ref. [1],

CA{b}_2=\sum _i{n}_i=0.044q{\rho }_{\text{s}}{d}_{\text{c}}\sum _i{a}_{\text{g}}^i=0.044q{\rho }_{\text{s}}{d}_{\text{c}}{A}_{\text{g}},

for Eq. (11) of Ref. [1], A_{\text{g}} is in m²,

for Eq. (15) of Ref. [1],

\frac{1}{6}\text{π}{\overline{d}}^3=\sum _i\frac{1}{6}\text{π}{d}_i^3{\omega }_i.

The major issue, that justifies this Comment, it is found in the calculation of a fundamental parameter for the approach, which is the specific surface area of recycled concrete aggregates (RCA), denoted as η, and referred several times in Ref. [1] as a “key parameter”.

For the sake of simplicity, Huang et al. [1], proposed a formula to estimate η from the granulometric curve of RCA. To that purpose Huang et al. [1] made use of a parameter that they called “average diameter for RCAs”. However it is arguable if the weighing factor to compute this parameter should be the number of particles instead of the volume/mass of a given size, or even if it should be the surface of a given size (as the aim is to estimate a specific surface) and further if the appropriate parameter is the average diameter of particles or the diameter of the average size particle. To overcome such discussion, let us focus on the fact that the goal is to estimate η from the granulometric curve of RCA. Following the notation adopted in Ref. [1],

(1)\eta =\frac{A_{\text{g}}}{m_{\text{x}}}=\frac{A_{\text{g}}}{\rho V_{\text{x}}},

where η is the specific surface area of RCAs (m²/kg), A_{\text{g}} is the surface area of all RCAs considered (m²), m_{\text{x}} is the mass of all RCAs considered (kg), ρ is the density of RCA (kg/m³) and V_{\text{x}} is the volume of all RCAs considered (m³).

The surface area and the volume of all RCAs considered, can be obtained through the sum of individual surface areas a_{\text{g}}^i (in m²) and volumes V_i (in m³), respectively. Then,

(2)\eta =\frac{{\displaystyle \sum _i{a}_{\text{g}}^i}}{\rho {\displaystyle \sum _i{V}_i}}.

Considering the RCAs particles as spheres, Eq. (2) can be written as

(3)\eta =\frac{{\displaystyle \sum _i\text{π}{d}_i{}^2}}{\rho {\displaystyle \sum _i\frac{1}{6}\text{π}{d}_i{}^3}}=\frac{{\displaystyle \sum _i{d}_i{}^2}}{{\displaystyle \frac{1}{6}}\rho {\displaystyle \sum _i{d}_i{}^3}},

where d_i is the diameter (m) of an individual particle.

Now, to compute the two summations in Equation (3), let us introduce the simplification of considering a group of particles with similar sizes represented by a characteristic value, desirably a central tendency measurement of the group. At this point it shall be noticed that in Ref. [2] the adopted central tendency measurement is the geometric mean. Thus, considering groups of particles,

(4)\begin{array}{rl}& \sum _i{d}_i^2=\sum _j{n}_j{d}_j^2,\\ & \sum _i{d}_i^3=\sum _j{n}_j{d}_j^3,\end{array}

where n_j is the number of particles in a certain group and d_j^{} is the characteristic size of the particles from that group (m). The remaining variables are as described before.

Considering groups constituted by RCA particles within the sizes of two sieve openings, enables us to estimate η from a granulometric curve. Such estimation will be based on the mass ratio of each RCA fraction,

(5){\omega }_j=\frac{m_j}{m_{\text{x}}}=\frac{\rho V_j}{\rho V_{\text{x}}}=\frac{V_j}{V_{\text{x}}},

where {\omega }_j is the mass ratio of a certain fraction (kg/kg), m_j is the mass of a certain fraction (kg) and V_j is the volume of a certain fraction (m³). The remaining variables are as described before.

If the characteristic size is a central tendency measurement, then the volume of a certain fraction, V_j (m³), can be approximated by

(6)V_j=n_j\frac{\text{π}}{6}{d}_j^3,

where n_j is the number of particles of a certain fraction and d_j^{} is as described before.

Replacing V_j from Eq. (6) in Eq. (5),

(7){\omega }_j=\frac{n_j{\displaystyle \frac{\text{π}}{6}}{d}_j^3}{V_{\text{x}}}.

Solving Eq. (7) to find n_j, we get

(8)n_j=\frac{6V_{\text{x}}}{\text{π}{d}_j^3}{\omega }_j.

Replacing n_j from Eq. (8) in Eq. (4)

(9)\begin{array}{rl}& \sum _i{d}_i{}^2=\sum _j\frac{6V_{\text{x}}}{\text{π}{d}_j^3}{\omega }_j{d}_j^2=\frac{6V_{\text{x}}}{\text{π}}\sum _j\frac{{\omega }_j}{d_j},\\ & \sum _i{d}_i^3=\sum _j\frac{6V_{\text{x}}}{\text{π}{d}_j{}^3}{\omega }_j{d}_j^3=\frac{6V_{\text{x}}}{\text{π}}\sum _j{\omega }_j.\end{array}

Finally, substituting the above summations in Eq. (3), while knowing that the sum of all {\omega }_j equals 1,

(10)\eta =\frac{{\displaystyle \frac{6V_{\text{x}}}{\text{π}}}{\displaystyle \sum _j{\displaystyle \frac{{\omega }_j}{d_j}}}}{{\displaystyle \frac{1}{6}}\rho {\displaystyle \frac{6V_{\text{x}}}{\text{π}}}}={\displaystyle \frac{6}{\rho }}{\displaystyle \sum _j{\displaystyle \frac{{\omega }_j}{d_j}},}

where η is the specific surface area of RCAs (m²/kg), ρ is the density of RCA (kg/m³), {\omega }_j is the mass ratio of a certain fraction (kg/kg) and d_j is the characteristic size of the particles for that fraction (m).

Using Eq. (10) instead of Eqs. (18) and (15) of Ref. [1], for the RCA considered in the case study presented by Huang et al. [1], an increase of 23% in the specific surface area of RCAs is expected. Therefore, the CO₂ sequestration, CA (kg), presented in Table 1 of Ref. [1], shall be amended to 11.3, 15.0, 19.0, and 25.1, for mixes B1, B2, B3 and B4, respectively. Nevertheless, in opposition to what is defended by Huang et al. [1], despite the increase in CO₂ sequestration due to the correction of the estimation for the specific surface area of RCAs, it is found that for the case study discussed in Ref. [1], the difference between CO₂ emission and sequestration increases in favor of the emission when higher contents of RCAs are used. Regardless of this, the environmental benefits of replacing natural aggregates by RCAs are undisputed and further, for service live times longer than the 50 years considered in the case study discussed by Huang et al. [1], there may be a turnaround in favor of the CO₂ sequestration. All carbonation depths after 50 years, in the case study presented in Ref. [1], although not declared, are anticipated to be less than 20 mm. The cover to reinforcement is usually higher than 20 mm. Thus, a service life of 100 years could be considered, without corrosion-induced carbonation problems, using the mixes defined in the case study discussed by Huang et al. [1]. Incorporating the estimation of specific surface area of RCAs through Eq. (10) and a service life of 100 years, while retaining the remaining parameters of that case study, CO₂ sequestration per unit volume of concrete (kg/m³) will be 8.8, 14.3, 18.3, 22.6, and 29.1 for mixes A, B1, B2, B3, and B4, respectively. For these values, the difference between CO₂ emission and sequestration is quite similar for all mixes (approximately 260 kg of CO₂ per cubic meter of concrete), regardless of having RCAs or not and of the RCA content.

References

[1] Huang K, Li A, Xia B, Ding T. Prediction on CO₂ uptake of recycled aggregate concrete . Frontiers of Structural and Civil Engineering, 2020, 14(3): 746– 759

[2] Miyake J, Matsushita H. Evaluation method for consistencies of mortars with various mixture proportions. Journal of Advanced Concrete Technology, 2007, 5(1): 87– 97

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Higher Education Press 2021.