A Practical Equation for the Elastic Modulus of Recycled Aggregate Concrete

Abstract

For greater sustainability in construction, coarse recycled aggregate concrete (RAC) is becoming popular as a replacement for natural aggregate concrete (NAC) in structures. The elastic modulus of concrete (E) is a fundamental parameter in structure design. However, the empirical equations for E of NAC cannot apply to RAC because E of RAC is lower than NAC of equal strength, which hinders the widespread use of RAC to a certain extent. This paper provides a practical equation for E of RAC based on a comprehensive statistical analysis of 1383 mixes from 154 publications, allowing designers to easily estimate E of RAC by known parameters at the design stage, such as compressive strength, replacement rate and quality of recycled aggregate. This equation is developed by introducing a reduction factor η into the empirical equation for NAC and verified by the additional experimental results. Compared with JGJ/T443-2018 (a Chinese standard), this paper provides a more reasonable and accurate estimate by analysing much more data and taking into account other factors, such as aggregate type and the volume ratio of aggregate to paste.

1. Introduction

The elastic modulus of concrete is a fundamental parameter for designing concrete structures. Thus, current building codes propose practical equations for the elastic modulus, such as Equations (1)–(3) [1,2,3]. The elastic modulus in these equations is a function of compressive strength, a known parameter at the design stage.

CEB-FIP : E_NAC,pred = 21500(f_cy/10)^1/3

(1)

ACI 318 : E_NAC,pred = 4730f_cy^0.5

(2)

GB 50010 : E_NAC,pred = 10⁵/(2.2 + 34.7/f_cu)

(3)

where E_NAC,pred is the estimation of elastic modulus of NAC, MPa; f_cy is the compressive strength measured on cylinders 150/300 mm at an age of 28 days, MPa; f_cu is the compressive strength measured on cubes of 150 mm size at an age of 28 days, MPa.

For greater sustainability in construction, RAC has been considered as a replacement for NAC in structures. However, due to the old mortar and crushed bricks in coarse recycled aggregate (RA), the elastic modulus of RAC is lower than NAC of equal compressive strength, meaning that the equations for the elastic modulus of NAC, such as Equations (1)–(3), cannot apply to RAC. Therefore, many equations for the elastic modulus of RAC have been developed [4,5,6,7,8,9,10,11]. However, most of them are not practical for the estimation as they use many parameters unknown at the design stage, such as the detailed mix proportion of concrete, the aggregate type, the cement type, the aggregate size, the elastic modulus of the control concrete and so on.

JGJ/T443-2018 [11] (a Chinese code for recycled concrete structures) proposes a practical equation, as shown in Equation (4), for the elastic modulus of RAC by introducing a reduction factor η that depends on the quality and replacement level of RA, as shown in Equation (5). This is justified by the fact that it takes into account the influence of the elastic modulus of the mixed aggregate that mainly depends on the porosity of the aggregate affected by the quality and replacement level of RA. However, there are two problems due to the limited data for the analysis (only about 500 mixes):

• It shows that Class I RA has no adverse effect on the elastic modulus. However, a little old mortar may be attached to Class I RA that reduces the elastic modulus, and Ohemeng et al. [4] report that RCA made with high-quality RA may gain equal or higher compressive strength but lower elastic modulus, which means η for Class I RA should be less than 1.
• It does not distinguish the influence of Class II and III RA on the elastic modulus. However, a significant difference in porosity between Class II and III RA may lead to a different η for them.

E_RAC,pred = ηE_NAC,pred = η(10⁵/(2.2 + 34.7/f_cu))

(4)

η = {1, for Class I RA; 0.9 + (0.3 − r)/7, for Class II and III RA}

(5)

where RA is classified by GB 25177-2010 [12]; E_RAC,pred is the estimation of elastic modulus of RAC, MPa; r is the replacement rate of RA by weight.

This paper does similar works with JGJ/T443-2018 but analyses more data to enable a better evaluation of the reduction factor η. A total of 1383 mixes from 154 publications are collected and analysed statistically. The correlation between η and r for different quality of RA is quantified. From this, a practical equation for the elastic modulus of RAC in the form of Equation (4) is proposed. Finally, the equation is validated by the additional laboratory tests. Designers and engineers can use the simple equation to determine the elastic modulus of RAC by known parameters at the design stage.

2. Materials and Methods

2.1. Data Collection

First, the publications related to the elastic modulus of RCA are collected.

Second, for each publication, the key information, such as the apparent density (ρ_a) and water absorption (w_a) of RA, the replacement rate of RA, the compressive strength and the elastic modulus at 28 days and the shape and size of specimens for strength test, is identified carefully and transcribed into a spreadsheet. We cross-check it to avoid incorrect entries or repeated entries.

Notes:

• The ρ_a can be calculated from the oven-dry density (ρ_od) and w_a, or the saturated surface dry density (ρ_ssd) and w_a, or the ρ_ssd and ρ_od based on Equations (6) and (7), although some publications give the ρ_od or ρ_ssd of RA rather than the ρ_a.
• This paper uses the weight replacement rate as JGJ/T443-2018 does. Some publications use the volume replacement rate while others use the weight replacement rate. In fact, there is little difference between the volume replacement rate and weight replacement rate in most cases.
• The size effect of strength is considered in this paper. The 150 mm cube compressive strength is the standard compressive strength in this paper. The conversion factors of compressive strength are shown in

  Table 1. Conversion factors of compressive strength [13,14,15,16].

  Size/Diameter × Height	Shape	Strength Grade
  		C20–C40	C50	C60	C70	C80
  150 mm	Cube	1
  100 mm	Cube	0.95
  50 mm × 100 mm	Cylinder	1.17	1.13	1.03	1.01	0.99
  75 mm × 150 mm	Cylinder	1.19	1.15	1.07	1.05	1.04
  100 mm × 200 mm	Cylinder	1.21	1.17	1.12	1.10	1.08
  120 mm × 240 mm	Cylinder	1.23	1.19	1.14	1.12	1.10
  150 mm × 300 mm	Cylinder	1.25	1.20	1.16	1.14	1.12
  160 mm × 320 mm	Cylinder	1.26	1.21	1.17	1.15	1.13
  100 mm × 300 mm	Prism	1.23	1.23	1.18	1.15	1.13
  120 mm × 360 mm	Prism	1.26	1.26	1.22	1.19	1.16
  150 mm × 300 mm	Prism	1.32	1.32	1.28	1.25	1.22

  [13,14,15,16] and similar conversions can be seen in References [17,18]. For example, for C60 concrete, according to Table 1, we can multiply the 100 mm × 200 mm cylinder compressive strength by the specific conversion factor 1.12 to obtain the 150 mm cube compressive strength. The specific conversion factor 1.12 derives from Reference [15]. In Reference [15], for C60 concrete, the 150 mm cube compressive strength is approximately 1.16 times the 150 mm × 300 mm cylinder compressive strength, which is also seen in CEB-FIP model code 2010 [1], while the 150 mm × 300 mm cylinder compressive strength is approximately 0.97 times the 100 mm × 200 mm cylinder compressive strength. Therefore, the 150 mm cube compressive strength can be considered as approximately 1.12 (≈1.16 × 0.97) times the 100 mm × 200 mm cylinder compressive strength. Different kinds of tested specimens for compressive strength and elastic modulus are adopted in different publications. The size effect on elastic modulus does not exist as the elastic modulus is the property of concrete in the elastic stage while the size effect is related to the concrete fracture [19]; however, the size effect on strength is significant. The influence factors include the cross-sectional shape, the cross-sectional diameter and the height to diameter ratio; however, the decrease in strength is not significant when the height to diameter ratio is larger than 2 [13,14].

ρ_a = ρ_od/(1 + ρ_od/1000 − ρ_ssd/1000)

(6)

w_a = 100(ρ_ssd/ρ_od − 1)

(7)

where ρ_a, ρ_od and ρ_ssd are the apparent density, oven-dried density and saturated surface dry density, respectively, (kg/m³); w_a is the water absorption, %.

2.2. Statistic Analysis

The elastic modulus of RCA normally decreases with the increasing replacement level of RA, the degree of which depends on the quality of RA. Therefore, before the statistical analysis, the data is divided into several groups according to the quality of RA. GB 25177-2010 [12] (a Chinese code for coarse recycled aggregate) provides a performance-based classification for RA, as shown in

Table 2. Physical property requirements of the performance-based classification [12].

RA Class	I	II	III	IV
Apparent density (kg/m3)	>2450	>2350	>2250	No limit
Water absorption (%)	<3	<5	<8

. We use it to classify data as JGJ/T443-2018 does. It is worth noting that GB 25177-2010 only specifies Class I, II and III RA; we add Class IV RA since we find that low-quality RA beyond the requirements of Class III RA can also produce usable concrete that meets the performance requirements, which uses for reference the work of Silva et al. [20]. It is also worth noting that “>2450” means the apparent density of Class I RA should be larger than 2450 kg/m³ and that if the apparent density of a RA is equal to 2450 kg/m³, the RA belongs to Class II RA rather than Class I RA.

The basic form of the equation we aim to develop is shown in Equation (8). The equation changes to Equation (3) when r = 0. Moreover, the coefficient k_i represents the loss in the elastic modulus due to RA. The k_i is different for each class of RA, as shown in Equation (9). Obviously, k₄ > k₃ > k₂ > k₁ > 0.

It seems that the k_i can be determined by linear regression based on Equation (10). However, there are problems. Here, we take the data from Luo et al. [21] and Fonseca et al. [22] as examples. As shown in Figure 1a, the elastic modulus of 100% RAC using Class I RA decreases slightly compared with NAC, while the elastic modulus of 100% RAC using Class III RA decreases significantly, which is in line with our expectations. However, when we fit the data based on Equation (10), there is an error that k₃ < 0 < k₁. This is because the elastic modulus of the control concrete in the work of Luo et al. (Class I RA) is much lower than the estimation from Equation (3) [21], while that of Fonseca et al. (Class III RA) is much higher [22]. The essence is that only the compressive strength of concrete, the quality class and replacement rate of RA are considered in the equation, but the other factors affecting the elastic modulus, such as aggregate type (e.g., basalt, limestone, etc.), the volume ratio of aggregate to paste, the volume ratio of coarse aggregate to fine aggregate, aggregate size and so on, are ignored. Therefore, a correction factor α, as shown in Equation (11), is introduced to Equation (12) instead of Equation (10) to consider the other factors, and E_RAC/αE_NAC,pred mainly depends on the quality class and replacement rate of RA, as shown in Equation (12). At this point, the accurate k_i can be gained through linear regression based on Equation (12), as shown in Figure 1b.

α shows the variation of E_NAC for a given compressive strength due to other factors, e.g., aggregate type and volume ratio of aggregate to paste. As shown in Figure 2, the value range of α is (0.65, 1.29), calculated through the statistical analysis of the 332 mixes of control concrete. It should be noted that α in eight mixes from the references [23,24,25,26,27] is beyond the range (μ − 3σ, μ + 3σ), where μ is the mean and σ is the Standard Deviation, so α in the eight mixes are outliers. The data in these references is marked in the database and is not involved in the statistical analysis. Then, a practical equation for the elastic modulus of RCA is in the form of Equations (13)–(15).

E_RAC,pred = ηE_NAC,pred = (1-k_ir)(10⁵/(2.2 + 34.7/f_cu))

(8)

k_i = {k₁, for Class I RA; k₂, for Class II RA; k₃, for Class III RA; k₄, for Class IV RA}

(9)

E_RAC/(10⁵/(2.2 + 34.7/f_cu)) = (1 − k_ir)

(10)

α = E_control/E_NAC,pred

(11)

E_RAC/(α (10⁵/ (2.2 + 34.7/f_cu))) = (1 − k_ir)

(12)

E_RAC,pred = 0.97(1 − k_ir)(10⁵/(2.2 + 34.7/f_cu))

(13)

E_RAC,max = 1.29(1 − k_ir)(10⁵/(2.2 + 34.7/f_cu))

(14)

E_RAC,min = 0.65(1 − k_ir)(10⁵/(2.2 + 34.7/f_cu))

(15)

where E_control is the elastic modulus of the control concrete and the control concrete is a NAC that uses the same mix as RAC but uses natural aggregate rather than RA; E_RAC is the measured/actual value of elastic modulus of RAC, MPa; E_RAC,pred is the estimation of elastic modulus of RAC, MPa; and E_RAC,max/E_RAC,min are the upper/lower bound value of estimation of elastic modulus of RAC, MPa.

2.3. Laboratory Tests for Verification of the Equation

The compressive strength and elastic modulus of RCA made with four classes of RA are measured, and the results are used for verification of the equation proposed in this paper.

2.3.1. Materials

The materials used are shown in

Table 3. Materials used in the laboratory tests.

	Materials Used
Cement	PO 42.5R
Water	Tap water
Fine aggregate	Natural river sand with medium size
Natural coarse aggregate	Crushed natural stone
Class I RA	Carbonated crushed concrete
Class II RA	Crushed concrete
Class III RA	Crushed concrete
Class IV RA	Crushed concrete + crushed bricks

. The properties of coarse aggregate are shown in

Table 4. Properties of coarse aggregate in the laboratory tests.

	Size (mm)	Gradation	Water Absorption (%)	Apparent Density (kg/m3)
NA	5–25	5–10 mm (20%) 10–16 mm (30%) 16–25 mm (50%)	0.7	2810
Class I RA			2.5	2650
Class II RA			3.6	2600
Class III RA			5.5	2590
Class IV RA			8.5	2450

. No admixture is used. RA is treated by presoaking and used under saturated surface dry (SSD) conditions.

2.3.2. Preparation of Specimens

Three groups of control concrete are prepared with water to cement ratios of 0.6, 0.5 and 0.4, respectively. The detailed mix proportions are shown in

Table 5. Mix proportions of the control concrete in the laboratory tests (kg/m³).

	Coarse Aggregate	Fine Aggregate	Cement	Water
Control-0.6	1088	725	367	220
Control-0.5	1096	644	440	220
Control-0.4	1122	578	500	200

. Sixty groups of RAC are prepared with water to cement ratios of 0.6, 0.5 and 0.4, weight replacement rates of 20%, 40%, 60%, 80%, 100% and four classes of RA, respectively. Control-0.6 means the control concrete prepared with the water to cement ratio of 0.6, while RAC-I-20-0.6 means RAC prepared with Class I RA, the weight replacement rate of 20% and a water to cement ratio of 0.6.

2.3.3. Test for Compressive Strength and Elastic Modulus

To save raw materials, three 100 mm cubes are cast for each group for the strength test and three 100 mm × 200 mm cylinders for each group are cast for the elastic modulus test. The specimens are cured in a standard curing room for 28 days and then their compressive strength and elastic modulus are measured according to GB 50081-2019 [175]. The 100 mm cube strength is converted to the 150 mm cube strength and the 100 mm × 200 mm cylinder strength according to Table 1.

3. Dataset

A total of 1383 mixes from 154 publications are collected, as listed in Supplementary Materials [21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174]. The dataset includes 1051 RAC mixes and 332 mixes of the control concrete. However, 43 RAC mixes of data are identified as outliers and not involved in the statistical analysis, as the elastic modulus of the control concrete in these publications is too high or too low [23,24,25,26,27].

Most RAC mixes use the conventional replacement method, while a few mixes (26 mixes) use the equivalent mortar volume (EMV) method [86,93,101,111,115,120,126,168]. The EMV method considers the old mortar in RA as a mortar rather than a part of coarse aggregate and adjusts the coarse aggregate and fresh mortar content of the mix accordingly to achieve the same total mortar volume as the control mix. Due to the same total mortar volume, the elastic modulus of the RAC mixes designed by the EMV method is independent of quality and replacement rate of RA and not lower than NAC of equal strength, as shown in Figure 3. However, studies of the EMV method are limited [176]. Therefore, this paper still focuses on the RAC mixes designed by the conventional method.

Figure 4a,b present the distribution of E_RAC/E_NAC,pred and the relationship between E_RAC and f_cu of 982 RAC mixes produced with different quality and replacement levels of RA, respectively. Ninety-five per cent of E_RAC are in the range (0.552E_NAC,pred, 1.168E_NAC,pred), while 95% of E_NAC are in the range (0.65E_NAC,pred, 1.29E_NAC,pred), as shown in Section 2.2 (Figure 2). A significant reduction in the elastic modulus due to RA can be seen. The lower bound value of E_RAC/E_NAC,pred in this work is 0.552 while the value calculated by R.V. Silva et al. is 0.61 [5]. The figure of 0.552 may be more accurate as we use much more data. If the quality and replacement level of RA in RAC are unknown, Equations (16)–(18) can be used to estimate the elastic modulus of RAC. Note that the use of increasing RA content has a significant impact on the elastic modulus, and more so if these exhibit low quality. Therefore, the prediction of the elastic modulus of RAC can be improved if the quality and replacement level of RA are taken into account.

E_RAC,pred = 0.86(10⁵/(2.2 + 34.7/f_cu))

(16)

E_RAC,max = 1.168(10⁵/(2.2 + 34.7/f_cu))

(17)

E_RAC,min = 0.552(10⁵/(2.2 + 34.7/f_cu))

(18)

4. Practical Equation for the Elastic Modulus

Figure 5a–h present the relationships between E_RAC/αE_NAC,pred, E_RAC/E_NAC,pred and r of RAC mixes produced with different quality of RA, respectively. Although the R² obtained in this work seems low, there is a very strong correlation between E_RAC/αE_NAC,pred and r considering the large sample size. It should be noted that R² is influenced by the sample size. From a statistical point of view, the critical value of R² decreases with the increase of sample size and R² > the critical value means there is a very strong correlation, and the critical value is 0.033 (0.1829²) when the sample size is 82 [177]. The R² obtained in this work is much higher than the critical value.

The results reveal that even if Class I RA is used, the elastic modulus of RAC is still lower than NAC and only slightly higher than RAC made with Class II RA, while the elastic modulus of RAC made with Class II RA is also only slightly higher than RAC made with Class III RA. However, it is acceptable that RAC made with Class I, II and III RA have a reduced value of elastic modulus up to approximately 20% at maximum compared to NAC of equal strength as the value is within the scatter band for NAC. It should be noted that the elastic modulus of RAC made with Class IV RA is significantly lower than NAC of equal strength when high RA replacement levels are used. Class IV RA shall be used with caution.

α shows the variation of E due to other factors, e.g., aggregate type and volume ratio of aggregate to paste. It shows the effectiveness of the introduction of α that the obtained k_i is consistent with our expectations and most of the RAC mixes (about 94%) are in the range proposed by this work. If the quality and replacement level of RA in RAC are known, Equations (19)–(24) can be used to estimate the elastic modulus of RAC.

It should be noted that the basic equation of E_NAC,pred uses Equation (3) proposed by the Chinese code GB 50010 [3]. Obviously, other basic equations such as Equations (1) and (2) can be also used, and the corresponding α and k_i can be easily gained by the same method as shown in Section 2.2.

E_RAC,pred = 0.97(1 − 0.1229r)(10⁵/(2.2 + 34.7/f_cu)), for Class I RA

(19)

E_RAC,pred = 0.97(1 − 0.1429r)(10⁵/(2.2 + 34.7/f_cu)), for Class II RA

(20)

E_RAC,pred = 0.97(1 − 0.1744r)(10⁵/(2.2 + 34.7/f_cu)), for Class III RA

(21)

E_RAC,pred = 0.97(1 − 0.2816r)(10⁵/(2.2 + 34.7/f_cu)), for Class IV RA

(22)

E_RAC,max = 1.33E_RAC,pred

(23)

E_RAC,min = 0.67E_RAC,pred

(24)

5. Verification of the Equation

The experimental results and the E_RAC,pred estimated by Equations (19)–(22) are listed in

Table 6. Experimental results and E_RAC,pred estimated by Equations (19)–(22).

	fc (MPa)				E (MPa)				ERAC,pred (MPa)	ERAC/ERAC,pred
	1	2	3	Mean	1	2	3	Mean
Control-0.6	41.3	42.9	42.8	42.3	33,600	31,800	30,500	31,967
Control-0.5	55.1	56.9	58	56.7	33,400	35,800	36,100	35,100
Control-0.4	68.3	70.8	65.6	68.2	39,100	38,000	37,100	38,067
RAC-I-20-0.6	35.8	42.2	37.9	38.6	26,700	31,800	29,700	29,400	30,539	0.96
RAC-I-40-0.6	39.3	41.8	35.6	38.9	30,600	29,500	26,800	28,967	29,829	0.97
RAC-I-60-0.6	37.5	35.8	38.9	37.4	29,300	29,200	29,700	29,400	28,725	1.02
RAC-I-80-0.6	38.0	38.3	37.3	37.9	30,400	27,900	26,800	28,367	28,066	1.01
RAC-I-100-0.6	36.5	38.9	39.5	38.3	27,400	27,600	29,100	28,033	27,392	1.02
RAC-I-20-0.5	47.1	49.1	50.3	48.8	31,400	32,900	32,700	32,333	32,508	0.99
RAC-I-40-0.5	53.1	54.9	47.0	51.7	31,000	28,800	33,700	31,167	32,118	0.97
RAC-I-60-0.5	47.5	51.7	48.4	49.2	30,400	30,500	32,000	30,967	30,925	1.00
RAC-I-80-0.5	54.5	53.4	46.9	51.6	31,400	30,500	31,300	31,067	30,449	1.02
RAC-I-100-0.5	54.0	49.1	48.0	50.4	31,400	30,800	29,600	30,600	29,450	1.04
RAC-I-20-0.4	52.7	59.7	62.7	58.4	35,800	36,300	34,500	35,533	33,858	1.05
RAC-I-40-0.4	61.2	52.7	66.5	60.1	34,600	33,600	35,700	34,633	33,212	1.04
RAC-I-60-0.4	58.6	57.7	61.2	59.2	33,400	33,600	35,200	34,067	32,244	1.06
RAC-I-80-0.4	59.0	57.6	56.8	57.8	33,100	33,200	34,500	33,600	31,233	1.08
RAC-I-100-0.4	59.5	68.4	65.3	64.4	32,700	33,200	34,500	33,467	31,064	1.08
RAC-II-20-0.6	36.1	31.7	28.8	32.2	28,200	29,200	29,000	28,800	28,749	1.00
RAC-II-40-0.6	32.1	31.0	31.0	31.4	29,100	29,200	28,700	29,000	27,661	1.05
RAC-II-60-0.6	38.0	36.3	34.2	36.2	27,900	27,900	27,400	27,733	28,069	0.99
RAC-II-80-0.6	35.7	34.4	32.9	34.3	28,200	28,900	28,100	28,400	26,758	1.06
RAC-II-100-0.6	35.7	36.9	34.1	35.6	23,700	25,400	27,800	25,633	26,180	0.98
RAC-II-20-0.5	46.9	48.8	46.2	47.3	31,400	31,200	31,300	31,300	32,120	0.97
RAC-II-40-0.5	43.4	44.9	44.6	44.3	30,400	31,900	31,000	31,100	30,656	1.01
RAC-II-60-0.5	44.6	45.5	43.1	44.4	30,900	31,200	31,300	31,133	29,744	1.05
RAC-II-80-0.5	44.1	39.7	40.1	41.3	29,700	30,500	31,700	30,633	28,258	1.08
RAC-II-100-0.5	48.0	45.6	49.8	47.8	29,700	27,700	30,600	29,333	28,414	1.03
RAC-II-20-0.4	55.5	56.2	50.5	54.1	35,200	33,600	35,700	34,833	33,158	1.05
RAC-II-40-0.4	54.1	53.6	56.1	54.6	35,200	35,100	34,100	34,800	32,253	1.08
RAC-II-60-0.4	58.7	52.3	61.3	57.4	34,200	33,600	34,800	34,200	31,625	1.08
RAC-II-80-0.4	52.3	57.2	50.1	53.2	33,300	34,400	33,300	33,667	30,120	1.12
RAC-II-100-0.4	54.5	47.5	60.3	54.1	30,300	31,700	33,700	31,900	29,260	1.09
RAC-III-20-0.6	33.2	35.2	35.8	34.7	27,500	29,200	29,000	28,567	29,264	0.98
RAC-III-40-0.6	32.4	34.4	36.0	34.3	27,200	27,300	27,700	27,400	28,087	0.98
RAC-III-60-0.6	31.7	34.1	32.9	32.9	24,000	24,800	25,500	24,767	26,684	0.93
RAC-III-80-0.6	28.4	35.2	32.4	32.0	22,300	24,000	24,800	23,700	25,413	0.93
RAC-III-100-0.6	36.3	29.8	29.4	31.8	21,100	25,400	23,500	23,333	24,341	0.96
RAC-III-20-0.5	49.6	45.9	47.0	47.5	31,000	30,800	32,400	31,400	31,945	0.98
RAC-III-40-0.5	42.6	47.3	47.5	45.8	30,000	29,800	29,900	29,900	30,509	0.98
RAC-III-60-0.5	45.6	42.6	46.9	45.0	26,300	28,000	27,200	27,167	29,237	0.93
RAC-III-80-0.5	44.9	45.9	44.9	45.2	26,700	27,100	25,600	26,467	28,130	0.94
RAC-III-100-0.5	46.5	43.4	39.1	43	23,500	24,000	26,000	24,500	26,632	0.92
RAC-III-20-0.4	54.1	55.3	60.9	56.8	34,200	34,400	34,800	34,467	33,300	1.04
RAC-III-40-0.4	58.0	58.0	52.7	56.2	32,600	33,600	33,700	33,300	32,031	1.04
RAC-III-60-0.4	51.4	53.5	49.7	51.5	30,000	30,600	30,700	30,433	30,226	1.01
RAC-III-80-0.4	54.2	53.2	46.5	51.3	29,300	28,900	29,000	29,067	29,018	1.00
RAC-III-100-0.4	46.5	52.5	45.6	48.2	28,000	27,200	26,500	27,233	27,427	0.99
RAC-IV-20-0.6	33.3	36.3	31.4	33.7	25,800	28,300	27,600	27,233	28,334	0.96
RAC-IV-40-0.6	32.7	32.8	32.7	32.7	26,100	27,300	28,000	27,133	26,402	1.03
RAC-IV-60-0.6	30.3	28.1	29.8	29.4	22,500	24,800	24,600	23,967	23,847	1.00
RAC-IV-80-0.6	33.7	31.7	34.1	33.2	23,600	23,400	23,400	23,467	23,149	1.01
RAC-IV-100-0.6	30.2	26.8	34.1	30.4	18,700	21,400	21,600	20,567	20,847	0.99
RAC-IV-20-0.5	44.9	45.6	47.3	45.9	28,500	28,900	29,300	28,900	30,972	0.93
RAC-IV-40-0.5	45.5	46.2	42.6	44.8	28,200	29,900	29,600	29,233	28,931	1.01
RAC-IV-60-0.5	45.2	40.8	45.1	43.7	25,100	26,100	26,200	25,800	26,924	0.96
RAC-IV-80-0.5	47.1	43.8	39.3	43.4	25,700	26,500	25,600	25,933	25,053	1.04
RAC-IV-100-0.5	37.5	40.3	37.9	38.6	23,300	21,000	25,100	23,133	22,481	1.03
RAC-IV-20-0.4	61.3	59.1	55.1	58.5	31,400	32,300	32,200	31,967	32,772	0.98
RAC-IV-40-0.4	51.7	51.7	54.3	52.6	31,000	31,600	31,900	31,500	30,095	1.05
RAC-IV-60-0.4	55.3	48.8	46.6	50.2	28,000	28,500	28,800	28,433	27,886	1.02
RAC-IV-80-0.4	46.9	55.9	51.9	51.6	25,600	27,800	28,800	27,400	26,157	1.05
RAC-IV-100-0.4	47.5	46.6	45.7	46.6	22,500	26,000	25,100	24,533	23,665	1.04

. As shown in Table 6, E_RAC/E_RAC,pred in the experiments are in the range (0.92, 1.12) which is much narrower than the range (0.67, 1.33) allowed by Equations (23) and (24). It verifies Equations (19)–(24) that the E_RAC,pred is near E_RAC. In order to see this more intuitively, E_RAC vs. E_RAC,pred is plotted in Figure 6.

6. Comparison with JGJ/T443-2018

Table 7. Values of η in JGJ/T443-2018 and this work when r = 1.

	Class I RA	Class II RA	Class III RA
JGJ/T443-2018 [11]	1	0.8	0.8
This work	0.85	0.83	0.8

shows values of the reduction factor η in JGJ/T443-2018 and this work for different quality of RA when r = 1, respectively. The η values in this work is more in line with our expectations as the η value for Class I RA is less than 1 and the η value for Class II RA is larger than that Class III RA, as shown in Table 7. Compared with this work, JGJ/T443 overestimates the elastic modulus of RAC using Class I RA and underestimates that of RAC using Class II RA. However, the estimation for the elastic modulus of RAC using Class III RA by JGJ/T443-2018 and this work is close.

7. Conclusions

Although RAC may exhibit similar compressive strength to NAC, as the RA content increases the elastic modulus decreases, the degree of which depends on the quality of RA. This paper aims to use the reduction factor η to quantify the loss of the elastic modulus and propose a practical equation for the elastic modulus of RAC based on a comprehensive statistical analysis of 1383 concrete mixes from 154 publications. Based on the results of this investigation, the following conclusions can be drawn:

• For a given compressive strength, the elastic modulus of RAC in most studies is in the range (0.552E_NAC,pred, 1.168E_NAC,pred). It should be noted that this prediction interval is applicable only when the compressive strength is known while the other factors are unknown.
• The correlation between the reduction factor η and the replacement rate for different quality of RA is determined. The results show that the reduced elastic modulus of RAC made with Class I, II or III RA is acceptable; however, the reduced elastic modulus of RAC made with high replacement rates of Class IV RA is so low that Class IV RA must be used with caution.
• The prediction interval (scatter band) of the elastic modulus of RAC is provided considering the variation of the elastic modulus due to other factors, e.g., aggregate type and volume ratio of aggregate to paste.
• JGJ/T443-2018 overestimates the elastic modulus of RAC made with Class I RA and underestimates that of RAC made with Class II RA.
• The experimental results verify the equation proposed in this work. If the replacement rate and quality (classified by the apparent density and water absorption) of RA are known, designers and engineers can use the simple equation to determine the elastic modulus of RAC by means of the compressive strength.

It should be noted that these conclusions only apply to RAC designed by the conventional method. The elastic modulus of RAC designed by the EMV method is not lower than NAC of equal strength due to the same mortar volume. However, the related studies are limited. Therefore, further studies need to be conducted to ensure the effectiveness of the EMV method and the reliability of the results.