1 Introduction

Among raw materials for concrete, coarse aggregate is the least expensive per unit weight, but it constitutes the most weight of concrete. In some places, such as the eastern and north-eastern states of India and Bangladesh, natural coarse aggregates for the manufacture of concrete are scarce (Akhtaruzzaman & Hasnat, 1983; Mansur et al., 1999; Rashid et al., 2009). This situation necessitates the search for alternative sources from local places, which has been regarded as an economical method that avoids excessive transportation costs. Crushed over-burnt clay bricks (COBCBs) are available in abundance in rural areas as they are solid waste from traditional brick production. High temperature exposure renders COBCBs lightweight, but some voids will form, which make the aggregate inferior to the conventional stone aggregates. As a result, the porous mixes made with brick aggregates are too vulnerable to sustain heavy loads (Debnath & Sarkar, 2020). Crushed clinker bricks are 33% lighter and more porous than ordinary crushed stones. In addition, compared with concrete made with natural aggregates, the unit weight of crushed brick concrete reduces by 9.5%, leading to a 7% loss on average in concrete compressive strength (Khaloo, 1994). To use COBCBs is one of the practical ways. COBCBs not only are economically sustainable, but also can be used to prepare more environmentally friendly concrete. Debnath and Sarkar studied the performance of pervious concrete pavement under fatigue loading (Debnath & Sarkar, 2020). It was found that the fatigue life increased with the decreasing size of the aggregate. It is because the aggregate of a smaller size results in less voids in the concrete mix.

LWC is defined as any aggregate with an oven-dry density of up to 1950 kg/m3, 25% lighter than NWC, of which the density is between 2200 and 2600 kg/m3 (Neville, 2012). The main specialties of LWC are its low density and thermal conductivity. Hence, LWC can effectively reduce the dimensions of the structure members, thereby minimizing the earthquake force acting on the building and economizing on the project expenditure. Akhtaruzzaman and Hasnat (1983) employed brick aggregates to fabricate high-grade high-quality concrete with a unit weight of about 2000 to 2080 kg/m3 and a modulus of elasticity about 30% lower than that of NWC. Mansur et al. (Mansur et al., 1999) manufactured four basic mixes of different grades ranging from 30 to 60 MPa to assess the applicability of crushed clay bricks as the coarse aggregates in concrete preparation. The results suggested that the concrete produced had extremely poor workability, and its modulus of elasticity was significantly decreased. Besides, compared with conventional concrete, the finished concrete had similar compressive strength, but higher tensile strength and a lower drying shrinkage. Khalaf and Devenny (2004) examined the thermal properties of brick aggregate concrete, and it was observed that at high temperatures, clay brick concrete behaved similarly to or even better than granite concrete. A good bond could be achieved between the brick aggregates and the cement paste due to the angular shape of the brick aggregates (Khalaf, 2006). Moreover, the compressive strength of the concrete made from crushed brick aggregates with a smaller density was 8–15% lower than that of the concrete prepared with granite aggregates. The modulus of rupture of the concrete made with crushed brick aggregates was approximately 8% less than that of the concrete constructed with granite aggregates. Previous research (Cachim, 2008; Dang et al., 2018; Debieb & Kenai, 2008) showed that as the brick replacement ratio increased, the mortar flowability reduced. The replacement with 10% and 20% bricks had no negative effect on the mortar compressive strength and slight effects on the mortar shrinkage. A 20% to 30% decrease in strength was found depending on the degree of substitution. Gautam and Jaysawal (Gautam & Jaysawal, 2018) investigated different concrete mixes prepared by substituting 25%, 50%, 75%, and 100% COBCBs by volume for granite aggregates. Results revealed that the concrete containing 25% COBCBs shared similar characteristics with granite aggregate concrete. Nematzadeh et al. (Nematzadeh & Baradaran-Nasiria, 2019; Nematzadeh et al., 2019) reported that replacing 100% of natural fine aggregates with recycled refractory bricks increased the compressive strength of the concrete by 25% at 800∘C. Additionally, silica fume (SF) showed good performance in retaining the compressive strength of heated concrete.

Recently, Debnath et al. (Debnath & Sarkar, 2020) have confirmed that the water-cement ratio of the pervious concrete made from crushed burnt brick fine aggregates should be within a specified limit of 0.3–0.32. Rashwan et al. (Rashwan et al., 2016) substituted the gravel aggregates with different volumes of COBCBs (0, 20, 50, 100%). It was found that the mix containing 20% COBCBs displayed an improvement in all its mechanical properties (e.g., compressive, tensile, and flexure strength), compared with conventional concrete. Moreover, COBCB aggregates had a greater effect on internal curing than other types of aggregates. Uddin et al. (2017) analyzed the flexural performance of 24 reinforced concrete beams made with recycled brick aggregates. The addition of recycled brick aggregates in concrete reduced neither the cracking moment capacity nor the ultimate moment capacity of reinforced concrete beams. ACI 318-19 (American Concrete Institute [ACI], 2019) provisions can predict the cracking and ultimate moment capacities of reinforced concrete beams made with recycled brick aggregates. The study of Rasol (2015) demonstrated that mortar without adding SF had lower strength than that containing SF prepared at the same water-cement ratio, and the addition of 5% SF improved the compressive strength. This improved bond is ascribed to the fact that reactive SF incorporated in the concrete mix converts the calcium hydroxide that tends to form on the surface of aggregate particles into calcium silicate hydrate. According to Wang et al. (Wang et al., 2021), the addition of 5% SF by weight increased the corresponding compressive strength by 14.4%. Praveen et al. (Praveen et al., 2016) evaluated the performance of concrete fabricated with the admixture of brick aggregates and micro-silica. Test results showed that the optimum dose of micro-silica was 10% when it was used to replace cement for M30 concrete.

In this paper, an experimental study was carried out as follows to clarify the behavior of LWC made from COBCBs:

  • Utilized COBCBs as coarse aggregates to produce structural LWC, and compared LWC with NWC.

  • Reinforced the concrete beams with different reinforcement ratios.

  • Analyzed the effects of SF on the concrete mix properties and the behavior of the beams.

It is expected that the results of this study will augment the remarkably limited number of research studies on the behavior of LWC made from COBCBs.

2 Experimental program

The following sub-sections will provide details on the properties of the various raw materials used as well as the test parameters studied in this study.

2.1 Materials

Ordinary Portland cement was used in all concrete mixes for preparing normal-strength concrete. Local medium-type sand was taken as fine aggregates. Local gravel and COBCBs were added as coarse aggregates to produce normal weight concrete (NWC) and lightweight concrete (LWC), respectively. COBCBs were reduced in size by using a Morse Jaw Crusher shown in Fig. 1. The properties of different types of the aggregates used in this study are detailed in Table 1. To provide concrete mixes with acceptable workability and strength, ADECRETE BVF of density 1210 kg/m3 was added as an additive to improve the mechanical properties of the mixes. Then, the slump test was done to evaluate workability. SF has an average particle size of 0.1 μm, its specific surface area is (12–15 m2/g), and its specific gravity is 2.2. High tensile steel bars with diameters 12 and 10 mm were selected as tension and compression reinforcing materials, respectively. Mild steel bars with a diameter of 8 mm were adopted as stirrups. The mechanical properties of the steel bars are given in Table 2. The values in the table are the averages of three standard specimens tested.

Fig. 1
figure 1

a Morse Jaw Crusher b Bricks before crushing c Bricks after crushing

Full size image
Table 1 Properties of the aggregates used
Full size table
Table 2 Mechanical properties of the steel used
Full size table

2.2 Tested beams

A total of fifteen reinforcement concrete (RC) beams were constructed, with a depth of 280 mm, a width of 120 mm and an overall length of 2000 mm. All beams were provided with 8 mm diameter steel shear stirrups spaced at 100 mm and reinforced with two 10 mm steel rebars at the top. The clear concrete cover was 25 mm. The beams were divided into five groups. Group A was NWC beams made from gravel aggregates, while the other groups were LWC beams made from COBCB aggregates that contained different SF content (0, 10, 15, 20%) by weight of cement. Each group had three beams with various tension reinforcement ratios, \(\rho\) = 1.15, 1.92, and 2.69%. The reinforcement details of the beams are concluded in Fig. 2. The beams were labelled as (X-Y-Z) according to the concrete type, SF content and the amount of longitudinal tensile reinforcement. The letters X, Y, and Z indicate NWC or LWC, SF content, and the number of reinforcing rebars, respectively. For example, N0-3 represents an NWC beam made from gravel aggregates without adding SF and reinforced with three steel bars at the bottom, while L15-5 corresponds to an LWC beam made from COBCB aggregates containing 15% SF and reinforced with five steel bars at the bottom. The details of each beam are presented in Table 3.

Fig. 2
figure 2

Details of the reinforcement of the tested beams (all dimensions in mm)

Full size image
Table 3 Details of the tested beams
Full size table

2.3 Mix design and specimen preparation

Five concrete mixes were designed to produce normal-strength concrete with 28-day cubic compressive strength of 25 MPa (N0, L0, L10, L15 and L20). Three concrete cubes of 150 mm side length were cast from each mix, and their compressive strength was examined. It should be noted that the cylinder compressive strength of concrete, \({f}_{c}\mathrm{^{\prime}}\), was calculated based on ACI 318-19 (ACI, 2019); \({f}_{c}^{\mathrm{^{\prime}}}=0. 8{f}_{cu}\). N0 is a normal-weight mix made from gravel coarse aggregates without adding SF. The rest of the mixes, L0, L10, L15, and L20, are lightweight mixes produced using COBCB aggregates containing 0, 10, 15, and 20% SF by weight of cement, respectively. The required free water to cement ratio is 0.48. It is worth mentioning that the water absorbed by COBCBs should be included in the mixing water (Table 1). The optimum dose of superplasticizer admixture ADECRETE BVF was determined, in order to achieve reasonable workability and compressive strength values. Table 4 describes the quantities of constituent materials in 1 m3 of the concrete mix.

Table 4 Mix proportion of constituents in 1 m3 of the concrete mix
Full size table

2.4 Test program and instrumentation

All beams were tested up to failure under three-point bending loading conditions over a clear span of 1800 mm using a testing machine (EMS 60-ton hydraulic actuator). The applied load was measured using a load cell with a capacity of 300 kN. An LVDT was positioned at the bottom mid-span to meter the corresponding deflections. In addition, three electrical strain gauges were attached to the concrete surface in the compression zone at depths of 35 mm, 80 mm, and 130 mm. Another one strain gauge was bonded to the steel tension bars (Fig. 2). The data measured by different monitoring devices were uploaded to a portable data logger (TDS-150), which was connected to a computer to record the readings at preset load intervals until the beam failed (Fig. 3). On the same day of the beam test, the concrete cubes were tested to determine the properties of the concrete. The increment of loading equaled 5 kN, and crack propagation was marked with the corresponding load values during the test.

Fig. 3
figure 3

Test setup

Full size image

3 Results and discussions

In this section, the experimental results will be discussed in terms of the properties of concrete mixes, crack pattern, failure mode, load–deflection response, deflection capacity, ductility, energy absorption, and strain in concrete and steel.

3.1 Density and compressive strength

Table 5 lists the density and the cube compressive strength (\({f}_{cu}\)) of all concrete mixes designed. On the one hand, it was observed that the concrete prepared from COBCB aggregates had a lower density than the gravel aggregate concrete. The density of the SF-containing mix L0 was 1910 kg/m3, while the density of the mix N0 was recorded 2587 kg/m3. The density declined by 26% when gravel aggregates were replaced with COBCB aggregates. It is attributed to the low density of the COBCB aggregate. The concrete density values presented in Table 5 are lower than those reported in the studies by Akhtaruzzaman and Hasnat (1983), and by Khalaf (2006). In both studies, the concrete made with crushed bricks showed a density ranging between 2000 and 2300 kg/m3. It is worth noting that SF had little effect on the density of the resultant concrete. On the other hand, the compressive strength of L0 was 16% lower than that of N0, which is due to the lower strength of COBCB aggregates, compared with that of gravel aggregates. As the SF content increased, the compressive strength improved. For example, the compressive strength of L10 containing 10% SF was 23% higher than that of L0 without adding SF. Furthermore, when the SF content was increased to 20% in the mix L20, the corresponding compressive strength was 45.59 MPa, representing a 66% increase over its counterpart L0.

Table 5 Density and compressive strength of all concrete mixes
Full size table

3.2 Strain distribution

The results of the distribution of strain over the depth for all tested beams are summarized in Fig. 4. Generally, all beams exhibits linear elasticity prior to tensile cracking of concrete, wherein the curvature or slope of the strain profile in tension equals that of the strain profile in compression. It suggests that the beam behavior follows the Bernoulli–Euler beam theory at small deflections. As expected, the tested beams underwent minimal shear stress at lower loads, resulting in a small shear deformation. Regarding the beams with a low reinforcement ratio, the inclined cracking started from bending cracks, which then rapidly extended up to the proximity of the neutral axis. Finally, the cracks developed rather slowly, leaving only an extremely narrow depth of the compression zone unaffected. The concrete available to participate in the tension field ought to be confined to the uncracked region in the compression zone of the beam to resist the applied load. A possible reason for failure is the crushing of the reduced compression zone in the beam. Therefore, the strain value increased as the baseplate accelerated and the height of the compression zone descended.

Fig. 4
figure 4

Strain distribution of the test beams: a beam N0-3, b beam L0-3 and c beam L10-3

Full size image

3.3 Crack patterns and modes of failure of the tested beams

Figure 5 depicts the typical crack patterns of all the tested beams. LWC beams showed clearly similar flexural behaviors to NWC beams. The first crack was initiated near the loading point. As the load increased, new cracks were formed and propagated toward the compression zone. With the further enlargement of the load, more cracks generated along the beam and the cracks in the shear spans acquired an inclination toward the central zone. Finally, the failure occurred when one or more cracks extended to the upper concrete fibers in the maximum moment zone. All beams exhibited flexural failure characterized by the yielding of steel bars on the tension side. Nevertheless, considerable crushing of concrete in the compression zone of the LWC beams took place after steel yielding (Fig. 6). It could be attributed to the weaker strength of lightweight aggregates (COBCBs) used in LWC beams, compared with that of gravel aggregates used in NWC beams. It is evident that the reinforcement ratio significantly influenced the crack propagation and failure mode of beams. A smaller crack width and depth were observed by naked eye as the number of longitudinal steel reinforcement bars increased. Regardless of the concrete type, beams with low reinforcement ratios, such as N0-3 and L0-3, exhibited not only larger deflections and more flexural cracks, but also more plastic deformations before the flexural failure. Thus, the severity of failure increased as the reinforcement ratio decreased. As for beams reinforced with high reinforcement ratios, such as L10-7, they displayed more flexural cracks with narrower widths than L10-3 and L10-5. These findings confirmed that a large reinforcement ratio restrained the width and length of the cracks by distributing the cracks efficiently along the span of the beam. It was noticed that fewer and thinner cracks in beams containing SF were in evidence. It is because SF enhances the compressive strength in SF containing beams. However, the failure mode was slightly affected by SF addition.

Fig. 5
figure 5figure 5

Crack patterns of the tested beams: a Group A; b Group B; c Group C; d Group D; e Group E

Full size image
Fig. 6
figure 6

Failure modes of the tested beams

Full size image

3.4 Cracking load and moment

The initial cracking load corresponded to the first visible flexural crack. It was observed that the first crack in each group was similar because the concrete compressive strength primarily governed the behavior of the beams at this stage. The use of LWC instead of NWC resulted in a slight reduction in the cracking load as it lowered the compressive strength. The cracking loads of L0-3, L0-5 and L0-7 were 20, 17 and 22% lower than N0-3, N0-5 and N0-7, respectively. However, beams in Group C with 15% SF content had a higher cracking load than their counterparts in Group B. It confirmed that the first crack was delayed by the introduction of SF to the concrete mix, which improved the compressive strength and, therefore, the tensile strength of concrete.

The experimental cracking moment (\({M}_{cr,exp}\)) was calculated corresponding to the first cracking load (\({P}_{cr}\)) using Eq. (1). However, the predicted cracking moment (\({M}_{cr,pre}\)) was estimated using the expression given in Eq. (2). The modulus of rupture (\({f}_{r})\) was determined with Eqs. (3 and 4) in accordance with ACI 318-19 (ACI, 2019) and Canadian CSA-A23.3-19 (Canadian Standards Association [CSA], 2019).

$${M}_{cr}=\frac{{\mathrm{p}}_{\mathrm{cr}}\mathrm{L}}{4}$$
(1)
$${M}_{cr}=\frac{{f}_{r}{I}_{g}}{{y}_{t}}$$
(2)
$${f}_{r,ACI}=0.62 \lambda \sqrt{{{f}_{c}}^{^{\prime}}}$$
(3)
$${f}_{r,CSA}=0.60 \lambda \sqrt{{{f}_{c}}^{^{\prime}}}$$
(4)

where \({I}_{g}\) is the moment of inertia of the gross concrete section, \({y}_{t}\) is the distance from the extreme tension fiber to the neutral axis, and \(\lambda\) is a reduction factor equal to 0.75 for LWC and 1.0 for NWC. Table 6 calculates the ratios of the experimental cracking moment (\({M}_{cr,exp}\)) to the cracking moment predicted by the ACI 318-19 and CSA-A23.3-19 design codes (\({M}_{cr,ACI}\) and \({M}_{cr,CSA}\)). By comparing the experimental and predicted cracking moment, it was observed that ACI 318-19 yielded conservative predictions with an average \({M}_{cr,exp}\)/\({M}_{cr,ACI}\) of 1.92 ± 0.36. However, CSA-A23.3-19 afforded tremendously conservative results with an average \({M}_{cr,exp}\)/\({M}_{cr,CSA}\) of 2.27 ± 0.40. This agreement demonstrated that the ACI 318-19 and CSA-A23.3-19 code equations and the recommended reduction factor (λ = 0.75) were acceptable for predicting the cracking moment of the LWC beams.

Table 6 Experimental and predicted cracking and ultimate moment
Full size table

3.5 Ultimate capacity

Table 6 provides information about the ultimate capacity of the tested beams. The replacement of gravel aggregates with COBCB aggregates had significant effects on the ultimate load of the tested beams. It was evident that the ultimate loads of beams L0-3, L0-5, and L0-7 were 76, 92 and 127 kN, lower than 87, 129 and 162 kN of beams N0-3, N0-5 and N0-7, respectively. As mentioned above, the reduction in the ultimate load was ascribed to the weaker strength of COBCB aggregates than that of gravel aggregates. Regardless of the concrete type and SF content, the beams reinforced with high reinforcement ratios showed a marked enhancement in the ultimate capacity, compared with those reinforced with lower reinforcement ratios. The phenomenon might clarify that as the reinforcement ratio increased, the beam stiffness was also improved. For example, as the reinforcement ratio enlarged from 1.15 to 1.92 and 2.69, the ultimate loads of beams L10-3, L10-5, and L10-7 augmented by about 21.90% and 74%, respectively. Additionally, the addition of 10% SF improved the ultimate capacity of beam L10-3, which was 17% higher than that of beam L0-3 without adding SF. By increasing the SF addition amount from 0 to 20%, the ultimate load increased from 76 to 121 kN for beams L0-3 and L20-3, respectively. This result was consistent with that reported by Praveen (Praveen et al., 2016); when micro-silica was added, an overall improvement in the mechanical properties of concrete was observed, which is because the micro-silica of pozzolanic nature formed calcium silicate hydrate (Zhang et al., 2008).

The moment capacities of the tested beams (\({M}_{u,exp}\)) were calculated using Eq. (5). The predicted moment capacities (\({M}_{u,pre}\)) were determined by Eq. (6). The parameters \({\alpha }_{1}\) and \({\beta }_{1}\) were computed using Eqs. (7 and 8) based on ACI 318-19 (ACI, 2019) and CSA-A23.3-19 (CSA, 2019), respectively.

$${M}_{u,exp}=\frac{{p}_{u}L}{4}$$
(5)
$${\alpha }_{1}{{{\beta }_{1} \lambda f}_{c}}^{^{\prime}}cb={A}_{s}{f}_{y}$$
(6a)
$${M}_{u,pre}={(A}_{s}{f}_{y})\left(d-\frac{{\beta }_{1}c}{2}\right)$$
(6b)
$${\alpha }_{1}=0.85$$
(7a)

from ACI 318-19 (ACI, 2019)

$${\alpha }_{1}=0.85-0.0015 \lambda {{f}_{c}}^{^{\prime}}$$
(7b)

from CSA- A23.3-19 (CSA, 2019)

$${\beta }_{1}=0.85-0.05\left(\frac{ \lambda {{f}_{c}}^{^{\prime}}-27.6}{7}\right)$$
(8a)

from ACI 318-19 (ACI, 2019)

$${\beta }_{1}=0.97-0.0025 \lambda {{f}_{c}}^{^{\prime}}$$
(8b)

from CSA- A23.3-19 (CSA, 2019) where As denotes the area of tensile steel reinforcement (mm2), \({f}_{y}\) refers to the yield strength of steel (MPa), \({{f}_{c}}^{^{\prime}}\) stands for the cylinder compressive strength of concrete (MPa), d represents the effective depth (mm), and b is the beam width. The accuracy of the available equations in ACI 318-19 and CSA-A23.3-19 design codes was assessed by comparing their predictions with the experimentally determined moment capacities of the 15 reinforced concrete beams. The safety factors included in all the ultimate equations were set to 1.0. The ratios of the experimental ultimate moment to the ultimate moment predicted by ACI 318-19 and CSA-A23.3-19 (\({M}_{u,exp}\)/\({M}_{u,ACI}\) and \({M}_{u,exp}\)/\({M}_{u,CSA}\), respectively) are summarized in Table 6. It can be concluded that both ACI 318-19 and CSA-A23.3-19 provisions achieved reasonable yet conservative predictions, with an average experimental-to-predicted ratio of 1.13 ± 0.04 and 1.08 ± 0.05 and a COV value of 3.73 and 4.68%, respectively. The comparison confirmed the applicability of ACI 318-19 and CSA-A23.3-19 code equations in designing steel-reinforced LWC beams made from COBCB aggregates.

3.6 Deflection

Figure 7 describes the relationship between the applied load and the mid-span deflection of each group. The load–deflection curves have two turning points. One is the cracking point, and the other one is the yield point. Hence, the load–deflection curve can be divided into three stages. The first stage related to the uncracked response of the beams, represented by a linear elastic portion with a steep slope using the gross moment of inertia of the concrete cross-section. As the applied load increased, another linear portion with a flatter slope emerged, indicating the cracked response of the tested beams. The secondary stiffness was affected by the reinforcement ratio. High stiffness was observed when a large reinforcement ratio was adopted. The reason is that the high reinforcement ratio stiffened the beam, and thus alleviated deflections (Uddin et al., 2017). After the steel yielded, the beam stiffness sharply decreased, and the mid-span deflection increased rapidly. As shown in Fig. 7a–e, all beams satisfy the requirements of Serviceability Limit States (SLS) for deflection (\(L/250\)=7.20 mm). The cracked stiffness of the beam L0-7 was lower than that of the beam N0-7 (Fig. 7a). Consequently, at the same load level, beam L0-7 deflected more than beam N0-7. Besides, it was detected that the yield strength of NWC beams was higher than that of LWC beams. The effect of SF on load–deflection curves with different main steel reinforcement ratios is illustrated in Fig. 7e–g. By increasing the SF content while keeping the reinforcement ratio constant, the flexural behavior and the stiffness were improved. For example, at load 100 kN, the mid-span deflection of beam L20-7 was 1.6 mm, much lower than that of beam L0-7 (7.8 mm) with the same reinforcement ratio of 2.69%. It is attributed to the fact that the SF added evidently enhanced the concrete properties, such as elastic modulus and compressive strength.

Fig. 7
figure 7

Load–deflection relationships of the tested beams: a Groups A and B; b Group C; c Group D; d Group E; e Effect of SF (ρ = 1.15%); f Effect of SF (ρ = 1.92%); g Effect of SF (ρ = 2.69%)

Full size image

The ACI 318–19 (ACI, 2019) equation for determining the maximum deflection at the mid-span of beams under three-point bending is defined by Eq. (9):

$${\Delta }_{u,ACI}=\frac{{P}_{u}{L}^{3}}{{48E}_{c}{I}_{e}}$$
(9a)
$${I}_{e}={I}_{cr}+({I}_{g}-{I}_{cr})\left(\frac{{M}_{cr}}{{M}_{u}}\right)\le {I}_{g}$$
(9b)
$${I}_{g}=\frac{{bh}^{3}}{12}$$
(9c)
$${I}_{cr}=\frac{{b(kd)}^{3}}{3}+{n}_{s}{A}_{s}{d}^{2}{(1-k)}^{2}$$
(9d)
$${k=\sqrt{{{(n}_{s}{\rho }_{s})}^{2}+2{(n}_{s}{\rho }_{s})}-(n}_{s}{\rho }_{s})$$
(9e)
$${n}_{s}=\frac{{E}_{s}}{{E}_{c}}$$
(9f)

where a is the shear span, \({P}_{u}\) is the ultimate load, L is the beam’s effective span, \({I}_{g}\), \({I}_{e}\) and \({I}_{cr}\) are the gross, effective and cracked moment of inertia of a reinforced concrete section, respectively. \(k\) is a factor that determines the height of the compressed area of concrete from the top surface. \({A}_{s}\) and \({\rho }_{s}\) are the total cross-sectional area and reinforcement ratio of the steel rebars, respectively. \({n}_{s}\) is the modular ratio between steel reinforcement and concrete. \({E}_{s}\) and \({E}_{c}\) are the elastic moduli of steel and concrete, respectively.

Besides, the CSA-A23.3-19 (CSA, 2019) equation for estimating the maximum deflection is expressed as follows:

$${\Delta }_{u,CSA}=\frac{{p}_{u}{L}^{3}}{{48E}_{c}{I}_{cr}} \left[1-8\left(1-\frac{{I}_{cr}}{{I}_{g}}\right){\left(\frac{{L}_{g}}{L}\right)}^{3}\right]$$
(10a)
$${L}_{g}=0.5\frac{{M}_{cr}L}{{M}_{u}}$$
(10b)

where \({L}_{g}\) is the distance from the edge support to the point where the applied service moment is equal to the cracking moment.

Table 7 provides the experimental mid-span deflection (\({\Delta }_{u,exp}\)) and those predicted by the ACI 318-19 and CSA-A23.3-19 design codes (\({\Delta }_{u,ACI}\) and\({\Delta }_{u,CSA}\), respectively). Moreover, the table also compares experimental ultimate deflections with those predicted by ACI 318-19 and CSA-A23.3-19. The defection predictions were in good agreement with the experimental values, as demonstrated by the average experimental-to-predicted deflection ratios of 1.67 ± 0.35 and 1.59 ± 0.35 (\({\Delta }_{u,exp}\)/\({\Delta }_{u,ACI}\) and \({\Delta }_{u,exp}\)/\({\Delta }_{u,CSA}\), respectively). This finding tallied with the results observed by Alhassan et al. (Alhassan et al., 2017). Thus, ACI 318-19 and CSA-A23.3-19 can conservatively predict the deflection of LWC beams made from COBCBs.

Table 7 Deflection, maximum strain, and ductility index
Full size table

3.7 Concrete and steel reinforcement strains

Figure 8 plots the relationships of the applied load with the top concrete strain and bottom steel strain. All beams behaved similarly prior to tensile cracking of the concrete, showing a linear elastic feature. In this stage, the slope of the strain profile in tension equaled that of the compression strain profile. It was evidenced by the fact that, at lower loads, the beam behavior followed the Bernoulli–Euler beam theory at small deflections. Generally, LWC beams made from COBCBs have larger strains than NWC beams made from gravel. In addition, the beams with high reinforcement ratios display lower concrete and steel strains at the same load level. The reason is that an increased reinforcement ratio improves the beam rigidity. Figure 8f depicts the influence of SF addition on the concrete and reinforcement strains. The concrete and steel strains decreased as the amount of SF increased, which is because the high tensile strength delayed beam cracking, and the higher modulus of elasticity reduced the induced strains. Besides, the steel bars containing SF had lower strains at early loading stages than their counterparts that did not add SF.

Fig. 8
figure 8

Load-strain relationships: a Group A; b Group B; c Group C; d Group D; e Group E; f Effect of SF (ρ = 1.15%); g Effect of SF (ρ = 1.92%); h Effect of SF (ρ = 2.69%)

Full size image

3.8 Ductility and energy absorption

In general, structural concrete elements are deformed severely before collapse. The ductility index \(\mu\) in steel-reinforced concrete is determined by the ratio of ultimate displacement \({\Delta }_{u}\) to that at the yielding of the steel reinforcement \({\Delta }_{y}\). According to Table 7, LWC beams had a higher ductility index µ than NWC beams. As stated above, the ultimate deflection of LWC beams was larger than that of NWC beams because the COBCB aggregate of weaker strength enlarged the deformation before failure. In addition, the ductility of the tested beams was reduced with the increasing reinforcement ratio (Fig. 9). Beams with the lowest reinforcement ratio (ρ = 1.15%) had the highest \(\mu\). Conversely, the lowest µ value was found in beams with a high reinforcement ratio (ρ = 2.69%). In fact, increasing the SF content improved the concrete compressive strength, enhanced the beam stiffness, and thereby lowered the maximum deflection. Therefore, a small number of cracks with narrow widths were observed. Furthermore, the ductility decreased as SF was added, but a significant enhancement in the strength of the beams was detected when SF was introduced to the concrete mix. Hence, toughness and energy absorption are more reasonable indicators in evaluating the influence of SF on the overall flexural performance of the LWC beams. There is a good agreement between the experimental results in this study and the results obtained by Uddin et al. (Uddin et al., 2017). The main aim of this study is to achieve a noticeable increase in concrete strength while maintaining adequate ductility.

Fig. 9
figure 9

Effect of different parameters on the ductility index µ

Full size image

4 Conclusions

In this study, the application potential of COBCBs as alternative coarse aggregates for conventional gravel aggregates in concrete was investigated. Flexural tests were performed on LWC beams with different reinforcement ratios and SF content, and the results were compared with those of NWC beams. Based on the results of this investigation, the following conclusions are drawn:

  1. 1.

    The density and compressive strength of the LWC beams made from COBCBs as coarse aggregates are 26% and 16% lower than those of the NWC beams made from gravel. However, the reduction in the compressive strength can be recouped by adding SF. Hence, the combined use of waste COBCBs and SF promises a sustainable approach to the construction of environmentally friendly LWC.

  2. 2.

    All LWC beams show a typical structural behavior similar to that of NWC beams. In addition, as the reinforcement ratio increases, the ultimate capacity improves. A 1.15% to 1.92% increase in the reinforcement ratio enhances the ultimate capacities of beams L10-3 and L10-5 by 21%.

  3. 3.

    LWC beams deform radically, which provides ample warning before failure. Moreover, the ductility of LWC beams is higher than that of NWC beams due to the weakness of COBCBs.

  4. 4.

    ACI 318-19 and CSA- A23.3-19 equations make conservative predictions of the cracking moment, ultimate moment, and deflection in LWC beams.

The test results of this study have verified that COBCBs can be used to produce structural LWC. This type of concrete is applicable to the construction of residential and non-residential buildings in seismic areas. In addition, LWC has application prospects in making structures as diverse as precast wall blocks and panels, homes on weak foundations, roof and building aprons, partitions, boats, shipbuilding, lightweight blocks/bricks, thin shell roof structures, roof section in high-rise structures, doors, bridge decks, girders, etc.