Flexural behavior of ECC hollow beams incorporating different synthetic fibers

Abstract

Twelve ECC beams with three different fiber types, along with four normal concrete beams, were tested in this study to evaluate the influence of cross-sectional hollowing on their flexural performance. The fiber types used were nylon monofilament (NM), low-cost untreated polyvinyl alcohol (PVA), and polypropylene (PP). Three different square hole sizes of 60, 80, and 100 mm with cross-sectional hollowing ratios of 0.16, 0.28, and 0.44, respectively, were adopted for each group of beams in addition to a solid beam. All beams were tested under four-point loading using a displacement-controlled testing machine. The test results showed that ECC beams can mostly withstand higher cracking and ultimate loads compared to their corresponding normal concrete versions. The results also showed that both the ductility and toughness of the ECC beams are higher than those of the normal concrete beams and that the ductility values of the hollow beams with a hole size of 60 mm are higher than those of the corresponding solid beams. Moreover, hollow ECC beams with hole sizes of 60 and 80 mm exhibited a higher ductility than a solid normal concrete beam.

Graphical abstract

Keywords

hollow beam / hollowing ratio / ECC / flexural strength / ductility / toughness

Introduction

Concrete has a low tensile strength, low ductility, and low energy absorption owing to its low toughness and microscopic size defects, which are highly expected to occur under local tensile stresses [1,2]. The inclusion of short randomly distributed fibers in small fractions (0.5%–2% by volume) was found to be a candidate solution to improve the tensile behavior of concrete. The inclusion of fibers can significantly improve the tensile strength, increase the energy absorption (toughness), and decrease the number of defects that make the material behave quasi-brittle. Moreover, in certain cases, it is difficult to place a sufficient number of reinforcing bars in thin-walled members. Therefore, fibers can be used as a partial substitution of the lost quantity of the reinforcement area. Many types of fiber are currently used. Synthetic fibers such as nylon-monofilaments, polypropylene (PP), and polyvinyl alcohol (PVA) have good resistance to alkali and are not affected by hydrated cement [3]. The excellent performance of these types of fibers is often reflected by their strain-hardening behavior beyond the first cracking when under tension, which is attributed to their potential for crack bridging [4–7].

During the last two decades, several types of new and superior fibrous concrete were introduced with attractive tensile and energy absorption characteristics. Engineered cementitious composites (ECCs) are modern types of fibrous concrete that contain no coarse particles. Instead, extremely fine fillers are used with large amounts of cementitious materials. Owing to the large amounts of fine materials, the fiber content of ECCs is lower than that required for other mixture types providing the required mechanical properties, such as a high tensile strength [8] and improved ductility [9,10], with a significantly high strain capacity (3%–5%) [11]. One of the most attractive characteristics of ECCs are their ability to control the crack width to less than 60 µm owing to the good stress distribution [12]. A vast number of studies on the application of ECCs in structural members have been conducted. ECCs have been used to modify the flexural behavior of the beams [13,14], improve the shear resistance of structural members [15] and the behavior of column beam connections during an earthquake [16], and as a solution to improving the abrasion resistance of concrete in hydraulic structures [17,18].

Although new types of concrete including ECCs have certain advantages, they also have some disadvantages, including the weight of the member and high costs. As another disadvantage, such types of materials consume large amounts of cement, which means that their production leads to higher carbon dioxide emissions. Reducing the size of the structural members will reduce the weight, cost, and of course, the carbon dioxide emitted because the amount of consumed cement will be reduced. To reduce the size of the structural member, its cross-sectional dimensions should be optimized in such a way that it balances the structural design requirements (strength and serviceability) and its weight. To improve the ductility, pultruded cellular sections and layered sandwich sections using fiber-reinforced polymers have been suggested in previous studies [19–21]. Hollow concrete sections were also introduced as candidates that may afford the required balance. The reduced sectional area will mostly result in a lower strength and weaker behavior under loads. However, fibers can be used to partially or fully substitute the loss of strength and performance produced by reducing the sectional area.

Several studies have been conducted on the torsional strength [22–24] of hollow reinforced concrete beams, whereas studies on the flexural performance of hollow beams are too limited [25]. The available studies have focused on normal concrete with either no fibers or reinforcement with steel fibers [26,27]. An ECC is composed completely of fine materials and is known for its superior ductility and flexural behavior compared to normal concrete. Thus, the use of such materials with optimized thin-walled sections may reduce the weight of the structure, keeping the strength comparable to that of solid normal concrete beams but with a much higher energy absorption capacity under loading. To the best of the authors’ knowledge, no previous studies have investigated the flexural behavior of ECC beams with hollow sections. Therefore, in the present research, an experimental program was directed for investigating the flexural behavior of hollow ECC beams containing three types of synthetic fibers. Using the tested beams, the load-deflection behavior, cracking and failure patterns, ductility, and toughness of the hollow beams with different wall thicknesses were investigated and compared to those of solid beams. Such light weight sections can be considered successful candidates in precast building construction.

Materials and methods

Concrete mixture and material properties

In this research, ECC mixtures were created using three different types of synthetic fibers: nylon monofilament (NM), low-cost untreated PVA, and PP. Table 1 lists the characteristics of the three types of fibers. In addition to the three ECC mixtures, a normal concrete mixture was prepared for comparison. Table 2 summarizes the material proportions of the four mixtures. The NM and PVA-ECC mixtures were mixed according to the M45, as outlined in Ref. [28], in which a 2% fiber content was used, whereas PP-ECC was mixed according to a mixture proposed by Zhang et al. [29] with a 3% fiber content.

The experimental program was composed of two stages. In the first stage, four series of mechanical property tests were conducted. First, standard 100 mm × 200 mm cylinders subjected to a uniaxial compression load were used to evaluate the compressive strength (f_{\mathrm{c}}^{\text{'}}) of concrete according to ASTM C39. Second, similar cylindrical specimens were subjected to an indirect tensile load (splitting tensile test) to evaluate the concrete tensile strength (f_{\mathrm{c}\mathrm{t}}) according to ASTM C 496. Third, similar specimens were subjected to a compression load to evaluate the Young’s modulus according to ASTM C469. Fourth, prisms of 100 mm × 100 mm × 350 mm were cast and tested according to ASTM C1609 to evaluate the flexural performance under four-point loading.

Configuration of solid and hollow beams

Sixteen beams were tested to investigate the flexural behavior of ECC beams with different longitudinal hole sizes and different fiber types. The beams were divided into four groups according to the type of fiber used. The beams of the first group were made of normal concrete (E group) for comparison purposes, whereas the beams of the other three groups were made of an ECC but with different types of fibers (NM, PVA, and PP). Three beams with square holes with side lengths of 60, 80, and 100 mm in addition to a solid beam were fabricated from each of the four groups. Table 3 lists the details of the 16 beams. The number following the group symbol represents the side length of the hole, where 0, 6, 8, and 10 refer to hole side lengths of 0, 60, 80, and 100 mm, respectively.

All tested beams are of square reinforced cross sections of 150 mm × 150 mm and a length of 850 mm, as shown in Fig. 1. The beams were reinforced with longitudinal and transverse deformed bars of 8 mm and 5.3 mm diameter, respectively. The average reinforcement ultimate and yield strength of the 8 mm diameter bars were 650 and 530 MPa, respectively, whereas for the 5.3 mm diameter bars they were 477 and 400 MPa, respectively. The clear concrete cover of the beams was 15 mm, which led to an average effective depth (d) of 131 mm. Fig. 1 illustrates the configuration and reinforcement details of the four different beams of each of the four groups.

Beam test setup

All beams were tested under four-point flexure loading until failure. The beams were supported on two cylindrical supports with a clear 750-mm span. The tests were conducted using a closed-loop servo-controlled INSTRON testing machine with a maximum capacity of 250 kN. The loading of the beams was conducted at a constant rate of 0.4 mm/min. Increased monotonic loading was applied through two steel cylinders attached to the crossing head. The deflection of the beams was measured using linear variable differential transformers (LVDTs) that were attached beneath the tested beam, as shown in Fig. 2. To determine the net center deflection, two dial gauges were used. One dial gage was used at the top of the free edge of the beam, and the other was attached to the tension side (100 mm from the support), as shown in Fig. 2.

Results of control tests

Compressive strength, splitting tensile strength, and modulus of elasticity

The three types of ECCs and the normal concrete mixtures were designed to achieve a 28-d cylinder compressive strength (f_{\mathrm{c}}^{\text{'}}) of approximately 35 MPa to eliminate the effect of the concrete strength on the flexural behavior of the beams. Table 3 summarizes the compressive strengths of the four mixtures obtained. Many previous studies have shown that the inclusion of fibers does not significantly influence the compressive strength of concrete [30–32]. Table 3 shows that, in general, the compressive strengths of the four mixtures were comparable.

In contrast to the compressive strength, the tensile strengths of the ECCs for all tested specimens of different fiber types were significantly improved compared to a normal concrete mixture. The percentage of improvement in splitting the tensile strength of the ECC mixtures compared to normal concrete ranges 44.5%–47%, as shown in Table 3. In spite of the differences in fiber tensile strength, all ECC mixtures showed almost equal splitting tensile strengths. In addition, because of the effect of the fibers, they all failed gradually rather than directly separating into two parts as for normal concrete. By contrast, the experimental results obtained in this research showed that the modulus of elasticity of the ECC is typically lower than that of concrete. This can be attributed to the absence of coarse aggregates.

Flexural test

The flexural tests on prisms made from the four mixtures were conducted in accordance with ASTM C1609. The beams were 100 mm × 100 mm × 350 mm in size and were tested under three-point loading with a clear 300-mm span. The load was applied at a rate of 0.075 mm/min up to a mid-span deflection of 1 mm, and a 0.4 mm/min loading rate was applied up to failure.

Table 4 shows the main parameters that were obtained from the test results, whereas Fig. 3 shows the development of the mid-span displacement of the beams. The flexural strength was calculated based on the linear elastic beam theory, as follows:

(1)f={\displaystyle \frac{PL}{b{H}^{\mathrm{2}}}},

where f is the specified strength (MPa), P is the characterized load (N), L is the span length (mm), and b and H are the width and depth of the beam (mm), respectively.

In the current study, the first peak strength (f₁) and ultimate flexural strength (f_p) were almost the same for beams of normal concrete and PVA-ECC, whereas f1 for the NM-ECC and PP-ECC represent 68% and 65% of the f_p, respectively. It was also observed that the tensile strength obtained from a splitting test (f_sp) is more than that obtained from a beam bending test f_p by 28%–35% for the three ECC mixtures and 21% for the normal concrete mixture.

The improvement of fiber on the flexural behavior is clearly reflected in the load–deflection behavior after the first crack. In the current study, the normal concrete and PVA-ECC prisms showed brittle behavior after cracking. By contrast, the NM-ECC and PP-ECC prisms showed different post-crack behaviors. The NM-ECC showed a strain softening, whereas the PP-ECC showed a hardening plateau before the softening zone. This can be attributed to the higher fiber content used in the PP-ECC mixture (3%) compared to the 2% used in the NM-ECC and PVA-ECC mixtures.

The post-cracking behavior can be specified as the residual strength at a specified deflection or toughness at the same point. In the current study, the flexural strength ratio (R_{T,\mathrm{150}}^{\mathrm{D}}) is calculated based on the toughness (T_{\mathrm{150}}^{\mathrm{D}}) of up to L/150, as follows:

(2)R_{T,\mathrm{150}}^{\mathrm{D}}={\displaystyle \frac{\mathrm{150}\times T_{\mathrm{150}}^{\mathrm{D}}}{f_{\mathrm{1}}\times b\times d^{\mathrm{2}}}}\times \mathrm{100}\mathrm{\%}\mathrm{.}

The toughness results showed that all ECC prisms have a high energy absorption compared to those made of normal concrete. The T_{\mathrm{150}}^{\mathrm{D}} of NM-ECC and PVA-ECC was more than 4-times the T_{\mathrm{150}}^{\mathrm{D}} of normal concrete, whereas the T_{\mathrm{150}}^{\mathrm{D}} of the PP-ECC was approximately 6-times that of normal concrete. However, the flexural strength ratio (R_{T,\mathrm{150}}^{\mathrm{D}}) was varied based on the first crack strength, which was small for NM-ECC and PP-ECC; hence, their R_{T,\mathrm{150}}^{\mathrm{D}} values were high. Table 4 shows the R_{T,\mathrm{150}}^{\mathrm{D}} of the three types of ECC mixtures compared to the normal concrete mixture, where the highest ratio was obtained for the NM-ECC.

Results of solid and hollow reinforced beams

Flexural strength

Two major stages are important in the beam design. First, the deflection of the beam under service loads should not detract from the appearance. In the second state, the beam should be safe under the worst-loading case. In this section, the tested beams are compared and assessed under both the ultimate and serviceability stages.

Serviceability stage

Under low loading conditions, the beam behaves elastically, where the compression and tensile stresses in concrete are small and proportional to the corresponding strains. At this stage, the section is mostly uncracked, where the stress at the extreme tension fiber is still less than the modulus of rupture. To observe the development of the flexural behavior of ECC beams compared to normal concrete beams, the tested normal concrete beams were theoretically analyzed according to the elastic bending theory. These beams were analyzed considering the target compressive strength, which is 30 MPa, and the experimental yield strength of the used steel bars, which is 530 MPa. By contrast, the modulus of elasticity (E_c) was calculated according to MC2010 [33] as follows:

(3)E_{\mathrm{c}}=\mathrm{21.5}\times {\mathrm{10}}^{\mathrm{3}}{\left({\displaystyle \frac{f_{\mathrm{c}}^{\prime }+\mathrm{6}.\mathrm{4}}{\mathrm{1}\mathrm{0}}}\right)}^{\mathrm{1}/\mathrm{3}}\mathrm{.}

The cracking bending strength is then elastically calculated through the following:

(4)M_{\mathrm{c}\mathrm{r}}={\displaystyle \frac{f_{\mathrm{r}}\times I_{\mathrm{g}}}{y_{\mathrm{t}}}}

where {\displaystyle \frac{I_{\mathrm{g}}}{y_{\mathrm{t}}}} is the section modulus of the beam.

The required modulus of rupture (f_1,ACI) is calculated according to ACI318-14 as follows:

(5)f_{\mathrm{1},\mathrm{A}\mathrm{C}\mathrm{I}}=\mathrm{0}.\mathrm{6}\mathrm{2}\sqrt{f_{\mathrm{c}}^{\prime }}\mathrm{.}

The maximum deflection at the center of the normal concrete beams before cracking can be calculated according to the elastic bending theory as

(6){\delta }_{\max }={\displaystyle \frac{\mathrm{Pa}}{\mathrm{12}{E}_{\mathrm{c}}I}}\left({\displaystyle \frac{-\mathrm{3}{\mathcal{L}}^{\mathrm{2}}}{\mathrm{4}}}+a^{\mathrm{2}}\right),

where P is the cracking load, L is the clear span, a is the distance between one point load and the closer support, and E_c and I are the concrete modulus of elasticity and the moment of inertia of the beam section, respectively.

The analysis of the tested solid and hollow beams showed that, in general, the theoretical cracking loads (P_cr,theo) of the normal concrete beams were less than those obtained experimentally for all beam groups. For the normal concrete beams, the P_cr,theo values were less than the experimental cracking loads (P_cr,test) by approximately 15%, 27%, 36%, and 21% for E0, E6, E8, and E10, respectively. The calculated cracking loads (P_cr,theo) were 9.9, 9.6, 9.2, and 8.0 kN, respectively, whereas the cracking loads obtained from the tested beams (P_cr,test) are as listed in Table 5. By contrast, for most cases, P_cr,test of ECC beams were much higher than those obtained theoretically, as shown in Fig. 4. It is clear that the values of P_cr,theo slightly decrease with an increase in the hollowing index, where the hollowing index (HI) refers to the ratio of the hole sectional area to the beam total sectional area (HI = A_hole/A_tot). Although the moment of inertia of the hollow beams is lower than that of the solid beams, the values of P_cr,test for the tested beams of group E showed a continuous increase with an increase in the hole size up to an HI of 0.28. This observation was also recorded for the PP-ECC beams and partially for the PVA-ECC beams, whereas those with NM fibers exhibited a continuous decrease in the cracking load with an increase in the hole size, as shown in Fig. 4. Although beams with hole indices of 0.16 and 0.28 (except for the NM group) showed encouraging results, the further increase in the hole size to an index of 0.44 resulted in a lower cracking load; however, it was still comparable to that of the corresponding solid beam. The maximum P_cr,test values were recorded for beams made from PP-ECC.

Ultimate stage

The ultimate moment capacity (M_{\mathrm{u},\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}}) for the solid normal concrete beam was calculated according to Eq. (7), where the tensile strength of concrete in the tension zone is assumed to be zero, and the reinforcement bars resist the applied tensile stresses. For comparison, the safety factors for the applied moments and materials were neglected. In the current study, the compression reinforcement was found to avoid yielding.

(7)M_{\mathrm{u},\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}}=\mathrm{0}.\mathrm{8}\mathrm{5}{f}_{\mathrm{c}}^{\prime }\mathrm{ba}\left(d-{\displaystyle \frac{a}{\mathrm{2}}}\right)+A_{\mathrm{s}}^{\prime }{E}_{\mathrm{s}}{\epsilon }_{\mathrm{s}}^{\prime }(d-d^{\prime })\mathrm{.}

The depth of the compression concrete block (a) can be calculated as

(\mathrm{0.85}{f}_{\mathrm{c}}^{\prime }b)a^{\mathrm{2}}+(\mathrm{0}.\mathrm{0}\mathrm{0}\mathrm{3}{A}_{\mathrm{s}}^{\prime }{E}_{\mathrm{s}}-A_{\mathrm{s}}{f}_{\mathrm{y}})a-(\mathrm{0}.\mathrm{0}\mathrm{0}\mathrm{3}{A}_{\mathrm{s}}^{\prime }{E}_{\mathrm{s}}{\beta }_{\mathrm{1}}{d}^{\prime })=\mathrm{0},

and

{\beta }_{\mathrm{1}}=\mathrm{0}.\mathrm{8}\mathrm{5}-{\displaystyle \frac{\mathrm{0}.\mathrm{0}\mathrm{5}(f_{\mathrm{c}}^{\prime }-\mathrm{2}\mathrm{8})}{\mathrm{7}}},

{\epsilon }_{\mathrm{s}}^{\prime }=\mathrm{0}.\mathrm{0}\mathrm{0}\mathrm{3}\left(\mathrm{1}-{\displaystyle \frac{{\beta }_{\mathrm{1}}{d}^{\prime }}{a}}\right),

where b, d, and d^{\prime } are the beam width, effective depth, and distance from the upper fiber of the beam to the center of the compression reinforcement, respectively. A_{\mathrm{s}} and A_{\mathrm{s}}^{\prime } are the cross-sectional areas of the tension and compression steel, respectively, whereas E_{\mathrm{s}} and {\epsilon }_{\mathrm{s}}^{\prime } are the modulus of elasticity and strain of the compression reinforcement, respectively.

A comparison of the stress block depth with the thickness of the top flange in the normal concrete hollow beams showed that the neutral axis is less than the flange thickness, which mathematically means that the hollow beams can be analyzed as a rectangular beam. This is because the concrete stress block in the tension zone is neglected, as mentioned above.

Based on the residual strength obtained from the flexural performance test, different cases can be assumed for ECC beams, where both fibers and reinforcement bars in the tension zone resist the tensile stress, and the linear stress distribution can be used to represent the compression zone [34-37]. It was found that the flexural maximum compressive strain is less than the strain corresponding to the peak stress during compression, which is 3400 με[37] . There are three resultant forces acting on the section. C_ECC acts on the compression zone resisted by the ECC, and three other resultant forces act on the tension zone (T_ECC1, T_ECC2, and T_s). T_ECC1 and T_ECC2 are the resistances by ECC according to the shape of the stress block, whereas Ts is the resistance by the reinforcement bars in the tension zone. The effect of the compression reinforcement is ignored owing to its small distance from the neutral axis, which results in an extremely small moment.

Therefore, the equilibrium balance can be introduced as follows:

(8)C_{\mathrm{E}\mathrm{C}\mathrm{C}}+T_{\mathrm{E}\mathrm{C}\mathrm{C}1}+T_{\mathrm{E}\mathrm{C}\mathrm{C}2}+T_{\mathrm{s}}=\mathrm{0},

where

C_{\mathrm{E}\mathrm{C}\mathrm{C}}={\displaystyle \frac{f_{\mathrm{t}}^{\prime }\times {(h-z_{\mathrm{s}}-c)}^{\mathrm{2}}}{\mathrm{2}\times n_{\mathrm{\epsilon }}\times z_{\mathrm{s}}}}\times b,

T_{\mathrm{E}\mathrm{C}\mathrm{C}\mathrm{1}}={\displaystyle \frac{f_{\mathrm{t}}^{\prime }\times n_{\mathrm{\epsilon }}\times z_{\mathrm{s}}}{\mathrm{2}}}\times b,

T_{\mathrm{E}\mathrm{C}\mathrm{C}\mathrm{2}}=f_{\mathrm{t}}^{\prime }\times [z_{\mathrm{s}}(\mathrm{1}-n_{\mathrm{\epsilon }})+c]\times b,

T_{\mathrm{s}}=A_{\mathrm{s}}\times f_{\mathrm{y}}\mathrm{.}

The neutral axis is the millstone for calculating the moment capacity. This can be achieved through the force equilibrium according to Eq. (8). The triangular portion of the tension stress [37] is computed as a result of the linear strain assumption and based on the yield strain ratio (nε) between the strain of the ECC (ε_ECC) and the yield strain of the reinforcement (ε_s), where n_{e= εECC/εs. To find the neutral axis, Eq. (8) shall be solved in terms of the unknown zs.}

Previous researchers have adopted many values of the yield strain. Lepech and Li [34] found that a 0.02% yield strain of an ECC is suitable for use in the design considerations. This value was used in the analysis of ECC beams in the current study. The yield stress corresponding to the mentioned strain was obtained from an experimental study. For the failure case, the strains obtained from the ECC of different fibers used in the current research were 0.07 for ε_NM-ECC and 0.04 for both ε_PVA-ECC and ε_PP-ECC.

Based on the acting forces on the stress diagram [37], with the location of the neutral axis obtained from Eq. (8), the beam moment capacity of the solid ECC beams was calculated as follows:

(9)\begin{array}{l}{M}_{u,\mathrm{E}\mathrm{C}\mathrm{C}}=\left(-C_{\mathrm{E}\mathrm{C}\mathrm{C}}\times {\displaystyle \frac{\mathrm{2}(h-z_{\mathrm{s}}-c)}{\mathrm{3}}}\right)+\left(T_{\mathrm{E}\mathrm{C}\mathrm{C}1}\times {\displaystyle \frac{(\mathrm{1}-n_{\mathrm{\epsilon }})\times z_{\mathrm{s}}+c}{\mathrm{2}}}+n_{\epsilon }\times z_{\mathrm{s}}\right)\\ +\left(T_{\mathrm{E}\mathrm{C}\mathrm{C}\mathrm{2}}\times {\displaystyle \frac{\mathrm{2}{n}_{\mathrm{\epsilon }}\times z_{\mathrm{s}}}{\mathrm{3}}}\right)\end{array}\mathrm{.}

The ultimate load capacity (P_u) of the tested beams is shown in Fig. 5. Except for the PP-ECC beams, it is clearly shown that the P_u of other ECC beams was increased for an HI value of 0.16. However, these load capacities decreased with an increase in HI beyond this limit. Different load capacities were recognized for PP-ECC beams, where P_u decreased with an increase in the HI. This may be due to the high bond strength of the PP fibers, which causes a high cracking load but early yielding of the fibers at the initial stage.

A theoretical analysis of the solid beams showed that the ECC beams analyzed based on Eq. (9) produced a 13% improvement over the normal concrete beam analyzed according to Eq. (7), whereas the experimental study showed that the improvements in the P_u of the NM-ECC, PVA-ECC, and PP-ECC beams compared to the normal concrete beams were 15%, 9%, and 23%, respectively. These improvements were higher for the hollow beams. Figure 6 shows a comparison between the ultimate load strength for the beams made from normal concrete to the beams of ECCs with different fiber types.

Load-deflection behavior

The expected deflection for all beams was 0.05 mm, as shown in Eq. (6), which is an extremely small value compared to those recorded for the experimental beams, as listed in Table 5. Figure 7 shows the development of the deflection induced from the applied load as a comparison among the beams made from different materials, whereas Fig. 8 shows the effect of the hole size on the behavior of the beams of the same materials.

The loading processes can be divided into three main stages based on the response of the beams (deflection). These are the elastic, strain hardening, and failure stages. In the elastic stage, it can be observed in Fig. 7(a) that the ECC-solid beams exhibited a stiffer behavior than normal concrete beams during the pre-cracking stage. This case is mostly valid for hollow beams regardless of the size of the hole. The superiority among the ECC beams at this stage was dependent on the HI. For solid beams and beams with an HI of 0.16, the NM-ECC beams showed the highest dP/dδ among the ECC beams, whereas the PP-ECC exhibited the lowest dP/dδ. By contrast, the PVA-ECC beams exhibited the highest dP/dδ for HI values of 0.28 and 0.44.

The elastic zone was then followed by a hardening plateau (displacement-hardening behavior), and concentrated microcracking then started to form at the points where the highest deflection occurred. For beams with a hole size of 100 mm (HI = 0.44), there was no hardening plateau for the normal concrete beam and an extremely limited plateau for ECC beams. This may be attributed to the localized shear cracks that were produced close to one support of the beams with the largest holes (HI = 0.44). The comparisons show that the normal, NM-ECC, and PVA-ECC beams with 60 and 80 mm holes have almost the same hardening plateau, as shown in Figs. 8(a)–8(c), whereas for PP-ECC beams, the plateau decreased with an increase in the hole size (Fig. 8(d)). The longest strain hardening was recorded for the PP-ECC solid beam, which can be attributed to the higher fiber content compared to the other mixtures.

Flexural ductility and toughness

Calculating the ductility ratios (μ) of the beams is difficult because of the difficulty in defining the yield point [38,39]. The ductility ratio was determined from load–deflection curves and is defined herein as the deflection corresponding to the ultimate load (δ_u) normalized by the deflection corresponding to the load at the yield point (δ_y), that is, (μ=δ_u/δ_y). The yield deflection is the deflection corresponding to the load obtained from the intersection of the secant line intersecting the load–deflection curve at 75% of the ultimate load and the horizontal line drawn from the ultimate load, whereas the ultimate deflection corresponds to 80% of the ultimate load at the post-peak zone [39]. Figure 9 illustrates the defined deflections of the two mentioned levels for one of the tested beams in this study (PP6). The ductility of all the other beams was calculated using the same procedure.

Figure 10 shows the ductility ratios (μ) for the four groups of beams. It is clearly shown that the μ values of ECC beams are noticeably higher than those of normal concrete beams for both solid and hollow sections. It is also shown in the figure that all beams with 60-mm holes exhibited a higher μ compared to their corresponding solid beams, whereas increasing the hole size to 80 mm led to lower values of μ for all beams. However, the μ values of the ECC beams with 80-mm holes are comparable to those of solid beams, which was not the case for normal concrete beams. Increasing the hole size to 100 mm led to a significant decrease in μ for all beams. This can be attributed to the localized shear cracks, as previously described.

Although the PP fibers have a smaller tensile strength than the other used fibers, the PP-ECC beams showed the highest ductility ratios compared to other solid beams and beams with 60-mm holes. On the other hand, NM-ECC and PVA-ECC beams showed similar ductility behaviors. The relation governing μ in the HI for the normal concrete hollow beams used in the experiments can be represented by Eq. (10), whereas Eq. (11) represents this relation for the experimental ECC beams. These regression formulas were derived from the experimental results of the current study and have determination coefficients of R₂= 0.92 and 0.99 for normal and ECC beams, respectively.

(10){\mu }_{\mathrm{N}}=-\mathrm{20}{(\mathrm{HI})}^{\mathrm{2}}+\mathrm{5.4}(\mathrm{HI})+\mathrm{2.67},

(11){\mu }_{\mathrm{E}\mathrm{C}\mathrm{C}}=-\mathrm{50}{(\mathrm{HI})}^{\mathrm{2}}+\mathrm{17.6}(\mathrm{HI})+\mathrm{3.78.}

Toughness is also an important reflector for the ability of beams to absorb the applied energy. Mathematically, the toughness can be defined as the total area under the load–deflection curve up to a certain level of loading. Figure 11 shows the toughness for the three loading stages. The toughness of the tested beam up to the yielding point is labeled T_y, the toughness up to the peak load is T_p, and the toughness at up to 80% of the peak load within the post-peak zone is labeled T_u-80.

For the ductility, the toughness values of the ECC beams were significantly higher than those of the normal concrete beams. This is not surprising because of the displacement hardening that characterizes the ECC behavior. Moreover, the T_p contributes a higher percentage to the total toughness compared to the T_y and T_u-80 percentages for the normal concrete and PVA-ECC beams, whereas the T_p percentages are shown to be less than those of T_u-80 for the NM-ECC and PP-ECC beams. This indicates that the contribution of the fibers beyond the peak load is more effective when NM or PP fibers are used. It should be noted that the PVA fiber used in this study is a low-cost untreated fiber.

Failure mode

Figure 12 shows the final cracking patterns of the 16 beams after failure. The first cracks were visually observed and detected using the load-deflection curves. The location of the first crack was found to be dependent on the size of the hole and the fiber presence. In general, the first crack of the solid beams was initiated within the mid-third of the beam span, showing pure flexural cracking. For ECC beams with a hole size of 60 mm, the first crack was also a pure flexural crack, whereas the corresponding normal concrete beam exhibited shear cracking at the far end of the outer third. By contrast, the first crack was initiated within the outer third of the span for PP-ECC and NM-ECC beams with a hole size of 80 mm, whereas it was within the mid-third of the corresponding PVA-ECC beam. For the beams with 100-mm holes, the dominant cracking and failure pattern was pure shear cracking.

ECC beams exhibited a much better cracking performance compared to normal concrete beams. As shown in Fig. 12, the PP-ECC and NM-ECC beams showed multi-fine flexural cracking with small crack widths and close crack spacings. These cracks were then propagated up to the flexural reinforcement level with an extremely small increment in crack width because of the crack bridging activity of the fibers. Then, during and after the increase in load, the cracks further propagated upward as flexural or shear–flexural cracks. Based on the opening size, some cracks were further propagated to the compression zone until failure. However, the normal concrete beams exhibited a lower number of wider and far-spaced cracks. Unlike that appearing on the compression faces of the normal concrete beams (Fig. 12(a)), the fiber bridging of the tension zone and the multi-cracking development of ECC beams led to lower compression stresses at the compression surface. Reaching the ultimate beam strength, the longitudinal reinforcement bars started to yield with a significant increase in crack opening width and deflection.

Conclusions

In this study, the flexural performances of solid and hollow normal concrete and ECC beams were investigated. Three types of fibers (NM, PVA, and PP) were used for the ECC beams, whereas three hole sizes were studied for the three groups of ECC beams and the normal concrete beams. The following conclusions summarize the most important results obtained from the experimental beams.

1) Despite their lower moment of inertia, the cracking loads of normal concrete, PVA-ECC, and PP-ECC hollow beams with hollowing indices of 0.16 and 0.28 were higher than their corresponding solid beams, whereas those with NM fibers exhibited a continuous decrease in cracking load with an increase in the hole size. The maximum cracking load values were recorded for PP-ECC beams, which were 14.9, 22.5, 27.1, and 17.9 kN for hollowing indices of 0, 0.16, 0.28, and 0.44, respectively.

2) The improvements in the ultimate load capacity of PVA-ECC, NM-ECC, and PP-ECC solid beams compared to the normal concrete solid beam were 9%, 15%, and 23%, respectively. These improvements were higher for hollow PVA-ECC and NM-ECC beams (17%–28%) compared to hollow normal concrete beams. Moreover, the ultimate load capacities of the hollow PVA-ECC and NM-ECC beams with hollowing indices of 0.16 and 0.28 were higher than that of a normal solid concrete beam.

3) The ECC solid beams exhibited stiffer load-deflection behavior than normal concrete beams during the pre-cracking stage. This case is almost valid for hollow beams regardless of the size of the hole. The hollow NM-ECC and PVA-ECC beams with hollowing indices of 0.16 and 0.28 showed almost the same hardening plateaus that were comparable or higher than their corresponding solid beams and solid normal concrete beams. By contrast, the hardening plateau decreased with an increase in the hole size for the PP-ECC beams but with longer hardening plateaus compared to other types of ECC and normal concrete beams.

4) Owing to their displacement hardening characteristics, both the ductility and toughness were noticeably higher for the solid and hollow ECC beams compared to normal concrete beams. Beams with a hollowing index of 0.16 exhibited a higher ductility compared to their corresponding solid beams, whereas the ductility decreased as the size of the hole increased. However, the ductility of hollow ECC beams with hollowing indices of 0.16 and 0.28 mm was still noticeably higher than that of the normal solid concrete beam.

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