Flexural Performance of Steel Reinforced ECC-Concrete Composite Beams Subjected to Freeze–Thaw Cycles

Table 1 lists the sixteen beams and the values of the two main parameters considered in this investigation, namely the ECC height replacement ratio, r_h and number of freeze–thaw cycles, n. Fig 1 shows the geometrical dimensions, reinforcement, materials used and supporting system test specimens. The specimen total span length l = 1000 mm, flexural-shear span length l_mv = 300 mm, pure flexural span length l_m = 300 mm. Cross-section width b and height h are 100 and 150 mm, respectively, the vertical distance of the cross-section bottom edge to the centroid of steel bars a_s is 25 mm, the cross-section effective height h₀ is 125 mm. The top steel reinforcement is 2φ10, h_e is the ECC replacement height and r_h is the ECC height replacement ratio, r_h = h_e/h₀. The bottom longitudinal reinforcement is 2φ12 for all test specimens. Each group notation is selected to identify the ECC height replacement ratio used (BA, BB, BC and BD represents r_h = 0, 0.30, 0.60 and 1.20, respectively) and the cycles n (0, 50, 100 and 150) of freeze–thaw. All specimens were loaded by two equal point loads and simply supported as shown in Fig. 1.

Displacement trancedusers were located at midspan, loading and supporting points to measure movements at these locations. The load was applied by a manual hydraulic jack and measured by a load transducer. Two electrical resistance strain acquisition units (DP3862) were used to capture strains at various stages of loading: one was connected to the load transducer while the other was used to capture strains from mid-span strain gauges attached to steel reinforcement. Equidistant dial indicators installed along the height of the beam cross-section at midspan were used to measure the average ECC/concrete strains. The size of cracks along the span was measured by crack width measurement instrument KON-FK (B) (Zhou 2013).

The rapid water freezing and thawing method was adopted (China Renewable Energy Engineering Institute 2006), the maximum and minimum temperatures at the core area of specimens should be controlled at 8 ± 2 °C and − 17 ± 2 °C, respectively, and every cycle should be accomplished within 4 h. The freeze–thaw test system was used to accomplish the required cycles. Once achieved the predetermined cycles, tests of concrete cubes, ECC (flat-plates for tension and prisms for compression), flexural specimens (concrete beams, ECC-concrete composite beams and ECC beams) were conducted as explained below.

Figure 3 (taking group BC for example) presents the cross-section average strain distributions at various loads, Fig. 3a–d for 0, 50, 100 and 150 freeze–thaw cycles, respectively.

As observed from Fig. 3, the cross-section strain is generally linearly distributed, validating the plane-section assumption and no delamination between concrete and ECC.

Figure 4 presents the specimens midspan moment-steel strain curves. As observed from Fig. 4, the steel bars of all specimens yielded. After yielding of steel reinforcement, the steel strains of group BA (reinforced concrete specimens) increase, even the load does not increase, indicating full but gradual collapse of test specimens. On the other hand, test specimens in group BD (reinforced ECC specimens), groups BB and BC (reinforced ECC-concrete composite specimens) are able to carry more moments beyond yielding of steel, indicating that ECC materials in tensile zone can provide tensile resistance together with steel bar.

Figure 5 presents the specimens midspan moment-deflection curves. Relative bending capacity and deflections with respect to control unfrozen reinforced concrete beams are presented in Table 6. M_u is the bending capacity of each specimen, M_u0 is the bending capacity of control unfrozen specimen in each group. M_q0 and d_q are the moment and the corresponding deflections under quasi-permanent combinations of unfrozen specimen (BA-0, BB-0, BC-0 and BD-0), respectively.

As observed from Fig. 5 and Table 6, the bending capacities decrease with the increase of freeze–thaw cycles regardless of the cross-section form. After 50, 100 and 150 cycles, the bending capacities of group BA are 97%, 93% and 69% of that of its control unfrozen specimen BA-0, respectively. The ultimate moments of group BB are 96%, 91% and 82% of that of its comparison control unfrozen specimen BB-0, respectively. The ultimate moments of group BC are 86%, 80% and 73% of that of its control unfrozen specimen BC-0 respectively. The ultimate moments of group BD are 93%, 91% and 90%, respectively, of that of its control unfrozen specimen BD-0. Deflections of specimens after 50 and 100 cycles are generally lower, but after 150 cycles are higher, than that of control unfrozen specimen. This observation is in agreement with a previous investigation (Ge et al. 2018) that showed that the positive effect of water conservation environment on the elastic modulus is greater than the negative effect of freeze–thaw less than 100 cycles.

Table 7 presents the comparisons of bending capacities and deflections, where the reinforced concrete specimens are taken as comparison specimen. M_uc is the bending capacities of control concrete specimen without ECC layer (BA-0, BA-50, BA-100 and BA-150) in each group. M_qc and d_q are the moment and corresponding deflection under quasi-permanent combinations of control concrete specimen, respectively.

As observed from Table 7, the bending capacities of ECC-concrete composite specimens (group BB and BC) and ECC specimens (group BD) are greater than that of concrete specimens (group BA). Compared with the control specimen BA-0, the bending capacities improvement of BB-0, BC-0 and BD-0 are 4%, 28% and 12%, respectively. Specimens subjected to 50, 100 and 150 cycles show the same trend. For unfrozen specimens, the deflections of specimen BB-0, BC-0 and BD-0 under the quasi-permanent moment combinations are 79%, 81% and 85% of that of the control concrete specimen BA-0, respectively. Similar trends to specimens subjected to 50, 100 and 150 cycles, illustrating the bending capacity and flexural stiffness are improved when the tension zone was replaced by ECC layer.

Figure 6 presents the tested maximum crack widths at the same height of steel reinforcement for various load. ω_max,lim is the crack width limit value (Liu et al. 2008) and τ_l is the crack widths amplification coefficient under long-term load action (China Academy of Building Research 2010) of reinforced concrete specimen, ω_max,lim/τ_l is the limit value under testing load. Table 9 presents the crack width of specimens under the quasi-permanent moment combinations of tested control concrete specimens. M_qc and ω_q are the moment under quasi-permanent combinations of specimen BA-0 and the corresponding crack width, respectively. The average crack spacing l_cr and number of cracks n_cr are also presented in Fig. 7.

As can be seen from Figs. 6, 7 and Table 8, for unfrozen specimens, the crack width under quasi-permanent moment combinations of specimen BB-0, BC-0 and BD-0 are 59%, 50% and 44% of that of the control concrete specimen BA-0, respectively, indicating that crack widths decrease as the ECC height replacement ratios increase. It is also noted that the crack widths under quasi-permanent moment combinations all meet the requirement of service state, less than 0.2 mm. The average crack spacing decreases while number of cracks increases as the ECC height replacement ratios increase, illustrating that the application of ECC can control the cracks distributed along the specimens tensile zone effectively.

Typical under-reinforced flexural failure occurred for all specimens where steel reinforcement yielded, followed by crushing of concrete/ECC in the compressive zone (concrete for reinforced concrete specimens (group BA) and ECC-concrete composite specimens (group BB and BC), ECC for reinforced ECC specimens (group BD)). Fig 8 presents the failure modes of representative specimens. For unfrozen concrete specimens (for example specimen BA-0), after yielding of steel reinforcement, several visible cracks occurred near failure and, finally, the concrete compressive zone crushed. For concrete specimens subjected to freeze–thaw cycles (for example specimen BA-150), large volume of mortars dropped out and gravels exposed, several visible cracks occurred in the tensile zone. After yielding of steel reinforcement, a major crack occurred near failure and, finally, the concrete compressive zone crushed. For unfrozen composite specimens (for example specimen BC-0), multi-cracks occurred in the tensile zone, with the increase of loading, many new cracks developed and, then the steel reinforcement yield, finally, the concrete compressive zone crushed. For composite specimens subjected to freeze–thaw cycles (for example specimen BC-50, BC-100 and BC-150), with increasing the freeze–thaw cycles, mortar dropped out, and the bottom ECC layer exposed more fiber while the upper concrete layer exposed more sand and gravel. After yielding of steel reinforcement, several visible cracks occurred near failure and, finally, the concrete compressive zone crushed. For ECC specimens, the initial characteristics were similar to ECC-concrete composite specimens. After yielding of steel reinforcement, the outermost layer of ECC specimens reached its ultimate strain and then crushed, but the fibers distributed in cementitious materials can hold the crushed ECC blocks in contact.

The following assumptions have been considered in developing the predictions of flexural performance of steel reinforced ECC-concrete composite beams subjected to freeze–thaw cycles:

The constitutive model of steel bars (China Academy of Building Research 2010) simplified to a bilinear curve is expressed as Eq. 1. ε_s and σ_s are the steel reinforcement’s strain and stress, respectively, E_s and f_sy are the modulus of elasticity and the yield strength, respectively, ε_sy and ε_su are the yield and ultimate tensile strain.

The tensile constitutive model of ECC (Li et al. 2001) simplified to a bilinear curve is shown in Fig. 9a and presented by Eq. 2 as below. ε_et and σ_et are the ECC material’s tensile strain and stress, respectively. ε_etc,n and ε_etu,n are the ECC material’s cracking and ultimate strain subjected to n freeze–thaw cycles, respectively. f_etc,n and f_etu,n are the cracking and ultimate stresses subjected to n freeze–thaw cycles, respectively.

The mechanical properties of ECC subjected to n freeze–thaw cycles established by regression analysis of the tested data are expressed as follows.

The compressive constitutive model of ECC (Yuan et al. 2013) simplified to a trilinear curve is shown in Fig. 9b and expressed by Eq. 7. ε_ec and σ_ec are the ECC material’s compressive strain and stress, respectively; f_ecp,n and f_ecu,n are the maximum (peak point) and ultimate (after peak point) stress, respectively; ε_ecp,n and ε_ecu,n are the strain corresponding to maximum and ultimate compressive stress, respectively, subjected to n freeze–thaw cycles.

The compressive values of ECC subjected to n freeze–thaw cycles as required by Eq. (7) established by regression analysis of the tested data are expressed as follows.

The compressive constitutive model of concrete (Hognestad 1951; Wang 2017) simplified to a parabolic curve is shown in Fig. 10a and expressed by Eq. 12. f_c,n and f_c,n are the maximum (peak point) and ultimate stress (after peak point), respectively; ε_co,n and ε_cu,n are the strain corresponding to maximum and ultimate stress, respectively, subjected to n freeze–thaw cycles. ε_c and σ_c are the concrete compressive strain and corresponding stress.

The predicted compressive performances of concrete subjected to n freeze–thaw cycles established by regression analysis of experimental data are expressed as follows.

The tensile constitutive model of concrete (China Academy of Building Research 2010; Cao et al. 2012) is simplified to a linear curve as shown in Fig. 10b and presented by Eq. 17 as below. ε_ctu,n and f_ctu,n are the concrete ultimate tensile strain and stress subjected to n freeze–thaw cycles, respectively. ε_ct and σ_ct are the strain and corresponding stress in tensile concrete, respectively.

The predicted tensile performances of concrete subjected to n freeze–thaw cycles established by regression analysis of experimental data are expressed as follows.

Comparisons of experimental and predicted mechanical performances of ECC and concrete subjected to n freeze–thaw cycles are shown in Fig. 11, where R² is the coefficient of determination.

As observed from Fig. 11, the coefficients of determination are, all, greater than 0.95, showing good agreement between the predicted critical values and experimental test results.

In this section of the paper, simplified formulas for bending capacities of ECC-concrete composite and ECC specimens are developed as summarized in Table 10, where the first row (I) presents the cross-section (a), strain distribution (b) as well as actual and simplified stress distributions (c) along the cross-section height of ECC-concrete composite specimen and ECC specimen, respectively, for failure mode ②.

Based on force equilibrium, Eq. (27) can be obtained, while Eq. (28) obtained according to the plane-section assumption. x_c and x_e are the height of concrete and ECC compressive stresses, respectively, x is the simplified height for compressive stress block (x = β_c,n x_c for ECC-concrete composite specimen and x = β_e,n x_e for ECC specimen), α_c,n, a_e,n, β_c,n and β_e,n are coefficients associated with the equivalent compressive stress distribution for concrete and ECC subjected to freeze–thaw cycles. Then, based on the resultant force and moment equivalent principle, Eqs. (29) and (30) can be obtained. Substituting the concrete compressive properties into Eqs. (29) and (30), α_c,n/a_e,n and β_c,n/β_e,n can be calculated as presented in Table 11.

Table 12 presents comparisons of tested and predicted bending capacity, where M_u,e, M_u,c are the experimental and predicted bending capacity, respectively.

As observed from Table 12, the average value and their variation coefficients of M_u,c/M_u,e are 0.93 and 0.06, respectively, indicating the predicted bending capacity agrees well with tested results.

Figure 14 represents the relationship curves of ultimate moment and curvature ductility against the steel reinforcement ratio. Five steel reinforcement ratios ρ_s, 0.4%, 0.8%, 1.2%, 1.6% and 2.4% are studied.

As observed from Fig. 14, with the increase of reinforcement ratio, the yield and ultimate moments gradually increase. The yield curvature increases, the ultimate curvature decreases and curvature ductility, thus, decreases gradually. The elastic energy dissipation increases, plastic energy dissipation decreases and energy dissipation ratio gradually decreases. After the reinforcement ratio exceed the maximum balanced reinforcement ratio ρ_sb1,n, the ultimate moment is equal to the yield moment and the plastic energy dissipation is also equal to the elastic energy dissipation.

Furthermore, with the increase of freeze–thaw cycles, the yield and the ultimate moments gradually decreases, the maximum balanced reinforcement ratio gradually decreases.

Figure 15 presents the relationship curves of ultimate moment and curvature ductility against the ECC height replacement ratio (0, 0.24, 0.48, 0.72, 0.96 and 1.20).

As observed from Fig. 15, with the increase of ECC replacement ratio, the yield and ultimate moment gradually increases. The yield curvature, first increase, and then decrease while the ultimate curvature, first decrease, then increase, and then decrease; the curvature ductility, first decreases, and then increases, except for specimens exhibited over-reinforced failure. The elastic energy dissipation, first increases, and then decrease, the plastic energy dissipation, first decreases, and then increase, the energy dissipation ratio, first decreases, and then increase.

Figure 16 shows the relationship curves of ultimate moment and curvature ductility against the ECC strength. Five ECC grades, f_etc,A = f_etu,A = 3.0 N mm ⁻², f_ecp,A = 30 N mm ⁻², f_etc,B = f_etu,B = 4.0 N mm ⁻², f_ecp,B = 35 N mm ⁻², f_etc,C = f_etu,C = 5.0 N mm ⁻², f_ecp,C = 40 N mm ⁻², f_etc,D = f_etu,D = 6.0 N mm ⁻², f_ecp,D = 45 N mm ⁻², f_etc,E = f_etu,E = 7.0 N mm ⁻², f_ecp,E = 50 N mm ⁻², ε_etc = 0.0003, ε_etu = 0.03, ε_ecp = 0.0036 and ε_ecu = 0.0054 are studied.

As observed from Fig. 16, with the improvement of ECC strength, the yield and ultimate moments gradually increase. The yield curvature gradually increases, the ultimate curvature gradually decreases, and hence the curvature ductility gradually decreases. The elastic energy dissipation increases, the plastic energy dissipation decreases, and hence the energy dissipation ratio gradually decreases.

Figure 17 shows the relationship curves of ultimate moment and curvature ductility against the concrete strength. Five concrete compressive strength f_c, 20.1, 23.4, 26.8, 29.6 and 32.4 N mm ⁻² are studied.

As observed from Fig. 17, with the improvement of concrete strength, the yield and ultimate moment gradually increases. The yield curvature gradually decreases, the ultimate curvature gradually increases, and hence the curvature ductility gradually increases. The elastic energy dissipation decreases, the plastic energy dissipation increases, hence the energy dissipation ratio gradually increases.