Punching shear behavior of steel fiber reinforced recycled coarse aggregate concrete two-way slab without shear reinforcement

Abstract

In this paper, the punching shear performance of 8 steel fiber reinforced recycled coarse aggregate concrete (SFRCAC) two-way slabs with a size of 1800 mm × 1800 mm × 150 mm was studied under local concentric load. The effects of RCA replacement ratio (r_g) and SF volume fraction (V_f) on the punching shear performance of SFRCAC two-way slabs were investigated. Digital Image Correlation (DIC) measurement and Acoustic Emission (AE) technique were introduced to collect pictures and relevant data during the punching shear test. The test results show that the SFRCAC two-way slab mainly exhibits punching shear failure and flexure failure under local concentric load. The punching shear failure space area of SFRCAC two-way slab has no obvious change with increasing r_g, however, show a gradual increase trend with increasing V_f. Both of the punching shear ultimate bearing capacity (P_u) and its deflection of SFRCAC two-way slab decrease with increasing r_g and increase with increasing V_f, respectively. Finally, through the regression analysis of the results from this study and the data collected from related literature, the influence of r_g and V_f on the P_u of two-way slabs were obtained, and the equations in GB 50010-2010, ACI 318-19, and Eurocode 2 Codes were amended, respectively. Furthermore, the amended equations were all applicable to predicted the ultimate bearing capacity of the ordinary concrete two-way slab, RCAC two-way slab, SFRC two-way slab, and SFRCAC two-way slab.

Graphical abstract

Keywords

recycled coarse aggregate / steel fiber reinforced recycled coarse aggregate concrete / two-way slab / punching shear / punching shear ultimate bearing capacity

1 Introduction

With the development of globalization, more and more countries are paying attention to the maintenance and sustainable development of the ecological environment. However, due to the reconstruction of old cities, earthquakes, floods, typhoons and other natural factors, the demolition of old buildings will produce a large amount of construction waste [1–3]. Relevant studies show that the construction sector of Europe is the major waste producer, which accounts for about 36% of extracted natural resources depletion [4]. Furthermore, most of the construction waste is usually transported to the landfill or piled up in the open air, resulting in a lot of environmental pollution [5–7]. From a win-win point of view, to find an effective way for effectively dealing with construction waste and reducing environmental pollution is very consistent with the concept of sustainable development advocated by the international community [8]. The idea of using recycled coarse aggregate (RCA) produced from waste concrete in construction waste to prepare RCA concrete (RCAC) should be put into practice.

However, RCA has many defects in material composition and physical properties, resulting in its lower mechanical properties and durability than natural coarse aggregate (NCA) [9–11]. Therefore, the application of RCAC in engineering has great limitations due to the reasons mentioned above [12]. Relevant research results show that the addition of steel fiber (SF) can significantly improve the basic properties of concrete [13–16]. Therefore, the idea of adding a certain amount of SFs into RCAC to enhance its performance and improve its application in engineering comes into being [17]. This kind of concrete prepared by adding SFs into RCAC is defined as SFRCAC.

Relevant studies show that the punching shear performance of two-way slabs can be affected by the area and position of the external load applied to the two-way slab, the concrete matrix strength, the effective span, the thickness of slabs, the shear reinforcement, the boundary conditions, the particle size and distribution of coarse aggregate [18–21]. Up to now, the research on the punching shear performance mainly focuses on the two-way slabs made of plain concrete, RCAC and SFRC. Through the study on punching failure response of slab-column connections, Habibi et al. [22] developed an analytical model to predict the post punching response. Based on the investigation on the connection of reinforced concrete slab-column connection, Ju et al. [23] addressed the dual demand curves and corresponding capacity curves to estimate the punching shear strength of a reinforced concrete flat slab. Ju et al. [24] proposed the punching shear strength formula of SFRC two-way slab based on deterministic and probabilistic methods. Xiao et al. [18] drew the conclusion that the ductility and punching shear ultimate bearing capacity (P_u) of RCAC two-way slab show a gradual decline with increasing replacement ratio (r_g). Reis et al. [25] showed that uncracked state stiffness of the two-way slab decrease with the increase of r_g. By studying the performance of the two-way slab formed by pouring two different types of recycled aggregate, Mahmoud et al. [26] obtained that the initial crack load and punching shear bearing capacity decrease with the decrease of RCA size. Francesconi et al. [27] came to the conclusion that the addition of RCA does not affect the punching failure characteristics of the two-way slab. According to the comparison of the measured test values with the design values calculated by the equations in different specifications, Sahoo and Singh [28] presented a prediction model for the ultimate punching strength of recycled concrete two-way slab. Yang et al. [29] found that compared with plain concrete, the addition of SF will improve the punching strength of two-way slabs and improve the development of cracks. In recent years, the researches on the structural performance and economic impact of SFRCAC show that SFRCAC has broad application prospects in civil engineering structures. However, the study on punching shear performance of SFRCAC two-way slab is relatively few. Xiao et al. [18] proposed that compared with RCAC two-way slab, the addition of SF improves its energy consumption and P_u. However, the systematic investigation of punching shear performance on SFRCAC two-way slab has not been reported. Previous studies on two-way slab properties mainly use the traditional measurement methods up to now. Such as, linear variable displacement transducer, stress sensor, inclinometer and strain gauge are usually used to measure the deflection, load, rotation angle of two-way slab and the strain of reinforcement and concrete, respectively. Digital Image Correlation (DIC) measurement is a new computer vision technology, which makes it possible to measure the displacement, deflection, strain and crack formation and propagation of specimen [30,31]. The Acoustic Emission (AE) technique is usually used to monitor the internal damage evolution of components during loading [32,33]. In this test, on the basis of traditional measuring instruments, DIC and AE technique were introduced to collect pictures and relevant data during the loading test of SFRCAC two-way slab for the first time, respectively.

The purpose of this paper is to bridge the current knowledge gap on punching shear performance of SFRCAC two-way slab structure. Therefore, the effects of r_g and V_f on the mechanical behavior, load–deflection curve, crack types, strain of reinforcement and concrete, overall failure mode and the range of internal punching shear failure space area of SFRCAC two-way slabs were studied, respectively. Finally, by analyzing and fitting the experimental data in this paper and related literature, the influence coefficient of recycled coarse aggregate and SF on the ultimate bearing capacity of the two-way slab under punching shear load was obtained, and the equations in the Codes of GB 50010-2010 [34], ACI 318-19 [35] and Eurocode 2 Codes [36] were amended, respectively. Furthermore, the amended equations were all applicable to predicted the ultimate bearing capacity of the ordinary concrete two-way slab, RCAC two-way slab, SFRC two-way slab and SFRCAC two-way slab.

2 Experimental program

2.1 Materials

The cement used in this test is Portland cement (P.O 42.5). A kind of natural river sand with the apparent density of 2552 kg/m³ and the fineness modulus of 2.68 was used as fine aggregate. The size distributions of aggregate are all shown in Fig.1. RCA and NCA are prepared from the waste concrete with compressive strength of 30–50 MPa and limestone gravels, respectively. The size range of coarse aggregate is 4.75 to 20 mm. The properties of coarse aggregate measured according to GB/T 25177-2010 [37] are shown in Tab.1. The properties of SF are shown in Tab.2. In this test, a water reducing agent with a measured water reduction rate of 25% was used, the dosage of which is shown in Tab.3. The reinforcements with a nominal diameter of 12 mm used in this test were HRB400E (Hot-rolled Ribbed Bar, f_yk = 400 MPa). The average yield strength, the average elastic modulus and the average yield strain of reinforcement were 399.62 MPa, 2.0 × 10⁵ MPa, and 1998 × 10 ⁻⁶, respectively, according to the test of 3 reinforcement specimens.

2.2 Test parameters and mixture proportions

In this test, the effects of r_g and V_f on punching shear performance of SFRCAC two-way slabs were investigated. Based on the higher water absorption of RCA, pre-wetting the RCA before mixing is necessary to control the actual water cement ratio of SFRCAC. Test results show that the water absorption of RCA reached 94.40% of the saturated water rate in the first 30 min and reached the maximum after 24 h. Therefore, the amount of water absorbed in the first 30 min was used as the amount of water used for pre-wetting. The mixture proportions, test plan and the basic mechanical properties of SFRCAC two-way slab matrix concrete are shown in Tab.3–Tab.5, respectively.

2.3 Details of test specimen preparation

The shaft mixer was used to mix all SFRCAC in this test. According to the Standards CECS 13:2009 [38] and GB/T 50080-2016 [39], the two-way slabs with length, width and depth of 1800, 1800, and 150 mm were poured. In addition, 6 cubic specimens with sides of 150 mm and 6 prisms with dimensions of 150 mm × 150 mm × 300 mm were cast to test f_cu, f_ts, f_c and E_c for each group, respectively.

The bi-directional tensile reinforcements of which the ratios were 0.999% and 1.099%, respectively, were configured at the bottom of SFRCAC two-way slab. The spacing of reinforcement and the thickness of concrete cover are 85 mm and 12 mm, respectively, as shown in Fig.2. The two-way slabs with formwork removed after pouring 24 h were cured with water for 28 d.

2.4 Test procedure

In this test, each two-way slab was tested on a 200 t multi-function loading testing machine, as shown in Fig.3. The two-way slab was simply supported on 20 spherical hinge supports uniformly distributed in a square pattern for loading. To prevent the spherical hinge supports from slipping during loading, four steel plates with round holes shown in Fig.4 were arranged on the rectangular supporting ring beam to fix the position of the spherical hinge supports.

The test methods were implemented in accordance with the standards CECS 13:2009 [38], JGT/472-2015 [40], and GB/T 50152-2012 [41]. Preloading was required before formal loading to ensure the normal operation of the test instrument and close contact between the two-way slab and spherical hinge supports. In this test, the loading rate of preloading and formal loading were both 2 mm/min. Formal loading adopted hierarchical loading with the grade of 10 and 30 kN before and after the initial cracking of two-way slabs, respectively. The test data were collected with the acquisition board after 5 min of loading at each level. To collect the data information of initial crack load and ultimate load as accurately as possible, the value of the loading grade was appropriately reduced when the load reached initial crack load and ultimate load, respectively.

To study the punching shear behavior of SFRCAC two-way slab, the measurements during the loading process mainly included punching shear load, deflection of the lower surface of the two-way slab, the strains of reinforcement and concrete, propagation and distribution of crack, and punching shear failure space area in the two-way slab. DIC measurement was used to measure concrete strains, the vertical deflection and the propagation and distribution of crack on the lower surface of SFRCAC two-way slab. The energy information generated by punching shear failure in the two-way slab needed to be collected by AE technique. The measuring points location of the reinforcement strain gauge, the AE probe and the concrete strain different points on the lower surface of the two-way slab are shown in Fig.5(a)–Fig.5(c), respectively. (Note: The AE probe measuring points of (1–8) and (9–12) are on the upper and lower surfaces of the two-way slab, respectively.)

3 Test results and analysis

3.1 Punching shear load–deflection curve

The test results show that the maximum deflection of SFRCAC two-way slab occurs at the center of the lower surface under the action of concentric punching shear load. The load–deflection curves of the lower surface center point of SFRCAC two-way slabs in Fig.6 all show the following four development stages: When the load is less than the initial crack load, the two-way slab is in the elastic working stage, and the deflection changes linearly with the increasing load. As the load continues to increase from the initial crack load to about 80% of P_u, the load–deflection curve tends to deviate from the vertical axis, and the load–deflection curve at this stage generally shows an approximate linear change. The reason is that the two-way slab is in the stage of crack generation, during which the number of cracks in this process gradual increases. Then, the load–deflection curve tends to the deflection axis more and more obviously from about 80% of P_u to the stage of P_u. The reason is that in this process, with the continuous increase of the load, the number of cracks on the lower surface of SFRCAC two-way slab basically does not increase, and the crack width develops rapidly. From the ultimate load to the stage when the punching shear cone is detached out, the load decreases rapidly and finally remains within a certain range until the end of the test. When the load is introduced path-controlled the hydraulic jack tries to increase the path, but the load cannot be increased further since the slab is broken. Therefore, it is obvious that the deflection increases rapidly after failure. The main reason for this process phenomenon is that after the punching shear cone is completely formed, only the SF not completely pulled out between the punching cone and the two-way slab and the tensile reinforcement at the bottom of SFRCAC two-way slab are stressed under the action of punching shear load.

It can be seen that the slope of the load–deflection curve in the rising stage of the curve, the initial crack load, P_u and the mid-span deflection corresponding to P_u of SFRCAC two-way slab in Fig.6(a) and Fig.6(b) all decrease gradually with increasing r_g and increase gradually with increasing V_f. Compared to the two-way slab with r_g = 0, when r_g are 30%, 50%, and 100%, the punching shear ultimate bearing capacity reduce by 1.82%, 3.36%, and 8.30%, respectively. Compared to the two-way slab with V_f = 0%, when V_f are 0.5%, 1.0%, 1.5%, and 2.0%, the punching shear ultimate bearing capacity increase by 12.50%, 24.55%, 37.28%, and 46.77%, respectively. The reason is that the addition of RCA and SF greatly changes the performance of matrix concrete. In this paper, the sample of concrete material after loading is analyzed by Scanning Electron Microscope (SEM) technique, as shown in Fig.7. RCA is composed of NCA covered with a layer of porous aged cement paste, and there is interfacial transition zone (ITZ) between RCA and mortar, as shown in Fig.7(a). In addition, there are some micro-cracks in RCA, which also lead to the strength and toughness of RCA being lower than those of NCA when bearing load. The addition of SF can greatly improve the strength of the matrix concrete and the ability to inhibit the development of cracks, as shown in Fig.7(b), which is beneficial to improve the bearing capacity and toughness of SFRCAC two-way slab.

3.2 Punching shear failure and cracking patterns

The punching shear failure pictures of SFRCAC two-way slab are shown in Fig.8. Under the action of local punching shear load, the final failure mode of SFRCAC two-way slab shown in Fig.8 presents the following characteristics. On the upper surface of two-way slab, the steel plate and its adjacent areas are embedded in the two-way slab area, and there are no cracks outside the area near the steel plate. On the lower surface of two-way slab, the lower surface corresponding to the load and the surrounding area within a certain range are punched out of other slab areas as a whole. Thus, it can be inferred that under local load, the punching shear cone is formed and punched out in the SFRCAC two-way slabs in this test, and the final failure mode shows the characteristics of punching shear failure.

The images of cracks on the lower surface during the punching shear failure of SFRCAC two-way slab collected by DIC measurement are shown in the Fig.9. According to the images of cracks and the test phenomenon of the two-way slab, the punching shear failure process of SFRCAC two-way slab can be roughly summarized into the following three stages, as shown in Fig.10. The first stage was elastic working stage which included from the initial loading to the first appearance of cracks, as shown in section o–a of Fig.10. In this process, the relationship between load and deflection of two-way slab showed a linear change. The second stage was the stage of cracks generation and development, as shown in section a–c of Fig.10. In the early stage of this process, the cracks were mainly radial bending cracks. Then, the circumferential punching shear cracks also gradually appeared and developed with the gradual increase of load, as shown in section a–b of Fig.10. At the later stage of this process, the number of radial and circumferential cracks did not increase, however, the width of crack near the midspan gradually increased with the increase of load, as shown in section b–c of Fig.10. The third stage was the process of punching shear cone being punched out, as shown in section c–d of Fig.10. The punching shear cone was completely formed inside the two-way slab when the punching shear load reached its maximum value. When the punching shear cone was detached out of the lower surface of the two-way slab, the punching shear load decreased rapidly and finally remained relatively stable within a certain range. For the two-way slab without SF, when the load reached a certain value, the punching shear cone formed instantly without warning, accompanied by a large and short burst sound. When the two-way slab with SFs cracked to a certain extent, its failure process started to be accompanied by the snapping sound of SFs being pulled out. The lower surface of the punching shear cone basically remained intact after the complete punching shear failure, and a few small pieces of concrete spalling occurred near the slab outside the edge of the punching shear cone.

The output diagrams of energy release positioning during the punching shear failure process of the two-way slab collected by AE technique are shown in the Fig.11. At present, GB 50010-2010 [34], ACI 318-19 [35] and Eurocode 2 Codes [36] all stipulate that the shape of the internal punching shear cone of plain concrete two-way slab is a truncated cone under punching shear failure. By observing Fig.8, Fig.9, and Fig.11, under the condition of fully verifying the definition on the punching shear cone shape of two-way slab in the above three Codes, it can also be found that the punching shear failure of SFRCAC two-way slab is also accompanied by certain bending failure. The schematic diagram of punching shear failure of SFRCAC two-way slab is shown in Fig.12, in which the truncated pyramid cone in the green part is the approximate shape of the punching shear cone in the two-way slab. Furthermore, the black lines in Fig.12 are the radial bending cracks and circumferential web shear oblique cracks on the lower surface of SFRCAC two-way slab under local concentric load. The output diagrams of energy release positioning in Fig.11(a)–Fig.11(d) show that the range of punching shear failure space area in the two-way slab has no obvious change and the number of internal damage energy release points trends to decrease with the increase of the r_g. The reason may be that the strength and stiffness of the matrix concrete gradually decrease with increasing of r_g, which leads to the gradual decrease of SFRCAC two-way slab P_u. The greater the stiffness of SFRCAC two-way slab is, the more energy will be released when punching shear failure occurs. The output diagrams of energy release positioning in Fig.11(d)–Fig.11(h) show that the range of punching shear failure space area and the number of internal damage energy release points in the two-way slab both show a gradually increasing trend with the increase of V_f. The reason is that SF can inhibit the development of cracks and improve the tensile and shear strength of concrete. In a certain range, the larger the V_f is, the higher the P_u of the two-way slab is, and the more energy is released when punching shear failure occurs.

3.3 Load and strain behavior

In this test, the strains generated by the reinforcement were measured by pasting strain gauges on the reinforcement. The location of the reinforcement measuring point is shown in Fig.5. Since the reinforcement strain and law of the corresponding measuring points at the two central axes of the two-way slab are basically consistent, here only the reinforcement strains at the measuring points 1 to 5 are taken for analysis, as shown in Fig.13. The strains of reinforcement at the same measuring point of different two-way slabs also show a gradually increasing trend under the same load with increasing r_g. The main reason is that compared with NCA, many defects of the RCA itself lead to the reduction of concrete elastic modulus, and the longitudinal reinforcement at the bottom of the slab is more involved in the force under the same punching shear load. The strains of reinforcement at the same measuring point of different two-way slabs show a gradually decreasing trend under the same load with increasing V_f. The main reason is that the reinforcements, SFs crossing both ends of the cracks and uncracked concrete jointly bear the tension at the cracks of the two-way slab. The higher the V_f is, the greater the stiffness of the two-way slab and the smaller the stress of the longitudinal tensile reinforcement are.

With the help of DIC measurement, concrete strains are extracted at different positions along the diagonal and central axis of the lower surface of SFRCAC two-way slab to analyze the development characteristics of concrete strain during the loading. The extraction positions of concrete strain measuring points of SFRCAC two-way slab are shown in Fig.5. Since the extracted locations of the concrete strain points on the lower surface of SFRCAC two-way slab are symmetric, this paper only analyzes the concrete strains at the measuring points 1 to 9, as shown in Fig.14. Among them, the concrete strains 1–5 and 6–9 are the radial tensile strains on the central axis and the circumferential tensile strains on the diagonal of the two-way slab under the punching shear load, respectively.

From the load–strain curves of concrete in Fig.14, it can be inferred that under the action of central load, the bottom surface concrete in SFRCAC two-way slab is mainly subjected to two kinds of stresses. The two stresses are the bending tensile stress caused by the central local load and the compressive stress generated by the membrane effect near the support caused by the deformation of the two-way slab. As closer the measuring point to the load, the larger the tensile strains and tensile stress values are. The circumferential concrete strain (measuring points 6–9) is always in a tensile state. The radial concrete strain value at the measuring point 1, which is further away from the load, gradually changes from negative to positive, indicating that the concrete at this point is subjected to compression in the early stage and tension in the later stage. The concrete strains corresponding to the initial crack load and ultimate load of SFRCAC two-way slab show a gradually decreasing trend with increasing r_g, and a gradually increasing trend with increasing V_f. The reason is that the deformation capacity and P_u of the two-way slab are improved due to the bridging effect of SF at the crack, and are reduced by the defects of RCA itself, such as micro-cracks, larger crush index and low strength.

3.4 Punching shear ultimate bearing capacity of steel fiber reinforced recycled coarse aggregate concrete two-way slab without shear reinforcement

The relationship between P_u1/P₀₁ (the change rate of P_u) and r_g in this test and Refs. [18,25,27,28] is statistically analyzed to study the effect of r_g on P_u of ordinary concrete or SFRC two-way slabs, as shown in Fig.15(a). P₀₁ is the P_u test value of ordinary concrete or SFRC two-way slab. P_u1 is the P_u test value of RCAC or SFRCAC two-way slab. And P_u1 has the same mixture proportions as P₀₁ except for r_g. The linear relationship between P_u1/P₀₁ and r_g can be obtained from Fig.15(a), as shown in Eq. (1) as follow:

(1)P_{\text{u}1}/\phantom{P_{\text{u}1}{P}_{01}}{P}_{01}=1-0.065r_{\text{g}}.

Relevant studies show that the effect of SF on the basic properties of concrete is mainly related to the length–diameter ratio (l_f/d_f) and V_f [42–44]. In this paper, λ_f is defined as the characteristic parameter of SF, which can be calculated by Eq. (2). Fig.15(b) shows the relationship between P_u2/P₀₂ (the change rate of P_u) and λ_f [18,45–48]. P₀₂ is the P_u test value of ordinary concrete or RCAC two-way slab. P_u2 is the P_u test value of SFRC or SFRCAC two-way slab. And P_u2 has the same mixture proportions as P₀₂ except for V_f. The linear relationship between P_u2/P₀₂ and λ_f can also be obtained from Fig.15(b), as shown in Eq. (3) as follow:

(2){\lambda }_{\text{f}}=V_{\text{f}}\cdot \left(l_{\text{f}}/d_{\text{f}}\right),

(3)P_{\text{u}2}/\phantom{P_{\text{u}2}{P}_{02}}{P}_{02}=1+0.426{\lambda }_{\text{f}}.

According to Fig.15 and Eqs. (1)–(3), it can be seen that the influence coefficient of recycled coarse aggregate and SF on the punching shear ultimate bearing capacity of the two-way slab under punching shear load is (1-0.065r_{\text{g}})(1+0.426{\lambda }_{\text{f}}).At present, the domestic and foreign Codes for calculating the P_u of ordinary concrete two-way slabs mainly include GB 50010-2010 [34], ACI (318-19) [35] and European Code 2 [36]. The calculation formulas on the punching shear ultimate bearing capacity of the two-way slab in the above three Codes are as follows:

Code of GB 50010-2010 [34]:

(4)P⩽\left(0.7{\beta }_h\cdot f_{\text{t}}\right)\cdot \eta \cdot {\mu }_{\text{m}}\cdot h_0,

(5)\eta =min\left\{0.4+\frac{1.2}{{\beta }_{\text{s}}},0.5+\frac{{\alpha }_{\text{s}}\cdot h_0}{4{\mu }_{\text{m}}}\right\},

where P is the design value of the punching shear strength of a two-way slab, kN. f_t is the design value of axial tensile strength of concrete, MPa. β_h is the influence coefficient of section height: when the depth (h) of two-way slab is not greater than 800 mm, take β_h is 1.0. When h is not less than 2000 mm, take β_h is 0.9. When 800 mm < h < 2000 mm, the value of β_h is determined by linear interpolation. h₀ is the average of the effective depths in the two orthogonal directions, mm. μ_m is the basic control perimeter at a distance of h₀/2 from the column’s borders or concentrated load, mm. β_s is the ratio of long to short side of the column, concentrated load, or reaction area (2 ≤ β_s ≤ 4). For the circular punching plane, β_s takes 2. The value of α_s is 40 for interior columns, 30 for edge columns, and 20 for corner columns.

Code of ACI 318-19 [35]:

(6)P=min\left\{\begin{array}{c}4{\lambda }_{\text{s}}\lambda {\mu }_{\text{m}}{h}_0\sqrt{f_{\text{c}}^{\prime }}\\ \left(2+\frac{4}{\beta }\right){\lambda }_{\text{s}}\lambda {\mu }_{\text{m}}{h}_0\sqrt{f_{\text{c}}^{\prime }}\\ \left(2+\frac{{\alpha }_{\text{s}}{h}_0}{{\mu }_m}\right){\lambda }_{\text{s}}\lambda {\mu }_{\text{m}}{h}_0\sqrt{f_{\text{c}}^{\prime }}\end{array}\right\},

where P is the design value of the punching shear strength of a two-way slab, kN. f_{\text{c}}^{\prime } is the characteristic compressive cylinder strength of concrete at 28 d, MPa. β is the ratio of long to short side of the column, concentrated load, or reaction area. λ is the modification factor to reflect the reduced mechanical properties of lightweight concrete relative to normal-weight concrete of the same compressive strength. The value of λ shall be taken as 1.0 for normal-weight concrete. λ_s is the size effect modification factor, shall be determined by Eq. (7) as follow:

(7){\lambda }_{\text{s}}=\sqrt{\frac{2}{1+{\displaystyle \frac{h_0}{10}}}}⩽1,

where h₀ is the average of the effective depths in the two orthogonal directions, mm. μ_m is the basic control perimeter at a distance of h₀/2 from the column’s borders or concentrated load, mm. The value of α_s is 40 for interior columns, 30 for edge columns, and 20 for corner columns.

Code of Eurocode 2 [36]:

(8)P=max\left\{\begin{array}{c}{C}_{\text{Rd,c}}k(100{\rho }_{\text{l}}{f}_{\text{ck}}{)}^{1/3}{u}_{\text{m}}{h}_0\\ 0.035k^{3/\phantom{32}2}{f_{\text{ck}}}^{1/\phantom{12}2}{u}_{\text{m}}{h}_0\end{array}\right\},

(9)k=1+\sqrt{\frac{200}{h_0}}⩽2.0,

(10){\rho }_{\text{l}}=\sqrt{{\rho }_{\text{l}x}\cdot {\rho }_{\text{l}y}}⩽0.02,

where P is the design value of the punching shear strength of a two-way slab, kN. f_ck is the characteristic compressive cylinder strength of concrete at 28 d, MPa. C_Rd,c = 0.18/γ_c, γ_c is the partial safety factor for concrete, γ_c = 1.0. ρ_lx and ρ_ly are the reinforcement ratios for longitudinal reinforcement in the two orthogonal directions, respectively, extending to a 2h₀ distance from the column’s borders. u_m is the basic control perimeter at a distance of 2h₀ from the column’s borders, mm. h₀ is the average of the effective depths in the two orthogonal directions, mm.

According to Eqs. (4)–(10), it can be seen that the Codes of GB 50010-2010, ACI 318-19, and Eurocode 2 all have no specific definitions for calculating the P_u of RCAC, SFRC, and SFRCAC two-way slabs. The predicted ultimate bearing capacities of the two-way slabs under punching shear load calculated according to GB 50010-2010, ACI 318-19, and Eurocode 2 Codes are shown in Tab.6. It can be seen from Tab.6 that the prediction values of the two-way slab ultimate bearing capacity based on the Codes of GB 50010-2010, ACI 318-19, and Eurocode 2 are all too conservative.

By analyzing the results from this study and the data collected from related literature, the relationship between P_e/P_i (i = 1,2,3) and α are shown in Fig.16. α = (1 − 0.065r_g)(1 + 0.426λ_f). In this paper, P₁₁, P₂₂ and P₃ are defined as the amended equations of the punching shear ultimate bearing capacity in GB 50010-2010, ACI 318-19, and Eurocode 2 Codes, respectively.

The following equations can be obtained according to Fig.16.

(11)P_{11}=P_1\cdot [2.114\cdot (1-0.065r_{\text{g}})(1+0.426{\lambda }_{\text{f}})],

(12)P_{22}=P_2\cdot [1.306\cdot (1-0.065r_{\text{g}})(1+0.426{\lambda }_{\text{f}})],

(13)P_{33}=P_3\cdot [1.792\cdot (1-0.065r_{\text{g}})(1+0.426{\lambda }_{\text{f}})].

The experimental values of the two-way slab P_u and its predicted value calculated according to Eqs. (11)–(13) are shown in Tab.7. The average values of P₁₁/P_e, P₂₂/P_e, and P₃₃/P_e are 1.021, 1.030, and 0.991, respectively. And the coefficient of variation for P₁₁/P_e, P₂₂/P_e, and P₃₃/P_e are 14.37%, 14.86%, and 11.60%, respectively. The above results show that the amended equations (P₁₁, P₂₂, and P₃₃) in GB 50010-2010, ACI 318-19, and Eurocode 2 Codes are all applicable to predict the P_u of ordinary concrete two-way slabs, recycled coarse aggregate concrete (RCAC) two-way slabs, SF reinforced concrete (SFRC) two-way slabs and SFRCAC two-way slabs.

4 Conclusions

In this paper, combined the traditional measurement methods with DIC and AE technique, the effects of r_g and V_f on punching shear performance of SFRCAC two-way slabs were experimentally investigated. Finally, through the regression analysis of the results from this study and the data collected from related literature, the influence of r_g and V_f on the P_u of two-way slabs were obtained, and the equations in GB 50010-2010, ACI 318-19, and Eurocode 2 Codes were amended, respectively. Furthermore, the amended equations were all applicable to predicted the ultimate bearing capacity of the ordinary concrete two-way slab, recycled coarse aggregate concrete two-way slab, SF reinforced concrete two-way slab and SFRCAC two-way slab. According to the test results and analysis, the following conclusions can be drawn.

1) The test data collected by DIC and AE technique show that the punching failure of SFRCAC two-way slabs is also accompanied by certain bending failure. The range of punching shear failure space area in the two-way slab have no obvious change with increasing r_g and show a gradually increasing trend with increasing V_f.

2) The initial crack load, the ultimate punching shear load and the mid-span deflection corresponding to the ultimate punching shear load of SFRCAC two-way slabs all decrease gradually with increasing r_g and increase gradually with increasing V_f. Compared to the two-way slab with r_g = 0, when r_g are 30%, 50%, and 100%, the punching shear ultimate bearing capacity reduce by 1.82%, 3.36%, and 8.30%, respectively. Compared to the two-way slab with V_f = 0%, when V_f are 0.5%, 1.0%, 1.5%, and 2.0%, the punching shear ultimate bearing capacity increase by 12.50%, 24.55%, 37.28%, and 46.77%, respectively.

(3) The strains of reinforcement at the same measuring point of different two-way slabs under the same load show a gradually increasing trend with increasing r_g and a gradually decreasing trend with increasing V_f.

(4) The concrete strains corresponding to the initial crack load and ultimate load of the two-way slab show a gradually decreasing trend with increasing r_g and a gradually increasing trend with increasing V_f.

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