Calculation on flexural capacity of recycled aggregate concrete beams

Abstract

Based on the constitutive relation of recycled aggregate concrete (RAC, referred to as recycled concrete), from the calculation formulas of the equivalent rectangular block parameters in the compression zone of recycled concrete beams under different recycled coarse aggregate replacement ratios, the calculation formulas of the key parameters 𝛼₁ and 𝛽₁ of recycled concrete are deduced. Based on 𝛼₁ and 𝛽₁, the flexural bearing capacity of recycled concrete beams is given. In addition, the nonlinear finite element method is applied, and the simulation results are compared with the calculation results to verify the accuracy of the calculation results. Then, the limit compression zone height and maximum reinforcement ratio of recycled concrete beams, as well as the variation characters of compression zone height and reinforcement ratio under certain size and load are analyzed and obtained.

Keywords

recycled aggregate concrete beam equivalent rectangular block flexural behavior nonlinear analysis

Introduction

Recycled aggregate concrete (referred to as “recycled concrete”) is concrete using recycled aggregate produced by crushing, sieving, and grading waste concrete blocks. It is a kind of ecological concrete used to partially or completely replace natural aggregates, and then add cementitious materials (Xiao, 2018). In China, about 1.297 billion tons to 1.704 billion tons of construction solid waste was discharged from 2013 to 2018. This has attracted the attention of many scholars. Until 2021, in China, a total of 146 projects had been approved by Natural Science Foundation (NSFC) (Xu et al., 2022). Only about 5%–10% of the discharged construction solid waste is recycled (Ghisellini et al., 2018). Recycling the solid waste of construction to produce recycled concrete is of great significance to the protection of resources and the environment. Also, it is significance to the realization of the sustainable development of the construction industry in China.

A large number of relevant research results show that on average, the flexural normal section of recycled concrete beams obeys the assumption of flat section during the failure process, and the failure form is basically similar to that of natural aggregate concrete (NC) beams; but the ultimate bearing capacity is slightly reduced and the deflection at failure is increased. The initial stiffness decreases and the crack width increases as the replacement ratio of recycled aggregate rises (Mahdi et al., 2015; Sato et al., 2007; Sindy et al., 2018). Through experiments and theoretical analysis, Zhao and Sun (2013) pointed out that when calculating the cracking moment of recycled concrete beams, the existing codes need to be modified. Through experiments, Zhang et al. (2016) and Yang et al. (2020) showed that recycled concrete beams conform to the assumption of a flat section during the loading process and have the similar pattern of conventional concrete cracking. Through experiments, Xiao et al. (2012) found that the stiffness of recycled concrete beams has been reduced under the same conditions. Through experiments, Wu et al. (2010) found that the mid-span deflection of recycled coarse aggregate concrete beams is greater than that of ordinary aggregate concrete beams. Tosic et al. (2016) established a flexural strength database based on the test results of 217 beams and validated the application of Eurocode 2 in designing recycled concrete beams. The results showed that the beam with stirrups needs further research. Through experiments, Choi et al. (2012) found that the maximum flexural strength of natural aggregate beams is 20% higher than that of recycled concrete beams. Due to the reduced interface strength between mortar and recycled coarse aggregate, the neutral axis of 100% recycled coarse aggregate beams is higher. Deng and Yun (2010) tested the practicability of present code of China in the calculation of recycled concrete beams and found the poor prediction of cracking moment, deflection and crack width. Through experiments, Deresa et al. (2020) found that the cracking moment decreases as the replacement ratio of recycled aggregate increases.

In summary, the current research on recycled concrete has found the performance of recycled concrete beams designed with conventional concrete specifications will be lower than expected because of the lower material property of recycled concrete. Even with the same strength, the constitutive properties of recycled concrete and conventional concrete are different, and the equivalent rectangular area coefficients α₁ and β₁ of the recycled concrete beam section based on the constitutive are different from those of conventional concrete. Therefore, the influence of the mechanical properties of recycled concrete on its components must be considered and included in the structural design. In this study, the effect of the variation in the constitutive relation of recycled concrete with the replacement ratio of RCA on flexural capacity of RAC beams is analyzed theoretically and numerically. The key parameters of the simplified calculation method are proposed. The authors hope this study can improve the design technique of RAC structures, and encourage the further studies in this field.

Comparative analysis of the constitutive relationships of recycled concrete

The difference between the flexural performance of recycled concrete beams and NC beams is mainly due to the different constitutive relationship of concrete. Referring to the constitutive structure of NC proposed by Guo (2004), Xiao (2007) took the replacement ratio of recycled coarse aggregate as an influencing factor and established the constitutive model shown in equation (1), which was adopted by Technical Code on The Application of Recycled Concrete (DG/TJ 08-2020-2007, 2007)

{\begin{array}{c} y = a_{r} x + (3 - 2 a_{r}) x^{2} + (a_{r} - 2) x^{3}, 0 \leq x \leq 1 \\ y = \frac{x}{b_{r} {(x - 1)}^{2} + x}, x \geq 1 \end{array}

(1)

Among them, x = ε/ε₀, ε is strain, ε₀ is the strain corresponding to the peak stress, y = σ/f_c, σ is stress, f_c is the axial compressive strength, and r is the replacement ratio of recycled coarse aggregate. For recycled concrete, a_r and b_r can be expressed by the rational equation of the replacement ratio of recycled coarse aggregate, and the values proposed by Xiao (2007) are

{\begin{array}{c} a_{r} = 2.2 (0.748 r^{2} - 1.231 r + 0.975) \\ b_{r} = 0.8 (7.6483 r + 1.142) \end{array}

(2)

The parameter values proposed by Xie et al. (2018) are

{\begin{array}{c} a_{r} = 0.3259 r^{2} - 0.7559 r + 1.2668 \\ b_{r} = 4.7657 r + 2.8905 \end{array}

(3)

In Code for Design of Concrete Structures (GB 50010-2010, 2015) the stress remains unchanged after the peak strain is exceeded. When the strength grade of concrete is lower than C50, the constitutive relationship is

{\begin{array}{c} y = 1 - (2 x - x^{2}), 0 \leq x \leq 1 \\ y = 1, x \geq 1 \end{array}

(4)

Wang and Xiao (2018) proposed the stress-strain relationship of recycled concrete confined by stirrups. This constitutive model reflects the influence of constraints on peak stress, peak strain and ultimate strain. Wang and Xiao (2018) proposed the stress-strain relationship of recycled concrete confined by stirrups. This constitutive model reflects the influence of constraints on peak stress, peak strain and ultimate strain.

Comparing the compressive stress-strain curve equations of recycled concrete given by the above scholars, equations (2) and (3) are currently given with the replacement ratio of recycled coarse aggregate as a variable and in good agreement with the test results. Choose equations (2) and (3) to calculate the stress-strain curve of recycled concrete under different recycled coarse aggregate replacement ratio, as shown in Figure 1, where the 0 replacement ratio of recycled coarse aggregate represents the compressive stress-strain curve of NC. For the rising section of the constitutive curve, the curve of equation (2) basically coincides with the curve of Specification for Design of Concrete Structures. When the replacement ratio of recycled coarse aggregate is 100%, the curves drawn by equations (2) and (3) are basically the same. The constitutive curves of equation (2) and equation (3) reflect the approximate range of constitutive dispersion of recycled concrete. When the restraint of the stirrups on the concrete increases, the deformability of recycled concrete will be improved. The constitutive curve of Wang and Xiao (2018) improved the deformability of recycled concrete due to the consideration of stirrup constraints. However, when the beam is loaded in flexure and is damaged, the restraint effect is less obvious. In the following, the nonlinear constitutive structure of conventional concrete, that is, literature (Choi and Yun, 2013) and literature (Choi et al., 2012) are used for analysis.

Figure 1.

Stress-strain curve of recycled concrete. (a). r = 0%; (b) r = 100%.

According to the previous study (Xiao, 2007), the peak strain of recycled concrete is desirable

ε_{0} = {0.00076 + {[(0.626 f_{c} - 4.33) \times 10^{0.7}]}^{0.5}} \cdot (1 - \frac{r}{B (r)})

(5)

Among them, r is the replacement ratio of recycled coarse aggregate, 𝑓_c is the axial compressive strength, (r) is a parameter, determined as

B (r) = 65.715 r^{2} - 109.43 r + 48.989

(6)

Conversion relationship between the cubic compressive strength of recycled concrete and the compressive strength of prisms (Wang and Xiao, 2018)

f_{c} = 0.76 f_{c u} (\frac{ρ}{2400}) (1 + \frac{r}{A (r)})

(7)

Among them, 𝑓_cu is the compressive strength of the cube, 𝜌 is the density, (r) is the parameter, and the value is

A (r) = - 89.338 r^{2} + 131.49 r - 37.572

(8)

Calculation of equivalent stress distribution of recycled concrete

In the Code for Design of Concrete Structures (GB 50010-2010, 2015), the nonlinear compressive stress distribution on the section can be equivalent to a rectangular distribution. The stress distribution of the single-reinforced concrete beam and the equivalent rectangular stress distribution are shown in Figure 2. The resultant force of the concrete internal compressive stress is 𝐶, and the distance between the center of the resultant force in the compression zone and the edge of the compression zone is 𝑦_c. The force 𝐶 and the distance 𝑦_c should remain identical before and after the equivalence process. Suppose the equivalent compressive stress of concrete is 𝛼₁𝑓_c, and the compression height in the equivalent rectangular stress graph is 𝛽_z, where x is the height of the compression zone, that is, 𝛽₁ is assumed as the ratio of the equivalent compression height to the compression height.

Figure 2.

Equivalent rectangular stress distribution. (a). r = 0%; (b). r = 100%.

As shown in Figure 2(a), when a concrete beam is flexural damaged, the pressure on the concrete in the compression zone is

C = b \int_{0}^{ξ_{n} h_{0}} σ_{y} d y

(9)

Among them, b is the beam width, h₀ is the effective height of the beam, and ξ_n is the height of the relative compression zone. Take x = ε/ε₀, ε₀ and ε_cu are the peak strain and ultimate strain of concrete, respectively. σ_y = σ_x integrates the compressive stress of concrete in the compression zone of the section as the pressure force in the compression zone

C = f_{c} b ξ_{n} h_{0} \frac{ε_{0}}{ε_{c u}} \int_{0}^{\frac{ε_{c u}}{ε_{0}}} \frac{σ_{x}}{f_{c}} d x

(10)

Bringing equation (10) into the constitutive equation (1) of recycled concrete, we get

C = f_{c} b ξ_{n} h_{0} \frac{ε_{0}}{ε_{c u}} (\int_{0}^{1} [a_{r} x + (3 - 2 a_{r}) x^{2} + (a_{r} - 2) x^{3}] d x + \int_{1}^{\frac{ε_{c u}}{ε_{0}}} \frac{x}{b_{r} {(x - 1)}^{2} + x} d x)

(11)

Among them, a_r and b_r are respectively the rising section coefficient and the falling section coefficient of the constitutive structure of recycled concrete. After integration, the pressure of the concrete in the compression zone is obtained

C = f_{c} b ξ_{n} h_{0} \frac{ε_{0}}{ε_{c u}} (\frac{1}{2} + \frac{a_{r}}{12} + \frac{1}{2 b_{r}} F_{1})

(12)

Where

F_{1}

and

F_{2}

are functions of

ε_{0}

ε_{c u}

and

b_{r}

, respectively

F_{1} = - 2 \arctan (F_{2}) (- 1 + 2 b_{r}) F_{2} + \ln [\frac{ϵ_{c u}}{ϵ_{0}} + b_{r} {(- 1 + \frac{ε_{c u}}{ε_{0}})}^{2}] + 2 \arctan {[1 + 2 b_{r} (- 1 + \frac{ε_{c u}}{ε_{0}})] F_{2}} (- 1 + 2 b_{r}) F_{2}

(13)

F_{2} = \frac{1}{\sqrt{- 1 + 4 b_{r}}}

(14)

The distance between the equivalent pressure force and the edge of the compression zone (𝑦_c) is calculated according to the moment balance $\sum M_{y} = 0$ as

y_{c} = ξ_{n} h_{0} - \frac{(\int_{0}^{1} [a_{r} x + (3 - 2 a_{r}) x^{2} + (a_{r} - 2) x^{3}] x d x + \int_{1}^{\frac{ε_{c u}}{ε_{0}}} \frac{x^{2}}{b_{r} {(x - 1)}^{2} + x} d x)}{(\int_{0}^{1} [a_{r} x + (3 - 2 a_{r}) x^{2} + (a_{r} - 2) x^{3}] d x + \int_{1}^{\frac{ε_{c u}}{ε_{0}}} \frac{x}{b_{r} {(x - 1)}^{2} + x} d x)}

(15)

The solution is

{y_{c} = ξ}_{n} h_{0} (1 - \frac{ε_{0}}{ε_{c u}} \frac{21 b_{r}^{2} + {2 a}_{r} b_{r}^{2} + 30 F_{3}}{5 b_{r} (6 b_{r} + a_{r} b_{r} + 6 F_{1})})

(16)

Where 𝐹₃ is a function of ε₀, ε_cu and b_r, respectively.

F_{3} = {[1 + 2 b_{r} (- 1 + \frac{ε_{c u}}{ε_{0}})] F_{2}} (1 - 4 b_{r} + 2 b_{r}^{2}) F_{2} + \frac{2 b_{r} ε_{c u}}{ε_{0}}

(17)

Incorporating equation (1) and equation (2) or equation (3) into equation (12) and equation (16), the equivalent stress diagram coefficients 𝛼₁ and 𝛽₁ of recycled concrete can be calculated, and the two have the following relationship with 𝐶 and 𝑦_c

β_{1} = \frac{2 y_{c}}{ξ_{n} h_{0}} = 2 - \frac{(42 + {4 a}_{r}) b_{r}^{2} + 60 F_{3}}{5 b_{r} [(6 + a_{r}) b_{r} + 6 F_{1}]}

(18)

α_{1} = \frac{C}{2 y_{c} f_{c} b} = \frac{1}{β_{1}} \frac{C}{{f_{c} b h}_{0} ξ_{n}} = \frac{5 ((6 + a_{r}) b_{r} + 6 F_{1}) b_{r} [(6 + a_{r}) b_{r} + 6 F_{1}]}{24 b_{r} ((21 + {2 a}_{r}) b_{r}^{2} + 30 F_{3} - 5 b_{r} [(6 + a_{r}) b_{r} + 6 F_{1}])}

(19)

In Code for Design of Concrete Structures (GB 50010-2010, 2015), the $α_{1}$ and $β_{1}$ calculation formulas are

α_{1} = \frac{1}{β_{1}} (1 - \frac{1 ε_{0}}{3 ε_{c u}})

(20)

β_{1} = \frac{1 - \frac{2 ε_{0}}{3 ε_{c u}} + \frac{1}{6} {(\frac{ε_{0}}{ε_{c u}})}^{2}}{1 - \frac{1 ε_{0}}{3 ε_{c u}}}

(21)

When the concrete strength grade is less than C50, the values of 𝛼₁ and 𝛽₁ calculated by equation (20) and equation (21) for NC are 0.969 and 0.824, respectively, and the approximate values 1.0 and 0.8 are taken in the specification. According to the equivalent method of equivalent rectangular block in the concrete pressure zone, the stress distribution is the same as that of the concrete stress-strain curve in [0, ε/ε_cu]. As shown in Figure 2, it can be known that 𝛼₁ and 𝛽₁ represent the height and the width of the equivalent rectangular block respectively.

Verification of calculation method of equivalent stress distribution through FEA

The finite element method was used to simulate the bending failure process of recycled concrete beams, and the experimental dimensions of recycled concrete beams by Wang and Zhang (2016) were used for modeling and simulation analysis.

In the finite element analysis, the concrete adopts a damage plastic constitutive model (Concrete Damaged Plastic Model). The model includes dilation angle (Dilation Angle) 𝜓, flow potential offset (Eccentricity) 𝜖, biaxial compression and uniaxial compression stress ratio σ_b0/σ_c0, invariant stress ratio 𝐾_𝑐, and viscosity coefficient 𝜇. The dilatancy angle is the angle between the actual plastic strain ε and the shear strain 𝛾. In the Mohr-Coulomb criterion, the plastic angle 𝜙 is replaced by the dilatancy angle 𝜓, and the potential function G of the Mohr-Coulomb criterion is (Drescher and Detournay, 1993)

G = \frac{1}{2} (σ_{1} - σ_{2}) + \frac{1}{2} (σ_{1} + σ_{3}) \sin ψ - c c o s ψ = 0

(22)

The three-dimensional model is used in the simulation, which is the three-dimensional stress state. The triaxial strength test data of recycled concrete obtained by Wang et al. (2021) is selected, and the above formula is used to fit the three-dimensional failure parameters of recycled concrete. The results are listed in Table 1. The dilatancy angle of recycled concrete gradually decreases with the increase in the replacement ratio of recycled coarse aggregate.

Table 1.

Three-dimensional failure parameters.

	Dilation angle (°)	Cohesion (MPa)	R²
NC	34.01	7.336	0.83
RC50	32.73	6.311	0.73
RC100	30.68	6.096	0.63

Using the data in Table 1 to regress, the dilatancy angle of recycled concrete and the replacement ratio of recycled coarse aggregate have the following linear relationship

ψ = - 3.33 r + 34.139, R^{2} = 0.98269

(23)

The axial compressive strength 𝑓_c and the tensile strength 𝑓_t are determined by the relationship between the strength grade of recycled concrete 𝑓_c and 𝑓_t in the Specifications for Design of Concrete Structures (GB 50010-2010, 2015) and Technical Specification for Application of Recycled Aggregate Concrete (DG/TJ 08-2020-2007, 2007), and the regression results are obtained as the following relationships

f_{t, R A C} = - 0.001429 f_{c, R A C}^{2} + 0.1026 f_{c, R A C} + 0.238, R^{2} = 1.00

(24)

Among them, 𝑓_t, RAC is the tensile strength of recycled concrete, and 𝑓_c, RAC is the compressive strength of recycled concrete.

Axial compressive strength is evaluated from the cubic compressive strength reported by Wang and Xiao (2018). From the cubic compressive strengths of 31.80 MPa and 31.27 MPa when the replacement ratio of recycled concrete is 0% and 100%, 𝑓_c is calculated to be 24.53 MPa and 24.65 MPa, respectively. Because the ratio of the axial compressive strength of recycled concrete to the cubic compressive strength is greater than that of natural aggregate concrete (Xiao, 2018), when the two cubic compressive strengths are similar, the axial compressive strength of recycled concrete is slightly higher. The calculated 𝑓_t of the two concretes are 2.44 MPa and 2.41 MPa, respectively. Select the stress and strain value at 0.3𝑓_c and 0.7𝑓_c to calculate the elastic modulus. The Poisson’s ratio of concrete shall be 0.2 according to Technical Regulations for Application of Recycled Aggregate Concrete. The beam span is 1.75 m, the cross-section width is 150 mm, and the height is 280 mm. Since the finite element model can reflect the influence of size, it can be verified with test results different from the actual size. The values used for the simulation of NC beams and 100% recycled coarse aggregate concrete (RAC100) beams are shown in Table 2.

Table 2.

Simulation parameters.

r	E (GPa)	v	ft (MPa)	fc (MPa)	$ψ$ (°)	$ϵ$	$σ_{b 0} / σ_{c 0}$	$K_{c}$	$μ$
0	37.42	0.2	2.44	24.53	34.14	0.1	1.16	2/3	0.005
100	31.31	0.2	2.41	24.65	30.81	0.1	1.16	2/3	0.005

The compression damage factor is calculated according to the formula in Abaqus Analysis User’s Manual (6.14) (SIMULIA, 2014), the compression damage factor 𝑑_c and the tensile damage factor 𝑑_t are respectively

d_{c} = \frac{(1 - β_{c}) {\tilde{ε}}_{c}^{i n} E_{0}}{σ_{c} + (1 - β_{c}) {\tilde{ε}}_{c}^{i n} E_{0}}

(25)

d_{t} = \frac{(1 - β_{t}) {\tilde{ε}}_{t}^{i n} E_{0}}{σ_{t} + (1 - β_{t}) {\tilde{ε}}_{t}^{i n} E_{0}}

(26)

Among them, 𝛽_c and 𝛽_t are the proportion of plastic strain in the inelastic strain during tension and compression respectively; ${\tilde{ε}}_{c}^{i n}$ and ${\tilde{ε}}_{t}^{i n}$ are the inelastic strain under tension and the inelastic strain under compression, respectively. Using equation (1) and incorporating the a_r and b_r parameters of equation (2), and the ε₀ of equation (5), the damage constitutive under different recycled coarse aggregate replacement ratios are calculated.

Based on the ABAQUS software, the finite element model for the recycled concrete beam is established shown in Figure 3(a), same as the experimental specimen in the previous literature (Wang and Xiao, 2018), and the longitudinal reinforcement and stirrup are shown in Figure 3(b). The width, height, and length directions of the model correspond to the X axis, Y axis and Z axis of the system coordinates respectively. In order to increase the accuracy of the calculation, while considering the calculation efficiency, the calculation unit is more finely meshed in the middle area of the beam.

Figure 3.

Recycled aggregate concrete beam mode. (a). Finite element mesh, (b). Rebar.

The reinforcement unit is embedded in the concrete. The load is applied by the distribution beam in the middle area, which increases linearly with the load step. Using static calculation, after each step of load is stabilized, the next level of load is applied, and the calculation step length is automatically optimized by the software, and the calculation is performed until the beam is broken.

The beam model was generated using a ABAQUS script program developed in Python. Concrete and reinforcement are modeled separately using C3D8R elements and T3D2 elements, respectively. Since the beam divided by the plane of longitudinal reinforcement bars and stirrups during generation, the entire model satisfies the conditions of map meshing, so the beam was meshed into regular hexahedral meshes. At the support positions of the beam, the nodes along the thickness direction are constrained with hinge and sliding constraints respectively. Reinforcement embedded in concrete by overlapping nodes.

The simulated flexural bearing capacities of concrete beams with 0% and 100% recycled coarse aggregate replacement ratios are 37.28kN·m and 29.97kN·m, respectively, and the test results are 34.90kN·m and 31.38kN·m, the errors are 6.8% and 4.5%, the simulation effect is good. Using the revised α₁ and β₁ in this paper, the calculated flexural bearing capacities of concrete beam are 33.13 MPa and 29.50 MPa at 0% and 100% replacement ratio of recycled aggregate, respectively, with errors of 5.1% and 6.0%, respectively. The prediction effect of the calculation formula is good. The flexural bearing capacities of concrete beams calculated by specification is 32.17 MPa and 32.12 MPa. When the replacement ratio of recycled aggregate increases from 0% to 100%, the flexural bearing capacity only changes by 0.1%, while the experimental result changes by 10%. And when the replacement ratio of recycled aggregate is 100%, the calculated value is higher than the experimental value. This may leady to poor safety.

In order to study the influence of recycled concrete on the bending performance of beams in engineering, the size of the finite element model was modified and the model shown in Figure 4(a) was established. The revised beam length is 6.43 m, and the span is 6m. The beam has a width of 300 mm and a height of 700 mm. The bottom longitudinal ribs are 2 HRB335 with the diameter of 22 mm and 2 HRB335 with the diameter of 18 mm, the top longitudinal rib is 2 HRB335 with the diameter of 18 mm, the stirrup is HPB235 with the diameter of 8 mm, and the spacing is 200 mm, as shown in Figure 4(b). The load is loaded by distribution beams, which are respectively loaded at a distance of 1.8 m from the support, and the shear-span ratio is between 1 and 3. The width, height and length of the beam correspond to the X axis, Y axis and Z axis of the system coordinates respectively. The material parameters of the concrete in the model still use the parameters in Table 2 of the material.

Figure 4.

Revised recycled aggregate concrete beam mode. (a). Finite element mesh, (b). Rebar.

The replacement ratios of recycled coarse aggregates of 0, 30%, 50%, and 100% are selected respectively, and the equal water-cement ratio design is adopted. The concrete stress-strain model of Xiao (2007) was select. The simulation results and calculation results of the limit bending moment of the beam after changing the parameters are shown in Table 3. In the table, M_us is the simulated value, and M_uc is the value calculated according to the revised

α_{1}

and

β_{1}

in this paper.

M_{u c} = α_{1} f_{c} b x (h_{0} - \frac{x}{2})

(27)

Where,

α_{1}

is the revised

α_{1}

in this paper. The simulation result is good. It can be seen from Table 3 that at the 100% replacement ratio of recycled aggregate, without considering the change of 𝛼₁ and 𝛽₁, the error between calculation and simulation is 16%; when considering the change of 𝛼₁ and 𝛽₁, the error is reduced to 4%. It is obtained by simulation that the reduction of the limit bending moment with the increase of the replacement ratio of recycled coarse aggregate is greater than that of NC, indicating that there are still some nonlinear characteristics that cannot be reflected in the calculation.

Table 3.

Comparison of simulation and calculation results.

r	M_us (kN·m)	M_uc (kN·m)	M_us/M_uc
0	372.60	314.29	1.186
30	347.76	313.34	1.110
50	339.48	312.78	1.085
100	322.92	311.59	1.036

Results and discussion

Effect of replacement ratio of RCA and compressive strength on 𝛼₁ and 𝛽₁

The influence of 𝑓_cu on ε_u is given in the specification (GB 50010-2010, 2015)

ε_{c u} = 0.0033 - (f_{c u} - 50) \times 10^{- 5}

(28)

The influence of r on ε₀ is given in equation (5). Using the equation (5), the contour of ε₀ is shown in Figure 5. It can be seen from Figure 7 that as the replacement ratio of recycled coarse aggregate increases, the peak strain increases with the increase in the compressive strength of the cube. From the experimental results of Xiao (2007), The variation of ε_cu with r is showed in Figure 6. It can be seen from the figure that the mean value of the data changes very little and has great fluctuations. The confidence band of data completely, shown in Figure 6, includes all data points, indicating that the data changes with the change of RCA replacement ratio are caused by the larger data dispersion. With equation (1) and the established stress-strain curve of recycled concrete under uniaxial action, when the strength of concrete with different recycled aggregate replacement ratios is 30 MPa, the descending section of the calculated stress-strain is significantly reduced after adding recycled aggregate.

Figure 5.

Influence of 𝑓_cu and 𝑟 on ɛ₀.

Figure 7.

Influence of 𝑓_𝑦 and 𝐸_𝑠 on x.

Figure 6.

The variation of ɛ_cu with 𝑟.

The height of the compression zone x is related to the 𝑓_y and 𝐸_s of the steel bars, and the relationship is shown in Figure 7. As 𝑓_y decreases and 𝐸_s increases, ε_n gradually increases. Taking equation (5) and equation (28) into equation (18) and equation (19), the parameters 𝛼₁ and 𝛽₁ of recycled aggregate concrete are derived.

Xiao’s experimental data (Xiao, 2007) is used to analyze the correlation between $f_{c u}$ and $ρ_{r}$ , and the Pearson correlation between them is 0.945. The correlation is significant at the level of 0.05 (double tail). Therefore, the $ρ_{r}$ in equation (7) can be removed, the relationship between $f_{c u}$ and $ρ_{r}$ can be obtained by linear fitting as

ρ_{r} = 0.0744 f_{c u} - 142.89, R^{2} = 0.90

(29)

Take it into equation (7), then obtained

f_{c} = (8.51 + 0.5047 f_{c u}) * (1 + \frac{r}{106 - 93.85 r^{2}}), R^{2} = 0.97

(30)

From equation (5), equation (6), equation (13), equation (14), equation (17), equation (18), equation (19), equation (28) and equation (30), $α_{1}$ and $β_{1}$ can be calculated. Since the final formulas of $α_{1}$ and $β_{1}$ are more complicated, selected calculating the values at different recycled aggregate replacement ratios and cubic compressive strengths and by fitting to obtain the equations. The following equation are obtained by fitting

α_{1} = 0.8024 - 0.5157 r + 0.002281 f_{c u} + 0.329 r^{2} + 0.002041 r \cdot f_{c u}, R^{2} = 0.995

(31)

β_{1} = 0.9401 - 0.1216 r + 0.001825 f_{c u} + 0.1062 r^{2} + 0.001538 r \cdot f_{c u}, R^{2} = 0.995

(32)

The changes as the influence of r and 𝑓_cu are shown in Figure 8(a) and Figure 8(b), respectively. When the replacement ratio of recycled aggregate is low, namely below 50 MPa, the decrease of 𝛼₁ is faster, and the decrease ratio gradually slows down with the increase of the replacement ratio. Under the same recycled aggregate replacement ratio, as the strength increases, the 𝛼₁ of recycled concrete slowly decreases. The variation range of 𝛼₁ is 0.27. 𝛽₁ decreases with the increase of the strength of recycled concrete, increases at first and then decreases with the increase of the replacement ratio of recycled aggregate. The variation range of 𝛽₁ is 0.167.

Figure 8.

Influence of 𝑓_𝑐u and 𝑟. (a). 𝛼₁, (b). 𝛽₁.

Using the ratio of the ultimate strain and the peak strain of the stress-strain curve of recycled concrete as a variable, use the different stress drop to determine the ultimate strain of recycled concrete, we can obtain the relation of 𝛼₁ and 𝛽₁ with the replacement ratio of recycled coarse aggregate and the stress drop amplitude at the limit state (σ_cu/𝑓_c), as shown in Figure 9. The light-colored curved surface in Figure 9 is the result of calculation using the parameters of equation (2), and the dark-colored curved surface is the result of calculation using equation (3). It can be seen from Figure 9 that the stress in the limit state has a greater impact on each parameter. As the stress increase during failure, 𝛼₁ shows an increasing trend, and 𝛽₁ shows a decreasing trend.

Figure 9.

Equivalent rectangular parametric surface of recycled concrete pressure zone. (a). 𝛼₁, (b). 𝛽₁.

In the study of Xiao (2007), when the stress of stress-strain curve is reduced to 85% of the peak stress, the corresponding strain is the ultimate strain, and the corresponding strain is shown in Figure 10. In Figure 10, the replacement ratio of zero recycled aggregate corresponds to the value in the specification. The 𝛼₁ and 𝛽₁ are shown in Figure 11, when the replacement ratio of recycled aggregate is 0% and 100%. From Figure 11, it can be seen that 𝛼₁ and 𝛽₁ decrease after mixing with recycled aggregate. When the replacement ratio of recycled coarse aggregate is 100%, the value of 𝛼₁ decreases by 2%, and the value of 𝛽₁ decreases by 6%. The value calculated by Wang and Xiao (2018) is in the middle of the value calculated by the standard and the value calculated by Wang and Xiao (2007) and Xie et al. (2018).

Figure 10.

Relationship between ultimate compressive strain and replacement ratio of recycled coarse aggregate.

Figure 11.

Comparison of 𝛼₁ and 𝛽₁ before and after add recycled aggregate.

When the replacement ratio of recycled coarse aggregate changes, the change of 𝛼₁ is expressed by the change of the rising section coefficient $a_{r}$ , the falling section coefficient $b_{r}$ of the stress-strain curve, and the ratio of the ultimate strain to the peak strain ε_r = ε_cu/ε₀

α_{1} = f (a_{r} (r), b_{r} (r), ε_{r} (r))

(33)

Therefore, the change of 𝛼₁ caused by the replacement ratio of recycled coarse aggregate r can be decomposed into the change of 𝛼₁ corresponding to the change of the rising section curve caused by r, the change of 𝛼₁ corresponding to the change of the falling section curve caused by r, and the ultimate strain caused by r, represented as $\frac{\partial α_{1}}{\partial a_{r}}$ , $\frac{\partial α_{1}}{\partial b_{r}}$ and $\frac{\partial α_{1}}{\partial ε_{r}}$ respectively

\frac{d α_{1}}{d r} = \frac{\partial α_{1}}{\partial a_{r}} d r + \frac{\partial α_{1}}{\partial b_{r}} d r + \frac{\partial α_{1}}{\partial ε_{r}} d r

(34)

Similarly, the change of 𝛽₁ caused by the replacement ratio of recycled coarse aggregate r is decomposed into the change of 𝛽₁ corresponding to the change of the rising section curve, the change of 𝛼₁ corresponding to the change of the falling section curve, and the ultimate strain caused by r respectively, using $\frac{\partial β_{1}}{\partial a_{r}}$ , $\frac{\partial β_{1}}{\partial b_{r}}$ and $\frac{\partial β_{1}}{\partial ε_{r}}$ to indicate

\frac{d β_{1}}{d r} = \frac{\partial β_{1}}{\partial a_{r}} d r + \frac{\partial β_{1}}{\partial b_{r}} d r + \frac{\partial β_{1}}{\partial ε_{r}} d r

(35)

Figure 12 is the effect of recycled aggregate replacement ratio on the coefficients of the rising and falling sections of the stress-strain curve. Using equation (31) and equation (32), take the partial derivatives of $α_{1}$ and $β_{1}$ to $a_{r}$ , $b_{r}$ and $ε_{r}$ , to obtain their effects on $α_{1}$ and $β_{1}$ , respectively. The changes of $\frac{\partial α_{1}}{\partial a_{r}}$ , $\frac{\partial α_{1}}{\partial b_{r}}$ and $\frac{\partial α_{1}}{\partial ε_{r}}$ are shown in Figure 12(a). It can be seen from Figure 12(a) that the changes of $\frac{\partial β_{1}}{\partial a_{r}}$ , $\frac{\partial β_{1}}{\partial b_{r}}$ and $\frac{\partial β_{1}}{\partial ε_{r}}$ are (−0.1193, 0.0271), (−4.6834, −0.5346) and (0.0209, 0.0246). $\frac{\partial α_{1}}{\partial b_{r}}$ has the largest change, indicating that the descending segment has the greatest impact on 𝛼₁. With the increase of the replacement ratio of recycled coarse aggregate, the change of the decreasing section of the stress-strain curve leads to a decrease of 𝛼₁, and the decreasing amplitude gradually slows down with the increase of the replacement ratio of recycled coarse aggregate. The obtained 𝛽₁ changes with the replacement ratio of recycled coarse aggregate, and the changes of $\frac{\partial β_{1}}{\partial a_{r}}$ , $\frac{\partial β_{1}}{\partial b_{r}}$ and $\frac{\partial β_{1}}{\partial ε_{r}}$ are shown in Figure 12(b). It can be seen from Figure 12(b) that the changes of $\frac{\partial β_{1}}{\partial a_{r}}$ , $\frac{\partial β_{1}}{\partial b_{r}}$ and $\frac{\partial β_{1}}{\partial ε_{r}}$ are (−0.0304, 0.1168), (−7.8230, –1.0352) and (0.0417, 0.0426). The large change of $\frac{\partial β_{1}}{\partial b_{r}}$ indicates that the descending segment has a greater impact on 𝛽₁. With the increase of the replacement ratio of recycled coarse aggregate, the change of the decreasing section of the stress-strain curve causes 𝛽₁ becomes larger, and the increasing range gradually increases with the increase of the replacement ratio of recycled coarse aggregate.

Figure 12.

Effect of recycled aggregate replacement ratio on the coefficients of the rising and falling sections of the stress-strain curve. (a). Coefficients of the rising sections, (b). Coefficients of the falling sections.

Effect of replacement ratio of RCA and compressive strength on bending capacity

When the beam fails, the crushing of the concrete in the compression zone and the yielding of the reinforcement in the tension zone occur simultaneously, the limiting relative height of the compression zone, is obtained from the cross-sectional stress distribution at the time of the failure (GB 50010-2010, 2015).

ξ_{b} = \frac{β_{1}}{1 + \frac{f_{y}}{E_{s} ε_{cu}}}

(36)

HRB400 steel reinforcements according to the Chinese standard are used, the $f_{y}$ and $E_{s}$ of which are 360 MPa and 2 × 10⁵ MPa respectively. 𝛽₁ and ε_cu of different replacement ratios of recycled aggregates are calculated with equation (21) and equation (28). The effect of replacement ratio of RCA and compressive strength on bending capacity were analyzed by the variable parameter analysis method, and the results are shown in Figure 13. The results of different replacement ratios of recycled aggregate and strength grades are shown in Figure 13(a).

Figure 13.

Variable parameter analysis results. (a). Maximum section resistance moment, (b). Maximum reinforcement ratio, (c). Maximum reinforcement ratio, (d). Relative pressure zone height, (e). Longitudinal reinforcement ratio.

It can be seen from Figure 13(a) that when the strength grade of recycled concrete is below 50 MPa, the increase of recycled aggregate leads to ξ_b a first decrease and then a slight increase. When the replacement ratio of recycled aggregate is 70%, ξ_b is the minimum, and it is reduced by 19% compared to natural concrete. When the replacement ratio larger than 70%, ξ_b increase by 2% than that in 70% replacement ratio. Relative to the previous decline, this stage can be considered to remain unchanged. The variation in the relative height of the compression zone is fitted as

ξ_{b} = 0.5039 - 0.2596 r + 0.1844 r^{2}, R^{2} = 0.98

(37)

Where, r is the replacement ratio of recycled aggregates. The slight increase in the later stage is due to the low elastic modulus of recycled concrete with the same strength as conventional concrete, which led the ε₀ of equation (5) increases with the increase of the replacement ratio of recycled aggregate. With the increase of the replacement ratio of recycled aggregates, the stress-strain drop stage becomes steeper. The combined effect of the two causes the ultimate strain of recycled concrete not to decrease monotonically, and cause ξ_b not to change in monotonically decreasing. Considering the balance condition of beam axial force ( $\sum X = 0$ ) and moment balance condition ( $\sum M = 0$ ) respectively, the simplified basic formula for calculating ultimate flexural bearing capacity of single-bar rectangular cross-section is obtained (GB 50010-2010, 2015)

α_{1} f_{c} b x = f_{y} A_{s}

(38)

M_{u} = α_{1} f_{c} b x (h_{0} - \frac{x}{2}) = f_{y} A_{s} (h_{0} - \frac{x}{2})

(39)

Since $ξ = \frac{x}{h_{0}}$ , brought $ξ_{b}$ into equation (38) and equation (39), it can be got

M_{u, \max} = α_{1} f_{c} b h_{0}^{2} ξ_{b} (1 - 0.5 ξ_{b})

(40)

The maximum sectional resistance moment M_u,max of recycled concrete under different strength grades of recycled concrete and the replacement ratio of recycled aggregate are calculated as shown in Figure 13(b).

From Figure 13(b), it can be seen that the strength grade of recycled concrete and the replacement ratio of recycled aggregate have an effect on M_u,max. The effect of strength grade to M_u,max is constant at different replacement ratios of recycled aggregates and M_u,max has an increase of 95kN·m for every 5 MPa strength grade increase.

Under the same strength grade, with the increase of the replacement ratio of recycled aggregates, M_u,max is gradually slowing parabolic decline, and the decline amplitude is at most 15.7%. Fit the surface, it can be got

M_{u, \max} = - 56.76 + 17.47 S_{g} - 152.6 r - 2.608 S_{g} \cdot r + 164.8 r^{2}, R^{2} = 0.99

(41)

Where S_g is the strength grade of concrete. The maximum reinforcement ratio of recycled concrete beams can be obtained by taking $ξ_{b}$ into equation (38) and equation (39), which is shown in equation (42)

ρ_{\max} = ξ_{b} \frac{α_{1} f_{c}}{f_{y}}

(42)

Figure 13(c) shows the 𝜌_max at different strength grades and the replacement ratios of recycled aggregates.

It can be seen from Figure 13(c) that both the strength grade of recycled concrete and the replacement ratio of recycled aggregate have effects on 𝜌_max. Among them, the effect of strength grade is relatively small. Under different replacement ratios of recycled aggregates, the strength grade increases by 0.4% for every 5 MPa increase. Under a same strength grade, with the increase of the replacement ratio of recycled aggregates, 𝜌_max shows a gradual slowing parabolic increase, and the increase amplitude is at most 20.4%. Fit the surface, it can be got

ρ_{\max} = - 0.00218 + 0.0007989 C - 0.009587 r - 0.0001542 C \cdot r + 0.01031 r^{2}, R^{2} = 0.99

(43)

From equation (38) and equation (39), these can be obtained

x = \frac{α_{1} f_{c} b h_{0} - \sqrt{{(α_{1} f_{c} b h_{0})}^{2} - 2 α_{1} f_{c} M_{u}}}{α_{1} f_{c} b}

(44)

A_{s} = \frac{α_{1} f_{c} b h_{0} - \sqrt{α_{1} f_{c} b (α_{1} f_{c} b {h_{0}}^{2} - 2 M_{u})}}{f_{y}}

(45)

Bring the parameters in a project into equation (38) and equation (39), the height x of the concrete compression zone and the reinforcement area at different ratios of recycled aggregate replacement can be determined. Referring to the Chinese specification for recycled concrete structures, HRB400 steel bars commonly used in buildings and C20 - C50 strength grade concrete are used. M_u takes 80kN·m. The section size of the beam selected 250 mm × 600 mm. The compressive strength of concrete of C20, C25, C30, C35, C40, C45 and C50 are 9.6 MPa, 11.9 MPa, 14.3 MPa, 16.7 MPa, 19.1 MPa, 21.1 MPa and 23.1 MPa (GB 50010-2010, 2015).

Since $ξ = \frac{x}{h_{0}}$ , from equation (41), it can be got

ξ = \frac{α_{1} f_{c} b h_{0} - \sqrt{{(α_{1} f_{c} b h_{0})}^{2} - 2 α_{1} f_{c} M_{u}}}{α_{1} f_{c} b h_{0}}

(46)

Since $ρ = \frac{A_{s}}{b h_{0}}$ , From equation (42), it can be got

ρ = \frac{α_{1} f_{c} b h_{0} - \sqrt{α_{1} f_{c} b (α_{1} f_{c} b {h_{0}}^{2} - 2 M_{u})}}{b h_{0} f_{y}}

(47)

Taking equation (27) and equation (29) into equation (33), it can be got

ξ_{b} = \frac{β_{1} E_{s} (f_{cu} - 380)}{E_{s} (f_{cu} - 380) - 100000 f_{y}}

(48)

Taking equation (45) into equation (37), it can be got

M_{u, \max} = \frac{0.5 b E_{s} f_{c} (f_{cu} - 380) h_{0} α_{1} β_{1} (200000 f_{y} + E_{s} (380 β_{1} - 2) - 760)}{{(E_{s} (f_{cu} - 380) - 100000 f_{y})}^{2}}

(49)

Taking equation (45) into equation (39), it can be got

\begin{array}{l} ρ_{\max} = \frac{E_{s} (3652 + 34.5 r - 3233.8 r^{2} + f_{cu} (207 + 1.95 r - 183 r^{2})) α_{1} β_{1}}{(E_{s} (f_{cu} - 380) - 100000 f_{y}) f_{y} (r^{2} - 1.13)} + \\ \frac{f_{cu}^{2} (0.505 r^{2} - 0.00538 r - 0.57) α_{1} β_{1}}{(E_{s} (f_{cu} - 380) - 100000 f_{y}) f_{y} (r^{2} - 1.13)} \end{array}

(50)

According to equation (43) into equation (47), variable parameter analysis results are shown in Figure 13. It can be seen from Figure 13(d) that the strength grade has a great influence on ξ, and with the increase of concrete strength grade, ξ gradually decreases. When the strength grade of concrete remains unchanged, with the increase of the replacement ratio of recycled aggregate, ξ shows an increasing trend. When the strength grade of concrete is lower, the effect of the replacement ratio of recycled aggregate is more pronounced. When the concrete strength grade is C20 and the beam with 100% recycled aggregate replacement ratio, ξ increases by 8%. When the concrete strength grade is C50 and the beam with 100% recycled aggregate replacement ratio, ξ increases by 4%. Fit the surface, it can be got

ξ = 1.66 - 0.06704 C + 0.06305 r + 0.0007513 C^{2} - 0.001268 C \cdot r, R^{2} = 0.97

(51)

The calculated relative pressure zone height ξ under different strength grades and the replacement ratio of recycled aggregate is shown in Figure 13(e).

It can be seen from Figure 13(e) that the strength grade has a great influence on 𝜌, and with the increase of concrete strength grade, 𝜌 gradually decreases. The increase of recycled aggregate leads to an increase in 𝜌, but the increase is small, only 0.35%. Fit the surface, it can be got

ρ = 3.18 \times 10^{- 3} - 1.42 \times 10^{- 5} C + 1.03 \times 10^{- 5} r + 1.50 \times 10^{- 7} C^{2} - 1.76 \times 10^{- 7} C \cdot r, R^{2} = 0.98

(52)

Conclusion

Based on the stress-strain relationship, peak strain and other concrete mechanical parameters of recycled concrete, calculation of recycled concrete beams under bending are analyzed. The value and change law of the relevant calculation parameters equivalent to the rectangular distribution of the compressive stress of recycled concrete beams are studied. The following conclusions can be obtained:

1. For recycled concrete with a strength grade lower than 50 MPa, based on the nonlinear constitutive of recycled concrete, the equivalent rectangular block parameters, 𝛼₁ and 𝛽₁ was be deduced. The parameter 𝛼₁ is increased significantly at first, and then keeps stable with the increase of replacement ratio of recycled aggregate. Besides, the decreasing trend is found for the parameter 𝛼₁ as the strength grade increases. When the above factors change, the maximum variation amplitude of 𝛼₁ is 27%. 𝛽₁ is increased in the initial stage and then decreased as the increase in the replacement ratio of recycled aggregate. And 𝛽₁ is decreased with the increase in the strength grade of recycled concrete. When the above factors change, the maximum variation amplitude of 𝛽₁ is 0.16.

2. It is verified by ABAQUS that the calculation method in this paper can better reflect the difference in flexural capacity of recycled concrete and conventional concrete beams, as well as different recycled concrete beams. At the 100% replacement ratio of recycled aggregate, without considering the change of 𝛼₁ and 𝛽₁, the error between calculation and simulation is 16%; when considering the change of 𝛼₁ and 𝛽₁, the error is reduced to 4%.

3. With the increase in replacement ratio of recycled aggregate, the relative height of the limiting compression zone ξ_b of recycled concrete is reduced by 19% at 70% recycled aggregate replacement ratio, and remain unchanged at higher replacement ratio. The ultimate flexural bearing capacity M_u,max, is reduced by a maximum of 15.7% as the replacement ratio of recycled aggregate increased from 0% to 100%. With the increase in replacement ratio of recycled aggregate, the maximum reinforcement ratio 𝜌_max is gradual parabolic increase, and the max amplitude is at most 20.4%. With the replacement ratio increase, the relative height of the limiting compression zone ξ increase and the reinforcement ratio 𝜌 decrease. Under the beam size and loads assumed in this paper, the change of ξ and 𝜌 are 4%–8% and 0.35%.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors would like to acknowledge the financial support of the National Natural Science Foundation (NSFC) of PR China (Nos. 52078370, 51778463).

ORCID iD

Tan Li

References

Choi

Yun

(2013) Long-term deflection and flexural behavior of reinforced concrete beams with recycled aggregate. Materials & Design 51: 742–750.

Choi

Yun

Kim

(2012) Flexural performance of reinforced recycled aggregate concrete beams. Magazine of Concrete Research 64(9): 837–848.

Deng

(2010) Experimental studies of flexural strength and mechanics performance for recycled concrete beam. 2nd International Conference on Waste Engineering and Management, Tongji Univ, Shanghai, Peoples R China, RILEM Publications.

Deresa

Demartino

, et al. (2020) A review of experimental results on structural performance of reinforced recycled aggregate concrete beams and columns. Advances in Structural Engineering 23(15): 3351–3369.

DG/TJ 08-2020-2007 (2007) Technical Code on the Application of Recycled Concrete. Shanghai: Tongji University Press.

Drescher

Detournay

(1993) Limit load in translational failure mechanisms for associative and nonassociative materials. Geotechnique 43(3): 443–456.

GB 50010-2010 (2015) Code for Design of Concrete Structures. Beijing, China: Architecture & Building Press.

Ghisellini

Liu

et al. (2018) Evaluating the transition towards cleaner production in the construction and demolition sector of China: a review. Journal of Cleaner Production 195: 418–434.

Guo

(2004) Strength and Constitutive Relations of Concrete-Principles and Applications. Beijing: China Construction Industry Press.

10.

Mahdi

Adam

Jeffery

et al. (2015) An experimental study on flexural strength of reinforced concrete beams with 100% recycled concrete aggregate. Engineering Structures 88: 154–162.

11.

Sato

Maruyama

Sogabe

, et al. (2007) Flexural behavior of reinforced recycled concrete beams. Journal of Advanced Concrete Technology 5(1):43–61.

12.

SIMULIA (2014) Abaqus analysis user’s guide.

13.

Sindy

Belen

Fernando

, et al. (2018) Flexural performance of reinforced concrete beams made with recycled concrete coarse aggregate. Engineering Structures 156: 32–45.

14.

Tosic

Marinkovic

Ignjatovic

(2016) A database on flexural and shear strength of reinforced recycled aggregate concrete beams and comparison to Eurocode 2 predictions. Construction and Building Materials 127: 932–944.

15.

Wang

Xiao

(2018) Evaluation of the stress-strain behavior of confined recycled aggregate concrete under monotonic dynamic loadings. Cement and Concrete Composites 87: 149–163.

16.

Wang

Zhang

(2016) Experiment on flexural behavior of recycled anti-bending concrete beam. Journal of Lanzhou University of Technology 42(2): 130–134.

17.

Wang

Deng

Xiao

, et al. (2021) Mechanical properties of recycled aggregate concrete under compression-shear stress state. Construction and Building Materials 271: 11.

18.

Wang

Xiao

Liu

, et al. (2022) Unloading and reloading stress-strain relationship of recycled aggregate concrete reinforced with steel/polypropylene fibers under uniaxial low-cycle loadings. Cement & Concrete Composites 131: 104597.

19.

Ding

Yang

(2010) Deflection of reinforced concrete beams with recycled coarse aggregate. 1st International Conference on Sustainable Urbanization (ICSU), Hong Kong Polytechn Univ, Fac Construct & Environm, Hong Kong, Peoples R China, Hong Kong Polytechnic Univ, Fac Construction & Environment.

20.

Xiao

(2007) Experimental investigation on complete stress-strain curve of recycled concrete under uniaxial loading. Journal of Tongji University(Natural Science) 11: 1445–1449.

21.

Xiao

(2018) Recycled Aggregate Concrete Structure. Berlin: Springer-Verlag.

22.

Xiao

Tawana

Huang

(2012) Review of studies on structural performance of recycled aggregate concrete in China. Science China Technological Sciences 55: 2727–2739.

23.

Xie

Ping

, et al. (2018) Analysis of stress-strain curves of recycled concrete under uniaxial compression. China Concrete and Cement Products (2): 95–100.

24.

Liu

Simi

, et al. (2022) Recycling and reuse of construction and demolition waste: from the perspective of national natural science foundation-supported research and research-driven application. Case Studies in Construction Materials 16:24.

25.

Yang

Park

Kim

, et al. (2020) Structural behavior of concrete beams containing recycled coarse aggregates under flexure. Advances in Materials Science and Engineering 2020: 8037131.

26.

Zhang

Peng

Liu

(2016) Experimental study on flexural behavior of modified recycled concrete beams. Proceedings of the 7th International Conference on Education, Management, Information and Computer Science (ICEMC 2017), Atlantis Press.

27.

Zhao

Sun

(2013) Experimental study of the recycled aggregate concrete beam flexural performance. In Kao

JCM

Sung

Chen

eds. Frontiers of Green Building, Materials and Civil Engineering Iii, Pts 1-3 368–370:1074-+ Switzerland: Trans Tech Publications Inc.

Calculation on flexural capacity of recycled aggregate concrete beams

Abstract

Keywords

Introduction

Comparative analysis of the constitutive relationships of recycled concrete

Calculation of equivalent stress distribution of recycled concrete

Verification of calculation method of equivalent stress distribution through FEA

Results and discussion

Effect of replacement ratio of RCA and compressive strength on 𝛼1 and 𝛽1

Effect of replacement ratio of RCA and compressive strength on bending capacity

Conclusion

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

References

Effect of replacement ratio of RCA and compressive strength on 𝛼₁ and 𝛽₁