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The main goal of this paper is to describe the mechanical behavior of the
*CDW* recycled concrete in compression, using an isotropic damage model adapted to the variation of the replacement rate of natural aggregates by recycled ones. The isotropic model by Mazars was used as a constitutive equation for the
*CDW* concrete and its adjustment parameters,
* A *and
*B*, were written as quadratic polynomials according to the aggregates replacement rate. The model was evaluated for conventional and recycled concretes. For the latter ones, the aggregates replacement ratios evaluated were 50% and 100%. The results show good approximation between the analytical and numerical values obtained with the adapted isotropic damage model and experimental concrete results for both compressive and flexural strength.

The description of the mechanical behavior of conventional concrete already has consistent analytical models in science. Models based on the theory of elasticity, plasticity, in the mechanics of fracture and damage and in their combinations, are able to describe the real phenomena in a broad sense. However, special concretes, such as recycled concretes, still need specific constitutive equations so to be analytically represented.

Recycled concrete, for example, shows a specific mechanical behavior as a consequence of the use of aggregates that show differentiated characteristics when compared to natural aggregates. The construction and demolition waste (CDW) composition and the aggregate production procedures result in the variability of the physical, chemical and mechanical characteristics of the aggregates that will considerably interfere in the mechanical behavior of the recycled concrete achieved.

Experimental studies of recycled concrete behavior have been carried out by number of researchers, evaluating concrete compressive and flexural strength [

Maruyama et al. [

The recycled concrete beam behavior under impact load was evaluated by Rao et al. [

It can thus be observed that the use of recycled aggregates from CDW for concrete production impairs the concrete properties in the hardened state due to specific characteristics, such as high heterogeneity of the recycled aggregates and their higher porosity [

In general the researches focusing on obtaining mathematical models that describe the recycled concrete behavior, are based on consistent models established for conventional concrete. The use of these models to design reinforced concrete members, despite being allowed by international standards, show some restrictions related to the type of the recycled aggregate and to the maximum replacement rate of the natural aggregate [

Xiao et al. [

Bhikshma and Kishore [

Du et al. [

The generalization of the conventional concrete constitutive models for recycled concretes is a big challenge for the researchers in this field. The variability in the gravimetric composition of recycled aggregates and the lack of experimental results are factors that hamper the broad validation of the existing analytical models.

Thus, the main goal of this study is to propose an analytical model that will incorporate the changes in the behavior of concrete resulting from the variation of the recycled aggregate contents and that will provide the adaptation and generalization needed due to the characteristics of the recycled aggregates. This study is also based on the hypothesis that an analytical model with parameters of explicit adjustment can be used. Furthermore, it can make possible such parameters sensitive to the variability of the recycled aggregate and be able to express the changes in the mechanical behavior of the recycled concrete depending on the aggregates replacement rate. Thereby this approach intends to describe the mechanical behavior of CDW recycled concrete in compression using the isotropic damage model by Mazars [

Seen from a mathematical point of view, the isotropic damage model proposed by Mazars [

Such a function for the uniaxial cases of load, can be written as follows

if

if

where,

σ = uniaxial strength

ε = deformation in the direction of load application

ε_{eq} = equivalent deformation

ε_{d}_{0} = peak deformation in tensile strength

E = initial longitudinal modulus of elasticity

D = damage

A and B = adjustment parameters that incorporate material characteristics

The contribution of each parameter in the mechanical behavior of the material can be obtained through an analysis of parametric influence, similar to the one carried out by Álvares [

The values of parameters A, B and ε_{d}_{0} were suggested by Mazars [

Using these intervals, Álvares [

Observing

・ the variation of ε_{d}_{0} (

・ the variation of B (

・ the variation of parameter A (

It can be observed that each parameter has its own specific influence to build the analytical stress-strain curve.

From the understanding of the parametric influence on, it is necessary to establish values for the parameters considering an experimental curve to be adjusted. For Álvares [

According to the second fundamental hypothesis of the Mazars model, the damage is caused only by the existence of stretching in at least one of the main directions of deformation [_{d}_{0}, corresponding to the peak stress, determines the beginning of the cracking of the analytical model and must be obtained through direct tensile strength or split tensile strength tests in cylindrical samples. Thus, it is necessary to get a definition of an equivalent deformation (ε_{eq}) to apply the model in compression loading situations.

The equivalent deformation that refers to the positive part of the main deformation in direction is defined by Equation (4) as follows

In the case of the split tension test (Equation (5)) and compression test (Equation (6)) we have

In Equation (6),

The values of parameters A and B can be found using a least square regression.

The damage parameters adjustment using the Mazars model allows a greater reliability of the prediction of the concrete mechanical properties. As seen before, important modifications occur in the behavior of the recycled concrete with the increase of the aggregate substitution rate, which indicates that this variable is of great importance to the adapting of the original model.

In this paper, the aggregate substitution rate (ASR) was added to the Mazars model as an independent variable directly associated to the parameters A and B. The adapted model will thus be the function of two independent variables ASR and ε, related respectively to the aggregate substitution rate and to the development of the deformation.

The relationship between the damage parameters (A and B) and the ASR was established based on the observation of experimental stress-strain curves. The variable ASR was evaluated in the interval of 0% to 100% in three points of its domain, the extreme limits 0% and 100% and the central point. The aimed relationship arises, therefore, from the curve that best adjusts the points that were evaluated and can be expressed by a polynomial function.

The proceeding that follows shows the stages of this evaluation

・ obtainment of the experimental curves

・ parametric identification of the experimental curves

・ obtainment of the functions for the curves “A versus ASR” and “B versus ASR”.

In this paper the experimental data that were used for the adapting of the Mazars model were obtained by Leite [

Leite [

・ Reference-0% of substitution rate, named here as REF

・ one mixture using 50% of recycled fine aggregate, named here as H-RFA

・ one mixture using 50% of recycled coarse aggregate, named here as H-RCA

・ one mixture using 100% of recycled fine aggregate, named here as F-RFA

・ one mixture using 100% of recycled coarse aggregate, named here as F-RCA

・ one mixture using 50% of recycled fine aggregate and 50% of recycled coarse aggregate, named here as H-RFCA.

The experimental curves were achieved from axial compression tests with displacement control at 28 days of age. Leite [

Applying a regression method to obtain the values of A and B parameters ensures the best adjustment of the model of the experimental data as well as it allows the evaluation of the quality of the adjustment achieved through R^{2}. According to Álvares [

where,

Err = global error;

_{i} e y_{i};

_{i} and the parameters of the model, in this case A and B.

The adjustment of the Mazars model resulted in a system of coupled equations, not linear, in order to fulfill the conditions established by Equation (7). The solution of systems like these needs iterative methods. So, the Levenberg-Marquardt method was chosen in this study. The initial values of the parameters A and B were the same that were used in conventional concrete as suggested by Mazars [

The behavior of the parameters of the analytical model in relation to the substitution of aggregates is observed by designing curves that adjust the three points previously chosen in the domain (0%, 50% and 100%). The choice of the adjustment function obeys the following criteria

・ the curve must necessarily pass through the 3 points that were obtained experimentally

・ the curve in the intervals between the points (0% to 50% and 50% to 100%) must have a linear or quadratic shape.

Using the average curves of axial and lateral stress-strain of the evaluated mixtures, Leite [

Using the previously presented methodology (Section 2.3), it was possible to obtain values for the parameters of the damage model from the experimental stress-strain curves. As follows,

For the mixtures with the water/cement ratio equal to 0.80 the values of the parameter A lie between 0.55 and 0.88 and of the parameter B between 1185.50 and 2057.15.

Using the average of the values that were obtained for the parameters A and B as shown, the curves “A versus ASR” and “B versus ASR” were drawn. Eight representative curves as follow that represent the behavior of each parameter regarding to the aggregates types-RFA and RCA- and the water/cement ratios −0.45 and 0.80 were found.

Thus, the model of isotropic damage proposed by Mazars [

Mixture | Sample | A | B | R² | |||
---|---|---|---|---|---|---|---|

w/c = 0.45 | w/c = 0.80 | w/c = 0.45 | w/c = 0.80 | w/c = 0.45 | w/c = 0.80 | ||

REF | 1 | 0.81 | 0.64 | 1116.99 | 1409.06 | 0.998 | 0.964 |

2 | 0.81 | 0.8 | 1063.88 | 1558.63 | 0.997 | 0.939 | |

3 | 0.84 | 0.61 | 1158.70 | 1315.03 | 0.993 | 0.942 | |

4 | - | 0.58 | - | 1415.78 | - | 0.939 | |

5 | - | 0.56 | - | 1185.49 | - | 0.901 | |

H-RFA | 1 | 0.91 | 0.68 | 1306.55 | 1289.42 | 0.976 | 0.986 |

2 | 0.85 | 0.65 | 1045.60 | 1293.74 | 0.995 | 0.974 | |

3 | 0.90 | 0.66 | 1471.89 | 1281.19 | 0.959 | 0.965 | |

4 | - | 0.66 | - | 1321.94 | - | 0.974 | |

F-RFA | 1 | 0.87 | 0.55 | 1435.43 | 1213.63 | 0.977 | 0.960 |

2 | 0.87 | 0.64 | 1523.85 | 1277.64 | 0.965 | 0.988 | |

3 | 0.86 | 0.60 | 1599.97 | 1273.67 | 0.963 | 0.984 | |

4 | - | 0.62 | - | 1203.07 | - | 0.983 | |

H-RCA | 1 | 0.79 | 0.59 | 1473.41 | 1509.98 | 0.988 | 0.998 |

2 | 0.84 | 0.62 | 1644.13 | 1409.49 | 0.963 | 0.990 | |

3 | 0.86 | 0.64 | 1917.65 | 1338.93 | 0.910 | 0.991 | |

4 | - | 0.55 | - | 1377.21 | - | 0.946 | |

F-RCA | 1 | 0.72 | 0.81 | 1718.38 | 1405.11 | 0.974 | 0.993 |

2 | 0.74 | 0.82 | 1809.93 | 1434.82 | 0.958 | 0.993 | |

3 | 1.00 | 0.85 | 1117.04 | 1515.78 | 0.970 | 0.999 | |

4 | - | 0.80 | - | 2057.15 | - | 0.999 | |

5 | - | 0.78 | - | 1868.70 | - | 0.998 | |

6 | - | 0.76 | - | 1607.14 | - | 0.984 | |

H-RFCA | 1 | 0.64 | 0.88 | 2261.52 | 1312.32 | 0.969 | 0.994 |

2 | 0.84 | 0.85 | 1558.64 | 1506.40 | 0.939 | 0.999 | |

3 | 0.82 | 0.85 | 1689.58 | 1506.32 | 0.931 | 0.992 |

・ Mixtures with the w/c = 0.45 and substitution of RFA

・ Mixtures with the w/c = 0.45 and substitution of RCA

・ Mixtures with the w/c = 0.80 and substitution of RFA

・ Mixtures with the w/c = 0.80 and substitution of RCA

The evaluation of the efficiency of the model created for the recycled concrete was done through the description of the experimental axial compression curves. The suggested model was implemented in the MATLAB® software. The original equation by Mazars [

It is possible to note that the model proposed by the authors (adapted Mazars) does not exactly describe individually any of the experimental curves for the mixtures with the water/cement of 0.45 as well as for the water/cement ratio of 0.80. However, the curves allow to observe that the adapted Mazars model is able to draw the approximate behavior of recycled concrete for the different substitution contents. This results in a generalized model with analytical curves that are very close to the experimental curves for all the mixtures.

The analytical model validated in the item 3.3 (Figures 6-10) was used in numerical simulations so to represent the behavior under compression of the recycled concrete. Through the finite element method studies of flexural tensile strength were simulated using the mixtures defined in item 2.1 referring to the water/cement ratio equal to 0.80.

The conditions of geometry and loading for the building of the model followed the guidelines of the Brazilian Standard NBR12142 [

The considerations assumed to build the numerical model using the DIANA® software are shown in

The adapted Mazars model was included in the analyses through stress-strain curves under compression obtained by the substitution of the equations of item 3.2 chosen according to the type of the mixture, in Equation (3), the original Mazars model. The behavior of flexural tensile strength after cracking was represented by a distributed cracking model using the function developed by Hordijk et al. (1986) apud [

Parameter | Value/Description |
---|---|

Finite element | Q8MEM |

Mesh (height × length) | 12 × 40 elements (size element = 0.0125 m) |

Loading | Displacement y = −0.001 m |

Type of loading | Incremental |

Model of cracking | Distributed-rotational |

Behavior under compression | Adapted Mazars |

Behavior under tension | With softening-Hordijk et al. apud [ |

Width of cracking band | h = 0.0176 m |

cracking (h) was calculated based on the dimensions of the finite element according to Equation (16) suggested by the DIANA® software user guide.

where,

S = finite element surface

The fracture energies (G_{f}) that were considered,

where,

G_{f} = fracture energy

b = parameter with value equal to 85.93;

b_{1} = parameter with value equal to 0.125;

b_{2} = parameter with value equal to 0.211;

d = maximum size of aggregate;

d_{20} = parameter with value equal to 20 mm;

t = cure time in days;

t_{30} = parameter with value equal to 30 days;

λ = parameter with value equal to 1.

Mixture | G_{f} (N/m) | f_{t} (MPa) (Experimental) | f_{t,fl} (MPa)^{1} (CEB-FIP) | f_{t,fl} (MPa)^{1} (Numerical) | Variation (%) |
---|---|---|---|---|---|

REF | 65.15 | 2.10 | 3.15 | 2.96 | −6.2% |

H-RFA | 76.17 | 1.70 | 2.55 | 2.58 | 1.0% |

F-RFA | 75.53 | 1.60 | 2.40 | 2.38 | −1.0% |

H-RCA | 73.68 | 1.80 | 2.70 | 2.67 | −1.2% |

F-RCA | 69.08 | 1.40 | 2.10 | 2.18 | 3.7% |

^{1}Flexural tensile strength.

where,

f_{t} = direct tensile strength;

f_{t,fl} = flexural tensile strength;

h_{b} = beam height (mm);

h_{0} = 100 mm.

In this article an isotropic damage model was applied for the description of the mechanical behavior of recycled concrete by means of adapting the parameters A and B described by Mazars [

・ The adapted Mazars model of isotropic damage is able to represent the mechanical behavior of recycled concrete under compression with good approximations. In this paper the determination coefficients found are higher than 0.90;

・ The hypothesis that the generalization of a constitutive analytical model for recycled concrete is possible through the manipulation of its parameters was confirmed. Using the studies of the influence of the parameters A and B to draw the stress-strain curves under compression it was possible to express through polynomial functions the variation of the values of these parameters with the increase of the replacement rate of the aggregates;

・ The methodology used allowed that the applying of the Mazars model could be done through the attribution of values of a single variable, replacement rate of the aggregates (ASR). The validation of the model that was created allowed to observe the proximity of the analytical curves, generated by the model in relation to the experimental curves.

The authors thank CAPES and CNPq for their financial support to this research.

Marcelo Pedreirada Silva,Magno TeixeiraMota,Anderson de Souza MatosGadéa,Mônica BatistaLeite,Koji de JesusNagahama, (2015) The Behavior of Recycled Concrete through the Application of an Isotropic Damage Model. Open Journal of Civil Engineering,05,339-351. doi: 10.4236/ojce.2015.53034