By using the Base Force Element Method (BFEM) on potential energy principle, a new numerical concrete model, random convex aggregate model, is presented in this paper to simulate the experiment under uniaxial compression for recycled aggregate concrete (RAC) which can also be referred to as recycled concrete. This model is considered as a heterogeneous composite which is composed of five mediums, including natural coarse aggregate, old mortar, new mortar, new interfacial transition zone (ITZ), and old ITZ. In order to simulate the damage processes of RAC, a curve damage model was adopted as the damage constitutive model and the strength theory of maximum tensile strain was used as the failure criterion in the BFEM on mesomechanics. The numerical results obtained in this paper which contained the uniaxial compressive strengths, size effects on strength, and damage processes of RAC are in agreement with experimental observations. The research works show that the random convex aggregate model and the BFEM with the curve damage model can be used for simulating the relationship between microstructure and mechanical properties of RAC.

Recycled aggregate concrete (RAC) is considered as a green building material which can alleviate the pressure of resource shortage. Since more and more researchers were attracted to carry out a series of experiments to explore the mechanical performances of RAC, some classical conclusions have been made over the micro-, meso-, and macroscales. However, testing always consumes a large amount of manpower, material, and financial resources, and the conclusions made by different researchers are not very coincident frequently.

Based on the concept of numerical concrete presented by Wittmann et al. [

However, the simulation of random circular aggregate model is more suitable for boulder concrete than crushed stone concrete. Although some studies on the random convex polygon aggregate model of concrete were done [

In recent years, a new type of FEM, the Base Force Element Method (BFEM), has been developed by Peng et al. [

The concept of base forces was proposed by Gao [

The Base Force Element Method (BFEM) on complementary energy principle uses the base forces as fundamental variables to establish control equations of the novel finite element method. In the literature [

The BFEM on potential energy principle uses the displacement gradients

A triangular element.

For the plane stress problem, it is necessary to replace

Generally, the nonlinear performance of concrete stress-strain curve can be mainly attributed to the continuous quasibrittle damage, caused by the initiation and propagation of microcracks under stress, rather than the plastic deformation of materials. Therefore, the RAC which is composed by different characteristics of natural coarse aggregate, new mortar, old mortar, and new and old interfacial transition zone (ITZ) on mesolevel can be described by the constitutive relation of elasticity mechanics.

According to the Lemaitre strain equivalent principle [

or

In order to reflect the damage processes of materials veritably, the damage degradation of recycled aggregate concrete is described by the revised piecewise curve damage model which was first presented by Qian and Zhou [

Revised piecewise curve of damage model.

In Figure

According to (

In this paper, the failure criterion of RAC is the strength theory of maximum tensile strain, which means

In order to obtain more optimized compaction and macroscopic strength of RAC, the Fuller grading curve was adopted to simulate the distribution of the aggregate model in this paper. Based on this curve, Walraven and Reinhardt [

In this present paper, three dimensions of specimens for RAC, contained 100 mm × 100 mm × 100 mm, 150 mm × 150 mm × 150 mm and 300 mm × 300 mm × 300 mm are used to simulate the uniaxial compression tests.

By the above mentioned method, the three-dimensional structure is schematized as a plane stress problem and the simplified sizes of specimens are 100 mm × 100 mm, 150 mm × 150 mm, and 300 mm × 300 mm.

For the specimens of 100 mm × 100 mm, the numbers of large aggregate (typical diameter is 17.5 mm), middle aggregate (typical diameter is 12.5 mm), and fine aggregate (typical diameter is 7.5 mm) in RAC are 3, 9, and 37, respectively.

Analogously, for the specimens of 150 mm × 150 mm, the numbers of large aggregate (typical diameter is 35 mm), middle aggregate (typical diameter is 20 mm), and fine aggregate (typical diameter is 10 mm) in RAC are 3, 10, and 59, respectively.

For the specimens of 300 mm × 300 mm, the numbers of large aggregate (typical diameter is 60 mm), middle aggregate (typical diameter is 30 mm), and fine aggregate (typical diameter is 12 mm) in RAC are 6, 21, and 159, respectively.

The random circular aggregate distribution model (presented in Figure

Random circular aggregate model of RAC.

A specimen of 100 mm × 100 mm

A specimen of 150 mm × 150 mm

A specimen of 300 mm × 300 mm

The formation of the random convex aggregate model for RAC is based on the random circular aggregate model which contained the data of the aggregate particle diameter, the number of different sizes of aggregates, and the thickness of old cement mortar.

Firstly, the basic framework of random convex aggregate can be generated by the internal access polygon of each aggregate boundary with the centre of circular aggregate inside.

Based on the basic framework of random convex aggregate, we insert several new vertexes which located in the area between circular aggregate and convex aggregate to constitute a new polygon. The new inserted vertex requires the following conditions to be satisfied:

The new vertex should not be beyond the scope of specimen.

The newly formed extensional polygon should be a convex polygon.

The newly formed aggregates have no overlap region with each other.

Using the method mentioned above, the two-dimensional random convex aggregate model for RAC (shown in Figure

Random convex polygon aggregate model of recycled aggregate concrete.

A specimen of 100 mm × 100 mm

A specimen of 150 mm × 150 mm

A specimen of 300 mm × 300 mm

In this paper, the projection method is applied to the attribute interval recognition of arbitrary element in RAC specimen. By using computer programming, we can judge the states of recycled coarse aggregate, new cement mortar, old cement mortar, new interfacial transition zone (ITZ), and old ITZ. The model is shown in Figure

Attribute interval recognition of convex polygon recycled coarse aggregate.

Based on the BFEM on potential energy principle for damage mechanics problem, this paper simulated the concrete test under uniaxial compression (shown in Figure

Compressive loading model.

Referring to the experimental results from [

Material parameters of numerical simulations.

Materials | Elastic modulus/GPa | Poisson’s ratio | Tensile strength/MPa | | | | | | | | |
---|---|---|---|---|---|---|---|---|---|---|---|

Natural aggregate | 70 | 0.16 | 10 | 0.1 | 5 | 10 | 1/6 | 5/6 | 5 | 1.7 | |

Old ITZ | 13 | 0.2 | 2 | 0.1 | 3 | 10 | 1/6 | 5/6 | 5 | 1.7 | |

Old cement mortar | 25 | 0.22 | 2.5 | 0.1 | 4 | 10 | 1/6 | 5/6 | 5 | 1.7 | |

New ITZ | 15 | 0.2 | 2 | 0.1 | 3 | 10 | 1/6 | 5/6 | 5 | 1.7 | |

New cement mortar | 30 | 0.22 | 3 | 0.1 | 4 | 10 | 1/6 | 5/6 | 5 | 1.7 | |

A specimen of 100 mm × 100 mm, a specimen of 150 mm × 150 mm, and a specimen of 300 mm × 300 mm are chosen as the representative models to observe the failure patterning of different size of RAC specimens by uniaxial compression, and they are shown in Table

The failure patterning of different size of RAC specimens under uniaxial compression.

Failure state of specimens | Initial state | Crack appears | Crack coalescence |
---|---|---|---|

A specimen of 100 mm × 100 mm | | | |

A specimen of 150 mm × 150 mm | | | |

A specimen of 300 mm × 300 mm | | | |

Three specimens of 100 mm × 100 mm with different random aggregate distributions are simulated, and the uniaxial compressive stress-strain curves are shown in Figure

Uniaxial compressive stress-strain curve of RAC specimens.

Specimens of 100 mm × 100 mm

Specimens of 150 mm × 150 mm

Specimens of 300 mm × 300 mm

Similarly, the uniaxial compressive stress-strain curves of three specimens of 150 mm × 150 mm and three specimens of 300 mm × 300 mm are shown in Figures

The calculation results are shown as follows:

The uniaxial compressive strengths of the three specimens of 100 mm × 100 mm are 26.44 MPa, 25.71 MPa, and 26.31 MPa, and the average strength is 26.15 MPa.

The uniaxial compressive strengths of the three specimens of 150 mm × 150 mm are 25.15 MPa, 25.21 MPa, and 25.10 MPa, and the average strength is 25.15 MPa.

The uniaxial compressive strengths of the three specimens of 300 mm × 300 mm are 23.24 MPa, 23.68 MPa, and 23.75 MPa, and the average strength is 23.56 MPa.

For the specimens of 100 mm × 100 mm, the uniaxial compressive strength of 26.15 MPa is coincided with the result of 26.7 MPa in the test [

To explore the size effect of uniaxial compressive strength with the same loading conditions, we calculate the average values of three specimens in the dimension of 100 mm × 100 mm, 150 mm × 150 mm, and 300 mm × 300 mm, respectively. The average compressive stress-strain curves are shown in Figure

The average uniaxial compressive strength of different sizes of RAC specimens.

Dimensions of RAC | Means of compressive strength/MPa |
---|---|

100 mm × 100 mm | 26.15 |

150 mm × 150 mm | 25.15 |

300 mm × 300 mm | 23.56 |

The average compressive stress-strain curves of RAC specimens in three dimensions.

The recycled aggregates are made from demolished concrete by a series of measures like crushing, cleaning, and grading. Due to the different degrees of processing technology, the contents of old mortar adhered on natural aggregates are uncertain.

As early as 1984, Rasheeduzzafar and Khan [

Compressive strengths of RAC with different mass contents of old mortar.

Mass contents of old mortar | Compressive strength/MPa |
---|---|

32% | 26.76 |

42% | 26.31 |

52% | 25.39 |

RAC models with different mass contents of old mortar.

Mass contents of 32%

Mass contents of 42%

Mass contents of 52%

Uniaxial compressive stress-strain curve of RAC specimens with different mass contents of old mortar.

Through the failure patterning of RAC specimens, we may discover that microcracks first appear in the ITZ between the zones of aggregate and cement mortar. Subsequently, the cracks will propagate, intersect, and run through the specimen till it is destroyed. The strength of interface performance plays an important role in the mechanical properties of recycled concrete materials. It is difficult to study the interfacial mechanical properties of recycled concrete materials by means of experiments, and the numerical analysis method will be a powerful analytical method. At present, the studies on the interfacial mechanical properties of recycled concrete materials by using numerical analysis method are relatively few.

In order to explore the influence of the tensile strength of ITZ, several numerical values were used by some researchers; for instance, the strength values of 1.25 MPa were applied to the concrete area between matrix and aggregate in the lattice model by Chiaia et al. [

The compressive stress-strain curves are shown in Figure

Compressive strengths of RAC with different tensile strengths of ITZ.

Tensile strength of ITZ/MPa | Compressive strength/MPa |
---|---|

1.25 | 23.13 |

2.0 | 26.36 |

2.4 | 27.75 |

The compressive stress-strain curve of RAC specimen of 100 mm × 100 mm with different tensile strengths of ITZ.

(1) This paper analyzed the uniaxial compressive strengths, size effects on strength, and damage processes of RAC using the Base Force Element Method (BFEM) on mesolevel. The numerical results show that the uniaxial compressive strength of RAC specimens decreases with increasing specimen size, and it is agreeing with the test results. The research works show that the random convex aggregate model and the BFEM with the curve damage model can be used for simulating the relationship between microstructure and mechanical properties of RAC.

(2) Taking the real graduation and content of recycled aggregates into consideration, this paper proposed a new model of numerical RAC, random convex aggregate, model which contains natural coarse aggregate, new mortar, new interfacial transition zone (ITZ), old mortar, and old ITZ. The model can reflect the characteristics of RAC specimens more authentically than the random circular aggregate model, and it is proved to be feasible by the numerical test result. The relationships of mesostructure and macroscopic mechanical performance of RAC can be analyzed in a simple and feasible way with this model.

(3) The failure pattern of numerical RAC under uniaxial compression shows that the destruction process of specimen can be described as the initiation, propagation, and cut-through of cracks at mesoscale level, which is in accordance with the real phenomena.

(4) The failure pattern also shows that the microcracks first appear in the area of interfacial transition zone (ITZ) with the increase of compressive loading; therefore, a hypothesis that ITZ is the weak part of RAC is raised by this study. Moreover, it can be seen clearly that the compressive strength of RAC specimen increases obviously as the tensile strength of ITZ increases in above qualitative analysis. However, more systemic experiments are necessary to be done to explore the contributions which ITZ made quantitatively in years to come.

(5) Three different mass contents are used in the RAC models to explore their influences on the uniaxial compressive strengths. The results indicated that the compressive strength of RAC specimen increases as the tensile strength of ITZ increases, and this may be due to the fact that the aggregates with low old mortar contents are much closer to the natural aggregates which make the mechanical property of RAC specimens much closer to the concrete.

The authors declare that there is no conflict of interests.

This work is supported by National Science Foundation of China (10972015, 11172015), Beijing Natural Science Foundation (8162008), and Preexploration Project of Key Laboratory of Urban Security and Disaster Engineering, Ministry of Education, Beijing University of Technology (USDE201404).