ES Materials & Manufacturing

ES Materials & Manufacturing, 2020, 9, 3-11

Published online: 28 Jun 2020

Received 14 Mar 2020, Accepted 26 Jun 2020

Jianmin Wang^{1*}, Yitao Fan^{1}, Chengfeng Zhu^{1}, Shuang Lu^{2} and Junzhe Liu^{3}

^{1} School of Civil and Environmental Engineering, Ningbo University, Ningbo, 315211, China

^{2} School of Civil Engineering, Harbin Institute of Technology, Harbin, 150090, China

^{3}School of Architecture Engineering, Qingdao Agricultural University. Qingdao, 266109, China.

ES Food & Agroforestry

**Abstract**: In order to study the bonding shear performance of the casting interface in the functionally gradient concrete (FGC), a multiphase mesoscopic finite element modelling method was proposed to simulate a sandwich FGC specimen with the normal weight concrete (NWC) casted on the hardened ceramsite lightweight aggregate concrete (LWAC) layer. Four kinds of phases were considered during modeling: coarse aggregates, mortar substrate, interface transition zone (ITZ) between the mortar and coarse aggregates, the casting interface transition zone (C-ITZ). Each phase in the model is endowed with the respective material property based on the constitutive damage plastic model (CDP). The structural characteristic of the C-ITZ that is related to the casting construction of the FGC were fully considered in the proposed modeling method. Based on the verification by corresponding experiments, the internal damage developing and the failure mechanism of the FGC model are effectively reflected by the simulation. For the designed FGC specimen corresponding to the experiment, the weak position are proved to be located on the C-ITZ. The damage developing and damage characteristic of the given FGC specimen are more related to the casting interval time of the FGC.

* Keywords:* functionally gradient concrete; mesoscopic finite element; interfacial bonding performance; lightweight aggregate

Functionally gradient material (FGM) is a new type of heterogeneous composite material, in which two or more different kinds of materials continuously and smoothly change from one side of the material to the other by advanced composite technology. In 1999, the concept of gradient was first introduced into the interface problem of cement-based concrete;^{[1]} and the research on the FGC has become an important branch of the engineering material in recent years.^{[2]} The application of the gradient concrete can effectively improve the synthetic performance of cement-based materials to solve the problem of the weaker interface, single functional, lower tensile strength, poor toughness and so on;^{[3]} and it also can extend the applicability of the concrete in complex and special engineering environments.^{[4]} The hybrid FGC, composed of the normal weight concrete (NWC) and the ceramsite lightweight aggregate concrete (LWAC), can effectively integrate the advantages of both types of concrete together. Akmaluddin *et al*.^{[5]} discussed the connection behavior of the hybrid precast concrete column and the sandwich concrete beam under the static loading. Ji *et al*.^{[6]} analyzed the variation of the mid-span deflection of the composite beam composed of the reactive powder concrete (RPC) and normal weight concrete (NWC) considering the influence of the prestressing degree, the RPC height and the NWC strength; the higher the pre-stressing degree, the longer the elastic stage before the crack, and the faster the stiffness in strengthening stage decreases after yielding. Campi *et al*.^{[7}^{,}^{8]} proposed a closed-form solution on two-layer beams considering the interlayer slip, in which a linear and non-proportional law relating interfacial shear tractions and slips is chosen to describe the interfacial behavior. As a kind of typical multiphase inhomogeneous material, the bonding performance and failure mechanism of FGC need thorough studies from multi perspectives.^{[9]}

For the simulation analysis, Yao *et al*.^{[10]} divided the recycled concrete into five components at the mesoscopic scale: old and new hardened mortar units, internal and external interface area units, and natural aggregate units; and established a two-dimensional randomly packing model of circular aggregate. A modeling method of two-dimensional mesoscopic scale random aggregate was proposed to establish the circular, oval, and polygon random aggregate models.^{[11]} Zhang *et al*.^{[12]} suggested the random walking algorithm for three-dimensional polygonal aggregate packing, and the distribution of aggregates was verified to satisfy the Fuller change curve. In fact, there is a typically physical structure for the interfacial layer in FGC which is important to guarantee the integration and coordination of the members. The structure of the interfacial layer is directly related to the construction technology, the casting interval time of the FGC members and so on. It is needed to carefully consider the physical structure and the material property of the interfacial layer in FGC to accurately simulate the performance of the FGC. In this paper, the sandwich FGC specimen model was designed with NWC cast on the ceramsite lightweight aggregate concrete (LWAC) in layers; and a multiphase mesoscopic finite element modeling method was proposed. The physical structure of the casting interface transition zone (C-ITZ) in FGC was specially modeled in detail and the mechanical performance of the FGC model was simulated based on the experimental results.

**2.1 Structural details of the FGC**

**Fig. 1** FGC specimen model and the experiment loading (a) The FGC model; and (b) experiment blocks and loading.

To study the interfacial bonding performance of FGC with NWC cast on the LWAC in layers, a sandwich specimen model is designed as shown in Fig. 1(a). The internal layer is LWAC substrate precast in advance, and two layers on both sides of the middle layer are NWC cast with a certain interval time late. The casting interface of the FGC is handled with the mortar retarder in the experiment. For a single kind of concrete material, it can be simulated at the mesoscopic scale as a composite is composed of the mortar substrate, coarse aggregate, the interface transition zone (ITZ) contacting the mortar and aggregates.

The modeled FGC is considered to be composed of four basic phases due to the special material property and structural detail of the C-ITZ. To describe the properties of the designed FGC model in detail, it can be divided into the normal aggregate (N-AGG), the mortar substrate (N-M) in NWC, ITZ between N-AGG and N-M (N-ITZ), the ceramsite lightweight coarse aggregate (L-AGG), the mortar substrate (L-M) in LWAC, ITZ between L-AGG and L-M (L-ITZ). Besides, the C-ITZ bonding between the NWC and LWAC is an important internal phase in the model.

**2.2 Coarse aggregates**

To build the two-dimensional mesoscopic model of the concrete, the three-dimensional gradation of the coarse aggregate in three-dimension must first be transformed to the two-dimensional. Based on the Fuller formula, the probability transforming the three-dimensional grading curve into that of the two-dimension specimen from a point with the aggregate diameter *Do* is expressed as,^{[13]}

(1)

in which *D*_{o }is the sieve diameter, *D _{max }*is the maximal aggregate size and

In the two-dimensional model, the probability distribution function *P _{c}* (

(2)

where *n _{i }*denotes the amount of coarse aggregates for a given diameter,

According to the distribution of particle sizes of the aggregates in the experiment, four gradation parameters are selected to calculate the amount of the ceramsite coarse aggregates and normal coarse aggregates in the FGC model. The sequential aggregate sizes are 2mm-5mm, 5mm-10mm, 10mm-15mm and 15mm-20mm.

**2.3 Modeling of the FGC**

To build the mesoscopic model of layered FGC, the throwing and locating of coarse aggregates, the building of ITZ surrounding coarse aggregates and C-ITZ between the NWC and LWAC layer are essential. The most important is the modeling of the C-ITZ because it is directly related to the processing method of the casting interface and the constructional procedure. The mortar retarder is used to handle the casting interface of the sandwich FGC blocks in the experiment. The handled interface before casting is shown in Fig. 2(a), which characterizes with some of the coarse ceramsite aggregates locally exposed out the casting surface. Therefore, this important structural detail of the casting interface should be characterized in modeling.