Application of finite element method on recycled aggregate concrete and reinforced recycled aggregate concrete A review

2.1. Modeling of Recycled Aggregate Concrete

2.1.1. Macro-Scale Modeling In the literature, researchers examine the macro-scale behavior of RAC in pure concrete state and in confined concrete state (concrete filled steel tube (CFST)). Hence, in this review paper, the subject of “Modeling of Recycled Aggregate Concrete” is divided into two parts as one can see in below considering the details given above.

2.1.1.1. Macro-Scale Behavior of RAC in Pure RAC State Etse et al. [21] improve a constitutive theory for RAC considering high temperature conditions. The theory is a material model of thermodynamically consistent gradient poroplastic and aims to predict the mechanical behavior of RAC [21]. In the research, the elevated temperatures (20200-400-600oC) and various RA ratios (0-30-60-100%) are concerned and the RAC simulation of the failure behavior under high temperature and the capability of the theory are demonstrated [21]. Dilbas [4], in his research, conducts some mechanical tests (compressive strength, splitting tensile strength and elasticity modulus) to define the mechanical behavior of RAC obtaining stress-strain data from zero to failure and beyond for mechanical tests [4]. Then, a homogeneous cantilever beam subjected to a point load is modeled in his research using the obtained mechanical properties and the mechanical behavior is examined under static loading conditions in Abaqus [4]. In his research, 3-dimensional (3D) non-linear FEA is considered, and pure plasticity is used to define the RAC properties in Abaqus [4]. Also, the results are verified with SAP 2000 FEA software. Choubey et al. [22] demonstrate the application of fracture models to RAC (double-K fracture model and fictitious crack model). The required parameters for the models are obtained in the equations given in the related literature and varying content of RA (0-30-50-70-100%) is considered [22]. It is concluded that the fracture models given in the literature for natural aggregate concrete (NAC) is suitable for RAC and the fracture parameters of RAC included RA from 0% to 100% can be determined using the models [22]. Also, some interesting results for NAC and RAC are found that the ratio of Pini/Pu (force when initial crack occurs/ultimate force) and KICini/KICun (initial cracking toughness/unstable fracture toughness) are constant for RAC and NAC [22]. Musiket et al. [23] present the fracture tests on notched RAC beams with different sizes under different high loading rates from 10−4/s to 10−2/s (Fig. 3) considering and combining two material models: viscoelastic model and

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Figure 5. Parts assembled (left), surface definition (right) and mean line of the interface [25].

Figure 6. Evaluation of the shear stress in the interface [25].

Figure 7. (a) Slab specimen on soil with expected crack surface; (b) edge-notched slab; and (c) one-third notched slab. Gray area in (b and c) denotes the ligament, while the white area is the pre-existing notch [9]. multi-phase composite model. Combining two material models, the rigidity of RAC is predicted for high loading rate conditions [23]. Force-crack mouth opening displacement (CMOD) curves are obtained from simulations, and the simulation model includes the fracture analysis criteria and eXtended Finite Element Method (XFEM) [23]. As a results, similar distributions of stress in the beams for different sizes are obtained, and the maximum loads estimated by the simulations are not close with test data [23]. Ripani et al. [24] study on a gradient plasticity theory reformulating Leon-Druger-Prager Model. The theory is widened to estimate the mechanical failure behavior of RAC, and the supposed theory is consistent with thermodynamic laws and considers the softening and hardening response behaviors [24]. In the modeling section, the supposed model and some numerical results are compared against experimental results given in the literature and the formulation of dual mixed FE is considered [24]. The formulation includes thermodynamically consistent gradient plasticity [24]. Also, the tests of uniaxial tensile and compression are adopted to FEM [24]. It is stated in conclusion that the proposed constitutive model presents the influence of RA addition on the behavior of failure response and reflects the sensitivity of RA [24] (Fig. 4). Ceia [25] researches the effect of RA on shear resistance. In the experimental work, many specimens including various RA ratios (0-20-50-100%) are produced [25]. In the

3D modeling section, Abaqus is used, two parts (upper and lower parts) are defined separately to model the shear test and then the parts are assembled in conformity with a behavior of linear elastic material [25] (Fig. 5). Cohesive bonding is considered for the surfaces of the specimens [25]. It is stated that the stiffness of differential in FEA is substantial for shear strength [25] (Fig. 6). Gaedicke et al. [9] propose an 3D approach which includes three subjects separately: Concrete slab flexural load capacity determination under mode I -the slab lies on elastic foundation-, crack growth and crack initiation. 3D slabs FEM is generated in Abaqus, and the slabs include cohesive crack elements along pre-defined paths [9] (Fig. 7). The bilinear softening for concrete is considered, and the model is simulated. Also, the results are verified experimentally [9]. It is concluded that 3D cohesive crack element can estimate the capacity of slabs under flexural loads on soils [9]. 2.1.1.2. Macro-Scale Behavior of RAC in Confined RAC State Tam et al. [26] use RAC in concrete-filled steel tubular (CFST) columns as a filling material and CFST columns has rectangular geometry. Then FEA is considered to model CFST columns in Abaqus [26]. An equation defined for stress-strain data for confined concrete proposed by Han et al. [26] is used in the model as a constitutive model parameter and it is stated that the equation gives good results for models when the damage plasticity model is used in Ab-

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Figure 9. A schematic view of the test assembly [27]. Figure 8. Comparison between the predicted and experimental ultimate strength [26]. aqus [26]. In the modeling part, steel jacket and concrete are modeled as shell and solid elements, respectively [26]. Also, surface-based interaction between the steel jacket and concrete is defined: In the normal direction and the tangential direction a contact pressure model and a Coulomb friction model, respectively [26]. In conclusion, it is stated that a FE model simulated for conventional concrete-filled steel tubes is possible to use for CFST with RAC, and satisfactory CFST results are found [26] (Fig. 8). Yang et al. [27] carry out an experimental and numerical studies on square CFST under lateral impact loads (Fig. 9). In this study, local damages and failure modes of specimens are examined [27]. The non-linear FEM for CFST is simulated in Abaqus, and explicit solver is considered. [27]. Damaged plasticity model is taken into account for modeling nonlinear behavior of concrete [27]. It is found that the failure mode of CFST is generally concave where the loads are applied to, and the shear failure with punching shear failure of CFST is observed [27]. Also, experimental, and numerical results are in good agreements is found [27]. Xiao et al. [28] use glass fiber reinforced plastic (GFRP) tubes and steel tubes to confine RAC in their research and apply axial compression force to concrete-filled tubes to determine the mechanical properties. Then, a concrete-filled tube FEM is simulated to examine the outer tube thickness and the core strength effect [28]. The non-linearity in FEM is accounted in ANSYS [28]. 3D solid element for outer tube is used and the element abilities are creep, plasticity, stress stiffening, swelling, large strain, and large deflection, and the name is solid45 [28]. Also, 3D solid element for core concrete is chosen and the name is solid65 [28]. Solid65 is for solid models including no rebars and the abilities of solid65 are crushing in compression, cracking, creep cracking in tension and plastic deformation [28]. It is concluded that the peak stress of recycled concrete filled steel tube increases when the thickness increases and no effect on the plastic stage is observed [28] (Fig. 10).

Figure 10. Effect of the outer tube thickness [28]. Xiang et al. [29] conduct a theoretical study on recycled aggregate concrete-filled steel tube stub columns. In the study, cold-formed hollow structural square steel tube is used, and nonlinear finite element model is simulated in Abaqus [29]. The stub column is subjected to axial compression. 3D eightnode solid elements with full integration (C3D8) are chosen for rigid plates and RAC, and the cold-formed steel tube is modeled with a shell element (S4) due to the small wall thickness in Abaqus [29]. For modeling the cold-formed steel material behavior, an idealized elastic-plastic stress-strain model proposed by Abdel-Rahman and Sivakumaran is considered [29]. This model indicates a multi-linear isotropic strain hardening rule [29]. The ascending part of RAC equivalent stress-strain is modeled according to Guo and Zhang equation [29]. Concrete damaged plasticity model in Abaqus

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Table 1. Comparisons of the ultimate compressive strengths determined by different methods [29]

is considered for RAC, and the surface-to-surface contact is used for the relation between the faces of steel jacket and core concrete [29]. In the research section on the friction coefficient, it is stated that the column under compression has no sensitivity with the friction coefficients although various friction coefficients (from 0.2 to 0.6) in FEM is considered [29]. In conclusion it is stated that the square CFST included RAC has similar mechanical behavior with the square CFST included conventional concrete, and the specification Eurocode 4 estimates the ultimate compressive strength of square CFST with a reasonable accuracy [29] (Table 1). Yang et al. [30] investigate the fire resistance of CFST included RAC (Fig. 11). In the analysis, typical temperature development, failure pattern, fire resistance and axial displacement of the specimens are determined [30]. In the simulation, RAC-filled square steel tubular columns is modeled in Abaqus [30]. According to the research, the model includes two main parts: thermal part (includes temperature development) and mechanical part (includes displacement, failure pattern, and fire resistance) [30]. In the model, the effects of radiation and heat convection on column is taken into account [30]. The thermal contact resistance between the core RAC and steel tube is considered in conformity of the suggestion of Ghojel [30]. In the heat transfer model, the core concrete and the steel jacket are modeled with linear 3D brick elements (DC3D8) and 3D shell elements (DS4), respectively [30]. Under high temperatures, plasticity model is used for steel tubes and the damaged plasticity model for core concrete is adopted [30]. The ‘Coulomb friction’ and ‘hard contact’ is chosen for the contact properties between core and steel, and geometric linearity is assumed for large lateral deflections [30]. In conclusion, it is stated that the temperature development and fire resistance, failure pattern and axial displacement of specimens with 50% RA are generally similar behavior with reference CFST, and the estimated response of CFST under fire is generally in good agreement with experiments [30].

Figure 11. Schematic diagram of the test set-up [30]. Geng et al. [31] examine the time-dependent behavior of CFST with RAC (50 MPa). In this paper, a CFST is modeled in Abaqus. Core concrete and steel tubes are considered in Abaqus as Timoshenko beam elements (B31) and the time-dependent behavior of concrete is formed considering the Fathifazl creep model [31]. Under compression, the concrete constitutive model in Abaqus with the UMAT subroutine is used [31]. As a results, FEM gives a good agreement with the numerical results and the FEA results with the maximum deviation 1.9‰ is obtained in comparison to the numerical results [31].

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Figure 12. Total chloride concentration along the depth of three concrete specimens with different aggregate shapes, after4yearsofexposure [32].

Figure 13. Chloride content-time of the specimen: (a) at cover depth=30 mmand (b) depth=50mm [32]. 2.1.2. Meso-Scale Modeling Du et al. [32], in their research, develop a heterogeneous model including mortar matrix, aggregate, and ITZ to examine chloride diffusivity of concrete, especially RAC [32]. In the model, aggregates are assumed as an impermeable material and the chloride diffusion occurs through the mortar matrix and ITZs [32]. The diffusivity parameters of components, such as mortar matrix and ITZs, are obtained in the literature, and the model simulated in Abaqus is validated with the test given in the literature [32]. The transient analysis is chosen, and the period is 4 years [32]. 4-node linear heat transfer quadrilateral elements are used for concrete [32]. As a results, it is concluded that three different aggregate shape (squared and circular, elliptical) don’t affect the chloride diffusion performances of RAC for the same aggregate volume ratio in concrete (Fig. 12) and, the chloride diffusion increases when ITZs thickness increases due to more porous structure and higher water/cement ratio of ITZ in comparison to the cement paste (Fig. 13) [32].

Kim et al. [33] conduct a series of numerical analysis on porous concrete pile (RAPP) produced with RA and compared the results with the numerical simulation results using Abaqus [33]. RAPP is modeled as a vertical drainage in Ref. [33]. In the modeling part, RAPP and the clay formation are simulated by using the Mohr–Coulomb model and the modified Cam clay model, respectively [33]. For all the components, 4-node bilinear displacement and the pore pressure element (CAX4P) is used [33]. It is stated that RAPP considerably contributes to enriching consolidation with supplying radial drainage [33]. Xiao et al. [34] examine the ITZs effects on stress-strain of RAC. In this paper, RAC is modeled in meso/micro scale in Abaqus (Fig. 14). The plastic-damage constitutive models are used, and the model is simulated to determine mechanical behavior (i.e., compression and tension) [34]. In Explicit step, ABAQUS/explicit quasi-static solver is used [34]. While defining the properties of ITZ and other parts, concrete damaged plasticity is considered and the properties of parts are based on experimental data (i.e., nano-indenta-

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Figure 15. Compressive stress–strain curves with different new mortar matrices [34]. tion tests) [34]. It is concluded that the mortar matrixes and ITZs has a significant role on failure patterns and stress– strain relationship of modeled RAC (MRAC) (Fig. 15) [34]. Xiao et al. [35] propose a model to define the RA effect on chloride diffusion in RAC using Abaqus (Fig. 16). In the simulation part, a five-phase composite for RAC is modeled (Fig. 17) (these phases are old and new ITZs, old and new mortar, and original aggregate) [35]. The transient analysis and the 8-node quadratic heat transfer quadrilateral element are chosen for the model [35]. It is stated that the suggested heterogeneous RAC FE model works well and gives realistic chloride diffusion results [35]. Wang et al. [11] study the influence of old concrete carbonation on ITZ properties of RAC. In this paper, old concretes with various water/binder ratios are considered and modeled and are carbonated [11]. Then, the peak load, the load–displacement curves, and the peak displacement are examined to define the effect of carbonation on modeled RAC [11]. The model is simulated in Abaqus and is verified

Figure 16. The chloride flow in modeling concrete [35]. with the test data [11]. In the modeling of mortar matrix and ITZ, the constitutive relationship of mortar matrix and ITZ is defined with damage plasticity model in Abaqus [11]. It is stated that ITZ properties have similarity with mortar matrix properties, however elastic modulus, and strength of ITZ are lower than the mortar matrix in the model [11]. On the other hand, in the modeling of natural aggregate (NA), NA is considered and modeled as an isotropic material [11]. In FEA, ABAQUS/explicit solver is used to solve FEM equations [11]. As a results, it is stated that ITZ properties of modeled RAC is considerably related with shape of RA, distribution of old mortar, and carbonation depth [11].

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Figure 18. The MRAC containing modeled RA and NA [10]. Figure 17. Five-phase composite sphere mode [35]. Ying et al. [10] investigate the effect of RA ratio on chloride diffusion in RAC using Abaqus (Fig. 18). The transient analysis and the 8-node quadratic heat transfer quadrilateral element are selected for FEM [10]. It is concluded that the consistent tendency for compressive strength and chloride migration in modeled RAC is observed and FEA results are verified with test results [10]. Xiao et al. [36] investigate RAC stress distribution while a pressure load is applied to RAC model in Abaqus. In FEA, overall mechanical properties, elastic stress distribution, damage localization and stress concentration are examined (Fig. 19) [36]. The static analysis in Abaqus is adopted to FEM and the linearity in the analysis is considered [36]. In conclusion, it is recommended that ITZ presents a strain softening behavior and the non-linearity in the analysis for ITZ should be considered [36].

Figure 19. Testing results on the MRAC under uniaxial loading by the digital image correlation: (a) horizontal field strain contour map; (b) crack pattern [36]. 2.1.3. Micro-Scale Modeling Jeong et al. [37] study on the time-dependent hydration phenomenon chemo-thermal modeling of mortars included RA and NA. In this paper experimental and theoretical

Figure 20. Illustration of geometrical configurations of M2-1 numerical EAG specimens, (a) cement matrix including 4149 sand grains and (b) mesh density [37].

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Figure 21. RAC graded slab models [38]. Table 2. Comparisons between ABAQUS simulation and experiment [38]

included rebars and concrete, and investigations on their behavior are implemented around the world. In the literature, in parallel, the reinforced recycled aggregate concrete (RRAC)behavior is examined widely, and especially the comparative studies on RRAC, and reinforced NAC (RNAC) are done. Researchers are generally inspired to determine the properties of RRAC under the static and the dynamic loading conditions to assess the properties of RRAC (i.e., punching). Hence, in this section, the papers on modeling of RRAC are reviewed in two sub-sections consisted of the static and the dynamic loading conditions.

3.1. Modeling of Reinforced Recycled Aggregate

analysis are conducted and the modified Arrhenius’ law and 3D FEA are considered [37]. In the modeling section, the Extracted Aggregate Groups (EAGs) concept is formed and has spherical geometry (Fig. 20) [37]. During the hydration process, the isotropic chemo-thermal features in the calorimeter device is considered [37]. Also, the pseudo-random geometric spherical packing algorithm is considered [37]. In this paper, the grains in the mortar are modeled and formed in Matlab-Comsolcode [37]. In the modeling, it is pointed out that the chemo-thermal modeling is in non-linear transient-state because the chemical reactions of cement paste have the non-linear features [37]. In conclusion, according to a user-written Matlab-Comsolcode FEA and the experimental results, the modified Arrhenius’ law is not useful for the recycling mortar hydration modeling [37]. Hence, a revision is need for the modified Arrhenius’ law if it is used for the recycling mortar hydration modeling [37].