Uniaxial mechanical behaviors of recycled coarse aggregate concretes cast with conventional and equivalent mortar volume methods

Abstract

Among the various kinds of adjustment methods to improve the material properties of recycled aggregate concrete (RAC), equivalent mortar volume (EMV) method is widely considered as economic and effective. This is mainly because that only an extra content of natural aggregates (NAs) is needed to be added in the mixture during fabricating RAC. To objectively evaluate the method, this study conducted a series of discrete element mesoscale simulations to illustrate and compare the mechanical behaviors and failure mechanisms for conventional and EMV methods designed RAC samples under uniaxial loadings. Particularly, the influences of the replacement ratio of RAs, the mixture’s water-to-cement ratio and the spatial location of coarse aggregates on the two RACs’ strength and deformation characteristics were analyzed. Additionally, generic expressions used for estimating the mechanical properties of conventional and EMV methods cast RAC samples were also tried to be established in the article. It was found by this study that: (a) As the replacement ratio grows, both the conventional RAC’s compressive strength and elastic modulus reduce monotonously, however, the tensile strength’s variation trend is highly dependent on the relative strength of new-to-old mortar; (b) Regardless of the RAC’s water-to-cement ratio, an EMV design method can always improve the elastic modulus of RAC effectively; (c) When the new mortar strength is lower than that of old mortar, adopting an EMV mix-design method notably improves the RAC’s tensile and compressive strengths, however, if the old mortar strength is obviously smaller, the EMV method’s enhancement to the concrete’s strength is limited; (d) Variabilities for compressive and tensile strengths of EMV method designed RAC samples are commonly higher than those of conventional RAC samples; and (e) Uniaxial mechanical property of RAC sample cast either using a conventional or EMV method can both be predicted with a same formulas.

Keywords

recycled aggregate concrete equivalent mortar volume method mesoscale discrete element modeling uniaxial compression and tension strength and deformation characteristics

Introduction

Entering into the new century, the civil engineering’s rapid development notably changes human being’s life. On the plus side, the urbanization process in the world continues to accelerate, consequently, people’s living and working environments improve greatly. While on the adverse side, construction and demolition activities often consume a large content of natural resources and also generate lots of solid wastes, which makes the earth operate highly-stressed. Taking China as an example, it was reported in the year of 2019 that, the urban population’s proportion had reached 60.6%, the annual consumptions for the cement, sand and gravel were, respectively, 1.2, 1.5 and 3.2 billion tonnes (NBSC, 2019), and simultaneously 0.2 billion tonnes of waste concrete was produced (Xie and Zhao, 2021).

Under above backgrounds, researchers in recent pay lots of attentions on the recycled aggregate concrete (RAC). Through breaking waste concrete, sieving out coarse recycled aggregates (RAs) and then using them to replace natural aggregates (NAs) during manufacturing fresh concrete, waste components are reasonably consumed, meanwhile, a new type of construction material is sustainably generated (Visintin et al., 2020; Xiao et al., 2018; Xie et al., 2018). From this view, RAC seems to be an ideal solution to tackle the difficulties in the field of civil engineering. But caused by the notably-different property of the parent material and the special crushing technique, coarse RAs’ physical and mechanical properties alter a lot, and they commonly have the following features as compared with NAs (Xiao et al., 2018): (a) RA’s attribution varies greatly among different particles; (b) a certain content of weak mortar is generally adhered on the aggregate surface; (c) a new type of old mortar-aggregate interfacial transition zone (ITZ) appears in RAs; and lastly (d) crushing damages and cracks occur in RAs, especially at the weak mortar region. These characters naturally affect the RAC’s material properties and make them hard to be estimated.

Since the invention of RAC in 1950s (Xiao et al., 2018), a considerable amount of investigations have been conducted to show the influence of incorporating RAs on the concrete’s physical, chemical, mechanical and durable properties. Pepe (2015), for instance, once analyzed the porosity, geometric shape, water absorption, particle density and strength of RAs, and found these indexes obtained from various sources were greatly different. Duan and Poon (2014) prepared RAs with various old mortar contents to make RAC cube and then tested the samples’ mechanical properties. It was observed that with the increasing of the old mortar content the RAC sample’s compressive strength and elastic modulus were both lower than those of cube fully made with NAs. The tensile strength, however, showed no definite tendency. More recently, with the aid of advanced test techniques such as scanning electron microscope and nanoindentation, Xiao et al. (2013a) investigated the old and new ITZs existed in RAC. They observed that the ITZ’s property was tightly correlated to the mortar’s property, while the elastic modulus of new ITZ almost kept to be 85% of that of new mortar, regardless of the water-to-cement ratio. To study the failure mode of RAC samples under axial compression, Xiao et al. (2013b) also proposed a novel concept named Modeled RAC, and through conducting direct compression tests they successfully found that the crack propagation of RAC under compression was highly dependent on the strength ratio of old mortar to new mortar. By tests, it is also evident to observe that the RAC’s mechanical and durable properties deteriorate significantly as compared with those of natural aggregate concrete (NAC) (Xiao et al., 2018). As summarized by Silva (2015a, 2015b, 2016), descending amplitudes for the RAC’s compressive and tensile strengths as well as the elastic modulus with a 100% RA replacement ratio were, respectively, 13.5%, 19.5% and 27.5% on average. At the same time, the RAC’s shrinkage coefficient and chloride diffusivity increased 39.8% and 22.0%.

To a certain extent, such a notable degeneration of the material’s property restricts the wide application of RAC. In China, for instance, it is recently reported that coarse RAs is primarily used in back-filling or roadbed construction, while only about 5% of RAs is applied in constructing load-bearing structures (Wu et al., 2019). To improve RAC’s material properties, many techniques today have been proposed by various scholars around the world (Xiao et al., 2018). Aggregate enhancement is one classical method. It is mainly aimed to treat RAs to reduce the content of old mortar with using particle-shaping (Li et al., 2006), acid-soaking (Katkhuda and Shatarat, 2016) or microwave heating (Xiao et al., 2012). Beside this, altering RAC’s mix proportions is another common method, which hopes to improve RAC through adjusting its constituents or mixing method. Because of the simpler operations and cheaper cost, the latter type of technique is preferentially recommended by main countries like Spanish, Canada and Australia (de Brito and Agrela, 2018). The present study herein also focuses on one such method named as equivalent mortar volume (EMV) method, which was originally proposed by Fathifazl’s group in 2009 (Fathifazl et al., 2009, 2011; Yu and Lin, 2020). As depicted in Figure 1(a) and (b), the volume content of the coarse aggregates in a conventional mixing method cast RAC sample (commonly implies producing RAC with saturated-dried RAs) is in fact reduced due to the appearance of old mortar on RAs. To fix this problem, the operation involved in an EMV method is to add equivalent amount of virgin aggregates to offset the old mortar’s influence during manufacturing fresh concrete (see Figure 1(c)).

Figure 1.

NAC, conventional method designed RAC and EMV method proportioned RAC. (a) NAC, (b) Conventional RAC, (c) EMV method designed RAC.

Many investigations have demonstrated the effectiveness of this method. For instance, during investigating the shear performance of reinforced RAC beams without stirrup, Fathifazl et al. (Fathifazl et al., 2009) found that there had no distinct difference between the failure mode, cracking and shear capacities of RAC and NAC beams if an EMV method was adopted for RAC. A group led by Emmanuel et al. (2002) also reported that RAC made with the EMV method commonly uses significantly less content of cement than conventional RAC or NAC with a comparable strength. With regard to the material’s durabilities, Abbs and his coworkers (2009) once fully studied the freeze-thaw, chloride penetration and carbonation properties of EMV method manufactured RAC mixtures with a water-to-binder ratio of 0.45. Their experimental results showed RAC mixed using an EMV method often had higher resistance, and can satisfy the current requirements for concrete exposed to severe environments.

Those pioneering studies have made great contributions to the understanding of the RAC’s EMV method. But for large area applications of RAC structures using such method, it should be pointed out that there still exist some aspects of works need to be performed. For instance, in accordance with the authors’ test experience, when the RA’s replacement ratio is high, the mixing process for an EMV method cast RAC component usually becomes difficult, this is probably because of the increasing solid constitution content, due to simultaneous inclusions of waste RAs and compensatory NAs. And after hardening, the number of coarse aggregate and ITZ categories in the sample also increases. Both of these differences affect the sample’s failure mode, as well as alter the concrete’s mechanical properties and their variabilities (Yu et al., 2021b), but available studies have yet not clearly reported them. In addition, it is clear to find from existing tests that the property for the old mortar attached on RAs is often lost. Commonly, this fact indicates that the strength ratio of new mortar to old mortar, which mostly affects the RAC’s mechanical property (Yu et al., 2021b), is not clear. As a result, the improving result for an EMV method has some uncertainties. And lastly, facing to actual designing and constructing RAC elements, concise formulas used to estimate uniaxial mechanical properties of EMV method designed RAC based on its constituents are always welcomed. But these formulas are not built up to now.

To add knowledge with related to these issues, this study tries to conduct some mesoscale computations to simulate the EMV method designed RAC samples under compression and tension. Similar with the works conducted by Wang et al., (2019, 2020), RAC at mesoscale level is considered as a composite material constituted by phases of new and old aggregates, mortar and ITZs. After building the RAC’s random aggregate model, a finite element method or discrete element method (DEM) commonly can be used to simulate the mechanical responses of concrete. In this study, the latter technique is adopted since it has been shown in previous literature (Tan et al., 2019; Nitka and Tejchman, 2020; Sinaie et al., 2018) together with our recent investigations (Yu et al., 2021a) that DEM has the following distinct advantages: (a) easy to represent different types of ITZs; (b) handy for explicitly expressing crack’s initialization and development; (c) reasonably simulate concrete’s lateral deformation changes; and (d) superior in describing the concrete material’s mechanical property indexes quantitatively. With using DEM, more recently, Tan et al. (Tan et al., 2019) successfully simulated the failure process of Modeled RAC plates under axial compression, and Zhang’s group (2021) innovatively discussed the crushing characters of recycled construction and demolition wastes used in road bases.

After clearly illustrating the methods used in this study, axial compressive and tensile loadings for conventional and EMV methods designed RACs will be simulated. Particularly, the impacts of the RA replacement ratio, the water-to-cement ratio of the mixture and the coarse aggregate’s spatial location on these two RACs’ strength and deformation characteristics are analyzed and compared in detail. In the last section of this paper, generic expressions used for predicting strengths and elastic moduli of conventional and EMV methods designed RAC specimens will be tentatively established. The authors think that the outcomes of this study will benefit to engineers well understanding the mechanical responses of EMV method designed RAC and their differences with conventional RAC together with estimating the two concretes’ mechanical properties during mix-design stage.

Mesoscale computational models

Random aggregate model

Three categories of concretes are modeled in this study, they are, respectively, NAC, RAC fabricated with a conventional method and RAC mixed using an EMV method. The main intent of this sub-section is to illustrate the establishment method for these concretes’ random aggregate models.

Before conducting such a work, mesoscale structures of the three concretes should be understood firstly. Today, it has been widely known that the traditional NAC is manufactured using raw materials of water, cement, sand, coarse aggregates and some admixtures. But in mesoscale simulations, these constituted materials can not all be explicitly modeled due to the limitation of the computation capacity. Generally, water, cement and sand are treated together to form a mortar phase, which finally leads NAC at mesoscale level being composited by phases of coarse aggregate, mortar and ITZs. For RAC cast by a conventional method, more various phases appear in the material. At this time, coarse aggregates, mortar and ITZs should be distinguished based on their original sources or connecting objects. Consequently, it makes the conventional RAC sample as a six-phase material constituted by new aggregates, old aggregates, new mortar, old mortar, new aggregate-new mortar ITZs and RA-new mortar ITZs (Note that in some recent study (Yu and Wu, 2019) the RA-new mortar ITZ is also separated as old aggregate-new mortar ITZ and old mortar-new mortar ITZ). Lastly, with regard to the RAC sample proportioned with an EMV method, its meso-structure is the most complex due to the inclusion of compensatory aggregates.

The coarse aggregate’s shape, size and content should also be ascertained prior of establishing mesoscale models. In this study, since NAC and RAC samples are both modeled as two-dimensional 100×100 mm squares, natural, recycled and compensatory aggregates appearing in these samples are assumed as circular for simplicity. Similar with the practices done in modeling works of (Wang et al., 2019, 2020; Yu et al., 2021a), the sizes and contents of coarse NAs and RAs in NAC and conventional RAC samples are supposed to follow the classical Walraven’s formulation:

\begin{array}{l} P_{c} (D < D_{0}) = P_{k} (1.065 D_{0}^{0.5} D_{\max}^{- 0.5} - 0.053 D_{0}^{4} D_{\max}^{- 4} - 0.012 D_{0}^{6} D_{\max}^{- 6} - \\ 0.045 D_{0}^{8} D_{\max}^{- 8} + 0.0025 D_{0}^{10} D_{\max}^{- 10}) \end{array}

(1)

in which P_c represents the area percent of coarse particles with a diameter D less than D₀; D is the circular aggregate’s diameter; P_k denotes the fraction of the total area occupied by coarse aggregates (usually 75%, Yu et al., 2021a); and lastly D_max is the maximum aggregate size, which keeps as 20 mm as per the calibration experiments of this study.

For RAC samples proportioned by an EMV method, its coarse aggregates’ size and content do not follow the Walraven’s formulation due to the addition of compensatory aggregates. In current simulations, the geometric size of compensatory aggregates is simply taken as 7.5 mm, while its total area content P_com is calculated according to the definition of the EMV method (Fathifazl et al., 2009):

P_{com} = ν η P_{k} V

(2)

in which η is the RA’s area replacement ratio (equals to volume replacement ratio since the out-plane thickness of the concrete sample is assumed as 1.0); ν is the average area ratio of adhered old mortar to RA, and it is supposed as 30% during all of the calculations; and V is the specimen volume.

The number of aggregates can then be acquired through equations (1) and (2). To build the random aggregate model, the recently-proposed “explicit movement of coarse aggregates” technique by the authors is adopted in this study (the advantages of such a method against with the traditional “take and place” method (Wang et al., 1999) had been illustrated clearly in our previous studies (Yu et al., 2019). This method is completely implemented on the commercial software of Particle Flow Code 2D (PFC2D), and those involved main procedures can be summarized as: (a) Keeping the width of the square as 100 mm, however, amplifying its height to generate a rectangle with a dimension of 100 × 200 mm. Then using the PFC2D software’s built-in command “wall generate” to create four pieces of bounding walls. (b) Maintaining the total number of the coarse aggregates unchanged, but increasing their sizes as 1.05 times of the initial ones (Note that the purpose of such a treatment is to avoid overlaps between adjacent particles, and the aggregate’s size will be recovered to the initial one in the subsequent step e). (c) Employing the package’s built-in command “ball generate” to place all aggregates into the rectangle. It should be mentioned that this command will automatically ignores some hard-to-place particles if the aggregate’s content is too high (Itasca, 2004). But in the present method because of the enlargement of the thrown zone in the first step, the aggregate’s placement is generally easy. (d) Giving aggregate a pretty large normal stiffness, then forcing the top and bottom bounding walls to move face to face until reaching a distance of 100 mm. During the walls’ motion, the aggregates are translated simultaneously, and the high stiffness will ensure that the overlaps between adjacent aggregates are very small. (e) Adjusting the adjacent aggregates’ distance and the aggregate-wall’s distance: these involve giving each aggregate a low velocity and an arbitrary translation direction together with shrinking the dimension of the particle back to the initial one to make aggregates apart. (f) Random aggregate models of NAC samples have been well established after completing above steps, but for RAC samples, one more step is often needed, that is, choosing compensatory aggregates and simulating RA’s adhering old mortar. It is realized by randomly selecting some of aggregates to be compensatory aggregates and RAs in line with the predefined volume ratio and dividing each RA circularly into a thin mortar shell and an old aggregate core. Figure 2 shows the example steps for building the random aggregate model of RAC sample designed with an EMV method.

Figure 2.

Generating mesoscale multiphase models for EMV method designed RAC.

Principles for mesoscale DEM

Discrete element method is one classical method, which was firstly proposed by Cundall and Hart (1992) in 1971 to simulate jointed rock’s failure process. Through recent years’ studies (Nitka and Tejchman, 2020; Tan et al., 2019; Sinaie et al., 2018), this method has also been demonstrated as an effective approach to model the concrete’s workabilities and mechanical properties. Similar with the finite element method, the analytical body in a discrete element analysis should also be discretized first. But the most notable distinction in this method is that the separated elements are usually rigid blocks or particles, where the deformation can not occur inside the element. The motion of computation body is finally realized by connecting these elements with contacts (see Figure 3).

Figure 3.

Discrete element model for an EMV method cast RAC sample. (a) Background mesh projection, (b) Various kinds of particles & contacts, (c) Cell composition for different contact models in PFC2D.

Discrete element simulations conducted in this article were again implemented on the PFC2D software. Circular particles with a mean diameter of 0.36 mm were chosen to discretize the square. To ensure the sample’s compactness, the particle’s size was allowed to float around the average with a variability coefficient of 10%, this finally produced an initial porosity of 5.0% of the sample. After finishing meshing, a background mesh projection method was adopted to determine the phase attribution for each particle and contact, since it has been reported by Ren et al. (2015) that such a technique can effectively reduce the disturb of irregular elements on the simulation results. Figure 3(a) shows an example mesh for an EMV method designed RAC sample using above treatments. In that mesh, rigid particles’ total number and deformable contacts’ total amount are, respectively, about 9.3 × 10⁴ and 27.3 × 10⁴.

As mentioned previously, contacts are usually adopted by the software of PFC2D to represent mutual interactions among discrete particles. For easily understanding, one contact can be treated as a combination of cells such as springs, gaps, dampers, frictions, and etc. In this paper, a total of two types of contact models were employed, those were, linear model (LM) and flat joint model (FJM). LM was chosen to model interactions happening between the concrete specimen and the two load platens, while FLM was adopted to describe interactions among adjacent rigid particles. The reasonableness of choosing these models to simulate the concrete’s uniaxial mechanical behaviors has once been verified in our previously-published studies (Yu et al., 2021a Yu et al., 2021b).

From Figure 3(c)-1, it is evident to find that a LM is commonly constituted by a pair of normal and shear springs, a pair of normal and shear dampers and one friction cell. Such an arrangement finally makes that the contact is always linear-elastic in the normal direction, and reaches its maximum capacity when the shear slippage achieves the value of δ_su. Comparing to the LM, the composition and mechanical response of the FLM are more complex. Prior to understanding this representation, another type of model named “linear parallel model (LPM)” should be introduced firstly. It can be seen in Figure 3(c)-2 that as compared with a LM only two parallel springs are added in a LPM. But it should be noted that these springs can only bear external forces with limited magnitude. Their capacities are, respectively, ascertained by the parameters of tensile strength σ_t, cohesive strength c and friction angle φ.

In both LM and LPM, mutual action among adjacent particle pieces in two-dimensional plane is treated as point-to-point contact. In a FJM, this interaction is, however, considered as line-to-line. As shown in Figure 3(c)-3, a FJM commonly divides the contact line into small separate elements. Before loading, each element independently deforms, and can under a partially damaged or broken state. When external force is applied, intact elements can be described by a LPM, while broken elements follow the LM. This special structure makes the mesoscale force displacement law for a FJM can be a weighted sum of the ones of LM and LPM. A detailed comparison for the mesoscale mechanical responses of these three models can be found in literature (Yu et al., 2021b).

Table 1 summarizes the main parameters used in LM and FJM. In this study, most of these parameters were determined in accordance with the values used in previous studies (Tan et al., 2019). The remaining three parameters E^*, σ_t and c should be calibrated through axial compression and tension tests.

Table 1.

Mesoscale parameters used in LM and FJM.

Mesoscale properties	Literature	This paper	Mesoscale properties	Literature	This paper
Linear model
Elastic modulus E^L	200 GPa	200 GPa	Stiffness ratio k^L	2–3.5	2
Friction coefficient μ_s^L	0–0.6	0.6	Normal damping ratio β_n^L	0.5	0.5
Flat-joint model
Effective modulus E^*	—	By test	Effective modulus of parallel spring E_p	E ^*	E ^*
Stiffness ratio k^*	2–3.5	3.1	Stiffness ratio of parallel spring k_p	k ^*	k ^*
Surface gap g_n	0–0.3	0	Tensile strength σ_t	—	By test
Friction coefficient μ_s	0–0.6	0.6	Cohesion strength c	—	By test
Normal damping ratio β_n	0.5	0.5	Friction angle φ	0–50°	26.7°
Shear damping ratio β_s	0	0	Radial element N	2–4	2

Determining mesoscale parameters of DEM

Reasonably choosing mesoscale parameters used in DEM has been stated as the most essential thing to ensure the mesoscale simulation’ objectivity (Tan et al., 2019). Due to the most complex composition, the EMV method designed RAC is taken in this section as an instance to illustrate how to determine the DEM’s parameters.

From Figures 1 and 2 it is not difficult to see that 10 various kinds of constitutive phases are simultaneously existed in a RAC sample proportioned by an EMV method. This finally leads 10 various contacts appearing in the DEM model. Those are, respectively: (a) new aggregate-new aggregate contact; (b) new mortar-new mortar contact; (c) new aggregate-new mortar contact; (d) old aggregate-old aggregate contact; (e) old mortar-old mortar contact; (f) old aggregate-old mortar contact; (g) new mortar-old mortar contact; (h) new mortar-old aggregate contact; (i) compensatory aggregate-compensatory aggregate contact; and (j) compensatory aggregate-new mortar contact. The former six types of connecting contacts are used to describe attributions of new concrete and RA’s parent concrete, the seventh and eighth contacts are adopted to describe the bonding between coarse RAs and new mortar; while the last two contacts are employed to describe the compensatory aggregates and their bonding to new mortar.

For each of above-listed contacts, there commonly exist three parameters (i.e. E^* , σ_t and c) should be determined. To simplify that process, the below hypotheses are made for this study’s calculations: (a) Coarse aggregates including new, old and compensatory aggregates are assumed to have a same attribution, their mesoscale parameters of σ_t, c and E^* are uniformly set to be 36 MPa, 48 MPa and 75 GPa, respectively in accordance with the values used in literature (Yu et al., 2021a). (b) The property of aggregate-mortar ITZ is supposed as positively correlated with that of its connecting mortar. In line with the microscopical test result reported by Xiao et al. (2013a), this ratio is supposed to be 0.8; (c) New mortar-old mortar ITZs are usually stronger than new aggregate-new mortar ITZs, and their parameters are often supposed as 0.85 times of those of new mortar. Following these rules, Table 2 has summarized the main parameters employed in the discrete element mesoscale model of an EMV method designed RAC.

Table 2.

Detailed parameters for the 10 types of contacts in EMV method mixed RAC.

Material	Contact type	E^* (GPa)	σ_t (MPa)	c (MPa)
Newly-poured concrete	New aggregate-new aggregate	75	36	48
	New mortar-new mortar	α _new	β _new	γ _new
	New aggregate-new mortar	0.80α_new	0.80β_new	0.80γ_new
RA’s parent concrete	Old aggregate-old aggregate	75	36	48
	Old mortar-old mortar	α _old	β _old	γ _old
	Old mortar-old mortar	0.80α_old	0.8β_old	0.8γ_old
Bonding between new mortar and RA pieces	Old aggregate-new mortar	0.80α_new	0.80β_new	0.80γ_new
Bonding between new mortar and RA pieces	Old mortar-new mortar	0.85α_new	0.85β_new	0.85γ_new
Bonding between new mortar and compensatory aggregates (CAs)	CA-CA	75	36	48
	CA-new mortar	0.80α_new	0.80β_new	0.80γ_new

Calibration & validation of computational models

The feasibility of using random aggregate model and DEM to model the uniaxial mechanical performance of NAC and conventional RAC samples in compression and tension loadings has once been checked in our study (Yu et al., 2021b). That verification contains two aspects of works, which are briefly summarized here:

a. Examining discrete element modeling results with experiments: A total number of 36 mortar, NAC and conventional RAC platens were manufactured in literature (Yu et al., 2021b). These samples were designed to possess same values of water-to-binder ratio and binder-to-sand ratio, which makes the mortar paste have an identical attribution. The total mass of coarse aggregates in NAC and RAC samples was also same. Before casting, coarse RAs were presoaked in clean water for 24 h to reach a saturated-surface dry state. In mesoscale computations, the modeled crack propagation, failure mode, mechanical behaviors of mortar paste and concrete samples under direct tension and compression were compared with the tested ones. It was finally found that not only the longitudinal mechanical responses but also the lateral deformable characters of mortar, NAC and RAC samples have been well reproduced.

b. The influences of various kinds of internal factors (including the new mortar’s strength, old mortar’s strength and content, crushing microcracks and etc.) on the RAC’s uniaxial mechanical performance were simulated using the calibrated DEM models, and they were also compared with the typical rules acquired through experiments. These investigations again demonstrate the DEM’s power. For instance, it was found from the numerical results that the strength ratio of new mortar to old mortar has a decisive influence on crack initialization and extension happened in conventional RAC. When the new mortar paste is weaker than the old mortar paste, micro-damage always happens at ITZs between old and new pastes, and then develops into the new paste. However, if the old mortar is weaker, crack initially occurs at the old aggregate-old mortar ITZs, then propagates into the old mortar and eventually into the new mortar. Lastly, when the old mortar is significantly weaker than the new mortar, almost all micro-damages are located within the weak old mortar. These findings perfectly agree with the observations reported by Xiao et al. (2013a) during their testing on Modeled RAC plates (see Figure 4).

Figure 4.

Micro-damage development around RA pieces in compression (Yu et al., 2021b). (a) Conventional RAC sample (old mortar strength > new mortar strength), (b) Conventional RAC sample (old mortar strength < new mortar strength), (c) Conventional RAC sample (old mortar strength << new mortar strength).

Modeling results of conventional RAC

Before evaluating the enhancement result of the EMV method, uniaxial mechanical behaviors for RAC cast with a conventional method must be first known. To achieve this goal, 750 conventional RAC samples were modeled in this section. Main variables among these samples include the RA replacement ratio (0, 30%, 50%, 70% and 100%) and the strength ratio of new to old mortar (The old mortar’s compressive strength kept as 41.06 MPa, but the new mortar strength could change from 27.14, 41.06–58.23 MPa; For each sample, mesoscale parameters for the old and new mortars can be ascertained in line with the data listed in Table 3). In addition, to alleviate the disturb of the coarse aggregate’s spatial locations on the discrete element simulations, NAs and RAs in every NAC and RAC samples should be randomly thrown a certain of times until stable mechanical responses are acquired. This finally leads 50 parallel samples for each combination of RA replacement ratio and strength ratio of new to old mortar. Figure 5 shows the detail procedures to determine the throw times.

Table 3.

Mesoscale parameters for the mortar phase and its corresponding mechanical properties.

E^* (GPa)	σ_t (MPa)	c (MPa)	Compressive strength (MPa)	Tensile strength (MPa)	Elastic modulus (GPa)
45	21.6	28.8	27.14	2.20	11.82
75	36	48	41.06	3.65	19.53
105	50.4	67.2	58.23	5.13	27.25

Figure 5.

Mechanical behavior for EMV method designed RAC with different aggregate distributions. (a) Comp. stress–axial strain curves, (b) Comp. stress-vol. strain curves, (c) Contact failures in compression, (d) Tensile stress–axial strain curves, (e) Contact failures in tension, (f) Mechanical index variability.

The stress-axial strain relations, stress-volumetric strain relations and stress-to-strength ratio-failure contact number relations for a total number of 50 RAC samples under compression are presented in Figure 5(a) to (c). Note that the RA replacement ratio and the new mortar strength among these samples are both identical with adopting values of 50% and 41.06 MPa, the only distinction is the coarse aggregate location. Correspondingly, Figure 5(d) and (e) present the stress-strain curves and failure contact number’s evolution curves under tensile loading. It can be seen from these plots that: (a) As the aggregate location changes, the linear ascending portions (up to almost 40% of the peak strength) of the compressive and tension load-deformation curves basically coincide. This implies that the elastic modulus and Poisson’s ratio for a concrete material are negligibly affected by the coarse aggregate distribution. (b) Concrete’s two mechanical strengths are both obviously affected by the NAs and RAs’ distributions. (c) The variability for the concrete’s volumetric strain is found as more notable than that of axial strain. (d) When the external force exceeds the concrete’s uniaxial load capacity, the variability of the axial stress usually grow with an increase in the axial deformation. To express the variation features of the stress-axial strain relations quantitatively, Figure 5(f) further show the mean value together with the coefficient of variation for the RAC’s compressive strength, elastic modulus and tensile strength against with the throw times. It is easy to find that the RAC’s elastic modulus stabilizes quite quickly, but the average value and the coefficient of variation for the compressive and tensile strengths still fluctuate significantly when the sample number is 10. Above 25, all mechanical properties, however, get stable. Thus, a choose of 50 times of random throws in this study’s computations is adequate to acquire stable mechanical results.

The variabilities of the conventional RAC’s compressive and tensile strengths with various contents of RAs and relative strengths of new to old mortar induced by the coarse aggregate location are summarized in Figure 6(a) and (b). Note in these figures that the RAC specimen with a zero RA replacement ratio always indicate a NAC sample. It can be seen that the variabilities of RAC’s compressive and tensile strengths usually locate in the ranges of 2.36%–3.19% and 6.41%–9.01%, which are both higher than the variabilities of NAC’s mechanical indexes. This observation is consistent with the results reported by Xiao et al. (2018) and Pacheco et al. (2019) during their experimental investigations on RAC’s uniaxial mechanical properties. As explained by those scholars, the reason for this phenomenon is probably because that more numbers of phases like old mortar and ITZs appear in RAC, which makes micro-damages and cracks develop more randomly, and finally affects the RAC’s macroscopic mechanical responses. Furthermore, it is evident to find through comparing subplots a&b that the variability for the RAC sample’s uniaxial strength index is on the whole the largest when the compressive strength of the new mortar paste is 58.23 MPa, and is the smallest as the strength of the new mortar paste is 41.06 MPa. This result shows that the strength ratio of new mortar to old mortar is an essential factor affecting the variability of the RAC’s uniaxial mechanical property. In general, RAC’s strength randomness is the smallest when new and old mortars have a same attribution.

Figure 6.

Property variability for conventional RAC with various relative strengths of new to old mortar. (a) Compressive strength, (b) Tensile strength.

Next the impact of the RA’s replacement level on conventional method designed RAC samples’ mechanical and deformation behaviors are emphatically discussed in this section. Figure 7 shows a case in which the strength of the new mortar (i.e. 58.23 MPa) is significantly higher than that of old mortar (i.e. 41.06 MPa). This corresponds to the commonest case in real employment of the RAC material, since RAs are usually produced from old year components. As previously mentioned, to avoid the adverse influence of the aggregate’s location on the current analyses, each curve depicted in Figure 7 denotes an average response for 50 parallel RAC samples under compression or tension. It can be found from this figure that:

a. With increasing the content of RAs, both the RAC’s compressive and tensile mechanical properties notably deteriorate: When the replacement ratio reaches up to 100%, the RAC’s compressive strength degenerates from 64.52 to 56.86 MPa with an amplitude of 11.8%, its elastic modulus decrease from 40.09 to 33.10 GPa with an amplitude of 17.4%, and the tensile strength decline notably from 4.45 MPa to 3.57 MPa with an amplitude of 19.8%. Obviously, the reduce rate of the RAC’s tensile strength is the fastest.

b. As the RA volume content grows from zero to 100%, the decreasing proportions of the RAC sample’s compression and tension stress-axial strain curves both become flat, which indicates that the RAC’s brittleness is generally higher than that of NAC. A group led by Wu et al. (2014) reported a similar observation during their tests.

c. Under a same stress to strength ratio, the RAC’s volumetric strain commonly grows as the RA replacement ratio increase, and the critical stress ratio (namely, the stress level where the sample volume transforms from compression to dilation) always declines. Both of these results show that incorporating RAs leads the RAC’s lateral deformation being larger.

d. Probably attributed to the function of the mortar adhering on the RAs, at the initial loading of the RAC sample, the occurrence moment for the internal damage commonly delays as the RA replacement ratio increases. Simultaneously, the total amount of failures in the sample always declines.

e. When external force exceeds the load capacity, failure contact content is usually larger in RAC samples.

Figure 7.

Mechanical behaviors for conventional RAC with various replacement ratios (fnew mortar > fold mortar). (a) Comp. stress-axial-strain curves, (b) Comp. stress-vol. strain curves, (c) Failed contacts in compression, (d) Tensile stress-axial strain curves, (e) Failed contacts in tension.

Figures 8 and 9 show the crack propagation processes for above conventional RAC samples with various RA replacement ratios (including 0, 30%, 50%, 70% and 100%) under axial compression and tension, respectively. It is clear to see from these figures that the uniaxial failure patterns of RAC are almost negligibly affected by the RA volume content: during compressive loading, main cracks develop primarily at vertical directions, and lastly divide the concrete square as small columns. While at tension loading, only one or two cracks are horizontally formed, and finally the sample’s whole deformation is located at the cracking region. But when taking a close look at the local parts of concrete samples depicted in Figures 8 and 9, it can be seen that notable differences still exist among the crack paths of NAC and RAC samples: For a NAC sample, cracks mainly originate at the new aggregate-new mortar ITZs, and they progressively propagate into mortar, but barely develop into the hard coarse aggregates. However, with regard to the RAC sample cast using a conventional method, stress-induced cracks occur initially at the connecting ITZs between old aggregate and old mortar, quickly pass through the old paste, and then enter into the new paste region. As the RA replacement ratio grows, the frequence for such phenomenons increases significantly. These results commonly illustrate that the weakest regions in one RAC sample change from the traditional new aggregate-new paste ITZs to be the old aggregate-old paste ITZs.

Figure 8.

Crack development process for conventional RAC samples under compression (f_{new mortar} > f_{old mortar}). (a) NAC, (b) RAC30, (c) RAC50, (d) RAC70. (e) RAC100.

Figure 9.

Crack development process for conventional RAC samples under tension (f_{new mortar} > f_{old mortar}). (a) NAC, (b) RAC30, (c) RAC50, (d) RAC70, (e) RAC100.

Lastly, Figures 10 and 11 display another two cases of compressive and tensile mechanical responses of RAC samples which the new mortar property is equal to or smaller than the old mortar property. Again each curve in the figures is an average of the responses of 50 parallel specimens. It can seen from these figures that the variation tendencies of the concrete’s compressive stress-strain curves and the stress-to-strength ratio-failure contact number relations against with the replacement ratio are similar with those in Figure 7, which shows that an inclusion of RAs in concrete always deteriorate the material’s compressive mechanical indexes. As explained by Xiao et al. (2013a, 2018), this is mainly because that, during compressive testing on RAC, the adhered mortar on RAs is often treated as “hard aggregate” to resist the external load, this makes severe damages and cracks frequently appear in this region. But due to the lower attribution of the old mortar, the RAC sample’s compressive strength and elastic modulus notably decline.

Figure 10.

Mechanical behaviors of conventional RAC with various replacement ratios (f_{new mortar} = f_{old mortar}). (a) Comp. stress-axial-strain curves, (b) Comp. stress-vol. strain curves, (c) Failed contacts in compression, (d) Tensile stress-axial strain curves, (e) Failed contacts in tension.

Figure 11.

Mechanical behaviors of conventional RAC with various replacement ratios (f_{new mortar} < f_{old mortar}). (a) Comp. stress-axial-strain curves, (b) Comp. stress-vol. strain curves, (c) Failed contacts in compression, (d) Tensile stress-axial strain curves, (e) Failed contacts in tension.

Besides above similarities, some significant changes also can be found through comparing the tensile mechanical behaviors of RAC mixtures with different strength ratios of new mortar to old mortar. As seen from Figure 10(d), as the old mortar strength is equal to new mortar strength, average tensile strengths for the five RAC samples with 0, 30%, 50%, 70% and 100% amount of RAs are, respectively, 3.07, 3.06, 2.99, 3.01 and 3.05 MPa. Obviously, RAC’s tensile strength is negligibly affected by the RA replacement ratio. But if reducing the new mortar strength to be obviously lower than that of old strength (see Figure 11(d)), mean tensile strengths of the RAC samples become as 1.73, 1.81, 1.76, 1.78 and 1.86 MPa. At this time, the RAC’s tensile strength presents an increasing trend with the growth of the replacement ratio. Both of these variation trends of the RAC’s tensile strength are different with that presented in Figure 8. These results show that the conventional RAC’s tensile mechanical response is highly sensitive to the relative strength of new-to-old mortar.

Simulation results for EMV method mixed RAC

To ensure a one-to-one correspondence with the conventional RAC samples (exclude the NAC samples) modeled in Section 3, a total amount of 600 RAC cubes cast with an EMV method are modeled in this section. Again, the RA replacement ratio, the strength ratio of new mortar to old mortar and the spatial location of coarse aggregates (including NAs, RAs and compensatory aggregates) are the main variables among these specimens.

The modification effect of the EMV method is firstly evaluated at a case where RAC has an identical strength of new and old mortars (i.e. the strength ratio of new mortar-to-old mortar is 1.0). Average tensile and compressive mechanical responses of these EMV method designed RAC samples with various RA contents have been presented in Figure 12. Combining with the numerical curves shown in Figure 7, it can be found that: (a) At this relative strength, the improvements for the strength and deformation indexes of RAC are very remarkable. The compressive strength, elastic modulus and tensile strength for the NAC material are, respectively, 48.90 MPa, 30.95 GPa and 3.06 MPa. With using a conventional mix method, these three mechanical properties for the RAC sample containing a 100% replacement ratio of RAs declines to be 44.96 MPa, 26.16 GPa and 3.05 MPa, but after adopting the EMV method, the same indexes for the RAC sample with a 100% RA replacement ratio change as 47.93 MPa, 30.03 GPa and 3.07 MPa. (b) For EMV method designed RAC samples with various RA replacement ratios, the descending and residual proportions of their compressive and tensile stress-strain relations always coincide with each other. This again shows the RAC’s mechanical responses almost completely recovery to the NAC’s level.

Figure 12.

Mechanical behaviors of EMV method designed RAC with various replacement ratios (f_{new mortar} = f_{old mortar}). (a) Comp. stress-axial-strain curves, (b) Comp. stress-vol. strain curves, (c) Failed contacts in compression, (d) Tensile stress-axial strain curves, (e) Failed contacts in tension.

Above numerical results also show that the influence of the content of ITZs on the concrete’s axial mechanical properties is commonly limited, since it is easy to find that the most notable difference between NAC and an EMV method proportioned RAC is that lots of old aggregate-mortar ITZs appears in the latter type of concrete. In accordance with the study results reported by (Yu et al., 2021a Yu et al., 2021b), the parameter of the ITZ content commonly does not alter the concrete’s strength greatly, but always affects the internal damages occur in the material. The current relations between the stress-to-strength ratio and the failure contact number, which are presented in Figure 12(c) and (e), verify this conclusion. At full loading range, the total number of failure contacts in RAC always grows with the increasing of the RA replacement ratio.

When the attribution of old mortar is significantly higher than the property of new mortar, the axial stress-strain relations together with the failure contact number’s evolution curves for the EMV method designed RAC samples have been depicted in Figure 13. The figure clearly shows that the average compressive strengths for the five RAC samples with a 0, 30%, 50%, 70% and 100% replacement ratio are, respectively, 32.45, 33.23, 33.20, 33.26 and 34.08 MPa, their mean elastic moduli are 20.35, 20.67, 20.87, 20.91 and 21.24 GPa, and the tensile strengths are 1.76, 1.82, 1.78, 1.79 and 1.87 MPa. Apparently, these numerical results again demonstrate that the EMV mix method is effective to enhance the RAC’s mechanical performance at such a strength combination of new and old mortars. The slight increasing tendency of the RAC’s mechanical property against with the RA replacement ratio is probably because the strong old mortar replaces the weak new mortar to bear external load. Attributed to the same reason, it is easy to observe that either under a compressive or tensile loading, the total number of the failure contacts in the concrete sample is always the lowest for RAC having a largest replacement ratio of RAs. This trend has a big difference with that appears in EMV method proportioned RAC samples with a 1.0 strength ratio of new-to-old mortar.

Figure 13.

Mechanical behaviors of EMV method designed RAC with various replacement ratios (f_{new mortar} < f_{old mortar}). (a) Comp. stress-axial-strain curves, (b) Comp. stress-vol. strain curves, (c) Failed contacts in compression, (d) Tensile stress-axial strain curves, (e) Failed contacts in tension.

Figure 14 presents the third case of stress-strain curves and stress-to-strength ratio-failure contact number relations for RAC samples mixed with an EMV method. In all of these samples, the new mortar is 58.23 MPa, which is apparently larger than that of old mortar attaching on the coarse RAs (namely 41.06 MPa). As clearly seen from the subplots, with an increase in the replacement ratio of RAs, the RAC’s peak strengths and deformable modulus present declining trends, and the failure contact numbers at full range of compression and tension commonly increase, which both indicates that the RAC’s mechanical performance is weaker than that of the NAC material. Taking a close look at the concrete’s compressive response, compressive strengths for the five RAC samples of Figure 14(a) are, respectively, 64.53, 62.85, 61.68, 60.63 and 59.44 MPa, where the same indexes for the conventional RAC samples are 64.53, 61.17, 59.94, 58.69 and 56.86 MPa, respectively (see figure a). From this data, it is easy to know that the EMV method has slightly improved the RAC’s mechanical property, but can not help RAC to recovery its mechanical property to that level of NAC.

Figure 14.

Mechanical behaviors of EMV method designed RAC with various replacement ratios (f_{new mortar} > f_{old mortar}). (a) Comp. stress-axial-strain curves, (b) Comp. stress-vol. strain curves, (c) Failed contacts in compression, (d) Tensile stress-axial strain curves, (e) Failed contacts in tension.

The limited improvement result of the EMV method in such a strength combination of new and old mortars is obviously due to the old mortar’s adverse influence. As stated in one of our previous article (Yu et al., 2021b), the RAC’s tensile and compressive mechanical properties will be sharply deteriorated when too weak attribution of phase is included in the mixture. In an EMV mix design method, the coarse aggregates’ volume ratio is effectively recovery through adding an equivalent amount of compensatory aggregates, but the weak attached mortar in fact has not been well treated. Thus, from a view of practice employment, the current results show that it is needed to adopt some special RA enhancement techniques such as carbonation and acid-washing to use together with the EMV method when the old mortar’s property is much lower than that of new mortar (which is frequently happened in high-strength RAC).

As typical instances, Figures 15 and 16 further show the crack developments for RAC samples of Figure 14 under uniaxial loading. Comparing these pictures with those depicted in Figures 8 and 9, it is evident to see that the failure shapes of the EMV method designed RAC samples under axial compression and tension do not change very much. The biggest difference is that more twisted cracks occur in the RAC samples cast using an EMV method. This is probably because that more numbers of ITZs and coarse aggregates appear in a narrow zone.

Figure 15.

Crack development for EMV method designed RAC samples under compression (f_{new mortar} > f_{old mortar}). (a) RAC30, (b) RAC50, (c) RAC70, (d) RAC100.

Figure 16.

Crack development for EMV method designed RAC samples under tension (f_{new mortar} > f_{old mortar}). (a) RAC30, (b) RAC50, (c) RAC70, (d) RAC100.

Lastly, Figure 17 displays the variabilities for the mechanical properties of the EMV method designed RAC samples. It is easily seen that: (a) The variability for the compressive and tensile strengths of RAC cast with an EMV method locate in the ranges of 2.41%–3.76%% and 6.77%–9.70%, which are both larger those of RAC cast with a conventional method. (b) The EMV method designed RAC’s mechanical property variability usually increases with the growth of the replacement ratio of RAs.

Figure 17.

Property variability for EMV method designed RAC with various relative strengths of new-to-old mortar. (a) Compressive strength, (b) Tensile strength.

Generic expressions for estimating uniaxial mechanical properties of RAC

After well illustrating the mechanical properties of conventional and EMV method cast RAC samples with various RA replacement ratios, some predictive expressions are tried to be established in the current section. This work is not only meaningful for actual practices of these two kinds of RACs in engineering, but also significant for correlating uniaxial mechanical properties of various kind of concretes like normal strength conventional concrete, lightweight aggregate concrete and recycled brick aggregate concrete (Bilir, 2016; de Brito and Agrela, 2018).

Before conducting such a work, two important aspects of knowledge should be briefly introduced in this section, since the following proposed generic formulas are primarily built based on them. The first one is a new waste concrete recycling technology, which was originally proposed by Wu’s research group and termed as recycled lump concrete (RLC) (Wu et al., 2018b; Yu and Wu, 2019). Figure 18(a) gives a detailed illustration for this material. It can be seen from the figure, in RLC, demolished concrete was coarsely broken as large-piece lumps, and then cast with freshly pouring concrete to form new components. And it is easy to find through comparing Figure 16(a) and (b) that the RLC is also constituted by phases of new and old mortar, aggregate and ITZ, but their assembling mode has a large difference with that of conventional RAC.

Figure 18.

Predicting mechanical properties of conventional method and EMV method designed RAC samples. (a) Recycled lump concrete, (b) Comparison between DEM calculation and Model prediction.

Through conducting extensive material tests (Wu et al., 2018a, 2018b, 2019) and some mesoscale discrete element simulations (Yu and Wu, 2019), Wu and his colleagues proposed the following expressions for ascertaining the mechanical properties of RLC as:

f_{c, RLC} = (1 - θ) \times f_{c, new concrete} + θ f_{c, old concrete}

(3)

f_{t, RLC} = (1 - θ) \times f_{t, new concrete} + θ f_{t, old concrete}

(4)

\frac{1}{E_{RLC}} = \frac{1 - \sqrt{θ}}{E_{new concrete}} + \frac{1}{(1 - \sqrt{θ} / \sqrt{θ}) E_{old concrete} + 1 / \frac{1}{k} + \frac{1}{E_{old concrete}}}

(5)

in which f_{c, RLC}, f_{t, RLC} and E_RLC are, respectively, combined compressive strength, tensile strength, and elastic modulus of the RLC, f_{c, new concrete}, f_{t, new concrete} and E_{new concrete} are corresponding mechanical properties of the new concrete, f_{c, old concrete}, f_{t, old concrete} and E_{old concrete} are mechanical properties of the old concrete, and finally θ is the mass replacement ratio of old concrete lumps (or waste utilization ratio). Generally, equations (3)–(4) indicate that uniaxial strengths of RLC can be easily determined by linear weight sum of the strengths of constituted new and old concretes. The structure of equation (5) is a little complex, but in fact it is a modified version of the Counto Model (see literature (Bilir, 2016; Wu et al., 2018b) for more details). The coefficient k is a parameter to consider the influence of micro-damages induced by lump crushing (Wu et al., 2018b).

Another issue is a historical subject, that is, how to predict uniaxial mechanical property of normal strength NAC accurately? The answer to this question is equally essential for concrete using recycled materials, since if those relations have be explicitly built, then they can be substituted into equations (3)–(5) to acquire predictive expressions correlating the macroscopic mechanical property of one recycled concrete to its constitutive phases’ mesoscale properties. Fortunately, in one of our previously-published articles, a series of simple expressions are established or confirmed through numerically-investigating the uniaxial mechanical properties of 287 cubes and comparing them with some existing experiments:

f_{c, * concrete} = 1.16 f_{c, * mortar} (0.714 A_{* aggregate} + 0.729)

(6)

f_{t, * concrete} = 0.83 f_{t, * mortar}

(7)

\frac{1}{E_{* concrete}} = \frac{1 - \sqrt{A_{* aggregate}}}{E_{* mortar}} + {[\frac{1 - \sqrt{A_{* aggregate}}}{\sqrt{A_{* aggregate}}} E_{* mortar} + E_{* aggregate}]}^{- 1}

(8)

Here the subscript *(=new or old) always indicates the concrete type; f_c,*concrete, f_t,*concrete and E_*concrete are, respectively, compressive strength, tensile strength and elastic modulus of conventional concrete; E_*aggregate and A_{* aggregate} are coarse aggregate’s elastic modulus and area ratio; and f_c,*mortar, f_t,*_mortar and E_*mortar are mechanical properties of the mortar.

For conventional method designed RAC samples, below expressions are existed for correlating the waste utilization ratio θ and the area ratios A of aggregates & mortars in new and old concretes to the global RA replacement ratio η and old mortar content ν:

θ = \frac{(1 - ν) η P_{k} ρ_{old aggregate} + ν η P_{k} ρ_{old mortar}}{(1 - η) P_{k} ρ_{new aggregate} + (1 - P_{k}) ρ_{new mortar} + (1 - ν) η P_{k} ρ_{old aggregate} + ν η P_{k} ρ_{old mortar}}

(9)

A_{new aggregate} = \frac{(1 - η) P_{k}}{1 - η P_{k}}

(10)

A_{old aggregate} = \frac{(1 - υ) η P_{k}}{η P_{k}} = 1 - υ

(11)

With regard to EMV method designed RAC sample, due to the inclusion of the compensatory aggregates, equations (9) and (10) should be replaced using the following formulas:

θ = \frac{(1 - ν) η P_{k} ρ_{old aggregate} + ν η P_{k} ρ_{old mortar}}{[(1 - η) P_{k} + ν η P_{k}] ρ_{new aggregate} + (1 - P_{k} - ν η P_{k}) ρ_{new mortar} + (1 - ν) η P_{k} ρ_{old aggregate} + ν η P_{k} ρ_{old mortar}}

(12)

A_{new aggregate} = \frac{(1 - η) P_{k} + ν η P_{k}}{1 - η P_{k}}

(13)

In equations (9)–(13), ρ denotes the density, and ρ_aggregate and ρ_mortar are assumed in this study as 2650 and 2100 kg/m³ in accordance with literature (Yu and Wu, 2019). Values of E_{* aggregate} and A_{* aggregate} are taken as 195.63 MPa and 96.61 GPa (data came from our previous article (Yu et al., 2021a)).

Using equations (3)–(13), the calculated average strengths and elastic moduli for the 1350 samples appearing in Modeling results of conventional RAC and Simulation results for EMV method mixed RAC can be compared with their DEM numerical averages depicted in Figure 7 and Figures 10 to 14. Figure 18(b) shows the comparison results. The figure shows that the three correlation coefficients for the mechanical properties are both larger than 0.95, which indicates that the model predicted strengths and elastic moduli are in well agreement with the DEM method calculate ones. The present section’s calculations also show that there exist generic models to determine the mechanical properties of various kinds of NACs and recycled concretes.

Conclusions

Two dimensional mesoscale discrete element modelings about RAC cubes under compression and tension were performed in this study to show the impacts of the strength ratio of new mortar to old mortar, the RA replacement ratio, the spatial locations of coarse NAs and RAs and the mix design method (including conventional method and EMV method) on the concrete’s uniaxial mechanical behaviors. The current works generate the following important conclusions:

a. With increasing the replacement ratio of RAs, both the compressive strength and elastic modulus of conventional RAC present a decreasing tendency. The variation trend of the RAC material’s axial tensile strength is, however, highly dependent on the strength ratio of new mortar to old mortar. When the old mortar attribution is higher than or equivalent to the new mortar property, the RAC sample’s tensile strength almost keeps unchanged as RA replacement ratio varies.

b. Regardless of the RAC mixture’s water-to-cement ratio, adopting an EMV cast method can always improve the material’s elastic modulus. But it should be noted that the enhancement result of this method to the uniaxial strengths is indefinite. When the property of the new mortar is lower than that property of old mortar, adopting an EMV mixing method notably improves the RAC’s tensile and compressive strengths, but when the old mortar strength is obviously smaller, the improving of the concrete’s strength is usually limited.

c. Attributed to the fact that more number of mesoscale phases existed in RAC materials, variabilities for mechanical properties of RAC are commonly higher than those of NAC. Besides, the variabilities for the compressive and tensile strengths of EMV method designed RAC samples were found as 0.05–0.89, 0.17–1.60 percentages larger than those of conventional RAC samples.

d. Uniaxial mechanical properties for NAC, RAC fabricated either using a conventional or EMV method, and recycled lump concrete can be predicted with same formulas.

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 research grants from China’s Natural Science Foundation (52008108, 52170800 and 52008107), Guangdong Basic and Applied Basic Research Foundation (2019A1515110481 and 2019A1515111032) and Key Research Project by Education Department of Guangdong Province (2018KZDXM068).

ORCID iD

Yu Zheng

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