Mesoscale modelling of recycled aggregate concrete under uniaxial compression of different strain rates

Abstract

Studying the compressive behaviour of recycled aggregate concrete (RAC) under different strain rates in a mesoscale model is of considerable interest. In the mesoscale model in this paper, RAC is regarded as a five-phase composite material mainly comprising natural aggregates, old interface transition zone (ITZ), old cement mortar, new ITZ and new cement mortar. The existence of pore defects is also considered. Random round aggregates and oval aggregate models of different recycled coarse aggregate replacement rates (0%, 25%, 50%, 75% and 100%) are constructed in the mesoscale RAC model. The uniaxial compressive behaviour of the mesoscale RAC model under different strain rates is numerically simulated. Numerical results show that the material properties of the ITZs have an impact on material damage. The compressive strength of recycled concrete increases with the strain rate, showing dynamic strain rate effects. The dynamic increase in strength is not only due to the material property, but also due to the inertia confinement. A mesoscale model of RAC with 1% porosity is then established to study the influence of initial micro-defects in RAC on its mechanical properties. The numerical results are compared with those of RAC without initial pore defects. These results indicate that the existence of pores considerably affects the formation and development of cracks under static and dynamic uniaxial compressions and weakens the compressive strength of RAC materials.

Keywords

recycled concrete aggregate distribution mesoscale modelling strain rate uniaxial compression

Introduction

Recycle aggregate concrete

Many new buildings have emerged with population growth and urbanisation acceleration. A large amount of new concrete is continuously poured. A huge demand for building materials has substantially burdened the natural supply of the earth and restricted the development of the construction industry. By contrast, demolished buildings generate a considerable amount of waste. Thus, processing these construction wastes not only needs a substantial amount of expenditure and labour but also requires additional land space, which puts remarkable pressure on environmental governance. The contradiction between the shortage of natural resources and the sustainable development of the construction industry has become increasingly serious. The use of recycled concrete aggregates in new concrete is an alternative method that can provide economic and environmental benefits (Sonawane and Pimplikar, 2013).

Recycled aggregate concrete (RAC) refers to concrete that utilises recycled aggregate produced by crushing waste concrete to replace natural aggregate in concrete partly or completely (Xiao, 2018). Recycled aggregate is the main component of the RAC material, and its defects will affect the mechanical properties of RAC. As early as the 1980 s, Hansen (1986) began systematic research on RAC and conducted experimental research on its stress–strain curve. Results showed that the strength of recycled concrete was 5%–30% lower than that of ordinary concrete. Subsequently, several scholars have conducted investigations on RAC. RAC research and technology have made considerable progress worldwide in recent years. Numerous experiments and numerical simulations have been conducted to study the mechanical properties of RAC, and certain results and conclusions have been obtained (Jayasuriya et al., 2020; Wang et al., 2021; Yu et al., 2021a and 2021b). In addition to static analysis, some scholars (Xiao et al., 2015; Liu et al., 2015) have also conducted research on the dynamic response of RAC.

Mesoscale modelling

The influence of coarse aggregate, fine aggregates and mortar inside concrete materials, as well as the actual internal defects of concrete materials, such as damages, inclusions and pores, are hardly considered by the research results obtained by traditional methods. With the development of high-speed computers and high-performance scanning equipment, many scholars (Chen et al., 2020; Grassl and Rempling, 2008; Rodrigues et al., 2016; Wang et al., 1999; Wang et al., 2015; Wang et al., 2018; Wu et al., 2020) have studied the internal damage properties of normal concrete materials from the microscopic and mesoscale levels. The unit size of concrete materials on the mesoscale is 10⁻³ to 10⁻¹ m, and the concrete comprises coarse aggregate, interface transition zone (ITZ) and cement mortar. Various forms of loads can be applied to the mesoscale model to study the heterogeneous behaviour of the concrete.

Many mesoscale models for concrete have been developed to analyse the static heterogeneous behaviour of concrete (Wu et al., 2021). In a mesoscale model, the most important parameters, such as the shape, size and distribution of course aggregates within the mortar matrix, significantly influence the mechanical behaviour of concrete (Wriggers and Moftah, 2006). Different aggregate shapes have been adopted in the numerical simulation. The simplest aggregate shape is circular (2 D) (Van Mier and Van Vliet, 2003) and spherical (3 D) (Wriggers and Moftah, 2006). Other shapes, such as oval and polygonal aggregates, have also been used in 2 D simulations. Wang et al. (1999) developed a procedure to generate random aggregate polygons for rounded and angular aggregates based on the Monte Carlo random sampling principle. The shapes of the randomly generated polygons were adjusted following the prescribed elongation ratios. Häfner et al. (2006) later improved their ellipsoid shape functions to generate complicated aggregate shapes. Different material models for the aggregate and the mortar, such as 2 D linear elastic analysis (Agioutantis et al., 2000; Häfner et al., 2006), nonlinear orthotropic fracture model (Kwan et al., 1999) and isotropic damage model (Wriggers and Moftah, 2006), have been employed to study the concrete behaviours. The mesoscale model has also been adopted to study the dynamic behaviour of concrete. (Song and Lu, 2012; Tu and Lu, 2011; Zhou and Hao, 2008a and b; Zhou et al., 2020). Similar to static simulation, different aggregate shapes and material models have been adopted. The dynamic mesoscale modelling revealed that the heterogeneity of concrete affects the dynamic increase factor (DIF) (Zhou and Hao, 2008a).

Different models have also been adopted considering their heterogeneity to study the static behaviour to predict the failure mechanism of RAC materials (Jayasuriya et al., 2020; Liu et al., 2015; Peng et al., 2020; Poon et al., 2004; Rodrigues et al., 2021; Yu et al., 2021a). Poon et al. (2004) studied the effect of ITZ on the compressive strength of RAC. Liu et al. (2015) investigated the mechanical behaviour of the ITZs under uniaxial compression with differently shaped aggregates. Peng et al. (2020) used the digital image processing technique to obtain the real aggregate and mortar distribution of RAC to construct a mesoscale model and then modelled the nonlinearity deformation, stress redistribution and crack propagation of RAC under uniaxial compression and tension. Jayasuriya et al. (2020) proposed a random aggregate generation approach. Yu et al. (2021a) adopted the discrete element method to model the RAC under uniaxial compression and tension. The main difference between RAC and ordinary concrete in mesoscale simulation is that RAC contains old aggregate and old mortar. Therefore, old and new ITZs emerge, thus complicating the mesoscale modelling of RAC.

ITZs play an important role in mesoscale modelling regardless of static or dynamic modelling and normal or recycled concrete. Simultaneously, the appearance and development of cracks are related to the spatial distribution of the coarse aggregate. Microcracks tend to start in the ITZ and propagate towards the mortar matrix until macrocrack formation.

Scope of the present study

Limited studies have been conducted to apply the mesoscale models in numerical simulations of different strain rates to investigate the dynamic material properties of RAC. Only a few investigations (Peng and Ying, 2018) have been found in the open literature. In these studies, the static and dynamic loadings are numerically analysed in mesoscale, wherein all the coarse aggregates are recycled aggregates. The numerical analysis of different replacement rates was not considered, and the influence of porosity was disregarded. The present paper aims to analyse the uniaxial compressive behaviour of the RAC mesoscale model under different strain rates (from 10⁻⁵/s (quasi-static loading) to 20/s (dynamic loading)). A five-phase mesoscale heterogeneous model, including natural aggregates, old ITZ, old cement mortar, new ITZ and new cement mortar, is constructed to model RAC materials. The typical numerical specimen size is 150 mm × 150 mm, which represents a 150 mm cube concrete specimen in China. Different recycled coarse aggregate replacement rates, namely, 0%, 25%, 50%, 75% and 100%, are constructed. The replacement rate of recycled aggregate by mass means the ratio of the mass of recycled aggregate to that of total coarse aggregates in percentage. 0% means normal concrete without additional recycled aggregate, whilst 100% means all the coarse aggregates are made from recycled concrete aggregates. The coarse aggregate is simply assumed to be circular and oval, with randomly distributed sizes according to aggregate gradation (cumulative percentage). Furthermore, a porosity of 1% is considered by constructing circular and oval voids in the model. The static and dynamic uniaxial compressive loadings of different strain rates are considered by adding displacement (low strain rates) or velocity (higher strain rates). The crack and failure processes and the ultimate compressive strength are obtained and compared for the different cases. The effect of ITZ parameters is studied, and the influence of porosity is also analysed.

Mesoscale RAC model

The fine aggregates are assumed to be natural fine aggregates, and only the coarse aggregates are replaced by recycled aggregate. Five replacement rates, namely, 0%, 25%, 50%, 75% and 100%, are considered. Aggregate size distribution is firstly determined in this section, and the RAC model is constructed assuming the presence of old mortar around the old aggregates. Random aggregates are then generated, and the circular and oval aggregate RAC models are constructed. Afterwards, the material model and the parameters for the five phases are specified, and the geometry and boundary conditions are given.

Aggregate size distribution

The aggregate particle size distribution is usually expressed in terms of the cumulative percentage passing through a series of sieve opening sizes. One of the most acceptable aggregate distributions is given by Fuller (Wriggers and Moftah, 2006) as follows:

P (d) = 100 {(\frac{d}{d_{\max}})}^{n}

(1)

where P(d) is the cumulative percentage passing a sieve with an aperture diameter of d and d_max is the maximum size of the aggregate particles and n is the exponent (n = 0.45–0.70). The typical maximum size of aggregates in practical concrete construction is approximately 31.5 mm to obtain high-quality concrete mix. In the present paper, d_max is 31.5 mm, and n is taken as 0.5.

In the numerical simulation, the grading curve expressed in equation (1) can be discretised into a certain number of segments (Lu and Tu, 2011), each covering a size range of [d_i, d_{i + 1}]. Thus, the amount (area in 2 D) of aggregates within each grading segment is,

A_{a, i} = \frac{P (d_{i + 1}) - P (d_{i})}{P (d_{\max}) - P (d_{\min})} \times A_{a}

(2)

where A_a is the total amount (area in 2 D) of aggregates in concrete. Assuming that the coarse aggregate with a particle size larger than 4.75 mm accounts for 40% of the total volume of the concrete, three segments, namely, (4.75 mm, 9.5 mm), (9.5 mm, 19 mm) and (19 mm, 31.5 mm), are considered in the present paper. Equations (1) and (2) indicate that in a 2 D specimen of 150 mm × 150 mm, aggregates with particle sizes of 4.75–9.5, 9.5–19 and 19–31.5 mm, respectively, accounted for 10.52%, 14.87% and 14.61% of the total area.

Simplified RAC model

Compared with natural aggregate, recycled aggregate has old cement mortar attached to the surface of old natural aggregate. Recycled aggregate concrete is a five-phase composite material comprising old aggregate, old mortar, new mortar, old ITZ and new ITZ. The simplified two-dimensional RAC model is shown in Figure 1. The old nature aggregate in the recycled coarse aggregate is assumed to be surrounded by old mortar.

Figure 1.

Simplified five-phase RAC model.

The mass content of the old mortar in the recycled aggregate is assumed to be 42% to calculate the thickness of the old mortar in Figure 1. The mass ratio of the old mortar w can be calculated as,

w = \frac{v_{s} \times ρ_{s}}{v_{s} \times ρ_{s} + v_{g} \times ρ_{g}}

(3)

where v_s and v_g are the volumes of old mortar and natural aggregates, respectively; ρ_s and ρ_g are densities of old mortar and old nature aggregate, respectively. The volume ratio of old mortar to old aggregate

\bar{w}

is as follows,

\bar{w} = \frac{ρ_{g} \times w}{ρ_{s} \times (1 - w)}

(4)

Accordingly, the thickness of the old mortar can be calculated as,

h = \frac{a - a \times \sqrt{\frac{1}{1 + \bar{w}}}}{2}

(5)

where a is the size of the entire recycled aggregate, including old aggregate and mortar, and h is the thickness of the old mortar, as shown in Figure 1.

Recycled aggregate particles contain two different ITZs, namely, the old ITZ and the new ITZ. The old ITZ is between the old aggregate and the old cement mortar layer; the new ITZ is between the old cement mortar layer and the new cement mortar layer, or between the natural aggregate and the new cement mortar layer. The ITZ thickness is in the magnitude of μm (20–50 μm). By contrast, if the finite elements with the size of 20–50 μm were employed in finite element meshing to represent those ITZ elements, then the computational cost will be markedly increased. Thus, the ITZ element size should be considered using the effective ITZ layer 0. The thickness of old and new ITZs is 0.2 mm in this paper to consider the calculation efficiency; that is, the thickness of the effective ITZ layer is 0.2 mm.

Random aggregate generation and RAC models

The circular- and oval-shaped aggregate particles are considered in the present study. Circular aggregates can be easily constructed. Firstly, uniformly distributed random numbers are set to determine the centres of the circles. The diameters are then randomly generated. Random numbers are generated for the oval-shaped aggregates to determine the position of the oval centre (x, y), long axial radius r_l, short axial radius r_s and the orientation angle of the long axis φ.

According to Fuller’s curve, the recycled aggregates and natural aggregate particles are put into the specimen in order from the largest to the smallest. The placement process of typical circular particles is as follows.

Step 1

Calculate the area of aggregates to be generated in the grading segment. Determine the replacement rate (r) and then distinguish recycled and natural aggregates according to r. Calculate the areas of recycled and natural aggregates at all segments.

Step 2

Generate a uniformly distributed random number to determine the position of the aggregate particle.

Step 3

Generate a random number defining the size of an aggregate particle assuming the particle size d is a uniformly random number between the size range of [d_i, d_{i + 1}]. The largest size range is placed first. The mortar thickness for recycled aggregate is calculated by equation (5).

Step 4

Check whether all the placement conditions are completely satisfied. The placement conditions include the overlap between any two particles, or overlap between a particle and any boundary is not allowed; a minimum gap size t must be provided between any two particles. Any unsuccessful particles should be avoided.

Step 5

Calculate the total area of the aggregate particles generated and compare it with the area within the current grading segment. If the former is less than the latter, then repeat from Step 2; otherwise, calculate the next grading segment.

Step 6

Repeat the above steps for the next grading segment until the total area of aggregates reaches a certain value, which means that all the particles are generated.

Following the above steps, the area ratio of aggregates in RAC with different replacement rates is calculated, as listed in Table 1. NCA(C) means circular natural coarse aggregate, where (C) means circular, and RCA50(C) means circular recycled coarse aggregate (replacement ratio r = 50%).

Table 1.

Area ratio of circle aggregates.

Ratio of aggregate	Recycle aggregate			Natural aggregate			Total
Ratio of aggregate	19–31.5 mm, %	9.5–19 mm, %	4.75–9.5 mm, %	19–31.5 mm, %	9.5–19 mm, %	4.75–9.5 mm, %	4.75–31.5 mm, %
NCA(C)	0.00	0.00	0.00	16.73	15.05	10.54	42.32
RCA25(C)	4.07	3.76	2.79	12.56	11.39	8.03	42.60
RCA50(C)	8.37	8.00	5.58	7.58	7.53	5.37	42.43
RCA75(C)	12.18	11.40	8.27	4.27	3.80	2.70	42.62
RCA100(C)	16.70	14.91	10.67	0.00	0.00	0.00	42.28

Similarly, oval aggregate models are constructed with (O) means oval. The area ratio is listed in Table 2. The constructed RAC model with different replacement rates for circular and oval aggregates are shown in Figure 2 andFigure 3, respectively. In the figures, red represents new natural aggregates, dark red represents old natural aggregate particles, green represents old mortar and brown represents new mortar; old ITZs are between dark red and green, and new ITZs are between green and brown, or between red and brown. In the subsequent simulation, the old and new nature aggregates have the same mechanical properties, and the same material model and parameters are adopted.

Table 2.

Area ratio of oval aggregates.

Ratio of aggregate	Recycle aggregate			Natural aggregate			Total
Ratio of aggregate	19–31.5 mm, %	9.5–19 mm, %	4.75–9.5 mm, %	19–31.5 mm, %	9.5–19 mm, %	4.75–9.5 mm, %	4.75–31.5 mm, %
NCA(O)	0.00	0.00	0.00	16.59	15.12	10.54	42.25
RCA25(O)	4.78	4.55	2.66	11.07	11.39	7.93	42.38
RCA50(O)	7.32	7.97	5.32	8.76	7.85	5.32	42.54
RCA75(O)	11.81	11.20	7.91	4.71	3.78	2.72	42.13
RCA100(O)	16.34	15.47	10.63	0.00	0.00	0.00	42.44

Figure 2.

RAC model of random circular aggregates with different replacement rates.

Figure 3.

RAC model of random oval aggregates with different replacement rates.

Pores are randomly put in the specimen to further consider their effects and those of microcracks and micro-defects on the mechanical properties of concrete materials. The pores are assumed to be circular and oval in the circular and oval aggregate models, respectively. The pore size is 1–2 mm. Typical aggregate particles of different shapes in the RAC model with r of 50% and porosity of 1% are shown in Figure 4.

Figure 4.

Mesoscale RAC model with pores (r = 50%, porosity =1%).

Material models for five phases

As one of the most widely used models for the concrete-like material, the K&C (Karagozian and Case) model (Malvar et al., 1997) is adopted to model all the five phases in the present mesoscale RAC model. The model introduces three strength surfaces, namely, initial yield, ultimate strength and residual failure surfaces, to determine the initial yield, ultimate and residual strengths of concrete under load, respectively. From the beginning of loading to concrete failure, the following three stages are observed: (1) elastic stage: the stress point does not reach the initial yield surface (YIELD); (2) strengthening stage: the stress point exceeds the initial yield strength surface but does not reach the ultimate strength surface (MAX); (3) softening stage: the stress point reaches the ultimate strength surface but does not reach the residual failure surface (RESIDUAL). The initial yield, ultimate strength and residual failure surfaces are determined by Equations (6)–(8), respectively.

Δ σ_{y} = a_{0 y} + \frac{P}{a_{1 y} + a_{2 y} P}

(6)

Δ σ_{m} = a_{0} + \frac{P}{a_{1} + a_{2} P}

(7)

Δ σ_{r} = \frac{P}{a_{1 f} + a_{2 f} P}

(8)

where

P = - (σ_{1} + σ_{2} + σ_{3}) / 3

, and

a_{0}

a_{1}

a_{2}

a_{0 y}

a_{1 y}

a_{2 y}

a_{1 f}

and

a_{2 f}

are the material parameters. According to the relevant recycled concrete test of Li et al. (2016), combined with the material parameters of each phase in RAC by Jayasuriya et al. (2020), the compressive strength of the new cement mortar matrix is assumed to be 42.5 MPa in the present study. Accordingly, the major parameters of the five phases in the RAC model listed in Table 3 are determined, whilst other parameters are automatically generated by the LS-DYNA software (LS-DYNA, 2007). The default dynamic increase factor (DIF) value in LS-DYNA is adopted. Notably, the old and new natural aggregates are assumed to have the same parameters.

Table 3.

Material constants of the five phases.

Different phases	Density(kg/m³)	Compressive strength (Mpa)	Tensile strength (Mpa)	Poisson’s ratio
Natural aggregate	2634.00	144.00	10.00	0.16
Old ITZ	2280.00	29.33	2.06	0.20
Old mortar	2280.00	39.10	2.76	0.22
New ITZ	2280.00	31.88	2.21	0.20
New mortar	2280.00	42.50	3.00	0.22

Geometry and boundary conditions

A standard concrete specimen measuring 150 mm × 150 mm × 150 mm in dimension, as usually used in laboratory tests in China, is considered. The specimen is modelled in a 2 D plane stress condition. A thin-plate configuration with a single layer of elements in the z-direction is adopted to allow the use of solid elements. The numerical specimen is a thin plate with an area of 150 mm × 150 mm and a thickness of 1 mm, as shown in Figure 5. The z-direction deformation is restricted on one side in the thickness direction. Triangular prism elements are adopted, with an element size of less or equal to 1 mm. The minimum element size is 0.2 mm because the thickness of ITZ is 0.2 mm. Overall, 59,650 elements and 30,126 nodes are found in the specimen. The lower boundary in the y-direction is fixed, whist the displacement or velocity boundary is added on the upper boundary. In quasi-static loading simulations, such as strain rates of 10⁻⁵/s and 10⁻³/s, the implicit calculation method and the linear displacement boundary are used (Figure 6 (a)). Meanwhile, in dynamic simulation, that is, strain rate of 10⁻¹/s and above, explicit dynamic analysis and velocity boundary are adopted (Figure 6 (b)). Similar finite models and boundary conditions can be found in Ref (Lu and Tu, 2011). All the analyses are performed using LS-DYNA (2007).

Figure 5.

Numerical specimen.

Figure 6.

Loading curves.

Numerical results and analysis

Numerical simulations of the above-mentioned mesoscale RAC models under uniaxial compressive loads of different strain rates are conducted using LS-DYNA (2007). Numerical results of random circular and oval RAC models with and without pores are presented in this section. The effects of the aggregate shape, replacement ratio and porosity are also analysed.

Random circular aggregate RAC model under uniaxial compression

The random circular mesoscale RAC models with recycled aggregate replacement rates of 0%, 25%, 50%, 75% and 100% (as shown in Figure 2), are initially numerically analysed. Uniaxial compressive loading of strain rates 10⁻⁵/s, 10⁻³/s, 10⁻¹/s, 1/s, 10/s and 20/s are added to the numerical RAC specimen (Figure 5). The ultimate compressive strength of the circular aggregate model with different replacement rates at each strain rate is shown in Figure 7. The ultimate compressive strength shows a downward trend as the recycled aggregate replacement rate increases. At high strain rates, the ultimate compressive strength significantly decreases as the replacement rate increases, whilst the decrease is relatively absent in the case of a low strain rate. Notably, the calculated strength value has certain randomness due to the randomness of the aggregate distribution. Therefore, a few data in Figure 8 are inconsistent with the predicted law, which is observed when the strain rate is low. The figure also demonstrates that the strength has significant increase as the strain rate rises, indicating the presence of the strain rate effect. Even in the stage of static loading, that is, implicit calculation with strain rates of 10⁻⁵/s and 10⁻³/s, the compressive strength shows strain rate effects, and the strength of strain rate 10⁻³/s is higher than that of strain rate 10⁻⁵/s. The relationship between the compressive strength and the strain rate in the range of 10⁻⁵/s to 20/s is linear. Notably, the DIF is considered in the adopted K&C model. The strain rate effect may be caused by the material properties, the inertial confinement and the mesoscale model.

Figure 7.

Compressive strength of circular aggregate RAC.

Figure 8.

Failure pattern of circular aggregate RAC under uniaxial compression.

Failure patterns of some typical cases are shown in Figure 8, where natural aggregates are removed due to the absence of damage within these aggregates. It shows that the failure pattern of the high strain rate cases is different from that of the low strain rate cases. Under the action of low strain rate, the failure process of the recycled concrete model is similar to the typical failure mode under static force, and a few main oblique cracks are formed. The stress concentration area during the loading process starts from weak old ITZs. The initial cracks extend through the new and old mortar areas to the nearby ITZs, and the fine cracks gradually penetrate through to form a small number of penetrating oblique main cracks, which reflects the failure mode under static loading. Under the action of high strain rate force, a large number of cracks distribute throughout the numerical specimen, the load-bearing capacity is then quickly lost and the phenomenon of crushing damage is consistent with the highly dynamic failure. Accordingly, the amount of cracks is significantly more than those under low strain rates. These results are consistent with the results from Zhou and Hao (2008b). By contrast, the crack pattern and failure mode remain unaffected by the recycled aggregate replacement rates. The failure modes of RAC with different replacement rates under the same strain rate are roughly similar. The crack pattern is mainly controlled by the coarse aggregate distribution.

Random oval aggregate RAC model under uniaxial compression and effect of ITZ strength

The random oval aggregate mesoscale RAC models in Figure 3 are also numerically analysed. The same loading cases as those in the previous section are calculated, and the ultimate compressive strengths of the oval aggregate RAC models with different replacement rates at different strain rates are shown in Figure 9, which is similar to that in Figure 7. The calculated strengths from the oval and circular aggregate models are compared. The comparison results reveal that the strength obtained from the oval aggregate model is slightly lower than that from the circular aggregate model. However, the slight difference is negligible.

Figure 9.

Compressive strength of oval aggregate RAC.

DIFs for all the above cases are calculated and compared with those from CEB and the default K&C DIF in Figure 10. The black line is the K&C DIF adopted in the present study to calculate the material DIF, while the red line is the DIF recommended by CEB. It can be found that the calculated DIFs are much higher than the material DIF, which means that the DIF is not only caused by the material properties, but also for other reasons. The contribution of inertial confinement is relatively large. On the other hand, the meso-scale modelling also yield higher DIF, as mentioned in the literature (Zhou and Hao, 2008b).

Figure 10.

Comparison of DIFs.

The failure pattern of some typical cases of the oval aggregate model is shown in Figure 11, whilst that of different strain rates is similar to Figure 8. Both figures reveal that the crack pattern is affected by the coarse aggregate distribution. The comparison of the circular and oval aggregate models shows that both models can be used to calculate the response of mesoscale RAC. Moreover, both models can yield reasonable crack patterns, and similar ultimate strengths can be obtained.

Figure 11.

Failure pattern of oval aggregate RAC under uniaxial compression.

The ITZ between the new and the old interface of RAC is relatively weak, and its strength may affect the ultimate strength of the RAC specimen. Thus, the ITZ strength effect on compressive strength is studied. Taking the random oval aggregate RAC model with a 50% replacement rate (RCA50(O)) as an example, the tensile and compressive strengths of the new and old ITZ are reduced or increased by 25%, whilst other parameters remain. Three mesoscale RAC models, namely, RCA50(O)75%ITZ, RCA50(O)100%ITZ and RCA50(O)125%ITZ, are applied by uniaxial compressive loads of strain rates 0.1/s, 1/s and 10/s. The influence of the ITZ strength on RAC compressive strength is studied and shown in Figure 12, which demonstrates the ultimate compressive strength of each mesoscale model under different strain rates. The results show that the change in mechanical parameters in the ITZ affects the dynamic mechanical properties of the material. RCA50(O)75%ITZ under the dynamic load of strain rate 0.1/s, 1/s and 10/s shows a reduction in overall compressive strength of the material by 6.82%, 5.44% and 2.99%, respectively, whilst NS-RCA50(O)125%ITZ increased the original ultimate compressive strength by 6.82%, 3.76% and 2.23%, respectively. This finding shows that improving the interface bonding area of recycled concrete materials is one of the keys to enhancing the overall mechanical properties. The stress concentration area of the material increases with the dynamic strain rate, and the influence of the ITZ strength on the material strength decreases.

Figure 12.

Effect of ITZ strength on compressive strength.

Porous RAC model under uniaxial compression

A total of 1% porosity is added to circular and oval RAC models to explore the effect of pores on the formation and development of cracks in RAC, and then similar loading cases are calculated. A circular aggregate RAC model with a porosity of 1% and a replacement rate of 50% (as shown in Figure 4 a) is simulated in this section. The crack propagation process with a strain rate of 1/s is compared with a non-porous RAC model with the same replacement rate in Figure 13. The mesoscale RAC model with pores has an additional stress concentration at 1.0 ms. The stress concentration areas initially appeared in the new and old ITZs in the RAC model without pores, whilst stress concentration around some pores in the porous RAC model is evident. The stress concentration area of the mesoscale RAC model with pores is larger than that of the model without pores at 1.6 ms and extends from one pore to the other. The numerical model with pore defects is substantially damaged at 2.0 ms, and the direction of crack extension is affected by the distribution of pores. Therefore, the existence of pores affects the formation and expansion of cracks. By contrast, the crack patterns of the two cases have certain similarities. Some cracks in the old and new ITZs and in the old and new mortars are similar in both cases.

Figure 13.

Comparison of crack propagation of circle aggregate RAC with and without pores.

The strength loss percentages of different circular RAC model cases are listed in Table 4. Compared with the non-porous aggregate model, the ultimate compressive strength of the defect-containing porous circular aggregate model of each replacement rate decreases under the uniaxial compressive load of different strain rates. The strength decline trend decreases as the strain rate increases. This trend is due to the rapid development of cracks at high strain rates. Therefore, the initial defects have relatively minimal effect. The effect of the recycled aggregate replacement ratio is not obvious. It should be mentioned that the calculated results are relatively scattered due to the arbitrary aggregate distribution.

Table 4.

Strength loss of porous circular aggregate RAC.

Strain rate\Replacement	0%	25%	50%	75%	100%
10⁻¹s⁻¹	10.24	7.74	9.06	11.00	7.96
1s⁻¹	7.23	5.47	6.07	6.99	6.00
10s⁻¹	3.88	3.62	3.84	3.28	3.45
20s⁻¹	3.63	3.30	3.78	2.98	2.74

Similarly, an oval aggregate RAC model with a porosity of 1% and a replacement rate of 50% (as shown in Figure 4 b) is calculated. The crack propagation process with a strain rate of 1/s is compared with a non-porous recycled concrete model with the same replacement rate in Figure 14. The crack pattern is similar to that in Figure 13. This finding indicates that the circular- and oval-shaped aggregate models can be adopted to obtain reasonable failure patterns. Moreover, the strength loss percentages of different oval RAC model cases are listed in Table 5. The comparison of Table 5 and Table 4 shows that the strength loss of the oval model is slightly larger than that of the circular model. Thus, oval pores produce stronger stress concentrations than circular pores. The real pore defects have different shapes. Therefore, oval pores may be more reasonable than circular pores. By contrast, no strength loss trend is observed for different replacement rates. The different strength loss percentages may be due to the random distribution of pores.

Figure 14.

Comparison of crack propagation of oval aggregate RAC with and without pores.

Table 5.

Strength loss of porous oval aggregate RAC.

Strain rate\Replacement	0%	25%	50%	75%	100%
10⁻¹s⁻¹	15.00	15.41	15.73	18.80	13.22
1s⁻¹	9.51	11.29	8.79	13.43	9.08
10s⁻¹	5.01	5.38	3.79	4.83	4.19
20s⁻¹	4.44	5.01	3.17	4.75	3.56

Typical stress–strain relationship

A typical stress–strain relationship is shown in Figure 15. PRCA50(O) denotes the porous oval aggregate model with a replacement ratio of 50%. The shape of the stress–strain relationship is similar for the other cases, but the peak value is different. The figure shows that the ultimate compressive strengths can be calculated with acceptable accuracy. The descending part of the curve can also be obtained. However, the shape of the stress–strain relationship still has certain problems. The change in Young’s modulus with strain rate is not observed; thus, the strain corresponding to the peak stress remarkably varies for different cases. The adopted K&C model still has certain problems in obtaining an accurate stress–strain relationship. However, the peak values of compressive strength and the crack formation and dynamic failure process can be obtained.

Figure 15.

Typical stress–strain relationship.

Conclusions

Random circular and oval aggregates are used in this paper to establish RAC models with different replacement rates. According to the different quasi-static and dynamic loading rates, implicit and explicit calculation methods are used to obtain the uniaxial compression behaviour of recycled concrete. Strain rate sensitivity is also analysed. Furthermore, the influence of pore defects on the compressive properties of RAC is considered. The following conclusions can be drawn from the numerical simulation.

1. The mesoscale RAC model shows dynamic strain rate sensitivity under axial compression. The ultimate compressive strength of RAC increases with the strain rate.

2. The shape of coarse aggregates affects the dynamic compressive performance of RAC. The oval aggregates of RAC yield lower strength than that of the circular aggregates of RAC, which means that the assumption of circular aggregates may slightly overestimate the RAC strength. However, the error is substantially small and acceptable. Thus, oval and circular aggregates yield similar results.

3. High recycled aggregate replacement ratios obtain low strength, which is observed when the strain rate is high. Such an observation is due to the relatively lower strength of recycled concrete aggregates than that of natural concrete. However, the reduction in strength under quasi-static loading is absent, which means the ideal mesoscale assumption of RCA may underestimate the strength reduction.

4. The strength of ITZ affects the strength of RAC. Thus, improving the ITZ properties of RAC materials is one of the keys to enhancing the overall mechanical properties. The influence of these properties decreases with the increase in strain rate.

5. The existence of pore defects affects the dynamic mechanical properties of RAC materials. Stress concentration areas often appear around the pores, which directly affect the formation and development of cracks and reduce the ultimate compressive strength of the RAC. The strength loss of the oval aggregate model is more evident than that of the circular aggregate model.

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: This work was supported by the General Programme of the National Natural Science Foundation of China (51678364).

ORCID iD

Xiao-Qing Zhou

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