1. INTRODUCTION
⌅Cemented
sand and gravel (CSG) is a cementitious material of a known strength
formed by mixing, paving, vibrating, and rolling a small amount of
cementing material together with unscreened and unwashed gravels at the
project site (11.
Feng, W. (2013) Research on characteristics of damming materials for
cemented gravel dam and engineering application, China Institute of
Water Resources and Hydropower Research, Beijing, China.
). Responding to the United Nations’ call for new, green building materials (22.
González-Fonteboa, B.; Seara-Paz, S.; de Brito, J.; González-Taboada,
I.; Martínez-Abella, F.; Vasco-Silva, R. (2018) Recycled concrete with
coarse recycled aggregate. An overview and analysis. Mater. Construcc. 68 [330], e151. https://doi.org/10.3989/mc.2018.13317.
),
CSG can be used in modern dam construction technology to pursue
efficient, low-cost construction while protecting natural resources.
This has become the development trend toward future dam construction
technology. CSG dam technology has been applied worldwide; permanent CSG
dams have been built in Japan, Turkey, Greece, France, and elsewhere.
It has also been gradually extended and applied in temporary works and
in parts of permanent works in China. CSG dams are usually applied in
areas where riverbeds provide abundant sand gravels. In order to broaden
its applicability to more dam types, artificial aggregates can be used
to replace natural aggregates for projects in riverbeds lacking natural
gravels. Compared with natural aggregates, artificial aggregates have
much larger surface areas owing to their multiple corner angles and
rough surfaces. The presence of unscreened aggregates in CSG
complexifies its aggregate characteristics; moreover, CSG properties are
different from those of ordinary concrete. Aggregate type, shape, and
grading are all important factors influencing the mechanical behavior of
concrete materials (33.
Shafigh, P.; Asadi, I.; Akhiani, A.R.; Mahyuddin, N.B.; Hashemi, M.
(2020) Thermal properties of cement mortar with different mix
proportions. Mater. Construcc. 70 [339], e224. https://doi.org/10.3989/mc.2020.09219.
, 44.
Jin, L.; Yu, W.; Du, X.; Yang, W. (2020) Meso-scale simulations of size
effect on concrete dyna-mic splitting tensile strength: Influence of
aggregate content and maximum aggregate size. Eng. Fract. Mech. 230, 106979. https://doi.org/10.1016/j.engfracmech.2020.106979.
).
Therefore, in order to provide a theoretical basis for CSG use in
engineering design, it is necessary to systematically study the
relationship between aggregate characteristics and CSG properties.
In
recent years, an increasing number of studies have focused on the
relationship between aggregate shapes and the resulting macroscopic
properties of composite materials. Huang (55.
Huang, X.F. (2010) Effect of coarse aggregate shape on concrete
physical and mechanical properties, Zhejiang University of Technology,
Zhengjiang, China (2010).
) proposed from his
experiments that the more sphere-like the shape of a coarse aggregate,
the greater the compressive strength and elastic modulus of the
resulting concrete. Guo (66.
Guo, D. (2016) Research on the main technical requirements of
high-quality concrete aggregates, Beijing University of Architecture,
Beijing, China (2016).
) found through experiments
that, with increasing fractions of irregular particles, the slump and
concrete strength of C30 and C50 concrete decrease. In research
performed by Sánchez-Roldán et al. (77.
Sánchez-Roldán, Z.; Valverde-Palacios, I.; Valverde-Espinosa, I.;
Martín-Morales, M. (2020) Microstructural analysis of concretes
manufactured with recycled coarse aggregates pre-soaked using different
methods. Mater. Construcc. 70 [339], e228. https://doi.org/10.3989/mc.2020.16919.
),
it was observed that recycled coarse aggregates (RCA) have less angular
shapes compared to natural aggregates; this characteristic, together
with better particle coupling, provides greater compactness to the whole
mixture. In addition to the shapes of aggregates, the shapes of other
components in concrete have also been investigated. Research conducted
by Zhang et al. (88.
Zhang, Y.; Yan, L.; Wang, S.; Xu, M. (2019) Impact of twisting
high-performance polyethylene fibre bundle reinforcements on the
mechanical characteristics of high-strength concrete. Mater. Construcc. 69 [334], e184. https://doi.org/10.3989/mc.2019.01418.
)
showed that the improved geometry of ultra-high-molecular-weight
polyethylene (UHMWPE) fibers can ensure their uniform distribution in a
matrix, significantly enhancing the splitting tensile strength and
residual compressive strength of the resulting concrete.
In terms of numerical simulation, Xiong and Xiao (99.
Xiong, X.Y.; Xiao, Q.S. (2019) A unified meso-scale simulation method
for concrete under both tension and compression based on Cohesive Zone
Model. J. Hydraul. Eng. 50, 448-462. https://doi.org/10.13243/j.cnki.slxb.20181061.
)
determined that round aggregates reduce the stress concentration
intensity inside concrete compared to irregular aggregates; this
suggests that the resulting concrete strength is relatively high, which
is consistent with experimental results. On the basis of numerical
simulation, Wang (1010.
Wang, X.F.; Yang, Z.J.; Yates, J.R.; Jivkov, A.P., Zhang, Ch.. (2015)
Monte Carlo simulations of mesoscale fracture modelling of concrete with
random aggregates and pores. Constr. Build. Mater. 75, 35-45. https://doi.org/10.1016/j.conbuildmat.2014.09.069.
)
proposed that the average peak stress of the tensile strength of round
aggregates is slightly higher than that of polygonal aggregates for the
same volume fraction of aggregates and pores. Numerical modeling by
Zheng et al. (1111.
Zheng, J.C.; Zhu, L.; Peng, G. (2013) Numerical simulation of concrete
axial tensile performance based on mesomechanics. Engineering Journal of
Wuhan University. 46, 188-193.
) implied that changes
in aggregate shape cause stress concentrations that affect the strength
of the concrete. Hou and Wang’s numerical modeling (1212. Hou, Y.X.; Wang, L.C. (2009) Generating method of random polygon aggregate in mesoscopic simulation of concrete. J. Archit. Civil. Eng. 26, 59-65.
)
found that aggregate shape has little effect on the compression
resistance of concrete. Although the above literature focuses on
concrete, it is applicable only to standard gradation; the gradation
characteristics of CSG with unscreened aggregates remain to be studied
further.
Separately, fractal theory was introduced into the study
of material structure, opening a new avenue for quantifying the
relationship between material complexity and macroscopic properties. Yu (1313. Yu, B.; Li, J. (2001) Some fractal characters of porous media. Fractals. 9 [3], 365-372. https://doi.org/10.1142/S0218348X01000804.
) described the statistical properties of porous media based on fractal theory and fractal technology. Zhang and Jin (1414. Zhang, J.X.; Jin, S.S. (2013) Micropore structure of cement concrete and its function, Science Press, Beijing, China.
) studied the application of fractal theory to concrete pore structures. Gao et al. (1515.
Gao, S.; Guo, Y.X.; Wu, B.Q. (2019) Research on Fractal characteristics
of the recycled fi-ne aggregate. Concrete. 6, 78-83. https://doi.org/10.3969/j.issn.1002-3550.2019.06.018.
) and Hu et al. (1616.
Hu, H-x.; Zhang, Q.; Ding, D-h. (2010) Study on the mechanical
properties of the concrete materials based on fractal theory. Concrete.
6, 31-33,36. https://doi.org/10.3969/j.issn.1002-3550.2010.06.009.
)
described and quantified the fractal characteristics of aggregate
appearance and outlines using the method of fractal dimensions. Li et
al. (1717.
Li, W.T.; Sun, H-q.; Xing, J. (2003) Theory of fractal applied to
concrete study. Journal of Hebei University of Technology. 32, 13-16.
) adopted fractal dimensions to describe the particle shape and gradation of concrete aggregates.
Based on different gradation characteristics of natural sand gravels at the project site, this study uses numerical simulation to obtain the maximum density gradation attainable by adding artificial aggregates. Fractal theory is applied to characterize aggregate properties and to further explore the effects of aggregate fractal characteristics on CSG macroscopic and mesoscopic mechanical behavior. This provides a theoretical basis for mix proportion design in other engineering applications.
2. MATERIALS AND METHODS
⌅2.1. Fractal Theory
⌅Fractal geometry (1818. Mandelbrot, B.B. (1982) The fractal geometry of nature. W. H. Freeman, New York.
)
was founded by the French-American mathematician, Benoit Mandelbrot. As
an emerging science describing the irregularity and complexity of
materials, it offers a new way to study the quantitative relationship
between aggregate complexity and the mechanical properties of CSG.
2.1.1 Fractal Model Based on Aggregate Gradation
⌅Aggregate gradation refers to the proportional relationship between the numbers of aggregate particles of different sizes. Traditional aggregates are divided into small stones (5-20 mm), medium stones (20-40 mm), large stones (40-80 mm) and super-large stones (80-150 mm) according to particle size. Such an irrational gradation indicates poor aggregate density, and reduces the performance of the composite material.
Based on the gradation method, a fractal model was established for aggregate gradation of CSG (1919.
Chang, Y.J. (2018) Fractal characteristics and the application for
asphalt mixture grading with the curve models. Journal of Heilongjiang
Institute of Technology. 32, 6-10. https://doi.org/10.19352/j.cnki.issn1671-4679.2018.06.002.
). The resulting fractal function for graded CSG aggregates is (Equation [1]):
where r represents the size of a sieve pore for grading particles; rmin and rmax represent the smallest and largest particle sizes, respectively; Dg represents the fractal dimension of the aggregate size mass distribution; and P0 represents the pass rate at the maximum nominal particle size. Because rmin is much smaller than rmax, Equation [1] can be simplified to Equation [2]:
In accordance with the above formula, the fractal dimension Dg of the aggregate gradation can be obtained.
2.1.2 Fractal Model Based on Aggregate Shape
⌅The
section of an aggregate is rough and complex with obvious fractal
characteristics; this can be represented by the box dimension. One of
the most widely used fractal dimensions, its mathematical expression is
as follows: supposing that is any non-empty bounded subset on R and Nδ is the minimum number of boxes of size δ that can cover the set F, the box dimension can be obtained through the following Equation [3] (1414. Zhang, J.X.; Jin, S.S. (2013) Micropore structure of cement concrete and its function, Science Press, Beijing, China.
):
where δ represents the unit measurement scale in a continuous distribution, i.e., a unit square used in the two-dimensional plane; Nδ represents the number of measurement scales, which is the number of small squares covering polygonal aggregates; and Dx represents the box dimension of an aggregate shape.
2.2. Random CSG Aggregate Model
⌅2.2.1 Generation of Random Aggregates
⌅In
the generation of random aggregates, a group of random variables
uniformly distributed on the interval [0, 1] were first generated by the
Monte Carlo method (20-2220.
Bai, W.; Peng, G. (2007) Monte-Carlo method aggregate random structures
for concretes by Ansys, Journal of Shihezi University (Natural
Science). 25, 504-507. https://doi.org/10.13880/j.cnki.65-1174/n.2007.04.014.
21.
Rong, M.D.; Guo, Z.Y.; Wu, X.Q. (2017) Ansys implementation of
two-dimensional and three-dimensional random aggregate model generated
by Monte Carlo method. Construction Machinery Technology and Management.
30, 71-73. https://doi.org/10.13824/j.cnki.cmtm.2017.11.019.
22. Li, Z.W. (2007) Monte Carlo simulation of related random variables. Stat. Decis. 5, 9-10.
). The probability density function with X was assumed to be as follows Equation [4]:
Random variables on any other intervals can be obtained from the transformation of random variables on the interval [0, 1]. For example, the uniformly distributed random variable Y on any interval [a, b] can be obtained by Y = a + (b - a) X. Thus, random variables that meet the uniform distribution on each interval were generated.
The position of aggregates within different particle size ranges in the test pieces was randomly determined using the Monte Carlo method. The number of aggregate particles was obtained from the gradation of concrete and the occupancy of aggregates was determined using the Fuller gradation theory based on the principle of maximum density.
According to the Walaraven Equation (2323.
Schlangen, E.; van Mier, J.G.M. (1992) Simple lattice model for
numerical simulation of fracture of concrete materials and structures. Mater. Struct. 25, 534-542. https://doi.org/10.1007/BF02472449.
),
a three-dimensional aggregate gradation curve can be transformed into a
two-dimensional planar aggregate gradation curve. The cumulative
distribution probability of aggregates with diameter D less than D0 was calculated as follows Equation [5]:
where Pk represents the occupancy fraction of aggregates, for which a value of 70% was used in this study. In accordance with Equation [5], the number of aggregate particles at various levels of the cross section can be calculated.
2.2.2 Inversion of Mesoscopic Material Parameters
⌅CSG test cubes of 100 mm × 100 mm × 100 mm were used in the experiment. Based on laboratory conditions, standard grade II aggregates were adopted with the mix proportions shown in Table 1. The test pieces were cured for 28 d for the uniaxial compression test. In the test, a universal testing machine and a displacement control method were used to obtain the stress-strain curve.
| Cement (kg/m3) | Flash (kg/m3) | Sand (kg/m3) | Water (kg/m3) | Aggregate (kg/m3) | Sand rate |
|---|---|---|---|---|---|
| 70 | 20 | 434 | 90 | 1736 | 0.2 |
From
a mesoscopic perspective, CSG can be seen as a three-phase composite
material composed of sand gravel aggregates, a mortar matrix, and
interfaces between the mortar matrix and the aggregates. In the
two-dimensional plane, it was assumed that the natural sand gravel
aggregates are round and the artificial sand gravel aggregates
polygonal. In this study, by generating aggregate random circles and
adhesive random circles with boundaries, the inner and outer circles
were divided into quadrants. The number of corner points for each
quadrant was determined, and the corner point coordinates were formed.
Finally, the corner points were connected to generate polygons (2424.
Guo, L.X.; Zhong, L.; Zheng, C.Y. (2019) Damage and destruction
research of recycled concrete with waste brick based on modified random
aggregate model. J. Basic Eng. 27, 1390-1398. https://doi.org/10.16058/j.issn.1005-0930.2019.06.018.
).
The constitutive relationship and failure criterion for mesoscopic component materials were selected simply. The constitutive model of each component adopted a linear elastic model while the failure criterion adopted the maximum stress criterion; that is, when the tensile stress in a material exceeds its maximum tensile strength, the material is assumed to crack.
In the finite element calculations, the material
parameters of each component included the tensile strength, elastic
modulus, and Poisson’s ratio. Since the parameters of meso-component
materials were difficult to measure, minimizing the difference between
stress-strain curves obtained from experiments and numerical simulation
was taken as the optimization goal to obtain the parameters by means of
inversion (25-2725.
Xiao, J.Z.; Du, J.T. (2008) Complete stress-strain curve of concrete
with different recycle coarse aggregates under uniaxial compression. J. Build. Mater. 11, 1445-1449. https://doi.org/10.3969/j.issn.1007-9629.2008.01.021.
26.
Peng, Y.J.; Wang, Y.H. (2006) Numerical analyses for fracture process
and failure mechanism of concrete on meso-level. Chin. Saf. Sci. J. 16, 110-114. https://doi.org/10.16265/j.cnki.issn1003-3033.2006.08.020.
27.
Shang, X.Y.; Yang, J.W.; Li, J.S. (2020) Fractal characteristics of
meso-failure cracks in re-cycled coarse aggregate concrete based on CT
image. Acta. Mater. Compos. Sin. https://doi.org/10.13801/j.cnki.fhclxb.20190917.002.
). The comparison between numerical simulation results and lab uniaxial compression tests is shown in Figure 1.
Figure 1 shows that the peak stress in the experiment is slightly lower than that in the numerical simulation and the strain values are basically the same. Moreover, the correlation coefficient between the two curves is very high. After failure, the measured curve shows a descent stage while the simulation results show brittle failure with less of a decline. This is caused by the unreasonable description of the yield failure criterion used; however, the numerical simulation described the main mechanical properties quite well. The values of the mesoscopic parameters obtained from inversion are shown in Table 2.
| Meso component | Elastic modulus (MPa) | Poisson’s ratio | Tensile strength (MPa) |
|---|---|---|---|
| Aggregate | 210 | 0.16 | 0.5 |
| Cement mortar | 65 | 0.20 | 0.5 |
| Interface | 32 | 0.16 | 0.4 |
Aggregate shape has a remarkable impact on the interface (2828. Prokopski, G.; Halbiniak, J. (2000) Interfacial transition zone in cementitious materials. Cem. Concr. Res. 30 [4], 579-583. https://doi.org/10.1016/S0008-8846(00)00210-6.
, 2929. Xu, Y.S. (2017) Research on mesoscopic model of concrete considering aggregate shape, Southeast University, Nanjing.
),
but because the interface occupied a very small proportion of the CSG,
the impact of aggregate characteristics on mesoscopic parameters was
ignored in this study.
3. RESULTS
⌅CSG
aggregates usually come from the project site and have round or
near-round shapes. In principle, they are used without screening, giving
rise to a complex gradation. The research of Feng (11.
Feng, W. (2013) Research on characteristics of damming materials for
cemented gravel dam and engineering application, China Institute of
Water Resources and Hydropower Research, Beijing, China.
)
showed that natural sand gravels at project sites have alternately
distributed sand and gravel layers with uneven gradation (see Figure 2), causing a significant strength decrease in the resulting CSG. Figure 2
shows the gradation and Fuller curves of the 12 groups of on-site
aggregates. The gradation of on-site aggregates deviates markedly from
the standard Fuller gradation. Therefore, the gradation must be adjusted
using artificial aggregates (3030.
Guo, L.; Zhang, Y.; Zhong, L.; Wang, M.; Zhu, X. (2020) Study on
macroscopic and mesoscopic mechanical behavior of CSG based on inversion
of mesoscopic material parameters. Sci. Eng. Compos. Mater. 27, 65-72. https://doi.org/10.1515/secm-2020-0007.
).
)).
For projects lacking natural riverbed sand gravels, artificial aggregates can be used to replace natural aggregates. Artificial aggregates are generally shaped as irregular polygons. Their surfaces are relatively rough and irregular with more edges and corners than natural aggregates. Artificial gravel aggregates supplement natural gravel aggregates at dam sites, allowing the aggregate gradation of CSG to be adjusted. In order to mix aggregates in a logical way, the aggregates’ characteristics must be quantified. Owing to the complex gradations and shapes of aggregates, fractal theory was introduced in this work to quantify their characteristics.
3.1. Fractal Characteristics Based on Aggregate Gradation
⌅The impact of aggregate gradation characteristics on CSG was compared with Fuller gradation, which was taken as the standard gradation (BZ) of aggregates and was combined with cemented sand and gravel site aggregates. The on-site gradations with sand rates of 29.2% and 38.8% were selected as control gradation 1 (DZ1) and control gradation 2 (DZ2), respectively. The cumulative percentage of particles passing the sieve is illustrated in Figure 2 and the cumulative screening rate is shown in Table 3.
| No. | Sieving particle size (mm) | |||||||
|---|---|---|---|---|---|---|---|---|
| 40 | 35 | 30 | 25 | 20 | 15 | 10 | 5 | |
| BZ | 100.0 | 94.0 | 87.0 | 79.0 | 71.0 | 61.0 | 50.0 | 35.0 |
| DZ1 | 100.0 | 93.0 | 85.5 | 77.4 | 68.6 | 61.3 | 52.3 | 39.9 |
| DZ2 | 100.0 | 93.8 | 87.2 | 79.9 | 71.8 | 65.4 | 57.4 | 45.9 |
Since the Fuller curve model was highly consistent with the power function curve, the cumulative aggregate distribution curve was transformed into the same form as Equation (2) to determine its fractal dimension. The aggregate standard gradation curve (BZ) is expressed as Equation [6]:
According to the above formula and Equation [2] , the fractal dimension of the standard gradation was 2.4951.
The fractal dimensions of the three gradations obtained are shown in Table 4. Figure 3 presents the fractal curves of the grading qualities obtained for the three aggregate grading curves listed in Table 3.
| No. | Slope K | Fractal dimension Dg | R2 |
|---|---|---|---|
| BZ | 0.5049 | 2.4951 | 1.000 |
| DZ1 | 0.4404 | 2.5596 | 0.993 |
| DZ2 | 0.3730 | 2.6270 | 0.990 |
Table 4 and Figure 3 show that, as the cumulative aggregate screening rate approaches the standard value, the curve steepens and the fractal dimension decreases. That is, for aggregates with significant fractal characteristics within the same scale range, the larger the fractal dimension, the poorer the gradation; conversely, the smaller the fractal dimension, the better the gradation.
3.2. Fractal Characteristics Based on Aggregate Shape
⌅Natural sand gravel aggregates are generally round and artificial aggregates are generally polygonal. In order to study the effect of the mix proportion of different shapes of sand gravel aggregates on the performance of CSG, the fractal characteristics of mixed aggregates were determined as listed in Table 5.
| No. | Aggregate proportion (%) | |
|---|---|---|
| Round | Polygonal | |
| LC1 | 0 | 100 |
| LC2 | 20 | 80 |
| LC3 | 40 | 60 |
| LC4 | 60 | 40 |
| LC5 | 80 | 100 |
| LC6 | 100 | 0 |
Based on Equation [3], the mixing ratios (LC1, LC2, LC3, LC4, LC5) of the above-mentioned five different shapes of aggregates are calculated, and the fractal dimension regression calculation results are shown in Figure 4 and Table 6. Since there were no polygonal aggregates in LC6, it was not required to calculate its fractal dimension.
Table 6 summarizes the fractal dimension regression results and Figure 4 shows the fractal curves for different aggregate shapes.
According to Table 6 and Figure 4, as the proportion of polygonal (artificial) aggregates in CSG decreases, aggregate shape complexity and fractal dimension decrease. That is, within the same scale range, the larger the fractal dimension, the more polygonal the artificial aggregates; conversely, the smaller the fractal dimension, the less the polygonal the artificial aggregates.
| No. | Fractal dimension Dx | R2 |
|---|---|---|
| LC1 | 1.7630 | 0.998 |
| LC2 | 1.6102 | 0.998 |
| LC3 | 1.5000 | 0.997 |
| LC4 | 1.3187 | 1.000 |
| LC5 | 1.1477 | 0.995 |
4. DISCUSSION
⌅Based on the results obtained, the following discussion examines the effects of aggregate characteristics on CSG mechanical behavior. In particular, the relationships between aggregate gradation and shape fractal dimensions and resulting CSG mechanical behavior are discussed.
4.1. Effect of Aggregate Gradation Fractal Dimension
⌅The effect of aggregate gradation on the mechanical behavior of CSG was studied based on the three aggregate gradations described in 3.1: the standard gradation (BZ), control gradation 1 (DZ1), and control gradation 2 (DZ2). The random aggregate models in which all aggregates were artificial (LC1) are shown in Figure 5 for the three gradations, and the corresponding stress-strain curves obtained from numerical simulations are shown in Figure 6.
As
the aggregate gradation approaches the standard gradation, the fractal
dimension of the aggregate gradation decreases and the peak stress
increases. Simultaneously, as the aggregate gradation improves, the
tangent slope of the stress-strain curve increases; that is, the elastic
modulus increases. This occurs because, as the aggregate gradation
approaches the standard gradation, the aggregate quantity increases,
improving the aggregate density; thus, both the strength and elastic
modulus increase. This is consistent with experimental results in the
literature (3131.
Ashraf, W.B.; Noor, M.A. (2011) Performance-evaluation of concrete
properties for different combined aggregate gradation approaches. Proce. Eng. 14, 2627-2634. https://doi.org/10.1016/j.proeng.2011.07.330.
) and validates the research method used in this study.
4.2. Effect of Aggregate Shape Fractal Dimension
⌅The effect of aggregate shape on the mechanical behavior of CSG was analyzed in accordance with the relationship between fractal characteristics and mechanical characteristic parameters. Figure 7 shows the models of different aggregate shapes under the standard gradation.
Figure 8 shows the stress-strain curves under uniaxial compression obtained for the models illustrated in Figure 7.
Figure 7 and Figure 8
show that, as the proportion of polygonal aggregates increases (i.e.,
as the aggregate shape fractal dimension increases), the peak stress and
the tangent slope of the stress-strain curve both decrease: that is,
the elastic modulus decreases. This is consistent with experimental
results in literature (32-3532. Du, C-B.; Sun, L-G. (2007) Numerical simulation of aggregate shapes of two-dimensional concrete and its application. J. Aerospace Eng. 20 [3], 172-178. https://doi.org/10.1061/(ASCE)0893-1321(2007)20:3(172).
33.
Du, C-B.; Sun, L-G.; Jiang, S.Y. (2013) Numerical simulation of
aggregate shapes of three-dimensional concrete and its application. J. Aerospace Eng. 26 [3], 515-527. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000181.
34.
Cui, W.; Yan, W-s.; Song, H-f.; Wu, W-l. (2020) DEM simulation of SCC
flow in L-Box set-up: Influence of coarse aggregate shape on SCC
flowability. Cem. Concr. Comp. 109, 103558. https://doi.org/10.1016/j.cemconcomp.2020.103558.
35.
Tian, M.Y. (2019) Numerical calculation of concrete uniaxial mechanical
properties based on mesoscale, Taiyuan University of Technology,
Taiyuan, China.
). There are several possible explanations for this phenomenon: the influence of corner edges and of stress concentration.
Considering
the impact of the corner edges, the area of the interfacial transition
zone (ITZ) units around the polygonal aggregates is larger than that
around the circular aggregates of the same volume. Under the same
stress, more ITZ units around the polygonal aggregates will show damage
and fracture than around the circular aggregates. This conclusion is
consistent with that in the reference works (99.
Xiong, X.Y.; Xiao, Q.S. (2019) A unified meso-scale simulation method
for concrete under both tension and compression based on Cohesive Zone
Model. J. Hydraul. Eng. 50, 448-462. https://doi.org/10.13243/j.cnki.slxb.20181061.
, 3636.
Chen, P.; Chen, X.; Wang, Y.; Wang, P. (2020) Preliminary study on the
upcycle of non-structural construction and demolition waste for waste
cleaning. Mater. Construcc. 70 [338], e220. https://doi.org/10.3989/mc.2020.13819.
, 3737. Chen, H.Q.; Ma, H.F.; Li, Y.C. (2007) Influence of random aggregate shapes on flexural strength of dam concrete. J. Chin. Inst. Water. Resour. Hydr. Res. 04, 241-246. https://doi.org/10.13244/j.cnki.jiwhr.2007.04.003.
).
Considering the impact of stress concentration, the stress distribution around polygonal aggregates is more concentrated than that around the circular aggregates. Therefore, ITZ units around the polygonal aggregates are more prone to damage and fracture. Furthermore, under the standard gradation, when the aggregate shapes are all round (LC6), i.e., when all the aggregates are natural sand gravel aggregates, the highest peak stress and elastic modulus are achieved. However, since this study focuses on project sites lacking natural sand gravels, this condition is difficult to achieve and is not considered further.
Figure 9 and Figure 10 present diagrams of the relationship between the fractal characteristics and mechanical characteristic parameters.
According to Figure 9 and Figure 10, for the same aggregate gradation fractal dimension, the CSG peak stress and elastic modulus both increase as the aggregate shape fractal dimension decreases. Conversely, for the same aggregate shape fractal dimension, the CSG peak stress and elastic modulus both decrease with the increase of the aggregate gradation fractal dimension.
For use in CSG, artificial aggregates are mixed into natural aggregates sourced from riverbeds. Considering the complex resulting aggregate characteristics, aggregate gradation and shape were quantified using fractal dimensions in this research. On one hand, the results obtained show that mixing artificial aggregates standardizes the resulting gradations, and that the closer a gradation is to the standard gradation, the better its CSG mechanical properties. On the other hand, excessive artificial aggregate content may degrade CSG mechanical properties. For project sites lacking natural aggregates, artificial aggregates should be added appropriately to achieve the best performance. When 20% artificial aggregate content was added under the standard gradation considered in this study, the elastic modulus and peak stress reached their maximum values; this scenario was suitable for on-site mixing. The method used in this study to investigate the impact of complex aggregates on CSG mechanical properties through fractal theory and numerical simulation can provide a theoretical reference for other CSG projects.
5. CONCLUSIONS
⌅In view of the complex characteristics of CSG aggregates, the concept of fractal dimensions was introduced to quantify aggregate gradation and shape. A two-dimensional random aggregate model of CSG was established, and mechanical properties of CSG under different aggregate gradation and shape fractal dimensions were studied through parameter inversion. The following conclusions were drawn:
The closer the aggregate gradation to the standard gradation, the smaller the fractal dimension of the aggregate gradation; as the proportion of polygonal aggregates increased, the aggregate shape fractal dimension increased.
According to uniaxial compression numerical testing, as the aggregate gradation fractal dimension decreased, both the peak stress and elastic modulus of CSG increased.
According to uniaxial compression numerical testing, as the aggregate shape fractal dimension increased, both the peak stress and elastic modulus of CSG decreased.
For mixing artificial aggregates with natural aggregates from riverbeds, a mix proportion for optimal mechanical properties was obtained; this could provide a theoretical basis for similar projects.
Due to the limited test methods available for this study, the mesoscopic numerical simulation technique in this work did not consider the effect of aggregate shape on interface performance; this topic requires further research in the future.