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A method for quantifying the packing function of particles in packed aggregate blend
Construction and Building Materials 188 (2018) 607–614
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A method for quantifying the packing function of particles in packed aggregate blend Yinghao Miao a,b,⇑, Sudi Wang b, Liyan Guo b, Juan Li b a b
National Center for Materials Service Safety, University of Science and Technology Beijing, 30 Xueyuan Road, Haidian District, Beijing 100083, China Beijing Key Laboratory of Transportation Engineering, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing 100124, China
h i g h l i g h t s The PCPV provides a new way to understand the composition of aggregate blend. The PCPV shows compaction energy and morphology independent. PB
The RC s
can be used to quantifying the packing functions of particles in blend. PB means major skeleton building function. i PB A negative RC s means major air voids filling function. i i
A positive RC s
a r t i c l e
i n f o
Article history: Received 6 May 2018 Received in revised form 20 August 2018 Accepted 22 August 2018
Keywords: Aggregate blend Packing function Air voids filling function Skeleton building function Packing volume Particle morphology
a b s t r a c t This paper proposes a method to quantify the packing function of particles in packed aggregate blend. Three indicators are defined to capture the composition of aggregate blend and the packing function of particles in packed aggregate blend, which are the percentage of contribution to the packing volume (PCPV), the percentage of contribution to the bulk volume (PCBV), and the relative change between the contribution of particles to the packing volume and that to the bulk volume (RC PB si ). Packing strateare developed based on the loose filling test, the dry-rodded test and the gies to quantify PCPV and RC PB si Superpave gyratory compactor (SGC) test. Two typical aggregates, one with good angularity (denoted as crushed stone) and the other with poor angularity (denoted as gravel), are selected for investigating the proposed method with 3 stone matrix asphalt (SMA) gradations and 3 asphalt concrete (AC) gradations. The test results show that the PCPV provides a new way to understand the composition of aggregate can be employed to quantitatively investigate the packing functions of the particles blend. The RC PB si represents the balance point between air voids filling funcin packed aggregate blend. The zero of RC PB si means more skeleton building function. And the bigtion and skeleton building function. A positive RC PB si the stronger the skeleton building function. A negative RC PB means major air voids filling ger RC PB si si the more significant the air voids filling function. The balance size for function. And the smaller RC PB si the SMA gradation with the nominal maximum particle size (NMPS) of 16 mm is 2.36 mm, which is also considered as the balance size for the reference upper limit and a designed gradations of AC with the NMPS of 26.5. The balance size for the reference gradation lower limit gradation of AC is bigger than 2.36 mm but smaller than 4.75 mm. The compact energy of the filling test and the particle morphology but significant effects on the air void content. The SGC test is rechave no impacts on the PCPV and RC PB si ommended to quantify the indicators. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction
⇑ Corresponding author at: National Center for Materials Service Safety, University of Science and Technology Beijing, 30 Xueyuan Road, Haidian District, Beijing 100083, China. E-mail address: [email protected] (Y. Miao). https://doi.org/10.1016/j.conbuildmat.2018.08.142 0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.
Aggregate blend is the main portion forming the skeleton of asphalt concrete and cement concrete. Suitable aggregate blend characteristics are important to ensure good field mixture performance. The grain size distribution is usually employed to describe the composition of aggregate blend, which is considered highly related to the mixture performance [1,2]. The optimizing direction
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is to obtain the maximum density in traditional gradation design. Fuller [3] proposed the gradation design method on the basis of the power function curve, which is known as the n method. Originally, 0.5 was adopted for n. Now 0.45 is usually used after many times modification [4]. However, not all mixture characteristics can be ensured merely in accordance with the principle of the maximum density. The packing characteristics of aggregate blend are also usually referenced to optimize the gradation [5,6]. Weymouth [7] analyzed the particle interference effects and proposed a method to improve the workability of concrete mixture. Some methods, such as the Bailey method and the coarse aggregate void filling (CAVF) method, included the volume parameters getting from packing tests to assess the packing characteristics of aggregate blend and improve the gradation design [8–11]. Aggregates are usually categorized into coarse aggregates and fine aggregates for separately assessing in gradation design. It is usually considered that the coarse aggregates is to form the skeleton and the fine is to fill the air voids [12]. However, there are many different criteria for discriminating the coarse and fine. Typically, the size of 4.75 mm or 2.36 mm is employed [13,14]. But the maximum particle size isn’t taken into account in that criterion. Brown et al. [15] proposed to use 4.75 mm to discriminate the coarse and fine particles for the stone matrix asphalt (SMA) with the nominal maximum particle size (NMPS) of 12.5 mm and 19 mm, and use the 2.36 mm for the SMA with the NMPS of 9.5 mm. In Bailey method, the size of 0.22 times of the NMPS was defined as the primary control sieve size (PCS) for discriminating the coarse and fine [8,9], while Lin [16] suggested using 0.25 times of the NMPS. However, the packing characteristics of aggregate blend are complicated. The concepts of coarse and fine aggregates can’t totally meet the needs of gradation optimization in practice. Kim et al. [17,18] proposed a new framework to analyze the composition features of aggregate blends, in which some particles was identified as dominant aggregate particles by the defined dominant aggregate size range (DASR). It was suggested that the DASR particles should be composed of coarse enough particles and the porosity of the DASR part should be no greater than 50%. The particles smaller than the DASR were considered to fill the voids between the DASR particles along with the binder and fillers. The particles larger than the DASR were thought to simply float in the mixture. The DASR identification was performed graphically and could be somewhat subjective. Guarina et al. [19] found some specific particles could disrupt the DASR structure. Then the ratio between the potentially disruptive interstitial component (IC) particles and the volume of DASR voids were referred to as the disruption factors to assess the potentials. Yideti et al. [20] divided the skeleton of unbound granular materials into two basic components, the load carrying skeleton (primary structure), built by the DASR particles, and the finer fraction (secondary structure). Then, a model describing the disruption potential (DP model) was proposed based on the division of the 2 components. The framework provided a new way to investigate the packing characteristics of aggregate blend. However, the function of each size particles could be different in the packed aggregate blend. And the packing function of aggregate particles is not always skeleton building or voids filling. The particles with given size might have both the 2 functions with different proportions. A quantitative framework in which the function of each size particles can be quantified might be more efficient for understanding the packing characteristics of aggregate blend. This paper focused on the concern about quantifying the packing function of particles in packed aggregate blend. A series of indicators were defined to capture the composition of aggregate blend and the packing function of particles in packed aggregate blend. Then, packing strategies to quantify the indicators were developed
based on the loose filling test, the dry-rodded test and the Superpave gyratory compactor (SGC) test. Six typical gradations as well as two kinds of typical aggregates, one with good angularity and the other with poor angularity, were selected to investigate the proposed method. The test results showed that the method proposed in this paper provided a quantitative way to understand the composition of aggregate blend and the packing function of particles in packed aggregate blend. 2. Definitions Employ A to represent an aggregate blend with given gradation and mass. The sieve sizes involved in the gradation are numbered in an ascending order as si (i = 0, 1, . . ., M), in which s0 means the sieve bottom, sM means the maximum aggregate particle size in the gradation. Then denote Asi as the particles of A passed sieve si+1 but retained on sieve si. Employ Asi sM to represent all the particles of A bigger than si. Denote the packing volume of A under given packing method as VP, which is composed of the bulk volume of all particles of A and the air voids volume between all the particles. Record the packing volume of ASi and ASi sM under the same packing method as V PSi and V PSi SM . Fig. 1 depicts the relationships between V Psi ; V PSi SM , and VP. The percentage of contribution to the packing volume (PCPV) is defined as Eq. (1) to describe the contribution of ASi SM to the packing volume of A. The contribution of Asi to the packing volume of A is defined as Eq. (2).
PCPV si sM ¼
V Psi sM VP
PCPV si ¼ PCPV si sM PCPV siþ1 sM
ð1Þ ð2Þ
Denote the total bulk volume of A as VB. Record the bulk volume of ASi SM as V Bsi sM . Then the percentage of contribution to the bulk volume (PCBV) is defined as Eq. (3) to describe the contribution of Asi sM to the total bulk volume of A. The contribution of Asi to the bulk volume of A is defined as Eq. (4).
PCBVsi sM ¼
PCBVsi ¼
VBsi VB
VBsi sM VB
ð3Þ
ð4Þ
Generally, the packing function is divided into skeleton building and air voids filling. The packing volume is composed of the bulk volume of the aggregate particles and the air voids volume between the particles. When adding an amount of given size particles to a blend, the packing structure of the blend will be changed. If there is only a decrease of air voids content but no packing volume increase, the function of the added particles can be totally considered as air voids filling. If the added particles increase the packing volume, and the increased proportion is bigger than their corresponding bulk volume proportion in the blend, they can be considered have skeleton building function. Mostly particles in each size, except the maximum size, have the 2 functions at the same time to various extents. The packing function of particles in packed aggregate blend can be quantitatively discriminated in accordance with the concepts of PCPV and PCBV. It can be considered that the major function of the particles of Asi is build the skeleton in the packed A when the value of PCPV si is bigger than that of PCBV si . If the value of PCPV si is smaller than that of PCBV si , the air voids filling function will be more than the skeleton building function for the particles of :. The relative change between the contri-
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VsPi VsPi+1 − sM
VsPi − sM
Asi+1 − sM
Asi − sM
VP = VsP0 − sM
A
Fig. 1. The relationships between V Psi ; V Psi sm ; and VP.
bution of Asi to the packing volume and that to the bulk volume can be defined as Eq. (5), which is convenient to be used for investigating the packing function of particles in packed aggregate blend. The zero of RC PB can be considered as the balance point between the si air voids filling function and skeleton building function. A positive means more skeleton building function. And the bigger RC PB RC PB si si the stronger the skeleton building function. A negative RC PB si means major air voids filling function. And the smaller RC PB the si more significant the air voids filling function.
RC PB ¼ si
PCPV si PCBV si PCBV si
(a) 13.2 mm
ð5Þ
(b) 9.5 mm
3. Materials 3.1. Aggregates The angularity characteristics of aggregates have potential effects on their packing characteristics [21,22]. Two kinds of typical aggregates with different angularity characteristics were employed to incorporate the angularity effects into this study. The crushed stone and manufactured sand were selected as aggregates with good angularity and the gravel and natural sand were selected as aggregates with poor angularity. The same mineral powder was used as filler for the 2 typical aggregates. Figs. 2 and 3 depict the typical particles of the aggregates with good angularity and poor
(c) 4.75 mm
(d) 1.18 mm
Fig. 2. Typical particles of the aggregates with good angularity.
(a) 13.2 mm
(b) 9.5 mm
(c) 4.75 mm
Fig. 3. Typical particles of the aggregates with poor angularity.
(d) 1.18 mm
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Table 1 Bulk density of aggregates (g/cm3). Size (mm)
Crushed stone
Gravel
Size (mm)
Manufactu-red Sand
Natural sand
Size (mm)
Mineral powder
26.5 19 16 13.2 9.5 4.75 2.36
2.810 2.793 2.799 2.802 2.796 2.790 2.737
2.597 2.572 2.546 2.538 2.581 2.565 2.501
1.18 0.6 0.3 0.15 0.075 / /
2.680 2.675 2.652 2.614 2.589 / /
2.594 2.528 2.566 2.535 2.614 / /
<0.075
2.806
Table 2 The selected gradations. Sieve Size (mm)
31.5 26.5 19 16 13.2 9.5 4.75 2.36 1.18 0.6 0.3 0.15 0.075
blend mixed only by particles bigger than si in accordance with the given gradation. So, the value of V Psi sM corresponding to Asi sM
Percent passing (%) SMAU
SMAD
SMAL
ACU
ACD
ACL
_ 100 100 100 85 65 32 24 22 18 15 14 12
_ 100 99.7 94.0 71.5 55.9 27.8 18.7 16.2 14.2 12.8 12.0 11.2
_ 100 100 90 65 45 20 15 14 12 10 9 8
100 100 90.0 80 73 63 52 42 32 25 18 13 7
100 99.3 79.1 72.2 65.3 52.5 38.9 28.8 20.6 14.5 10.1 7.6 6.5
100 95 75 62 53 43 32 25 18 13 8 5 3
angularity respectively. The bulk density of each aggregate was determined in accordance with the ‘‘Test Methods of Aggregate for Highway Engineering (JTG E42-2005)” of China [23]. Table 1 lists the bulk density values of the aggregates with different size. 3.2. Selected gradations Two kinds of typical gradations, for SMA and for dense asphalt concrete (AC), were selected to investigate the contributions of particles to the blend packing volume. The NMPS of the SMA gradation and that of the AC gradation are 16 mm and 25 mm respectively. The reference upper limit, the reference lower limit, and a designed gradation of each gradation type were selected in accordance with the ‘‘Specifications for Design of Highway Asphalt Pavement (JTG D50-2006)” of China [24] for following investigations, which were denoted as SMAU, SMAL SMAD, ACU, ACL, and ACD. The detailed information of the six gradations is presented in Table 2. Both the aggregates with good angularity (denoted as crushed stone) and those with poor angularity (denoted as gravel) were blended in accordance with the 6 gradations for packing tests. 4. Packing tests to quantify PCPV 4.1. Packing strategies Packing strategies to quantify PCPV were developed based on 3 packing test methods, the loose filling test, the dry-rodded test, and the SGC test. The loose filling test and dry-rodded test were performed in accordance with the 0309-2005 method in the ‘‘Test Methods of Aggregate for Highway Engineering (JTG E42-2005)” of China [23]. Following is the strategy to quantify PCPV by the loose filling test or the dry-rodded test. Firstly, the aggregate blend with given gradation filled in the cylindrical measure can be denoted as A. Thus the corresponding VP is the volume of the cylindrical measure. Secondly, fill the cylindrical measure up using the aggregate
can be calculated using the filled mass and the mass proportion of particles bigger than si in A. Then the PCPV of Asi sM can be obtained by Eq. (1). The air void content of A (denoted as Va) and that of Asi sM (denoted as V asi sM ) can also be obtained by the filling tests. In this paper, a 5 L cylindrical measure was selected to do the loose filling test and dry-rodded test. For the loose filling test, let the aggregate blend free fall from a height of 50 mm above the top of the cylindrical measure until the measure is filled up. Then flatten the surface and weight the mass of the aggregate in the measure for further usage. For the dry-rodded test, the measure is filled up with 3 layers and each layer is evenly rodded 25 times. Then weight the mass of the aggregate in the measure after flattening the surface. The SGC is commonly used to make HMA specimens. It also can be employed to compact unbound materials [25,26]. The compaction energy can be controlled more precisely by the SGC than the loose filling and dry-rodded, which can lower the test error due to the operator. A strategy to quantify PCPV by the SGC test is proposed through trial and error. Denote 3 kg aggregate blend with given gradation as A. Compact A 25 gyrations in a mold with a diameter of 150 mm. Record the packing volume, which is the corresponding VP. Take 3 kg aggregate blend mixed only by particles bigger than si in accordance with the given gradation to compact 25 gyrations and record the packing volume. So, the value of V Psi sM corresponding to AsisM can be calculated using the packing volume and the mass proportion of particles bigger than si in A. Then the PCPV of Asi sM can be obtained by Eq. (1). The corresponding values of V asi sM can also be obtained at the same time.
4.2. Packing tests The loose filling test, dry-rodded test and SGC test were carried out in accordance with the corresponding strategies using the crushed stone blends with gradation of SMAD and ACD to investigate the potential differences between the 3 packing tests in quantifying PCPV. The PCPV si sM and V asi sM are depicted in Figs. 4 and 5 respectively. As can be seen in Fig. 4, the PCPV si sM of SMAD shows a fast increase and then gradually tends to a stable value. The addition of mineral powder finally increases the PCPV si sM to 100%. The PCPV si sM of ACD shows an increase slower than that of SMAD and then gradually tends to 100%. The curves of PCPV si sM obtained from the three different packing tests closely match each other for both SMAD and ACD. The variance homogeneity tests were conducted with the confidence level of 0.05 to determine whether the results of PCPV si sM from different packing tests can be considered consistent. The P values of the tests, presented in Table 3, are 0.978 and 0.988 for SMAD and ACD respectively, which indicate that different packing test methods have no impacts on the PCPV results.
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Y. Miao et al. / Construction and Building Materials 188 (2018) 607–614 Table 3 PCPV si sM (%) and the P value of statistical test. Sieve size (mm)
SMAD
13.2 9.5 4.75 2.36 1.18 0.6 0.3 0.15 0.075 <0.075
ACD
Loose
Rodded
SGC
P value
Loose
Rodded
SGC
P value
\ 54.33 85.09 94.11 95.21 95.43 95.11 95.17 94.43 100
\ 54.28 86.15 94.90 96.95 97.24 98.14 96.98 96.95 100
35.00 53.37 85.22 94.16 95.49 96.69 98.27 96.75 96.96 100
0.978
\ 60.51 75.45 85.05 90.44 94.70 97.69 97.15 96.66 100
\ 60.63 76.12 86.78 91.53 95.73 98.05 98.25 98.45 100
45.17 58.03 74.28 84.47 90.67 95.41 98.09 98.35 98.57 100
0.988
As shown in Fig. 5, the values of V asi sM are totally different from
precisely controlling and easily performing. Therefore, the following investigation was carried out by the SGC test.
each packing test for both SMAD and ACD, which could be attributed to the different compaction energy of the 3 packing tests. The loose filling test results in the biggest V asi sM for both SMAD and
4.3. Analysis of the contributions to packing volume
ACD among the 3 packing tests, followed by the dry-rodded test, then the SGC test. However, all the V asi sM obtained from the 3 pack-
The PCPV si sM of crushed stone blends and gravel blends with all the 6 gradations are depicted in Fig. 6. As comparison, the gradations presented by the percentage of accumulated retained (PAR) are also depicted in Fig. 6. Generally, the gradation of aggregate blend is captured by mass. However, aggregate particles fill a space by volume. Different aggregate blends with the same gradation in mass (GM) usually have different gradations in volume for the different densities. Actually, the PCBV si sM is the PAR expression of a gradation in bulk volume. So all the corresponding PCBV si sM curves are also incorporated in Fig. 6. As can be seen, both the PCBV si sM curve of crushed stone and that of gravel are closely match the GM curve for each gradation, which can be attributed to the similar bulk densities of the particles with different sizes for both the crushed stone and gravel. However, the curves of PCPV si sM are totally different from those of GM and PCBV si sM for all the SMA and the AC gradations, which means PCPV si sM provides a new way to understand the composition of aggregate blend. As shown in Fig. 6, there are very little differences between the PCPV si sM curve of crushed stone and that of gravel for each gradation, which presents the morphology of aggregate particles has no influence on the PCPV. Fig. 7 presents the V asi sM of crushed stone blends and gravel
ing tests gradually decreases with the addition of smaller particles in a similar way for each gradation. As above mentioned, the compaction energy has no impact on the PCPV results, and the compaction energy can be controlled more precisely by SGC than the other 2 methods so that the test error due to the operator can be lowered. Hence the SGC test could be a good choice for quantifying PCPV with the consideration of
100 90
i M
PCPVs -s (%)
80 70 SMAD Loose
60
SMAD Rodded
50
SMAD SGC
40
ACD Rodded
ACD Loose ACD SGC
30 13.2
9.5
4.75
2.36
1.18 0.6 Sieve Size (mm)
0.3
0.15
0.075
blends with all the gradations. As shown in Fig. 7, the V asi sM grad-
0
ually decreases with the addition of the smaller particles for each aggregate type and gradation. In comparison with crushed stone blends, the gravel blends with the corresponding gradation exhi-
Fig. 4. The PCPV si sM from different packing tests.
50
SMAD Rodded
45
Vsa-s (%)
i M
i M
a Vs -s
30
30 25
20
20
4.75
2.36
1.18
0.6
0.3
0.15
0.075
ACD SGC
35
25
9.5
ACD Rodded
40
35
15 13.2
ACD Loose
45
SMAD SGC
40
(%)
50
SMAD Loose
0
15 13.2
9.5
4.75
Sieve Size (mm)
2.36
1.18
0.6
Sieve Size (mm)
(a) SMA gradations Fig. 5. The air void contents under different tests.
(b) AC gradations
0.3
0.15
0.075
0
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Y. Miao et al. / Construction and Building Materials 188 (2018) 607–614
bits remarkably lower V asi sM , which indicates that particle morphology has significant effect on the air void content of packed aggregate blend.
accordance with the test results of the crushed stone blends for the morphology of aggregate particles has no influence on PCPV). As shown in Fig. 8, the values of RC PB corresponding to particles si of 2.36 mm are very close to 0 for all the 3 SMA gradations. The value substantially particles of 4.75 mm and bigger have a RC PB si
4.4. Packing function analysis
greater than 0 while most particles smaller than 2.36 mm correcan be employed to As above mentioned, the indicator of RC PB si investigate the packing functions of the particles in packed aggre-
ered as the balance size between air voids filling function and skeleton building function for the SMA gradations. The skeleton of the packed SMA blend is mainly built by the particles bigger
100
100
90
90
80
80
70
70 Percent (%)
Percent (%)
for each gradation gate blend. Fig. 8 depicts the values of RC PB si with crushed stone (Following investigations are only in
spond to a big negative RC PB si . The size of 2.36 mm could be consid-
60 50 40
20 10 13.2
9.5
4.75
2.36
1.18
0.6
0.3
0.15
0.075
50 40
GM Crushed stone PCBV Gravel PCBV Crushed stone PCPV Gravel PCPV
30
60
GM Crushed stone PCBV Gravel PCBV Crushed stone PCPV Gravel PCPV
30 20 10 13.2
0
9.5
4.75
2.36
Sieve Size (mm)
100
100
90
90
80
80
70
70
60 50 40 30 20 4.75
2.36
1.18
0.6
0.3
0.15
0.075
20 10 13.2
0
9.5
4.75
2.36
90
80
80
70
70 Percent (%)
Percent (%)
0.6
0.3
0.15
0.075
0
(d) ACD 100
60 50 40 30 20 0.6
0.3
0.15
0.075
60 50 40
GM Crushed stone PCBV Gravel PCBV Crushed stone PCPV Gravel PCPV 1.18
1.18
Sieve Size (mm)
90
2.36
0
GM Crushed stone PCBV Gravel PCBV Crushed stone PCPV Gravel PCPV
30
100
4.75
0.075
50
(c) SMAD
9.5
0.15
60
Sieve Size (mm)
10 13.2
0.3
40
GM Crushed stone PCBV Gravel PCBV Crushed stone PCPV Gravel PCPV 9.5
0.6
(b) ACU
Percent (%)
Percent (%)
(a) SMAU
10 13.2
1.18
Sieve Size (mm)
GM Crushed stone PCBV Gravel PCBV Crushed stone PCPV Gravel PCPV
30 20 0
10 13.2
9.5
4.75
2.36
Sieve Size (mm)
1.18
0.6
Sieve Size (mm)
(f) ACL
(e) SMAL Fig. 6. The PCPV, GM, and PCBV curves of all the gradations.
0.3
0.15
0.075
0
613
40
40
35
35
30
30
V a -s (%) s
SMAU Crushed stone
25
i M
i M
V as -s (%)
Y. Miao et al. / Construction and Building Materials 188 (2018) 607–614
SMAU Gravel SMAD Crushed stone
20
25 20
SMAD Gravel 15
SMAL Gravel 10 13.2
9.5
4.75
ACD Crushed stone ACD Gravel
SMAL Crushed stone
15
ACU Crushed stone ACU Gravel
ACL Crushed stone ACL Gravel
2.36
1.18
0.6
0.3
0.15
0.075
0
10 13.2
9.5
4.75
Sieve size (mm)
2.36
1.18
0.6
0.3
0.15
0.075
0
Sieve size (mm)
(a) SMA gradations
(b) AC gradations
Fig. 7. The air void contents of different aggregate blends.
50
SMAU
SMAD
SMAL
0
-100
i
RCsP-B (%)
-50
-150 -200 -250 -300
13.2 9.5 4.75 2.36 1.18 0.6 0.3 0.15 0.075 0
As can been seen from Fig. 8, the values of RC sPB corresponding i to the particles of 2.36 mm are very close to 0 for the gradations of ACU and ACD. Though that for the gradation of ACL is substantially less than 0, the RC PB switches from positive to negative at the size si of 2.36 mm. The size of 2.36 mm could be considered as the balance size between air voids filling function and skeleton building function for the gradations of ACU and ACD. That for the gradation of ACL is bigger than 2.36 mm but smaller than 4.75 mm, which can’t be captured precisely by the sieve size. It also can be seen that
(a) SMA gradations 40 ACU
20
ACD
ACL
(%)
corresponding to the particles less than 0.15 mm are significantly increase from ACU to ACD and ACL, which means the air voids filling function of the smaller particles is more significant in the coarse gradation than in the fine gradation.
i
RCs
P-B
which means slight increase of the balance size. The RC PB values si
-20
-60 -80 -100
the RC PB value corresponding to the particles of 2.36 mm si increases with the gradation tending to coarse from ACU to ACL,
0
-40
when the amount of the added particles is very small. The test errors could compromise the increase of packing volume due to the addition of the smaller particles. Secondly, the small amount addition of the smaller particles may reduce the interlock action between the coarse particles. Hence, the particles can be compacted closer with the same compact energy. The increase of packing volume due to the addition of the smaller particles could also be compromised by this effect.
13.2 9.5 4.75 2.36 1.18 0.6 0.3 0.15 0.075 0
5. Discussions
(b) AC gradations Fig. 8. The difference of and and PleaseCheck
than 2.36 mm. The major function of the particles smaller than 2.36 mm is to fill the air voids of the packed SMA blend. And the particles have a total filling function when the corresponding RC PB decreases to -100%. si It should be noted that several
As can be seen from above analysis, the PCPV, proposed in this paper, provides a new way to capture the composition of aggregate blend. It is morphology and compact energy independent and easy to quantify by any packing test. Furthermore, the indictor of RC PB si is defined on the basis of the PCPV, which can be used to quantitatively characterize the packing function of particles in a packed aggregate blend. The RC PB can be used to discriminate the partisi cles with skeleton building function and those with the air voids value can also filling function. Moreover, the amount of the RC PB si
RC PB si
values for SMA gradations
are less than 100%, which means the corresponding PCPV si values are negative. A negative PCPV si presents a decrease in the packing volume with the addition of the particles of size si. The tests and the data are carefully reviewed to obtain proper explanations for that phenomenon. Firstly, the PCPV si is calculated by PCPV siþ1 sM and PCPV si sM , which are determined by different packing tests. So the value of PCPV si is very sensitive to the packing test errors
be employed to compare the function significance between particles with different size. For the particles with skeleton building means the stronger function. For the parfunction, the bigger RC PB si means the ticles with air voids filling function, the smaller RC PB si stronger function. The method proposed in this paper provides a new analysis framework for quantitatively capturing the packing function of particles in a packed aggregate blend, which is potentially helpful to improve the method of aggregate blend design.
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6. Conclusions A series of indicators including PCPV, PCBV, and RC PB are si defined for characterizing the packing function of particles in packed aggregate blend. Then the packing strategies are proposed to quantify the indicators using the loose filling test, dry-rodded test and SGC test. Two typical aggregates, crushed stone and gravel, are selected for investigating the proposed method with 3 SMA gradations and 3 AC gradations. Some conclusions can be drawn as following. (1). The PCPV provides a new way to describe the composition of packed aggregate blend. The major function of in in A is to build the skeleton when the corresponding value of PCPV si is bigger than that of PCBV si . Conversely, the major function of Asi in A is to fill the air voids when the corresponding value of PCPV si is smaller than that of PCBV si . (2). The RC PB si , defined on the basis of the PCPV, can be used to quantitatively characterize the packing function of particles means the in a packed aggregate blend. The zero of RC PB si balance of the air voids filling function and skeleton building function. A positive value and a negative value of RC PB si mean major skeleton building function and major air voids presents filling function respectively. The amount of RC PB si the extent of each function. (3). The balance size for the SMA gradation with the NMPS of 16 mm is 2.36 mm. Meanwhile, the balance size for the AC gradation with NMPS of 26.5 mm depends on the specific grain distribution. For the reference upper limit and the designed gradation, the balance size is 2.6 mm. For the reference lower limit, the balance size is bigger than 2.36 mm but smaller than 4.75 mm, which can’t be presented exactly by the sieve size. (4). The PCPV shows compaction energy independent. Therefore, any packing test can be employed to quantify PCPV and RC PB si . However, the Va of packed aggregate blend depends on the compaction energy. So a fixed packing test should be selected to ensure the comparability of the test results of Va. The packing strategy based on the SGC test is recommended, of which the errors due to test operators can be better controlled. (5). The particles’ morphology has no impacts on PCPV and RC PB si but significant impacts on Va. The gravel blends with all the 6 gradations have smaller Va than the corresponding crushed stone blends. 7. Conflict of interest None. References [1] I. Mehmetaj, E. Luga, Optimization of Particle Size Distribution of Concrete Aggregates. International Balkans Conference on Challenges of Civil Engineering, 3-Bccce, 19–21, 2016, Epoka University.
[2] J.P. Bilodeau, C.O. Plamondon, G. Doré, Estimation of resilient modulus of unbound granular materials used as pavement base: combined effect of grainsize distribution and aggregate source frictional properties, Mater. Struct. 49 (10) (2016) 1–11. [3] Fuller, William B. (1906). A Treatise on Concrete, Plain and Reinforced: Materials, Construction, and Design of Concrete and Reinforced Concrete, Frederick Winslow Taylor, Sanford Eleazer Thompson, New York:John Wiley & Sons, Proportioning Concrete (Chapter 11), pp183–215. [4] Y. Zhao, The study on the composition of asphalt mixture Doctoral dissertation, Southeast University, 2005. [5] G.J. Hao, M.K. Ding, R.B. Ren, Study on the SGC and inter-lock analysis in improvement of stage filling, J. Shandong Jianzhu Univ. 36 (1) (2008) 3–10. [6] Y.M. Zhang, S.F. Chen, G.W. Hu, Coarse aggregate gradation design of asphalt mixture by gradually filling test, J. Wuhan Univ. Technol. 33 (11) (2011) 44– 143. [7] C.A.G. Weymouth, Effects of particle interference in mortars and concretes, Rock Products. 36 (2) (1933) 26–31. [8] W.R. Vavrik, W.J. Pine, G. Huber, S.H. Carpenter, The Bailey method of gradation evaluation: the influence of aggregate gradation and packing characteristics on voids in the mineral aggregate, J. Assoc. Asphalt Pav. Technol. 70 (2001) 132–175. [9] W.R. Vavrik, G. Huber, W.J. Pine, S.H. Carpenter, R. Bailey, Bailey method for gradation selection in HMA mixture design, Transport. Res. E-Circular (2002) E-C044. [10] X. Zhang, S. Wang, K. Wu, D. Wang, The CAVF method of asphalt mixture composition design, Highway 12 (2001) 17–21. [11] Sha. Qinglin, Design and Construction of Multi-Crushed Stone of Asphalt Concrete SAC, Communications Press, China, 2005. [12] Peng Bo, Study on Geometric Characteristics and Structure of Asphalt Mixture Aggregate Doctoral dissertation, Chang’an University, 2008. [13] F.L. Roberts, P.S. Kandhal, E.R. Brown, D. Lee, T.W. Kennedy, Hot mix asphalt materials, mixture design and construction, second edition, 1996, Construction Equipment. [14] L.W. Shi, D.Y. Wang, X. Cai, Z.Y. Wu, Distribution characteristics of coarse aggregate contacts based on digital image processing technique, China J. Highway Transp. 27 (8) (2014) 23–31. [15] E.R. Brown, L.A. Cooley, Designing Stone Matrix Asphalt Mixtures for RutResistant Pavements (NCHRP Report 425), Transportation Research Board, 1999. [16] X. Lin, The formula for the better aggregate composition of asphalt concrete, East China Highway 1 (2003) 82–84. [17] S. Kim, R. Roque, A. Guarin, B. Birgisson, Identification and assessment of the dominant aggregate size range (DASR) of asphalt mixture, J. Assoc. Asphalt Pav. Technol. 75 (2006) 789–814. [18] S. Kim, A. Guarin, R. Roque, B. Birgisson, Laboratory evaluation for rutting performance based on the DASR porosity of asphalt mixture, Road Mater. Pavem. Des. 9 (3) (2008) 421–440. [19] A. Guarin, R. Reynaldo, S. Kim, S. Okan, Disruption factor of asphalt mixtures, Int. J. Pave. Eng. 14 (5) (2013) 472–485. [20] T.F. Yideti, B. Birgisson, D. Jelagin, A. Guarin, Packing theory-based framework to evaluate permanent deformation of unbound granular materials, Int.J.Pave. Eng. 14 (3) (2013) 309–320. [21] H. Wang, Y. Bu, D. Wang, M. Oeser, 3d characterisation of the grain sphericity and angularity with the aid of computed tomography, Bauingenieur 90 (2015) 436–443. [22] H. Wang, D. Wang, P. Liu, J. Hu, C. Schulze, M. Oeser, Development of morphological properties of road surfacing aggregates during the polishing process, Int. J. Pave. Eng. 18 (4) (2017) 367–380. [23] Ministry of Transport, China, Test Methods of Aggregate for Highway Engineering (JTG E42-2005), China Communications Press, Beijing, 2005. [24] Ministry of Transport, China, Specifications for Design of Highway Asphalt Pavement (JTG D50-2006), China Communications Press, Beijing, 2006. [25] B. Sukumaran, C. Kumpel, C. Cary, A. Bagriacik, R. Cohen, S. Rossi et al., Superpave gyratory compactor as a compaction predictor tool for unbound material., 2014, ISAP Asphalt Pavement Design Conference. [26] N. Roohi Sefidmazgi, H. Bahia, Mechanisms Controlling Shearing Resistance of Mixtures in the Superpave Gyratory Compactor. Transportation Research Board 94th Annual Meeting, 2015.
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
A method for quantifying the packing function of particles in packed aggregate blend Yinghao Miao a,b,⇑, Sudi Wang b, Liyan Guo b, Juan Li b a b
National Center for Materials Service Safety, University of Science and Technology Beijing, 30 Xueyuan Road, Haidian District, Beijing 100083, China Beijing Key Laboratory of Transportation Engineering, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing 100124, China
h i g h l i g h t s The PCPV provides a new way to understand the composition of aggregate blend. The PCPV shows compaction energy and morphology independent. PB
The RC s
can be used to quantifying the packing functions of particles in blend. PB means major skeleton building function. i PB A negative RC s means major air voids filling function. i i
A positive RC s
a r t i c l e
i n f o
Article history: Received 6 May 2018 Received in revised form 20 August 2018 Accepted 22 August 2018
Keywords: Aggregate blend Packing function Air voids filling function Skeleton building function Packing volume Particle morphology
a b s t r a c t This paper proposes a method to quantify the packing function of particles in packed aggregate blend. Three indicators are defined to capture the composition of aggregate blend and the packing function of particles in packed aggregate blend, which are the percentage of contribution to the packing volume (PCPV), the percentage of contribution to the bulk volume (PCBV), and the relative change between the contribution of particles to the packing volume and that to the bulk volume (RC PB si ). Packing strateare developed based on the loose filling test, the dry-rodded test and the gies to quantify PCPV and RC PB si Superpave gyratory compactor (SGC) test. Two typical aggregates, one with good angularity (denoted as crushed stone) and the other with poor angularity (denoted as gravel), are selected for investigating the proposed method with 3 stone matrix asphalt (SMA) gradations and 3 asphalt concrete (AC) gradations. The test results show that the PCPV provides a new way to understand the composition of aggregate can be employed to quantitatively investigate the packing functions of the particles blend. The RC PB si represents the balance point between air voids filling funcin packed aggregate blend. The zero of RC PB si means more skeleton building function. And the bigtion and skeleton building function. A positive RC PB si the stronger the skeleton building function. A negative RC PB means major air voids filling ger RC PB si si the more significant the air voids filling function. The balance size for function. And the smaller RC PB si the SMA gradation with the nominal maximum particle size (NMPS) of 16 mm is 2.36 mm, which is also considered as the balance size for the reference upper limit and a designed gradations of AC with the NMPS of 26.5. The balance size for the reference gradation lower limit gradation of AC is bigger than 2.36 mm but smaller than 4.75 mm. The compact energy of the filling test and the particle morphology but significant effects on the air void content. The SGC test is rechave no impacts on the PCPV and RC PB si ommended to quantify the indicators. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction
⇑ Corresponding author at: National Center for Materials Service Safety, University of Science and Technology Beijing, 30 Xueyuan Road, Haidian District, Beijing 100083, China. E-mail address: [email protected] (Y. Miao). https://doi.org/10.1016/j.conbuildmat.2018.08.142 0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.
Aggregate blend is the main portion forming the skeleton of asphalt concrete and cement concrete. Suitable aggregate blend characteristics are important to ensure good field mixture performance. The grain size distribution is usually employed to describe the composition of aggregate blend, which is considered highly related to the mixture performance [1,2]. The optimizing direction
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is to obtain the maximum density in traditional gradation design. Fuller [3] proposed the gradation design method on the basis of the power function curve, which is known as the n method. Originally, 0.5 was adopted for n. Now 0.45 is usually used after many times modification [4]. However, not all mixture characteristics can be ensured merely in accordance with the principle of the maximum density. The packing characteristics of aggregate blend are also usually referenced to optimize the gradation [5,6]. Weymouth [7] analyzed the particle interference effects and proposed a method to improve the workability of concrete mixture. Some methods, such as the Bailey method and the coarse aggregate void filling (CAVF) method, included the volume parameters getting from packing tests to assess the packing characteristics of aggregate blend and improve the gradation design [8–11]. Aggregates are usually categorized into coarse aggregates and fine aggregates for separately assessing in gradation design. It is usually considered that the coarse aggregates is to form the skeleton and the fine is to fill the air voids [12]. However, there are many different criteria for discriminating the coarse and fine. Typically, the size of 4.75 mm or 2.36 mm is employed [13,14]. But the maximum particle size isn’t taken into account in that criterion. Brown et al. [15] proposed to use 4.75 mm to discriminate the coarse and fine particles for the stone matrix asphalt (SMA) with the nominal maximum particle size (NMPS) of 12.5 mm and 19 mm, and use the 2.36 mm for the SMA with the NMPS of 9.5 mm. In Bailey method, the size of 0.22 times of the NMPS was defined as the primary control sieve size (PCS) for discriminating the coarse and fine [8,9], while Lin [16] suggested using 0.25 times of the NMPS. However, the packing characteristics of aggregate blend are complicated. The concepts of coarse and fine aggregates can’t totally meet the needs of gradation optimization in practice. Kim et al. [17,18] proposed a new framework to analyze the composition features of aggregate blends, in which some particles was identified as dominant aggregate particles by the defined dominant aggregate size range (DASR). It was suggested that the DASR particles should be composed of coarse enough particles and the porosity of the DASR part should be no greater than 50%. The particles smaller than the DASR were considered to fill the voids between the DASR particles along with the binder and fillers. The particles larger than the DASR were thought to simply float in the mixture. The DASR identification was performed graphically and could be somewhat subjective. Guarina et al. [19] found some specific particles could disrupt the DASR structure. Then the ratio between the potentially disruptive interstitial component (IC) particles and the volume of DASR voids were referred to as the disruption factors to assess the potentials. Yideti et al. [20] divided the skeleton of unbound granular materials into two basic components, the load carrying skeleton (primary structure), built by the DASR particles, and the finer fraction (secondary structure). Then, a model describing the disruption potential (DP model) was proposed based on the division of the 2 components. The framework provided a new way to investigate the packing characteristics of aggregate blend. However, the function of each size particles could be different in the packed aggregate blend. And the packing function of aggregate particles is not always skeleton building or voids filling. The particles with given size might have both the 2 functions with different proportions. A quantitative framework in which the function of each size particles can be quantified might be more efficient for understanding the packing characteristics of aggregate blend. This paper focused on the concern about quantifying the packing function of particles in packed aggregate blend. A series of indicators were defined to capture the composition of aggregate blend and the packing function of particles in packed aggregate blend. Then, packing strategies to quantify the indicators were developed
based on the loose filling test, the dry-rodded test and the Superpave gyratory compactor (SGC) test. Six typical gradations as well as two kinds of typical aggregates, one with good angularity and the other with poor angularity, were selected to investigate the proposed method. The test results showed that the method proposed in this paper provided a quantitative way to understand the composition of aggregate blend and the packing function of particles in packed aggregate blend. 2. Definitions Employ A to represent an aggregate blend with given gradation and mass. The sieve sizes involved in the gradation are numbered in an ascending order as si (i = 0, 1, . . ., M), in which s0 means the sieve bottom, sM means the maximum aggregate particle size in the gradation. Then denote Asi as the particles of A passed sieve si+1 but retained on sieve si. Employ Asi sM to represent all the particles of A bigger than si. Denote the packing volume of A under given packing method as VP, which is composed of the bulk volume of all particles of A and the air voids volume between all the particles. Record the packing volume of ASi and ASi sM under the same packing method as V PSi and V PSi SM . Fig. 1 depicts the relationships between V Psi ; V PSi SM , and VP. The percentage of contribution to the packing volume (PCPV) is defined as Eq. (1) to describe the contribution of ASi SM to the packing volume of A. The contribution of Asi to the packing volume of A is defined as Eq. (2).
PCPV si sM ¼
V Psi sM VP
PCPV si ¼ PCPV si sM PCPV siþ1 sM
ð1Þ ð2Þ
Denote the total bulk volume of A as VB. Record the bulk volume of ASi SM as V Bsi sM . Then the percentage of contribution to the bulk volume (PCBV) is defined as Eq. (3) to describe the contribution of Asi sM to the total bulk volume of A. The contribution of Asi to the bulk volume of A is defined as Eq. (4).
PCBVsi sM ¼
PCBVsi ¼
VBsi VB
VBsi sM VB
ð3Þ
ð4Þ
Generally, the packing function is divided into skeleton building and air voids filling. The packing volume is composed of the bulk volume of the aggregate particles and the air voids volume between the particles. When adding an amount of given size particles to a blend, the packing structure of the blend will be changed. If there is only a decrease of air voids content but no packing volume increase, the function of the added particles can be totally considered as air voids filling. If the added particles increase the packing volume, and the increased proportion is bigger than their corresponding bulk volume proportion in the blend, they can be considered have skeleton building function. Mostly particles in each size, except the maximum size, have the 2 functions at the same time to various extents. The packing function of particles in packed aggregate blend can be quantitatively discriminated in accordance with the concepts of PCPV and PCBV. It can be considered that the major function of the particles of Asi is build the skeleton in the packed A when the value of PCPV si is bigger than that of PCBV si . If the value of PCPV si is smaller than that of PCBV si , the air voids filling function will be more than the skeleton building function for the particles of :. The relative change between the contri-
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VsPi VsPi+1 − sM
VsPi − sM
Asi+1 − sM
Asi − sM
VP = VsP0 − sM
A
Fig. 1. The relationships between V Psi ; V Psi sm ; and VP.
bution of Asi to the packing volume and that to the bulk volume can be defined as Eq. (5), which is convenient to be used for investigating the packing function of particles in packed aggregate blend. The zero of RC PB can be considered as the balance point between the si air voids filling function and skeleton building function. A positive means more skeleton building function. And the bigger RC PB RC PB si si the stronger the skeleton building function. A negative RC PB si means major air voids filling function. And the smaller RC PB the si more significant the air voids filling function.
RC PB ¼ si
PCPV si PCBV si PCBV si
(a) 13.2 mm
ð5Þ
(b) 9.5 mm
3. Materials 3.1. Aggregates The angularity characteristics of aggregates have potential effects on their packing characteristics [21,22]. Two kinds of typical aggregates with different angularity characteristics were employed to incorporate the angularity effects into this study. The crushed stone and manufactured sand were selected as aggregates with good angularity and the gravel and natural sand were selected as aggregates with poor angularity. The same mineral powder was used as filler for the 2 typical aggregates. Figs. 2 and 3 depict the typical particles of the aggregates with good angularity and poor
(c) 4.75 mm
(d) 1.18 mm
Fig. 2. Typical particles of the aggregates with good angularity.
(a) 13.2 mm
(b) 9.5 mm
(c) 4.75 mm
Fig. 3. Typical particles of the aggregates with poor angularity.
(d) 1.18 mm
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Table 1 Bulk density of aggregates (g/cm3). Size (mm)
Crushed stone
Gravel
Size (mm)
Manufactu-red Sand
Natural sand
Size (mm)
Mineral powder
26.5 19 16 13.2 9.5 4.75 2.36
2.810 2.793 2.799 2.802 2.796 2.790 2.737
2.597 2.572 2.546 2.538 2.581 2.565 2.501
1.18 0.6 0.3 0.15 0.075 / /
2.680 2.675 2.652 2.614 2.589 / /
2.594 2.528 2.566 2.535 2.614 / /
<0.075
2.806
Table 2 The selected gradations. Sieve Size (mm)
31.5 26.5 19 16 13.2 9.5 4.75 2.36 1.18 0.6 0.3 0.15 0.075
blend mixed only by particles bigger than si in accordance with the given gradation. So, the value of V Psi sM corresponding to Asi sM
Percent passing (%) SMAU
SMAD
SMAL
ACU
ACD
ACL
_ 100 100 100 85 65 32 24 22 18 15 14 12
_ 100 99.7 94.0 71.5 55.9 27.8 18.7 16.2 14.2 12.8 12.0 11.2
_ 100 100 90 65 45 20 15 14 12 10 9 8
100 100 90.0 80 73 63 52 42 32 25 18 13 7
100 99.3 79.1 72.2 65.3 52.5 38.9 28.8 20.6 14.5 10.1 7.6 6.5
100 95 75 62 53 43 32 25 18 13 8 5 3
angularity respectively. The bulk density of each aggregate was determined in accordance with the ‘‘Test Methods of Aggregate for Highway Engineering (JTG E42-2005)” of China [23]. Table 1 lists the bulk density values of the aggregates with different size. 3.2. Selected gradations Two kinds of typical gradations, for SMA and for dense asphalt concrete (AC), were selected to investigate the contributions of particles to the blend packing volume. The NMPS of the SMA gradation and that of the AC gradation are 16 mm and 25 mm respectively. The reference upper limit, the reference lower limit, and a designed gradation of each gradation type were selected in accordance with the ‘‘Specifications for Design of Highway Asphalt Pavement (JTG D50-2006)” of China [24] for following investigations, which were denoted as SMAU, SMAL SMAD, ACU, ACL, and ACD. The detailed information of the six gradations is presented in Table 2. Both the aggregates with good angularity (denoted as crushed stone) and those with poor angularity (denoted as gravel) were blended in accordance with the 6 gradations for packing tests. 4. Packing tests to quantify PCPV 4.1. Packing strategies Packing strategies to quantify PCPV were developed based on 3 packing test methods, the loose filling test, the dry-rodded test, and the SGC test. The loose filling test and dry-rodded test were performed in accordance with the 0309-2005 method in the ‘‘Test Methods of Aggregate for Highway Engineering (JTG E42-2005)” of China [23]. Following is the strategy to quantify PCPV by the loose filling test or the dry-rodded test. Firstly, the aggregate blend with given gradation filled in the cylindrical measure can be denoted as A. Thus the corresponding VP is the volume of the cylindrical measure. Secondly, fill the cylindrical measure up using the aggregate
can be calculated using the filled mass and the mass proportion of particles bigger than si in A. Then the PCPV of Asi sM can be obtained by Eq. (1). The air void content of A (denoted as Va) and that of Asi sM (denoted as V asi sM ) can also be obtained by the filling tests. In this paper, a 5 L cylindrical measure was selected to do the loose filling test and dry-rodded test. For the loose filling test, let the aggregate blend free fall from a height of 50 mm above the top of the cylindrical measure until the measure is filled up. Then flatten the surface and weight the mass of the aggregate in the measure for further usage. For the dry-rodded test, the measure is filled up with 3 layers and each layer is evenly rodded 25 times. Then weight the mass of the aggregate in the measure after flattening the surface. The SGC is commonly used to make HMA specimens. It also can be employed to compact unbound materials [25,26]. The compaction energy can be controlled more precisely by the SGC than the loose filling and dry-rodded, which can lower the test error due to the operator. A strategy to quantify PCPV by the SGC test is proposed through trial and error. Denote 3 kg aggregate blend with given gradation as A. Compact A 25 gyrations in a mold with a diameter of 150 mm. Record the packing volume, which is the corresponding VP. Take 3 kg aggregate blend mixed only by particles bigger than si in accordance with the given gradation to compact 25 gyrations and record the packing volume. So, the value of V Psi sM corresponding to AsisM can be calculated using the packing volume and the mass proportion of particles bigger than si in A. Then the PCPV of Asi sM can be obtained by Eq. (1). The corresponding values of V asi sM can also be obtained at the same time.
4.2. Packing tests The loose filling test, dry-rodded test and SGC test were carried out in accordance with the corresponding strategies using the crushed stone blends with gradation of SMAD and ACD to investigate the potential differences between the 3 packing tests in quantifying PCPV. The PCPV si sM and V asi sM are depicted in Figs. 4 and 5 respectively. As can be seen in Fig. 4, the PCPV si sM of SMAD shows a fast increase and then gradually tends to a stable value. The addition of mineral powder finally increases the PCPV si sM to 100%. The PCPV si sM of ACD shows an increase slower than that of SMAD and then gradually tends to 100%. The curves of PCPV si sM obtained from the three different packing tests closely match each other for both SMAD and ACD. The variance homogeneity tests were conducted with the confidence level of 0.05 to determine whether the results of PCPV si sM from different packing tests can be considered consistent. The P values of the tests, presented in Table 3, are 0.978 and 0.988 for SMAD and ACD respectively, which indicate that different packing test methods have no impacts on the PCPV results.
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Y. Miao et al. / Construction and Building Materials 188 (2018) 607–614 Table 3 PCPV si sM (%) and the P value of statistical test. Sieve size (mm)
SMAD
13.2 9.5 4.75 2.36 1.18 0.6 0.3 0.15 0.075 <0.075
ACD
Loose
Rodded
SGC
P value
Loose
Rodded
SGC
P value
\ 54.33 85.09 94.11 95.21 95.43 95.11 95.17 94.43 100
\ 54.28 86.15 94.90 96.95 97.24 98.14 96.98 96.95 100
35.00 53.37 85.22 94.16 95.49 96.69 98.27 96.75 96.96 100
0.978
\ 60.51 75.45 85.05 90.44 94.70 97.69 97.15 96.66 100
\ 60.63 76.12 86.78 91.53 95.73 98.05 98.25 98.45 100
45.17 58.03 74.28 84.47 90.67 95.41 98.09 98.35 98.57 100
0.988
As shown in Fig. 5, the values of V asi sM are totally different from
precisely controlling and easily performing. Therefore, the following investigation was carried out by the SGC test.
each packing test for both SMAD and ACD, which could be attributed to the different compaction energy of the 3 packing tests. The loose filling test results in the biggest V asi sM for both SMAD and
4.3. Analysis of the contributions to packing volume
ACD among the 3 packing tests, followed by the dry-rodded test, then the SGC test. However, all the V asi sM obtained from the 3 pack-
The PCPV si sM of crushed stone blends and gravel blends with all the 6 gradations are depicted in Fig. 6. As comparison, the gradations presented by the percentage of accumulated retained (PAR) are also depicted in Fig. 6. Generally, the gradation of aggregate blend is captured by mass. However, aggregate particles fill a space by volume. Different aggregate blends with the same gradation in mass (GM) usually have different gradations in volume for the different densities. Actually, the PCBV si sM is the PAR expression of a gradation in bulk volume. So all the corresponding PCBV si sM curves are also incorporated in Fig. 6. As can be seen, both the PCBV si sM curve of crushed stone and that of gravel are closely match the GM curve for each gradation, which can be attributed to the similar bulk densities of the particles with different sizes for both the crushed stone and gravel. However, the curves of PCPV si sM are totally different from those of GM and PCBV si sM for all the SMA and the AC gradations, which means PCPV si sM provides a new way to understand the composition of aggregate blend. As shown in Fig. 6, there are very little differences between the PCPV si sM curve of crushed stone and that of gravel for each gradation, which presents the morphology of aggregate particles has no influence on the PCPV. Fig. 7 presents the V asi sM of crushed stone blends and gravel
ing tests gradually decreases with the addition of smaller particles in a similar way for each gradation. As above mentioned, the compaction energy has no impact on the PCPV results, and the compaction energy can be controlled more precisely by SGC than the other 2 methods so that the test error due to the operator can be lowered. Hence the SGC test could be a good choice for quantifying PCPV with the consideration of
100 90
i M
PCPVs -s (%)
80 70 SMAD Loose
60
SMAD Rodded
50
SMAD SGC
40
ACD Rodded
ACD Loose ACD SGC
30 13.2
9.5
4.75
2.36
1.18 0.6 Sieve Size (mm)
0.3
0.15
0.075
blends with all the gradations. As shown in Fig. 7, the V asi sM grad-
0
ually decreases with the addition of the smaller particles for each aggregate type and gradation. In comparison with crushed stone blends, the gravel blends with the corresponding gradation exhi-
Fig. 4. The PCPV si sM from different packing tests.
50
SMAD Rodded
45
Vsa-s (%)
i M
i M
a Vs -s
30
30 25
20
20
4.75
2.36
1.18
0.6
0.3
0.15
0.075
ACD SGC
35
25
9.5
ACD Rodded
40
35
15 13.2
ACD Loose
45
SMAD SGC
40
(%)
50
SMAD Loose
0
15 13.2
9.5
4.75
Sieve Size (mm)
2.36
1.18
0.6
Sieve Size (mm)
(a) SMA gradations Fig. 5. The air void contents under different tests.
(b) AC gradations
0.3
0.15
0.075
0
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Y. Miao et al. / Construction and Building Materials 188 (2018) 607–614
bits remarkably lower V asi sM , which indicates that particle morphology has significant effect on the air void content of packed aggregate blend.
accordance with the test results of the crushed stone blends for the morphology of aggregate particles has no influence on PCPV). As shown in Fig. 8, the values of RC PB corresponding to particles si of 2.36 mm are very close to 0 for all the 3 SMA gradations. The value substantially particles of 4.75 mm and bigger have a RC PB si
4.4. Packing function analysis
greater than 0 while most particles smaller than 2.36 mm correcan be employed to As above mentioned, the indicator of RC PB si investigate the packing functions of the particles in packed aggre-
ered as the balance size between air voids filling function and skeleton building function for the SMA gradations. The skeleton of the packed SMA blend is mainly built by the particles bigger
100
100
90
90
80
80
70
70 Percent (%)
Percent (%)
for each gradation gate blend. Fig. 8 depicts the values of RC PB si with crushed stone (Following investigations are only in
spond to a big negative RC PB si . The size of 2.36 mm could be consid-
60 50 40
20 10 13.2
9.5
4.75
2.36
1.18
0.6
0.3
0.15
0.075
50 40
GM Crushed stone PCBV Gravel PCBV Crushed stone PCPV Gravel PCPV
30
60
GM Crushed stone PCBV Gravel PCBV Crushed stone PCPV Gravel PCPV
30 20 10 13.2
0
9.5
4.75
2.36
Sieve Size (mm)
100
100
90
90
80
80
70
70
60 50 40 30 20 4.75
2.36
1.18
0.6
0.3
0.15
0.075
20 10 13.2
0
9.5
4.75
2.36
90
80
80
70
70 Percent (%)
Percent (%)
0.6
0.3
0.15
0.075
0
(d) ACD 100
60 50 40 30 20 0.6
0.3
0.15
0.075
60 50 40
GM Crushed stone PCBV Gravel PCBV Crushed stone PCPV Gravel PCPV 1.18
1.18
Sieve Size (mm)
90
2.36
0
GM Crushed stone PCBV Gravel PCBV Crushed stone PCPV Gravel PCPV
30
100
4.75
0.075
50
(c) SMAD
9.5
0.15
60
Sieve Size (mm)
10 13.2
0.3
40
GM Crushed stone PCBV Gravel PCBV Crushed stone PCPV Gravel PCPV 9.5
0.6
(b) ACU
Percent (%)
Percent (%)
(a) SMAU
10 13.2
1.18
Sieve Size (mm)
GM Crushed stone PCBV Gravel PCBV Crushed stone PCPV Gravel PCPV
30 20 0
10 13.2
9.5
4.75
2.36
Sieve Size (mm)
1.18
0.6
Sieve Size (mm)
(f) ACL
(e) SMAL Fig. 6. The PCPV, GM, and PCBV curves of all the gradations.
0.3
0.15
0.075
0
613
40
40
35
35
30
30
V a -s (%) s
SMAU Crushed stone
25
i M
i M
V as -s (%)
Y. Miao et al. / Construction and Building Materials 188 (2018) 607–614
SMAU Gravel SMAD Crushed stone
20
25 20
SMAD Gravel 15
SMAL Gravel 10 13.2
9.5
4.75
ACD Crushed stone ACD Gravel
SMAL Crushed stone
15
ACU Crushed stone ACU Gravel
ACL Crushed stone ACL Gravel
2.36
1.18
0.6
0.3
0.15
0.075
0
10 13.2
9.5
4.75
Sieve size (mm)
2.36
1.18
0.6
0.3
0.15
0.075
0
Sieve size (mm)
(a) SMA gradations
(b) AC gradations
Fig. 7. The air void contents of different aggregate blends.
50
SMAU
SMAD
SMAL
0
-100
i
RCsP-B (%)
-50
-150 -200 -250 -300
13.2 9.5 4.75 2.36 1.18 0.6 0.3 0.15 0.075 0
As can been seen from Fig. 8, the values of RC sPB corresponding i to the particles of 2.36 mm are very close to 0 for the gradations of ACU and ACD. Though that for the gradation of ACL is substantially less than 0, the RC PB switches from positive to negative at the size si of 2.36 mm. The size of 2.36 mm could be considered as the balance size between air voids filling function and skeleton building function for the gradations of ACU and ACD. That for the gradation of ACL is bigger than 2.36 mm but smaller than 4.75 mm, which can’t be captured precisely by the sieve size. It also can be seen that
(a) SMA gradations 40 ACU
20
ACD
ACL
(%)
corresponding to the particles less than 0.15 mm are significantly increase from ACU to ACD and ACL, which means the air voids filling function of the smaller particles is more significant in the coarse gradation than in the fine gradation.
i
RCs
P-B
which means slight increase of the balance size. The RC PB values si
-20
-60 -80 -100
the RC PB value corresponding to the particles of 2.36 mm si increases with the gradation tending to coarse from ACU to ACL,
0
-40
when the amount of the added particles is very small. The test errors could compromise the increase of packing volume due to the addition of the smaller particles. Secondly, the small amount addition of the smaller particles may reduce the interlock action between the coarse particles. Hence, the particles can be compacted closer with the same compact energy. The increase of packing volume due to the addition of the smaller particles could also be compromised by this effect.
13.2 9.5 4.75 2.36 1.18 0.6 0.3 0.15 0.075 0
5. Discussions
(b) AC gradations Fig. 8. The difference of and and PleaseCheck
than 2.36 mm. The major function of the particles smaller than 2.36 mm is to fill the air voids of the packed SMA blend. And the particles have a total filling function when the corresponding RC PB decreases to -100%. si It should be noted that several
As can be seen from above analysis, the PCPV, proposed in this paper, provides a new way to capture the composition of aggregate blend. It is morphology and compact energy independent and easy to quantify by any packing test. Furthermore, the indictor of RC PB si is defined on the basis of the PCPV, which can be used to quantitatively characterize the packing function of particles in a packed aggregate blend. The RC PB can be used to discriminate the partisi cles with skeleton building function and those with the air voids value can also filling function. Moreover, the amount of the RC PB si
RC PB si
values for SMA gradations
are less than 100%, which means the corresponding PCPV si values are negative. A negative PCPV si presents a decrease in the packing volume with the addition of the particles of size si. The tests and the data are carefully reviewed to obtain proper explanations for that phenomenon. Firstly, the PCPV si is calculated by PCPV siþ1 sM and PCPV si sM , which are determined by different packing tests. So the value of PCPV si is very sensitive to the packing test errors
be employed to compare the function significance between particles with different size. For the particles with skeleton building means the stronger function. For the parfunction, the bigger RC PB si means the ticles with air voids filling function, the smaller RC PB si stronger function. The method proposed in this paper provides a new analysis framework for quantitatively capturing the packing function of particles in a packed aggregate blend, which is potentially helpful to improve the method of aggregate blend design.
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Y. Miao et al. / Construction and Building Materials 188 (2018) 607–614
6. Conclusions A series of indicators including PCPV, PCBV, and RC PB are si defined for characterizing the packing function of particles in packed aggregate blend. Then the packing strategies are proposed to quantify the indicators using the loose filling test, dry-rodded test and SGC test. Two typical aggregates, crushed stone and gravel, are selected for investigating the proposed method with 3 SMA gradations and 3 AC gradations. Some conclusions can be drawn as following. (1). The PCPV provides a new way to describe the composition of packed aggregate blend. The major function of in in A is to build the skeleton when the corresponding value of PCPV si is bigger than that of PCBV si . Conversely, the major function of Asi in A is to fill the air voids when the corresponding value of PCPV si is smaller than that of PCBV si . (2). The RC PB si , defined on the basis of the PCPV, can be used to quantitatively characterize the packing function of particles means the in a packed aggregate blend. The zero of RC PB si balance of the air voids filling function and skeleton building function. A positive value and a negative value of RC PB si mean major skeleton building function and major air voids presents filling function respectively. The amount of RC PB si the extent of each function. (3). The balance size for the SMA gradation with the NMPS of 16 mm is 2.36 mm. Meanwhile, the balance size for the AC gradation with NMPS of 26.5 mm depends on the specific grain distribution. For the reference upper limit and the designed gradation, the balance size is 2.6 mm. For the reference lower limit, the balance size is bigger than 2.36 mm but smaller than 4.75 mm, which can’t be presented exactly by the sieve size. (4). The PCPV shows compaction energy independent. Therefore, any packing test can be employed to quantify PCPV and RC PB si . However, the Va of packed aggregate blend depends on the compaction energy. So a fixed packing test should be selected to ensure the comparability of the test results of Va. The packing strategy based on the SGC test is recommended, of which the errors due to test operators can be better controlled. (5). The particles’ morphology has no impacts on PCPV and RC PB si but significant impacts on Va. The gravel blends with all the 6 gradations have smaller Va than the corresponding crushed stone blends. 7. Conflict of interest None. References [1] I. Mehmetaj, E. Luga, Optimization of Particle Size Distribution of Concrete Aggregates. International Balkans Conference on Challenges of Civil Engineering, 3-Bccce, 19–21, 2016, Epoka University.
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