The Bearing and Breakage Characteristics of Crushed Stone Aggregates in the Bedding Course of Permeable Roads

*e current study of permeable roads helps address urban flooding in Chinese cities caused by frequent heavy rainfall and build smart cities with sponge-like functionality. Crushed stone is widely used in constructing the bedding course of permeable roads because it has good water permeability. Experiments on the compaction of crushed stone were carried out by considering the impact of particle size and gradation to examine the strength and particle breakage characteristics of crushed stone and evaluate its use as the aggregate in the bedding course of permeable roads. *e compaction process can be divided into two stages, i.e., the preliminary compaction stage and the particle crushing and intensive compaction stage. *e latter consists of an alternating cycle of compacting and crushing. *e particle size distribution after crushing can be described analogously to the Talbot continuous gradation equation. Single particle size samples are subject to earlier and stronger particle breakage than the mixed particle size sample, which are affected by both compaction level and loading speed.*is study has important application value, and it provides experimental support for the study of materials for urban permeable roads.


Introduction
e National Meteorological Center of China Meteorological Administration issued multiple rainstorm yellow alerts since July 2020, and flooding has ravaged the streets of many Chinese cities (Figure 1). ere is a rising demand for sponge-like smart cities [1][2][3], the construction of which requires permeable roads as their underpinning. In fact, permeable roads are massively built throughout the world since the 1980s to prevent urban flooding.
German started the research and development of permeable roads since 1980 and intends to convert >95% of its roads to permeable roads in the early 21st century. e Kinki area of Japan began to install permeable pavements in 1993, and presently in Japan, permeable pavements are widely used in major and minor roads, branch roads, express roads, pedestrian streets, and outdoor spaces (e.g., plazas and parks). China introduced the concept of permeable road in the 1990s and gradually began its application in major cities since 2000. e "Engineering Technical Code for Rain Utilization in Building and Sub-District"( GB50400-2006) issued in 2007 gave regulations on the design, construction, and management of permeable roads [4].
Meng et al. [5] conducted a field survey on the permeability of permeable roads in Shanghai to summarize their application and analyze the factors affecting the actual permeability. Liu [6] studied permeable roads with regard to structural type, road performance, etc. Lu et al. [7,8] devised a permeameter to investigate the flow characteristics of permeable pavement mixtures under different hydraulic gradient. e results show that Darcy's law is not applicable to analyzing the directional water transport of permeable pavement materials. Instead, the Reynolds number of permeable pavement materials increases with rising hydraulic gradient, and the water flows in permeable pavement materials transition from Darcy flow to non-Darcy flow. Wang [9] summarized the advantages of permeable concrete pavement and analyzed the factors affecting its mechanical strength, e.g., aggregate particle size, water-binder ratio, silica fume, adhesive layer strength, and method of the forming process. Borgwardt et al. [10,11] studied the longterm permeability of permeable concrete and brick pavements on-site. ey found that permeability depends on the joint material, and permeability is noticeably better when larger aggregates are used. ese prior works demonstrate that the permeability of roads relies heavily on the particle size and gradation of the aggregates. Nevertheless, it must be noted that aggregates can be crushed when they are subject to pressure. Few studies investigated the road bearing ability affected by the crushing of aggregates.
Crushed stone is widely used in constructing the bedding course of permeable roads because it has good water permeability, allows smooth transition of diffusive stress and load, and is readily available and can be obtained locally. is work studied the compaction performance and particle breakage characteristics of crushed stone as the aggregate of permeable roads and analyzed how they are influenced by particle size, gradation, etc. is study can provide experimental support for the study of materials for urban permeable roads, help address urban flooding in Chinese cities caused by frequent heavy rainfall, and can help build smart cities with sponge-like functionality.

Equipment.
e compaction test system of crushed stone aggregate ( Figure 2) includes a home-made compaction device, a loading system, and a data acquisition system. e compaction device is composed of a hollow piston, a cylinder tube, a bottom plate, and other components. e cylinder is 400 mm in height and has an inner and outer diameter of 160 and 180 mm, respectively. e hollow piston is 250 mm in height. e loading system is a WDW-100D universal electronic testing machine produced by the Jinan Huaxin Yuanda Test Equipment Co., Ltd., which has a maximum testing force of 100 kN with a control accuracy of 1% for testing force, displacement, and speed. During the test, the compaction device was placed in the lower chamber of the WDW-100D testing machine, and the load was applied as the indenter on the testing machine which pressed the hollow piston cover.

Sample Preparation.
Test samples were prepared with broken mudstone particles of different sizes. According to the ASTM test standard [12], the maximum particle size in the compaction cylinder must not be greater than 1/3 of the inner diameter of the cylinder. e current test used a sorting sieve to allocate the stone particles into the following groups: 10-15 mm, 15-20 mm, 20-25 mm, and 25-30 mm ( Figure 3).
Single-size particle samples and the mixed-size particle sample were both compacted in this experiment to study the effect of particle size and gradation on the results. Single-size particle samples were prepared from the 15-20 mm, 20-25 mm, and 25-30 mm particle groups. Mixed-size particle sample was prepared from a 1 : 1 : 1 : 1 mixture of 10-15 mm, 15-20 mm, 20-25 mm, and 25-30 mm particles. For all test schemes, stone particles with a total mass of 2000 g were charged into the compaction device. Table 1 shows the mass of particles with different sizes in each test scheme.
In order to study the influence of compaction level and loading speed on the test results, in this work, the compaction level was tested at 10 mm, 20 mm, 30 mm, and 40 mm and the loading speed was tested at 1 mm/min, 2 mm/min, 4 mm/min, and 6 mm/min. All tests were performed in triplicate, and the average value was taken as the result to ensure the accuracy of the test results. Figure 4 shows the test process. e stone particles were thoroughly mixed and then charged into the compaction cylinder, after which the sample was gently compressed and the sample height was measured. e hollow piston and piston cap were then installed. e compaction device was placed in the lower chamber of the WDW-100D testing machine, and an initial load of 0.02 kN was applied. e reading of the scale paper was then recorded, and the sample height was calculated. Afterward, the compaction level was attained at the set loading speed. e crushed particles were then discharged and sorted into groups with a size of 0-2 mm, 2-5 mm, 5-10 mm, 10-15 mm, 15-2 0 mm, 20-25 mm, and 25-30 mm, respectively.

Results
Because various factors (particle size, gradation, and compaction level, etc.) were considered in the test, the following demonstrates the test result with 40 mm compaction and 2 mm/min loading speed as an example to illustrate the strength characteristics, particle breakage characteristics, and particle size changes.    e second stage corresponds to particle crushing and compaction, and the curves clearly differentiated as the particle size of the samples varied. Cycles alternating between compacting and crushing were clearly visible. e time in the second stage varied for samples with different particle sizes. In addition, particle size also affected the loading force. When the compaction level was 40 mm, the 15-20 mm particles required the largest force (58.48 kN), whereas the 20-25 mm particles required the smallest force (44.48 kN). However, the direct correlation between loading force and particle size was not verified in this study.

Strength Characteristics.
By comparison, the mixed size particle sample had the worst strength in the first stage of compaction and demonstrated higher strength than the 20-25 mm particles only at the end of the compaction test, but its strength was always lower than the other two samples.  the particle size of the sample. e 20-25 mm particles had a relatively low stress of 5.13 MPa, but the 15-20 mm particles had a higher stress of 6.75 MPa. In addition, larger particle sizes generally corresponded to earlier initiation of cracking. e stress-strain curves of single particle size samples were almost parallel, which indicated minimal difference in elastic modulus. e mixed-size particle sample had a maximum stress of 5.74 Mpa, and its stress-strain curve largely overlapped to that of the 20-25 mm particles. Its initiation of cracking was slightly later compared with the 20-25 mm particle sample.
It can be seen from Figures 5(a) and 5(b) that fluctuation in both force and stress was the largest for 25-30 mm particles. It can be inferred that the larger particle size gives rise to greater particle crushing during compaction.

Particle Size Distribution after Compaction.
e stability of the sample after compaction and crushing depends on the particle size distribution [13,14]. Figure 6 shows the redistribution of particle size after the sample was loaded and crushed. It can be seen from the figure that for all samples, the structure after crushing still mainly consisted of the original large particles, and the total amount of secondary particles generated after loading accounted for less than 50%. e generated secondary particles did not impair but in fact enhanced the stability of the structure because smaller particles gradually filled the pores in the sample. Figure 6 shows that the particle size distribution after crushing can be expressed analogously to the Talbot continuous gradation equation [15] as a power function of the particle size ratio (d/d max ). Table 2 shows that after compaction, the continuous gradation sample has a larger coefficient of the particle size distribution function than the discontinuous gradation sample and the single particle size sample. In addition, for the single particle size sample after compaction, the coefficient of the particle size distribution function decreases with rising particle size.
As shown in Table 2, the particle size distribution of the sample after crushing can be expressed as where coefficient a and the power exponent b are both related to the particle breakage characteristics of the particles. erefore, the redistribution of particle size may be predicted based on the particle breakage characteristics of the sample.

Characteristics and Calculation of Particle Breakage.
Before compaction, particles are arranged in a disorderly manner with poor contact that is mainly point-to-point and point-to-surface [16][17][18]. e structure is constructed by large particles and relatively loose, with relatively large internal pores. As the axial stress increases, the pores are compressed or filled with small particles. Particle breakage becomes obvious, and some large particles are fragmented to produce secondary smaller particles, as seen in Figure 7. e changes in particle size distribution give rise to the relative displacement between particles as well as their rearrangement. Particles gradually enter stable surface-to-surface contact and meta-stable contact. It could be seen that the particle breakage characteristics and the change of particle size strongly affect the stability of the sample structure.
Quantitative indicators are needed to measure and analyze particle breakage [19][20][21][22][23][24]. Because it is difficult to test gradation during compaction, the current experiment only measured particle breakage after compaction was finished. Confining pressure and other factors in the compaction process were not considered. Particle breakage is thus quantified by B g according to Marsal as follows [19]: where ∆W k is the difference in the content between particles of a certain size before and after compaction and B g is the degree of particle breakage, calculated as the sum of particle content increment and expressed as a percentage.

e Influence of Particle Size and Gradation on Particle
Breakage. As the particle size and gradation vary, particles are arranged very differently after the samples are charged in the test instrument, and the contact between particles also differs. As a result, particles are crushed in different ways during compaction. Hence, particle size and gradation both affect particle breakage [25]. Table 3 shows the difference in particle size content as well as the particle breakage for samples compacted to 40 mm at a loading speed of 2 mm/min. e particle breakage is above 43% for all single-size particle samples and about 20% for the mixed-size particle sample. at is, singlesize particle samples are more severely crushed than the mixed-size particle sample. In single-size particle samples, particles are in rigid contact and more likely crushed after compaction. In contrast, small particles fill the pores between large particles to form semirigid contact in the mixed particle size sample. Particle breakage is thus less during compaction, and the sample has higher structural stability. It has been stipulated for the bedding course of roads that particle breakage must not be greater than 26% when the maximum particle size is less than 60 mm [26]. erefore, in paving the bedding course, the crushed stone in the aggregate should not adopt a single particle size but use a mixed particle size.

e Effect of Compaction Level on Particle Breakage.
Aside from particle size and gradation, the compaction level after loading also affects the particle breakage of samples. Samples were compacted to 10, 20, 30, and 40 mm and then sieved to determine the particle breakage. Table 4 lists the change in particle size content before and after compaction to different levels. Figure 8 shows the relationship between particle breakage and compaction level for different samples. It can Advances in Civil Engineering 5 be seen from Figure 8(a) that particle breakage increased with a rising compaction level for both single particle size samples and the mixed particle size sample. e slopes of the curves at different loading stages vary slightly. e compaction can be divided into four stages each with a 10 mm increment. In the first stage, the mixed particle size sample only had a low breakage of 3%, the 15-20 mm particles had a breakage of 9%, and the 20-25 mm and 25-30 mm particles had the highest breakage of 11%. In the second stage, the 20-25 mm particles had a breakage of 18%, much higher than that of the 15-20 mm particles (9%), 25-30 mm particles (6%), and the mixed particles (4.5%). In the third stage,

Conclusions
e current study on permeable roads helps build smart cities with sponge-like functionality to address urban flooding in Chinese cities caused by frequent heavy rainfall. Experiments on the compaction of crushed stone were   Advances in Civil Engineering carried out by considering the impact of particle size and gradation to examine the strength and particle breakage characteristics of crushed stone and evaluate its use as the aggregate in the bedding course of permeable roads. e following can be concluded: (1) e force-time curve can be divided into two stages, i.e., the preliminary compaction stage and the particle crushing and intensive compaction stage. e latter consists of an alternating cycle of compacting and crushing. (2) e mixed particle size sample has no advantage compared with the single particle size samples with regard to strength because its initiation of particle cracking is much later during the compaction process. (3) e particle size distribution after crushing can be described analogously to the Talbot continuous gradation equation. e coefficient and the power exponent are related to the particle breakage characteristics of the sample. (4) Particle crushing commonly falls into four categories: complete crushing, complete rupture, partial damage, and surface grinding.
(5) Single particle size samples are subject to stronger particle breakage than the mixed particle size sample, and both the compaction level and the loading speed affect particle breakage. In view of appropriate regulations of the bedding course, the crushed stone aggregate for permeable roads should consist of particles of mixed size.

Data Availability
e data used to support the findings of this study are available from the author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.