Construction and Building Materials 494 (2025) 143552
Contents lists available at ScienceDirect
Construction and Building Materials
journal homepage: www.elsevier.com/locate/conbuildmat
The influence of aggregate gradation on the macro-micro damage evolution
characteristics of concrete after the action of abrasion
Yang Li *, Haisheng Zha , Yanlong Li , Ruijun Wang , Kai Kong
State Key Laboratory of Water Engineering Ecology and Environment in Arid Area, Xi’an University of Technology, Xi’an, Shaanxi 710048, China
A R T I C L E I N F O
A B S T R A C T
Keywords:
Aggregate gradation
Abrasion resistance performance
3D scanning
ITZ thickness
Griffith’s microcrack theory
Concrete structures in engineering applications are subject to erosion damage by high-speed sand-laden water
flow, resulting in surface spalling, microcrack propagation, and mechanical property degradation, which
severely threaten structural durability. However, systematic studies on the influence of aggregate gradation on
the abrasion resistance of concrete under high-speed sand-laden water flow remain limited. In this study, granite
and marble aggregate concretes were selected as research objects, and three aggregate gradations were designed.
Through compressive strength tests, abrasion tests, 3D scanning, microhardness, and scanning electron micro­
scope (SEM) analysis, the influence mechanism of aggregate gradation on the macro- and micro-abrasion
resistance of concrete was investigated. A theoretical relationship between Interface Transition Zone (ITZ)
thickness and macroscopic performance parameters was established. The results indicate that the abrasion
damage gradually extends from the surface erosion zone toward the central mortar erosion zone, and the
aggregate content significantly influences the damage evolution. With the increase of fine aggregate proportion,
the concrete’s mass loss and abrasion depth first decrease and then increase, while the compressive and abrasion
resistance strengths first increase and then decrease. When the fine aggregate proportion is 40 %, the concrete
exhibits optimal performance, with a cumulative 48 h abrasion strength loss of only 14.86–15.10 %, the ITZ
thickness reaching a minimum of 4.90μm to 5.92μm, and the highest corresponding microhardness. The fitting
model established based on Griffith’s microcrack theory further shows that ITZ thickness is significantly and
linearly negatively correlated with macroscopic mechanical parameters, with an average fitting deviation of no
more than 3.04 %, demonstrating high accuracy.
1. Introduction
Large-scale hydroelectric power stations, water conveyance tunnels,
and other hydraulic engineering projects provide security for the
fundamental water resources on which human survival depends [1]. The
safe operation of hydraulic structures is crucial for water storage and
transportation, Hydraulic structures operate in extremely harsh envi­
ronments, leading to significantly shortened service lives [2,3]. Abra­
sion damage is the primary factor causing other issues, with
approximately 70 % of dam spillway structures experiencing varying
degrees of abrasion damage [4]. The abrasion resistance of concrete
mainly depends on aggregate parameters, mix proportion, mechanical
properties, cement type and dosage, fiber content, surface treatment,
and porosity [5–7].
With the large-scale construction of high-head and high-discharge
hydraulic projects, the abrasion problem of conventional concrete
under complex hydraulic conditions has become increasingly promi­
nent. As the primary constituent of concrete, the gradation character­
istics of aggregates directly affect its compactness, ITZ properties, and
overall abrasion resistance [8]. Optimizing aggregate gradation is
therefore a key factor in ensuring the durability and operational safety of
hydraulic structures [9]. Scholars have been devoted to the effects of
aggregate properties on concrete performance [10–12]. The size effect
induced by aggregate gradation is considered one of the key factors
influencing the mechanical properties of concrete. Increasing the
maximum aggregate size can enhance fracture energy under high
loading rates and reduce the sensitivity of splitting tensile strength to
size effects [13,14–16]. Aggregate shape and content significantly affect
impact energy dissipation [17]. Moreover, aggregate types such as
recycled aggregate [18], waste glass aggregate [19,20], and desert sand
* Corresponding author.
E-mail addresses: LY1990120311@163.com (Y. Li), 18691080790@163.com (H. Zha), liyanlong@xaut.edu.cn (Y. Li), wrj7163@xaut.edu.cn (R. Wang),
kk15689757321@163.com (K. Kong).
https://doi.org/10.1016/j.conbuildmat.2025.143552
Received 28 June 2025; Received in revised form 27 August 2025; Accepted 6 September 2025
Available online 9 September 2025
0950-0618/© 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Y. Li et al.
Construction and Building Materials 494 (2025) 143552
[21], along with their pretreatment methods, can alter the phase
composition, degree of carbonation, and porosity at the microscale,
thereby influencing the mechanical and durability properties of con­
crete. Zheng et al. [22] demonstrated that aggregate content, maximum
particle size, and gradation curve significantly affect concrete strength.
Talat et al. [23] further compared the performance of ten aggregate
gradations in porous mixtures, finding that porosity and abrasion loss
were not strongly correlated. In addition, experimental studies
confirmed that the coarse-to-fine aggregate ratio [24] and abrasion
angle [25] are important parameters governing the abrasion resistance
of concrete.
Significant progress has also been made in experimental methods
and theoretical modeling of concrete abrasion damage and ITZ thick­
ness. Tang et al. [26] employed molecular simulations to reveal the
mechanical behavior, microstructure, and erosion resistance mecha­
nisms of recycled aggregate concrete ITZ. Yin et al. [27] clarified the
strength variation mechanisms of ITZ at different spatial positions and
established a strength prediction model based on ITZ pore structure
characteristics, spatial heterogeneity, and water-to-cement ratio pa­
rameters. Advances in microscopic detection technologies have further
facilitated the characterization of the internal structural evolution of
concrete. Techniques such as microhardness testing [28], 3D scanning
[29], digital image analysis [30], and X-ray computed tomography [31]
have been widely applied to quantify ITZ properties, aggregate
morphology, and internal damage. Under harsh service conditions such
as freeze–thaw cycles [32], salt-frost environments [21], and long-term
water flow erosion [33]. Su et al. [34] proposed corresponding char­
acterization methods and performance prediction models, and explored
the influence of strength, aggregate parameters, flow velocity, and
sediment concentration on the abrasion resistance of concrete.
However, systematic studies on the regulation of macroscopic
abrasion resistance and the microstructural ITZ evolution mechanisms
influenced by aggregate gradation are still lacking. In this study, con­
crete prepared with granite and marble aggregates from real engineer­
ing projects was used as the research object, and three aggregate
gradations were designed. Based on high-speed underwater steel ball
abrasion tests and SEM, and supported by Griffith’s microcrack theory,
the abrasion resistance, microhardness, and ITZ thickness of concrete
were systematically analyzed. The quantitative influence mechanism of
aggregate gradation on the macro–micro evolution process during
abrasion was further explored. This study aims to provide a theoretical
foundation for optimizing aggregate gradation of concrete under prac­
tical service conditions, and to offer scientific foundation for enhancing
the durability and service life of hydraulic structures.
2. Materials and methods
2.1. Methodology
This paper studies the abrasion resistance, microhardness and ITZ
thickness of granite and marble concrete under different aggregate
gradations. To better represent the overall steps, a schematic diagram
was drawn, as shown in Fig. 1.
2.2. Materials
The cement used was P.O 42.5 medium heat portland cement, the
main chemical composition and properties of which are listed in Table 1.
The selected class II fly ash’s main chemical composition and properties
are presented in Table 2. Natural river sand with a fineness modulus of
2.75 was used as the fine aggregate, and its principal performance
indices are given in Table 3. Two types of coarse aggregate granite and
marble with particle size ranges of 5–10 mm, 10–20 mm, and 20–30 mm
were employed, and the morphologies of these coarse aggregates are
shown in Fig. 2. The admixtures comprised a DH9 air-entraining agent
and a GK-3000 polycarboxylate high performance superplasticizer. The
mixing water was ordinary tap water.
3D scanning test (every 12h)
Abrasion resistance test
Compressive resistance test
SEM
Aggregate
50mm
ITZ
100m
m
Mortar
Concrete slicing and coring treatment
after abrasion
Microhardness
Fig. 1. Technology roadmap.
2
Test area
(1mm interval)
Y. Li et al.
Construction and Building Materials 494 (2025) 143552
Table 1
Main chemical composition and properties of cement.
Strength class
Main chemical composition (%)
Compressive strength(MPa)
Setting time(min)
CaO
SiO2
P.O 42.5
58.53
24.73
Al2O3
3-d
28-d
Initial set
Final set
4.48
22.8
43.6
205
249
Density
(g⋅cm− 3)
Stability
3.16
Qualified
Table 2
Main chemical composition and performance of fly ash.
Main chemical composition (%)
SiO2
56.6
Fe2O3
Al2O3
CaO
7.6
21.3
4.2
Density
(g⋅cm− 3)
Specific surface area(cm2/g)
Water demand ratio(%)
Fineness (%)
Firing loss (%)
2.1
3400
102
18.0
3.6
50 %, respectively. On this basis, experiments were carried out to
investigate the effects of aggregate gradation on concrete abrasion
resistance, ITZ thickness, and microstructural properties. The coarse
aggregate gradation curves adopted in this study are shown in Fig. 3.
Table 3
Technical performance indices of fine aggregates.
Fineness
modulus
Apparent density
(kg⋅m− 3)
2.75
2540
Packing density
(kg⋅m− 3)
Loose
Tightness
1480
1785
Silt content
(%)
2.4. Test methods
1.3
2.4.1. Compressive strength test
To evaluate the relationship between the abrasion resistance and
mechanical strength of hydraulic concrete, the compressive strength
was tested in accordance with the Chinese standard DL/T 5150–2017
"Technical specification for testing hydraulic concrete" [38]. Before
abrasion, cubic specimens of 100 mm× 100 mm× 100 mm were pre­
pared. Core sampling was carried out using a drilling machine to obtain
cylindrical specimens with dimensions of Φ 50 mm×h100mm. The
Fig. 2. Aggregate morphology.
2.3. Experimental proportion
The gradation of aggregate particle size directly affects the density
and abrasion resistance of concrete. This study uses the improved
gradation model based on Dinger-Funk proposed by Cao [35] and Li
[36] for aggregate configuration. Typically, the maximum particle size
should not exceed 1/4–1/3 of the thickness of the concrete specimen. A
stepwise binary mixing method is employed, starting with small-volume
aggregate with a particle size of 5–10 mm as a variable to maximize the
concrete’s packing density [37]. As shown in Table 4, three continuous
gradation schemes were designed, with mass ratios of 5–10 mm,
10–20 mm, and 20–30 mm aggregates set to 30:40:30, 40:30:30, and
50:30:20, corresponding to small aggregate dosages of 30 %, 40 %, and
Fig. 3. Coarse aggregate gradation.
Table 4
The mix proportion of concrete with different coarse aggregate gradations.
Group
G1
G2
G3
M1
2
M3
Water-binder ratio
0.35
0.35
0.35
0.35
0.35
0.35
Sand ratio
(%)
Fly ash
(%)
Water reducing agent (%)
33
33
33
33
33
33
20
20
20
20
20
20
0.7
0.7
0.7
0.7
0.7
0.7
Air entraining agent
(%)
1 m3concrete material quantity（kg/m3）
Water
Cement
Fly ash
Sand
0.02
0.02
0.02
0.02
0.02
0.02
120
120
120
120
120
120
274
274
274
274
274
274
69
69
69
69
69
69
610
610
610
610
610
610
3
Stone (mm)
5–10
10–20
20–30
371.4
495.2
619
371.4
495.2
619
495.2
371.4
371.4
495.2
371.4
371.4
371.4
371.4
247.6
371.4
371.4
247.6
Y. Li et al.
Construction and Building Materials 494 (2025) 143552
compressive strength test of concrete was conducted using the
WAW-1000 universal testing machine, and the loading rate was set at
0.4 MPa/s.
indentation.
2.4.5. SEM
The JSM-6700 F scanning electron microscope was used to assess the
effect of aggregate gradation on the internal microstructure of concrete
specimens after abrasion, and representative images were selected to
measure the average thickness of the ITZ, with 25 micrographs acquired
for each specimen group. First, aggregate and cement paste samples that
met the test requirements were sectioned from the abrasion damaged
regions of the specimens, and surface dust was removed using com­
pressed gas, the samples were then mounted onto specimen stubs with
double-sided adhesive tape and connected with conductive gold paste to
ensure sufficient electrical conductivity. Next, an ion sputter coater was
used to deposit a thin gold layer on the samples to improve imaging
quality. Finally, the prepared specimens were placed in the SEM
observation chamber for analysis.
2.4.2. Abrasion resistance test
According to the Chinese standard DL/T 5150–2017 "Technical
specification for testing hydraulic concrete" [38], the high-speed un­
derwater steel-ball method was employed to evaluate concrete abrasion
resistance. The abrasion specimens measured Φ300 mm × h100 mm,
and the test apparatus is shown in Fig. 1. Before testing, the cured
specimens were fully immersed in water for over 48 h, their surface
moisture was wiped off, and the initial mass was recorded. During the
test, steel balls were placed on the concrete surface to simulate erosive
particles. A total of 70 balls were used, comprising 10 with a diameter of
25.4 ± 0.1 mm, 35 with a diameter of 19.1 ± 0.1 mm, and 25 with a
diameter of 12.7 ± 0.1 mm. The balls were made of high-hardness
grinding steel with a Rockwell hardness ≥ 60. The apparatus was
operated at a rotational speed of 4000 r/min, with a near-bed flow ve­
locity of approximately 3.8 m/s [39]. The standard test duration was
720 min, with an intermittent operation period of 120 min. After each
720 min test cycle, the specimens were removed to measure the mass
loss. These steps were repeated until the total abrasion time reached
2880 min. The mass loss rate and abrasion resistance strength of the
specimens were calculated using Eq. (1) and Eq. (2), respectively.
△M =
m0 －m1
× 100
m0
3. Test results
3.1. Compressive strength
Fig. 4 shows the compressive strength of concrete before and after
abrasion. This figure clearly indicates that with the increase in the
proportion of small-sized coarse aggregates, the compressive strength of
concrete initially increases and then decreases. Before abrasion, the G2
specimen exhibited the highest compressive strength of 50.27 MPa.
Compared with G2, the compressive strengths of the G1 and G3 speci­
mens decreased by 21.92 % and 13.31 %, respectively. The compressive
strength variation trend of the M1 to M3 specimens is similar to that of
the G1 to G3 specimens. Before abrasion, the M1 group specimens
exhibited the lowest compressive strength of 38.96 MPa. With the in­
crease in the proportion of small-sized coarse aggregates, the compres­
sive strengths of the M2 and M3 specimens increased by 18.45 % and
2.39 %, respectively. After 48 h of abrasion, the G2 and M2 group
specimens still maintained the highest compressive strengths, at
32.32 MPa and 24.33 MPa, respectively. Compared with the values
before abrasion, their compressive strengths decreased by 35.71 % and
47.28 %, respectively, which represented the smallest reduction ratios.
This strength variation is not only related to the content of smallsized aggregates but also closely associated with the aggregate skel­
eton structure formed by different gradations [22]. When the proportion
of small-sized aggregates is too low, it is insufficient to fill the internal
voids of the concrete, resulting in fewer contact points between
(1)
Where △M(%) is the mass loss rate, m0(kg) is the initial mass of the
specimen, m1(kg) is the mass of the specimens after abrasion.
fa =
tA
△m
(2)
Where fa(MPa) is the abrasion resistance strength, A(m2) is the abrasion
area, t(h) is the abrasion time, △m(kg) is the mass loss of the specimen
after t time.
2.4.3. 3D scanning test
3D scanning test is a detection method based on multiple line beam
lasers to obtain 3D point cloud data on the surface of objects, which is
mainly used to collect point cloud data on the surface morphology of
concrete specimens after abrasion [40]. Before scanning, mark points
with diameter of 6 mm and 3 mm were uniformly pasted on the concrete
surface successively. A handheld 3D scanner was used to scan the sur­
face of the specimen through mark point mode, and then the laser face
mode was switched to scan again, and grid analysis was carried out to
output cloud point data and polygonal mesh model.
2.4.4. Microhardness test
An HVS-1000 microhardness tester was used for the tests, and the
results are expressed in Vickers Hardness (HV) [41]. Before testing, a
cutting machine was used to extract specimens along the direction
perpendicular to the abraded surface of the specimens, and measure­
ment points on the cut samples were marked at 1 mm intervals. After
multiple stages of polishing, the samples were placed under the micro­
hardness tester, a load of 4.90 N was applied for a dwell time of 10 s. The
indentations were observed through a 400 × microscope objective, with
the schematic of the test shown in Fig. 1. This test primarily measured
the microhardness of the aggregate, the ITZ, and the mortar regions of
the samples, with the HV values calculated according to Eq. (3).
HV =
F 2Fsin2α
=
d2
S
(3)
Where HV(MPa) is the microhardness value, F(N) is the test load, S
(mm2) is the indentation area, α(◦ ) is the angle between the indenter,
take 136◦ , d(mm) is the arithmetic mean of the diagonal of the
Fig. 4. Compressive strength of concrete before and after abrasion.
4
Y. Li et al.
Construction and Building Materials 494 (2025) 143552
aggregates, reduced plastic viscosity of the mortar, and the formation of
a suspension-dense structure dominated by cement paste. In this case,
loads are more likely to be transferred through the paste and the ITZ,
leading to stress concentration, the development of more microcracks,
and lower strength. Conversely, when the proportion of small-sized
aggregates is too high, the main skeleton effect of the aggregates is
weakened, and the strength relies more on the mortar matrix [42]. The
larger specific surface area produces a thicker ITZ, which ultimately
reduces the load-bearing capacity of the concrete. When the proportion
of small-sized aggregates is 40 %, a denser and more interlocked skel­
eton structure is formed, optimizing the load transfer path and allowing
the coarse aggregate skeleton to bear more pressure, thereby exhibiting
the highest compressive strength [43].
and characterized by localized depressions formed by the abrasion of
edge aggregates. The aggregate exposure region bounded by a yellow
dashed line and representing a transitional state in which the aggregate
surface has undergone slight wear. The core mortar erosion region
bounded by a blue dashed line, which features selective wear of the
cement mortar while the coarse aggregate remains relatively intact and
still fully coated, with no obvious aggregate exposure.
The specimen initial state exhibited a well-leveled surface, with the
cement mortar fully encapsulating the aggregate and no interfacial de­
fects. During the early stage of the abrasion (0–12 h), wear was domi­
nated by the mortar layer. In the mid-stage (12–36 h), it transitioned to a
composite wear phase of the concrete matrix, characterized by an
increased exposure ratio of coarse aggregate and the formation of
abrasion pits at the edge region with a maximum depth of 30.54 mm.
The density of pits in the exposed region decreased, with only localized
aggregate exposure. The central region remained relatively intact,
dominated by slightly protruding aggregates. In the final stage
(36–48 h), degradation of the ITZ caused the abrasion damage to reach
its peak, with a maximum wear depth at the edge region of up to
44.33 cm. These abrasion-damage features are closely related to the
3.2. Apparent damage morphology
Fig. 5 shows the damage evolution behavior of the concrete apparent
morphology during the abrasion process. Under sustained abrasion, the
abrasion surface of the specimen is divided into three typical damage
regions [44]. The surface pitting region bounded by a red dashed line
Fig. 5. The evolution of the apparent morphology of the specimen.
5
Y. Li et al.
Construction and Building Materials 494 (2025) 143552
dynamics of the underwater steel-ball method [45], whereby during the
test, the impeller drives the steel balls at 4000 rpm to generate a cen­
trifugal field, resulting in a significantly higher concentration of steel
balls at the specimen edges than at the center. This spatial distribution
difference leads to an increase in the abrasion energy per unit area at the
outer margin. After 48 h of abrasion, the surface pits on the specimen
exhibited pronounced irregularity and the aggregate exposure area
reached its maximum, indicating that the irregular geometry of the
eroded surface accelerates subsequent abrasion damage.
The possible reason for this phenomenon is that the aggregate
gradation alters the stability of the internal structure and the energy
dissipation characteristics of concrete during abrasion, thereby signifi­
cantly affecting its abrasion resistance [46]. This is manifested in the
irregular destructive patterns of mass loss and surface morphology.
When the proportion of small-sized aggregates is excessively high or
low, the mechanical interlock between coarse aggregates is weakened.
In the relatively weak ITZ and mortar regions on the concrete surface,
the probability of aggregate failure increases, and the stress concentra­
tion at the edges of the exposed pits is intensified, further aggravating
the mass loss of concrete [47]. In contrast, an appropriate increase in the
proportion of fine aggregates can improve overall compactness and
matrix continuity, thereby alleviating local stress concentration and
reducing mass loss.
decreased and then increased. At 0–24 h, the G2 specimen had the
lowest mass loss rate at 4.89 %, while the M2 specimen had the lowest at
6.42 %. After 48 h of abrasion, the cumulative abrasion rates of G2 and
M2 reached 10.59 % and 14.05 %, respectively, which were the lowest
among their respective aggregate groups. The results demonstrated a
clear positive correlation with time. This indicates a nonlinear rela­
tionship between aggregate gradation parameters and abrasion resis­
tance, that is either excessively high or low proportions of small-sized
aggregate reduce the abrasion resistance of concrete.
The fundamental reason for the differences in concrete mass loss
caused by aggregate gradation lies in the effect of gradation variation on
the weak mortar matrix and ITZ at the concrete surface [48]. When the
proportion of small-sized aggregates is either too low or too high, a
thicker ITZ is formed. The spalling of large-sized aggregates is one of the
main causes of mass loss. Under the combined action of high-speed steel
balls and water flow abrasion, the dense ITZ interfaces and mortar
matrix are more prone to synergistic damage, leading to aggregate
displacement or complete detachment. The stress concentration at the
edges of the exposed pits is then intensified, resulting in further dete­
rioration of the concrete. When the proportion of small-sized aggregates
is 40 %, the impact energy of the steel balls is more evenly dispersed,
and the damage mainly manifests as gradual deterioration of the mortar
layer with only a few exposed aggregates (Fig. 5), resulting in lower
mass loss per unit area.
3.3. Abrasion resistance test
3.3.2. Abrasion resistance
Fig. 7 shows the abrasion resistance strength of concrete under
different abrasion times. After 24 h of abrasion, the abrasion resistance
strength of the G2 specimens was 1.97 MPa, and that of the M2 speci­
mens was 1.51 MPa, both being the highest values among their
respective groups. Compared with the values at 12 h of abrasion, the
strength of the two groups decreased by 7.89 % and 7.14 %, respec­
tively. After 48 h of abrasion, the cumulative loss rates of abrasion
resistance strength for G2 and M2, with a 40 % proportion of small-sized
aggregates, were the lowest, at 14.86 % and 15.10 %, respectively.
Compared with G2, the abrasion resistance strength of G1 and G3
decreased by 19.23 % and 15.92 %, respectively, after 48 h. Similarly,
compared with M2, the abrasion resistance strength of M1 and M3
decreased by 11.29 % and 27.78 %, respectively. The abrasion resis­
tance strength of the specimens exhibited a trend of first increasing and
then decreasing with the increasing proportion of small-sized aggre­
gates, which is consistent with the variation pattern of compressive
3.3.1. Mass loss
Fig. 6 shows the mass loss and mass loss rate of concrete under
different abrasion times. The mass of the specimens was measured at
12 h intervals to accurately capture the variation patterns of mass loss
rate over time. As shown in Fig. 6a, the overall mass loss of granite
aggregate concrete is lower than that of marble aggregate concrete.
After 48 h of abrasion, the mass loss of the G2 group was 1.86 kg.
Compared with the G2 group, the mass losses of the G1 and G3 groups
increased by 23.12 % and 16.13 %, respectively. Before abrasion, the
mass of the M2 was 17.44 kg, the cumulative mass loss after abrasion
was 2.45 kg. The M3 specimen exhibited the highest cumulative mass
loss, reaching 3.15 kg. Compared with the M2 group, the cumulative
mass losses of the M1 and M3 specimens increased by 12.24 % and
28.57 %, respectively.
As shown in Fig. 6b, when the proportion of small-sized aggregate
increased from 30 % to 50 %, the mass loss rate of concrete first
20
M3
0
14
G3
G2
G1 Mass loss(kg)
1
2
3
G1
12
10
4
M3
G2
M2
6
4
0
M
1
48
Ab
ras 36
ion
G1
M3
8
2
48
h
G3
G2
M2
G3
36
h
M
1
Mass loss rate(%)
M3
M2
M
1
M2
16
h
12
G3
M
1
G1
G2
24
h
18
(a) Mass loss
tim 24
e (h
)
12
G1
G2
(b) Mass loss rate
Fig. 6. Mass loss and mass loss rate of the specimens after abrasion.
6
G3
M1
M2
M3
Y. Li et al.
Construction and Building Materials 494 (2025) 143552
the proportion of mortar in the concrete matrix, but the limited strength
of the mortar cannot provide sufficient load-bearing capacity. Under
sustained abrasion, both of these conditions accelerate the failure of the
concrete surface and significantly reduce its abrasion resistance strength
[49].
3.3.3. Abrasion depth
Fig. 8 and Fig. 9 shows the 3D topography cloud maps of the concrete
after abrasion, with the color gradient revealing the spatial distribution
characteristics of abrasion damage. The abrasion depth spectrum ranges
from shallow to deep as follows, purple, blue, green, yellow, and red
[50]. To quantitatively investigate the effect of aggregate gradation on
concrete abrasion depth, the point-cloud data acquired after each 12 h
abrasion interval were analyzed to compute the average abrasion depth,
as shown in Fig. 10. Before abrasion, the abrasion depth of the speci­
mens approached 0 mm, indicating that in the absence of external
forces, the concrete surface exhibited no pits and the uniformity and
compactness of the internal structure remained intact. After 24 h of
abrasion, the cloud maps exhibited significant changes in color gradients
(Fig. 8). With the deep purple areas in the central regions of all specimen
groups substantially reduced; multiple blue protrusions indicate that the
mortar layer had been eroded, leading to exposure of coarse aggregates,
and small green regions appeared at the edges. At this time, the G2 group
exhibited the minimum average abrasion depth of 5.97 mm. Compared
with G2, the average abrasion depths of G1 and G3 increased by 10.89 %
and 4.69 %, respectively. The average abrasion depth of marble aggre­
gate concrete was slightly greater than that of granite aggregate con­
crete. The M2 exhibited an abrasion depth of 6.60 mm. Compared with
Fig. 7. Abrasion resistance strength of concrete after different abrasion times.
strength. This phenomenon may originate from the interfacial mecha­
nism of concrete, wherein the bond performance between coarse
aggregate and cement paste is governed by the interfacial yield stress
and the plastic viscosity of the paste. A 30 % incorporation of small-sized
aggregates leads to a heterogeneous aggregate–mortar distribution that
more readily induces a porous structure, forming weak zones with stress
concentration. A 50 % incorporation of small-sized aggregates increases
0
-10
-20
-30
-40
-150
-100
-50
X
0
0
50
50
100
100
150
150
-50
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-150
-50
-100
-150
0
100
150
-100
-50
Y
50
X
100
150
0
-10
-20
-30
-40
-150
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Y
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X
0
0
50
50
100
100
-100
-50
48h
Grinding depth(mm)
X
0
-10
-20
-30
-40
-150
-100
-50
X
0
0
50
50
100
100
150
150
-50
-100
-150
-50
-100
-150
0
0
50
100
150
Grinding depth(mm)
0
-10
-20
-30
-40
-150
150
-50
-100
-150
-50
-100
-150
0
50
100
150
-100
Y
-50
X
50
100
0
-10
-20
-30
-40
-150
150
-100
Y
-50
X
0
0
50
50
100
100
M2
0
-10
-20
-30
-40
-150
-100
Y
50
Y
-50
X
100
Grinding depth(mm)
24h
Grinding depth(mm)
M1
150
0
Grinding depth(mm)
50
Grinding depth(mm)
48h
Grinding depth(mm)
X
0
0
-10
-20
-30
-40
-150
150
0
-10
-20
-30
-40
-150
-100
-50
X
0
0
50
50
100
100
150
150
-50
-100
-150
-50
-100
-150
0
0
50
100
150
0
-10
-20
-30
-40
-150
-100
-50
Y
50
X
100
150
0
-10
-20
-30
-40
-150
-100
Y
Fig. 8. 3D surface morphology cloud map of the specimen after abrasion.
7
150
150
-50
-100
-150
-50
-100
-150
0
0
50
100
150
Y
50
100
150
Y
M3
Grinding depth(mm)
-50
0
-10
-20
-30
-40
-150
G3
Grinding depth(mm)
-100
Grinding depth(mm)
0
-10
-20
-30
-40
-150
G2
Grinding depth(mm)
24h
Grinding depth(mm)
G1
-50
X
0
0
50
50
100
100
150
150
-50
-100
-150
-50
-100
-150
0
0
50
100
150
Y
50
Y
100
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Y. Li et al.
Construction and Building Materials 494 (2025) 143552
G1
G2
Grinding depth(mm)
150
150
100
100
0
-16.50
-16.50 -16.50
-50
-50
-20.63
-20.63 -20.63
-100
-100
-24.75
-24.75 -24.75
-28.88
-28.88 -28.88
-150
-150
150
-150
-150
-24.75
Y
-150
Y
-100
Y
-100
Y
-20.63
-28.88
-150
-100
-50
150
100
100
50
50
0
0
X
50
100
M2
Grinding depth(mm)
150
0
0.000
150150
-100
-100
-150
-150
100100
-11.25
-100
-50
0
X
50
100
150
-50
0
X
0.000
0
50
X
50
100
100
150
150
M3
Grinding
depth(mm)
Grinding
depth(mm)
0.000
0.000
-5.625
-5.625
-5.625
-11.25
-11.25
-11.25
-16.88
-16.88
-16.88
-16.88
-22.50
0 0
-22.50
-22.50
-22.50
-50 -50
-28.13
-28.13
-28.13
-33.75
-33.75
-33.75
-39.38
-39.38
-39.38
-28.13
-33.75
-100-100
-39.38
-150
-100
-50
50 50
Y
Y
Y
-50
-150
-100
Grinding depth(mm)
-5.625
-50
-33.00 -33.00
-33.00
-33.00
X
-12.38 -12.38
0
-50
M1
-12.38
50
-50
150
-8.250 -8.250
50
-16.50
100
-8.250
-12.38
-8.250
0
50
-4.125 -4.125
100
0
0
-4.125
100
50
-50
0.000
0.000
150
50
-100
Grinding depth(mm)
Grinding depth(mm)
0.000
150
-4.125
-150
G3
Grinding depth(mm)
0.000
-150-150
-45.00
-150
-45.00
-45.00
-45.00
-100
-50
0
50
100
150
-150-150 -100-100 -50 -50
0 0
X
50 50 100100 150150
Fig. 9. Cloud map of the abraded surface of the specimen after 48 h of abrasion.
and yellow areas, with very few red areas and smooth color transitions.
After 48 h of abrasion, the average abrasion depths of G2 and M2 were
12.26 mm and 13.98 mm, respectively, both of which are the smallest
within their groups. A 40 % proportion of small-sized aggregates pro­
vides a denser concrete skeleton structure that effectively disperses the
abrasion energy imparted by the steel balls and delays the progression of
abrasion induced damage. Specimens with 30 % and 50 % small-sized
aggregate content exhibited higher initial pit densities, which could
not alleviate stress concentration during abrasion and became the
dominant factor in later-stage abrasion damage. Significantly acceler­
ating the deterioration of the concrete structure and resulting in
increased average abrasion depths. This also validates the influence
pattern of aggregate gradation on the compressive strength and abrasion
resistance strength of the specimens.
3.4. Microscopic test
3.4.1. ITZ thickness
After the specimens were ground for 48 h, the microscopic mor­
phologies of coarse aggregates, ITZ and mortar were observed by SEM at
magnifications ranging from 400 to 2500 times. The obtained image is
binarized to form a darker contrast. ITZ and the matrix are distinguished
according to the microstructure characteristics and contrast differences.
ITZ is manifested as a darker ring-shaped area around the coarse
aggregate. The ITZ thickness of each group of specimens was measured
using image software (Fig. 11). The width of ITZ microcracks may be
affected by the cutting method, resulting in uneven ITZ microcracks.
Therefore, the reliability of the test results was verified by statistical
methods, and the average width (WC), standard deviation (δ), coefficient
of variation (CV), and extreme values (WC, max and WC, min) of the
microcracks were shown in Table 5.
Fig. 10. Average abrasion depth of the specimen after abrasion.
M2, the abrasion depths of M1 and M3 increased by 1.97 % and 4.39 %,
respectively.
After 48 h of abrasion, the growth rate of abrasion depth increased to
0.26–0.43 mm/h. The abrasion damage extended from the peripheral
weak zones further toward the central regions, with most of the blue
areas transitioning to green and the red areas at the edges expanding,
indicating an increase in damage depth. It is worth noting that in Fig. 9,
the G2 and M2 specimens exhibit relatively high proportions of green
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Y. Li et al.
Construction and Building Materials 494 (2025) 143552
Fig. 11. SEM image of the specimen.
9
Y. Li et al.
Construction and Building Materials 494 (2025) 143552
Fig. 11. (continued).
10
Y. Li et al.
Construction and Building Materials 494 (2025) 143552
aggregate concrete. As shown in Fig. 12d-f, at the 1 mm measurement
point, the M2 group exhibited an average ITZ microhardness of
77.4 MPa, and relative to M2, the microhardness values of the M1 and
M3 groups at 1 mm decreased by 9.95 % and 19.38 %, respectively. At
the 14 mm measurement point, the ITZ microhardness values of all
groups approached 97 MPa, with M2 still presenting the highest
microhardness, representing an increase of 26.36 % compared to the
1 mm region. The internal damage depths for the M1, M2, and M3
groups were 8–9 mm, 7–8 mm, and 9–10 mm, respectively. This phe­
nomenon can be explained by the microbleeding effect during specimen
formation, which creates a distribution gradient within the internal
aggregate-cement paste system. When the proportion of small-sized
aggregates is 30 % and 50 %, the workability of the cement paste is
adversely affected. The adsorption of moisture on the aggregate surfaces
creates distinct water-rich layers, leading to pronounced heterogeneity
in the internal concrete structure. The variation in ITZ thickness leads to
differentiated microhardness in concrete under abrasion [53].
Table 5
Statistical parameters of ITZ thickness.
Specimen
WC(μm)
δ(μm)
CV(%)
WC，max(μm)
WC，min(μm)
G1
G2
G3
M1
M2
M3
7.19
4.9
6.69
6.67
5.92
7.79
0.15
0.03
0.06
0.06
0.03
0.11
7.89
5.21
5.93
6.77
6.18
6.04
13.02
6.32
8.33
8.47
7.59
13.69
3.75
2.33
3.29
2.70
1.51
3.74
After 48 h of abrasion, the average ITZ thicknesses of specimens G1G3 were 7.19 μm, 4.90 μm, and 6.69 μm, respectively. Small-sized ag­
gregates exhibit a greater specific surface area and more contact in­
terfaces than large-sized aggregates. Therefore, the bonding strength
between the G2 aggregates and the mortar is relatively stronger,
resulting in a smaller ITZ thickness. Compared with G2, the average ITZ
thicknesses of G1 and G3 increased by 46.73 % and 36.53 %, respec­
tively. Due to differences in the hydrophilicity of aggregate surfaces, the
ITZ of granite aggregate concrete is denser and thinner than that of
marble aggregate concrete. The M2 group exhibited a maximum ITZ
thickness of 7.59 μm and an average thickness of 5.92 μm after 48 h of
abrasion, compared with M2, the average ITZ thicknesses of M1 and M3
increased by 12.67 % and 31.59 %, respectively. This observation is
consistent with the findings of Wang et al. [51], which indicate that an
increase in ITZ thickness leads to a reduction in the abrasion resistance
of concrete. When the bonding strength between the aggregate and the
cement paste is low, under the combined action of water flow and
steel-ball abrasion, the degradation of the ITZ is accelerated. Resulting
in increased aggregate spalling and crack propagation in the concrete,
thereby exacerbating abrasion damage. When the proportion of
small-sized aggregates is 40 %, the concrete exhibits a narrower ITZ
thickness.
3.4.3. Abrasion damage gradient
The parameter Ki is introduced to describe the variation trend of
microhardness when the local area changes from i to i + 1 [54]. The
parameter Ki is the slope of the relationship between microhardness and
the distance of the measurement point when the local area changes from
i to i + 1：
Ki =
HV i+1 − HV i
di
(4)
Where HVi and HVi+1 is the microhardness values in local region i and
region i + 1, di is the distance between local region i and region i + 1.
In Eq. (4), a Ki value greater than 0 indicates that, as the local area
changes from i to i + 1, the microhardness increases, while a Ki value
less than 0 indicates that, as the local area changes from i to i + 1, the
microhardness decreases. When Ki > 0, it signifies that concrete abra­
sion damage exhibits a spatial gradient distribution characteristic, with
larger Ki values indicating more pronounced gradient features. Fig. 13
shows The damage gradient of concrete after abrasion. Specimens near
the surface damage region exhibit more prominent spatial damage
gradients. In concretes with the same aggregate type, within region 1 the
G2 and M2 groups exhibit the lowest K1 values of 5.05 N⋅mm− 1 and
4.63 N⋅mm− 1, respectively, indicating the smallest spatial damage
gradient and a stronger ability to maintain structural integrity under
continuous abrasion. As shown in Fig. 13a, the Ki value of G2 in regions
2–7 gradually decreases from 3.98 N⋅mm− 1 to 2.30 N⋅mm− 1 and stabi­
lizes in regions 8–12, demonstrating that after 48 h of abrasion, G2 re­
tains good integrity and compactness. As shown in Fig. 13b, the Ki value
of M2 in regions 2–10 gradually decreases from 4.00 N⋅mm− 1 to
0.80 N⋅mm− 1 and approaches 0 in regions 11–12, validating previous
experimental findings. In addition, due to the higher microhardness and
greater hydrophilicity of granite aggregate concrete, it exhibits superior
abrasion resistance performance and smaller damage gradients.
3.4.2. Microhardness
Fig. 12 shows the microhardness distribution of aggregates, ITZ, and
mortar at varying depths after 48 h abrasion. Microhardness testing
commenced from coarse aggregates 1 mm beneath the abraded surface,
with statistically averaged hardness values calculated for each depth.
The ITZ manifests as a microcrack-prone weak region characterized by
sparse clinker particles, abundant microdefects, and oriented enrich­
ment of plate-like calcium hydroxide crystals. Its thickness was deter­
mined by identifying abrupt transition zones in the hardness profile
[52].
As shown in Fig. 12a-c, as the measurement points gradually move
away from the coarse aggregate, the microhardness in all regions of
granite aggregate concrete exhibits a trend of initially increasing and
then gradually stabilizing. The microhardness of the ITZ fluctuates
regularly with measurement point depth, indicating that it is more
susceptible to structural damage under abrasion. At the 1 mm mea­
surement point, the average microhardness of the ITZ in the G2 group is
84.4 MPa, compared with G2, the microhardness at 1 mm in the G1 and
G3 groups decreases by 11.02 % and 3.55 %, respectively. At the 14 mm
measurement point, the microhardness values of the ITZ for all groups
are close to 106 MPa, with G2 still having the highest microhardness,
which is 25.95 % higher than that at the 1 mm region. The microhard­
ness of the ITZ gradually increases within the range of 1–6 mm, while no
significant differences are observed in the range of 7–14 mm, indicating
that under abrasion, internal damage in the concrete has a certain
threshold. When the microhardness of the ITZ stabilizes in a specific
region, it can be considered that the specimen is undamaged. The in­
ternal damage depths for G1-G3 are 8–9 mm, 6–7 mm, and 8–9 mm,
respectively.
The distribution pattern of the ITZ microhardness in marble aggre­
gate concrete is similar to that in granite aggregate concrete, but the
microhardness values are generally lower than those of granite
4. Discussions
4.1. The thickness of ITZ estimated by Griffith’s microcrack theory
Griffith’s microcrack theory holds that there are many small cracks
or defects in actual materials, and material failure begins with the
largest crack [55]. Based on the ITZ thickness data measured by SEM,
when the concrete is subjected to abrasion, the relatively weak ITZ first
generates stress concentration under the action of external force, local
cracks begin to expand, and gradually extend to the concrete matrix
until they penetrate. Since the composition of the base concrete and the
water-cement ratio remain unchanged, it can be considered that γ re­
mains constant. However, the change in the gradation of coarse aggre­
gates will cause changes in the ITZ thickness, ultimately leading to
11
Y. Li et al.
Construction and Building Materials 494 (2025) 143552
Fig. 12. The microhardness of the specimens after 48 h of abrasion.
12
Construction and Building Materials 494 (2025) 143552
Y. Li et al.
Fig. 13. Abrasion damage gradient of concrete after abrasion.
alterations in the compressive strength and elastic modulus of the con­
crete. As shown in Eq. (5), the thickness of ITZ (C) is negatively corre­
lated with the compressive strength (σ ), and positively correlated with
the elastic modulus (E) and the fracture surface energy (γ).
C=
2Eγ
are slightly larger than those for marble aggregate concrete. However,
the overall error ranges of all groups remain relatively small.
4.2. The relationship between ITZ thickness and compressive strength
(5)
π(σ )2
The simple linear regression model between ITZ thickness and
compressive strength is expressed as Eq. (6), where Y represents the
compressive strength and X represents the ITZ thickness. As shown in
the fitting results (Fig. 15), the trend of ITZ thickness is inversely pro­
portional to the trend of compressive strength, indicating a strong linear
correlation for both. When granite is used as aggregate, the ITZ thickness
increases from 5.00 μm to 7.00 μm, while the compressive strength
decreases from 32.09 MPa to 22.54 MPa. When marble is used as
aggregate, the ITZ thickness increases from 6 μm to 8 μm, and the
compressive strength decreases from 23.44 MPa to 18.13 MPa. This
trend is consistent with the actual measured values of compressive
strength, where the increase in ITZ thickness weakens the bond between
coarse aggregate and cement matrix, affects the structural integrity, and
ultimately leads to a reduction in overall strength [56]. Therefore,
optimizing the ITZ microstructure through aggregate gradation can
effectively improve the compressive strength of concrete.
where σ (MPa) is the compressive strength of concrete, E(GPa) is the
elastic modulus, γ(J/m²) is the surface energy of the crack per unit area,
C(μm) is the ITZ thickness.
The measured values of ITZ thickness, compressive strength of
specimens and elastic modulus were substituted into Eq. (5) to obtain
the fracture surface energy of granite and marble aggregate concrete of
different gradations respectively. The relevant parameters are shown in
Table 6. The fracture surface energies of granite aggregate and marble
aggregate concretes are 4.15 J/m² and 3.63 J/m², respectively. Based on
the previously obtained relevant parameters and Eq. (5), the calculated
ITZ thickness values for each group of specimens are shown in Table 7. It
can be seen that as the proportion of small-sized aggregates increases
from 30 % to 50 %, the ITZ thickness exhibits a trend of first decreasing
and then increasing. At a 40 % incorporation of small-sized aggregates,
both the ITZ thickness and the macroscopic performance of the concrete
are optimal. Fig. 14 shows the linear fitting relationship between the
calculated and measured ITZ thickness values. When the coarse aggre­
gate is granite, the average deviation between the measured and
calculated ITZ thickness values is 3.04 %, with the largest deviation of
6.13 % occurring in G3 and the smallest deviation of 0.56 % in G1.
When the coarse aggregate is marble, the average deviation between the
measured and calculated ITZ thickness values is 1.18 %, with the
maximum deviation of 2.40 % in M1 and the minimum deviation of
0.51 % in M2. The calculation deviations for granite aggregate concrete
Y = AX + B
4.3. The relationship between ITZ thickness and elastic modulus
Fig. 16 shows the relationship between ITZ thickness and elastic
modulus of concrete. When the ITZ thickness is minimal, the elastic
modulus of the concrete is maximal, and the elastic modulus decreases
as the ITZ thickness increases. For granite aggregate concrete, as the ITZ
thickness increases from 5.00 μm to 7.00 μm, the elastic modulus of the
concrete decreases from 19.44 GPa to 13.08 GPa, representing a
reduction rate of approximately 3.18 GPa/μm. For marble aggregate
concrete, as the ITZ thickness increases from 6 μm to 8 μm, the elastic
modulus decreases from 14.37 GPa to 11.14 GPa, with a reduction rate
of approximately 1.62 GPa/μm. These calculated results are consistent
with the findings reported in the literature [57]. A decrease in ITZ
thickness implies an increased contact area between aggregate and
cement matrix, thereby enhancing the bond strength at the aggregate
and matrix interface. This improved bond strength more effectively
Table 6
Basic parameters of concrete after 48 h of abrasion.
Aggregate
type
Group
Compressive
strength
(MPa)
Elastic
modulus
(GPa)
Average
thickness
of ITZ(μm)
γ(J⋅m− 2)
Granite
Marble
G1~G3
M1~M3
24.67
20.46
14.79
12.29
6.26
6.79
4.15
3.63
(6)
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Construction and Building Materials 494 (2025) 143552
Table 7
Calculated ITZ thickness of concrete after 48 h of abrasion.
Aggregate type
Granite
Marble
Group
G1
G2
G3
M1
M2
M3
γ(J⋅m− 2)
4.15
3.63
Compressive strength (MPa)
20.94
32.32
21.74
19.6
24.33
17.46
Elastic modulus (GPa)
11.85
19.84
12.69
11.34
15.21
10.33
Average thickness of ITZ (μm)
Calculated value
Measured
value
7.15
5.02
7.10
6.83
5.95
7.84
7.19
4.9
6.69
6.67
5.92
7.79
transfers stress under sustained loading, reduces stress concentration,
and consequently increases the overall elastic modulus of the concrete.
4.4. The relationship between ITZ thickness and abrasion resistance
strength
Fig. 17 shows the relationship between ITZ thickness and abrasion
resistance strength of concrete. As shown in Fig. 17, there exists a sig­
nificant relationship between the ITZ thickness and the abrasion resis­
tance strength of concrete. The fitting results demonstrate that the
abrasion resistance strength of concrete is maximal when ITZ thickness
is minimal, and the abrasion resistance strength decreases with
increasing ITZ thickness. For granite aggregate concrete, when the ITZ
thickness increases from 5.00 μm to 7.00 μm, the abrasion resistance
strength decreases by 13.33 %. For marble aggregate concrete, when the
ITZ thickness increases from 6.00 μm to 8.00 μm, the abrasion resistance
strength decreases by 19.12 %. These fitting results are consistent with
the findings in the literature, At 40 % proportion of small-sized aggre­
gates, the abrasion-resistance strength of concrete is significantly
enhanced and the ITZ thickness is reduced. An increase in ITZ thickness
implies the potential inclusion of more pores and microcracks, which
weakens the bond between the mortar and the aggregate. When abra­
sion loads act on the concrete surface, they can weaken the local loadbearing capacity of the concrete matrix, leading to an increase in
microcrack number and their rapid propagation inward, thereby accel­
erating the abrasion damage of the concrete [58].
Fig. 14. Relation between calculated and measured ITZ thickness values.
Fig. 15. Relation between ITZ thickness and compressive strength.
14
Y. Li et al.
Construction and Building Materials 494 (2025) 143552
Fig. 16. Relation between ITZ thickness and elastic modulus.
Fig. 17. Relation between ITZ thickness and abrasion resistance strength.
5. Conclusions
(2) Under high-speed underwater abrasion, the abrasion damage of
concrete exhibits a multi-stage evolution, expanding from the peripheral
erosion zones toward the central mortar erosion zones. Concrete with
40 % small-sized aggregates demonstrated the most uniform damage
distribution, the lowest cumulative mass loss, and the slowest rate of
damage depth propagation, with a minimum expansion rate of
0.26 mm/h.
(3) Variations in small-sized aggregate content significantly influ­
ence the ITZ by altering the compactness of the aggregate skeleton and
interfacial properties. As the proportion of small-sized aggregates
increased, ITZ thickness showed a trend of initially decreasing and then
increasing, while microhardness exhibited the opposite trend of initially
increasing and then decreasing. Concrete under abrasion exhibited
distinct spatial damage gradients and an internal damage depth
threshold.
This study systematically analyzed the macro-micro performance
evolution of granite and marble aggregate concrete under high-speed
water flow abrasion by setting three coarse aggregate gradations, and
further revealed the intrinsic relationship between ITZ thickness and
concrete abrasion damage based on Griffith’s microcrack theory. The
main conclusions are as follows:
(1) The content of small-sized aggregates is a key factor affecting the
compressive strength and abrasion resistance of concrete. A small-sized
aggregate proportion of 40 % was found to be optimal, corresponding to
concrete with the highest compressive strength and the best abrasion
resistance. Due to the higher intrinsic strength of granite aggregates,
specimens generally exhibited superior overall performance compared
to marble aggregate concrete.
15
Y. Li et al.
Construction and Building Materials 494 (2025) 143552
(4) The ITZ thickness in concrete after abrasion is significantly and
linearly negatively correlated with elastic modulus, compressive
strength, and abrasion resistance. The model showed high predictive
accuracy, with an average error ranging from 1.18 % to 3.04 %, theo­
retically confirming that microscopic ITZ degradation is one of the
fundamental causes of the decline in macroscopic mechanical perfor­
mance and reduced abrasion resistance.
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CRediT authorship contribution statement
Ruijun Wang: Validation, Investigation, Data curation. Yanlong Li:
Project administration, Investigation, Data curation. Kai Kong: Vali­
dation, Formal analysis. Haisheng Zha: Writing – original draft,
Investigation, Formal analysis, Data curation. Yang Li: Writing – review
& editing, Methodology, Funding acquisition, Conceptualization.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Acknowledgments
This study was financially supported by the Joint Funds of the Na­
tional Natural Science Foundation of China (Program No. U23A20673),
the National Natural Science Foundation of China (Program No.
52479134), the Local Service Special Program of Shaanxi Provincial
Department of Education (Program No. 24JE018), the Key Research and
Development Program of Shaanxi Province (Program No. 2025SFYBXM-538).
Data availability
Data will be made available on request.
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