Compressive stress-strain relationship of limestone calcined clay cement-based UHPC matrix

Full text

Compressive stress-strain relationship of limestone calcined clay
cement-based UHPC matrix
Kunjie Fan
a,*
, Peng Du
b
, Yao Yao
a,c,**
a
School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710072, China
b
School of Science, Xi’an University of Architecture and Technology, Xi’an 710055, China
c
School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China
ARTICLE INFO
Keywords:
Limestone calcined clay cement (LC
3
)
Ultra-high performance concrete (UHPC)
Limestone powder
Calcined clay
Compressive stress-strain relationship
ABSTRACT
Limestone calcined clay cement-based ultra-high performance concrete (LC
3
-UHPC) was found to
possess excellent eco-efciency and mechanical properties. However, the effect of the substitution
rate and the calcined clay to limestone powder ratio on the compressive stress-strain relationship
of LC
3
-UHPC matrix remains unclear. This study tested the uniaxial compressive stress-strain
relationships of LC
3
-UHPC matrix with different mix proportions. DTG, SEM-EDS, and MIP
have been performed to investigate the hydration process and microstructures. The results show
that LC
3
-UHPC matrix achieves optimal mechanical performance with a 1:2 calcined clay to
limestone powder ratio and a 30 % substitution rate of limestone calcined clay (LC
2
) for cement in
this study, while the typical calcined clay to limestone powder ratio for LC
3
-based normal con-
crete is 2:1. With the optimal mix, the 28-day compressive strength of 104 MPa can be achieved
without employing any special curing, silica fume or bers. Furthermore, adding an appropriate
amount of LC
2
(no more than 30 %) to UHPC matrix is found to reduce the nonlinearity of
compressive stress-strain relationships, thereby minimizing the plastic deformation of LC
3
-UHPC
matrix. At last, the uniaxial compressive constitutive model proposed by Popovics is used to
formulate the compressive stress-strain relationships of LC
3
-UHPC matrix. It should be noted that
the compressive stress-strain relationship of LC
3
-UHPC matrix is inuenced by many factors, such
as the chemical composition of raw materials, particle packing density, and the presence of silica
fume. Therefore, the optimal mix proportion obtained in this study is not applicable to all sce-
narios. Nonetheless, this study can provide a reference for the mix proportion design and me-
chanical performance analysis of LC
3
-UHPC.
1. Introduction
As the demand for sustainable and resilient infrastructure grows, the superior properties of ultra-high performance concrete
(UHPC), such as its high compressive strength (≥120 MPa under 28-day standard curing), exceptional durability, and reduced
maintenance requirements, position it as a key trend in the future of the construction industry[1–4]. However, the cement con-
sumption in UHPC is three to four times that of normal concrete, leading to a signicant increase in CO
2
emissions. Therefore, it is
* Corresponding author.
** Corresponding author at: School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710072,
China.
E-mail addresses: kunjie.fan@nwpu.edu.cn (K. Fan), yaoy@xauat.edu.cn (Y. Yao).
Contents lists available at ScienceDirect
Case Studies in Construction Materials
journal homepage: www.elsevier.com/locate/cscm
https://doi.org/10.1016/j.cscm.2025.e04274
Received 6 November 2024; Received in revised form 30 December 2024; Accepted 16 January 2025
Case Studies in Construction Materials 22 (2025) e04274
Available online 17 January 2025
2214-5095/© 2025 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license
( http://creativecommons.org/licenses/by/4.0/ ).

necessary to develop more sustainable alternatives to ordinary Portland cement, to mitigate UHPC’s ecological footprint[5,6].
Limestone calcined clay cement (LC
3
) has emerged as one of the most viable substitutes[7].
LC
3
is a recently developed ternary blended cement in which the mass ratio of calcined clay to limestone powder is usually
optimized at 2:1, and a proper amount of gypsum is added to balance the sulfate[8–10]. In LC
3
, the calcined clay serves as a pozzolanic
material, undergoing reactions with portlandite (CH), water, and sulfate to form calcium aluminium silicate hydrates (C-A-S-H),
ettringite (AFt), and monosulfate (AFm) phases[11]. Adding limestone powder to cement results in a reaction between calcite and
tricalcium aluminate (C
3
A) from the clinker, as well as with the aluminate phase in calcined clay, leading to the formation of
hemi-carboaluminate (Hc) and mono-carboaluminate (Mc) phases[12]. Studies on LC
3
-based concrete have shown that it possesses
mechanical properties comparable to or even better than those of ordinary Portland cement - based concrete[13–15]. Considering
limestone and clay are abundant and widely available with substantial reserves across the globe[16], therefore, using limestone
calcined clay (LC
2
) to replace a portion of the cement in UHPC is a potential solution to enhance the cost-effectiveness and envi-
ronmental sustainability of UHPC.
Currently, there have been some scholars prepared and characterized of limestone calcined clay cement-based ultra-high perfor-
mance concrete (LC
3
-UHPC). Sun et al.[17] found that when the added amount of LC
2
reaches 56.8 % of the cementitious materials, the
corrosion resistance properties of LC
3
-UHPC are optimized, and the addition of LC
2
can decrease the environmental impact by 37.1 %
compared to normal UHPC. The results of Dong et al.[18] show that when the substitution level is lower than 40 %, the mechanical
properties at 28 days are still comparable to or even higher than the reference sample. Liu et al.[19] investigated LC
3
-UHPC with high
cement substitution rate and the optimized mix proportion achieves the maximum compressive strength under steam curing, about
146.05 MPa, when the substitution rate is about 55 %. Based on the results of the above studies, it can be concluded that LC
3
-UHPC not
only demonstrates its environmental advantages but also exhibits uncompromised performance.
Although LC
3
-UHPC shows great potential for application, there are still some issues that need to be addressed before it can be
widely adopted in practical engineering. First of all, the effect of the substitution rate and the ratio between calcined clay and limestone
powder in LC
2
, on the uniaxial compressive stress-strain relationship of LC
3
-UHPC remains unclear. The compressive stress-strain
relationship of concrete is fundamental for structural design and analysis. It provides a mathematical description of concrete
behavior under different stress levels, enabling the prediction and simulation of structural responses under load. Another issue is the
application of silica fume in LC
3
-UHPC. Due to the microlling and nucleation effects, silica fume appears to be an essential ingredient
in most research on LC
3
-UHPC[17–21]. However, as an industrial by-product, silica fume has issues with quality inconsistency and
limited production capacity[22]. As a result, the addition of silica fume may restrict the future development of LC
3
-UHPC. On the other
hand, research has shown that calcined clay is a supplementary cementitious material (SCM) that can replace silica fume[23].
Consequently, it is possible to omit silica fume in LC
3
-UHPC, simplifying the raw materials and making them more economical and
stable.
According to the analysis above, the main aim of this study is to investigate the impacts of different mix proportions, including
varying substitution rates of LC
2
for cement and the ratio of calcined clay to limestone powder, on the uniaxial compressive stress-
strain relationship of LC
3
-UHPC matrix without the addition of silica fume. The reason for selecting the LC
3
-UHPC matrix rather
than ber-reinforced LC
3
-UHPC as the research subject is to exclude the inuence of the mix proportion on the LC
3
-UHPC matrix-ber
interaction, thereby focusing on the critical issue of how the mix proportion affects the compressive stress-strain relationship of the
LC
3
-UHPC matrix. In addition, DTG, SEM-EDS, and MIP were employed to analyze the corresponding hydration process and micro-
structures of LC
3
-UHPC matrix. Finally, the optimal mix proportion for LC
3
-UHPC matrix without the addition of silica fume will be
proposed. Based on the experimental results and the constitutive model proposed by Popovics[24], the uniaxial compressive
stress-strain relationship for LC
3
-UHPC matrix will be formulated in this study.
2. Materials and test methods
2.1. Materials
The raw materials used in this study include P.O.52.5 ordinary Portland cement, calcined clay, limestone powder, gypsum, quartz
sand, and superplasticizer. The chemical compositions of cement, calcined clay and limestone powder are listed in Table 1. The
apparent morphology of calcined clay and limestone powder under SEM are illustrated in Fig. 1. The mesh sizes of calcined clay and
limestone powder are respectively 800 mesh and 600 mesh. Quartz sand is used as the ne aggregate and its SiO
2
content exceeds
98 %. Particle size distributions of cement, calcined clay, limestone powder and quartz sand are shown in Fig. 2. In order to ensure the
good workability of the developed UHPC mixtures, a polycarboxylate superplasticizer (SP, HLX-standard type), purchased from Shanxi
Feike New Materials Technology Co., Ltd., is utilized in this study.
Table 1
Chemical compositions of cement, calcined clay and limestone powder (%).
Oxide SiO
2
Al
2
O
3
Fe
2
O
3
TiO
2
CaO MgO K
2
O Na
2
O SO
3
LOI
Cement 19.19 4.21 3.30 - 65.01 1.57 0.78 0.08 2.72 2.50
Calcined clay 54.50 43.50 0.50 0.20 0.10 0.05 0.50 0.05 - 2.01
Limestone powder 0.24 0.05 0.05 0.01 54.83 0.32 0.01 0.01 - 43.96
K. Fan et al.
Case Studies in Construction Materials 22 (2025) e04274
2

Fig. 1. The SEM images of raw materials: (a) calcined clay, (b) limestone powder.
Fig. 2. The cumulative particle size distribution curves of raw materials.
Table 2
Mix proportions of LC
3
-UHPC matrix.
Number Cement (%) Calcined clay (%) Limestone Powder (%) Gypsum (%) SP (%) B/S W/B
REF 100 0.0 0.0 0.00 0.40 1 0.2
LS30 70 0.0 30.0 1.50 0.25 1 0.2
CC30 70 30.0 0.0 1.50 2.50 1 0.2
LC
3
5/10 85 5.0 10.0 0.75 0.50 1 0.2
LC
3
10/5 85 10.0 5.0 0.75 1.00 1 0.2
LC
3
10/20 70 10.0 20.0 1.50 0.40 1 0.2
LC
3
20/10 70 20.0 10.0 1.50 2.20 1 0.2
LC
3
15/30 55 15.0 30.0 2.25 1.00 1 0.2
LC
3
30/15 55 30.0 15.0 2.25 2.80 1 0.2
K. Fan et al.
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2.2. Mixture proportion and sample preparation
The mix design for LC
3
-UHPC matrix is outlined in Table 2, with a water-to-binder ratio (W/B) of 0.2 and a sand-to-binder ratio (S/
B) of 1. There are 12 groups of mixes in this study, designated as follows: REF (no calcined clay or limestone powder), LS30 (30 %
substitution rate of limestone powder for cement), CC30 (30 % substitution rate of calcined clay for cement), and LC
3
X/Y for the
remaining groups, where X and Y represent the respective percentages of calcined clay and limestone powder in the total cementitious
materials. Gypsum was added at a rate of 5 % of the LC
2
dosage to supply additional sulfate. This strategy aims to inhibit the rapid
reaction of C
3
A with water, thus preventing the ash setting of concrete [25]. The uidity of LC
3
-UHPC was controlled within the range
of 250 mm ±10 mm via SP with various mixing amounts. No bers were incorporated into LC
3
-UHPC to avoid the inuence of bers
on the hydration reaction and microstructure.
The stirring procedure for LC
3
-UHPC matrix is delineated in Fig. 3. Firstly, the cement, calcined clay, limestone powder, gypsum,
and quartz sand were mixed in the JJ20 cement mortar mixer for 3 min at a speed of 62.5 r/min. Subsequently, the mixed solution,
consisting of 50 % water and all SP, was introduced and stirred at 62.5 r/min for 1 min. Then, residual water was added to ush the
remaining SP on the inner wall of the beaker. After that, the mixed solution was stirred at 62.5 r/min for 3 min, after which the stirring
speed was increased to 125 r/min for 2 min. Next, the mixture was cast into cylinder molds with a diameter of 50 mm and a height of
100 mm. The pouring process can be divided into three steps under the vibration on a high-frequency vibration table. The specimens
with molds were kept under standard room conditions (95 %RH, 20 ±1◦C) in the rst 24 hours. After being demolded, the specimens
were cured in water at 20◦C for 28 days.
2.3. Testing methods
The owability test was implemented based on the ASTM C1437 [26]. According to the Chinese standard GB/T 50081–2019 [27],
the uniaxial compression test was conducted on the specimens to obtain the uniaxial compressive stress-strain relationship. The test
was conducted using a TES microcomputer-controlled electronic universal testing machine with a capacity of 600 kN. Specimens were
subjected to uniaxial compression at a constant displacement rate of 0.12 mm/min. Each specimen was preloaded to around 30 % of
the compressive strength to prevent loading eccentricity and system relaxation. The contact strain test method was adopted in this
study, with the deformation measuring device being detailed in Fig. 4.
After the uniaxial compression test at 28 days, the mortar specimens were crushed and immersed in isopropanol to stop hydration
for 48 hours. The samples were then placed in a vacuum drying chamber and subjected to a temperature of 60◦C for 48 hours. For DTG
analysis, the samples were crushed and the powders that passed through a 200-mesh sieve were collected. Approximately 13 mg of
powder was employed for DTG analysis. The sample was heated from 30◦C to 1000◦C at a rate of 10 ◦C/min under the protection of the
N
2
atmosphere. SEM-EDS was conducted with the aid of ZEISS GeminiSEM 500 (Carl Zeiss). After the at fragments were collected
from the dried fragments, the gold spraying treatment was performed on the sample’s surface to enhance the conductivity. MIP test
was used to analyze the pore structure of hydration products. The pore size distributions were measured via Auto Pore IV9500 (Mike
Company). The pore size test range was 5 nm to 800
μ
m, and the test pressure ranged from 0.1 psi to 30000 psi.
3. Results and discussion
3.1. Flowability
The owability of mixtures with different proportions are illustrated in Fig. 5. Due to the multilayered, ake-like structure and high
specic surface area of calcined clay, as shown in Fig. 1(a), its addition to UHPC mixtures typically reduces owability. It has been
observed that incorporating 30 % calcined clay (CC30 group) requires more superplasticizer to achieve a owability similar to that of
the reference group, aligning with previous research ndings [28]. Even with a dosage of superplasticizer as high as 2.5 %, the
owability of CC30 mixture was only 242 mm. Conversely, the presence of limestone particles is seen to reduce ow resistance and
improve workability. The addition of 30 % limestone powder (LS30 group) increased the owability of the mixture with less super-
plasticizer compared to the REF group. This improvement is likely due to the ball effect during the mixing process, caused by the
relatively smooth surface of the limestone particles, as shown in Fig. 1(b). The CaCO
3
particles release entrapped water between
coarser particles[29–31], therefore making more water available to aid in the owability[32].
Based on the analysis above, limestone powder positively affects owability, while calcined clay has a negative effect. Therefore,
when the substitution rate of limestone calcined clay (LC
2
) for cement is xed, the mass ratio of calcined clay to limestone powder
signicantly inuences owability. For example, at a substitution rate of 30 %, the LC
3
10/20 group, where the mass ratio of calcined
clay to limestone powder is 1:2, exhibits higher owability (256 mm) with the minimum superplasticizer dosage (0.4 %). In com-
parison, the LC
3
20/10 group, where the mass ratio of calcined clay to limestone powder is 2:1, shows lower owability (247 mm) with
Fig. 3. The stirring procedure.
K. Fan et al.
Case Studies in Construction Materials 22 (2025) e04274
4

a high superplasticizer dosage (2.2 %).
3.2. Hydration and microstructure
3.2.1. DTG analysis
Fig. 6 shows the DTG curves of samples with different proportions at 28 days of age. From Fig. 6, it can be seen that the mass loss
rate of the samples varies at different temperatures, with signicant mass losses occurring in three distinct temperature ranges. The
rst mass loss occurs between 50 ◦C and 200 ◦C. In this range, the mass loss is mainly caused by the evaporation of physically adsorbed
Fig. 4. The schematic diagram of the deformation measuring device.
Fig. 5. Flowability test.
K. Fan et al.
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5

water and the decomposition of C-(A)-S-H, ettringite (AFt), and carboaluminate (AFm)[33].
The second major mass loss occurs between 400 ◦C and 450 ◦C. During this period, the main cause of mass loss is the dehydration of
Ca(OH)₂[34]. It can be observed that in this temperature range, the mass loss of the samples decreases with the increase in the amount
of calcined clay, because the greater the amount of calcined clay, the more Ca(OH)₂ is consumed by the pozzolanic reaction[18]. In
contrast, the addition of limestone powder increases the mass loss in this temperature range, because limestone powder provides
nucleation sites for cement hydration, allowing more cement particles to participate in the reaction and generate more calcium hy-
droxide[35].
Fig. 6. DTG curves of UHPC at 28d: (a) REF, CC30, LS30, (b) LC3-UHPC.
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The third major mass loss occurs between 600 ◦C and 750 ◦C, where the main cause of the mass loss is the decomposition of
CaCO₃[34]. Since the main component of limestone powder is calcium carbonate, incorporating more limestone powder leads to
increased mass loss at this stage. Additionally, from Fig. 6(b), it can be seen that when the increase in limestone powder content is the
same, the difference in mass loss in this temperature range between the LC
3
5/10 group and the LC
3
10/20 group is smaller than the
difference between the LC
3
10/20 group and the LC
3
15/30 group. This indicates that after the limestone powder content exceeds 20 %,
its participation in hydration decreases, and more limestone powder particles primarily act as llers[36].
3.2.2. SEM-EDS analysis
Fig. 7 shows the Al/Ca and Si/Ca ratios of hydration products of REF group and LC
3
10/20 group at 28 days obtained through EDS
analysis. The criteria for selecting data points in Fig. 7 are as follows: For each sample, six observation areas with evenly distributed
hydration products are selected (microstructures without signicant voids, unhydrated clinker particles, or noticeable foreign parti-
cles). Five points are then randomly selected within each area, resulting in a total of 30 points for testing. Compared with REF, both of
Al/Ca and Si/Ca ratios are signicantly higher in LC
3
systems. The hydration products of REF are primarily a mixture of Calcium
Silicate Hydrate (C-S-H) and portlandite (CH). In the case of LC
3
10/20 group, there is a synergistic effect between limestone powder
and calcined clay that leads to the consumption of CH and the production of carboaluminate (Hc) and mono-carboaluminate (Mc).
Consequently, the predominant hydration products in LC
3
10/20 group are a blend of C-S-H, C-A-S-H, AFt, Hc and Mc phases, which is
in consistent with the SEM results. As illustrated in Fig. 8, a smaller quantity of hydration products adheres to the micropores of REF,
while the micropores of LC
3
10/20 are lled with hydration products such as Mc, AFt, and CH. This lling effect renes the micro-pores
and densies the matrix. This observation can be explained by the fact that both calcined clay and limestone powder supply a sub-
stantial amount of reactive aluminum phase and calcite in LC
3
-UHPC system. This abundance facilitates the swift formation and
stabilization of Hc and Mc phases, which, in turn, helps to stabilize AFt[8,18].
3.2.3. MIP analysis
Fig. 9 shows the pore size distributions of LC
3
-UHPC matrix at 28 days. It can be seen from Fig. 9(a) that both calcined clay and
limestone powder can rene the micropores (0–100 nm), with calcined clay having a more pronounced effect. However, while 30 %
calcined clay signicantly renes the micropores, it also introduces more mesopores (100–10,000 nm). This may be due to its high
water absorption rate and the corresponding negative impact on the mixture’s workability, indicating that the amount of calcined clay
used in LC
3
-UHPC should be limited. Comparing Fig. 9(a) and Fig. 9(b), it can be seen that the combined use of calcined clay and
limestone powder (LC
3
10/20) has a more signicant effect on rening the pore structure than using either one alone (CC30/LS30).
This demonstrates the synergistic effect between the two and the effectiveness of the LC
3
-UHPC matrix. However, it is important to
note that the replacement rate also has a signicant impact on the pore renement effect. On one hand, when the replacement rate is
low (LC
3
5/10), the pore renement effect is relatively less pronounced. On the other hand, if the replacement rate is too high (LC
3
15/
Fig. 7. The 2D scatter diagram of hydration products of REF and LC
3
10/20 at 28d.
K. Fan et al.
Case Studies in Construction Materials 22 (2025) e04274
7

30), more mesopores (100–10,000 nm) are introduced, which may be due to the high water absorption rate of the calcined clay, as
previously analyzed. It is also noteworthy that the negative effects of high amounts of calcined clay on the pore structure and
workability were not observed in previous studies on LC
3
based normal concrete. This could be attributed to the fact that LC
3
-UHPC
matrix has a very low water-cement ratio, making it more sensitive to changes in water content.
3.3. Uniaxial compressive behavior
3.3.1. Failure pattern
In the uniaxial compressive strength test, specimens of LC
3
-UHPC matrix exhibited similar failure patterns. Initially, as the load was
applied, no apparent cracks were observed on the surfaces of the specimens. When the specimens were loaded to 80 % of the peak load,
tiny longitudinal cracks appeared at both ends, accompanied by a faint splitting sound. As the load neared the peak, the longitudinal
cracks continued to extend, the number of cracks increased, and portions of the surface layer began to ake off. As the load continued
to increase, the width of the cracks widened, and the fractures extended longitudinally until they penetrated the specimen, resulting in
brittle failure, as shown in Fig. 10. The main body of the specimens maintained certain structural integrity, with only a few fragments
falling off.
3.3.2. Compressive strength
The 28-day compressive strength of specimens with different mix proportions is illustrated in Fig. 11. It should be noted that the
measured compressive strength is not as high as those reported for UHPC specimens. This is because no silica fume or bers were
added, and only standard curing was adopted. The focus of this study is the inuence of LC
2
on the UHPC matrix.
Incorporating 30 % limestone powder (LS30 group) results in an increase in compressive strength compared to the REF group. This
improvement is due to limestone powder’s ability to effectively ll the voids between cementitious materials, enhance owability, and
provide nucleation sites for hydration products during the hydration process[37,38]. These benets outweigh the negative impact of
the dilution effect caused by substituting limestone powder for cement. Conversely, incorporating 30 % calcined clay (CC30 group)
reduces the compressive strength compared to the REF group. On one hand, calcined clay reacts with CH to form hydration products
such as C-S-H, calcium aluminate hydrate (C-A-H), and C-A-S-H. These additional hydration products ll the matrix’s pores, resulting
Fig. 8. The SEM images of UHPC at 28d: (a)REF, (b)LC
3
10/20.
K. Fan et al.
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8

in a denser microstructure. However, on the other hand, the high absorption also has negative impacts on the hydration process and the
mixture’s owability[23].
When both calcined clay and limestone powder are added to UHPC matrix, synergistic reactions occur among the cement clinker,
calcined clay, limestone powder, and gypsum, in addition to their individual effects. In the LC
3
ternary system, limestone powder can
provide nucleation sites for the precipitation of hydration products, accelerating the hydration of both calcined clay and clinker
(especially C
3
S) at an early stage, and react with aluminate phases (from clinker or calcined clay) and Ca(OH)
2
to form hemicarbonate
(Hc) and monocarbonate (Mc), thereby stabilizing ettringite[12,39]. Due to these synergistic reactions, at the same replacement rate
Fig. 9. Pore size distributions of LC
3
-UHPC at 28 days.
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(30 %), the strength of the LC
3
10/20 group is higher than that of both the CC30 and LS30 groups, demonstrating the effectiveness of
the LC
3
-UHPC system. However, the strength of the LC
3
20/10 group is lower than that of the LC
3
10/20 group due to the excessive
amount of calcined clay, which decreases the mixture’s owability, while the LC
3
5/10 and LC
3
10/5 groups, with lower amounts of
calcined clay, exhibit comparable compressive strength to the optimal LC
3
10/20 group. The compressive strength of the LC
3
30/15
group is lowest among all groups due to the dilution effect caused by high substitution rate of LC
2
and excessive amount of calcined
clay.
3.3.3. Compressive stress-strain relationship
Fig. 12(a) and Table 3 present the measured compressive stress-strain curves of LC
3
-UHPC matrix at 28 days, along with the
corresponding values of compressive strength, elastic modulus, and peak strain. As shown in Fig. 12(a) and Table 3, except for the
LC
3
15/30 and LC
3
30/15 groups, all other mixes exhibit similar or even better compressive mechanical properties compared to the REF
group. Mixes with higher compressive strength also possess higher elastic modulus and lower peak strain, which could be attributed to
more complete hydration and the renement of pore structure. Among them, the LC
3
10/20 group shows the best uniaxial compressive
mechanical performance.
In addition to the differences in mechanical properties, it is also observed that the shapes of the curves vary between different
mixes. To better quantify the differences in the compressive stress-strain curves among the different mixes and provide a reference for
Fig. 10. Typical failure patterns of specimens (a) LC
3
10/20, (b) LC
3
15/30, (c) LC
3
30/15.
Fig. 11. Compressive strength of LC
3
-UHPC at 28 days.
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10

future related studies, the concrete constitutive model proposed by Popovics[24], as shown in Eq. (1), is used to assess the nonlinearity
of the compressive stress-strain curves of the specimens.
σ
fc
=
ε
ε
c
n
n−1+(
ε
ε
c)n(1)
Fig. 12. Compressive stress-strain curves of LC
3
-UHPC: (a) measured curves, (b) normalized curves.
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where
σ
,
ε
are stress and strain, respectively; fc is compressive strength;
ε
c is peak strain; n is a parameter related to the nonlinearity of
the stress-strain curves.
First, all stress-strain curves were normalized, meaning the actual stress and strain values were divided by the corresponding axial
compressive strength and peak strain, respectively, for comparison. The results are shown in Fig. 12(b). It can be seen that the degree of
nonlinearity of the normalized stress-strain curves varies between different mixes. Then, based on Eq.(1), all the normalized stress-
strain curves were tted, and the nonlinearity parameter n was determined.
The tting results for the n values and the corresponding R² values are shown in Table 3. A larger n value indicates a lower degree of
nonlinearity and a smaller curvature[40]. As shown in Fig. 12(b) and Table 3, adding 30 % calcined clay has little effect on the n value
compared to the REF group, while adding 30 % limestone powder signicantly reduces the n value of the stress-strain curve, thereby
increasing its nonlinearity[40,41]. Unlike single incorporation, the combined use of calcined clay and limestone powder, i.e., using LC
2
to replace cement, increases the n value of the uniaxial compressive stress-strain curve, thereby reducing its nonlinearity, which may
be related to the synergistic effect between the two. It is noteworthy that the ratio between calcined clay and limestone powder has
little effect on the n value, whereas the replacement rate has a more signicant impact. As the replacement rate increases from 15 % to
45 %, the n value gradually decreases to a level close to that of the REF group. Based on the above analysis, it can be concluded that
adding an appropriate amount of LC
2
(no more than 30 %) to UHPC matrix helps reduce the nonlinearity of its axial compressive
stress-strain relationship. Based on Eq.(1) and the data in Table 3, the measured uniaxial compressive stress-strain curves of LC
3
-UHPC
in Fig. 12(a) can be effectively formulated, providing a reference for related research in the future.
4. Conclusions
In this paper, the uniaxial compressive stress-strain relationships of LC
3
-UHPC matrix with different mix proportions were tested.
The hydration process and microstructures were analyzed by various techniques. A uniaxial compressive constitutive model proposed
by Popovics was used to formulate the compressive stress-strain relationships of LC
3
-UHPC matrix and quantify the difference among
the curves. Based on the obtained results, the following conclusions can be drawn:
(1) Unlike LC
3
based normal concrete, LC
3
-UHPC matrix has a very low water-cement ratio, making it highly sensitive to changes in
water content. Therefore, the amount of calcined clay in LC
3
-UHPC matrix should not be too high; otherwise, the high water
absorption rate of calcined clay could lead to reduced workability and deterioration of compressive mechanical properties. As a
result, LC
3
-UHPC matrix achieves optimal mechanical performance with a 1:2 calcined clay to limestone powder ratio and a
30 % substitution rate of LC
2
for cement in this study, while the typical calcined clay to limestone powder ratio for LC
3
-based
normal concrete is 2:1.
(2) The optimal mix proportion identied in this study is LC
3
10/20 group (10 % calcined clay, 20 % limestone powder), which
exhibits the highest compressive strength and elastic modulus, showing increases of 16 % and 44 %, respectively, compared to
that of the reference group. The LC
3
10/20 group achieves a 28-day compressive strength of 104 MPa under standard curing,
without applying any silica fume or bers, which indicates its great potential in practical engineering. Furthermore, the LC
3
15/
30 group (15 % calcined clay, 30 % limestone powder), featuring a 45 % substitution rate of LC
2
for cement, exhibits only a
11 % decrease in compressive strength compared to the reference group, underscoring its notable environmentally friendly
characteristics.
(3) Adding an appropriate amount of LC
2
(no more than 30 %) to UHPC matrix helps reduce the nonlinearity of its compressive
stress-strain relationship, thereby minimizing the plastic deformation of UHPC matrix. The nonlinearity of the compressive
stress-strain curve is related to the replacement rate of LC
2
for cement. As the replacement rate increases from 15 % to 45 %, the
nonlinearity parameter n of the compressive stress-strain relationship gradually decreases to a value close to that of the
reference group. Additionally, the uniaxial compressive constitutive model proposed by Popovics has been proven to formulate
the compressive stress-strain relationship of LC
3
-UHPC matrix in this study well. The specic parameters of the constitutive
model have been summarized in Table 3, providing a reference for related research in the future.
Table 3
Constitutive parameters of LC
3
-UHPC under uniaxial compression.
Number Compressive strength (MPa) Elastic modulus(GPa) Peak strain(‰) Nonlinearity parameter-n Curve tting-R
2
REF 90.20 47.26 2.15 9.21 0.9980
LS30 94.45 60.58 2.08 3.72 0.9994
CC30 86.99 46.08 2.20 6.90 0.9995
LC
3
5/10 102.26 65.25 1.54 35.51 0.9984
LC
3
10/5 99.51 62.12 1.62 33.68 0.9998
LC
3
10/20 104.62 68.00 1.41 14.39 0.9986
LC
3
20/10 88.42 51.72 1.85 16.39 0.9988
LC
3
15/30 80.29 56.31 1.60 9.94 0.9997
LC
3
30/15 71.05 43.52 1.79 11.73 0.9997
K. Fan et al.
Case Studies in Construction Materials 22 (2025) e04274
12

CRediT authorship contribution statement
Kunjie Fan: Writing – review & editing, Writing – original draft, Supervision, Project administration, Funding acquisition, Formal
analysis, Conceptualization. Peng Du: Writing – original draft, Resources, Methodology, Investigation, Formal analysis, Data curation.
Yao Yao: Supervision, Project administration, Funding acquisition, Conceptualization.
Declaration of Competing Interest
The authors declare that they have no known competing nancial interests or personal relationships that could have appeared to
inuence the work reported in this paper.
Acknowledgments
The authors would like to acknowledge the nancial supports received from the Natural Science Basic Research Program of Shaanxi
Province (Grant No. 2023-JC-QN-0456), the Fundamental Research Funds for the Central Universities (Grant No. NWPU-
G2021KY05101), the "Scientists+Engineers" Team Construction Project of Qinchuangyuan, Shaanxi Province (Grant No. 2022KXJ-
094), and the Shaanxi Science and Technology Innovation Team (Grant No. 2022TD-05).
Data availability
Data will be made available on request.
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