Abstract
Developing seawater sea-sand concrete can address the challenges arising from the lack of freshwater and river/manufactured sand for making concrete on-site for sustainable marine and coastal construction. To eliminate the corrosion risk of steel fibers while maintaining the high ductility of concrete, this study aims to develop a new type of ultra-high-performance seawater sea-sand concrete (UHP-SSC) by using ultra-high-molecular-weight polyethylene fibers. The effect of fiber content (0%, 0.5%, 1.0%, and 1.5% by volume) on the mechanical performance and cracking characteristics of UHP-SSC was experimentally investigated. The results showed that as the fiber content increases, the tensile strength and strain capacity of UHP-SSC significantly increase, while the compressive strength slightly decreases (but still over 130 MPa). The stochastic nature of the crack width was characterized by the Weibull distribution. A probabilistic model was used to model the evolution of the crack width for UHP-SSC at different strain levels. The model showed good agreement with the experimental results, and it can be used to estimate the allowed tensile strain of UHP-SSC in practical applications for a given limit of crack width and cumulative probability. The findings in this study provide insights into the future design of UHP-SSC in marine and coastal applications.
Keywords
Introduction
Reinforced concrete structures play an important role in marine and costal infrastructures, such as bridges, ports, and offshore platforms. The corrosion risk of steel reinforcements in marine environment and the lack of freshwater and river/manufactured sand for making concrete on-site are two major challenges for reinforced concrete structures in marine and costal applications (Xiao et al., 2017, 2019; Zhang et al., 2019a). To address these challenges, seawater sea-sand concrete (SSC) structure reinforced with fiber-reinforced polymer (FRP) composites (FRP-SSC) was proposed by Teng and co-workers (Teng, 2014; Teng et al., 2011), and the concept has been proven to be attractive (Dong et al., 2020; Li et al., 2018; Wang et al., 2017, 2018; Zeng et al., 2020; Zhou et al., 2019a).
Ultra-high-performance concrete (UHPC) is a special kind of high-performance fiber-reinforced cementitious composites (HPFRCC) featuring high compressive strength (≥120 MPa as per the Chinese standard (T/CBMF37, 2018) or ≥150 MPa as per the ACI report (ACI, 2018), high tensile strength, and superior durability (Li et al., 2020; Shaikh et al., 2020; Shi et al., 2015; Su et al., 2020; Wille et al., 2011). Compared to ordinary concrete, UHPC shows much lower water permeability and higher resistance to chloride penetration (Li et al., 2020). Steel fibers are generally used in UHPC to provide high energy absorption prior to tensile fracture and multiple fine cracks prior to crack localization (Figure 1) (Naaman, 2003; Wille et al., 2011); therefore, conventional UHPC is not suitable to be used in marine environment due to the fiber corrosion. Recently, (Teng et al., 2019) developed ultra-high-performance seawater sea-sand concrete (UHP-SSC) without fibers to eliminate the corrosion problem of steel fibers. However, as high-strength concrete is more brittle than normal-strength concrete, the failure mode of FRP-reinforced UHP-SSC (without fibers) can be more brittle than that of FRP-reinforced normal-strength SSC if the failure is governed by concrete crushing.

Tensile strain-hardening and multiple cracking of HPFRCC (Naaman, 2003). As a kind of HPFRCC, UHPC shows high energy absorption prior to tensile fracture and multiple cracking prior to crack localization.
To address the above challenge, it is essential to develop a new type of ductile UHP-SSC without the corrosion risk of steel fibers. The ductility in concrete can be improved by fiber reinforcement based on the micromechanical design theory (Huang et al., 2018b, 2019a; Li and Leung, 1992; Lin et al., 2018; Yu et al., 2018a, 2018b; Yu et al., 2020a). It has been proven that the resiliency and durability of structural members can be significantly improved by using ductile concrete (Huang et al., 2017a, 2019b, 2019c, 2020; Li, 2019; Li et al., 2016; Lu et al., 2018; Mechtcherine, 2013; van Zijl and Slowik, 2017; Xu et al., 2017). Ultra-high-molecular-weight polyethylene (PE) fibers were widely used in high-tensile-strength ductile concrete (Chen et al., 2018, 2020; Ding et al., 2019; He et al., 2017; Yu et al., 2018d; Zhang et al., 2019b, 2020; Zhou et al., 2019b), and therefore there is a great interest to develop ductile UHP-SSC with PE fibers to avoid the corrosion risk of reinforcing fibers.
For FRP-SSC structures, the crack width of SSC and its distribution are important for the deformation compatibility between FRP and concrete, and also control the water permeability of concrete (Lepech and Li, 2009; Liu et al., 2016; Wang et al., 1997; Wu et al., 2020; Ye, 2003; Yu et al., 2017). For the sake of reliable applications of UHP-SSC, it is desirable to describe the stochastic nature of crack widths based on the probabilistic approach. The Weibull distribution is well known to satisfactorily fit the distribution of matrix flaw sizes in cement-based materials (Kanda et al., 2000; Spearing and Zok, 1993; Wu and Li, 1995) and it can describe the stochastic nature of several static and fatigue parameters of strain-hardening fiber-reinforced concrete (Huang, 2018; Huang et al., 2017b, 2018a). Therefore, it is of interest to know whether the Weibull distribution is suitable for describing the stochastic characteristics of cracks in UHP-SSC. Additionally, it is helpful to use a probabilistic-based method to model the crack width evolution of UHP-SSC.
To fill the above knowledge gaps, this study aims to develop ductile UHP-SSC by incorporating PE fibers. The effect of fiber content (0-1.5 vol.%) on the mechanical performance and cracking characteristics were comprehensively evaluated. A probabilistic method was used to analyze and model the stochastic nature of crack widths of UHP-SSC at different strain levels.
Materials and methods
Mix proportion
Table 1 shows the four mixes with different fiber volume fractions. Portland cement, micro silica, seawater, sea-sand, superplasticizers and ultra-high-molecular-weight polyethylene (PE) fibers (Table 2) were used. In the mix ID, the number stands for the volume content of PE fiber. The sea-sand with the maximum particle size of 1.18 mm (Figure 2) was used, which was obtained from a local coast. Some seashell particles can be observed in the used sea-sand.
Mix design of UHP-SSC (weight ratio).
CEM I Portland cement 52.5N as per BS EN 197-1 (BSI, 2011);
Silica content over 92%;
The seawater was made of freshwater and dissolved commercial sea-salt with a concentration of 36 g/L as suggested in (Teng et al., 2019);
Polycarboxylate ether (PCE) type superplasticizers (solid content).
Nominal properties of ultra-high-molecular-weight polyethylene (PE) fibers.

Sea-sand with maximum particle sizes of 1.18 mm. Some seashell particles can be observed.
For the fresh property, the mini-slump flow diameters as per the ASTM C1437 (ASTM, 2007) for all the mixes in Table 1 were 160–170 mm, and no fiber agglomeration or ingredient segregation was observed during mixing and casting.
Sampling and testing
Curing
All the samples were cast in stainless steel molds and demolded after 24 h, and then cured at the temperature of 23°C and relative humidity of 95% until 28-day age (ASTM, 2016). Though heat curing under atmospheric pressure and autoclave curing regimes are widely used for making UHPC (Shi et al., 2015), the standard room temperature curing was used in the present study to ensure the wide application of UHP-SSC.
Compressive strength
Three 50 mm×50 mm×50 mm cubes for each group were prepared to determine the compressive strength of UHP-SSC, and the loading rate was 0.6 MPa/s as per ASTM C109 (ASTM, 2013).
Tensile performance
According to a recommendation by the Japan Society of Civil Engineers (JSCE, 2008), dumbbell samples (Figure 3) were prepared for the direct tension test. A 25-kN servo-hydraulic MTSTM 810 testing system was used for the tension test and the loading rate was 0.5 mm/min (JSCE, 2008). A pair of linear variable displacement transducers were attached to the dumbbell samples with an 80-mm gauge length to measure the tensile strain.

Specimen dimensions for direct tension test.
Crack pattern recording
To record the crack pattern of UHP-SSC during the tension test, a 24.2-megapixel camera (Canon EOS 6D Mark ii) was used to take photos within the gauge length (Figure 3), and a resolution of around 15 μm per pixel was achieved. Then, Adobe Photoshop was used to analyze the crack widths at different strain levels. Details of the method can be found in (Lu et al., 2016; Yu et al., 2018c).
Analysis of cracking characteristics
With the photos showing crack pattern of UHP-SSC under different tensile strain levels, the crack widths were first analyzed based on the Weibull distribution, as the crack width can be treated as a positive random variable. Then, a probabilistic model to describe the crack width development with increasing strain levels was introduced and validated. Specifically, for the Weibull distribution, the cumulative distribution function CDF (Fw(w)) can be expressed as (Ross, 2017):
where w is crack width (variable); λ and k are the scale and shape parameters, respectively.
Mechanical performance of UHP-SSC
Compressive strength
The compressive strength of UHP-SSC is summarized in Figure 4. As the PE fiber content increased, the compressive strength of UHP-SSC slightly decreased. The average compressive strength of PE0.0%, PE0.5%, PE1.0%, and PE1.5% was 140.9 MPa, 140.8 MPa, 137.7 MPa, and 131.7 MPa, respectively (Figure 4); all these values fulfill the requirement of the minimum characteristic strength ≥ 120 MPa as per the Chinese standard for UHPC (T/CBMF37, 2018).

Compressive strength of UHP-SSC. A summary of the effect of polymer fiber volume content on compressive strength based on the data from the literature is also shown for discussion. Generally, for high-strength concrete with the compressive strength over 70 MPa, an increasing fiber content up to 2 vol.% slightly decreases the compressive strength.
Adding steel fibers (Larsen and Thorstensen, 2020; Liu et al., 2020) or replacing polymer fibers by steel fibers (Yu et al., 2019) in concrete generally increase its compressive strength, while the overall influence of polymer fibers on the compressive strength of concrete is delicate: the fibers can lower the matrix compactness (negative effect) but can also bridge the micro-cracks (positive effect) (Bentur and Mindess, 2007). Figure 4 also summarizes the effect of polymer fiber volume content on the compressive strength based on the data from the literature reporting concrete with fiber over 0.5 vol.% (Al-mashhadani et al., 2018; Çavdar, 2014; Choi et al., 2017; Kakooei et al., 2012; Wang et al., 2019, 2020; Yu et al., 2020b). Specially, three kinds of widely-used polymer fibers including PE, polyvinyl alcohol (PVA) and polypropylene (PP) were showed. As indicated from this figure, for high-strength concrete with the compressive strength over 70 MPa, an increasing fiber content up to 2 vol.% slightly decreases the compressive strength; for normal-strength concrete, both increasing and decreasing trends were reported. This observation may be due to the fact that high-strength concrete is sensitive to the matrix compactness, and therefore the negative effect of adding polymer fibers (lowering the matrix compactness) dominates.
Tensile performance
The tensile performance of UHP-SSC is summarized in Figure 5. The tensile stress-strain curves of all the samples and the cracking characteristics of the typical sample (corresponding to the highlighted curve) for each group are presented in Figure 6. Tensile strain-hardening behavior can be observed for all the three groups with fibers.

Tensile performance of UHP-SSC: (a) strength and (b) strain capacity. As the fiber content increases, the tensile strength and strain capacity of UHP-SSC increase.

Tensile stress-strain curves and cracking characteristics of UHP-SSC: (a) PE0.5%; (b) PE1.0%; and (c) PE1.5%. Tensile strain-hardening and multiple cracking can be observed for UHP-SSC with fiber content from 0.5 vol.% to 1.5 vol.%.
In concrete reinforced with hydrophobic fiber (such as PE fiber in this study), the fiber/matrix interaction can be considered as pure friction (Lin et al., 1999). For this kind of fiber-reinforced concrete, the ultimate tensile strength (σcu) can be calculated as (Lin et al., 1999):
where τ0 is the fiber/matrix interfacial frictional bond, f is the snubbing coefficient reflecting the effect of fiber inclination, and Vf, Lf, and df are the content, length, and diameter of fibers, respectively. According to equation (2), the tensile strength is proportional to the fiber content (Vf), which supports the observation in Figure 5(a): the tensile strength of UHP-SSC increases from about 4 MPa for PE0.5% to about 8 MPa for PE1.5%. Additionally, as the fiber content increases from 0.5 vol.% to 1.5 vol.%, the tensile strain capacity also increases significantly (Figure 5(b)). The tensile strain capacities of PE1.0% and PE1.5% are 1.8% and 4.6%, respectively; these values are 3.5 and 9.2 times that of PE0.5%, respectively (Figure 5(b)). It should be pointed out that, an excess fiber dosage in fiber-reinforced concrete can lead to difficulty in fiber dispersion and make equation (2) invalid.
For strain-hardening cement-based materials, the cracking characteristics (e.g. the distribution and evolution of crack width) are also important for practical applications (Huang et al., 2020). In the next section, the cracking characteristics of all the tensile samples are further analyzed and modeled based on a probabilistic approach proposed by the authors (Huang et al., 2021).
Cracking characteristics of UHP-SSC and probabilistic modeling
Crack pattern at different strain levels
To investigate the cracking characteristics of UHP-SSC, the recorded digital photos at five strain levels (from A to E) were selected. Specifically, the strain level A is 0.2%, which reflects the strain level of UHP-SSC under the serviceability stage and is set the same for all the samples; the strain level E is the ultimate tensile strain capacity. The strain levels B, C, and D divide the strain range between A and E into quarters. For example, if the tensile strain capacity of the sample is 0.77%, the strain levels A, B, C, D, and E are 0.2%, 0.34%, 0.48%, 0.63%, and 0.77%, respectively.
From the recorded digital photos at different strain levels, the crack number and crack width can be obtained for all the tensile samples, which are presented in Figures 7 to 9. Since the resolution of the photos was 15 μm per pixel (Section 2.2), the step of the crack-width groups was set to be 15 μm. It should be pointed out that only two samples are presented in Figure 7 for group PE0.5%, as the photos of the third sample are not clear enough (not in focus) for crack analysis.

Crack widths and numbers of UHP-SSC at different strain levels: (a) PE0.5%-1, and (b) PE0.5%-2.

Crack widths and numbers of UHP-SSC at different strain levels: (a) PE1.0%-1, (b) PE1.0%-2, and (c) PE1.0%-3.

Crack widths and numbers of UHP-SSC at different strain levels: (a) PE1.5%-1, (b) PE1.5%-2, and (c) PE1.5%-3.
Distribution of crack width
For the crack widths and numbers presented in Figures 7 to 9, the cumulative distribution functions (CDF, equation (1)) of Weibull distributions was used to fit the cumulative distributions of crack widths at all the strain levels. The fitting distribution parameters (Weibull scale parameter λ and Weibull shape parameter k) and the corresponding correlation coefficients (rWeibull) of best fit are listed in Table 3. The value of rWeibull ranges from 0.866 to 0.996, which indicates that the Weibull distribution can be used to describe the crack width distribution at various strain levels for UHP-SSC, at least for the materials used and the fiber content studied (0.5–1.5 vol.%). In the next section, the fitted Weibull distribution is used in the modeling for the evolution of crack width distribution with increasing tensile strain.
Fitting Weibull parameters of crack width distributions of UHP-SSC.
Probabilistic modeling of crack width with increasing tensile strain
As presented in Table 3, the Weibull scale parameter λ versus tensile strain ε relation (i.e. λ–ε relation) can be described using a linear fit. The correlation coefficient r of the linear fit ranges from 0.827 to 0.989, which indicates the λ–ε relation could be considered as a linear correlation. In Weibull distribution, there is a positive correlation between λ and crack width. It can be seen in Table 3 that the value of λ increases as the tensile strain increases, which means that the crack width of UHP-SSC increases with increasing tensile strain. In the following, the simplified linear relation between λ and ε (i.e. λ–ε relation in Table 3) will be used for probabilistic modeling.
The average value of Weibull shape parameters k (i.e. kavg) at different strain levels for each sample is listed in Table 3. In general, the variation of the k values at different strain levels is limited for each sample, except for a few data points. Here, for simplicity, the Weibull shape parameter k is assumed to be a constant (i.e. the average value kavg) for each sample. The effect of such a simplification on the modeling results will be discussed later.
By introducing the linear λ-ε relation and kavg into the Weibull CDF (equation (1)), the CDF of crack width w at a given tensile strain ε can be expressed as:
where a and b are the linear fit parameters of λ-ε relation in Table 3. For each sample, the crack width development can be described by equation (3) after giving the values of a, b, and kavg.
To validate the model, the correlation coefficient (rModel) between equation (3) and the cumulative distribution of the measured crack widths was calculated for each strain level of every tensile sample. In Figure 10, the rModel versus rWeibull (Weibull best-fit correlation coefficient in Table 3) relation is plotted and an equality line is also presented. It can be seen that in general, the values of rModel are very close to those of rWeibull in most cases, which indicates that the equation (3) can be used to describe the crack width distribution at different strain levels for UHP-SSC. Additionally, it is reasonable to treat the Weibull shape parameter k as a constant (kavg) for each tensile sample.

The model correlation coefficient (rModel) is close to the Weibull Best-fit correlation coefficient (rWeibull) in most cases.
For each sample in Table 3, the crack width distributions at different strain levels can be calculated after giving the values of a, b, and kavg in equation (3). The best-fit results (i.e. PDFBest-fit) and model results (i.e. PDFModel) of probability density curves for PE0.5%, PE1.0%, and PE1.5% are plotted in Figures 11 to 13, respectively. Besides, the crack width versus tensile strain relation (i.e. w–ε relation) at three different cumulative probabilities (i.e. 0%, 50%, and 95%) are also presented in Figures 11 to 13. In general, the model results show good agreement with the best-fit results, which also indicates that this method can successfully model the crack development of UHP-SSC. Furthermore, for a given crack width limit and cumulative probability, the proposed model can be used to estimate the allowed tensile strain of UHP-SSC in practical applications.

Best-fit and model results of crack-width distributions of PE0.5% show good agreement: (a) PE-0.5%-1; and (b) PE-0.5%-2.

Best-fit and model results of crack-width distributions of PE1.0% show good agreement: (a) PE-1.0%-1; (b) PE-1.0%-2; and (c) PE-1.0%-3.

Best-fit and model results of crack-width distributions of PE1.5% show good agreement: (a) PE-1.5%-1; (b) PE-1.5%-2; and (c) PE-1.5%-3.
Conclusion
This study investigates the effect of fiber content (0–1.5 vol.%) on the mechanical performance and cracking characteristics of ultra-high-performance seawater sea-sand concrete (UHP-SSC). According to the materials used and results obtained, the following conclusions can be drawn.
(1) Ductile UHP-SSC was developed, which showed tensile strain-hardening behavior and 28-day compressive strength over 130 MPa. With an increasing fiber content, both tensile strength and strain capacity significantly increased, while the compressive strength slightly decreased.
(2) The Weibull distribution was found to be suitable for describing the crack width distribution of UHP-SSC, at least for the mixes with 0.5–1.5 vol.% fibers.
(3) A probabilistic model was used to model the evolution of the crack width distribution of UHP-SSC at different strain levels. The model results showed good agreement with the experimental results, and it can be used to estimate the critical tensile strain of UHP-SSC in practical applications for a given crack width limit and cumulative probability.
These findings provide new insights into the future design of UHP-SSC in marine and coastal applications. Future research on the long-term performance of UHP-SSC is recommended.
Footnotes
Acknowledgements
Bo-Tao Huang acknowledges the support by The Hong Kong Polytechnic University Postdoctoral Fellowships Scheme (No.: YW4K). The authors would also express their appreciation to Dr. Yu Xiang, Mr. Ji-Xiang Zhu and Mr. Ke-Fan Weng at The Hong Kong Polytechnic University for their assistance in experiment.
Authors’ note
Jing Yu is currently affiliated with the School of Civil Engineering, Sun Yat-Sen University, Guangzhou 510275, PR China.
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was supported by the Hong Kong Research Grants Council (No.: T22-502/18-R).
