Ultra-high-performance concrete (UHPC) with adapted rheology continues to attract interest considering the requirement for novel processing techniques such as self-consolidating, pumping, spraying, and three-dimensional (3D) printing. The rheology of UHPC is complex due to its high solid volume fraction, low water content, and wide range of constituent materials that affect its flow properties. This work provides guidance for tailoring the mixture proportioning of UHPC to secure proper rheological properties and performance of UHPC for various applications. In the first part of this work, key physical, physicochemical, and chemical factors that can affect the rheological properties of UHPC are discussed. Rheological measurement methods and interpretation of the test results are provided to accurately determine the rheological parameters. The effects of constituent materials on the yield stress, viscosity, thixotropy, and structural build-up of UHPC are elaborated. The rheological parameters can increase by up to 100 times with the decrease in water-to-binder ratio. Such an increase can be reduced to less than 10 times through optimization of the particle size distribution and selection of superplasticizer. Rheology control strategies for UHPC for various applications are outlined. Multiple chemical admixtures with an organized molecular architecture must be used to achieve contradictory rheological requirements (e.g., low yield stress but high viscosity; low dynamic yield stress but high static yield stress). Finally, challenges and future demands to fine-tune the rheological properties of sustainable UHPC are showcased. Of special interest in future studies is the interaction between low-clinker binder and chemical admixtures and its effect on the microstructure of fresh UHPC.
Le Teng, Kamal H. Khayat, Jiaping Liu.
Recent Advances in the Rheological Properties of Ultra-High-Performance Concrete: A Critical Review.
Engineering, 2026, 61 (6) : 7-28 DOI:10.1016/j.eng.2025.04.011
Ultra-high-performance concrete (UHPC) is an advanced composite material with a high strength-to-weight ratio and outstanding durability [1]. Its compressive strength, tensile strength, and energy dissipation capacity can be 120-200 MPa, 5-15 MPa, and 55-95 kJ·m−3, respectively [2,3]. The permeability of chloride ions and oxygen can be 200 and 100 folds lower than that of conventional concrete, respectively [4]. Considering such superior performance, UHPC has been widely used in civil engineering including bridge constructions, high-rise buildings, airport runways, railways, stadiums, and offshore structures [1],[5], [6], [7], [8], [9].
Compared with mechanical performance and durability, less work has been conducted to tailor the rheological properties of UHPC to enhance the mixing and processing aspects. First, the higher flowability of UHPC is expected to facilitate casting, placement, and consolidation, which is not straightforward considering its very low water content and high solid volume fraction. The workability of UHPC can be enhanced by optimizing the particle size distribution (PSD) and using adequate chemical admixtures including superplasticizers [10,11]. For the PSD, two main questions should be concerned: ① How to change the PSD to minimize the negative effect of the low water-to-binder ratio (w/b) on the rheological properties, and ② to what extent the flowability can be improved by adjusting the PSD in low-w/b mixtures. The answers should be related to particle packing, which is directly affected by the physical properties of the binder composition and sand in use [12]. When a superplasticizer is used, the key question is how to secure its high dispersion efficiency in the binder materials. We can expect that the answer is closely related to its affinity with the particle surface, which can be considered the physicochemical effect [12,13].
The development of concrete construction technology increases the demand to tailor the viscosity in addition to the yield stress. For example, many cast-in-place structures necessitate a self-consolidating consistency for the ease of casting and filling of the formwork, especially those with congested reinforcement [14]. Viscosity adjustment is required in self-consolidating UHPC to avoid fiber segregation and enhance fiber alignment [15]. Tailoring the selection of constituent materials and mixture proportioning of UHPC to balance these contradictory properties is complex.
In time-dependent casting processes such as three-dimensional (3D) printing or shotcrete, a rapid change in rheological properties is required. For example, the yield stress of shotcrete should rapidly increase after spraying to resist sagging on sloped surfaces [16]. Similarly, the extrusion-based 3D printing concrete should have a low yield stress to secure the ease of extrusion and pumping but a high yield stress to enhance the shape stability and buildability during printing [17], [18], [19]. This contradiction introduces additional complications to the above questions, where the particle-flocculation-induced thixotropy (physical and physicochemical effects) and hydration-induced rigidification (chemical effect) must be considered [12,20]. In this process, it is widely accepted that the formation of early-age hydration products and consumption of superplasticizer due to the tricalcium aluminate (C3A) and tricalcium silicate (C3S) reaction can greatly affect the PSD and solid volume fraction of the fresh mixture, which can increase the yield stress and viscosity [12,21].
The main challenge to improve the rheological properties of UHPC is to elucidate the relationship between mixture design (i.e., constituent materials and mixture proportioning) and rheological parameters (i.e., yield stress, viscosity, thixotropy, and structural build-up). The rheological properties directly depend on the microstructure of the fresh material. This review begins with a discussion of recent analytical models to underline how the rheological properties can be characterized by physical, physicochemical, and chemical factors from a microstructural viewpoint. Evaluation methods to accurately determine the rheological properties are reviewed. In this frame, the effects of w/b, cementitious materials, sand, chemical admixtures, and fiber on the physical and chemical microstructural factors are discussed. Then, interconnections of these factors are analyzed to understand the influence of the same mixture design factor on different rheological parameters, which is essential to balance the contradictory rheological requirements in processing applications. Finally, the rheological properties of UHPC designated for various infrastructural constructions and rehabilitations and the corresponding tuning strategies are summarized.
2. Theoretical frame to analyze the rheological parameters in the microstructure view
Fresh UHPC is a solid suspension of sand and fiber in cement paste. The rheological properties of UHPC can be determined by the rheological characteristics of cement paste and the physical characteristics of sand and fiber when there are only physical interactions among cement paste, sand, and fiber. Therefore, this study first discusses the effect of key microstructural factors on the rheological properties of the paste phase. Then, the discussion is extended from the paste scale to the fiber composite of the UHPC scale.
2.1. Cement paste scale
2.1.1. Dynamic yield stress
The dynamic yield stress in the macroscopic flow initiation reflects the required finite energy to break the percolated network of interacting particles at the end of the mixing process [22,23]. The slump test is widely used to measure flow initiation. Bouvet et al. [24] established the relationship between slump flow and yield stress using numerical simulation. Considering the incompressible characteristic of concrete, the flow behavior is governed by the mass and momentum conservation equations, as shown in Eqs. (1), (2), respectively. The mass conservation law reflects that the concrete mass remains constant at any displacement for a system without the incorporation of additional matter. Consequently, the final flow radius (Rf) can be related to the initial radius (Ri), height of the cone (Hi), and final height (Hf) of the material (i.e., $R_{\mathrm{f}}^{2}=R_{\mathrm{i}}^{2} \frac{\mathrm{~d} H_{\mathrm{i}}}{\mathrm{~d} H_{\mathrm{f}}}$) for similar Ri and Hi values [25]. The momentum conservation states that the momentum change rate of the fluid in an elemental volume over time is equal to the sum of different forces on the components.
where ρ (kg·m−3) is the density of the cement paste, T (s) is time, ∇ is the Nabla operator, v (m·s−2) is the flow velocity, p (Pa) is the pressure, μ (Pa·s) is the viscosity, and g (m·s−2) is the gravity acceleration.
In the microscopic view, the formation of a percolated network is primarily governed by the attractive colloidal interaction and particle contact interaction [22,26,27]. The latter occurs when the solid volume fraction exceeds the percolation volume fraction, which holds for UHPC [28]. Van der Waals force becomes dominant in an attractive colloidal interaction when particles are near one another [26]. The primary factors that influence the contact interaction involve the particle packing density and particle contact number. Flatt and Bowen [29] quantitively identified the influence of key factors on the yield stress of the paste, as shown in the following equation:
$\tau_{\mathrm{c}} \cong m \cdot \frac{A_{0} a^{*}}{d_{50}^{2} H^{2}} \cdot \frac{\varphi^{2}\left(\varphi-\varphi_{0}\right)}{\varphi_{\mathrm{m}}\left(\varphi_{\mathrm{m}}-\varphi\right)}$
where τcp (Pa) is the dynamic yield stress of the cement paste, m is the PSD function, A0 (J) is the non-retarded Hamaker constant, a* (m) is the curvature radius of the contact point determined by the particle of cementitious materials, H (m) is the surface distance between particles, d50 (m) is the median diameter of particles, φ is the solid volume fraction, φ0 is the percolation volume fraction, and φm is the maximum packing density. The attractive colloidal interaction is inversely proportional to the power two of particle distance. The contact interaction of solid particles increases with decreasing particle size, decreasing packing density, or increasing solid volume fraction.
2.1.2. Residual viscosity
The residual viscosity reflects the energy dissipation in addition to the finite energy of the yield stress, which can be calculated using the following equation [30]:
where μapp (Pa·s) is the apparent viscosity, μcp (Pa·s) is the residual viscosity of the cement paste, τ0 (Pa) is the dynamic yield stress, and $\dot{\gamma}$ (s−1) is the shear rate. When cement-based materials exhibit a Bingham flow behavior, the residual viscosity becomes equal to the plastic viscosity.
The residual viscosity is governed by the hydrodynamic interactions, frictional contacts among particles, and particle inertia interaction [30,31]. The residual viscosity can be determined using the Krueger-Dougherty model, where the hydrodynamic interaction is related to the particle separation distance, and the frictional contacts correlate to the packing density and solid volume fraction of cement particles, as shown in the following equation [32]:
where μp (Pa·s) is the viscosity of the interstitial pore solution, M is a parameter related to the particle characteristics, and [η] is the intrinsic viscosity of the cement paste. The effect of inertia interaction is not considered at a relatively low shear rate due to its limited influence [30,31].
2.1.3. Structural build-up and thixotropy
The structural build-up of UHPC is reflected through the evolution of static yield stress with rest time. The colloidal flocculation and bridging effect of hydration products are the underlying mechanisms of the structural build-up [20]. As shown in Fig. 1, solid particles are well dispersed at the end of mixing. Once at rest, the colloidal interaction can cause particle flocculation, which rapidly increases the static yield stress in a short time (< 5 min). In the scale of hours, the hydration products (e.g., ettringite and metastable calcium silicate hydrate (C-S-H)) can gradually bridge adjacent particles to further increase the particle connections [33]. The particle flocculation and early-age bridging can be broken down after applying adequate shear energy, which makes the fresh material exhibit a thixotropic behavior [34]. The Fa and Fb correspond to the strong and weak bridging forces of early-age hydration products, respectively. Further increases in the amount of hydration products with time can result in inter-particle connections (rigidification), where further mixing of the plastic material cannot reverse the increase in static yield stress [33,35].
Lecompte and Perrot [36] proposed a theoretical frame to determine the static yield stress (τs) at a given rest time, as shown in Eq. (6). The hydration-induced bridging effect was characterized using the increase in solid volume fraction over time (t). Lowke [37] established the theoretical mode of thixotropy, which is defined by the particle flocculation rate, where the surface coverage ratio (θ) referring to the particle surface separation, and the solid volume fraction and particle packing are considered, as presented in Eq. (7). The φm value is usually considered a constant value in these two equations, possibly due to the limited effect of ettringite particles on the cement PSD, because ettringite has a greatly smaller particle size than cement [38]. However, silica fume, which is widely used in UHPC, also has a smaller particle size than cement. Therefore, it is an open question whether φm remains constant or greatly changes with time.
where x indicates the hydrated cement volume, α(t) is the hydration degree, trest (s) is the rest time, Athix (Pa·s−1) is the rate of particle flocculation, and C1 and C2 are constants fitted using experimental results.
2.1.4. Key factors to influence the rheological property
According to the proposed theoretical frame, the dynamic yield stress and residual viscosity can be considered a product of a function of the separation distance and a function of the solid volume fraction and particle packing [27,39,40]. The colloidal interaction closely correlates to the physicochemical-related surface force, which is dominated by the particle surface distance. The increased particle surface distance has a higher effect on reducing the dynamic yield stress than the residual viscosity due to the inverse proportion to the second power.
The solid volume fraction and particle packing are physical factors. The former is directly influenced by w/b, whereas the latter is an intrinsic property determined by the physical characteristics of constituent solid materials. In general, the increased solid volume fraction and reduced particle packing have a greater effect on increasing dynamic yield stress than the residual viscosity [32]. In addition, the viscosity of an interstitial pore solution can only influence the residual viscosity of the paste.
The key physical and physicochemical factors influencing thixotropy are similar to those of the dynamic yield stress. The increased particle surface distance, increased particle packing, and decreased solid volume fraction can decrease the thixotropy. In the case of structural build-up, the chemical influence induced by early-age hydration kinetics should be considered. Ettringite can rapidly form after the first contact between cementitious materials and water [41]. The formation of ettringite with a high specific surface area can reduce the adsorption of superplasticizer molecules onto the cementitious materials and free superplasticizer molecules in pore solution, which decreases the particle surface distance. The hydrates can also increase the solid volume fraction and change the particle packing density. However, the variation of particle packing with time is not considered in Eq. (6).
2.2. From paste to UHPC
The addition of fine aggregate and fiber to the cement paste can be considered incorporating non-colloidal and non-Brownian solid particles into the yield stress fluid. The reason is that the cementitious material particle can be ignored because its particle size is 100-1000 times lower than that of fine aggregate and fiber [28,42]. In most cases, there is no or very weak chemical interaction among cement paste, aggregate, and fiber. Therefore, the volume fraction, size, and shape of fine aggregate and fiber are key factors that affect the dynamic yield stress and residual viscosity of UHPC of a given cement paste [43], [44], [45], as elaborated in 4.3 Aggregate, 4.4 Fibers.
The ratio of the static yield stress of UHPC to that of cement paste should be equal to the ratio of the dynamic yield stress of UHPC to that of cement paste when there is no specific chemical interaction among cement paste, aggregate, and fiber [28,44]. Once the effect of fine aggregate and fiber on the dynamic yield stress has been determined, the structural build-up of UHPC can be predicted by the structural build-up of the paste phase [28,44]. The theoretical framework to estimate the thixotropy of cement paste, as shown in Eq. (7), can be applied to calculate the thixotropy of the composite material of the UHPC. The influence of fine aggregate and fiber on the solid volume fraction should be considered in addition to the cementitious materials [37].
3. Rheological characterization of UHPC
3.1. Dynamic yield stress and residual viscosity
Dynamic yield stress and residual viscosity can be determined using the flow curve [46]. The accurate measurement associated with the interpretation of the flow curve is not easy because some artifacts can be involved during testing. Pre-shearing is applied with an adequate duration to break flocculated particles before measuring the flow curve. As shown in Fig. 2(a), two protocols are widely used: ① The pre-shear rate is maintained at the maximum shear rate set for the flow curve measurement [47,48], and ② the pre-shear rate gradually increases to the maximum shear rate [49,50]. Ley-Hernández and Feys [51] and Ley-Hernández et al. [52] indicated that the second pre-shearing protocol might cause shear-induced structure formation in some cases, which can overestimate the yield stress and residual viscosity. The pre-shearing should be stopped when the material reaches an equilibrium state to reduce the risk of particle migration. The optimal pre-shearing duration can vary with the materials. A period of approximately 30 s is recommended for self-consolidating UHPC [15,34,53]. Thiedeitz et al. [46] proposed that the increased solid volume fraction and decreased superplasticizer content required a longer pre-shearing duration for particle deflocculation.
The stepwise or straightforward decrease in shear rate was applied to measure the flow curve immediately after pre-shearing, as plotted in Fig. 2(a). In general, the stepwise reduction can provide more accurate results because the equilibrium torque measured at each stage is used to determine the shear stress, which can prevent the erroneous result of shear thickening [54]. For self-consolidating UHPC, steel fibers can migrate toward the outer cylinder where the shear rate is low, which can underestimate the rheological properties of UHPC [55], as deduced by comparing the white circles and black squares in Fig. 2(b) [56]. To decrease the risk of particle migration, the shear rate and period for the pre-shearing should be reduced. For stiff UHPC, a plug flow, which reflects that part of the material is not sheared, can occur during the measurement and aggravate the shear-thickening behavior, as Fig. 2(b) [56] shows by comparing the black squares and triangles. Such measurement artifacts can be eliminated using the plug radius to substitute the outer radius or using an interactive procedure based on the matching correction of the yield stress and shear radius [54,57].
Depending on the mixture composition and constituent materials, UHPC can exhibit a Bingham flow behavior at a relatively low shear rate and a shear-thickening nonlinear flow behavior in other cases. Fig. 3(a) [53] shows examples of the flow curves of self-consolidating UHPC with silica fume (0%, 5%, 10%, 15%, 20%, and 25%) and 2% steel fibers, and exhibited a shear-thickening behavior, especially when the cement replacement mass ratio of silica fume was lower than 15%. For UHPC with nanoclay (0%-2%) and 2% steel fiber in 3D printing, which has a relatively high yield stress, the shear-thinning behavior can be observed, as shown in Fig. 3(b) [58].
UHPC can be considered a dense non-Brownian suspension due to the high solid volume fraction [59]. The rheological flow curve of such suspension has three different shear rate-dependent stages, namely shear thinning at a low shear rate followed by a Bingham fluid behavior at an intermediate shear rate and shear thickening at a high shear rate [59,60]. Shear thinning is caused by the shear-induced ordering of particles [60]. In this stage, cement particles do not have direct contact with one another because there is a repulsive layer barrier around the particles (steric interaction). For stiff UHPC, the distance between cement particles is limited due to the use of a relatively low superplasticizer dosage. This distance can increase after applying additional shear stress, which can reduce the effective volume fraction of solid particles to decrease the apparent viscosity [59,60]. For self-consolidating UHPC, the incorporation of a high superplasticizer dosage secures the highly dispersed cement particles, which can limit the effect of the applied shear stress on the dispersion of cement particles [61]. Therefore, the self-consolidating UHPC is less likely to exhibit a shear-thinning behavior in the measurement.
The underlying mechanism of the shear-thickening behavior is the formation of a transient cluster of cement particles when the applied shear stress (also known as hydrodynamic force) overcomes the repulsive stress between cement particles [31,62,63]. The applied shear stress that enables the direct contact of cement particles is defined as the critical shear stress, which can be reduced by improving the particle dispersion [64,65]. The self-consolidating UHPC exhibits a greater dispersion of cement particles than the stiff UHPC due to the use of a higher superplasticizer dosage. Brown et al. [66] proposed an alternative possible mechanism that a high yield stress could hide the shear-thickening behavior. As a result, the self-consolidating UHPC is more likely to show a shear-thickening behavior than the stiff UHPC. Wu et al. [53] proposed that the increase in silica fume content in replacement of cement in UHPC with a 0.18 water-to-cement ratio (w/c) could reduce the intensity of shear thickening. The reason may be that the use of fine particles (e.g., silica fume) can increase the critical shear stress of the UHPC system because the increase in particle packing can decrease the strength of the flocculated structure of fresh UHPC [64,67].
Table 1 summarizes the flow modes to determine the dynamic yield stress and residual viscosity of these UHPC mixtures [68,69]. The Bingham model has a lower sensitivity to small measurement errors compared with the Herschel-Bulkley (H-B) and modified Bingham (M-B) models, which should be considered first to describe the rheological behavior of UHPC. H-B and M-B models are used to characterize the flow curve when the nonlinear behavior cannot be ignored.
Fig. 4 [53], [58] compares the dynamic yield stress determined using these two models. For the shear-thickening behavior, the M-B model can obtain a lower dynamic yield stress than the H-B model, and their difference increases with the increase in the intensity of shear thickening. This result is consistent with the findings in Refs. [69,70], where the H-B model can overestimate the yield stress when the fresh material is not under extreme shear thickening (n < 2). The yield stress determined using the M-B model is closer to that estimated using the mini-slump flow test than that obtained using the H-B model. Therefore, the M-B model is more appropriate to characterize the shear-thickening behavior of UHPC. In the case of the shear-thinning behavior, the M-B model obtains a greater yield stress than the H-B model. However, which model can obtain a more accurate result remains unclear because the yield stress cannot be determined using a mini-slump flow test for the non-flowable material. The increase in the intensity of shear thinning can increase the difference between dynamic yield stress determined using these two models compared with the increase in the intensity of shear thickening at the same level.
3.2. Structural build-up and thixotropy
The structural build-up of UHPC can be characterized by the evolution of static yield stress with rest time. The shear rate controlled method is widely applied to determine the static yield stress, where a low constant shear rate of 0.001-0.050 s−1 is used for cement paste [71], [72], [73] and 0.01-0.10 s−1 for UHPC [47,58,74]. The shear stress linearly increased and subsequently gradually reduced to equilibrium, and the peak value is the static yield stress, as plotted in Fig. 5(a) [47]. The increase in shear rate can decrease the static yield stress in the measurement [75]. Theoretically, the shear rate should be minimized, but using a very low shear rate may not accurately determine static yield stress due to continuous structuration [75].
Roussel et al. [20] proposed a model to show that the static yield stress linearly increased with time for cement-based materials, where the hydration rate could be considered a constant value in the dormant period. Perrot et al. [76] extended this model by considering the cement hydration process in the acceleration period to describe the quick increase in static yield stress. Previous studies [55],[77], [78], [79] on UHPC showed that the static yield stress quickly increased at a very early age (i.e., within 5 min) due to the particle flocculation and a subsequent linear increase over rest time during the first hour after the end of mixing, as presented in Fig. 5(b) [58]. Teng et al. [77] added a parameter of τfloc (the rapid growth of static yield stress at an early age, Pa) to describe the particle-flocculation-induced yield stress increment, as presented in Table 2 [20], [76], [77].
Thixotropy that refers to the reversible component of structural build-up can be determined by the variation of the discrepancy between static and dynamic yield stress, breakdown area, and hysteretic loop area with rest time. In the case of measurement of the structural breakdown area, four different constant shear rates of 0.5-3.0 s−1 are recommended to shear the material after rest [80], [81], [82]. The structural breakdown area is determined by the area enveloped by the curve consisting of peak and equilibrium shear stresses at various shear rates, as indicated in Eq. (8). Tuyan et al. [82] showed that the structural breakdown area (Abd; J·m−3) was more appropriate to assess the thixotropy of concrete with a relatively high yield stress based on the correlation between thixotropy and formwork pressure:
where τp(N) (Pa) is the maximum yield stress at different shear rates; τe(N) (Pa) is the equilibrium static yield stress at different shear rates; N is the normalized shear rate; $\dot{\gamma}_{\max }$ (s−1) is the maximum shear rate; and $\dot{\gamma}_{\min }$ (s−1) is the minimum shear rate.
The test procedure to determine the hysteresis loop involves the increase in shear rate to a certain value followed by reducing the shear rate to zero with no pre-shearing [49,83]. The maximum shear rates are 25-100 s−1 for cement paste [49,83] and 1-5 s−1 for concrete [81,84]. The enclosed area between ascending and descending curves is defined as the hysteresis loop, as presented in the following equation:
where Ahl (J·m−3) is the hysteresis loop area; τa(N) (Pa) and τd(N) (Pa) are the shear stress in ascending and descending curves, respectively. The main artifact of this test is the plug flow, especially for UHPC with high yield stress due to the lack of pre-shearing [54].
4. Influence of constituents on the rheological properties of UHPC
4.1. Water-to-binder ratio
The typical w/b of UHPC is 0.14-0.24 [1]. Increasing w/b can decrease the yield stress and residual viscosity because the decrease in solid volume fraction decreases the crowding effect and contact among solid particles [85,86]. The yield stress can significantly increase when w/b is lower than a critical value possibly because the solid volume fraction approaches the divergent particle packing [23]. For example, Wang et al. [85] noted that the yield stress increased from 245 to 1610 Pa when w/b decreased from 0.20 to 0.18 for UHPC with 1.6% superplasticizer, whereas such value only increased from 30 to 245 Pa with the decrease in w/b from 0.24 to 0.20, as presented in Fig. 6(a) [85]. Furthermore, the incorporation of superplasticizer can reduce the critical value of w/b. Therefore, the effect of w/b on the yield stress depends on the surface coverage of the superplasticizer. However, few studies focused on the effect of the molecular structure of the superplasticizer on the critical value of w/b. It can be assumed that the increase in adsorption layer thickness can further reduce the critical w/b value at the saturated surface coverage, which is worth investigating in a future study. Fig. 6(b) [85] indicates that the decrease in w/b from 0.24 to 0.18 increased the residual viscosity from 10 to 25 Pa·s, which demonstrates that the yield stress is more sensitive to variations of solid volume fraction than the viscosity.
The structural build-up and thixotropy increase with the decrease in w/b. Ma et al. [86] noted that the hysteresis loop area increased by 35% when w/b decreased from 0.22 to 0.18. Navarrete et al. [33] attributed this result to the increased solid volume fraction instead of the higher bridging effect of early-age hydration products due to slight variations in the growth rate of cement particles. Decreasing w/b necessitates a greater demand for superplasticizers, which can hinder structural build-up at rest, as elaborated in Section 4.5.1.
4.2. Cementitious materials
4.2.1. Cement
Theoretically, the packing density only depends on the PSD and particle morphology. The improvement of the cement PSD can decrease the yield stress and viscosity. For example, Chen and Kwan [87] reported that using fine cement particles measuring 3.1 μm in d50 to replace 20% of the cement particles with d50 of 12.4 μm reduced the yield stress by 40% for cement paste with 0.22 w/b. Dils et al. [88] investigated the influence of the cement particle fineness on the rheological properties of cement paste. The results showed that the decrease in d50 from 18.6 to 13.1 μm decreased the yield stress by 10% due to the increase in particle packing. However, further reduction of d50 of cement particles from 13.1 to 9.9 μm increased the dynamic yield stress from 2.5 to 11 Pa, respectively. The possible reasons are as follows: ① The incorporation of fine particles at a high volume can push apart the large particles to cause the loosening effect, which results in a lower particle packing density; ② the high specific surface area of fine particles can increase the superplasticizer consumption to decrease the particle surface distance. The finding in Ref. [88] also showed that the variation of cement fineness had a higher effect on the dynamic yield stress than the residual viscosity.
From the physical and physicochemical viewpoint, the cement fineness has a similar effect on the static yield stress compared to the dynamic yield stress. From the chemical viewpoint, the decreased fineness can positively influence the hydration-induced bridging effect because more nucleation sites can lead to a higher structural build-up. Moreover, incorporating cement with a higher C3A content is more effective in enhancing the structural build-up due to the rapid formation of the ettringite network [89].
4.2.2. Supplementary cementitious materials
Incorporating the supplementary cementitious materials (SCMs) has a marked effect on the rheological properties of UHPC [90]. The silica fume measuring 0.1-0.3 μm in d50 is the most common SCM to achieve the great mechanical performance of UHPC. The dispersion of silica fume can greatly affect the rheological properties of UHPC. Mao et al. [91] reported that the use of high densified silica fume with d50 of 100 μm resulted in higher yield stress and viscosity, whereas the yield stress and viscosity first decreased and subsequently increased with increasing content of moderate densified or raw silica fume. The latter phenomenon is consistent with the experimental results in Ref. [92], where for cement paste with 0.19 w/b, increasing the silica fume content from 0 to 15% by mass of binder decreased the yield stress from 4.3 to 0.1 Pa. However, the dynamic yield stress increased to 64.8 Pa when the silica fume content further increased from 15% to 35% [92]. The finding in Ref. [93] also showed that using silica fume to replace 15% cement by mass led to the lowest flowability of UHPC. The widely used SCMs include fly ash and ground granulated blast furnace slag with d50 of 5-30 μm, which is in the same order as cement particles. Mehdipour and Khayat [94] proposed that the use of 40%-50% fly ash or ground granulated blast furnace slag to replace cement led to a higher packing density of 0.67-0.73 than the mixture without SCM (packing density: 0.58), which reduced the superplasticizer demand by 40%. Furthermore, fly ash with a spherical shape can provide the “ball bearing effect,” which is more effective in increasing the packing density and decreasing the dynamic yield stress and plastic viscosity than the ground granulated blast furnace slag with an irregular shape. Arunothayan et al. [58] showed that the dynamic yield stress of UHPC made with 0.16 w/b was 31 Pa when fly ash was used to substitute for 60% cement; such value was 138 Pa when the same content of ground granulated blast furnace slag was used to replace cement. Enhancing particle packing using SCM can also decrease the residual viscosity. However, the decreasing amplitude is in the order of one, which is less pronounced than the yield stress with the change in the order of 10 [58,92,95]. Thus, the packing density has a higher effect on the yield stress than the residual viscosity.
In theory, the PSD is a physical factor that affects the packing density of cementitious materials. However, the PSD can affect the packing density in both physical and physicochemical aspects because the variation of cementitious material size can change the specific surface area to affect the adsorption of superplasticizer molecules [96]. Mehdipour and Khayat [97] established correlations among the specific surface area, packing density, and PSD, as presented in Fig. 7. The PSD was described using the modified Andreasen and Andersen model, as written in the following equation, where the q value referred to a higher content of fine particles and a wider PSD:
where Di (μm) is the particle size of the ith size class; PDi is the volume fraction with a particle size lower than Di; and Dmax and Dmin (μm) are the maximum and minimum particle sizes, respectively. The results showed that the decrease in q from 0.28 to 0.22 or the increase in specific surface area (SSA) from 425 to 1600 m2·kg−1 enhanced the packing density because the voids among large particles could be filled by fine particles [97]. However, the packing density decreased with a further decrease in q value or an increase in specific surface area due to the loosening effect and lower superplasticizer adsorption coverage [98,99]. Yin et al. [100] proposed a physicochemical packing method by considering the cement hydration process. More studies can focus on the influence of the pozzolanic reaction of SCMs on the physicochemical packing density.
Based on the above discussion, the yield stress and viscosity of cement paste can be reduced by 1-10 times by improving the packing density of cementitious materials. To obtain a high packing density, a q value of 0.21-0.235 for cement paste is recommended. Furthermore, the suggested replacement ratio of SCMs with d50 less than 5 μm is lower than 15%. This ratio can increase to 60% when SCMs with d50 of 10-30 μm are incorporated.
The influence of SCM on the structural build-up depends on the early-age hydration process in addition to the particle packing density. For fly ash and ground granulated blast furnace slag with a relatively low chemical reactivity, Navarrete et al. [33] reported that the packing density played a dominant role in the structural build-up. Arunothayan et al. [101] stated that the structural build-up of UHPC decreased by 15% when 60% of cement was replaced with ground granulated blast furnace slag by mass. Such decrease was 80% when the cement replacement mass ratio was 60% with the use of fly ash. The inferior influence of ground granulated blast furnace slag on reducing the structural build-up compared with fly ash can be attributed to its irregular shape and higher pozzolanic activity. In the case of silica fume, Yuan et al. [73] noted that the structural build-up was enhanced by 85% with the use of 5% silica fume due to the promotion of cement hydration at an early age. However, Huang et al. [102] reported that increasing the silica fume content from 0 to 1% by mass of binder reduced the structural build-up by 15% when the paste was tested at 10 °C. This result can be attributed to the fact that the influence of silica fume on increasing the particle packing density plays a dominant role in the structural build-up at rest, especially due to the reduced kinetics of cement hydration at an early age at a low temperature, where silica fume can promote cement hydration.
4.2.3. Fillers
The inert filler in micro-scale can be incorporated to increase the particle packing density and resulting decreased residual viscosity and yield stress. The common fillers include quartz and limestone powders that measure 5-30 μm in d50 [103,104]. The incorporation of 20% limestone can reduce the yield stress and viscosity by 25% and 15%, respectively [105]. Reducing the fineness of limestone powder can weaken its effect on decreasing the yield stress and viscosity, as shown in Fig. 8 [105], because using the coarse filler can reduce the loosening effect and Van der Waal force in the cement suspensions, which can also increase the yield stress. Furthermore, the loosening effect of the nano-scale filler is more pronounced compared with micro particles, which can greatly increase the yield stress and residual viscosity. For example, Teng et al. [77] reported that incorporating 0.4% nanoclay increased the yield stress from 40 to 175 Pa. Wu et al. [106] stated that the mini-slump flow of UHPC made with 6.4% nano-CaCO3 was 160 mm, which was lower than 220 mm for UHPC prepared without nanomaterial.
Incorporating an inert micro filler such as limestone powder can reduce the structural build-up due to the increased particle packing and decreased cement hydration at an early age. For example, Zhang et al. [107] reported that the structural build-up decreased by 65% when 40% limestone powder measuring 15 μm in diameter replaced the cement by mass. The use of nanomaterial as filler can provide a seeding effect to enhance the cement hydration process at an early age. Furthermore, some nanomaterials such as nanoclay can provide electrostatic attraction, which can exert positive effect on particle flocculation. For example, Teng et al. [77] reported that the addition of 0.4% nanoclay caused a 135% increase in the structural build-up within 5 min and a 250% enhancement in increasing the rate of static yield stress over time.
4.3. Aggregate
Proprietary UHPC uses quartz sand that is 150-600 μm in diameter [1]. Considering the high cost of quartz sand, many researchers developed non-proprietary UHPC using conventional concrete sand with a maximum diameter of 4.75 mm, including masonry sand, river sand, manufactured sand, lightweight sand, and recycled sand. The rheological properties of UHPC are affected by fine aggregate because it accounts for 20%-60% of the total volume of UHPC [1,108], and it is 10-103 larger than cementitious materials. The yield stress and viscosity of mortar mixture can be influenced by the solid volume fraction and packing density of fine aggregate for a given paste, as shown in Eqs. (11) [40,109] and (12) [110,111], respectively.
where τm (Pa) is the yield stress of mortar, φa is the solid volume fraction of fine aggregate, φam is the packing density of fine aggregate, η is the ratio of the divergence and maximum packing fraction, μm (Pa·s) is the plastic viscosity of mortar, and qam is a parameter related to φam.
The yield stress is reduced by increasing the packing density of fine aggregate, which depends on the PSD and morphology of the sand. Tai et al. [112] proposed that a combination of 70% sand A with particle sizes of 80-200 μm and 30% sand B with particle sizes of 400-800 μm could provide an optimal packing density. Such a sand combination resulted in a mini-slump flow of 270 mm compared with 230 mm for UHPC made with 80% sand A and 20% sand B.
The optimal PSD of fine aggregate can be determined using a modified Andreasen and Andersen model, as shown in Eq. (10) [113]. Meng et al. [113] proposed that the proper gradation of sand with a maximum particle size of 4.75 mm could be achieved by setting the q value to be 0.23. Many studies [83,96,114] noted that the optimal sand gradation also depended on the PSD of cementitious materials. Liu et al. [115] established the relationship among packing density, maximum sand size, and q value for UHPC mixtures, as shown in Fig. 9. The optimal value of maximum sand size increased from 1.25 to 6.61 mm when q increased from 0.17 to 0.25.
The morphology of fine aggregate can be characterized by the aspect ratio, circularity, and convexity [116]. Hafid et al. [117] noted that the aspect ratio was the dominant morphological parameter to influence the particle packing density and rheological properties of concrete. As shown in Fig. 10(a) [117], the increase in aspect ratio from 1.5 to 2.2 led to an approximately 0.1 decrease in the packing density of fine aggregate, which can increase the yield stress by an order of 10. This finding elucidates the results that the addition of manufactured and recycled sands with a higher aspect ratio reduces the flowability and enhances the yield stress and viscosity of UHPC compared with the river sand [118,119]. Furthermore, the decrease in the aspect ratio of fine aggregate can reduce the effect of the solid volume fraction on the yield stress, as shown in Fig. 10(b) [117].
The increased fine aggregate volume can enhance the yield stress and residual viscosity of the suspending mortar considering the increased solid volume fraction, as shown in Fig. 11 [40,117]. The critical value of sand volume fraction is 30%-40%, below which the yield stress and residual viscosity can moderately increase with φa. Beyond the critical φa value, a significant growth in yield stress and viscosity can occur because the frictional contacts and interlocking effect of fine aggregate become dominant due to the decrease in paste film thickness when the solid volume fraction approaches the divergent volume fraction (0.8φam) [109,120]. For UHPC with a constant solid volume fraction of cementitious materials and sand, the increase in sand volume fraction can decrease the yield stress and viscosity. For example, Meng et al. [113] reported that the increase in binder-to-sand ratio from 0.7 to 1.3 (i.e., a decrease in sand volume fraction from 0.47 to 0.33) increased the superplasticizer demand from 0.18% to 0.3%, for self-consolidating UHPC.
In addition to the PSD and morphology of fine aggregate, water absorption plays a great role in the rheological properties of UHPC. Porous lightweight sand with 15%-25% water absorption can be incorporated for internal curing to reduce autogenous shrinkage and enhance the mechanical performance of UHPC [121,122]. Using lightweight sand to replace 25% of normal-density river sand decreased the yield stress by 30% and the plastic viscosity by 20% for UHPC with 0.17 w/b [123]. This result can be attributed to the lubrication effect, where part of pre-absorbed water can break away from lightweight sand during mixing [121,124].
In general, the yield stress and viscosity can be reduced by 1-10 times with the adjustment of size distribution, morphology, and volume fraction of sand when the sand volume fraction is higher than 30%. The lower maximum sand size of 1.00-4.75 mm and the q value of all solid particles (i.e., cementitious materials, filler, and sand) of 0.17-0.25 are suggested with the decreased fineness of cementitious materials and fillers and increased binder-to-sand ratio. When the sand volume fraction is less than 30%, the change in sand characteristics has a limited effect on the yield stress and viscosity of UHPC.
The fine aggregate has a similar effect on increasing the static yield stress to the dynamic yield stress if there is no chemical reaction between cement and fine aggregate [44]. The structural build-up of UHPC can be determined by the product of the structural build-up of the paste phase and the function of the fine aggregate volume fraction, as presented in the following equation [44]:
where Asb.m and Asb.cp (Pa·s−1) are the structural build-up rate of mortar and paste phases of UHPC, respectively. Some special aggregates can chemically interact with cement paste. For example, De Vlieger [125] showed that the structural build-up rate increased by 85% when 50% natural sand was replaced by recycled sand by volume. The reason can be that the non-hydrated cement particles on the recycled sand surface can enhance cement hydration in addition to the irregular shape and high water absorption of the recycled sand.
4.4. Fibers
4.4.1. Rigid fibers
Rigid steel and flexible polyethylene fibers can be used to enhance the tensile strength and toughness of UHPC [3],[126], [127], [128]. In the case of rigid steel fiber, the mini-slump flow can decrease from 220 to 100 mm with an increase in fiber volume from 1% to 3% due to the reduced packing density caused by the wedging effect, wall effect, loosening effect, and connecting effect and internal friction of the fiber [129]. Martinie et al. [130] showed that the influence of rigid steel fiber on the yield stress of UHPC (τuhpc) could be quantified using Eq. (14), where the relative packing density of the fiber could be correlated to the fiber volume fraction and aspect ratio, as expressed in Eq. (15):
where Pf refers to the total volume fraction of the fiber and aggregate, r is the aspect ratio of the rigid fiber (ratio of length to diameter), and φf is the fiber volume fraction.
Fig. 12 [130] presents the relationship between relative yield stress and relative packing density of fiber. A critical relative packing density of 0.6 was observed, beyond which the effect of rigid fibers on the relative yield stress became significant. For conventional steel fibers with an aspect ratio of 65 (13/0.2), the critical fiber volume content is approximately 3.5%. Fan et al. [131] showed that the packing density of UHPC decreased from 0.795 to 0.765 with the change in fiber shape from straight to hooked-end for UHPC with 3% steel fiber and a constant aspect ratio of 65. Therefore, the fiber shape is a key parameter that affects the relative packing density of fibers. However, such a parameter is not considered in Eq. (15), which may explain the scattered results for relative packing fraction values of 0.6-0.8 [130]. Du et al. [132] showed that the flowability decreased from 195 to 155 mm with the increase in surface roughness for cement paste made with 3% steel fiber. However, the effect of the surface roughness is not considered in Eqs. (14), (15). Therefore, a parameter related to the fiber surface roughness must be introduced into the term of Pf to improve the prediction accuracy of the yield stress of fiber-reinforced UHPC, which can be a future study topic.
For straight steel fibers with an aspect ratio of 65, Khayat et al. [133] reported that the increase in fiber content from 0 to 3.25% increased the plastic viscosity of UHPC from 7 to 22 Pa·s. Jia et al. [134] found that the effect of the fiber shape on the viscosity of UHPC was limited when the fiber content was lower than 1.5%. In general, the effect of rigid fiber on the viscosity is less known than the yield stress because the yield stress is easier to measure using the simple spread test. The co-axial rheometer with a relatively high gap distance between the vane and wall of the testing bowl can be used to determine the residual viscosity of fiber-reinforced UHPC [130]. Using this rheometer, the following possible artifacts should be carefully considered: ① plug flow induced by the fiber agglomeration; ② flow-induced fiber alignment. After accurately measuring the viscosity, one can investigate the influence of rigid fiber characteristics on the residual viscosity of flowable and stiff UHPC. Furthermore, the correlation between the viscosity of cement paste and the viscosity of the fiber-reinforced UHPC matrix must be established.
4.4.2. Flexible fibers
Flexible synthetic fibers can be used to reduce shrinkage and enhance the toughness of UHPC. However, they commonly have a greater influence on reducing the flowability than rigid fibers due to their high aspect ratio [135], [136], [137], [138]. The main difference in effect between rigid and flexible fibers on the rheological properties of UHPC is that flexible fibers can deform in the mortar phase, which affects the packing density of UHPC in addition to the fiber volume and morphology. Sultangaliyeva et al. [139] showed that the deformation of flexible fibers could be characterized using the average effective length (Leff). Leff can be influenced by the elastic modulus (Ef), diameter (D), and length (L) of fiber and the yield stress of UHPC, as expressed in the following equation:
The authors of Ref. [139] proposed a physical model to determine the fiber-induced yield stress amplification based on the relative packing density of deformed flexible fibers:
The effect of fibers on the yield stress can be mitigated by increasing the yield stress of the suspending mortar and decreasing the aspect ratio and elastic modulus of the selected fiber. The critical relative packing density that can greatly influence the yield stress of UHPC is approximately 0.15 for flexible fiber, which indicates that the effect of synthetic fibers becomes significant when this threshold value is exceeded. For flexible fibers with an aspect ratio of 750 (18/0.024), which are widely used in ductile UHPC, the critical fiber volume is approximately 1% when the mortar phase of UHPC has a self-consolidating consistency. In addition to the physical interaction between fiber-to-fiber and fiber-to-matrix, some studies [135,136] noted that the use of synthetic fibers could adsorb some of the superplasticizer molecules, so the flowability decreased, especially if the fibers had high contents of hydrophilic groups.
The incorporation of synthetic fibers can increase the residual viscosity of UHPC [140,141]. Meng and Khayat [141] reported that for UHPC with a mini-slump flow of (280 ± 10) mm, the residual viscosity increased from 45 to 55 Pa·s when 0.5% straight steel fibers with an aspect ratio of 65 were replaced by polyvinyl alcohol fibers with an aspect ratio of 210 (8/0.038). This increase can be due to the higher aspect ratio that can increase the frictional contact between fiber and solid particles. Similar to the rigid fiber, there is no analytical model to determine the effect of synthetic fibers on the viscosity. Further investigations can be developed based on the relative packing density of deformed fibers to fill this knowledge gap.
4.4.3. Effect of fiber on the thixotropy and structural build-up
When there is only a physical interaction between cement paste and fibers, it is sufficient to use the structural build-up of the paste phase of UHPC to predict the structural build-up of fiber-reinforced UHPC because the static yield stress and dynamic yield stress have the same dependence on the volume fraction and packing density of the fibers [39]. Some researchers coated a nanomaterial onto the fiber surface to enhance the fiber-matrix interface [132,142]. The seeding influence of nanomaterial can accelerate cement hydration at an early age and lead to greater structural build-up. Further investigation is required to address this aspect.
4.5. Chemical admixtures
4.5.1. Superplasticizer
A superplasticizer such as polycarboxylate ether superplasticizer (PCE) is a key chemical admixture required to secure the proper flowability of UHPC [11]. The conventional PCE has a comb shape with a negatively charged backbone and non-ionic side chains, which can provide electrostatic repulsion and steric hindrance, respectively [143,144]. Such interactions can decrease the colloidal attractive interaction by increasing the particle surface distance, which decreases the yield stress and viscosity of UHPC, as shown in Fig. 13(a) [145]. Previous studies proposed that the average particle surface distance (H) could be quantified using the surface coverage (θ) and average layer thickness of adsorbed PCE (Hp), as shown in the following equation:
where H0 (nm) is the particle surface distance for the paste prepared without PCE. In general, increasing θ and Hp values can increase the distance between cement particles [23,30].
Sha et al. [146] stated that the first-order factor to affect the particle surface separation distance was the surface coverage in most practical situations, which was proportional to the adsorbed PCE amount for a given binder composition and content. As shown in Fig. 13(b) [147], the adsorbed PCE amount rapidly increased with the increase in PCE dosage when a low dosage of PCE was incorporated. Once the adsorbed PCE amount reached approximately 1.5-2.0 mg·gcement−1, a further increase in PCE dosage could have a limited effect on its adsorption because all particle surfaces were occupied by the PCE monolayer [147]. Thus, the influence of PCE on the rheological properties of UHPC depends on the layer thickness of PCE after the surface becomes saturated, which causes a limited change in yield stress, as shown in Fig. 13(a) [145].
The molecular architecture of PCE necessitates a meticulous design to enhance the binder particle dispersion. The structure of PCE varies with the length and stiffness of the backbone; the length, stiffness, and density of the side chain; and the type and density of the anchoring groups [143,148,149]. In the case of the backbone, the longer length can increase the adsorption affinity of PCE, whereas a lower stiffness is preferred to increase the layer thickness of PCE [150,151]. A relatively long and dense side chain is more appropriate due to the increased PCE steric hindrance [152,153]. However, an optimal value exists because the anchoring group can be shielded when the side chain of PCE is too long and dense [152,153].
The most common anchoring group in PCE is the carboxyl (COO−) group, which is effective in increasing the adsorption affinity of PCE onto cement particles. Zhang et al. [145] showed that UHPC paste prepared with cement and silica fume and made with PCE containing phosphate (PO42−) and COO− groups could exhibit lower yield stress and residual viscosity than that made with PCE with only a COO− group. This finding can be attributed to the fact that the PO42− group can provide a higher adsorption capacity onto silica fume particles to achieve uniform dispersion compared with COO− group. Similar preferential adsorption of PCE was reported in Ref. [13]. As discussed in Section 4.2, non-proprietary UHPC can be prepared with ternary and even quaternary cementitious materials. Therefore, it is necessary to tailor the combination of anchoring groups of PCE depending on the binder system for UHPC. The charge density should be determined by the demand of the applications because the increase in charge density can provide higher and faster adsorption onto the cement particles, and rapid workability decreases with time [154].
Many studies reported that the incorporation of PCE can decrease the structural build-up due to the increased particle separation distance and decreased early-age hydration [155], [156], [157], [158]. For example, Qian [155] stated that cement paste with 0.4% PCE exhibited five times less structural build-up than the reference cement paste made without PCE. However, the same authors also found that incorporating PCE at a relatively low dosage of 0.2% led to 4.5 times more structural build-up than the reference mixture. The different effect of PCE on the structural build-up is related to the PCE surface coverage. When the surface coverage is high, the increase in PCE can greatly reduce the number of pseudo-contact points due to the higher layers of PCE adsorption [155]. At low PCE surface coverage, Qian [155] attributed the higher flocculated state with the increase in PCE content to the fact that side chains could bridge the adjacent agglomerates at the pseudo-contact point. However, Nicia et al. [38] noted that the decrease in PCE side chain length led to a higher structural build-up, which was opposite to the viewpoint proposed by Qian [155]. Nicia et al. [38] found that the addition of PCE could increase the specific surface area of particles due to the formation of ettringite. The specific surface area was linearly proportional to the structural build-up. Therefore, the PCE-induced formation of ettringite has a dominant effect on the structural build-up at an early age. Furthermore, Sha et al. [159] reported that the delayed addition of PCE could reduce the formation of ettringites, which decreases the increasing amplitude of the specific surface area. Therefore, the PCE addition time is the key to controlling the structural build-up at the early age.
From the molecular architecture of PCE, the anchoring group can affect the structural build-up in addition to the side chain length. Nicia et al. [38] noted that the increase in anionic charge ratio could lead to a higher structural build-up at the early age because PCE can promote the formation of fine ettringite with the high specific surface of ettringite. The decrease in the adsorption rate of PCE onto cement particles is critical to decrease the structural build-up because more PCE can adsorb onto the hydration products to reduce their bridging effect. Zhang et al. [160] developed the acrylate-based post-acting PCE to achieve long fluidity retention because the COO− groups gradually formed and adsorbed onto the cement particles and hydration products. However, the addition of post-acting PCE with an inappropriate molecular structure cannot effectively reduce the structural build-up of UHPC. Due to the relatively high content of conventional PCE in UHPC, the interaction between conventional and post-acting PCEs can increase flocculation of particles because of the following reasons: ① A bridging effect can form between adsorbed conventional PCE and unabsorbed post-acting PCE [155]; ② the non-adsorbed polymer at the early age can increase the attractive depletion force [161]. Furthermore, the molecular structure of post-acting PCE can affect the hydrolysis rate, which is directly related to the early-age hydration process. Consequently, further studies are required to evaluate the influence of the molecular structure of post-acting PCE on the structural build-up of UHPC.
4.5.2. Viscosity-modifying admixtures
Viscosity-modifying admixture (VMA) can be critical to tailor the rheology of UHPC for complex casting processes, such as underwater casting and shooting [50,162,163]. Widely used VMAs have a long linear backbone and high molecular weight, which are approximately 100-fold higher than those of PCE [164]. The working mechanism of VMA is closely related to its adsorption affinity onto the particle surface of cementitious materials [165]. If VMA can effectively adsorb onto cement particles, the long polymer chains can simultaneously bridge several cement particles, which results in up to 10-fold higher yield stress than plain UHPC without VMA [50,77]. The non-adsorbed VMA is effective in increasing the viscosity of the interstitial pore solution, possibly because of the following mechanisms: ① The swelling and association of the polymer of VMA can increase the interaction between polymers and solvent [14,166]; ② VMA polymers can entangle with each other to form a polymer network when the VMA content exceeds a critical concentration, as shown in Fig. 14(a) [164]. This issue can greatly increase the hydrodynamic diameter of the VMA polymer [167]. The second mechanism has a higher effect on increasing the pore solution viscosity than the first mechanism, as shown in Fig. 14(b) [164]. In general, the bridging effect of adsorbed VMA polymers has a higher effect on increasing the yield stress, whereas the residual viscosity of UHPC is mainly affected by the swelling, association, and entanglement of non-adsorbed VMA. It should be mentioned that increasing amplitude of UHPC viscosity is lower than that of the viscosity of interstitial pore solution with the incorporation of VMA [167], [168], [169], [170]. The possible reason is that the formation of a hydrodynamic lubrication layer of non-adsorbed VMA polymer can increase the particle surface distance [167,168,170].
The changes in backbone length, density of the anchoring group, and type of VMA can greatly affect the rheological properties of cement-based materials. Qiao et al. [171] reported that the increase in molecular weight of VMA from 1.3 × 106 to 3.2 × 106 g·mol−1 (i.e., longer backbone length) increased the yield stress and residual viscosity by 165% and 70%, respectively. This result is consistent with the findings in Ref. [172], where diutan gum can better increase the yield stress and residual viscosity than welan gum because the molecular weight of diutan gum is approximately fivefold higher than that of welan gum. In most cases, VMAs with a stronger adsorption group and higher charge density are more effective in enhancing the yield stress and residual viscosity [34,173]. Chen et al. [173] reported that there was an optimal charge density of VMA because dense charge density can lead VMA to adsorb onto a cement particle instead of several particles. Furthermore, the bridging effect should reach the highest level when half of the particle surface is covered by VMA [28].
When UHPC is made with a constant superplasticizer content, the structural build-up and thixotropy can increase with the use of VMA due to the bridging force and formation of the polymer network [50,77,78]. For example, Teng et al. [77] reported that UHPC prepared with 0.9% welan gum exhibited a 250% higher structural build-up at rest than the reference mixture made without welan gum. Meanwhile, the early-age hydration process can be delayed and reduced with the addition of VMA because the adsorbed VMA can decrease the nucleation site for hydration products [78,174]. The lower bridging effect is expected to reduce the irreversible component of the structural build-up.
4.5.3. Compatibility between VMA and PCE
VMA and PCE are often combined to tailor the rheological properties of UHPC, for example, self-consolidating UHPC and UHPC for 3D printing. The effect of VMA and PCE is sensitive to their adsorption behaviors onto the particle surface of cementitious materials. The combined incorporation of these admixtures can cause a fierce competitive adsorption phenomenon due to the insufficient place for polymer adsorption onto binder materials [28,34,164]. Previous studies have shown that the adsorption of PCE can gradually desorb the VMA polymers after attaining surface saturation, as shown in Fig. 15(a) [34]. For non-ionic cellulose-based VMA that can present a relatively low surface affinity, the use of PCE at high dosage can maintain most of the VMA that remains in the interstitial pore solution [34,175]. Anionic welan gum and diutan gum, which have a high surface affinity, can effectively adsorb onto cement particles even when the PCE content is 10 times higher than the VMA content [34].
The competitive adsorption between VMA and PCE can be an advantage in tailoring the rheological properties in some cases. For example, Fig. 15(b) [34] presents that the combined use of VMA and PCE can enhance the residual viscosity without affecting the yield stress of UHPC. This can be because the adsorbed PCE governs the yield stress, whereas the VMA remaining in the interstitial pore solution contributes to increasing plastic viscosity [34,164,175]. However, it was found that the combined use of anionic welan gum and PCE at relatively high content is more effective in increasing the residual viscosity than the incorporation of a combination of non-ionic cellulose-based VMA and PCE [34]. This might be because the hydrodynamic lubrication layer formed by the increased non-adsorbed VMA and PCE can reduce the direct contact of particles [30]. Previous studies have also shown that the excessive amount of non-adsorbed VMA and PCE can induce attractive depletion forces to increase the flocculation of particles and yield stress [161], which can cause undesirable rheological properties of UHPC in some conditions.
The structural build-up can be affected by the competitive adsorption between VMA and PCE. As shown in Fig. 16 [34], using welan gum or diutan gum with PCE greatly increases the structural build-up of UHPC without influencing the initial flowability, possibly because the bridging force of the adsorbed polymer can strengthen the polymer network. In the case of cellulose-based VMA, the increase in structural build-up is limited due to the relatively low adsorption of cellulose-based VMA in the presence of PCE. Chen et al. [176] suggested that using acrylate-based VMA could maintain the effect of VMA on increasing the yield stress for a longer time because the acylate group gradually hydrolyzed into the COO− groups in the alkaline environment, which could increase the VMA adsorption capacity onto the cement particles and hydration products. Therefore, such an admixture is promising to enhance the structural build-up of UHPC without increasing the PCE demand. The method to control the hydrolysis rate and understudy the mechanism of the competitive adsorption between post-acting VMA and PCE requires a more comprehensive investigation. Furthermore, there is no general rule to elucidate the influence of competitive adsorption between VMA and PCE on the rheological properties of UHPC. The main challenge is to decouple the influence of adsorbed and non-adsorbed VMA and PCE on the microstructure and consequence rheological properties. Possible methods to distinguish the concentrations of VMA and PCE include the combination of total organic carbon and dynamic light scattering measurements or total organic carbon and ultraviolet-visible tests [147,175]. However, both methods are sensitive to the VMA and PCE size. Therefore, further studies are required to focus on this area. It is essential to investigate the synergetic effect of VMA and PCE on the bridging effect of early-age hydrates, which can facilitate the tuning of the molecular architecture of VMA and PCE to tailor the rheological properties of UHPC.
4.6. Superabsorbent polymers
Superabsorbent polymers (SAPs) are effective internal curing agents for UHPC to mitigate autogenous shrinkage [177], [178], [179]. However, SAP can affect the rheological properties. Ma et al. [86] reported that an increase in SAP content from 0 to 0.6% increased the residual viscosity and thixotropy by at most 90% and 240%, respectively, for cement paste made with a constant w/b of 0.22. Incorporating SAP necessitates a higher water or superplasticizer demand to secure the proper initial flowability [86,180]. When extra water is added to compensate for low flowability due to the use of SAP, the sorption behavior of SAP plays a dominant role in influencing the rheological properties compared with the shape and PSD of SAP [181,182]. Retentive SAP that slowly absorbs water without rapid release at an early age can greatly increase the yield stress and residual viscosity of UHPC. A slight increase or even decrease in such rheological parameters can be obtained using self-releasing SAP, which exhibits rapid water adsorption followed by immediate water desorption [181,183].
Liu et al. [181] reported that the increase in the mean particle size of self-releasing SAP from 95 to 470 μm could lead to 10% higher yield stress at 15 min due to the longer water absorption duration. Furthermore, the authors noted that UHPC containing pre-absorbed SAP exhibited 10%-20% lower dynamic yield stress than UHPC prepared with dry SAP because the desorption of water immediately occurred after dry SAP had been added to the mixture [181]. However, the SAP precondition has a limited effect on thixotropy [181]. When an additional superplasticizer is incorporated to compensate for the flowability loss caused by SAP, the effect of SAP on the rheological properties can be reduced. Chen et al. [184] showed that the yield stress of cement paste at 30 min increased by approximately 400% with the addition of 0.2% SAP; however, such an increase was limited to approximately 115% with the incorporation of 0.2% SAP and an additional 0.2% superplasticizer, possibly because superplasticizer can reduce water absorption and provide a steric hindrance effect. Oh and Choi [185] reported that the increasing superplasticizer content reduced the contribution of the PSD and shape of SAP on the rheological properties.
Further investigations to establish the relationships among the water sorption kinetics, change in packing density, and variation in solid volume fraction of SAP over time are of special interest. A more comprehensive study about the effect of water sorption on the bridging effect of early-age hydrates in UHPC with various binder systems is also required.
5. UHPC with adapted rheology
5.1. Improvement of the fiber distribution
The tensile and flexural properties of UHPC are closely related to fiber dispersion and orientation, which are greatly affected by the rheological properties of the suspending UHPC mortar [2],[186], [187], [188]. For self-consolidating UHPC, it is critical to tailor the residual viscosity to improve the fiber uniformity to secure an adequate fiber-matrix bond strength [48,189]. The optimal residual viscosity can vary with fiber characteristics. For steel fibers with a 65 aspect ratio, the optimal residual viscosity was 30-40, 40-55, and 55-65 Pa·s for UHPC with 1%, 2%, and 3% fiber contents, respectively, as shown in Fig. 17(a) [15].
The combination of special casting methods to promote fiber alignment and adjustments of rheological properties can improve the fiber distribution and alignment along the principle tensile stress direction [188,190,191], which can significantly improve the cracking bridging capacity of fiber. For example, using a 30° chute can promote the shear flow of self-consolidating UHPC, where the hydrodynamic stress can result in fiber alignment. The low yield stress necessitates a relatively high shear zone, whereas the proper residual viscosity is required to drive the fiber without a significant decrease in flow velocity. The plastic viscosity that corresponds to the best fiber alignment increased from 40 to 65 Pa·s with the increase in fiber content from 1% to 3% in UHPC prepared with w/b of 0.2, as shown in Fig. 17(b) [15]. Huang et al. [191] proposed an L-shape device with a restricted horizontal outlet to promote fiber alignment along the principle tensile stress direction of cast prismatic elements. For self-consolidating UHPC made with 2% steel fiber, a plastic viscosity of the suspending mortar of UHPC higher than 45 Pa·s was necessary to avoid separating fibers and mortar at the horizontal outlet of the L-shape device [190]. When the yield stress of UHPC is higher than 40 Pa, a lower plastic viscosity is preferred to prevent fiber agglomeration [190]. In these studies [15,48,190], the rheological properties of the mortar phase were tailored based on the following procedures: ① tuning the type and content of cementitious materials and fine aggregates to increase the packing density and reduce the PCE demand. The PSD of solid particles can be determined using the modified Andreasen and Andersen model. The optimal PSD modulus is 0.17-0.25 [114,115,192]. In general, the smaller particle size necessitates a lower value of PSD modulus to achieve a high packing density. ② Adjusting the combinations of VMA and PCE to obtain the desirable dynamic yield stress and residual viscosity.
Limited studies have investigated methods to promote flexible fiber alignment. Most studies concentrated on the improvement of rigid fiber alignment. Moreover, the proposed casting methods to improve the fiber dispersion and orientation are limited to the material scale. In structural applications, large dimensions and the presence of reinforcing steel bars can influence the flow characteristics of UHPC. Therefore, further studies should be undertaken to address these challenges.
5.2. Thin-bonded UHPC overlay for structural rehabilitation
UHPC in cast-in-place structural rehabilitation should exhibit special rheological properties due to the complicated shapes, congested reinforcing steel, restricted area for consolidation, and sometimes contradictory rheology requirements for the mixing, placement, and consolidation of the material. In the case of thin-bonded bridge overlay rehabilitation, the rapid particle flocculation of UHPC is essential because flocculation-induced thixotropy can prevent sagging of flowable UHPC on inclined surfaces [193]. Du et al. [74] showed that the incorporation of 0.2% nanoclay by mass of binder in self-consolidating UHPC could increase τfloc by 700%, which is necessary for UHPC placement on bridge decks with a slope of 2%. Khayat et al. [194] proposed the following equation to determine the minimum necessary yield stress (τIP) of fresh mixture to prevent the flow of concrete on inclined surfaces:
$\tau_{\mathrm{IP}}=\rho \cdot g \cdot h \cdot \sin \alpha$
where α (%) is the slope of the bridge deck, and h (mm) is the thin-bonded overlay thickness. The authors conducted field testing to establish an empirical correlation between the slope of the bridge deck and the fluidity of UHPC [133]. For example, for a bridge deck with a slope of 2%, a 40 mm thick UHPC overlay should have a maximum mini-slump flow of 150 mm after 25 jolting to prevent the material from sagging.
For sprayable UHPC that can be used to repair inclined or vertical surfaces, fresh UHPC is expected to have a relatively low viscosity for ease of pumping but a high static yield stress to secure adequate repair thickness after shotcrete application [195]. Chen et al. [196] proposed to evaluate shootability using the ratio of static yield stress to plastic viscosity. Lee and Yoo [197] developed a low-viscosity UHPC to enhance the pumping efficiency. The low viscosity was achieved using coarse cement with a fineness of 1800-2000 cm2·g−1 and coarse silica fume with a fineness of 100 000 cm2·g−1. Many studies [196,198,199] showed that VMA could be used to enhance the buildability of sprayable UHPC. Cui et al. [199] reported that the incorporation of 0.07% cellulose-based VMA could successfully spray a 50 mm thick UHPC layer onto wall elements with a slope of 75°. Dickinson et al. [198] indicated that the sprayed UHPC layer thickness increased from 1.6 to 9.2 mm with the increase in VMA content from 0 to 0.6% by mass of binder. The effect of VMA on enhancing the shootability highly depends on the type and content of VMA. VMA that can enhance the static yield stress without greatly increasing the viscosity is desirable for such an application. Chen et al. [196] showed that cellulose-based VMA was more suitable to develop sprayable than inorganic VMA.
In general, the strategy to control the rheological property of UHPC for the thin-bonded UHPC overlay rehabilitation is similar to the method in Section 5.1. Specifically, one should pay more attention to the effect of various organic VMA types on the thixotropy and structural build-up of UHPC.
5.3. Three-dimensional printing
Extrusion-based 3D concrete printing is an automated process of constructing the concrete element layer by layer without formwork [200]. Such a novel construction process requires special fresh properties. The proper pumpability and extrudability necessitate relatively low yield stress and viscosity. Then, the yield stress immediately after extrusion should be sufficiently high to resist flow and deformation of extruded layers. A high structural build-up at rest is required to prevent local deformation and buckling of the rising structure. Gu and Khayat [201] proposed that the extrudability of printed cement-based materials was a function of the yield stress after mixing and initial increase of yield stress after 5 min of rest, as presented in Fig. 18(a). In terms of buildability, Roussel [18] proposed that the failure pattern was plastic deformation when the height of the printed element was less than the critical height, as shown in Fig. 18(b). The minimum structural build-up rate to resist plastic deformation can be determined by the printing speed and dimension of each layer of the printed element, as shown in the following equation [18]:
where Ḣ (m·s−1) is the rising speed of each layer. A self-buckling failure mode can occur after the construction height exceeds the critical height, especially when the elastic modulus (E) of fresh material is lower than the critical value, as shown in the following equation [18]:
$E>\frac{2 \rho g h}{\sqrt{3} \gamma_{c}}(1+\nu)$
where γc is the shear strain at flow onset, and ν is the Poisson coefficient.
UHPC made using various binders and chemical admixtures to tailor the rheological properties can be successfully printed [101,202,203]. For example, Jia et al. [105] showed that the use of 20% limestone powder by mass of binder with d50 of 7 μm can enhance the early-age extrudability by 15%-20% without hindering the buildability. Arunothayan et al. [101] proposed that the combined use of nanoclay and PCE can obtain the desirable printing properties for 3D printing UHPC made with various SCMs. Extensive experiments to seek the optimal admixture characteristics are the main shortcomings of this method. A physical-informed neutral network that can assess the thixotropy of cement paste is a prospective solution to design 3D printing UHPC [204]. Jiao et al. [205], De Schutter et al. [206], and Zhang et al. [207] proposed a novel concept of using active rheology control that could externally trigger signals to adjust the rheological properties of cement paste in real time. This concept included the addition of magnetic particles, redox-responsive chemical admixtures, and temperature-sensitive polymers in cementitious materials and applying the corresponding external triggers (e.g., electromagnetic field and temperature) [205], [206], [207]. For example, when an external magnetic field was applied, a cement paste containing 3% Fe3O4 exhibited 300% higher structural build-up than the mixture prepared without magnetic particles [205]. The cement paste made with 7.5% carbonyl iron particles had a 750% higher structural build-up than that with 5% Fe3O4 and magnetic interventions [208]. De Schutter et al. [206] reported that the use of PCE containing a redox-responsive group led to a sixfold increase in structural build-up compared with a cement paste with conventional PCE after applying an external voltage. Zhang et al. [207] used the temperature as the external trigger to tailor the rheological properties of cement paste containing VMA. The results showed that the static yield stress at 30 min of rest time increased from 21 to 112 Pa with the incorporation of 0.1%-cellulose-based VMA and an increase in temperature from 15 to 35 °C. The active rheology control strategy of the combination of carbonyl iron particles and electromagnetic field was successfully upscaled from paste to mortar [209]. However, the increase in sand volume can reduce the response efficiency of carbonyl iron particles. In general, further upscaling investigation and optimization of special responsive admixture and external trigger signals will be of great interest for complex fiber-reinforced materials such as UHPC.
6. Conclusions
The rheology of UHPC is complicated due to its low water content, high solid volume fraction, and wide range of constituent materials. To understand and enhance the fresh performance of UHPC, this work comprehensively reviewed the rheological properties of UHPC. This review included the analysis of key physical and chemical factors that influence the performance, test procedures to evaluate the rheological parameters, and the effect of various constituent materials on the rheological properties. Furthermore, the required rheological properties to successfully apply UHPC across various applications were summarized. Based on the above discussion, the key findings are as follows:
(1) The solid volume fraction, packing density, and particle surface distance are the primary physical and physicochemical factors that affect the dynamic yield stress and residual viscosity (or plastic viscosity in the case of linear Bingham flow) of UHPC. The same variations of these factors exert greater influence on the dynamic yield stress than the residual viscosity. When characterizing thixotropy and structural build-up at rest, one should consider the chemical effect of early-age hydration.
(2) The M-B model is more appropriate to determine the rheological parameters of shear-thickening UHPC than the H-B model because the latter model can overestimate the rheological parameters of UHPC. In the case of shearing-thinning UHPC, the M-B model can yield higher rheological parameters than the H-B model.
(3) The structural build-up of UHPC can be characterized by the evolution of static yield stress with rest time. A constant shear rate of 0.01-0.10 s−1 is recommended to determine the static yield stress of UHPC. The UHPC thixotropy can be determined by the difference between static and dynamic yield stress, structural breakdown area, and hysteresis loop. The last method may not obtain an accurate result for highly thixotropic UHPC because it is more difficult to precisely consider the plug flow effect.
(4) The w/b factor is the most significant factor to influence the rheological properties of UHPC. The yield stress and viscosity can be increased by 1-100 times with the decrease in w/b. The use of SCMs at proper cement substitution rates can enhance the packing density of the powder materials, leading to 1-10 times lower yield stress and viscosity. To obtain a high packing density, the recommended range of PSD modulus of cementitious materials in the modified Andreasen and Andersen model is 0.210-0.235. The incorporation of SCMs with high pozzolanic reactivity can promote early-age hydration and consequently greater structural build-up despite the improved particle packing.
(5) The rheological properties of fiber-reinforced UHPC can be determined by the product of the paste rheology and function of the volume fraction and packing density of sand and fiber. For UHPC with a sand volume fraction above 30%, the packing density can be greatly improved by tailoring the size distribution and aspect ratio of the sand, which can decrease the yield stress and viscosity by 1-10 times. For the fiber packing density, key fiber parameters that affect the rheology include the aspect ratio and conformation. The flexible fiber conformation is influenced by the rheological property of the suspending mortar in addition to the fiber dimension and elastic modulus.
(6) PCE and VMA are used to enhance the performance of UHPC. The action mechanism of PCE and VMA is closely related to their affinity onto the particle surface of cementitious materials, which can be controlled by the molecular architecture of the admixture. Adsorbed admixtures can affect the colloidal interactions and early-age hydration kinetics of the binder. Non-adsorbed admixtures can affect the viscosity of the pore solution and contact interaction among solid particles. Contradictory rheological requirements can be achieved by tailoring the competitive adsorption between PCE and VMA.
(7) SAP can be used for internal curing to reduce autogenous shrinkage. The high water absorption of SAP and its effect on reducing flowability can be offset by water or superplasticizer addition. The effect of SAP on the rheological properties of UHPC depends on the water sorption kinetics, which is closely related to the type and size of SAP and the pore solution properties (e.g., ions, VMA, and PCE concentrations).
(8) UHPC with adapted rheology can be achieved by selecting the binder system and fine aggregate that can enhance the packing density of the system. The recommended value of PSD modulus of all solid materials (i.e., cementitious materials, filler, and sand) for a high packing density is 0.17-0.25. The optimal PSD modulus decreases with decreasing particle size. Proper selection of PCE molecular architecture and specialty admixtures (e.g., VMA) can also be used to modify the particle interaction and pore solution properties. Active on-demand rheology control is a promising approach to modify the rheological properties of UHPC.
7. Future work
The following challenges should be considered in future studies to successfully design and process UHPC.
·Future studies that target the use of novel binders with a low clinker factor, manufactured sand, and recycled sand and fiber in UHPC will help increase the sustainability of UHPC. The effect of these raw materials on rheological properties should be investigated.
·When UHPC exhibits relatively high yield stress and nonlinear flow behavior, strategies to eliminate the plug flow effect should be studied when determining the dynamic yield stress and residual viscosity.
·The influence of the alignment and agglomeration of fibers with various shapes, dimensions, surface roughness characteristics, and elastic moduli on the yield stress and residual viscosity of UHPC should be analyzed.
·The individual contributions of the adsorbed and unabsorbed polymers (e.g., VMA and PCE) on the rheology of UHPC should be determined when the combinations of chemical admixtures are in use. Special attention should focus on the competitive adsorption between PCE and VMA in formulating complex cement-based materials, such as UHPC with a reduced clinker factor.
·The influence of early-age hydration in sustainable UHPC on the consumption of chemical admixtures should be evaluated. Furthermore, the effect of chemical admixtures on the morphology of early-age hydrates should be characterized.
·The effect of the interaction between the adsorption of chemical admixtures and early-age hydration kinetics on the evolution of the microstructure of sustainable UHPC over time should be determined. In addition, it is important to investigate how to tailor the molecular architecture and formulate novel chemical admixtures to control the real-time rheological properties of UHPC.
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