Insights into the viscoelastic properties of cement paste based on SAOS technique

Understanding the viscoelastic properties of cement paste is beneficial to pumping, formwork casting and 3D printing of cement-based materials. This paper presents new insights into the viscoelastic properties of cement paste with various compositions. Several parameters, including critical strain, storage modulus and viscoelastic yield stress obtained from small amplitude oscillatory shear (SAOS) test, are selected to characterize the viscoelasticity of fresh cementitious paste. Results reveal that increasing water-to-cement (w/c) ratio reduces the storage modulus at linear viscoelastic region (LVER) and viscoelastic yield stress of cement paste, whereas higher w/c increases the critical strain. The replacement of cement by fly ash has no significant influence on the critical strain of cement paste. Due to the improvement of cohesive bonding between cement particles by nanoparticles, the incorporation of nano-Fe 3 O 4 particles results in an increase in the storage modulus at LVER, critical strain and viscoelastic yield stress. The critical strain of cement paste gradually increases with the concentration of polycarboxylate ether (PCE) superplasticizer, which possibly can be attributed to the interactions and entan-glement of PCE molecules adsorbed onto the solid particles. By contrast, cement pastes with low PCE additions exhibit an increase in the viscoelastic yield stress, while higher PCE additions significantly decrease the storage modulus at LVER and viscoelastic yield stress of cement paste.


Introduction
With the development and widely application of innovative types of concrete, e.g., self-compacting concrete (SCC) and ultra-high performance concrete (UHPC), the rheological behavior of fresh cement-based materials has gained increasing interest by researchers and engineers [1][2][3][4][5].It is commonly recognized that fresh cement-based material is regarded as a non-Newtonian suspension with yield stress, which shows viscoelastic behavior under an external shear stress lower than the yield stress and starts to flow at relatively high shear stress.The flow behavior of cementitious materials can be characterized by Bingham model [6], Modified Bingham model [7], or Herschel-Bulkley model [8].The rheological properties are the fundamental physical parameters of fresh cement-based materials, which can be used as efficient indicators to guide mixture proportion design [9,10], describe static and dynamic stability [11], and predict pumping pressure and formwork filling [12,13].
As fresh cement-based materials are supposed to exhibit dynamic flow behavior during the construction process from mixing, transporting, pumping and formwork casting, most researchers mainly focused on the measurements, calculations and applications of rheological parameters such as yield stress and plastic viscosity.The viscoelastic behavior rarely received scientific attention until the increased application of self-compacting concrete and even the recent development of 3D concrete printing technologies.For example, the features of self-compacting concrete during formwork filling, without external vibration, are related to the evolution of viscoelasticity and structuration of the material [14][15][16].With regards to 3D concrete printing, a class of digital fabrication technology, the sufficient bonding strength between two extruded layers and the fast evolution of the mechanical strength of each extruded layer are also correlated to the development of viscoelasticity of fresh cement-based materials [17][18][19].
The viscoelasticity of fresh cement-based materials can be monitored by a rheometer through operating stress growth test, creep recovery test, small amplitude oscillatory shearing (SAOS) test, etc. [20][21][22].For the stress growth test, the most popular protocol is applying a constant low shear rate, with the value ranging from 0.001 s − 1 to 0.05 s − 1 for cement paste and 0.01 s − 1 to 0.1 s − 1 for mortar and concrete [19], respectively.The resulting shear stress over time is captured, and the peak shear stress is determined as the static yield stress.The evolution of the static yield stress can be used to characterize the change of the viscoelasticity of fresh cement-based materials with time.Creep recovery test is generally achieved by applying a series of external shear stress levels and monitoring the subsequent change of viscosity [20,23].The critical shear stress where the resultant viscosity starts to decrease is regarded as the static yield stress.The creep recovery test is usually applied to highly thixotropic materials.Unfortunately, both stress growth test and creep recovery test only give the overall structure's macroscopic response, and the insights into the microstructure of cement-based materials cannot be revealed.
SAOS, by applying an oscillatory shear strain or shear stress and monitoring the response of storage modulus, loss modulus and phase angle, is an advanced technique to understand the microstructural behavior of viscoelastic materials [24][25][26].SAOS test generally includes strain-sweep, frequency sweep and time sweep modes.Specifically, strain sweep test is used to determine the microstructural response (e.g., storage modulus, critical strain and viscoelastic stress) and the linear viscoelastic region (LVER), while frequency sweep aims at gathering the information on the stability of suspensions.By contrast, time sweep test is used to quantitatively describe the evolution of structural build-up of a material over time [27,28].More recently, the SAOS technique was successfully employed to monitor the responsive structural evolution of cementitious paste to an external magnetic field [25,29,30], which is helpful to achieve the goal of active rheology control and active stiffening control of cement-based materials [31,32].However, previous experimental results reveal that the critical strain, indicating the deformation capacity of the connections between solid particles, shows a reverse relationship with the increase of water-to-cement (w/c) ratio and the addition of superplasticizer [33,34], and no systematic study in literature is available to interpret this phenomenon.This limits the understanding of viscoelastic behavior of cementitious materials and further restricts the rheology and stiffness control of cement-based materials during casting process.
To fill this research gap, this present paper gives new insights into the viscoelastic properties of cement paste with various compositions.The critical strain, storage modulus and viscoelastic yield stress obtained from small amplitude oscillatory shear (SAOS) test are used to evaluate the viscoelasticity of fresh cement paste.The influence of superplasticizer on the viscoelastic properties of cement pastes with different binder compositions (i.e., pure cement paste, cement paste with 25 vol.% fly ash, and cement paste with 3 wt.%nano-Fe 3 O 4 particles) is experimentally investigated and then discussed.This study provides an in-depth understanding on the microstructural response and viscoelastic properties of fresh cement-based materials, which contributes to the achievement of active control of rheology/stiffness in the process of pumping, formwork filling and 3D concrete printing.

Materials and mix proportions
CEM I 52.5 N Portland cement (OPC) with specific gravity and median particle size (D50) of 3.20 and 7.20 μm, respectively, was used.The utilized fly ash (FA) is from a power plant in Belgium.The specific gravity and median size of the fly ash are 2.22 and 8.01 μm, respectively.The chemical composition and particle size distribution of the cement and fly ash are shown in Table 1 and Fig. 1, respectively.Spherical nano-Fe 3 O 4 particles (MNPs) from US Research Nanomaterials, Inc, were used.According to the manufacturer, the average particle size and specific gravity of the nano-Fe 3 O 4 particles are 20-30 nm and 4.95, respectively.The zeta potential of the nano-Fe 3 O 4 particles dispersed in water measured by a Malvern Zetasizer instrument is -2.27 ± 0.03 mV.A commercial polycarboxylate ether (PCE) superplasticizer with a solid concentration of 35% (MasterGlenium 51, BASF, Netherlands) was employed.All samples were prepared using de-ionized water.
Three batches of cement paste with different cementitious compositions, w/c and PCE dosages were prepared.The cementitious compositions include pure cement paste, cement paste with 25% fly ash (by volume of cement), and cement paste with 3% MNPs (by mass of cement).The dosage of PCE varies from 0% up to 0.6% by the mass of powder, depending on the cementitious composition.The mix proportions of the prepared cement pastes are presented in Table 2.The mix is designated as cementitious composition-w/c-PCE dosage.For example, 25FA-40-0.4%PCErefers to cement paste with fly ash replacement of 25%, w/c of 0.40 and PCE dosage of 0.4%.All cement pastes were mixed using a rotational rheometer (MCR 52, Anton Paar) equipped with a helix geometry [25].This mixing method provides a repeatable initial state of paste samples with the same mix proportion [35].

Oscillatory strain sweep test
The viscoelastic properties of cement paste are evaluated by using a parallel plate rotational rheometer (MCR 102, Anton Paar).The diameter of the plate and the gap are 20 mm and 1 mm, respectively.After pouring the sample into the plate of the rheometer and adjusting the upper plate to the measurement position, a pre-shear with shear rate of 100 s − 1 was first applied for 30 s to eliminate the residual stress during the gap adjustment and destroy the possible agglomeration structures.This is followed by a rest period lasting for 10 s to ensure the sample reaching an equilibrium state.Afterwards, an oscillatory strain sweep test with shear strain γ logarithmically sweeping from 0.0001% to 100% and constant frequency of 2 Hz was performed.The rheological test of each mix proportion was repeated for three times, and the error bar in the following figures indicates the standard deviation of three measurements.During the entire rheometric test, the temperature is fixed at 20 • C.
A typical oscillatory strain sweep test result is presented in Fig. 2. With the shear strain γ sweeping from 0.0001% to 100%, the storage modulus G' and loss modulus G'' are directly recorded by the rheometer, while the elastic stress τ e is calculated by τ e = γ⋅G'.It can be observed from Fig. 2 that the storage modulus and loss modulus remain unchanged at relatively low shear strain, and the elastic stress increases linearly, defined as linear viscoelastic region (LVER).The storage modulus is always higher than the loss modulus during the LVER.This indicates that the internal microstructure of the suspension is maintained [24].That is, the suspension acts as a solid and the storage modulus is independent of the shear strain.When the shear strain is higher than a critical value, the storage modulus starts to decline and the elastic stress deviates.The critical strain is the length of the LVER, indicating the deformation of the weakest connections between solid particles (which are well recognized by the bridges of early hydration products such as C-S-H and metastable ettringite [28,36,37]).It can be used as a measurement of the deformation capacity of a suspension.The higher the critical strain is, the larger the deformation capacity of the suspension is.The storage modulus at LVER, which can be calculated as the average value of the plateau within 10%, is the ability of energy stored, indicating the elastic behavior of a suspension.Higher G' indicates higher strength or mechanical rigidity of the suspension.The elastic stress at the deviation of the elastic behavior is defined as viscoelastic yield stress τ e,l [33,35], which can be used as an indicator of the micro-mechanical strength of interparticle connections.In this study, the viscoelastic properties of cement paste are characterized by considering the critical strain, the storage modulus at LVER and the viscoelastic yield stress.The evolution of storage modulus, loss modulus and elastic stress at shear strain higher than the critical strain is beyond the scope of this paper.

Influence of w/c on viscoelasticity
The influence of w/c on the viscoelastic properties of plain cement paste is presented in Fig. 3. From Fig. 3 (a), it can be seen that the linear region of the elastic stress at low shear strains shifts to the top left with decreasing w/c, indicating higher storage modulus at LVER of cement paste with lower w/c.Indeed, reducing w/c from 0.45 to 0.40 increases the storage modulus at LVER from ~ 15 kPa to ~ 60 kPa, while it exhibits a more significant increase with the continuous decrease of w/c from 0.40 to 0.35.This is in good agreement with the fact that the stiffness of cement paste increases with the increase of particle volume fraction, and the increase rate is accelerated at high particle volume fractions [4,38,39].The critical strain of the plain cement paste shows less significant influence with increasing w/c from 0.35 to 0.40, which can be clearly observed from Fig. 3 (b), while increasing w/c from 0.40 to 0.45 slightly increases the critical strain, revealing a slight increase in the deformation capacity.Yuan et al. [22] and Ukrainczyk et al. [26] also observed a w/c-dependent behavior of critical strain of cement paste.From the viewpoint of viscoelastic yield stress, it exhibits a significant decrease with increasing w/c from 0.35 to 0.40, mainly contributed by the reduction of the storage modulus at LVER.Further increasing w/c has no significant influence on the viscoelastic yield stress, due to the compensation between the increase of critical strain and the reduction of storage modulus at LVER.This indicates that the plain cement pastes with w/c of 0.40 and 0.45 possibly have almost similar micro-mechanical strength of connections (i.e., --C-S-H and/ or ettringite bridges) between cement particles.

OPC paste and FA-OPC paste
The influence of PCE dosages on the viscoelastic properties of plain cement paste and fly ash incorporated cement paste is shown in Fig. 4 (a) and (b), respectively.Prior to describing the superplasticizer effect, it can first be observed that the volumetric replacement of cement by fly ash significantly decreases the storage modulus at LVER, with the magnitude declining from 60 kPa to 17 kPa, but has no big influence on the critical strain of the cement paste, with the value only increasing from 0.001% to 0.002%.This indicates that the cement paste becomes softer after volumetric replacing cement by fly ash, while the deformation capacity of the interparticle connections is not significantly altered.The viscoelastic yield stress decreases from 0.8 Pa to 0.5 Pa, indicating that the incorporation of fly ash reduces the micro-mechanical strength of the connections between solid particles and/or agglomerates.This is consistent with the fact that the addition of fly ash generally improves   the flowability and rheological properties of fresh cement-based materials due to the micro-filling and ball bearing effect of spherical fly ash particles [40,41].The presence of PCE plays a considerable role in the viscoelastic properties of cement paste.On the one hand, the addition of PCE gradually increases the magnitude of the critical strain, irrespective of the cementitious composition.This refers to the enhanced deformation capacity of interparticle connections in the PCE-containing suspensions.On the other hand, the addition of 0.2% PCE shows no influence on the storage modulus at LVER of both OPC paste and FA-OPC paste, indicating the insignificant change of rigidity of the microstructure.This is in good agreement with the findings in [42,43], which demonstrate that the shear stress or yield stress at low PCE additions exhibit less change or even higher values compared to those without PCE.However, with further increasing the PCE dosage from 0.2% to 0.4%, the storage modulus at LVER decreases from 545 kPa to 6.6 kPa, and from 18 kPa to 0.3 kPa for the OPC paste and FA-OPC paste, respectively.As a result, the addition of 0.2% PCE undoubtedly increases the viscoelastic yield stress of cement paste, and further increasing PCE dosage to 0.4% reduces the viscoelastic yield stress, while their values are still higher than that of cement pastes without PCE.Note that this observation is independent of the cement paste medium, which can be clearly observed from Fig. 6

(b) (see later).
It should be mentioned that the storage modulus of cement pastes with higher PCE dosage exhibits non-linear behavior at extremely low oscillatory shear strain, as reflected by the fluctuant elastic stress of FA-OPC paste with 0.4% PCE in Fig. 4.This probably can be attributed to the high liquid-like properties of the cement pastes, which exert a very low resistance to the oscillatory strain.Consequently, the extremely low induced torque possibly exceeds the sensitivity limits of the torque sensor of the rheometer, and therefore the instrument noise results in the non-linear behavior of the storage modulus and elastic stress at extremely low shear strain [44].

MNPs-OPC paste
Fig. 5 shows the evolution of elastic stress of MNPs-OPC paste with various PCE dosages.It can be observed that the replacement of cement with MNPs shows an increased effect on the storage modulus at LVER, with the magnitude increasing from 600 kPa to 780 kPa, whereas the critical strain is significantly increased.The results indicate that the stiffness of the cement paste is slightly increased with the replacement of cement by MNPs, and the deformation capacity of interparticle connections is dramatically improved.As a result, the micro-mechanical strength of the connections between solid particles is enhanced, as reflected by the significant increase of viscoelastic yield stress from 11 Pa to 41 Pa, as illustrated in Fig. 6(b) (see later).This possibly can be contributed by the physical nature, i.e., non-porous morphology and hydrophobic properties of the nano-Fe 3 O 4 particles.For this reason, Sikora et al. [45] stated that the addition of nano-Fe 3 O 4 particles showed no significant reduction effect on the workability of mortar.
From Fig. 5, it can be observed that the addition of PCE from 0% to 0.4% gradually decreases the storage modulus at LVER of the MNPs-OPC paste from 780 kPa to 320 kPa.Owing to the increase of the critical strain, the viscoelastic yield stress increases from 41 Pa to 72 Pa with the addition of PCE from 0% to 0.4%.This means that the addition of PCE at low dosages results in a reduction in the stiffness of the MNPs incorporated cement paste, while a significant increase in the deformation capacity and micro-mechanical strength of interparticle connections can still be observed.This behavior is in good agreement with the results of plain cement paste and fly ash incorporated cement paste in Fig. 4. For the MNPs-OPC paste with 0.5% PCE, the linear region of elastic stress exhibits a large shift towards the right.In other words, the elastic stress of the MNPs-OPC paste is significantly decreased with the addition of 0.5% PCE.Indeed, the storage modulus at LVER decreases from 320 kPa to 2.5 kPa with increasing PCE from 0.4% to 0.5%.In spite of the significant increase of the critical strain, the viscoelastic yield stress declines from 72 Pa to 13 Pa.This indicates that the stiffness and the micromechanical strength of the connections between solid particles and/or agglomerates considerably decreased after the PCE dosage exceeding 0.4%, while the deformation capacity of the interparticle connections shows an improvement behavior.Further increasing the PCE dosage reduces the storage modulus at LVER and viscoelastic yield stress but increases the critical strain of MNPs-OPC paste.The fluctuant behavior of elastic stress at extremely low shear strain is also present for the MNPs-incorporating cement pastes with high PCE dosages, as shown in Fig. 5.
In summary, the influence of PCE dosages on the critical strain and viscoelastic yield stress of the studied cement pastes is presented in Fig. 6.It can be seen that the critical strain has a general exponential relationship with the concentration of PCE.This indicates that the Fig. 5. Evolution of elastic stress of MNPs-OPC paste with various PCE dosages.Error bar indicates the standard deviation.

D. Jiao and G. De Schutter
addition of PCE increases the critical strain of cement paste, regardless of the cementitious composition.This is consistent with the observations in [22,28].The effect of PCE dosage on the viscoelastic yield stress of cement paste depends on the cementitious composition.For the plain cement paste and fly ash incorporated cement paste, the viscoelastic yield stress significantly increases with the addition of 0.2% PCE, while the inclusion of 0.4% PCE reduces the viscoelastic yield stress due to the dramatic reduction in the storage modulus.In the case of cement paste with MNPs, the viscoelastic yield stress continually increases until the PCE dosage reaching up to 0.4%, whereas the addition of 0.5% PCE contributes to an evident decrease in the viscoelastic yield stress, which can be attributed to the plasticizing effect of PCE molecules on the cement paste.

Discussion
As aforementioned, the storage modulus at LVER indicates the rigidity of a cementitious suspension.The higher (or lower) the storage modulus, the stiffer (or softer) the suspension tends to be.The critical strain describes the deformation capacity of the connections between solid particles and/or agglomerates in a cementitious suspension.A higher critical strain means that a greater oscillatory strain is required to destroy the interparticle connections.Note that higher critical strain does not necessarily mean higher stiffness of the paste.That is, a cementitious suspension with lower stiffness can still possibly possess higher critical strain.The viscoelastic yield stress, which depends on the magnitude of both storage modulus and critical strain, is a quantitative parameter characterizing the strength of the connections between solid particles.It is widely recognized that the interparticle connections corresponding to the critical strain from SAOS test are the early hydration product bridges between cement particles such as C-S-H and ettringite [25,28,33,36,46].
For the pure cement paste, the critical strain is the shear strain required to break the C-S-H and/or ettringite bonding between cement particles to initiate the relative motions of particles and terminate the linear elastic behavior of the suspension.This can be clearly illustrated from the schematic diagram of interparticle interactions in Fig. 7 (a).The critical strain shows little difference with increasing w/c from 0.35 to 0.40, while a slight increase in the critical strain is observed at w/c of 0.45.With the increase of w/c and simultaneously reduction of particle volume fraction, the dissolution rate of cement particles increases, and thus increasing the concentration of Ca 2+ ions [47], resulting in more initial C-S-H and ettringite bonds.Furthermore, the C-S-H gel in a cement paste with lower particle volume fraction possibly becomes less fragile [26].Consequently, the deformation capacity of the C-S-H bridges increases, and thus a slightly higher critical strain is observed at the cement paste with higher w/c.With regard to the viscoelastic yield stress, it is decreased with the increase of w/c due to the reduction of storage modulus at LVER caused by the decreased particle volume fraction.
In the case of cement paste containing PCE, the PCE molecules are absorbed onto the surface of cement particles.Owing to the entanglement of PCE molecules with each other, as shown in Fig. 7 (b), and the possible enhancement of the C-S-H bridges due to the Ca-Si enriched colloidal surface [48][49][50], the cohesive bonding between cement particles is improved, and thus the deformation capacity of the connections is improved.This requires a relatively high oscillatory shear strain to facilitate the particles to move or rotate, and thereby a gradual increase in the critical strain with increasing the concentration of PCE is observed.The viscoelastic yield stress shows PCE concentration dependency.At relatively low PCE additions, it is assumed that the layer of PCE molecules cannot fully cover the surface of cement particles, resulting in the cement paste exhibiting more bigger particles and/or agglomerates [43].In this case, the cement particles are bonded by not only early hydration productions, but also electrostatic forces and even van der Waals forces.Thus, the viscoelastic yield stress describing the micro-mechanical strength of interparticle connections is even higher than that of cement paste without PCE.At relatively high PCE additions, however, multi-layers of PCE molecules might be formed onto the surface of cement particles, leading to a stronger steric hindrance effect.Consequently, the bridging distance between cement particles increases, and the number of sites available for nucleation decreases.In this case, though the cohesive bonding between particles is strong, as reflected by the high critical strain, the colloidal interactions are significantly decreased.Therefore, a dramatic reduction in the storage modulus and thus the viscoelastic yield stress is obtained.
After volumetric replacement of cement by fly ash (in the absence of superplasticizer), the interparticle distance of the cement paste is increased due to the lower specific gravity of fly ash compared to cement particles.On this basis, more free water acting as lubrication effect is generated, and the liquid-like properties of the cement paste are accordingly improved.In addition, the number of bridges of early hydration products is reduced due to the combination of dilution effect and pozzolanic effect of fly ash, as presented in Fig. 7 (c).Therefore, the fly ash incorporated cement pastes exhibit lower stiffness, reflected by the smaller storage modulus at LVER and lower viscoelastic yield stress than that of the pure cement paste.In spite of the increase in the interparticle distance and the decrease in the number of early hydration product bridges, the micro-strength of the bridges between solid particles is possibly not obviously altered.Consequently, the critical strain shows insignificant change after the replacement of cement by fly ash.With the addition of PCE, the fly ash incorporated cement pastes exhibit similar change of critical strain, storage modulus at LVER and viscoelastic yield stress to the pure cement pastes, which can also be attributed to the adsorption and entanglement of PCE molecules.
As for the MNPs-containing cement paste without PCE, on the one side, the incorporation of MNPs increases the water requirement due to the ultra-high specific surface area of the nanoparticles, increasing the solid-like properties and thus the storage modulus at LVER of the cement paste.The physical nature of magnetic nano-Fe 3 O 4 particles tending to form small agglomerates should be also responsible for the stiffness increase of the suspension [45,51].On the other side, the presence of the nano-Fe 3 O 4 particles provides more available nucleation sites for the formation of C -S -H and/or ettringite bridges, as presented in Fig. 7 (d), resulting in an improvement in the cohesive bonding between cement particles.This increases the deformation capacity of the interparticle connections and thus the critical strain of cement paste.In the presence of PCE, it probably has no significant plasticizing effect on the dispersion of nano-Fe 3 O 4 particles, as reflected by the small negative zeta potential charge of the nanoparticles.Instead, the nanoparticles are distributed in the voids between cement particles as small agglomerates [51].Therefore, the MNPs-OPC paste with low PCE additions shows higher stiffness, and it needs a relatively higher dosage of PCE to improve the liquid-like properties of the suspension, compared to pure cement pastes and fly ash cement binary pastes.The significant decrease of the viscoelastic yield stress at PCE content higher than 0.5% can be attributed to the plasticizing effect of PCE on cement particles.

Conclusions
This paper discusses the viscoelastic properties of fresh cementitious paste based on the critical strain, storage modulus at LVER and viscoelastic yield stress obtained from small amplitude oscillatory shear (SAOS) test.The following conclusions can be reached: (1) Increasing w/c reduces the storage modulus at LVER and viscoelastic yield stress of cement paste.The critical strain shows no significant change with the w/c varying from 0.35 to 0.4, while a relatively high critical strain is observed for the cement paste with w/c of 0.45, possibly due to the formation of more C-S-H and ettringite bonds between cement particles.
(2) The replacement of cement by fly ash decreases the storage modulus at LVER and viscoelastic yield stress because of the increase in the interparticle distance.The critical strain of fly ash cement paste is in the same order to that of pure cement paste.The addition of nano-Fe 3 O 4 particles increases the water requirement and tends to form small agglomerates, resulting in an increase in the storage modulus at LVER and viscoelastic yield stress.The increase of critical strain can be possibly explained by the modification of cohesive bonds between cement parby the nanoparticles.(3) The addition of PCE increases the critical strain of cement paste, irrespective of the cementitious composition, which can be attributed to the intertwining of PCE molecules adsorbed onto the solid particles.Low PCE additions can increase the viscoelastic yield stress, while for the pastes with high PCE additions, the storage modulus at LVER and the viscoelastic yield stress are significantly decreased.
To achieve the rheology control of cementitious materials during construction process in real-time, more research should be further conducted to understand the viscoelasticity and the underlying mechanisms of cement-based materials concerning the influence of different mineral admixtures, aggregates, and chemical admixtures.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .
Fig. 1.Particle size distribution of the Portland cement and fly ash.

Fig. 3 .Fig. 4 .
Fig. 3. Influence of w/c on the (a) evolution of elastic stress and (b) critical strain and viscoelastic yield stress of plain cement paste.Error bar indicates the standard deviation.

Table 1
Chemical composition of the cement and fly ash (% by mass).
D. Jiao and G. De Schutter

Table 2
Mix proportions of cement pastes prepared in this study.Typical oscillatory strain sweep measurement result (Mix.OPC-35-0PCE).LVER is the linear viscoelastic region, and τ e,l is the viscoelastic yield stress.