Complex Modulus characterization of an Optimized Binder with SCMs: proposition of an enhanced Cement formulation to improve Stiffness Behavior and Durability of Mortars and Concretes

Materials optimization is an aspect of continuous endeavor for civil engineering in many applications, especially in construction where the materials’ durability and mechanical performance are crucial for structural integrity. Structures such as aerogenerators, both towers and foundations, are highly exposed to cyclic loads with a broad range of frequencies and levels. The improvement of the stiffness behavior can significantly enhance their fatigue resistance and consequently durability. This paper aims to evaluate the impact of a high-performance binder optimization, using supplementary cementitious materials (SCMs) to improve the mechanical behavior of mortars and concretes, by improving stiffness response under cyclic loadings, which is related to durability and fatigue life-service. Static tests (axial compressive and splitting tensile strengths) were conducted as well as cyclic stiffness tests that were proposed as a new methodology for these kinds of materials, which may better relate the mechanical behavior in field applications. The proposition consists of complex modulus tests, under sinusoidal loading, either in pure compression and pure tension, adopting low (0.1–1 Hz) and mid-range (1–25 Hz) loading frequencies. The results show that the optimized binder resulted in a superior material with up to 23% stiffer loading response and 13.8% more energy storage elastically, with also inferences on improved durability, which is expected to delay pathological manifestations, and extended fatigue-life. The proposed testing protocol obtained results compatible with the literature and seems applicable for evaluating the dynamic behavior of cementitious materials.


Introduction
The extension of the service life and the durability of cementitious materials is a continuous endeavor in materials science and civil construction.For this, the incorporation of supplementary cementitious materials (SCMs) has become increasingly popular in recent years due to their environmental appeal, with the potential to reduce greenhouse gas (GHG) emissions, also due to its ability to influence and even improve several properties in the composites, such as mechanical behavior (compressive and splitting tensile strengths, elasticity modulus, and Poisson's ratio), materials microstructure (pore sizes distribution, hydration products and transition zone), fresh state (workability, setting-time, and bleeding) as well as durability, pathological manifestation resistance and even fatigue life-service [3,7,9,19,21,28,31].
Over time, repeated loads can cause cracks and degradation, leading to a gradual loss of supporting capacity and increasing the energy dissipation within cyclic loads [24,45].In addition, the measurement of strain can be used to assess the cracking and damage (degradation status) of cementitious materials under different loading conditions.Fatigue testing and structural modeling design require a thorough understanding of the frequency-dependent behavior of materials to accurately predict their long-term performance [24,29,34,35,37,45].
In the renewable energy sector, the optimization of the structural materials used in the aerogenerators' towers and foundations (mostly concrete and grouts, which is a kind of mortar with improved fluidity and performance) is a strategic aspect to enhance efficiency in power generation [5,14,29].Such structures are crucial to ensuring the stability of the entire system, by resisting cyclic loading in different stress levels, temperatures and frequencies.They must be able to resist those loads, derived from high speeds winds, vibrations, seismic activity, varying loading regimes (from compression to tension) and frequencies, their own weight and the mechanical system as well, sustaining the nacelle, rotors and blades [5,24,29,45].
Studies [15,29,32,33,46] have shown that the improvement of the modulus of cementitious materials used in aerogenerator towers and foundations can lead to significant improvements in durability.
Kuo and Zhuang [29] also presented evaluations on high-performance concrete for aerogenerators foundations.It was found that a higher modulus of elasticity, compared to the usual values for normal-strength concrete, were more suitable for that application having an improved resistance to the mechanical and environmental incident loads from the aerogenerators' usual operation.
These findings emphasize the importance of enhancing mechanical behavior for those applications, especially concerning aerogenerators or other applications subjected to cyclic loading.
The complex modulus, which is a measurement of material stiffness for viscoelastic materials (and corresponds to the modulus of elasticity in perfect linear elasticity), is a crucial parameter to be accounted for, due to its ability to broader evaluate mechanical behavior [8,32].It contains information on classical global stiffness and on the amount of dissipated energy during mechanical loading.Classical stiffness is evaluated from the absolute value of the complex modulus, also known in the literature as "dynamic modulus", even if inertial effects are not present during tests.
Meanwhile, the proportion of dissipated and stored mechanical energy, during a load cycle, can be evaluated from measurements such as the phase angle of the complex modulus, the storage modulus (real part of the complex modulus) and the loss modulus (the imaginary part of the complex modulus) [8].Complex modulus is also related to aspects of fatigue resistance, also providing insights into aspects of pathological mechanisms and materials' durability [27].A deeper understanding of the complex modulus and the fatigue behavior is necessary to develop more durable and sustainable structures, with more engineered materials.
With respect to SCMs, silica fume (SF) and glass powder (GP) are considered by literature as two effective materials for improving the properties of cementitious materials, by replacing content of the ordinary Portland cement (OPC), with a significant focus on binder optimizations by its incorporation [6,19,41,43].
The GP addition has also shown potential for improving similar properties [3,4,6,7,19,23].It can enhance the compressive and flexural strength of concrete, reduce its permeability [3,7] improve the workability and water retention [19] and increase the flexural and compressive strength at early ages [7,28,38].GP has been found to be an effective SCM for enhancing the mechanical and fresh-state properties of cementitious materials, with long-term effects [6,7,27,38].
Literature reports a wide range of optimizations for cementitious materials depending on the application.The increase in modulus has been demonstrated as a valid approach resulting in improved durability, by reducing cracking and increasing stiffness [16,32].It is an important material property that affects the materials' strain response under different loading conditions, in which case its study is crucial for understanding the pathological manifestations mechanisms and fatigue-life.
This paper aims to evaluate the influence of a binder optimization, achieved through the incorporation of SCMs, on the dynamic stiffness behavior of cementitious materials (concretes and mortars), which will be assessed by analyzing the complex modulus.To achieve this, the optimization adopted an approach with the addition of silica fume and glass powder as SCMs, also aiming to enhance stiffness, durability and delay pathologies manifestations (modulus degradation and cracks).The binders were tested both in concrete and mortar using the same mix design derived from an in-site aerogenerator foundation.As a reference binder, a conventional OPC formulation was used (CEM I).The optimization involved the addition of GP and SF as a replacement for OPC.The experimental program comprised static tests, such as compressive strength and splitting tensile strengths, in addition to dynamic characterization, with complex modulus tests, under low (0.1-1 Hz) and midrange (1-25 Hz) loading frequencies, in pure compression and tension.
By analyzing the mechanical behavior, this paper aims to provide better insights into the complex modulus properties with respect to cementitious materials' mechanical behavior and durability.Ultimately, this research could lead to the development of more sustainable, efficient, and durable structures as it focuses on the mechanical behavior related to fatigue, which is a mechanism for pathological manifestations in structures subjected to cyclic or dynamic loadings [17,22,36].

Experimental Program
The experimental program consists of three main stages: (i) the specimens' fabrication for characterization testing; (ii) the assembly and adjustment of the dynamic press setting for the splitting tensile testing and complex modulus analysis (CMA); and (iii) the testing procedures itself, comprising uniaxial compressive strength, splitting tensile strength, and CMA at different frequencies.All tests were conducted in a controlled temperature environment adopting a temperature of 19 °C ± 0.50, with a minimum of 4 h allocated prior to the tests beginning to ensure temperature stabilization and heat flow equalization [25,40].

Materials
The specimens were cast using two different binder formulations, with the first being a commercial formulation of OPC as a reference.The choice of CEM I as the OPC type was deliberate, as it does not contain any SCMs in its manufacturing process, thus avoiding any undesired influences.The second formulation was designed based on recommendations for optimizing durability, microstructure, fatigue life, and modulus of elasticity [6,7,27].Table 1 provides the detailed formulations for the binders utilized in this study.
The incorporation of GP and SF has usually a positive effect on the microstructure, with the enhancement of the modulus [4,6,7,19,27,39].The proposed optimized formulation also had a low-carbon design, with a 28% clinker consumption reduction, which is also significant for sustainability aspects [3,7,46].
The cement CEM I 52.5N employed complied with the European standard EN 197-1 [11].The GP was obtained from demolition glass waste, of a waste disposal plant in Caen, France.The crushing and sieving process was repeated until achieving a diameter lower than 63 μm.The SF used complies with EN 13,263-1 & 2 [10].It has a spherical aspect with an absolute density of 2.24 g.cm −3 and a specific surface area of 225 m 2 /g with high purity.Other parameters and testing are presented in Table 2.
The silica fume used in this study meets all EN 13263-1 and 2 [10] requirements.With 96% ± 2 of SiO 2 and 0.14% ± 0.05 of elemental Si, it is highly pure and crucial for concrete performance.Na 2 O eq. content of 0.50% ± 0.1 and SO 3 content of 0.27% ± 0.50 are acceptable, signifying the absence of harmful impurities.The activity index at 28 days is ≥ 101%, indicating efficient pozzolanic reactivity.Additionally, the observed loss on ignition of 2% ± 0.5 proves thermal stability, critical for manufacturing and the product behavior.
The fillers' density was determined using a helium pycnometer and the particle size distribution (PSD) was by the wet process of EN 993-1 [12].The specific surface area was determined using the Brunauer-Emmett-Teller method (BET), based on the EN ISO 18757 [13].These results are presented in Table 3.
Comparing these results to literature, the specific gravity values of the OPC and GP were within the typical range reported, with suitability for use as raw materials.However, the high BET surface area of SF was significant and exceeds the conventional values, suggesting that the SF is highly reactive and with a high level of fineness, which is beneficial to improve the mechanical behavior and durability.
The importance of the fineness of binder and its constituents cannot be overstated, as it directly affects the microstructure and mechanical properties of the resulting concrete.Finer materials tend to improve the final density and porosity due to an enhanced pozzolanic reaction and pore filling.Therefore, it is crucial to consider not only the maximum diameter but also the entire particle size distribution (PSD) when selecting raw materials.The complete PSD curves, presented in Fig. 1, provide a more comprehensive view, which can aid in optimizing the mix design for improved performance.
The results demonstrate a continuous distribution of the OPC, falling between those of the GP and SF.This observation suggests that the addition of GP may not have a significant effect on the porosity of the product, except for the influence of hydration reactions.In contrast, the addition of SF may lead to improvements in microstructure.These findings may provide initial evidence of the potential benefits of SF incoporation.However, further investigations are needed to fully understand the mechanisms behind these observations and to optimize these incorporations [19,39,46].Figure 2 presents the current methodology through the experimental procedure abstract.
After the characterization of the raw materials, the concrete specimens were cast and left to cure for 24 h before being demolded.They were then placed in a humid chamber with a temperature of 22 °C and relative humidity of 50%, which is a common practice in the industry to simulate realworld conditions and avoid leaching of the material during curing [25,40].
It is worth noting that despite the differences in binders used in the specimens, both formulations aimed to maintain the same mix design parameters and mixture procedures.This approach allowed for a more direct comparison of the effects of each binder on the mechanical properties of the specimens.The water/binder ratio was kept constant at 0.45, with a binder consumption of 350 kg/m 3 for all mixtures.These details are summarized in Table 4.By keeping the same mix design, the study sought to isolate the effects of the binders on the properties of the resulting concrete and mortars.
In terms of geometry, two sizes of specimens were cast for this experimental program.The first one was a (i) regular cylindrical size of 11 cm × 22 cm, used in regular compressive strength tests.The second one was a (ii) smaller cylindrical version, with 39 mm × 88 mm, required to obtain a specimen with a lower rupture loading, under 25 kN, due to the loading limitations of the dynamic press.The regular-size specimens were meant for the compressive strength tests, while the smaller ones were used for the tensile strength and CMA tests.
For the last, to ensure that the mechanical properties of the binder optimization were properly characterized using the smaller specimens (39 × 88 mm), it was necessary to maintain the elementary representative volume (ERV).For this, it was excluded the coarse aggregates from the mix design formulation, in which case its incorporation could result in specimen size effects, overwhelming the mechanical behavior prior the cementitious matrix influence.
Therefore, a minimum proportion of 1:10 between the maximum diameter of the fine aggregate and the diameter of the specimen was maintained, according to standard recommendations for size effects reduction, complaining with ASTM C192 [1].By adopting this approach, an ERV was achieved, and the smaller specimens could be used to evaluate the tensile strength and the complex modulus, under pure tension and compression loading conditions, with a high level of accuracy.

Static and Dynamic Press Sets
The experimental program comprised tests in two different laboratories.At first, it was conducted the static testing, using a three-column compression testing machine with a maximum load of 4000 kN, equipped with a digital control system, a load cell with a precision of ± 0.5% of the load cell, and an axial extensometer with an accuracy of ± 0.01 mm and a displacement rate of 0.01-100 mm/min.This testing set was specifically intended for conducting compressive strength tests on the concrete specimens.Figure 3 shows the tests apparatus in the French laboratory.
Secondly, it was used a Universal Testing Machine dynamic press (UTM-25), a servo-hydraulic equipped with a high-speed data acquisition system and real-time digital control system, capable of measuring mechanical properties precisely under cyclic loading, with a maximum load capacity of 25 kN and displacement resolution of 0.1 μm.This machine allowed for the accurate measurement of complex modulus and phase angle using  dynamic mechanical analysis (DMA), with the capability of applying a sinusoidal load up to a frequency of 100 Hz, facilitating the characterization of the viscoelastic behavior of cementitious materials.This second testing set was inteded for analyzing the splitting tensile strength and complex modulus.Figure 4 presents the UTM-25 and the adapted test apparatus in the Brazilian laboratory.
Concerning the connection between endplates and specimens, both for compression and tension tests, it was used a bicomponent epoxy structural adhesive to connect the upper and bottom endplates to the specimen surface.It was assured to maintain a fine layer, by having a minimum applied load (0.1 kN) with the fresh glue positioned.
The positioning of the three Linear Variable Differential Transformers (LVDT) used to measure displacement was also modified.The first reading was taken at the bottom endplate to measure minor deformation throughout the tests, and the other two were in contact with the upper plate, to get their average.The specimen deformation could then be assessed using Eqs. 1 and 2, allowing for precise measurements.
The P i (t) variable represents the reading of each LVDT position recorded over time, while the Initial Position refers to the initial position of each of the three data loggers when no load was applied.
The testing set was adapted to make possible the mechanical characterization through dynamical tests in reduced specimens.The precise deformation measurement was possible due to the modifications of the LVDTs positioning and its position-capturing process as well. (1)

InitialSpecimenHeight
(2) This new assembly has the potential to expand the testing possibilities, being an innovative technique, by reducing the specimens' rupture loading, making feasible the use of smaller specimens and maintaining the ERV.

Complex Modulus Analysis: Theoretical Concepts and Test Requirements
Cementitious materials can be considered complex viscoelastic materials whose mechanical properties are dependent on the complex modulus, which is a fundamental attribute to characterize responses to stress and deformation.The accurate determination of this parameter is critical for understanding the mechanical behavior and ensuring durability in practical applications.Concrete and mortars have the ability to partially store and partially dissipate mechanical energy under cyclic loadings whereas the increase in this energy dissipation is a possible indicator of the degradation of the material [27,30,35,37].The phase angle, between other properties, is a direct measure of energy dissipation [8]. Figure 5 demonstrates the modeling of a sinusoidal loading test and its corresponding strain response.By utilizing these modeling techniques, researchers can gain a better understanding of the viscoelastic behavior of concrete and optimize its mechanical properties for various applications, which can enhance durability and long-term performance.
Figure 5a shows the stress applied to a specimen at a defined frequency (f) in the blue illustration, followed by its corresponding reading signal in Fig. 5b (stress vs. time).Similarly, the red illustration portrays the strain response, specifically the axial strain, along with its respective readings (strain vs. time).Equations ( 3) and (4) describe the modeled stress and strain signal as a function of time.Equation ( 5) presents the fundamental concept of the absolute value of complex modulus, while Eq. ( 6) provides the specific definitions for its components, namely the storage modulus and the loss modulus.
where as: (t) = Stress function along the time; The phase angle ( ) represents the angular lag between the stress and strain signals and is a fundamental characteristic of viscoelastic materials, which is closely related to the concept of complex modulus.In the frequency domain, the complex modulus describes the behavior of the elastic The |E * | , also named and reported as dynamic modulus, is a measure of the stiffness of a material under dynamic loading conditions.It is calculated from the real and imaginary parts of the complex modulus.The real part represents the material's ability to store energy elastically, also known as the storage modulus.The imaginary part corresponds to the material's characteristic to dissipate energy, also called the loss modulus.It is important to note that despite being called the dynamic modulus, there are no inertial effects involved [8,29,37].
Concerning the specifics of the CMA tests, the smaller specimens (39 mm × 88 mm) were fabricated to meet the reduced cylindrical geometry required to fit the limitations of the servo-hydraulic universal testing machine (UTM-25), which was capable of handling a 25 kN maximum loading capacity.
For the experimental control, it was used of a dynamic mechanical analyzer controller (DMA) to record the loading and LVDTs' positions responses under different loading conditions.The collected data was analyzed externally using an interpolation routine to ensure the most accurate and precise results for the complex modulus and its phase angle.
To ensure the accuracy of the results, the interpolation routine utilizes more complex equations to provide where as: (t) = stress function along the time; (t) = strain function along the time; = angular velocity, in the frequency domain; |E * | = absolute value of complex modulus; = phase angle, based on signals' delay; n = number cycles per sweep, for average; A , A = amplitude in phase, for stress and strain; (7)  These definitions are widely used in literature, particularly in the field of signal processing and analysis [8,26].The CMA testing was conducted with loading control using a sinusoidal loading shape, reported as the most usual method for such applications [27,35,37] at various frequencies, ranging from 0.1 to 25 Hz.The resulting loadings and displacement positions signals were recorded, to evaluate the complex modulus of the material by further analysis, through the curves interpolation, according to the method discussed above.
The chosen frequency range encompassed both the low and mid-frequency range only, avoiding potential dynamic effects on the readings (frequencies higher than 25 Hz), as recommended by ASTM E1876 [2].A careful selection of the frequency range is crucial to obtain reliable and accurate results for the characterization of the viscoelastic behavior.Additional testing parameters are presented in Table 5.
The fck is the characteristic cylinder compressive strength and fyk is the mean cylinder compressive strength, accord- ing to EN1992-1-1 [18].The low-frequency range investigates the viscoelastic behavior under slow deformations and attempts to characterize the viscous behavior, leading to the dissipation of mechanical energy.On the other hand, the mid-frequency demonstrates the behavior closer to an elastic solid.
The range of frequencies selected for CMA is essential for the accurate characterization, as it determines the degree of deformation, once the frequency range can have a significant impact on the resulting complex modulus values and phase angles of materials [8,26,27,30,35].

Results and Discussion
At sections 3.1 and 3.2, it is presented the results and analysis of the compressive strength and splitting tensile strength of the concretes and mortars, discussing their implications and findings in detail.Finally, at Sect. 3.3 is presented the results of the CMA, for the mortars characterization and insigths on its viscoelastic behavior.

Compressive Strength results for Concrete formulations
Figure 6 shows the results of the compressive tests conducted at 28 and 90 days.The test results for both concrete formulations, M1 and M2, show the first effect of the optimization on the mechanical properties.The optimization of concrete materials using SF and GP has been shown to have significant effects on the mechanical properties, pathological manifestations, and durability of the materials.As shown in Fig. 6, M1 exhibited higher compressive strength values at both 28 and 90 days, with higher average strength, in both ages.M2 showed lower compressive strength values for the same period.The standard deviation for both formulations was within an acceptable range, indicating consistency in the testing process with attention to a much lower variance for 90 days.
The lower compressive strength values of M2 are attributed to the 35% OPC replacement with GP (30%) and SF (5%).However, it is important to note that the optimization aimed at improving the strain response throughout the complex modulus parameter of the material, and not necessarily the compressive strength is gonna follow the same trend.Thus, the reduction in compressive strength observed in M2 should be considered in light of the potential benefits in terms of complex modulus improvement.
For the last, it is important to note that it was a decrease in strength reduction from 28 to 90 days.The GP addition is reported by literature as having a long-term effect.According to literature [3,19,28], the GP addition in concrete can lead to higher compressive strength and durability properties, including resistance to water absorption, chloride penetration, and carbonation, even after 365 days of exposure.Therefore, the GP incorporation can still be a suitable OPC replacement, leading to improved mechanical and durability in the long term, having M2 a higher compressive strength increase (11.00%) compared to M1 (3.50%) in this analysis period of time (28 to 90 days).Different authors [23,38] have examined the effect of GP on concrete durability and concluded that its addition can improve the resistance to chemical attack, frost and thaw cycles, and alkali-silica reaction (ASR), common causes of pathologies in structures.The review also noted that the use of GP in concrete can contribute to sustainable development, by reducing waste from glass manufacturing and decreasing the GHG of the industry [3,4,7].
In addition, the use of SF and GP has also been shown to improve the resistance of concrete to various pathologies, such as sulfate attack, alkali-silica reaction, and chloride penetration [6,19,20,28].Thus, a comprehensive evaluation of the durability and resistance to pathological manifestations of the optimized concrete formulation is warranted in future studies, beyond the compressive strength parameter.Despite the compressive strength decrease (36% and 33% for 28 and 90 days, respectively), M2 remains suitable for structural applications.

Splitting Tensile Strength results of Mortars formulations
Figure 7 displays the results of the splitting tensile tests performed on mortar specimens at 90 days.The results demonstrate the effect of the optimization on the splitting tensile strength of the materials.Similar to compressive strength results, the tensile strength of M1 and M2, provided similar behavior with a more complete picture of the statical mechanical properties.M1 exhibited higher tensile strength values, compared to M2 with a 31% reduction, being worthy noting with a lower decrease compared to the reductions visualized in compressive strength results (36% and 33%).The standard deviation for both formulations was within an acceptable range, indicating consistency.Additionaly, M2 presented a lower variance, as visualized in Fig. 7c, by the closer boxplot boundaries, indicating a more homogeneous material likewise.
It is reported by literature a correlation between both parameters (compressive and tensile strength), with tensile strength approximately 10% of the compressive strength.The results visualized were consistent with this relationship, with M2 showing a higher proportion (8.47%) compared to M1 (7.81%).It should be noted that the OPC replacement resulted in a similar reduction in tensile strength, compared to compressive strength.However, as previously discussed, the optimization was aimed at improving the complex modulus, the desired optimization parameter.

Complex Modulus for Pure Compression (Compressive Stresses)
Figure 8 presents the first results for the absolute value of complex modulus ( |E * | ) with its respective phase angle ( ).The presented values correspond to the average of the different sweep frequencies, for low (0.1 to 1 Hz) and mid-range (1 to 25 Hz) frequencies.
In regards to the modulus, the main optimization parameter, the results in Fig. 8a show that M2 consistently had a higher AVCM average compared to M1.Specifically, there was an 18% increase in |E * | and a 7% increase in com- paring both formulations.These findings suggest that the optimization was successful in making M2 stiffer than M1, which is a desirable outcome.It is worth noting that a higher AVCM is considered advantageous for enhancing the material's durability and resistance to pathological manifestations [15,16,32].
Concerning the variance, the M2 results exhibited a higher standard deviation, of 0.52 GPa, compared to M1, 0.45 GPa, with a percentage standard deviation of 2.86% and 4.01% respectively.This implies that despite its higher absolute deviation, M2 had a better uniformity and homogeneity, suggesting that the optimized binder resulted in more consistent and homogeneous properties.These findings comply with literature reporting the benefits of GP and SF incorporation to improve their mechanical properties and durability [3,19,23].
Regarding the , M2 showed a more pronounced increase in the low-frequency range, suggesting a more energyabsorbing behavior, tending to dissipate more energy than lower phase angles in low frequencies (< 1 Hz), by 7%.The increase in stiffness observed in M2 is attributed to the optimization proposed, which is known to improve the strength and stiffness when added in appropriate proportions.
These findings have important implications for structural design and construction, and future research may explore further optimization strategies to achieve the desired balance between strength, stiffness and energy-absorbing capacity, aligned with parameters of durability and resistance to pathological manifestations [23,38].Figure 9 presents the individual results of |E * | with its respective , over the test- ing frequencies.
The results of the complex modulus tests demonstrated that the optimized binder formulation, M2, consistently exhibited a higher complex modulus than M1 across all sweep frequencies, with an average value of 15.48 GPa, similar to the previous average, with no intersections.This finding indicates that M2 has a higher stiffness than M1, which could potentially improve the material's durability and resistance to pathological manifestations such as cracking and modulus degradation [29,35].
Furthermore, it was mostly observed an uptrend tendency in the low frequencies range for both parameters, which is in agreement with previous studies that have found an increase in the stiffness of concrete and closer to elasticity as the frequency increases [14,34].However, there were divergent values, it should be noted that there was an exception for M2 |E * |, with a downtrend in lowfrequencies and some values at 25 Hz, which could potentially be attributed to dynamic effects from the testing set, labeled as outliers in Fig. 8.
Upon analysis of the results for , it was observed that both formulations, M1 and M2, had very similar readings with not much significant difference between them, and a mean of 1.05°.Also, no statistical difference was found by ANOVA, comparing both phase angle series, even with a significance level of 99%.However, it was found that the loading frequency achieved the highest phase at 10 Hz, with the higher values for modulus.The phase angle is a direct function of the loss modulus, and the higher phase angle indicates a greater ability to dissipate energy, according to the presented equations in Eq. 5.In general, the phase angle for M2 was mostly higher than that of M1, which suggests that the optimized binder has a greater ability to dissipate energy.This finding is consistent with literature that reported an increase in the energy dissipation ability of concrete with those additions [19].
The behavior of increasing complex modulus with frequency up to 1-10 Hz, followed by a plateau, is resported as usual for viscoelastic materials, usually explained by the microstructure alignment, where further changes in frequency do not affect the modulus significantly, which literature can provide insight in similar aspects [14,34,36].This is typically attributed to the increased stiffness of the material as the microstructure becomes more ordered at higher frequencies.However, it is important to note that there is some variability in the results, as indicated by the standard deviations.This variability may be due to several factors, including measurement error, heterogeneity in the material, and experimental conditions.
Overall, these results suggest that the OPC replacement process has led to improvements in the mechanical properties of M2 and that these improvements are frequency dependent.For the last, the results at 10 Hz produced the highest phase angle for both materials (M1 and M2), having a greater ability to dissipate energy [24,30,35].This behavior is worthy of further investigation, having possible implications on fatigue behavior.The results obtained demonstrate that M2 has a similar consistently higher modulus (16.92 GPa) compared to M1 (14.01 GPa).Individually, it had similar results both for low and mid-range frequencies.This significant increase resulted in a stiffer material even for tensile stress and can improve durability and reduce the susceptibility to pathological manifestations such as cracking.Furthermore, the standard deviation of M2's complex modulus (1.116 GPa / 6.3%) was higher than M1 (0.586 GPa / 4.09%), indicating more variability, which is possible attributed to test variations and misreadings.

Complex Modulus for Pure Tension (Tensile Stresses)
The phase angle of M1 and M2 also exhibits differences.M1's average phase angle is 1.32°, while M2's is 1.10°.This lower value of phase angle for M2 indicates that it is less prone to energy dissipation compared to M1.The standard deviation for M2 (0.329°) is lower than M1 (0.355°), suggesting a more consistent and homogeneous mechanical behavior.The higher complex modulus and lower phase angle of M2 indicate improved stiffness and lower energy dissipation properties compared to M1, which could lead to superior behavior also in tensile loading regime.Figure 11 presents the individual results over the frequencies.
M2 exhibited a consistently higher modulus compared to M1 across all sweeping frequencies, and the 10 Hz frequency presented the lowest modulus and highest phase angle for M2.The results of |E * | showed a gradual increase with frequency after 10 Hz, with a decrease in the values for the phase angles.The average results of the M2 phase angle indicated a more elastic behavior for pure tension compared to M1, with generally lower values.It provides insights on the importance of understanding the materials' behavior under different loading conditions, as it can significantly impact structural performance and durability.
It was also observed that the phase angle increased with decreasing frequency for low frequencies, which diverged from the previous results obtained under pure compression.It suggests the mechanical behavior is dependent on the loading applied and the loading frequency is an important aspect in the resulting mechanical properties.The gradual increase in modulus with frequency after 10 Hz is consistent with the mechanical behavior in pure compression, by the plateau effect [14,36].
The high standard deviations in both complex modulus and phase angle indicate significant variability in the results.This variability can occur due to variations on the samples, environmental and temperature conditions, and eventually due to measurement errors.Also, no statistical difference was found (ANOVA), comparing phase angle series, even with a significance level of 99%.The overall trends in the results are consistent with the expected behavior of viscoelastic materials.The complex modulus and phase angle are dependent on the frequency and temperature, as shown in previous studies on viscoelastic materials [8,26].
The pure tension results demonstrate that M1 exhibited behavior closer to viscosity at lower frequencies, while M2 showed a more elastic response, consistent with the expected behavior of viscoelastic materials.These results demonstrate the importance of understanding the frequency-dependent mechanical behavior of these materials, and also it demonstrates to have implications in the structural designs for specific applications.
The findings of this paper were aligned with the literature for the importance of understanding the mechanical behavior of viscoelastic materials, at different frequencies and temperatures [6,19,23,27,34,35].Moreover, these results offer valuable insights into the viscoelastic behavior and complex modulus, which can be beneficial for structural design and the development of enhanced modulus optimization techniques.This knowledge is particularly valuable in applications where increased stiffness and improved durability are desired.Additionally, the experimental insights and reliable data obtained can aid in accurate modeling and analysis.

Conclusion
This paper aimed to assess the impact of a binder optimization on the dynamic stiffness behavior evaluated using the complex modulus.The optimized binder was composed also of OPC, having additions of silica fume and glass powder as SCMs, aiming to enhance stiffness and durability.The binders were tested both in concretes and mortars using the same mix design derived from an in-site aerogenerator foundation.Also, it was proposed an adjusted method for complex modulus characterization of cementitious materials.
The results obtained demonstrate that the optimized binder had a positive effect on the mechanical properties compared to OPC.In the statical tests, it was observed that although there was a decrease in strength due to a reduction in clinker content, this effect was less significant for longer ages, specifically at 90 days (due to the GP longterm hydration).Nonetheless, all obtained results for compressive and tensile strength remain suitable for structural applications.The complex modulus findings showed M2 a stiffer material with an increase in the energy dissipation ability for compression, and a decrease for tension.Also, it was presented a comprehensive overview of its implications on durability, pathological manifestation resistance and even fatigue life.
Indeed, the proposed characterization method and the materials characterization results (complex modulus) achieved experimental outcomes consistent with literature.These findings may have valuable implications for applications that require strain hardening, durability enhancement, and fatigue resistance.The conclusions can be summarized as follows: • The compressive and splitting tensile strengths decreased by an average of 33% and 31%, which is attributed to the OPC replacement (30% GP and 5% SF) and consequently to the clinker reduction.However, the proposed binder achieved relevant strength levels, making feasible the use of dosage techniques to achieve similar strength levels for further mix designs; • By characterizing the complex modulus and phase angle of two binders, M1 and M2, under pure compressive and tensile stresses, it was demonstrated that these materials can exhibit distinct results within frequencies, demonstrating a frequency-dependent behavior.These insights are crucial for developing more resilient and durable materials and for predicting degradation mechanisms; • The optimization resulted in a higher complex modulus for M2, stiffer than M1.It was also demonstrated that a higher complex modulus is considered an advantage for improving the material's durability concerning its mechanical behavior; • Aside from the modulus increase, the optimized binder (M2) demonstrated a higher implicating a higher loss modulus (more viscoelastic behavior), which is not a usual behavior in literature from stiffer materials; • The SCMs' addition proved to have a major effect on the mechanical response.It was seen an up to 37% variation in the complex modulus for the same loading regimes between the assessed materials, with a 23% increase of M2 modulus in compression, beyond its usual implications on durability.
85 Page 14 of 15 These findings provided valuable insights into the modelling, design and engineering of concrete structures, as well as for the understanding and prediction of mechanical behavior and durability over time.The M2 binder, applied in mortar, showed a better performance, with improved stiffness and durability.Also, with a focus on fatigue behavior, it may indicate a possible improved performance in that same aspect.The complex modulus of M2 was consistently higher than M1 across all sweep frequencies and loading regimes, indicating that the optimization has resulted in more stiffer, stable and predictable material behavior.
As a final contribution, to fully understand the relationship between mechanical behavior and durability, further research may lead to further insights.For this, it is suggested research with a focus on (i) fatigue testing, to supplement the modulus characterization and to quantify degradation over time, (ii) modulus characterization over different loadings amplitudes (stress levels) and temperatures, providing insights into different stress levels and freeze-thaw cycles throughout years and seasons, for long-term effects, and (iii) durability tests, to substantiate claims of improved resistance to pathological manifestations.These future research suggestions can provide a more holistic assessment of the long-term structural performance and can help guide the development of materials with tailored properties.

Fig. 3 A
Fig. 3 A Three-Column Compression Testing Machine (a) with its Digital Control System (b) (t) = Strain function along the time; 0 = Stress amplitude, of the sinusoidal shape; 0 = Strain amplitude, similarly; f = Loading frequency of the tests; = Angular velocity, with = 2 f ; = Phase angle, the signals' delay; |E * | = Absolute value of complex modulus; E' = Real part of complex modulus (Storage Modulus); E" = Imaginary part (Loss Modulus).
6) E � = |E * | cos ; E �� = |E * |sen modulus with respect to the strain and stress signals.Eq. 5 defines the relationship between the Absolute value of complex modulus ( |E * | ), and Eq. 6 presents the definitions for Storage ( |E ′ | ) and Loss Modulus (|E ′′ |).These equations have been extensively utilized in literature to model viscoelastic behavior.

Fig. 4
Fig. 4 Dynamic Press (a), testing set for Tension and Compression (b) LVDTs Assembly in detail (c) amplitude out of phase, for stress and strain; C , C = linear component resulting from drift or damage; D , D = stress and strain offset (mean values).

Fig. 5
Fig. 5 Complex Modulus Test Schematic (a) and Data Modeling in Time-Domain (b)

Fig. 8
Fig. 8 Results of |E * | (a) and (b) in pure compression for low and mid-frequencies

Fig. 9 Fig. 10
Fig. 9 Individual results of |E * | and in Pure Compression versus Loading Frequencies

Figure 10
Figure 10 presents results for |E * | with its respective for pure tension.The presented values correspond to the average

Fig. 11
Fig. 11 Individual results of |E * | and in Pure Tension versus Loading Frequencies

Table 1
Proposed Binders Formulations

Table 3
Characterization of the Raw Powder Materials Fig. 1 PSDs of the Cement, Glass Powder and Silica Fume

Table 5
CMA Testing Parameters