# Effect of Moisture Condition of Structural Lightweight Concretes on Specified Values of Static and Dynamic Modulus of Elasticity

^{*}

## Abstract

**:**

_{d}), specified by ultrasonic pulse velocity measurements, is often used, especially for concrete built into construction, to estimate the static modulus of elasticity (E

_{c,s}). However, the most commonly used Equations for such estimations do not take into account the influence of concrete moisture. The aim of this paper was to establish this influence for two series of structural lightweight aggregate concrete (LWAC) varying in their strength (40.2 and 54.3 MPa) and density (1690 and 1780 kg/m

^{3}). The effect of LWAC moisture content turned out to be much more pronounced in the case of dynamic modulus measurements than for static ones. The achieved results indicate that the moisture content of the concrete should be taken into consideration in modulus measurements as well as in Equations estimating E

_{c,s}on the basis of E

_{d}specified by the ultrasonic pulse velocity method. The static modulus of LWACs was lower on average by 11 and 24% in relation to dynamic modulus, respectively when measured in air-dried and water-saturated conditions. The influence of LWAC moisture content on the relationship between specified static and dynamic moduli was not affected by the type of tested lightweight concrete.

## 1. Introduction

- tangent initial modulus specified at stress equaled to 0 (E
_{0}[1]), - secant initial modulus determined at the first cycle (E
_{c,0}[12]); - secant stabilized modulus determined after the third cycle (E
_{c,s}[12]). - Besides the static moduli, mentioned above, a dynamic modulus (E
_{d}) is also specified for concrete. It is carried out in non-destructive tests causing vibrations in concrete, which result in stresses being vanishingly small. For this reason, the value of the dynamic and static initial moduli are often equated [2] and their values are bigger than the static secant modulus, which is the basic parameter used for designing the process of a concrete structure.

_{c,s}and E

_{d}, dedicated also to LWAC, were proposed by Swamy and Popovics, respectively [2]. In Equation (3), additionally concrete density (ρ) and a constant depending on the unit system were taken into consideration (k). Nevertheless, parameter k was specified for units in psi (0.23), while in SI is unidentified [18].

_{c,s}and E

_{d}may be significantly different from estimations given by the proposed relationships [19,20,21,22,23,24,25,26]. For example, the ratio of static and dynamic moduli of normal-weight concretes determined in water-saturated conditions, calculated on the basis of data given in [26], ranged from 0.72 to 0.76. Other concretes of the same compositions but cured in air and tested in air-dried conditions showed visibly higher ratios of 0.79–0.87. As a result, Equation (1) gives an overestimated value of static modulus on average by 10% for concretes cured in water and tested in saturated conditions, while it seems to be accurate enough for concretes cured in air and tested in air-dry conditions. In the first case, the estimated values were higher by 2.5–3.5 GPa, while in the second case, the differences were up to 0.6 GPa. Verification of Equation (2) gives much bigger differences in estimation. The calculated value of static modulus was higher in relation to the measured value on average by 25 and 10%, respectively for concretes cured in water and cured in air. As a result, the values of static modulus were overestimated even by up to 9 GPa. The results given in [22,23] proved that both relationships overestimate the values of static modulus in comparison to the measured values and Equation (2) gives much higher results. The estimated E

_{c,s}was higher by up 50% and the difference in overestimation of the static modulus was up to 15 GPa. In turn, the analysis of results for structural lightweight concretes, presented in [24,25], shows much lower differences in measured values of dynamic and static moduli (0 to 4 GPa) than for NWACs reported in [22,23,26] (4 to 17 GPa). Therefore, for the reported LWACs, the above-mentioned relations underestimate a value of E

_{c,s}. by up to 4.5 GPa (on average by 12%) and 3.0 GPa (on average by 8%), respectively when applied Equations (1) and (2). It should be noted that the difference between measured and estimated values of static modulus of elasticity was higher when the initial moisture content of the lightweight aggregate was bigger. Such an observation may be explained by the different microstructure of LWACs with aggregates of different initial moisture content. As it was proved in [9,27], the less initial moisture content of LWA, the better adhesion between cement paste and the aggregate and the more linear stress–strain relationship.

_{c,s}and E

_{d}are independent of the method of curing, air entrainment, cement type or test condition [2,18], the results presented in [26] indicate that the relationships between dynamic and static moduli may be dependent on the concrete moisture condition. Nevertheless, this thesis should be proved in research, as concrete reported in [26], although had the same compositions, in fact, had considerably different microstructure and mechanical properties due to different curing conditions.

_{c,s}and E

_{d}may be less considerable than for normal-weight concrete.

## 2. Materials and Methods

^{3}; the bulk density tested in accordance to EN 1097-6 [31], 730 kg/m

^{3}; the water absorption, determined according to EN 1097-6 [30] after immersion in water for 24 and 72 h reached 18.8 and 25.3%, respectively. Analyzing the above properties of the lightweight aggregate and comparing them to properties of other lightweight aggregates [2,32,33,34,35,36], it should be stated that despite rather high-water absorption, it reveals relatively high crushing resistance which made this LWA one of the most suitable for structural concretes.

_{c,s}) was tested according to Method B of the standard EN 12390-13 [12] firstly and then the dynamic modulus (E

_{d}) was specified using ultrasonic pulse velocity method as described in EN 12504-4 [40]. Therefore, to determine the loading and unloading range for testing the secant modulus, 3 cylinders of each concrete series were subjected to compressive strength test at the beginning. As a result, for each concrete series, the mean value of compressive strength (f

_{cm, cyl}) was calculated. Finally, the nominal lower stress (σ

_{p}) and the nominal upper stress (σ

_{a}) were assumed as 0.5 MPa and f

_{cm, cyl}/3, respectively. The standard scheme of loading and unloading cycles, as well as an example of cycles registered at testing, are presented in Figure 3. The testing procedure according to Method B consists of three loading cycles in the stress range from the lower stress σ

_{p}up to the upper stress σ

_{a.}The stabilized secant modulus of elasticity was determined according to Equation (4), where σ

_{a}

^{m}and σ

_{b}

^{m}are stress values measured at the third cycle, while ε

_{a,3}and ε

_{p,2}are corresponding strains.

_{cm, cyl}/3) that is significantly lower than the fatigue strength. As was stated in [2,10,11], cyclic loading under the fatigue strength should not affect a test result. Such behavior of tested lightweight concretes under cyclic load was also proved in this research. One selected specimen of each concrete series was subjected three times to tests of static modulus of elasticity in different arrangements of sensors in relation to a specimen and a specimen in relation to the machine platens. The measurement repeatability was satisfactory and showed no visible effect of multiple cyclic loading on a specified result of the test.

## 3. Results

#### 3.1. Results of Preliminary Tests at the Standard Age of 28 Days

^{3}, respectively for series LC1 and LC2. Meanwhile, the corresponding average oven-dried density was 1680 and 1770 kg/m

^{3}. Any individual result did not differ from the mean value of more than 20 kg/m

^{3}.

#### 3.2. Results of Main Tests at the Age of Three Years

^{3}, respectively for series LC1 and LC2. Meanwhile, the corresponding average density under the water-saturated conditions were 1860 and 1920 kg/m

^{3}, and the corresponding average oven-dried density was 1690 and 1780 kg/m

^{3}. Any individual result did not differ from the mean value more than 20 kg/m

^{3}.

#### 3.2.1. Static Secant Modulus of Elasticity

#### 3.2.2. Dynamic Modulus of Elasticity

## 4. Discussion

#### 4.1. Relationship between Static Secant and Dynamic Moduli of Elasticity

_{c,s}and E

_{d}determined for individual specimens tested in air-dried conditions ranged from 0.85 to 0.93, while specified in water-saturated conditions ranged from 0.71 to 0.80. The effect of the concrete series was not observed. As a result, the average ratio E

_{c,s}/ E

_{d}was assessed as 0.89 and 0.76 for air-dried conditions and water-saturated conditions, respectively. In both cases, the standard deviation of the ratio was 0.03. The obtained ratio values for tested lightweight concretes were slightly lower than those calculated for LWACs reported in [24,25]. On the other hand, the obtained E

_{c,s}/ E

_{d}turned out to be insignificantly higher than those calculated on the basis of data given in [26] for normal-weight concretes and much higher when compared to those calculated for NWACs reported in [22,23]. As in the case of [26], in this research, the value of E

_{c,s}/ E

_{d}determined in air-dried conditions was considerably higher than for water-saturated concretes. The above comparison of ratios achieved and calculated on the basis of reported data indicates that E

_{c,s}/ E

_{d}is affected by both moisture content and the homogeneity of the concrete composite structure. The less homogeneous structure of a composite (the weaker bond between cement paste and aggregate or the bigger difference in stiffness of these two constituents materials or the bigger extent of concrete degradation due to detrimental exposure), the lower the ratio.

_{c,s}, on average by 6 and 3%, respectively.

#### 4.2. The Influence of Moisture Content on Specified Values of Modulus of Elasticity

_{c,s}determined in water-saturated conditions were higher than the values tested in the air-dried conditions by only 2% on average. Meanwhile, for the dynamic modulus, such a mean increment was as high as 19%. No visible influence of the concrete series was observed.

_{c,}

_{s}of normal-weight concrete tested in water saturated condition ranged from 12 to 32% in relation to the dry condition. It should be noted that although the referred concretes had similar strength to those tested in this research, the porosity structure of composites was different. To achieve a similar strength level of concrete made of a more porous aggregate, it is necessary to use cement paste tighter than in the case of normal-weight concrete. Therefore, in saturated condition there is less water in the cement matrix of LWAC than of NWAC. Moreover, the bond between aggregate and cement paste in LWAC is usually better. However, when comparing the results achieved in this research to those referred to in [9] for lightweight concrete, a certain quantitative difference is also observed for the effect of moisture content on the static modulus of elasticity. As it was revealed in [9], E

_{c,s}determined in water-saturated conditions was bigger by 4 up to 14% in relation to results measured in air-dried condition. In this case, the explanation of a more pronounced moisture influence on the modulus in [9] is the much higher moisture content of lightweight concretes in air-dried conditions (5.7–7.8%). Meanwhile, in this research, due to longer time of drying in air (almost three years), LWACs tested in dry conditions had a relatively small moisture content (1.2–1.7%). As a result, in [9], air-dried conditions meant the saturation extent was 62–73%, and in this study, it ranged from 12 to 22%. Such a comparison may prove the conclusions given in [13] that static modulus of elasticity may decrease with increasing the moisture content to a certain level of concrete saturation with water (50–70%) and then may increase up to the full saturation.

## 5. Conclusions

_{c,s}and E

_{d}is influenced by both moisture content and the homogeneity of concrete composite structure. As a result, the tested lightweight concrete, despite their higher water absorption in comparison to NWACs, did not show a bigger effect of their moisture content on the specified values of static modulus of elasticity, probably due to better LWACs’ structural homogeneity and its more tight cement matrix. Nevertheless, it should be stated that the influence of the moisture content of concrete on its modulus of elasticity is not as unequivocal as in the case of compressive strength tests.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Load cycles for determination on secant modulus of elasticity: (

**a**) Theoretical cycles acc. to EN 12390-13 (Method B); (

**b**) Example of registered carried out load cycles for a specimen of concrete series LC1.

**Figure 4.**A concrete specimen with the measuring apparatus for determination of secant modulus of elasticity according to EN 12390-13.

**Figure 5.**A concrete specimen with the measuring apparatus for determination of dynamic modulus of elasticity according to ultrasonic pulse velocity method.

**Figure 6.**Specimens of lightweight concrete after compressive strength test: (

**a**) General view; (

**b**) Fracture form.

**Figure 7.**Relationship between ultrasonic pulse velocity (V) and dynamic (E

_{d}) moduli of elasticity is determined in air-dried and water saturated conditions.

**Figure 8.**Values of static secant (E

_{c,s}) and dynamic (E

_{d}) moduli of elasticity determined for concrete LC1 in air-dried and water-saturated conditions.

**Figure 9.**Values of static secant (E

_{c,s}) and dynamic (E

_{d}) moduli of elasticity determined for concrete LC2 in air-dried and water-saturated conditions.

**Figure 10.**Relationship between static secant (E

_{c,s}) and dynamic (E

_{d}) moduli of elasticity determined in air-dried and water saturated conditions.

**Figure 11.**The effect of moisture condition on specified values of static secant and dynamic moduli of elasticity determined in air-dried conditions (E

_{ad}) and water-saturated conditions (E

_{ws}).

Series | LWA 4/8 mm in Dry Condition | Water for Initial Wetting of LWA | Natural Sand 0/2 mm | Cement | Water | Superplasticizor |
---|---|---|---|---|---|---|

LC1 | 576 | 98 | 570 | 377 | 208 | 0 |

LC2 | 576 | 98 | 570 | 470 | 174 | 1.9 |

**Table 2.**Test type; cylindrical specimens’ number and age; standard procedure for each concrete series.

Test | Specimens Number | Concrete Age | Standard Procedure |
---|---|---|---|

Water saturated density | 3 | 28 days | EN 12390-7 [38] |

Oven dry density | |||

As received density | |||

Oven dry density | 3 | 3 years | |

Water saturated density | |||

Compressive Strength | 6 | 28 days | EN 12390-3 [39] |

3 | 3 years | ||

Static modulus of elasticity | 3 | 28 days | EN 12390-13 [12] |

Static modulus of elasticity | 3 | 3 years | EN 12390-13 [12] |

Dynamic modulus of elasticity | EN 12504-4 [40] |

Concrete Series | Specimen’ Number | Secant Modulus of Elasticity, GPa | ||||
---|---|---|---|---|---|---|

Air Dry Condition | Water Saturated Condition | |||||

E_{c,si} * | E_{c,si} | E_{c,s} | E_{c,si} | E_{c,s} | ||

LC1 | 1 | 18.1 | 17.9 | 18.3 | 18.4 | 18.4 |

1’ | 17.9 | |||||

1” | 17.7 | |||||

2 | - | 18.7 | 19.2 | |||

3 | - | 18.3 | 17.8 | |||

LC2 | 1 | 21.4 | 21.3 | 21.9 | 22.8 | 22.8 |

1’ | 21.7 | |||||

1” | 20.8 | |||||

2 | - | 22.5 | 22.8 | |||

3 | - | 21.9 | 22.7 |

Concrete Series | Specimen’ Number | Measurement * | Path Length, mm | Ultrasonic Pulse Velocity, m/s | |||||
---|---|---|---|---|---|---|---|---|---|

Air Dry Condition | Water Saturated Condition | ||||||||

V_{i} | V_{m} | V | V_{i} | V_{m} | V | ||||

LC1 | 1 | L | 295 | 3665 | 4032 | ||||

T | 151 | 3801 | 3721 | 4167 | 4106 | ||||

T’ | 151 | 3697 | 4119 | ||||||

2 | L | 296 | 3565 | 4042 | |||||

T | 150 | 3663 | 3648 | 3706 | 3872 | 3979 | 4042 | ||

T’ | 150 | 3716 | 4022 | ||||||

3 | L | 296 | 3727 | 4051 | |||||

T | 151 | 3789 | 3748 | 3963 | 4041 | ||||

T’ | 151 | 3727 | 4109 | ||||||

LC2 | 1 | L | 301 | 3890 | 4242 | ||||

T | 150 | 3953 | 3893 | 4242 | 4280 | ||||

T’ | 150 | 3835 | 4357 | ||||||

2 | L | 298 | 3953 | 4291 | |||||

T | 150 | 3944 | 3941 | 3904 | 4191 | 4227 | 4259 | ||

T’ | 150 | 3925 | 4200 | ||||||

3 | L | 296 | 3935 | 4242 | |||||

T | 151 | 3953 | 3880 | 4258 | 4269 | ||||

T’ | 151 | 3751 | 4308 |

Concrete Series | Specimen’ Number | Measurement * | Path Length, mm | Dynamic Modulus of Elasticity, GPa | |||||
---|---|---|---|---|---|---|---|---|---|

Air Dry Condition | Water Saturated Condition | ||||||||

E_{di} | E_{dm} | E_{d} | E_{di} | E_{dm} | E_{d} | ||||

LC1 | 1 | L | 295 | 20.4 | 24.7 | ||||

T | 151 | 22.0 | 21.1 | 26.4 | 25.6 | ||||

T’ | 151 | 20.8 | 25.8 | ||||||

2 | L | 296 | 19.3 | 24.8 | |||||

T | 150 | 20.4 | 20.3 | 20.9 | 22.8 | 24.1 | 24.9 | ||

T’ | 150 | 21.0 | 24.6 | ||||||

3 | L | 296 | 21.1 | 25.0 | |||||

T | 151 | 21.8 | 21.4 | 23.9 | 24.8 | ||||

T’ | 151 | 21.1 | 25.7 | ||||||

LC2 | 1 | L | 301 | 24.2 | 28.8 | ||||

T | 150 | 25.0 | 24.3 | 28.8 | 29.4 | ||||

T’ | 150 | 23.6 | 30.4 | ||||||

2 | L | 298 | 25.0 | 29.5 | |||||

T | 150 | 24.9 | 24.9 | 24.4 | 28.1 | 28.6 | 29.1 | ||

T’ | 150 | 24.7 | 28.3 | ||||||

3 | L | 296 | 24.8 | 28.8 | |||||

T | 151 | 25.0 | 24.1 | 29.0 | 29.2 | ||||

T’ | 151 | 22.5 | 29.7 |

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## Share and Cite

**MDPI and ACS Style**

Domagała, L.; Sieja, K.
Effect of Moisture Condition of Structural Lightweight Concretes on Specified Values of Static and Dynamic Modulus of Elasticity. *Materials* **2023**, *16*, 4299.
https://doi.org/10.3390/ma16124299

**AMA Style**

Domagała L, Sieja K.
Effect of Moisture Condition of Structural Lightweight Concretes on Specified Values of Static and Dynamic Modulus of Elasticity. *Materials*. 2023; 16(12):4299.
https://doi.org/10.3390/ma16124299

**Chicago/Turabian Style**

Domagała, Lucyna, and Kinga Sieja.
2023. "Effect of Moisture Condition of Structural Lightweight Concretes on Specified Values of Static and Dynamic Modulus of Elasticity" *Materials* 16, no. 12: 4299.
https://doi.org/10.3390/ma16124299