Influence of the load frequency and moisture content on fatigue deterioration of high‐strength concrete

With the expansion of offshore wind energy systems, the number of fatigue‐loaded concrete structures exposed to high moisture contents has significantly increased in the last decades. Investigations in the literature show a strong reduction of fatigue resistance with increasing moisture content of the concrete. However, a detailed quantified understanding of the influence of the moisture content and the underlying damage mechanisms is still lacking. In a conjoint project as part of the priority program SPP 2020 funded by the German Research Foundation (DFG), the water‐induced fatigue damage are investigated. In this paper, the results of compressive fatigue testes on high‐strength specimens with different moisture contents are presented. The cyclical loading was carried out at three different load frequencies and maximum stress levels, respectively. The results show that the damaging effect due to fatigue loading at high moisture content is more pronounced with decreasing stress levels and decreasing frequencies. Considering the strain development and acoustic emissions the results indicate that different damage mechanisms are acting with increasing moisture content of concrete. These mechanisms are elaborated in this paper.


Introduction
The fatigue behaviour of concrete has become an important subject of interest in the last few decades, especially with the expansion of offshore wind energy systems.Such structures are subjected to a high number of load cycles during their service life.The offshore exposure of such structures leads to higher moisture contents in the concrete compared to onshore wind energy systems.Only few investigations are documented in the literature regarding the influence of the moisture content on the fatigue resistance of concrete.For instance, Nygard et al. [1] and Muguruma et al. [2] carried out fatigue tests on concrete specimens with different compressive strengths, stored in air and under water.Their results showed a significant reduction of the fatigue resistance of concrete stored and tested under water compared to those subjected to dry conditions.Tomann et al. [3] carried out fatigue investigations on high-strength concrete specimens with different moisture contents, tested in air and under water.The results showed that the fatigue resistance decreases with increasing moisture content in the concrete.Oneschkow et al. [4] investigated the fatigue behaviour of concrete in dry and wet conditions at different stress levels.The results suggested that the influence of moisture content increases with decreasing maximum stress levels.
It is well known that the load frequency has a certain influence on the fatigue behaviour of concrete tested in dry condition.Higher load frequencies lead to higher numbers of cycles to failure for maximum stress level Smax > 0.80 [4][5][6][7].A reversal of the influence of the load frequency was observed at a maximum stress level of Smax < 0.80.Schneider et al. [7] postulated that the excessive increase in temperature during the fatigue tests is responsible for the reduction in the numbers of cycles to failure at higher load frequency.For specimens submerged in water, increasing load frequencies always lead to higher numbers of cycles to failure [8].However, Hohberg [5] suspected that the influence of load frequency on specimens with higher moisture content reverses at maximum stress levels between Smax = 0.45 -0.50.
The well-known s-shaped strain and stiffness developments have been used in the latest research as damage indicators to characterise the fatigue behaviour of concrete [3,4,9,12].According to Hümme [12], specimens with high moisture content show a higher gradient of strain in phase II compared to dry specimens.Tomann et al. [3] also observed that an increase of the moisture content in concrete leads to a stronger stiffness degradation per load cycle in phase II.This negative effect of moisture content on the stiffness development of concrete is more pronounced at lower load frequencies, as reported in [13].
In addition to strain-dependent damage indicators, acoustic emission measurements provide further information concerning the damage process in the concretes microstructure.According to [3], the number of acoustic emission (AE) hits significantly increases with increasing moisture content in the concrete microstructure.Additionally, the point of occurrence of the AE hits in the sinusoidal load curve shifts from the region of the maximum stress level towards the minimum stress level.These differences in the point of occurrence are explained by additional fatigue damage mechanisms which are acting with increasing moisture content in concrete [13].
Several hypotheses concerning water-induced damage mechanisms due to the fatigue loading are documented in the literature.For instance, Muguruma et al. [2] and Tait [14] proposed that water present in the microcracks creates a wedging effect during fatigue loading, which ultimately reduces the internal friction of the system.In contrast, Sørensen et al. [15], Pesch [16] and Tomann [17] assumed that pore water pressure can build up due to water redistribution in the pore systems, which has a negative effect on the fatigue resistance.Despite all these findings regarding the influence of moisture content, a detailed understanding of the water-induced damage mechanisms due to fatigue loading is still missing.Additionally, there is a pronounced lack of knowledge concerning the influence of the load frequency on the fatigue behaviour of concrete with high moisture content.
A joint research project is conducted at the Institute of Building Materials Science, Leibniz University Hannover, to investigate the influence of the moisture content on the compressive fatigue behaviour of high-strength concrete.The project is a part of the priority programme SPP 2020 'Cyclic Deterioration of High-Performance Concrete in an Experimental-Virtual Lab', funded by the German Research Foundation (DFG).The main objective of the project is to identify and model the damage mechanisms that occur in the concrete with high moisture content.
In this paper, the results of compressive fatigue tests on high-strength concrete with two different moisture contents are presented.The specimens are subjected to different maximum stress levels Smax and load frequencies.The number of cycles to failure were determined and discussed with respect to the S-N curves of fib Model Code 2020 [18].Additionally, the strain development and acoustic emission signals are analysed as damage indicators, to obtain insights into the water-induced damage mechanisms due to fatigue loading.

2
Experimental investigation

Concrete composition and specimen preparation
The fatigue testes were carried out on the reference highstrength concrete (RH1) of the priority programme SPP 2020 (see Table 1).The compressive strength at the age of 28 days was determined after underwater storage as fcm,cube= 114 MPa using three cubic specimens with an edge length of 150 mm [19].Cylindrical specimens with a height of h = 180 mm and a diameter of d = 60 mm were used in the fatigue investigations.The concrete was filled into PVC formworks in two equal layers which were mechanically compacted using a vibrating table.Specimens to be water-saturated (designation WS) were immersed in water immediately after the concreting process.After two days, the formworks of all specimens were removed, and the specimens with the higher moisture content (WS) were kept stored underwater until testing.The specimens with the lower moisture content (Cl 65) were stored permanently in a climate chamber under standard air conditions (20°C, 65% RH) from the concreting process until testing.At an age of 14 days, the top and bottom surfaces of all specimens were cut and prepared by grinding and polishing to achieve a uniform stress distribution.All specimens were sealed except the top and bottom surface just before testing using epoxy resin to prevent drying during the fatigue tests.

Experimental set-up and test programme
The experimental investigations were carried out using a class 0.5 sevro-hydraulic testing machine according to ISO 7500-1 [20] equipped with a 2.5 MN actuator.The axial deformations were measured using three laser distance sensors and three linear variable differential transformers (LVDT) which were placed on the circumference of the specimen at angles of 0°, 120° and 240°, see Figure 1.All strain measurements are given as mean value from the three sensors.The reference compressive strength was determined prior to the cyclic tests as mean value of three specimens from the same batch, with the same geometry and the same moisture content as the specimens used in the fatigue tests.The tests were conducted force-controlled using a monotonically increased stress rate of 0.5 MPa/s.The mean reference compressive strength per batch was used for the determination of the stress levels (Si = σc,i/fcm,ref).
The dynamic modulus of elasticity Edyn was also determined before fatigue testing by using the resonance analysis system RA100 Concrete from Lang Sensorik.The specific material properties of the used specimens with moisture contents Cl 65 and WS are given in Table 2 as mean values.At the beginning of the compressive fatigue tests, the load was increased monotonically up to the mean stress level Smean and then the full amplitude was applied from the first sinusoidal load cycle.The minimum stress level was kept constant at Smin = 0.05 for all tests.The cyclic tests were carried out at three different maximum stress levels Smax = 0.65, 0.75 and 0.80 and three different load frequencies ft = 0.1, 1.0 and 10.0 Hz, respectively.

Data analysis
The fatigue resistance of concrete with two different moisture contents (Cl 65 und WS) is first analysed with respect to the numbers of cycles to failure.Additionally, the strain developments were analysed as damage indicators.These include the stain values for all full cycles except the last cycle before failure because of the high unstable state of the microstructure (cf.[4]).The peak strains were determined using peak analyses of sinusoidal strain curves measured by the three laser distance sensors.These three peak strains were averaged to obtain the mean strain for each specimen.The strain development under compressive fatigue loading shows a typical s-shaped curves, with a strong increase in phase I, a quasi linear increase in phase II and again a strong increase in phase III until failure.In the following, the gradient of the strain development in phase II, i.e. strain increase per load cycle, are taken as a damage indicator.For each test, these are determined between the values of N/Nf = 0.20 and 0.80 (cf.Equation ( 1)).The total change of strain is analysed as additional parameter and calculated according to Eq. ( 2).
In addition to the strain-dependent damage indicator, the AE hits are analysed as further damage indicator and discussed in context with the s-shaped strain development.
The average hits per cycles (av.hits) are used as a parameter for the damage indicator.Hereby, the number of the recorded AE hits during the entire fatigue test are summarized and dived by the total number of load cycles.Moreover, the point of occurrence in the sinusoidal load curve is analysed as an additional significant parameter.

Numbers of cycles to failure
The values of the numbers of cycles to failure for both moisture contents Cl 65 and WS are presented in Figure 2. Furthermore, the S-N curves according to the draft of fib Model Code 2020 [18] for dry and wet condition are shown.
It can be seen from the figure that the numbers of cycles to failure for both moisture contents exceed the predictions of fib Model Code 2020.At maximum stress level of 0.80, specimens of both moisture contents show almost the same values of numbers of cycles to failure Nf.The largest difference in the numbers of cycles to failure between the both moisture contents occur at the lowest maximum stress level of Smax = 0.65 (Δ log Nf = 1.79).Please note that the result of the moisture content Cl 65 at maximums stress level of Smax = 0.65 refers to one run-out specimen (i.e.without failure), with the actual number of cycles to failure being higher than the given value.Thus, the water-induced fatigue damage increases more strongly with reducing stress level.The intensification of the negative effect of moisture with decreasing maximum stress level confirms the findings of Oneschkow et al. [4].Figure 3 shows the influence of the load frequency on the numbers of cycles to failure at the maximum stress level Smax of 0.75.For all load frequencies, the number of cycles to failure of the specimens with high moisture contents is lower compared to specimens with the low moisture content.As can be further seen, the effect of the load frequency is less pronounced for the dry samples (Cl 65).The highest load frequency of ft = 10 Hz is leading to the lowest numbers of cycles to failure, thus being in line with the literature [4,6].For water-saturated specimens (WS), lower load frequencies lead to lower numbers of cycles to failure.The differences between moisture contents and thus the effect of water-induced fatigue damage increases with decreasing load frequencies.

Development of strains
The influence of the maximum stress level on the gradient of strain in phase II for both moisture contents Cl 65 and WS is shown in Figure 4.It can be seen that the values of gradient of strain in phase II for water-saturated specimens are higher than for the dry specimens, except those at Smax = 0.80.Specimens of both moisture contents show a lower strain increase per load cycle in phase II with decreasing stress levels.However, the differences between both moisture contents strongly increases with decreasing stress levels.The influence of the load frequency on the gradient of strain development in phase II is shown in Figure 5 for both moisture contents.For the lower moisture content (Cl 65), the maximum gradient of strain slightly increases in average from 3.3 x 10 -5 at ft = 10 Hz to 4.4 x 10 -5 at ft = 0.1 Hz (Δ grad Ԑmax = 1.1 x 10 -5 ).In contrast, specimens with higher moisture content (WS) show a significantly higher increase of the gradient with decreasing load frequencies (Δ grad Ԑmax = 1.4 x 10 -3 ).Thus, the difference in the gradient of strain development between the both moisture contents increase with decreasing load frequencies, which correlates well with the results of the numbers of cycles to failure.Furthermore, the mean value of the total strain increases with decreasing stress level for both moisture contents.Whereby the reduction is significantly higher for dry specimens.The higher value of the total growth of strain at lower moisture content and with decreasing the stress level confirm the findings of Hümme [5].Regarding the influence of load frequency, dry specimens show a higher total growth of strain than specimens submerged in water at all load frequencies.Moreover, lower load frequency leads to a lower total growth of strain for both moisture contents.However, the decrease of the total growth of strain of the water-saturated specimens is less pronounced than those of the dry specimens.

Acoustic emission signals
In addition to the development of strain, the AE hits are analysed to obtain in-depth information about the damage mechanisms involved in the degradation process.Figures 6 und 7 show the development of the AE hits over the entire fatigue test for a representative specimen of the moisture contents Cl 65 and WS, respectively.The blue points represent the hits in the descending branch of the sinusoidal load (unloading), while the purple points represent the ascending branch (loading).The grey area schematically represents the well-known s-shaped strain development.The fatigue tests were conducted at a maximum stress level of Smax = 0.75 and a load frequency of ft = 1 Hz.
The water-saturated specimens shows a much higher value of average hits per cycle compared to the dry specimen (Cl 65: av.hits = 0.2; WS: av.hits = 11.9).Due to the different moisture contents, different point of occurrence of the AE hits are detected as shown in Figures 6  and 7.For dry specimens (Cl 65), the detected hits in phase I and II occur mainly in the region between the strains at maximum stress level Smax and mean stress level Smean (cf. Figure 6).The number of hits increases significantly in phase III before failure.Regarding the point of occurrence in the sinusoidal load curve, the recorded hits of dry specimens are mostly located in the descending branch of the sinusoidal load pattern.However, a higher number of hits in the ascending branch of the sinusoidal load was detected in the end of phase II and in phase III.In contrast, the hits in phases I and II of the water-saturated specimens mostly occur in the strain area between the mean stress level Smean and the minimum stress level Smin (cf. Figure 7), i.e. during unloading.The majority of those hits are additionally recorded in the ascending branch of the sinusoidal load.In phase III, a mixture of hits in the strain area between the maximum and minimum stress levels is detectable.These hits occur in the ascending as well as in the descending branch of the sinusoidal load.The differences in the results of AE hits clearly indicate that different damage mechanisms act with the increasing moisture content in concrete.

Conclusions
The fatigue behaviour of a high strength concrete with two different moisture contents was investigated in a joint research project.The fatigue tests were conducted at three different stress levels Smax = 0.65, 0.75 and 0.80.The minimum stress level was kept constant at Smin = 0.05.The influence of the load frequency on the water-induced fatigue damage was investigated using three load frequencies ft = 0.1 Hz, 1.0 Hz and 10 Hz, respectively.The main results can be summarised as follows:  Higher moisture content leads to a lower numbers of cycles to failure.Additionally, a higher gradient of strain in phase II, i.e. the increase of strain per load cycle, and a strong reduction of the total growth of strain was observed for the higher moisture content.


A strong reduction of the number of cycles to failure due to water-induced fatigue damages was observed for lower stress levels and lower load frequencies.


For both investigated moisture contents, the gradient of strain in phase II was lower at lower stress levels and lower load frequencies.Additionally, the total growth of strain decreases with decreasing stress level and load frequency.Where the total growth of strain of water-saturated specimens decrease in a less pronounced way than specimens in dry condition.


The results of the AE hits show differences concerning the number of recorded hits and the point of occurrence for the investigated moisture contents in concrete.This indicates that there are different damage mechanisms acting with increasing moisture contents in the microstructure of the concrete.
Overall, the obtained results reveal a notable influence of the test frequencies and stress level on the water-induced fatigue damage.In the next stages of the research project, a detailed analysis of the characteristics of AE hits is necessary to get more insights into the water-induced damage mechanisms.Moreover, further investigations of porosity, pore size distribution and nanoscale moisture deviations by means of NMR (nuclear magnetic resonance) techniques, will be conducted to obtain more detailed information about the nature of the damage processes on the micro and nano scale.In parallel, a numerical investigation will be conducted to simulate the water-induced damage processes.First approaches can be found in [18,21].

Figure 1
Figure 1 Test setup The data sampling rate was set between 100 Hz and 300 Hz depending on the load frequency.To obtain insights into the damage mechanisms by means of acoustic emission signals, six sensors with a frequency response within the range of 125 kHz to 750 kHz were attached to the specimens at an angular distance of 60° from one another, alternating in the upper and lower third of the specimen height.A specific threshold of 40 dB was used to separate the useful signal from the background noise.

Figure 2
Figure 2 Logarithmic number of cycle to failure Nf for samples with different moisture content (WS -water saturated; Cl 65 -samples stored at 65 % relative humidity) at different max.stress levels Smax

Figure 3
Figure 3 Influence of load frequency ft on the number of cycles to failure Nf for samples with different moisture content (WS -water saturated; Cl 65 -samples stored at 65 % relative humidity)

Figure 4
Figure 4Influence of max.stress level Smax on maximum gradient of strain in phase II for the investigated moisture contents (WS -water saturated; Cl 65 -samples stored at 65 % relative humidity)

Figure 5
Figure 5 Influence of load frequency ft on the gradient of strain in phase II for different moisture contents (WS -water saturated; Cl 65 -samples stored at 65 % relative humidity)

Table 1
Concrete compositions

Table 2
Mean values of investigated sample batches