Long‐term deformations of concrete under cyclic‐mechanical and cyclic‐hygric exposures

Long‐term deformations of concrete structures are actually calculated by creep models using the mean stress level and the time‐average ambient humidity. However, temporally varying mechanical and hygric exposures which occur in practice are suspected to increase the time‐dependent strains. Nevertheless, these influences have not been sufficiently investigated so far.


Introduction
The long-term deformations expected during the service life of concrete structures are calculated using prediction models, such as those given in Eurocode 2 [1], fib Model Code 2010 [2] or ACI 209R [3], which are in good agreement with laboratory results under constant-mechanical loads and constant climatic conditions.In practice, however, concrete structures are often exposed to mechanical creep loads which are superimposed by cyclic loads, e.g. as a result of traffic.Similarly, the climatic conditions, i.e. relative humidity (RH) and temperature, vary in a cyclic manner depending on the time of the day and the season.Measurements of existing concrete bridges have shown that long-term deformations can significantly exceed those predicted by the previously mentioned models, which give considerable reason to suspect that the varying exposures increase the deformations that actually occur [4][5].However, the effects of varying mechanical, hygric and thermal exposures on the long-term deformations of concrete have barely been investigated and are usually (and most likely wrongly) treated as negligible.
In general, the total strain of concrete due to a constantmechanical loading consists of a stress-dependent strain component (i.e.elastic and creep strain) and a stress-independent strain component (i.e.shrinkage and thermal strain).The prediction models contained in Eurocode 2 [1] are limited to constant-mechanical loadings.Thus, the design is done considering a mean-value, average constantmechanical loading.The fib Model Code 2010 [2], however, provides in addition to a prediction model for constant-mechanical loadings, which is in principle similar to that of Eurocode 2 [1], the following equation for calculating the stress-dependent strain due to a cyclic-mechanical loading with a maximum stress of 0.6•fck: This equation is composed of two added terms: the first term describes the elastic strain component as a constant strain resulting from the maximum cyclic stress (σc,max).
The second term describes the strain resulting from the function of creep considering the mean cyclic stress (σc,mean).Results of investigations comparing total strains due to constant-and cyclic-mechanical loading at maximum stress levels Smax ≤ 0.60 (with Si = σc,i/fcm) indicate that the mean stress level approach of fib Model Code 2010 [2] underestimates the total strains observed in cyclic-mechanical tests [6][7].Kern et al. [8][9] conducted comparable investigations on sealed specimens and focused in particular on the time-dependent strains, i.e. the elastic strains were subtracted from the total strains.It was shown that the time-dependent strains due to cyclicmechanical loading are higher than those due to constantmechanical loading at the corresponding constant mean stress level (Screep = Smean) for maximum cyclic stress levels of Smax = 0.35 and 0.45.
The influence of varying relative humidity is also not directly considered in the prediction models given by Eurocode 2 [1] and Model Code 2010 [2].The design is done considering seasonal variations by using the time-average of the ambient humidity (RHmean) within the limits of applicability of relative humidities between 40 and 100 %.However, a few studies indicated that the strains measured at cyclic ambient humidity are higher than those at the corresponding constant mean value humidity RHmean.
In these studies, differentiation is usually made between creep and shrinkage strains, so that the shrinkage strain of a specimen without mechanical loading is subtracted from the time-dependent strain in order to calculate the creep strain.Regarding the effect of cyclic ambient humidity on the creep strains, results obtained by Hansen [10] and Müller and Pristl [11] revealed that the creep strains at the end of loading are increased by approx.20 % due to cyclic ambient humidity compared to constant RHmean.This is in line with previous experimental investigations of the authors [12], which showed that creep strains are increased up to a factor of 1.6 at the end of loading due to cyclic ambient humidity compared to those at constant RHmean.Hereby, the influence of cyclic ambient humidity increases with a lower initial moisture content of the concrete.
Furthermore, models given by Bažant [13][14][15][16] describe the additional strain due to cyclic-mechanical or -hygric loading.However, these models were validated only on a small database available in literature.Furthermore, to the knowledge of the authors, there are no experimental studies in which cyclic-mechanical and -hygric loadings are considered coupled.
As it can be seen from this short literature overview, the influences of either cyclic-mechanical or -hygric loading and especially their coupling, i.e. cyclic-mechanical and -hygric loading on the time-dependent strains of concrete are still insufficiently investigated.In the paper at hand, the results of cyclic-mechanical and -hygric loading, separately, and those of the coupled cyclic-mechanical and -hygric loading are presented.Based on these results, existing modelling approaches will be extended in the next steps of the ongoing research project to include the influences of cyclic-mechanical and -hygric loading.

Concrete composition and specimens
All investigations were carried out on a normal strength concrete C30/37 (composition see Table 1).The specimens were cast in several batches with 28-day mean compressive strengths tested according to DIN EN 12390-3 [17] of fcm,cyl = 29.4MPa (batch 1), fcm,cyl = 31.8MPa (batch 2) and fcm,cyl = 34.0MPa (batch 5), respectively.The specimens of batch 3 and batch 4 were used for other investigations not included in this paper.
All tests were conducted on cylindrical specimens with a height of h = 180 mm and a diameter of d = 60 mm.Therefore, polyvinyl chloride (PVC) formworks were filled with two equally high layers of concrete.Each layer was mechanically compacted using a vibrating table.In order to prevent disturbed areas at the ends of the specimens, the latter were cast with a height of h = 230 mm and later cut to the final height.After casting, the specimens were stored at 20 °C in boxes with wet cloths to avoid drying.After five weeks, the specimens were demoulded and cut to the final height of 180 mm.The loaded test surfaces were plan-parallel ground and polished to achieve a uniform stress distribution during mechanical loading.Subsequently, the specimens were sealed with layers of plastic wrap and aluminium-coated butyl tape, in order to prevent drying, and stored at 20 °C until testing.This conditioning scheme ensured a defined initial moisture content in the concrete pores of approx.100 % (referred to as V100).All tests were conducted on specimens with a minimum concrete age of 180 days to ensure nearly complete hydration and avoid additional hardening of the concrete during testing.

Experimental set-up
The creep tests were performed in a creep testing machine (cf.[8]).The stress was monotonically increased up to the creep stress level Screep and maintained constant afterwards until the specimens were unloaded.An electromechanical universal testing machine was used for the cyclicmechanical tests.Here, the stress was monotonically increased up to the mean stress level Smean and, subsequently, the load oscillation, defined by the mean stress level Smean, the amplitude and the frequency ft, was started.Hereby, the full amplitude was applied directly in the first load cycle.
All creep tests were conducted in a climate room at 20 ± 1 °C and 65 ± 5 % RH.The existing creep testing machines were modified with a climatic control system for the creep tests at cyclic ambient humidity (cf.[18]).A climatic chamber was constructed around the creep specimens, connected by a pipe system to a container of saturated salt solution.The ambient humidity in the climatic chamber was adjusted to a constant target value by utilising saturated salt solutions and two integrated fans.The ambient humidity was cycled by a cyclic change of the salt solutions potassium nitrate and magnesium chloride.Using these salt solutions, the ambient humidity in the climatic chamber was adjusted to RHmax = 90 ± 5 % and RHmin = 40 ± 5 %.The temperature was constant at 22 ± 1 °C and, thus, slightly increased compared to the surrounding climate.
In principle, the same climatic control system was used, as described previously, for the coupled cyclic-mechanical and -hygric tests with the ambient humidity changing between RHmax and RHmin (see Fig. 1, centre).The cyclic-mechanical tests could not be performed in a climate room, therefore, the development of a new climatic control system to ensure parallel tests of specimens at a constant ambient humidity at RHmean was also necessary (see Fig. 1, top).In this case, a climatic chamber and an annular container filled with a saturated potassium iodide solution were constructed around the specimen.Additionally, the strains of a sealed specimen without loading (see Fig. 1, bottom) were measured to evaluate effects from potential temperature fluctuations and thus thermal strains.However, such temperature fluctuations and resulting strains were negligible during the test duration, thus, the measurements will not discussed in further detail.The axial deformations of the specimens were measured continuously during the tests using three linear variable differential transformers (LVDTs) positioned on the circumference of the specimen at angles of 0°, 120° and 240°.In addition, the axial force, the axial stroke of the actuator, the RH and temperature of the ambient air were measured.The data sampling rate of the deformations, the force and stroke was 1 Hz for the constant-mechanical investigations and 10 Hz for the cyclic-mechanical investigations.The ambient humidity and temperature were recorded with a sampling rate of 0.1 Hz.

Test programme
The mean reference compressive strength fcm,ref was determined force-controlled on parallel specimens immediately before testing, as the mean value of three cylindrical specimens each.The mean reference compressive strengths fcm,ref at the age of loading are summarised in Table 2.The mean reference compressive strength per batch was used for the determination of the stress levels (Si = σc,i/fcm,ref) of the mechanical loading.The test programme is given in Table 3 regarding the mechanical and hygric loadings during the tests and was structured in three experimental blocks (EB).The loading duration in all tests was 91 days.Please note that different batches were used for EB1, EB2 and EB3, respectively.Due to the limited testing capacities, the tests of EB2 had to be tested in two consecutive time slots, resulting in two different ages of loading.
In the first experimental block (EB1), the influence of the cyclic-mechanical loading was investigated in comparison to constant-mechanical loading, see Table 3.The stress levels in the cyclic-mechanical tests were Smax = 0.35 and Smin = 0.05 and the test frequency was ft = 0.1 Hz, with the stress being sinusoidally oscillated.Creep tests with constant stress levels of Screep = Smax and Screep = Smean were conducted for comparison with the cyclic-mechanical tests.Sealed specimens were used for all these investigations where drying was prevented using an aluminiumcoated butyl tape.
In the second experimental block (EB2), the influence of the cyclic ambient humidity was investigated.The mechanical loading was constant at Screep = 0.35.The focus of these tests was to quantify the effect of cyclic ambient humidity on the time-dependent strains in comparison to those at the corresponding constant mean humidity RHmean.Therefore, specimens were tested unsealed at a standard climate with a constant ambient humidity of RHmean = 65 % and at cyclic ambient humidity between RHmax = 90 % and RHmin = 40 %, see Table 3.One humidity cycle was defined as a period of 14 days at RHmax followed by 14 days at RHmin, thus, 28 days in total.The change in ambient humidity followed a square waveform.In the third experimental block (EB3), the coupled influence of cyclic-mechanical and -hygric loading was analysed.Therefore, constant-mechanical and cyclic-mechanical loadings were comparatively investigated at a constant humidity of RHmean = 65 % and at a cyclic-hygric loading of RHmax = 90 % and RHmin = 40 %.Only single tests were carried out in EB3 due to limited testing capacities.

Data analysis
The axial deformations were continuously measured using three LVDTs per specimen (see Sec. 2.2), from which the mean value was calculated for each specimen.The measured deformations Δl obtained by the LVDTs were normalized by the initial measuring length l = 118 mm to calculate the strains ε.In a next step, the temporal development of the peak strains of the cyclic-mechanical curves at the maximum stress level Smax were obtained by peak analyses.
The total strains due to constant or cyclic-mechanical loading consist of an elastic and a time-dependent strain component.The elastic strain component was defined as the strain at the time when the creep stress level Screep was reached or, in the case of cyclic-mechanical loading, as the strain when the maximum stress level Smax was reached in the first load cycle.The time-dependent strain was determined by subtracting the elastic strain component from the total strains due to the loading at the creep (constantmechanical) or maximum stress level (cyclic-mechanical).Thus, the shrinkage strains are also included in the timedependent strains.
In EB1 and EB2, the time-dependent strains are mean curves of specimens tested at the same mechanical and hygric loading, respectively.While in EB3, the time-dependent strains are only from one specimen tested at the same mechanical and hygric loading.

Influence of cyclic-mechanical loading
Fig. 2 shows the time-dependent strains due to cyclic-mechanical loading together with the time-dependent strains due to two different creep stress levels: strains at mean and maximum stress level.Overall, the strains of the unsealed specimens are higher compared to those of the sealed specimens, which was expected due to the additional drying of concrete.Considering the sealed specimens, it can be seen that the strains due to cyclic-mechanical loading are increased up to a factor of 1.9 compared to the strains at constant mean stress level (Screep = Smean).Furthermore, the strains of the sealed specimens due to cyclic-mechanical loading are closer (but slightly smaller) to the strains at constant maximum stress level (Screep = Smax).
By contrast, the strains due to cyclic-mechanical loading even exceed the strains due to constant-mechanical loading at maximum stress level (Screep = Smax) for the unsealed specimens.This result indicates that the influence of cyclic-mechanical loading is increased by the additional drying of the concrete and/or the resulting lower moisture content due to drying.This is in line with investigations on sealed specimens with a lower initial moisture content of approx.75 % (referred to as V75), showing that time-dependent strains due to cyclic-mechanical loading may exceed those due to constant-mechanical loading at Screep = Smax [9].
These results reveal that the practice of modelling the time-dependent strain due to cyclic-mechanical loading by using the mean stress level Smean, such as that given in Eurocode 2 [1] or fib Model Code 2010 [2], is not adequate.A transfer to the usage of the maximum stress level Smax delivers more accurate results, but also does not seem to be suitable to simulate the different deformation mechanisms, especially for concrete structures that are exposed to drying.

Influence of cyclic ambient humidity
The time-dependent strains due to a constant-mechanical loading at Screep = 0.35 at constant (yellow) and cyclic ambient humidity (blue) from batch 2 and batch 5 are shown in Fig. 3.The modulus of elasticity of batch 5 was higher than the one of batch 2, therefore, the time-dependent strains differ slightly from each other.
It can be seen that the time-dependent strains due to cyclic ambient humidity result in a cyclic strain response despite the constant-mechanical stress of 35 %.This demonstrates that concrete even swells under load.Similar results were presented by Cagnon et al. [19].However, swelling of concrete under load is not considered in current modelling approaches [1][2][3].Comparing the strains at constant RHmean and at cyclic ambient humidity, it is apparent that the slope of the cyclic strain curve in the first period at RHmax is smaller than the slope of the constant curve.After a change of the hygric loading to RHmin, the slope of the cyclic strain curve increases and the creep rate is significantly increased.At the end of the first humidity cycle (28 days), the strain at cyclic ambient humidity is in the same range as or slightly higher than the strain of the specimens at constant ambient humidity.This difference increases progressively after the second (56 days) and third humidity cycle (84 days).
It can be assumed that the difference between the cyclicand constant-hygric curve will be more significant with further humidity cycles.
At the end of loading, the time-dependent strains of the V100 specimens at cyclic and constant ambient humidity presented for batch 2 are in the same range, while the strains at cyclic ambient humidity slightly exceed those at constant ambient humidity for batch 5. Investigations on specimens with a lower initial moisture content of approx.65 % (referred to as V65) showed that creep strains are increased up to a factor of 1.6 due to cyclic ambient humidity compared to those at constant RHmean, see [12].These results reveal that the practice of modelling the time-dependent strains at a constant mean ambient humidity (time-average) using current design approaches, e.g.given in Eurocode 2 [1] or fib Model Code 2010 [2], is not suitable.

Coupled influence of cyclic-mechanical and cyclic-hygric loading
In addition to the influence of cyclic-mechanical loading at a constant ambient humidity shown in Sec.3.1 and the influence of cyclic ambient humidity at a constant-mechanical loading shown in Sec.3.2, the focus of this section is on the coupled influence of cyclic-mechanical and -hygric loading.Therefore, Fig. 4 shows the time-dependent strains due to cyclic-mechanical loading of unsealed specimens together with those due to constant-mechanical loading at maximum stress level Screep = Smax.As detailed in Fig. 2, the strains due to constant-mechanical loading at mean stress level Screep = Smean are significantly smaller and not comparable to those due to cyclic loading.Thus, they are not included in Fig. 4. The strains at constant ambient humidity are presented in yellow and those at cyclic ambient humidity in blue.Regarding constant ambient humidity, the strains due to cyclic-mechanical loading slightly exceed those due to constant-mechanical loading at Screep = Smax, as has already been shown in Fig. 2. Concerning constant-mechanical loading, the strains at cyclic ambient humidity increasingly exceed those at constant ambient humidity with each humidity cycle, as has already been presented in Fig. 3.
Comparing the strains due to cyclic-mechanical loading at cyclic ambient humidity (i.e. in the coupled tests) to those at constant RHmean in Fig. 4, it is apparent that the slope of the cyclic-hygric strain curve is smaller at RHmax and steeper at RHmin compared to the slope of the constanthygric curve.This is comparable to the results at constantmechanical loading.However, the strain curve due to cyclic-mechanical loading at cyclic ambient humidity remains below the one at constant ambient humidity for the complete loading duration.The results indicate that the first humidity cycle is decisive for the difference between the constant-and cyclic-hygric curve.
It can also be seen that the strain developments at cyclic ambient humidity due to constant-and cyclic-mechanical loading are quite similar for the first period of 14 days.
After the first change of hygric loading from RHmax to RHmin until the end of loading, the strains due to constant-mechanical loading exceed those due to cyclic-mechanical loading.Overall, this seems to be dominantly caused by the stronger increase in strain for constant-mechanical loading compared to cyclic-mechanical loading in the (drying) periods at RHmin.By contrast, the reduction of strain in the (swelling) periods at RHmax seems to be less affected by the type of mechanical loading (constant or cyclic).
It is important to note that the coupled influence was investigated here for the first time and only on a single specimen.Therefore, the results have to be verified in the future to derive general relations.

Conclusions and outlook
The objective of the investigations presented in this paper was to examine the influences of cyclic-mechanical and -hygric loading as well as their coupled influence on the long-term deformations of concrete.The time-dependent strains due to cyclic-mechanical and -hygric loading were compared with the corresponding constant mean loading (Smean or RHmean), regarding the usage of average mechanical loading and hygric boundary conditions in current design approaches (e.g.Eurocode 2 [1] or fib Model Code 2010 [2]).A normal-strength concrete C30/37 with an initial moisture content of approx.100 % (V100) was used in the investigations.
The overall results can be summarised as follows:


The time-dependent strains due to cyclic-mechanical loading are generally higher than those due to constant-mechanical loading at an equal mean stress level (Screep = Smean) for sealed and unsealed specimens.In the case of constant-mechanical loading at constant maximum stress level (Screep = Smax; with Smax being derived from the corresponding cyclic tests), the time-dependent strains are quite similar to those due to cyclic-mechanical loading.If the concrete is subjected to drying, the time-dependent strains due to cyclicmechanical loading can even exceed those due to constant-mechanical loading at an equal maximum stress level (Screep = Smax). Cyclic ambient humidity results in a cyclic strain response.The results demonstrate that concrete can swell even under a constant-mechanical loading of Screep = 0.35.


The time-dependent strains due to constant-mechanical loading of Screep = 0.35 at cyclic ambient humidity with time exceed those at constant ambient humidity at RHmean.Investigations shown in [12] on specimens with lower initial moisture contents confirm this result and show that the creep strains can be increased significantly up to a factor of 1.6 after 91 days compared to those due to constant RHmean. In the case of cyclic-humidity, the time-dependent strains due to constant-mechanical loading at Screep = 0.35 are higher than those due to cyclicmechanical loading.Here, the drying periods lead to a stronger increase in the strain for constantmechanical loading, while rare differences between both types of mechanical-loading are visible in the swelling periods.
The results reveal that the mean stress level concept and the assumption of a constant mean ambient humidity for the prediction of long-term strains in current design approaches are not suitable.As a conceivable consequence, variations in the mechanical loads and in the ambient humidity might lead to serious damage and safety risks of deflection-sensible structures.Therefore, it is necessary to improve the current deformation prediction models.Based on these results, appropriate approaches will be developed in the next step.

Figure 1
Figure 1 Experimental set-up for cyclic-mechanical tests at constant (top) and cyclic ambient humidity (centre).

Figure 2
Figure 2 Time-dependent strains due cyclic-and constant-mechanical loading sealed and at constant ambient humidity.

Figure 3
Figure 3 Time-dependent strains due to constant-mechanical loading at constant and cyclic ambient humidity.

Figure 4
Figure 4 Time-dependent strains due to cyclic-and constant-mechanical loading at constant and cyclic ambient humidity.

Table 1
Concrete composition

Table 2
Mean values of reference compressive strengths fcm,ref at the age of loading.

Table 3
Overview of the experimental blocks (EB).