Cyclic Deterioration of High‐performance Concrete – Findings of the Priority Programme SPP 2020

Modern high‐performance concretes with ever‐higher compressive strengths allow the construction of slender structures which are exposed to higher fatigue‐relevant loads. Current fatigue design rules include a high reduction of the fatigue resistance, which increases with increasing concrete strength. Thus, the fatigue verification becomes crucial for the realisation of such concrete structures. However, there is still a lack of knowledge regarding the damage mechanisms which hinders a substantial improvement of the fatigue design rules. The objective of the priority programme SPP 2020 is to gain more knowledge concerning the fatigue behaviour of high‐performance concretes and damage mechanisms in a strong network of different research institutions. The investigation of the concrete fatigue behaviour is challenging because of the multiple interdependence of influences on the concrete fatigue behaviour, and the damage effects occurring on different scales. Highly instrumented experiments combined with the latest microstructural investigation techniques and numerical modelling on different scales are used to explore the fatigue damage mechanisms. The scope of the priority programme SPP 2020 is outlined and selected results from the projects involved are presented in this paper.


Introduction
Recent developments in concrete technology have allowed the production and usage of concrete with ever-higher strengths in more filigree and slender structures with reduced self-weight.Fatigue resistance is relevant for the design of these structures, and even more for those that are inevitably subjected to oscillating loads, such as bridges and wind turbines.However, currently valid standards contain high reduction values for the fatigue resistance of high-strength concretes [1][2][3].Concurrently, the reduction in the fatigue resistance of high-strength concretes increases with increasing concrete strength.These conservative rules are historically rooted in concerns about the increasing brittleness of concretes with increasing strength subjected to fatigue loading [4].Thus, more knowledge is needed concerning the fatigue behaviour and damage processes especially in high-strength and ultrahigh-strength concretes to alleviate concerns and further develop the design codes.
Therefore, the aim of the priority programme SPP 2020 "Cyclic Deterioration of High-Performance Concrete in an Experimental-Virtual-Lab" is to gain more basic knowledge about the degradation mechanisms in the concrete's microstructure.In the past, fatigue investigations in literature mainly focused on the numbers of cycles to failure.Damage indicators were partly recorded, but rarely analysed in detail.Thus, fatigue damage was a kind of black box, at the end of which was failure.
A new approach for understanding the mechanisms of concrete fatigue was established in [5].The influences of maximum stress level, frequency and waveform were systematically investigated focusing not on the load cycles to failure but on the strain and stiffness development.The results clearly demonstrated that these influences can also be identified in both damage indicators, thus, pointing to a new promising research approach.Based on these investigations and on literature, it also became clear that different influences on the fatigue behaviour interact with each other, making the whole topic very complex.Furthermore, it was assumed that fatigue damage occurs on a very small scale [5].Thus, fatigue damage is not completely continuously detectable in fatigue tests.Time-discrete methods, such as microscopy or computer tomography, are additionally necessary, which substantially increase the time and effort required for the necessary research programme.Nevertheless, damage on the smallest scale would hardly be experimentally recorded.
A collaborative project with a large number of participants was considered to be the most target-oriented in order to

Abstract
Modern high-performance concretes with ever-higher compressive strengths allow the construction of slender structures which are exposed to higher fatigue-relevant loads.Current fatigue design rules include a high reduction of the fatigue resistance, which increases with increasing concrete strength.Thus, the fatigue verification becomes crucial for the realisation of such concrete structures.However, there is still a lack of knowledge regarding the damage mechanisms which hinders a substantial improvement of the fatigue design rules.The objective of the priority programme SPP 2020 is to gain more knowledge concerning the fatigue behaviour of high-performance concretes and damage mechanisms in a strong network of different research institutions.The investigation of the concrete fatigue behaviour is challenging because of the multiple interdependence of influences on the concrete fatigue behaviour, and the damage effects occurring on different scales.Highly instrumented experiments combined with the latest microstructural investigation techniques and numerical modelling on different scales are used to explore the fatigue damage mechanisms.The scope of the priority programme SPP 2020 is outlined and selected results from the projects involved are presented in this paper.close significant parts of the existing knowledge gap.Furthermore, a close collaboration between building materials and numerical mechanic scientists was scheduled in order to gain more knowledge even on very small scales.The idea was to calibrate multiscale numerical models on a higher scale by means of experiments and get additional information about the possible damage processes on a lower scale by means of the model, which cannot be directly observed in experimental investigations.Furthermore, the concrete's fatigue behaviour or, rather, the damage processes should be numerically predictable until fatigue failure.Thus, in addition to the huge efforts in experimental investigations to capture, understand and describe the material degradation processes of high-performance concretes, the numerical modelling and computation is the second block for the Experimental-Virtual-Lab to model and predict the fatigue damage development in concrete.Consequently, when applying for funding, tandem projects were requested with a materialand a simulation-focused partial project.
The priority programme was approved in 2016, then put out to tender, and the approved projects started in 2017 in a first period of a duration of three years.The second period started in 2020.Overall, the fatigue behaviour of high-performance concretes and the connected damage mechanisms have been investigated in 23 tandem projects.An overview of the funded projects can be found on the homepage of the SPP 2020 [6].As is often the case with priority programmes, projects with rather different objectives were approved.These range from various concrete strength grades to different types of loading (compression, tension, bending) or loading scenarios, plain concrete or concrete with (micro or macro) steel, carbon or polyvinyl alcohol (PVA) fibres with different geometries and different measurement and microstructural analysis techniques applied.These diversities are also reflected in the spectrum of numerical investigation methods.This paper gives an overview of the objective and research within the SPP 2020.In section 2, the reference concretes are presented and a brief overview of the main methods applied in the various projects is given.Selected results of different projects are presented briefly in section 3 as spotlight results in order to give an impression of the range of the investigations conducted and results obtained.More detailed research results can be found in the references provided or the individual project publications [6].

2
Materials and Test Methods

Materials
Two reference high-performance concretes with focus on the strength grade were developed and used within most of the projects of the SPP 2020: one high-strength concrete (HPC) and one ultra-high-strength concrete (UHPC).
The aim was to achieve a good comparability of the research results despite the different objectives of the individual projects.The composition of the ultra-high-strength concrete is essentially the same as that of the UHPC of the SPP 1182 [7].The reference HPC (named "RH1" within the SPP 2020) has a mean compressive strength of fcm,cube = 112 N/mm² and the reference UHPC (named "RU1") of fcm,cube = 158 N/mm² [8].The reference HPC has been classified as C 80/95 according to [9] and the reference UHPC as C 130/140 according to [10].Further results of the standard compression tests will be continuously collected until the end of the programme.The compositions of both concretes are given in Table 1.More detailed information on the raw materials can be found in [8].Steel fibres are typically used for high-strength and ultrahigh-strength concretes to reduce the material's brittleness and improve the fatigue life.Thus, the influence of these fibres on the damage evolution in fatigue loading is focused on in some of the projects within the SPP 2020.
Here, one of the two reference concrete mixtures was modified for the addition of fibres and used when possible or considered in a reasonably complementary way.Steel fibres of different sizes and geometries were investigated, with an attempt to partially harmonize the type of fibres and experiments between the projects.Two projects also include carbon fibres and one project focused on high ductility concrete with PVA fibres.Detailed information about the concrete composition used respectively can be found in the publications of the individual projects.

Methods
The methods applied are as diverse as the objectives of the projects.Most of the compressive, tensile and bending tests were conducted on small-scale specimens (cylinders, bone-shaped, prisms) with dimensions in the range of centimetres up to decimetres.The scope of all experimental investigations was not only to determine the numbers of cycles to failure but measure the damage development due to different types of loading, boundary conditions or material properties.Thus, these experiments were often conducted in a highly instrumented manner in order to record as many damage indicators as possible.Such macroscopically measured damage indicators are, for example, the developments of strain, stiffness, dissipated energy, specimen temperature and acoustic emission.Two set-ups for compressive tests and tensile tests used within the SPP 2020 are exemplarily shown in Figure 1 and 2.  In addition, special test methods were applied in individual projects.Pull-out tests on single or groups of fibres were conducted in order to investigate the combined bearing capacity regarding the bond between fibre and concrete [13].Dynamic mechanical analysis (DMA) was applied using a piezo-electric actuator on very small specimens in order to investigate the damage development of the concrete under compressive loading using very high load frequencies [14].
To gain more knowledge concerning the damage processes in the concrete, microstructural analyses techniques are used in an attempt to make the fatigue damage visible.As these analyses techniques are mostly destructive tests, they cannot be applied continuously, but the fatigue tests have to be stopped and specimens prepared to get time-discrete insights into the concrete's microstructure.However, this is challenging, especially concerning compressive fatigue damage, which occurs throughout the concrete microstructure until shortly before fatigue failure and, thus, is not as discrete as cracks.
Methods such as light microscopy, computer tomography, or scanning and transmission electron microscopy are used to visualise fatigue damage in individual projects.In addition, nuclear magnetic resonance spectroscopy, mercury intrusion porosimetry or gas adsorption are used to characterise fatigue damage in preloaded specimens compared to pristine specimens.The idea is to gather as much knowledge as possible by combining different microstructural analysis techniques.Accordingly, it is necessary to use these methods at their technologic limits.
The microstructural results obtained are analysed together with the continuously macroscopically measured damage indicators to describe the complete damage process up to fatigue failure.
Currently, a round robin test is being conducted with the objective to test and evaluate the significance and comparability of different microstructural analyses techniques.Therefore, compressive fatigue tests were centrally conducted on specimens of the reference high-strength concrete.Afterwards, samples were prepared from these pre-damaged specimens and sent to the different participants.The fatigue-induced damage is investigated in their laboratories using different microstructural methods for the purpose of comparison between the different methods.The results are currently under joint analyses and will be published soon.
Three benchmarks are conducted in the field of numerical modelling in order to compare the significance and efficiency of different modelling approaches pursued by the different projects.The three benchmarks deal with fibre pull-out, three-point bending and compressive fatigue loading.A first collaborative publication from two SPP 2020 projects [15] reports on three different numerical models for fibre-reinforced HPC validated by single-fibre pull-out experiments with different embedding lengths and compared regarding efficiency and computational costs.

Comparison of reference HPC and UHPC
The influence of compressive strength on the fatigue resistance is controversially discussed in the literature.Several researchers assume that the fatigue resistance decreases with increasing concrete strength.Thus, the compressive fatigue resistance of the reference HPC and UHPC was investigated comparatively [8].The investigations were performed on cylindrical specimens at stress levels Smax = 0.85 and 0.75 and Smin = 0.05 at a constant test frequency of ft = 1 Hz.The specimens were produced from two batches (a and b) of each concrete type, respectively.Two laboratories were involved.
The results in Figure 3 show that the UHPC reached higher mean numbers of cycles to failure than the HPC at both stress levels.Moreover, this result was found to be statistically significant at the lower level.A batch influence was identified on the reference compressive strength obtained from the monotonically increasing loading tests.This influence was not found in the number of cycles to failure due to the estimation of the fatigue stresses for each batch, based on the respective reference compressive strength.The fatigue damage indicators strain and stiffness exhibit a different material-dependent behaviour for the two concretes.The damage evolution of the UHPC was less pronounced than that of the HPC shown by, for example, a smaller increase in strain and smaller decrease in stiffness per load cycle overall; a higher fatigue sensitivity was not found for UHPC compared to HPC.This finding is confirmed by analyses based on a broad database from the literature [16].These results contradict the approach of a strengthdependent reduction of the compressive fatigue reference strength in current design codes.

Microstructural influences due to concrete composition
The influence of different high-strength concrete compositions on the fatigue behaviour is presented in [17].The composition of the reference HPC (RH1) was systematically adjusted in order to modify the microstructure.The compressive fatigue tests were conducted at two maximum stress levels Smax = 0.85 and 0.70 with Smin = 0.05.The test frequency was ft = 1.0 Hz.It is shown that higher w/c ratios impair the fatigue behaviour, and fatigue-resistant coarse aggregates improve the fatigue resistance compared to mortars, especially at lower stress levels.In addition, the influence of silica fume was investigated by partially replacing the cement by silica fume [17].The damage indicators strain, stiffness, dissipated energy and acoustic emission hits were analysed comparatively.
The development of the cumulated acoustic emission hits are shown in Figure 4.The specimens with silica fume reached significantly higher numbers of cycles to failure and, thus, silica fume increases the fatigue resistance.This is traced back to an improved bond between the aggregates and mortar matrix (interfacial transition zone) and an improved mortar matrix.Furthermore, silica fume leads to fewer acoustic emissions at the higher stress level ( Stepwise developments of the cumulated acoustic emission hits are observable after an initial phase, which are more pronounced for the concrete with silica fume.These stepwise jumps of the hits are not noticeable in the additionally evaluated strain and stiffness developments [17].
It is assumed that the hits within these jumps are caused by widespread submicro damage events which are not yet visible in the strain and stiffness developments.A finite element model with a gradient-enhanced equivalent strain-based damage model combined with a fatigue model was developed to predict the fatigue behaviour in the concrete mesostructure.The comparison of the experimentally and computationally determined developments of strain reveal good agreement, whereby the number of cycles to failure and the characteristics of the strain development are well depicted [11].

Influence of moisture content
The results in [18] already showed a significant reduction of the fatigue resistance of HPC with increasing moisture content of the concrete.A clear indication of differences in damage mechanisms with increasing moisture content was observed from acoustic emission measurements.In the second period of SPP 2020, the influence of the loading frequency on the compressive fatigue behaviour of concrete with different moisture contents was investigated using the reference HPC [19].Immediately after the concreting process, the specimens were stored underwater (WS) or in a climate chamber (Cl 65) to adjust the two different moisture contents.The stress levels were kept constant at Smax = 0.75 and Smin = 0.05.The cyclic loading was applied with test frequencies of ft = 0.1, 1.0 and 10 Hz, respectively, for both moisture contents.
The results in Figure 5 show that specimens with a high moisture content WS reached notably lower numbers of cycles to failure compared to specimens with low moisture content Cl 65 at all test frequencies.The smallest difference is visible at ft = 10 Hz.It is obvious that the numbers of cycles to failure decrease strongly with decreasing test frequency for the specimens with the high moisture content WS.Thus, the difference between both moisture contents increases significantly with decreasing test frequency.
The well-known s-shaped stiffness development curve with phases I-III was analysed as an additional damage indicator.The results showed a higher stiffness degradation per load cycle in phase II and, thus, a higher damaging effect with increasing moisture content and lower test frequency.
Figure 5 Influence of the test frequency on the logarithmic number of cycles to failure of specimens with two different moisture contents A numerical simulation model was developed by using a phase-field approach to damage in combination with a porous media theory [18].Additionally, the progressive deterioration of the fatigue resistance of the concrete due to the moisture content was modelled by determining a local lifetime variable.It was shown that the simulation tools developed can predict the behaviour of high-strength concrete with different moisture contents and compare well with experimental results.

Concrete behaviour under model II loading
The cylindrical punch-through shear test has been readapted for a systematic and consistent study of concrete under mode II loading (Figure 6(a)) [20].Since the material behaviour under shear stress is strongly dependent on the concurrent lateral compressive load level, a novel test set-up was developed to allow the simultaneous control of shear and compression loading as well as simple applicability in monotonic and fatigue tests.Testing under compressive-shear loading (mode II) offers the advantage of precise load determination and a small, well-defined fracture surface, which can provide a decisive benefit in the investigation of fatigue-specific degradation effects.The monotonic behaviour of the reference high-strength concrete under mode II loading is shown in Figure 6(b).
The shear strength and post-peak strength (largely determined by friction between inner concrete cylinder and outer concrete ring) rise with the increasing lateral compressive load level, while the initial stiffness is largely unaffected.The influence of the lateral compressive load under mode II loading on the fatigue life is depicted in Figure 6(c).
The number of cycles to failure remains nearly uniform for the load levels studied, indicating that there is no influence of the compressive stress on the mean fatigue life as long as the increase in shear strength is considered.Furthermore, it appears that the scatter of the results decreases with increasing lateral compressive loading.The reason for this could be an increasing homogenisation of the stresses along the shear surface with increasing lateral compressive loading.Further investigations, for example, on the scatter-sensitive load sequence effect, show great potential and will be conducted in the future.
A thermodynamically consistent model is proposed in [21] that captures the inelastic behaviour including three-dimensional kinematics in response to monotonic, cyclic and fatigue loading histories.It allows the simulation of material degradation under subcritical pulsating loading and has been embedded in a microplane framework and a lattice discrete particle model to simulate the fatigue-induced triaxial stress redistribution.

Characterising fatigue of high-performance concrete using DMA
The DMA is used within this project to characterise the behaviour of HPC before and after uniaxial compressive fatigue loading.Accordingly, a DMA set-up for cylindrical concrete cores was designed (Figure 7).The piezo-electric actuator allows for harmonic excitation frequencies from 0.1 to 1000 Hz at small strain amplitudes for the characterisation of the linear material's response.The complex Young's modulus and the complex Poisson's ratio are obtained from the amplitudes and phases (uniaxial stress-strain and axial strain-circumferential strain) measured.The absolute values of the frequency-dependent complex quantities (E * ,  * ) show a weak dispersive behaviour, i.e. a viscoelastic "signature".The damaged samples could be well characterised through the small amplitude excitation, resulting in a significant decrease in |E * | and an increase in | * | (Figure 7).Similar trends are observed for the intrinsic attenuation of the HPC sample measured in the loss factors [22].The highlighted results are one step towards a more detailed experimental characterisation of the fatigue-damage processes in highstrength concrete.
In addition, the simulation of hydro-mechanical interaction between (fluid-filled) fractures and the surrounding matrix domain, which is strongly dependent on the dynamical properties of the fracture fluid and the solid matrix (transient pressure diffusion, non-linear fracture deformation) was performed [23].To improve the numerical stability of the resulting equation systems, two algorithms were proposed and consistently implemented for the coupling of hybrid-dimensional elements with a surrounding bulk matrix and tested throughout different numerical experiments.

Nanoscale formation of ettringite induced by fatigue damage of ultra-high-strength concrete
Considering the fact that every single load cycle during fatigue testing introduces a permanent strain into the material, it must be connected to irreversible changes on the micro-or nanoscale.Scanning and transmission electron microscopy were conducted on UHPC and pure binder samples from various states of compressive fatigue damage to investigate these changes down to their origins [24].
Needle-shaped objects with dark material contrast were found which form in the binder matrix even after the early onset of fatigue damage (Figure 8).While they retain their original size of ca.200 nm in length and 30 nm in width, they continuously increase in number as fatigue damage progresses.Additionally, their material contrast with respect to the surrounding binder material becomes increasingly dark.Using spatially resolved x-ray spectroscopy in transmission electron microscopy, it was found that these structural changes preferentially occur in areas with comparatively high contents of aluminium and sulphur, especially surrounding nanoscale cracks.
These findings indicate that progressing fatigue damage of UHPC on the macroscale correlates with the formation of ettringite crystals on the nanoscale.Ettringite (Ca6Al2(SO4)3(OH)12 .26 H2O) is a rare mineral that plays a crucial role in the early stages of the setting of cementitious materials.A delayed formation of ettringite in hardened concrete, however, is known to be detrimental to the durability of the material.A continuous dissolution and crystallization of ettringite can exert pressure on the surrounding calcium silicate hydrate of the binder matrix, resulting in a solidification and, eventually, the formation of nanoscale cracks.Based on the experimental results, a rheological bonded particle model was developed to apply and investigate the changes to the mesoscopic scale [24].[24] and a spatially resolved x-ray spectroscopy map of aluminium distribution (right) [24] surrounding a nanoscale crack.Scale markers are 500 nm.

Fibre-reinforced Concrete
Tensile degradation of high-strength concrete with and without micro steel fibres Cyclic tensile tests were conducted on notched prismatic specimens (40 x 40 x 160 mm³) of the reference highstrength concrete with and without micro steel fibres to determine the influence of the latter on the fatigue behaviour [12].The vertical strains of the specimens were measured using strain gauges.Figure 9 exemplarily shows a comparison of the developments of strain at a maximum stress level of 70 % fct,max and minimum stress level of 35 % fct,min for a fibre-free specimen (a) and a fibre-reinforced specimen (b).The strain of the fibre-reinforced specimen grows only marginally in phase I and no noticeable increase in strain can be seen in phase II in comparison to the specimen without fibres.Due to the limited numbers of acting load cycles in the tests, the transition to phase III was not reached.A particular focus in this project was the characterisation of the microcrack behaviour during cyclic loading and to gain knowledge concerning the starting point of microcracks.For this purpose, thick sections cut vertically were prepared from specimens after defined numbers of load cycles and examined microscopically.The microscopic analyses showed that the number of cracks increased continuously with the increasing number of cycles [12].Furthermore, most microcracks initiated in the interfacial transition zone between the aggregate and the hardened cement paste in the fibre-reinforced and fibre-free highstrength concrete.In the case of high-strength concrete without steel fibres, wider and longer cracks and, thus, a larger total crack area was found.In the steel fibre-reinforced concrete, more cracks were found, but these cracks were smaller and shorter, i.e. more finely distributed.It is assumed that the bridging effect between the crack faces of the micro steel fibres leads to the finer distribution of microcracks under cyclic loading.
As a first step, a multilevel finite element model for steelfibre-reinforced concrete was presented in [25] which allows for the prediction of the post-cracking response of fibre-reinforced structural members.In contrast to the guidelines, which suggest that the response of steel fibrereinforced concrete should be derived indirectly using bending tests, the post-cracking response was derived directly from the actual fibre properties.The proposed finite element discrete fracture model considers the imperfect closure of cracks during cyclic loading, which manifests itself as hysteresis loops in load-displacement curves.
Failure of ultra-high-performance fibre-reinforced concrete under cyclic tensile loading Fibres in UHPC lead to a considerable post-cracking (monotonic) tensile strength, which can be taken into account for designing UHPC components under static loads.Thereby, the design of a fibre reinforcement for UHPC (i.e.geometry and tensile strength) should lead to fibre pullout.Therefore, ultra-high-performance fibre-reinforced concrete (UHPFRC) usually requires high-strength micro steel fibres.Monotonic pull-out tests and calculations in [26] on the reference ultra-high-strength concrete with fibres showed that the fibre stresses were always smaller than the tensile strength of the fibre material.However, the results also show that fibre rupture occurs under cyclic loading.The occurrence of fibre rupture depends generally on the orientation of the fibre to the stress flow in the UHPC and the load amplitude.
Since the results in [26] were based on small-scale samples, and it was not clear whether the fibre rupture also occurs on real scale components, a test programme has been set up for so-called UHPFRC demonstrators that represent component alike specimens.The demonstrators used are notched beams with a span of 3.0 m, a height of 30 cm and a width of 15 cm.The concrete mixture and fibre type remained the same as in [26].Figure 10 shows the evolution of the CMOD (crack mouth opening displacement) depending on the load cycles.The abrupt growth of the CMOD after about 1,800,000 load cycles points out that fibres might have been ruptured.Afterwards, the beam could only withstand a few additional load cycles until failure.
After the test, the crack was opened to examine the fibres that bridged the crack.The examination was done with a digital microscope and a 200-times magnification.Two images are integrated in Figure 10.Both images show that the fibre channel is not empty and the steel of the fibre is noticeable.Thus, the hypothesis of fibre rupture in UHPFRC beams under cyclic loading is supported by this result.Since fibre rupture should be avoided for UHPFRC in general, the design of the fibres needs to be conducted thoroughly, considering all conditions of a UHPFRC component.

Bending fatigue behaviour of high-strength concrete with steel fibres
The bending fatigue behaviour of the reference HPC was also analysed in order to find suitable damage indicators for the modelling of low-and high cycle fatigue.Notched HPC beams with a compressive strength of about 90 MPa with fibre contents of 0, 23, 57 and 115 kg/m³ hookedend macro steel fibres were tested in 3-point bending tests according to DIN EN 14651 for the experiments [27].Several unloading/reloading cycles were carried out in the crack-opening phase to quantify and describe the degradation during testing.
Figure 11 shows the development of the residual stiffness in the low-cycle tests, i.e. the gradient of the unloading/reloading cycles over the crack opening (CMOD) for all fibre contents.It can be seen that this damage indicator gives good discriminatory power regarding fibre contents, especially in the initial phase with small crack widths.The selectivity defined by the stiffness curve decreases for larger crack openings from about 0.5 mm.However, it is also shown in [28] that from this point onwards, better distinguishability between the fibre contents can be achieved by the damage energy absorbed in cracking up to specific crack openings.
To establish a numerical model to represent the bending fatigue behaviour of reinforced HPC, an elasto-plastic phase-field model based on the variational formulation of fracture in elasto-plastic material using a Drucker-Prager yield criterion to account for the asymmetric tension-compression behaviour of pure HPC was firstly developed in [29].This model also shows good accuracy in the load vs. CMOD curves and residual stiffness vs. CMOD curves from the aforementioned low-cycle tests of fibre-free HPC in [28].A phenomenological material model was then proposed in [28], based on a superposition of transverse isotropic elasto-plasticity and that phase-field model for pure HPC.
It is able to reproduce the main characteristics of the experimental results and was successfully validated using the degradation of the residual stiffness shown in Figure 11.
Behaviour of carbon short fibre-reinforced concrete under bending and tensile loading The mechanical behaviour of short carbon fibre-reinforced concrete subjected to tensile and bending load was investigated [30].Orientation of the fibres in the material resulting in high uniaxial strength properties can be achieved by processing a mixture of concrete containing 1 or 3 vol% of short carbon fibres with a diameter of less than 10 μm in a three-dimensional printing manner.Different measurement techniques, such as computer tomography validating fibre alignment in the material and high-resolution digital image correlation, provide data serving as input for numerical computations.Here, a multiscale approach considering the scale of the carbon fibres besides the specimen scale is used to analyse the mechanical behaviour of the carbon short fibre-reinforced concrete.Regarding the numerical model, the macroscopic workpiece is discretised and the carbon fibre scale is resolved by representative volume elements (RVEs) in terms of a computational-homogenisation approach.Here, the (local) material law in each macroscopic point is determined numerically with the help of the solution of cell problems posed in the RVE at that point.Based on the numerical analysis of the undamaged material and detailed convergence studies on the RVE and mesh size, further aspects, such as incorporation of cracks on the scale of the RVEs as observed in specimens having undergone static and/or cyclic loading, will lead to a better understanding of the influence of local cracks on the durability of the carbon fibre-reinforced UHPC.

Conclusive Remarks
This paper gives an overview of the research activities on the "Cyclic Deterioration of High-Performance Concrete in an Experimental-Virtual-Lab" within the SPP 2020.Different spotlight results for this are presented which were obtained in the different tandem projects with their special objectives.
The overarching results of the SPP 2020 obtained so far can be summarised as follows: 1) Different influences on the fatigue behaviour of concrete interact with each other.This multiple interdependence of influences increases the complexity of the research subject, also for numerical modelling.Regarding investigations, this means that other boundary conditions have to kept constant or comparable in order to obtain reliable results concerning a certain problem or influence.But the results obtained are possibly not transferable to other boundary conditions.Thus, the effort to get reliable results is enormous.Within the SPP 2020, the influence of the moisture content of the concrete was found as another of the decisive influences in compressive fatigue.2) Fatigue damage in concrete, especially due to compressive fatigue loading, occurs and develops across scales, starting at extremely small scales, perhaps nanoscale.Cracks develop and become detectable relatively late in the fatigue process.Thus, there is a considerable difference compared to the damage propagation due to bending and tensile loading, where discrete cracks are more pronounced.This also affects the methods of the numerical modelling.3) Overall, the results show that fatigue damage is differently pronounced compared to damage due to monotonically increased loading.4) The usage of fibres can lead to an improved fatigue behaviour of the concrete under bending and tensile fatigue loading due to a more finely distributed crack pattern in the microstructure.
Care must be taken in the design of the fibre reinforcement that fibre pull-out and not fibre rupture occurs in case of fatigue loading.5) Concerning the fatigue-induced damage progress in concrete, microstructural analysis techniques have their limits in terms of applicability and resolution, and, thus, in terms of their informative value.Computer tomography (commercial devices), which was expected to provide new insights into the damaged concrete microstructure at the beginning of the priority programme, does not (yet) achieve the necessary resolutions for the specimen geometries required to make visible the extremely small damages on a submicro scale.6) By combining time-discrete microstructural analyses with macroscopically and continuously measured damage indicators, new knowledge has been gained despite the existing applicability limits of single methods.This might also be a promising approach for other research fields where technical limits have to be overcome.7) The material modelling of concrete or, rather, concrete microstructure, and the modelling of concrete damage was brought more into focus by the SPP 2020.Here, different modelling approaches were transferred to concrete and further developed, which has considerably advanced the field of research.Furthermore, close collaborations were established between building material and numerical mechanic scientists which will remain and have a lasting effect on the research sector.
New findings concerning the fatigue behaviour of high-performance concretes and insights into the damaged concrete microstructure were gained, and new modelling approaches were developed within the framework of the SPP 2020.Thus, the knowledge gap has been considerably narrowed.The priority programme is still running and will provide further insights into fatigue-induced damage processes.Furthermore, the comparative evaluations of the microstructural analyses methods within the round robin test should also be very interesting for further building materials research.Other publications from the SPP 2020 projects can be found on the SPP 2020 homepage [6].

Figure 3
Figure 3 Number of cycles to failure of HPC and UHPC [8].
Figure 4(a)).By contrast, considerably more acoustic hits occur at the lower stress level (Figure 4(b)).

Figure 6
Figure 6 a) Punch-through shear test with controllable lateral compressive loading and test results regarding b) monotonic behaviour and c) fatigue life[20]

Figure 7
Figure 7 Experimental set-up of forced oscillation measurements and complex Young's modulus and Poisson's ratio.

Figure 8
Figure8Top row: transmission electron microscopy micrographs of ettringite nanocrystals in the binder matrix of pristine UHPC (left), after early-stage fatigue (middle) and late-stage fatigue (right).Scale marker is 200 nm.Bottom row: transmission electron microscopy micrograph (left)[24] and a spatially resolved x-ray spectroscopy map of aluminium distribution (right)[24] surrounding a nanoscale crack.Scale markers are 500 nm.

Figure 9
Figure 9 Strain development at maximum and minimum stress level of (a) HPC without fibres and (b) with micro steel fibres.

Figure 10
Figure 10 Evolution of CMOD depending on the load cycles and ruptured fibres

Figure 11
Figure 11 Development of the residual stiffness si of HPC beams with different fibre contents, (a) overview and (b) zoom on the initial cracking phase [28].

Table 1
Composition of reference HPC and UHPC