Autogenous self‐healing of concrete: Experimental design and test methodsA review

Cracks in concrete structures can serve as pathways for aggressive chemical substances that can lead to a progressive deterioration of the cement stone as well as of the reinforcement, affecting the load capacity, service life and useability of concrete structures. However, concrete and reinforced concrete exhibit an intrinsic ability to heal cracks, defined as autogenous self‐healing. This effect includes the precipitation of calcium carbonate in the presence of water and CO2 and is accompanied by continued hydration, swelling, and mechanical blocking of the crack pathway. Experiments led to the inclusion of crack sealing by autogenous self‐healing in Eurocode 1992–3 for water retaining concrete structures. However, despite code restrictions, autogenous self‐healing of concrete shows limited effectiveness in practice. This indicates the need for further research to provide engineers with reliable design rules. Therefore, this study aims for giving a broad literature review on the state‐of‐the‐art knowledge on autogenous self‐healing, the boundary conditions, consensus, and controversy of processes and factors influencing the efficiency of autogenous self‐healing. Regarding the transferability of laboratory results to real concrete constructions, materials, crack initiation techniques, experimental concepts, and methods for assessing the effectiveness of autogenous self‐healing are discussed and recommendations for future experiments are set.

material in the world. [1][2][3] However, due to its low tensile strength the formation of cracks from micro to macro scale due to load and load independent deformation caused by, for example, shrinkage, is unavoidable. Furthermore, it is necessary to reinforce concrete for many applications. Typically, inside concrete components steel bars bring the required tensile strength into the structure. This material is commonly known as reinforced concrete. The high pH of cement phases and pore solutions around 13.5 protects the rebars from corroding by the formation of a passive layer on the surface of the steel. [3][4][5] Thus, reinforced concrete could be considered a durable composite material. However, cracks can act as pathways for aggressive chemical substances that can lead to a progressive deterioration of the cement stone as well as of the rebars, affecting the load capacity, service life and useability of concrete structures. 6,7 Concrete and reinforced concrete exhibit an intrinsic ability to heal cracks, defined by RILEM technical committee as "autogenous self-healing." 8 This effect includes the precipitation of calcium carbonate in the presence of water and CO 2 and is accompanied by continued hydration, swelling, and mechanical blocking of the crack pathway. Autogenous self-healing has been investigated by many researchers since the 1980's 9-13 as a possibility to restore load capacity, durability, and useability of concrete structures. These experiments led to the formulation of Eurocode 1992-3 14 that regulates the boundary conditions, crack widths and hydraulic gradients under which autogenous self-healing is likely to occur. For reinforced concrete structures that have an increased demand on durability, the maximum crack width w max is limited to 300 μm. For water retaining concrete structures w max is further limited to 200 μm with respect to the ratio of water head to wall thickness. However, in practice it is observed that cracks in accordance with the restriction do not heal. 15 Problems might be that laboratory results have not been verified at real concrete structures as of today, there still is a lack of a comprehensive understanding of processes that influence the efficiency of autogenous self-healing or even worse, cracks do not heal because the boundary conditions are neglected on-site. Furthermore, as proof of the appropriate application of the restrictions the calculated crack width w k is set equal to w max according to Eurocode 1992-1-1, 16 which can have severe consequences for the efficiency of autogenous self-healing. 15,17 The scattering of crack widths due to crack geometry, temperature, loading and so forth is neglected and, as a matter of fact, it is accepted that for w k of 200 μm 20% of the measured crack widths can be greater than the actual restriction of 200 μm. These issues are just some examples for the increase of publications on autogenous self-healing of cracked concrete since the 1990's, while a prominent increase of interest can be observed since 2010 ( Figure 1). Therefore, this study aims at reviewing and discussing the current scientific consensus and controversy on parameters affecting autogenous self-healing, materials, experimental designs, and methods applied to assess the healing efficiency of cracked concrete. To guide the reader through this document self-explanatory icons were designed that represent certain aspects within the workflow of autogenous self-healing experiments ( Figure 2).

Swelling
Swelling of concrete is a slow and theoretically partly reversible process caused by water adsorption of the cement stone. 10,11 Thus, a crack sealed due to swelling can become leaky again in a dry period and close again in the presence F I G U R E 3 Schematic overview of possible causes of autogenous self-healing of water or sufficient humidity. In practice, however, it is difficult to determine the isolated effect of swelling of concrete without measuring superimposed processes such as autogenous shrinkage, excessive calcite precipitation, or continued hydration. For instance, Meichsner 10 measured the volumetric flow rate through a separating crack that was healed under flow conditions and then exposed to a dry environment for at least 1 week. As expected, the crack became leaky after the dry period. Accordingly, the experiment was repeated four times whereas with every repetition the increase of the volumetric flow rate became less pronounced. Therefore, swelling is not a completely reversible process. However, it must be addressed that superimposed effects such as CaCO 3 precipitation in air cannot be excluded for this experimental setup. According to Edvardsen 11 swelling is of little importance for crack closing of cracks wider ≥100 μm. The author gives a crack width reduction of 6 μm which was obtained through a sample calculation assuming a penetration depth of 30 mm and a maximum swelling of 0.1 mm*m −1 . This contradicts with results from Meichsner 10 who measured swelling with 0.3 mm*m −1 on samples that were submerged in water. Based on this and an assumed penetration depth of approx. 42 mm the latter author gives a theoretical crack width reduction of 25 μm. Therefore, differences in the sample calculations of Meichsner 10 and Edvardsen 11 can be explained by the lack of reliable data on the penetration depth and assumed degree of swelling. Roig-Flores et al. 26 found out that cracks can close by up to 8% when exposed to 95% relative humidity (RH) and 20 • C. However, when the environment was sufficiently dry (RH ∼ 45%) the crack width increased by up to 46% due to drying shrinkage. The initial crack widths are given with w < 300 μm but were not further limited. This makes it difficult to compare the measured value with Meichsners 10 and Edvardsens 11 theoretical values. Interestingly, however, experiments in humidity chambers could provide a possibility to quantify the effect of swelling without the superimposed effects of continued hydration, calcite precipitation, or clogging of the flow path. However, it must be addressed that moisture and liquid water, water pressure, temperature, and physical properties of the samples could result in different values for swelling. Finally, it can be concluded that for cracks restricted by Eurocode 1992-3 14 a maximum of 6% to 25% of the initial crack width (w ∼ 100 μm) could be closed due to swelling. To date, however, there still is a lack of reliable data on swelling with respect to autogenous self-healing.

Continued hydration
Continued hydration describes the hydration reaction of freshly exposed unhydrated cement particles after cracking. The growth of the hydration products into voids could seal cracks. According to Ritzmann 27 the hydration depth of cement particles is 5 μm after 28 days of hydration. During longer hydration periods particles up to 10 μm can hydrate completely. 28 The particle sizes of cement range from 0 to 100 μm whereas the exact particle size distribution depends on the desired properties of the cement such as for instance early age strength. The average grain size of CEM I/32.5 is in the range of 10 to 20 μm. 3 Therefore, especially with concrete at a young age, unhydrated cement particles are available for continued hydration when the particles are exposed to additional water. Therefore, continued hydration and its effect on autogenous self-healing has been studied. 21,22,[29][30][31] Some studies assign the uncertain effect of autogenous self-healing in practice to an excessive overgrinding of modern cements and suggest an optimized average cement grain size to improve the effect of continued hydration. 21,32 However, a practical relevance for this suggestion is questionable concerning the impact on concrete properties such as strength. According to Edvardsen 11 continued hydration is of minor importance for crack closing as no proof for it could be seen in her experimental study with cracked CEM I/32.5 R, CEM III/A 32.5 N (45% ground blast furnace slag [BFS]), and CEM III/A 32.5 N LH/SR (22% BFS) concretes subjected to continuous water flow. In case hydration products were washed away or overlooked she also provides an example calculation. Assuming a uniform particle diameter of 50 μm, a volume doubling for complete hydration and a hydration degree of 5% after 3 days, a crack width reduction of approx. 6 μm can be calculated for complete hydration. Therefore, the author states that continued hydration and swelling of concrete are in a similar range (compare Section 2.1) and only of importance for cracks ≪ 100 μm.
Some experimental studies aimed at isolating the effect of continued hydration, whereas special precautions must be taken to avoid excessive carbonation. Typically, experiments are carried out with deionized water and under a CO 2 free atmosphere. 29, 33 Yuan et al. 21 found continued hydration for CEM I mortar specimens in the range of 12 to 22 μm after 7 days of self-healing in water immersion. The initial crack width was ∼300 μm and the sample age 28 days. The authors also state, that continued hydration is the main mechanism of healing during the first 7 days of healing. Afterwards excessive carbonation is taking over. However, the water chemistry and atmospheric conditions are not clearly stated. Thus, this apparently delayed carbonation could be caused by the kinetics of dissolution of CO 2 in deionized water. Huang et al. 30,31 give a value of 30 to 35% of 10 μm cracks in CEM I cement paste that could be healed by capillary suction of water or Ca(OH) 2 solution under a CO 2 free atmosphere after an exposure time of 250 h. A higher healing efficiency was achieved for CEM III cement with approx. 60% of 10 μm cracks healed by capillary suction of Ca(OH) 2 solution. Generally healing was more efficient in Ca(OH) 2 solution. Interestingly, for both water and Ca(OH) 2 solution the hydration is fastest in the first 48 h and slows down distinctly afterwards. This could affect rapid flow reduction in permeability experiments (compare Section 4.3). Yet, differences between the authors could be assigned to the variable experimental approaches and materials. However, the scattering of ∼3 to 22 μm of possible crack width reduction by continued hydration is severe and should be investigated in further research. An influence of the initial crack width seems possible. Furthermore, it is desirable to study crack width reduction through continued hydration of specimens that were subjected to a permeation test. Respectively, the adhesion force of hydration products and critical water pressure that can be withstand could be determined. To obtain results that are transferable to real structures, concrete samples instead of mortar or paste should be used.
Huang et al. 30,31 characterized the phases that formed due to continued hydration chemically and mineralogically (see above for experimental conditions). The authors subdivided the hydration products into gel-like and crystal-like hydration products. For CEM I cement, the phases formed by continued hydration amount to approx. 78% to crystal-like Ca(OH) 2 (CH) and 5% CaCO 3 and 17% to gel-like calcium-silicate-hydrate (CSH) as determined by x-ray diffraction (XRD) and thermogravimetric analysis/differential thermal analysis (TG/DTA). For CEM III cement the phase content is different. Respectively, approx. 6% CH, 7.5% mono (Ca 4 Al 2 (CO 3 )(OH) 12 *5H 2 O) and hemi-carboaluminate (Ca 4 Al 2 (CO 3 ) 0.5 (OH) 13 *5.5H 2 O), 9.5% Ettringite (Ca 6 Al 2 (SO 4 ) 3 (OH) 12 *26 H 2 O), 20% CaCO 3 , and 57% CSH were determined by XRD and TG/DTA. A general depletion of Si 4+ in the hydration products compared to the cement stone matrix was measured by environmental scanning electron microscopy (ESEM). This was attributed to the slower diffusion of Si 4+ with respect to Ca 2+ . Detected CaCO 3 and mono-and hemi-carboaluminate was assigned to the successive reaction of CH with atmospheric CO 2 after the experiment was terminated. Concerning the different phase composition that is formed by continued hydration, it could be assumed that the cement type impacts the extend of carbonation secondarily through the CH content in the hydration margin, since CH is the main source of Ca 2+ ions which are required for carbonation. 11 This effect could be accompanied by a generally lower content of CH in cements incorporating pozzolanic or latent hydraulic replacements such as fly ash or ground blast furnace slag (compare Section 2.3). Yet, the understanding of the impact of continued hydration on carbonation and the dove-tailing of these two healing processes is little. For instance, it remains questionable whether primary carbonation of CH and unhydrated cement clinker phases in the cement stone matrix exposed at the crack wall takes places before any continued hydration.
Since cements incorporating pozzolanic or latent hydraulic supplementary cementitious materials show a slower hydration process, the potential for enhanced continued hydration was widely discussed in the literature. 24,25,29,[34][35][36][37] According to van Tittelboom et al. 29 best self-healing results can be obtained by cements incorporating blast furnace slag or fly ash replacement and thus showed a lower hydration degree at the testing age of 55 days compared to ordinary Portland cement. Respectively, the latter authors found that increasing the water/cement (W/C) ratio had the opposite effect. The results base on the assumption that only continued hydration is responsible for the flow reduction in the permeability experiments that were carried out with cracked mortar specimens and deionized water in a CO 2 free environment. However, it must be addressed that mineralogical and chemical proof was not given in the study and the possibility of physical clogging of the flow path was not discussed. Moreover, the results are in contradiction with findings of Maes 22 who states that the extend of continued hydration is independent from the used cement type. The author refers to experiments with CEM I and CEM III mortar specimens that were subjected to healing in deionized water immersion at the age of 24 days. The healing was then measured in terms of crack width measurements. Thus, differences between the authors could also be assigned to the age of the specimens and the subjective crack width measurement technique. Nevertheless, the supportive effect on continued hydration through the partial replacement of Portland cement with fly ash was also found in other studies. [34][35][36][37][38] Zhou et al. 36 even recommend the incorporation of 40% fly ash in cement to obtain best self-healing results. However, these studies have in common that the effect of continued hydration was investigated by compressive strength tests, porosity, hydration degree or Cl − diffusion coefficient measurements. Thus, the results are based on measurements of physical properties that are not relevant for the flow reduction of through cracked concrete. Respectively, Termkhajornkit et al. 35 states that his results are only applicable to the healing of micro-cracked cement paste and does, for example, account for the regain of strength 36,39 whereas the ability of continued hydration to heal wider cracks is questionable. Regardless the controversial results concerning continued hydration it can be concluded that hydration reactions are possibly of major importance for healing cracks with w ≪ 100 μm. With respect to a comprehensive numerical modeling of autogenous self-healing further research is required to improve the understanding of continued hydration, dove-tailing of chemical processes and the impact on carbonation.

Calcium-carbonate formation
It is widely accepted that calcium carbonate precipitation is the main mechanism of autogenous self-healing when cracked concrete is healed in liquid fresh water with a pH ≈ 7 in equilibrium to a CO 2 rich atmosphere such as air. 10,11,[19][20][21][22] Ca 2+ ions from the concrete react with carbonate species in the water and precipitate as calcite as soon as the solubility is exceeded. Edvardsen 11 showed that under the aforementioned conditions calcite is the thermodynamically stable structure of CaCO 3 and can close cracks up to 200 μm width completely when specimens are subjected to water flow for a few days to several weeks. It is also the only cause of autogenous self-healing that could be proven by the authors chemical and mineralogical analysis of healing products after the experiments were terminated. Edvardsen 11 further determined that the extent of flow reduction is independent from the cement type, additives increasing the Ca 2+ content and the concentration of carbonate species in the permeating water. This is in accordance with results from Meichsner. 10 Measurements of the chemical composition of the permeated water further showed that there is always an excess of HCO 3 − , CO 3 2− , and Ca 2+ ions available for calcite formation. However, it was observed in other studies that the partial replacement of Portland cement by ground blast furnace slag or fly ash reduces the amount of formed calcite. 19,29,40 This was assigned to a limited availability of Ca 2+ ions that mainly originate from portlandite (compare Section 2.2). On the other hand, Suleiman et al. 41 showed that cements with added limestone powder exhibit a higher maximum healable crack width by calcite precipitation compared to Portland cement references. Moreover, the authors showed that for limestone cements, the measured Ca 2+ concentration in the deionized water of the immersion tests was higher than for Portland cement. Thus, limestone additives could promote calcium carbonate formation. However, the latter results contradict the finding of Edvardsen 11 and Meichsner. 10 Furthermore, these studies are based on mortar or concrete specimens that were submerged in water for healing while the extend of healing was measured by surface crack width measurements. In contrast, Meichsner 10 and Edvardsen 11 conducted permeation experiments. Thus, differences could be assigned to the experimental approach and assessment technique of autogenous self-healing. However, it is desirable that Edvardsens 11 and Meichsners 10 results are verified on modern cements which typically have a low Portland cement content and can contain different cementitious supplementary materials.
Generally, calcite precipitation or dissolution depends on the pH value, temperature and the partial pressure of CO 2 (pCO 2 ). 3,11 Regarding the equilibrium of the CaCO 3 -CO 2 -H 2 O system the solubility of calcite increases with lowering of the pH value, decreasing temperature and increasing pCO 2 . Thus, in practice autogenous self-healing approaches cannot be applied when concrete attacking water with a pH value <5.5 or > 40 mg*l −1 CO 2 is present as recommended by the Germen board for reinforced concrete (DAfStb). 42 However, assuming the concentration of Ca 2+ ions in the crack to be constant (thus equal to one in the solubility calculation) one can calculate a critical pH ≈ 6.6 for calcite dissolution at 25 • C and 1 atm. Pressure concerning the pH dependency of the CO 3 2− concentration of water in equilibrium with air. Therefore, the aforementioned recommendation 42 can be considered rather optimistic. In permeation experiments calcite precipitation is also influenced by the crack width w and the water pressure p. 11 Both affect calcite growth indirectly through the pH change of the permeating water. Several crystallographic studies [43][44][45][46] confirm that the calcite growth rate is independent from flow velocity but decreases with increasing pH-value. Accordingly, a wider crack and a higher hydraulic pressure leads to an increase of flow velocity, reducing the contact time of water with concrete and thus a less prominent increase of the pH-value. Edvardsens 11 experiments confirmed this theoretical approach as absolute flow reduction was higher for 300 μm cracks than for 200 or 100 μm cracks. However, smaller cracks are more likely to close completely and show a higher relative flow reduction as the volumetric flow rate is proportional to the third power of crack width (Q ∼ w 3 , compare Section 4.3.2). Therefore, Eurocode 1992-3 14 restricts crack widths and hydraulic gradients and set both in relation so that autogenous self-healing for water retaining concrete structures should be likely. However, the measurement of crack width can be highly varied and subjective depending on the authors.
Additionally, calcite growth is often described as a two-phase kinetic process. 11,19 First, a fast surface-controlled growth of CaCO 3 . Second, a slow diffusion-controlled growth since Ca 2+ ions must diffuse through an already formed layer of CaCO 3 for further calcite growth. In the second phase the influence of crack width and hydraulic gradient on the flow reduction was found to be not relevant. 11 This perception was derived from characteristic volumetric flow rate curves as a function of time (compare Section 4.3), 11 while also crack width measurements of specimens submerged in water revealed two phases of a crack closing rate. 29 However, in water immersion experiments the pH value of the water increases, and the carbonate ion concentration decreases with time and could therefore also impact calcite growth. Moreover, as of today, this model lacks directly determined growth rates and Ca 2+ diffusion coefficients which would help to fully understand the healing process through calcite precipitation. This could further lead to a comprehensive chemical and transport modeling of autogenous self-healing, for example, with the PHREEQC 47 modeling tool. Furthermore, a fingerprint of the change in water chemistry during specific phases of the autogenous self-healing process could be generated.
Moreover, calcite growth can be influenced by the water chemistry. In many cases water has no tap water quality when it permeates through a separating crack in concrete structures. Thus, it is possible that water originates from soil or organic rich ground and contains increased quantities of dissolved organic matter (DOM). Chave and Suess 48 showed that DOM inhibits the growth of CaCO 3 by occupation of nucleation sites. Moreover, it was reported that phosphates and sulfates also inhibit calcite growth. 49,50 These findings could be reality in many construction environments and a decisive factor for the reliability of autogenous self-healing. However, these findings must be verified by experiments with through cracked concrete. Chemical monitoring of water permeating through cracks in real concrete constructions could help to enclose further inhibiting factors of calcite growth. However, a detailed review of the literature is necessary concerning chemical inhibition of calcite growth which is out of the scope of this study. The influence of seawater on calcium-carbonate formation is discussed in detail in Section 4.4.

Blocking
This cause of autogenous self-healing can only apply when a fluid flows through a crack. Loose particles from the crack walls and/or particles in the permeating water can cause the clogging of flow paths whereas the blocking is likely to occur at bottlenecks of the three-dimensional crack geometry. The width of bottlenecks can be significantly influenced by the gradation curve and aggregate size of concrete as further discussed in Section 4.3.4. As published by Clear 9 in 1985, rapid flow reduction in the first 7 days of permeation experiments is mainly due to this effect. However, without showing evidence. In contrast, Edvardsen 11 could not determine any sign of mechanical clogging in her experimental study and assigned the rapid flow reduction to the first stage of calcite formation (compare Sections 2.3 and 4.3). Yet, there is no study showing proof of the blocking of flow paths which generally could be a difficult task. Specimens must be prepared and cut in slices to allow an investigation of the crack interior. Thus, the probability of obtaining a slice showing evidence is low. Moreover, particles could loosen due to the preparation procedure. It is also likely that particles in blocked crack parts act as nucleation sites for calcite growth and are therefore overlooked. As of today, some authors still claim that blocking of flow paths is the main cause of early flow reduction. 15 Regarding the latter authors, this controversial statement could originate from experiments with water enriched in particles such as cement powder, bentonite, or silica fume. In such experiments the leaking time is significantly reduced. 11 However, in practice it is often not possible to enrich water with particles. Moreover, this could be counterproductive in terms of calcite precipitation as the crack can partially fall dry behind a blocked part of the crack. If particles are loosened or washed out after a while autogenous self-healing processes could no longer be effective due to the hydration degree of the concrete. 15 Correspondingly, cracks could leak again.

MATERIALS
The transmission of laboratory results to real concrete structures is difficult but should be a major goal to provide engineers with a reliable tool to assess the effectiveness of autogenous self-healing. However, cement-paste and mortar specimens of variable composition are frequently used to evaluate the effectiveness of autogenous self-healing as of today. Furthermore, different crack initiation techniques and adjusted crack widths can be found in the literature. This is discussed in the following sections concerning the transferability of laboratory results to real concrete structures. An overview of experimental design parameters of selected studies is given in Table 1. These parameters can be assessed by the reader after completing this section.

Specimen properties
3.  60 However, the wall thickness must be greater when certain pressure gradients I and maximum water column heights h w are exceeded. For h w >3 m ≤ 10 m, the concrete walls must be ≥400 mm < 660 mm. Respectively, a sample depth of 400 mm can be regarded as the minimum wall thickness of water retaining concrete components exposed to up to 1 bar water pressure. On construction sites, a limiting factor for autogenous self-healing can also be the crack length that can be >1 m. 10 It is likely that such cracks are neither evenly permeated nor continuously healed and therefore remain leaky for a longer period of time or do not heal completely as observed in practice. However, crack lengths >1 m are difficult to produce and to investigate in the laboratory. It is worth mentioning that the results of autogenous self-healing experiments have been extrapolated to cracks of arbitrary lengths to date, whereas only a few large scale experiments were carried out and remain to be verified. 11,56 Therefore, scaling experiments that aim at quantifying the effect of crack lengths and sample thickness on autogenous self-healing results could potentially lead to the introduction of a scaling factor to current self-healing criteria. > 5 min are exposed due to cracking and thus the ability of continued hydration to take place, while calcium carbonate formation could be promoted by the quantity of Ca(OH) 2 . Accordingly, autogenous self-healing data of specimens with different cement content such as paste, mortar, and concrete specimens are not comparable regarding the chemical causes of autogenous self-healing. Moreover, differences can also be expected for the swelling ability, the particles that form due to the cracking process and the crack geometry itself ( Figure 6, compare Section 4.3). From a practical point of view, concrete specimens should be used when tests aim at transferring laboratory results to real structures. For this purpose, the cement content of concrete mixes should be within the range of the applicable standard and exposure conditions. 3 For water-retaining concrete structures, a minimum cement content of ≥280 kg*m −3 is recommended according to the DAfStb standard. 60 Regarding DIN EN 206-1 61 and DIN 1045-2, 42 this minimum cement content must be further increased under certain exposure conditions.

Cement type & supplementary cementitious materials
According to Edvardsen, 11 the cement type, pozzolanic, latent hydraulic supplementary cementitious materials and other additives that affect the availability of Ca 2+ such as fly ash, ground blast furnace slag or limestone powder do not affect the extent of autogenous self-healing, respectively, the calcite precipitation. However, this finding is controversially discussed in the literature (compare Sections 2.2 and 2.3). Therefore, Edvardsens 11 results should be verified on modern cements, which typically have a reduced clinker content. As of today, cement types are not restricted by code regulations that consider autogenous self-healing of through cracks.

Aggregate volume & gradation curve
The tortuosity and effective crack length of through cracks in cementitious materials are significantly influenced by both aggregate volume and gradation curve. 10,12,13 Accordingly, permeability and autogenous self-healing of cement paste, mortar, and concrete are not comparable (compare Section 4.3). A similar argumentation accounts for concrete samples with different aggregate volumes and gradation curves since tortuosity superimposes the general high scatter of permeability experiments. Therefore, gradation curve and maximum aggregate size should be held constant within a test series and in the range of the applying code. According to DAfStb standard 60 for water retaining concrete the maximum grain size is restricted to ≤32 mm for a wall thickness of 400 mm.

W/C ratio
According to the DAfStb standard 60 for water retaining concrete structures, the W/C ratio should be ≤0.60 for a structural thickness of 400 mm. When seawater exposure applies the max. W/C ratio should further be restricted to ≤0.45 for XS3 and ≤0.55 for XS1 according to DIN EN 206-1, 61 and DIN 1045-2. 42 It is also reported that the tortuosity of cracks in cementitious materials decreases with decreasing W/C ratio 62 (compare Section 4.3). Moreover, a low W/C ratio leads to less hydrated cement (compare Section 2.2), which may affect autogenous self-healing by continued hydration. 55 Therefore, for reasons of transferability to real concrete structures, the W/C ratio should be in the range of the applicable standard and kept constant within a test series.

Concrete age
The testing age, respectively, the hydration degree of concrete specimens can have a significant effect on the efficiency of autogenous self-healing. It has been reported that autogenous self-healing is most effective for young concretes. [63][64][65] However, current code regulations 14,42 do not restrict autogenous self-healing to cracks that form solely by early age crack formation, for example, due to shrinkage. De Belie et al. 19 reviewed studies attributing the deceasing healing efficiency to the increasing amount of CSH phases formed over time due to the slow pozzolanic reaction. This argumentation is based on the lower solubility of CSH compared to Ca(OH) 2 which could limit the availability of Ca 2+ for calcium-carbonate precipitation at higher hydration degrees. However, this contradicts with results of other studies that showed that autogenous self-healing is independent of the cement type and cementitious supplementary materials, 10,11 as both affect the initial CH and CSH concentration. Accordingly, it remains unclear which explicit process limits the efficiency of autogenous self-healing at higher concrete age. Therefore, systematic experiments with different sample ages should be performed in the future. It is worth noting that most reviewed publications started with permeation experiments after 28 days of curing Table 1. In practice, concrete structures are also frequently exposed to water after 28 days of curing.

Crack initiation & crack width
Autogenous self-healing approaches can be applied when water retaining concrete structures show early load-independent cracking, which is mainly due to constrained stresses resulting from temperature profiles within the concrete element, plastic-, drying-, chemical-, and autogenous shrinkage. 4,11,66 When through cracks are formed the constrained stress shows a uniform tensile-stress distribution. 4,67 Generally, the crack generation technique impacts the crack geometry due to different stress states. 68 Since the permeability of cracked concrete is sensitive to the crack geometry (compare Section 4.3) results of permeability experiments are affected by the cracking technique. Therefore, cracks in laboratory concrete should be initiated according to the stress state of the cracking mechanism. Moreover, it is unlikely that crack walls rotate in real constructions after cracking. Thus, the parallelism of crack walls should always be given to conserve the initial crack geometry. This is not the case when the initial crack width is readjusted, or specimens are put back together after cracking. In general, crack widths should be in the range of 100, 200, and 300 μm as these are the restricted widths by Eurocode 1992-3. 14 Moreover, the coefficient of variation (COV) of the measured mean surface crack width of a test series should be <4%, if one aims at assessing the effect of different crack geometries on permeation. 59 Variation of the initial flow of samples can then be assigned to variation of the crack geometry. However, it must be mentioned that in reality cracks in concrete often show a branching that can reduce the spatial crack width and increase the crack length which could promote autogenous self-healing. Accordingly, different fibers and reinforcement close to the surface were tested in different studies. 11,12,19,54,69 Edvardsen 11 found that steal fibers increase the surface crack width. In her study, only reinforcement close to the surface promoted crack branching and was effective in reducing the initial flow and the healing time but was dependent on the degree of reinforcement. On the other hand, it was reported that fibers reduce the permeability by up to 90% and reinforcement only by 30%. 12 However, the effect was found to depend on the fiber type (steal, polyacrylonitrile, polyvinyl-alcohol [PVA]) and the volume of fibers. In addition, Mechtcherine et al. 54 reported that finer fibers (glass and carbon fibers) lead to the formation of finer but more cracks. Also the precipitation of CaCO 3 is influenced by the presence of fibers (PVA) which act as nucleation sites. 69 However, further systematic experiments are desirable.
In the past couple of years deep learning neural network based image analysis tools were proposed among others by Cha et al. 70,71 to overcome limitations of crack detection by human-eye visual inspection on construction sites. The latter authors conclude that crack detection by bounding-boxes-based image recognition with convolutional neural networks (CNN) and faster region-based convolutional neural networks (R-CNN) is a precise and reliable tool for crack detection under different environmental conditions such as shadow, bright light and so forth whereas with the R-CNN method the amount of training data could be significantly reduced. However, the detection based on bounding-boxes is too coarse to quantify defects such as the crack length and width, which requires pixel-level crack segmentation. 72,73 For instance, Kang et al. 74 modified a R-CNN algorithm to allow for a crack segmentation into pixels and further measurement of the crack thickness and length by pixel analysis. The latter authors achieved an accuracy of 93%. Additionally, it has been shown that modified R-CNN algorithms can accurately detect cracks in the range of 90 to 200 μm in real-time from unmanned autonomous vehicles such as drones. 75 It would be desirable to test these methods in future studies on cracks in real structures that are intended to be healed by autogenous self-healing.
In the following paragraphs common cracking methods ( Figure 4) are discussed, considering the above-mentioned requirements for the stress state and preservation of the crack geometry. An overview of the pros and cons is given in Table 2.
In most recent publications cylindrical specimens were cracked by tensile splitting test (TST). 25,26,29,33,51,58,76,77 This method is easy to use, fast, and has a uniform tensile-stress distribution according to simulations, 78 while only the margins subjected to loading show small areas of compressive stress regimes that most authors consider negligible. However, crack width must be monitored by linear variable displacement transformers (LVDT) during crack initiation to stop loading when the desired width is reached, while cracks can then partially close again after unloading by up to 32% to 72%. 52 Furthermore, it was reported that cracks open on one side and then propagate through the sample, which is why the crack width must be controlled on both flat sides of the cylinder during a TST. 76 Respectively, the tensile stress distribution is not as uniform from a practical point of view. Moreover, it is likely that rotation of the crack walls occurs when the crack width is readjusted after crack initiation or crack walls "snap-back" due to unloading. This can cause the clogging of flow paths due to wedged particles or crack surfaces and should be avoided in permeation experiments. However, this is not important when specimens are simply submerged in water for healing. To protect samples from breaking apart the cylinders can be coated by epoxy or other reinforcing materials such as done by van Tittelboom et al. 33 Alternatively, 3 or 4 point-bending tests (PBT) are recommended by some studies. 68,79 This method is also easy to use and fast but shows a nonuniform tensile-stress distribution as compressive stresses apply on the loading face. Mostly lab sized prismatic samples are cracked with this method, whereas for instance Danner et al. 80 used PBT-techniques to initiate cracking on several meter long concrete beams. However, it can be difficult to keep the specimen attached after cracking. Therefore, a thin coating of carbon fiber plastic can be applied on the loading face to protect the samples from breaking apart as reported by some authors. 57,59,81 In other studies, 21,31,55 the specimens were only pre-cracked to avoid breaking apart, which means that the loading was stopped as soon as a small crack tip opened. With the latter, crack width reduced after unloading. 55,57 For plastic coated specimens crack width must be readjusted after crack initiation, whereas for completely separated specimens the crack must be reassembled. Therefore, rotation of crack walls is unavoidable with the consequences for permeation experiments that were outlined above. For active crack width control special retainers are widely used. 7,57,59,80 However, it was reported that elastic creep of readjusted cracks can lead to the partial closure of the opening with time, while the absolute extent of elastic creep depends on the exact restraining method. 59 Therefore, relaxation time and the extent of elastic creep should be monitored before self-healing or permeation experiments are carried out to eliminate this effect. Another approach is to fix crack width by applying an epoxy coating such as done by Yuan et al. 21 Epoxy coatings show negligible elastic creep, but special care must be taken to ensure that the resin does not flow into the crack. Generally, it is rather unusual to perform permeability tests with prismatic specimens that were cracked by PBT, while most studies use such specimens for self-healing experiments in water immersion. However, van Mullem et al. 59 and Gruyaert et al. 57 proposed a special permeation test setup with active crack width control that was also tested in a round-robin test series. 81 Prismatic (160 × 40 × 40 mm 3 ) samples are coated by a carbon fiber plastic on the loading side, crack width is readjusted and restrained after crack initiation and the crack sides are sealed with methylacrylate. Water flows then through a hole in the center of the sample, before entering the crack. A major disadvantage of this method is the increased contact time of water with concrete due to the flow path through the half length of the specimen before entering the crack. This can influence autogenous self-healing due to an increased pH value and increased Ca 2+ availability in the water. Moreover, the triangular crack shape of this method produces bottlenecks at the narrowest part. This method might be suitable for short permeability experiments, for instance to investigate the impact of crack geometry on permeability but is not suitable for long time autogenous self-healing experiments due to the disadvantages outlined above.
Another approach are compressive strength tests for crack initiation. This method can be considered completely unsuitable for crack initiation as the stress distribution is contradictory to the requirements mentioned above. Moreover, specimens often show multiple cracking, displacement, and deterioration after the test. Furthermore, it is not possible to fix or adjust crack widths. Therefore, the extent of healing cannot be compared to the initial crack width and thus the extent of healing cannot be assessed.
Direct tensile tests are rather uncommon for crack initiation. However, this method provides pure tensile stress, while the biggest disadvantage is the complete separation of the specimen after cracking or the partial closure of cracks after unloading. 54 Respectively, the sample must be reassembled, and the crack width readjusted, or the flow path can be blocked due to the "snapping back" of the crack walls. Moreover, for large scale specimens' custom setups are needed. However, the mechanism of crack initiation is the most realistic one regarding early load-independent cracking. Edvardsen 11 developed an experimental setup based on the latter crack inducing technique ( Figure 5). To avoid an uncontrolled separation of the sample or "snapping back," the tensile stress is applied in small steps by rotating nuts on threaded rods that simultaneously act as crack width retainers. The tensile force is brought into the concrete through cast in curved threaded rods, while thick metal plates at the back side of the concrete specimen provides sufficient counter force. However, it is important to allow for relaxation after each step of increasing the tensile stress until crack initiation. The exact location of cracking is then given by notches in the specimen that result from the special casting framework.
The greatest advantage of this setup is the maintained parallelism of the crack walls that are hold in position during the crack initiation. The greatest disadvantages are the complexity and time-consuming crack initiation. Furthermore, the size of the setups must be varied when scaling experiments are aimed at. However, this setup can be used as a framework for concrete casting, crack initiation and permeability experiments. However, stress rates and relaxation times are not given in Edvardsens 11 study and therefore must be approached by trial and error in further research following this test design. In future setups acoustic emission techniques could guide the crack initiation process and could allow an assessment of damage growth in the concrete specimen. 82

INFLUENCE OF DIFFERENT EXPOSURE CONDITIONS ON AUTOGENOUS SELF-HEALING
After working in the process theory of autogenous self-healing, material selection, casting, curing, and cracking of the specimens, the samples must be exposed to a healing environment to initiate autogenous self-healing ( Table 3). The healing environment, its possibilities and limitations should be clarified in advance of any experiment to avoid disturbance of the workflow. In addition, it is particularly useful for the reader of self-healing literature to be aware of different exposure conditions and corresponding experimental variables that can affect autogenous self-healing results to avoid misinterpretation of experimental data. In the following sections an overview of commonly applied exposure conditions is given, and the possibilities and limitations are discussed.  • Surface crack width measurement.

Submersion in water of through cracked concrete specimens
In many studies 21,24,25,41,83,84 cracked concrete specimens are submerged in water to investigate the extend of autogenous self-healing for the sake of simplicity. Therefore, instead of measuring the permeability, surface crack width measurements are mostly carried out. Thus, watertightness cannot be accessed ( Figure 6) and only swelling, continued hydration and calcite precipitation apply in these experiments. Only in a few studies 25,26 healing was initiated in water immersion experiments and the watertightness tested after defined healing periods in permeability tests. These experiments only allow for blocking of the crack during the watertightness evaluation. Moreover, the healing process is terminated as the samples are moved into a permeability setup. This provides multiple error sources such as change of the crack width, contact to atmospheric CO 2 and so forth. Respectively, it is difficult to compare results with continuously permeated concrete specimens. The main mechanism of autogenous self-healing of samples immersed in tap water under atmospheric conditions is the precipitation of calcite. 20,83 However, only little is known about the impact of the container size, respectively, the water volume on the temporal availability of relevant carbonate ions and pH development during such experiments. Both could affect the self-healing results (compare Section 2.3). Maes 22 showed that samples submerged in deionized water exhibit a much slower self-healing rate as mainly continued hydration applies. However, it is not clear from the authors study whether the experimental setup was exposed to atmospheric conditions. One can conclude that carbonate species must be present in the water for calcite precipitation to take place and the kinetics of dissolution of CO 2 in the water is too slow to be recognized by the experiment. When the samples are submerged in artificial seawater the self-healing mechanism changes (compare Section 4.5). All immersion tests in tap water have in common that calcite precipitation mainly takes place at the surface of the specimen adjacent to the crack opening and not in the sample interior. This seems to depend on the initial crack width, since 200 μm cracks show CaCO 3 at the crack opening while 400 μm cracks show CaCO 3 precipitates along the whole crack path. 24,25 On the other hand, permeation experiments by Edvardsen 11 showed calcite precipitation along the whole crack path regardless of the crack width. Thus, due to the lack of motion in water F I G U R E 6 Schematic illustration of the workflow of freshwater immersion and permeability experiments for different sample types, see text for detailed description of the parameters immersion experiments there must be a depletion of relevant ions inside of the crack. A mechanism is proposed by Palin et al. 25 Respectively, carbonate species quickly deplete in the interior which leads to the formation of a concentration gradient and the movement of Ca 2+ ions toward the crack opening. Therefore, excessive calcite precipitation takes places at the concentration front. However, the depletion of carbonate ions is only effective for crack widths ≤200 μm.

Cyclic submersion in water of through cracked concrete specimens/wet & dry cycles
It was reported 20,22,26,69,83 that the self-healing rate in the first days of a healing process is faster with cyclic water immersion and drying periods (typically repeated cycles of 12 h water immersion 12 h air exposure) compared to continuous water immersion. Generally, swelling, continued hydration and calcite precipitation are the only causes of self-healing that apply in these experiments. However, the main mechanism of self-healing remains the precipitation of calcite when tap water in equilibrium with atmosphere is used for healing. Calcite precipitates at the crack opening (compare Section 4.1) whereas the interior mainly shows continuous hydration. 69 According to Maes,22 calcite precipitation at the crack opening is accelerated due to the direct contact of the concrete to atmospheric CO 2 . However, it is not addressed that the solubility of calcite could also be exceeded due to evaporation of water on the specimen's surface and therefore lead to the faster precipitation of calcite in the beginning of the healing process. Interestingly, the absolute extend of self-healing remains controversial. According to Roig-Flores et al., 26,83 cyclically submerged specimens exhibit a lower maximum healed crack width after a healing period of 42 days compared to continuously submerged samples although healing was faster in the first 7 days. Suleiman et al. 20 could not determine any difference after 9 month. Thus, the healing period itself can be addressed as a possible reason for the contradictory results. Especially for the second, diffusion-controlled phase of calcite growth, the constant availability of the transport medium water could be beneficial (compare Section 2.3). Therefore, controlled wet & dry cycles are only of interest to simulate the influence of tidal zones on autogenous self-healing in cracked concrete but not for application as a healing accelerator on construction sites. Moreover, from a practical point of view, it is important that cracks carry water continuously as uncontrolled dry periods can stop the self-healing process (compare Sections 2.1 and 4.4).

Permeation of through cracked concrete
In many concrete structures such as underground garages or water tanks concrete walls hold back water on one side to ensure the functionality of the construction. Thus, separating cracks are permeated when water pressure applies to only one side of the wall ( Figure 6). In such a situation all causes of autogenous self-healing apply simultaneous, since the blocking of flow paths with particles is only possible when specimens are subjected to water flow. Typically, permeation curves exhibit a rapid decrease of the volumetric flow rate in the first ∼48 h of exposure, while at later stages a minimum is asymptotically approached. 10,11,15,51,53 When freshwater in equilibrium with air permeates through a crack, calcite precipitation is the main mechanism of healing and deposits along the whole crack path, whereas the healing effectiveness depends on the initial crack width and the hydraulic gradient. 11 Accordingly, a two-stage model of the kinetics of calcite growth is often concerned (compare Section 2.3). Gruyaert et al. 57 found that increasing the water pressure from 0.05 to 2 bars on cracks that were already healed can cause the cracks to leak again. Reinhardt and Jooss 77 showed that flow reduction is most effective at higher temperatures of the permeating fresh water (up to 80 • C). This can be explained by the decreasing solubility of calcite with increasing temperature and a higher flow velocity due to a decreased viscosity of the water (compare Section 2.3). Thus, the increase of the pH of the permeating water is less pronounced and the calcite growth rate is higher. Furthermore, there is a greater supply of ions due to a higher flow rate. Tsukamoto and Wörner 12 investigated the effect of viscosity of different fluids such as different hydro carbons on autogenous self-healing. In this way the influence of continued hydration and carbonation could be excluded and limited to swelling and blocking of the flow path. Interestingly, the authors found that for liquids with a lower viscosity than water self-healing can only be expected for crack width < 100 μm. Therefore, it can be concluded that the effectiveness of blocking of flow paths is highly dependent on the viscosity of the permeating fluid.
Other permeation experiments were carried out with fresh water of different hardness, 10,11 deionized water, 20,22,29,33,55 and synthetic seawater. 22,24,25 Water hardness was found to have no influence on the extent of self-healing. The use of deionized water causes mainly continued hydration. When synthetic seawater is used the mechanism of the chemical causes of autogenous self-healing change (compare Section 4.5).
In general, two approaches can be differentiated to describe water flow through cracked concrete. First, permeation through a homogeneous and porous medium according to Darcy (compare Section 4.3.1). Second, permeation through a smooth gap according to Hagen-Poiseuille (compare Section 4.3.2). Both are discrete solutions of the partial differential Navier-Stokes equations which describe the motion of viscous fluids and thus can be used to investigate permeation of water through bulk concrete, cracked concrete, and the extend of self-healing of cracked concrete. In most experiments, cracked concrete specimens are permeated from top to bottom or bottom to top by a uniform fluid flow. However, Meichsner and Röhling 15 point out that the assumption of a uniform flow through the crack, continuous reduction of the flow effective cross section through autogenous self-healing and the universal transfer of laboratory results to real structures are a risk in the current design rules. The The following condition of the experimental setup must be met in order to apply Darcy's Law 58,87,88 : (a) the specimen is completely saturated with the permeating fluid, (b) both specimen surfaces are in contact with the permeating fluid, (c) flow is laminar, (d) the fluid is incompressible, and (e) the hydraulic gradient is only consumed for flow through the crack or interior of the sample.
Hydraulic conductivity of cement paste is reported with 10 −15 to 10 −12 [m*s −1 ], 89-91 while Nokken and Hooten 91 state that this range is also valid for mortar and concrete. In contrast, Wang et al. 51 gives conductivity-coefficients for concrete in the range of 10 −12 to 10 −11 [m*s −1 ]. A detailed discussion of the controversy is given by Wu, 92,93 who also reported a more complex distinction of parameters influencing the permeability of cementitious materials. Thus, (a) a reduction of cement paste volume, porosity, increased tortuosity by aggregates reduce the permeability, (b) densification of the cement matrix by incorporation of ground blast furnace slag and limestone powder reduce permeability, (c) the presence of interfacial transition zone between cement stone and aggregates (ITZ), and (d) connectivity of ITZ increases permeability. 68 Furthermore, the influence of aspects (c) and (d) increases rapidly with volume of aggregates. For an aggregate volume > 35% it is reported that the impact of the ITZ exceeds permeability reducing aspects such as the densification or pore reduction. 93 The increase of hydraulic conductivity-coefficients of cement paste, mortar, normal strength concrete (NSC) to high strength concrete (HSC) measured by Aldea et al. 52,76 with associated aggregate volumes of 0%, 50%, 74%, and 77% agrees with these results.
Darcy's law is also applied to fractured rocks or concrete with through cracks. 29,33,[51][52][53]58,76,88 When it comes to flow through cracks the rock or concrete matrix and the crack surfaces are considered impermeable. Thus, as an approximation the fluid flow occurs only through the crack. A comparison of the hydraulic conductivity-coefficients of cracked and uncracked concrete shows that this assumption is correct. For cracked concrete with a crack width of 300 to 400 μm, k f is given in the range of 10 −4 bis 10 −5 [m*s −1 ]. 51,76 A similar argumentation accounts for transport by diffusion and capillary suction. 68 Wang et al. 51 and Aldea et al. 52,53,76 investigated the influence of different crack widths on the hydraulic conductivity k f . According to Wang et al. the influence of cracks is only significant for w ≥ 50 μm with a slightly increased conductivity coefficient of 10 −10 [m*s −1 ] compared to uncracked concrete. However, the author only investigated one concrete specimen per crack width. Furthermore, the crack length l orthogonal to the flow lines was variable and not recorded by measurements. Aldea et al. report that the increase of conductivity-coefficient is only significant for w ≥ 100 μm although a similar test setup was used. As already highlighted by Mengel et al. 68 critical crack widths w c < < 50 μm for water permeation are reported by other authors. 22,[94][95][96] For instance, w c ≈ 10 μm is reported by Louis. 94 Interestingly, the same w c for chloride penetration is reported by Maes. 22 Differences might be due to different experimental setups, hydraulic gradients and measurement techniques of the crack width used by different authors. For instance, crack widths measured with electrical displacement transformers such as linear variable displacement transformers (LVDT) include the crack processing zone in the measurements. This technique consistently overestimates the crack width by 30 to 100 μm compared to optical measurements. 17,97 Another study reports an overestimation by the factor of 2.5. 96 Unless the controversy about w c it can be concluded that for crack widths restricted by Eurocode 1992-3 14 permeability is predominated by the crack.
Beside the crack width w, crack length orthogonal to the flow direction (l) is listed by Wang et al. 51 as an influencing factor on the conductivity coefficient whereas the need for further research was pointed out by the authors as l was variable in the experiments but not systematically measured. Crack length parallel to the flow direction (d), respectively, the sample thickness is reported by Aldea et al. 76 to have little to no influence on k f . That this is not the case is shown in Section 4.3.2 in detail. Additionally, it must be added that both Aldea et al. 76 and Wang et al. 51 investigated only a few samples and the specimen's diameter and thickness was very small Table 1. Generally, it is recognizable that in permeability self-healing studies of the past decade, sample size and dimension stayed small. Thus, results are likely influenced by inhomogeneities along the crack paths ( Figure 6).

Permeation according to Hagen-Poiseuille
The As previously mentioned, studies following the Darcy approach showed a dependence of the permeability on the crack width w. The rapid increase of hydraulic conductivity coefficients with w can be assigned to the fact that the volumetric flow rate Q is proportional to the third power of w which was confirmed among others by Edvardsen. 11 The influence of However, in practice the three-dimensional crack width, tortuosity and roughness show a significant scattering. Experiments with the same experimental design parameters and similar measured surface crack widths can result in totally different values. Therefore, different approaches and ranges of values can be found in the literature (Table 4). Constant values in the range of 0.125 to 0.25 are proposed by Edvardsen, 11 Meichsner 10 and Clear. 9 Tsukamoto and Wörner 12 and Ripphausen et al. 13 suggest a variable correction factor depending on the gradation curve and crack width. Louis 94 introduced a correction factor depending on the relative roughness K/D h . With K the absolute roughness and D h the hydraulic diameter that is equal to two times w. Lately another approach was issued by Akhavan et al. 96 building on Louis 94 results. The authors propound to include a tortuosity factor T determined by the mean height of crack surface asperities and the effective length of the crack. The authors found in the range of 0.163 to 0.229 which is in accordance with Edvardsens 11 results.
However, it must be noted that the experiments of Akhavan et al. 96 were carried out on mortar samples with a diameter of 89 mm and a thickness of only 25 mm. Thus, this approach needs to be verified on thicker concrete specimens. Yet, for real concrete structures it is impossible. However, it is proof for the widely accepted influence of crack geometry, roughness and tortuosity on permeability of cracked cement-based materials. Compare Section 4.3.4 for a detailed discussion of the influencing factors on crack geometry, roughness and tortuosity.

4.3.3
Characteristics of flow through cracked concrete For Re < 2300 flow is laminar. For 2300 < Re < 3000 a transmission zone is stated, whereas for Re > 3500 flow is purely turbulent. 58,85,98 To distinguish between parallel and nonparallel flow the relative roughness K/D h must be considered (compare Section 4.3.2). According to Lomize 11,99 flow is parallel for K/D h <0.032, whereas above this value nonparallel flow is present which still can be laminar. Concerning Louis's equation (Table 4) and applying ≈ 0.25 as suggested by Edvardsen 11 a relative roughness of ≥0.48 can be calculated for through cracks in concrete. Thus, fluid flow through cracked concrete in general is nonparallel. Furthermore, transition from laminar to turbulent flow regimes occurs at lower Re values with increasing relative roughness. 85 For K/D h ≈ 0.5 a critical Re of 450 can be calculated according to Rissler. 85,100 To approximate the transition of the flow regime as a function of the critical hydraulic gradient I c [without unit], crack width w [m], and kinematic viscosity [m 2 *s −1 ] of the fluid and acceleration due to gravity g [m*s −2 ], the following equations for nonparallel and parallel flow are given by Wittke 85 (Table 5).
Applied to crack widths according to the restrictions of Eurocode 1992-3 14 it can be seen that the transition from laminar to turbulent flow occurs at rather high hydraulic gradients. For a common structural thickness of 400 mm this results in a critical pressure of ∼1.6 bars for 300 μm, ∼ 5.5 bars for 200 μm, and ∼ 44.2 bars for 100 μm cracks (calculated TA B L E 5 Calculation of the critical hydraulic gradient for the transmission from laminar to turbulent for parallel and nonparallel flow 85

Flow condition Critical Hydraulic Gradient I c [−]
Nonparallel-K/D h ≥0.032 I c = 11000 * v 2 g * w 3 Parallel-K/D h <0.032 with a kinematic viscosity of 1.002*10 −6 [m 2 *s −1 ] at 20 • C). These pressures should not be exceeded in experiments and are unlikely to be reached in realistic construction environments. 11,94 Furthermore, for w > 300 μm and Re > 100 Shin et al. 58 propose the calculation of the true water head accounting for head losses due to the experimental set up. Above the critical Re and w a variation of up to 40% of the applied water head was determined due to the energy losses caused by the change of flow lines in the experimental setup. Accordingly, permeation results of specimens with w max > 300 μm obtained with different test-setups are not comparable regardless of the composition and crack geometry. Therefore, the limitation to crack widths ≤300 μm can be formulated as a design criterion for future experiments.

4.3.4
Crack geometry, roughness, and tortuosity of through cracks in concrete In the previous sections it was shown that fluid transport through concrete with a separating crack is mainly characterized by the crack itself. The precise crack geometry, roughness, and tortuosity restrict the volumetric flow rate and are often summarized in the correction factor following the Hagen-Poiseuille approach. However, these flow reducing parameters scatter severely even when the same experimental design was used. 11 Furthermore, crack geometry, roughness, and tortuosity are influenced by variables of concrete mixtures and design criteria. For instance, crack geometry can be strongly influenced by the aggregate size due to grains that partly stand out of the crack surfaces. This effect can locally reduce the crack width and provide bottlenecks for the blocking of the flow path and nucleation of calcite. 10,12 At the same time the flow path becomes more tortuous, respectively, the effective crack length l effctive increases 12,13,96 ( Figure 6). On the other hand, it was reported that higher W/C ratios reduce tortuosity. 62 Therefore, it is difficult to compare experimental results when aggregate size, gradation curve and/or W/C ratio are different and superimpose on the generally high scattering of permeability tests. In real concrete structures the reinforcement plays another important role. It was shown by several studies that crack width decreases at the bars 101-103 whereas the crack width at the surface is generally wider but dependent on the concrete cover. 103,104 Accordingly, Akhavan et al. 96 reported for mortar samples without reinforcement that the surface crack width is 13% greater than the interior crack width. However, the latter authors investigated only one cross section of the crack per sample and results must be verified on concrete specimens. In general, it is difficult to find reliable data of the crack width in the interior of concrete specimens as a function of composition. Moreover, there is a lack of a calculation method that allows to estimate the crack geometry as already stated by Mengel et al. 68 Thus, concerning the transmission of laboratory results to real structures, concrete composition (cement type, aggregates, W/C ratio, etc.), 10,12,13,62 degree, and assemblage of reinforcement and concrete cover 13,102-104 need to be considered and carefully documented. As a matter of fact, most studies on autogenous self-healing did not investigate the crack width in the interior of the samples but only considered surface crack width. This is due to the problem that crack width measurements in the interior are destructive. A solution could be provided by the application of x-ray μ-CT which was already used in some studies. 41,105,106 This technique will be discussed in detail (compare Section 5.3). For a more detailed description of the influencing factors on crack geometry, roughness and tortuosity reference is set to Mengel et al. 68

Exposure to humidity
Roig-Flores et al. 26 exposed concrete samples to different degrees of relative humidity (RH). Specimens subjected to 95% RH showed a decrease of w by 8% whereas at 40% RH w increased by up to 46%. In both cases neither continued hydration nor calcite precipitation was proven. Respectively, at high RH swelling of the concrete occurred whereas the samples shrunk due to drying at low RH (compare Section 2.1). Other studies confirm that continued hydration and calcite precipitation do not occur in humid environments. 19,20,39,69,83 However, it must be addressed that concrete incorporating super-adsorbent polymers (SAP) shows the ability of continued hydration and calcite precipitation in humid environments. A detailed discussion is out of the scope of this study. Reference is set to Snoeck et al. 55,69 and Gruyaert et al. 57

Exposure to seawater
Some studies 22,24,25,80 investigated the influence of seawater on autogenous self-healing. Especially in marine environments crack healing is of great importance, since cracks >10 μm can lead to an increased chloride ingress and thus an accelerated deterioration of the reinforcement. 22,107 Moreover, permeating seawater can impair the functionality of tunnel elements or other concrete structures that must be watertight. The most abundant ions in seawater are Cl − , Na + , SO 4 2− , Mg 2+ , Ca 2+ , K + , and HCO 3 − in a descending order whereas the concentration of HCO 3 − is roughly the same for seawater and groundwater in equilibrium with the atmosphere. Mg 2+ shows up to 880 times higher concentrations in seawater than in tap water. 108,109 Therefore, it is not surprising that different chemical causes of autogenous self-healing apply than in freshwater environments. Experimental studies 22,24,25 show that brucite (Mg(OH) 2 ) veined with gypsum (CaSO 4 *2H 2 O), hydrophilite (CaCl 2 ), and ettringite forms directly on the sample surface next to the crack opening when cracked mortar specimens are immersed in artificial seawater for healing. Mg-ions in the water quickly react with hydroxide ions leaching from portlandite and precipitate in form of brucite due to its low solubility. Precipitation of accessory phases such as hydrophilite, gypsum and ettringite is related to the presence of sulfates and sodium chloride in the water. However, the formation of these minerals showed no effect on the rate of self-healing. 22 On top of the brucite layer aragonite deposits which is thermodynamically stabilized by the presence of Mg-ions. 50,[110][111][112][113] Respectively, the presence of a high Mg 2+ concentration changes the autogenous self-healing mechanism to the above-mentioned sequence. In contrast, Danner et al. 80 found calcite on top of the brucite layer when he investigated concrete beams that were exposed to a marine tidal environment in a Norwegian fjord for 25 years. Thus, the extensive timespan, a cyclic exposure to the atmosphere or other factors imposed by the realistic marine environment may lead to a structural change of aragonite to calcite.
As of today, the influence of different cement types on the extent of autogenous self-healing in marine water is controversial. Palin et al. 24 found that autogenous self-healing of CEM I mortar specimens in artificial seawater is more effective than in fresh water. Accordingly, cracks up to 600 μm could be healed in seawater and up to 150 μm in freshwater. Interestingly, mortar samples based on CEM III showed an inverse behavior. Crack widths up to 400 μm could be healed in freshwater and up to 100 μm in seawater. This effect was assigned to the lower content of portlandite and lower porosity of CEM III samples and a blocking effect of the brucite layer that might inhibits further leaching of Ca-ions. However, the study lacks chemical prove according to the blocking effect of brucite with respect to the Ca 2+ diffusion. In contrast, Danner et al. 80 found no difference in the extend of self-healing for different concrete compositions and report the maximum healed crack width with 200 μm. Concerning the experimental setup it must further be addressed that most experiments were carried out on mortar specimens that were immersed in artificial seawater for self-healing. Accordingly, most healing was observed at the crack opening (compare Section 4.1, Figure 6) and no mechanical blocking could apply. Only Palin et al. 25 tested the watertightness in a permeation experiment. However, the mortar samples were submerged in artificial seawater for 28 and 56 days to initiate self-healing and only subjected to a permeability test of 30 min. Thus, the results need to be verified on continuous permeability experiments of cracked concrete. As of today, the scientific knowledge of self-healing of cracked concrete in marine environments is not satisfactory to quantify explicit boundary conditions and transfer results to real concrete structures.

Conclusion of the causes and limitations of autogenous self-healing
In general, autogenous self-healing is based on the reaction of water and concrete in the restricted space of a separating crack of a certain width. Water, concrete, and crack geometry are influenced by various variables that could affect the efficiency of autogenous self-healing. These variables were discussed in the Sections 2, 3, and 4 and are summarized in Table 6 for the sake of clarity.

ASSESSMENT OF THE EFFICIENCY OF AUTOGENOUS SELF-HEALING
The extent of autogenous self-healing can be assessed by different approaches such as for instance permeation experiments, 10,11,54,77 surface crack width measurements, 22,41,56,80 crack width measurements along a cross section, 96,101 regain of strength measurements, 29,39,69,114 and propagation of ultra-sonic signals. 21,33,114,115 These methods will be discussed in the following sections.

Recovery of watertightness
Permeability experiments allow an indirect assessment of the efficiency of autogenous-self-healing by measuring the volumetric flow rate at certain time Q t and relating it to the initial volumetric flow rate Q 0 (Equation 7). To determine Q 0 the sample should be water saturated prior to the experiment and time should be given until the flow stabilizes. Accordingly, Edvardsen 11 used the average volumetric flow rate of the first 5 min as Q 0 . Generally, experimental setups can be subdivided into two groups 79 : (1) experiments with a constant water head and (2) with a falling water head. Both methods can be used to evaluate self-healing when the test setup is designed according to the theoretical conditions of either Darcy or Poiseuille (compare Section 4.3). As previously discussed, autogenous self-healing can also be initiated by water immersion of concrete samples (compare Section 4.1). The samples can then be subjected to a permeability test after defined healing periods. Another approach is to initiate healing by the water flow itself inside the permeability test-setup. With the latter a continuous permeation curve can be obtained, and more importantly mechanical blocking and washing out of healing products applies during the whole experiment (compare Section 2). The extent of healing S(Q) [%] can be expressed by the quotient of the volumetric flow rate at time t Q t divided by the initial volumetric flow rate Q 0 (Equation 7).
Thus, for a completely healed crack, Q t is equal to 0. Respectively, S t (Q) is equal to 100% after a healing period of the length t. However, specimens with a similar crack width can show a severe scatter of the volumetric flow rate due to variable crack geometries. 11,59 Therefore, it is crucial to assign Q 0 and Q t to a specific sample and not to a generalized mean TA B L E 7 Overview of the arguments concerning permeability experiments as an evaluation method of the efficiency of autogenous self-healing

Recovery of watertightness
Permeability test • Realistic self-healing environment for water retaining concrete structures.
• Determination of the watertightness.
• Combined healing and monitoring of the extent of self-healing.
• No mineralogical and chemical information of the healing products.
• Measuring the permeated water volume indirectly through weight measurements might be the most practicable way. However, it must be addressed that washed out particles can cause a significant error. Therefore, the volumetric flow rate should also be determined by water level measurements or flow meters. The main advantage of permeation experiments is the water flow itself, which is a crucial factor in water retaining concrete structures. It is also the only method that allows an assessment of the regain of watertightness after a healing period which is an important measure for useability and durability. However, it is not possible to assess the extent and locality of internal healing directly without deterioration of the sample. Thus, water might still be able to reach the rebar and cause corrosion, although a crack exhibits no more water flow. Therefore, permeation experiments should be combined with chemical and mineralogical investigation, for example, of cross sections of the healed crack or the crack surfaces. The pros and cons of this method are summarized in Table 7.

Surface crack healing
Measurements of the crack closing rate at the surface of a specimen are usually done by either digital or optical (such as polarized-, reflected light-, stereo-microscopy) light microscopic methods but can also be carried out by photography or electron microscopy. 41,56,83 The pros and cons of these methods are summarized in Table 8. All approaches have in common that to evaluate crack closing the crack width is determined just before and after a healing period. The extent of healing is then given by the absolute value of the average crack width after the healing period or expressed as the percentage with respect to the initial width. Alternatively, the crack area A or the pixels of the crack can be determined with image analysis. Generally, it is crucial that the crack width is kept constant during the experiment and the measurements are conducted at the same location. Respectively, setups that use retainers must monitor the relaxation time and the extent of elastic creep before starting any experiment (compare Section 3.2). For a regularly monitoring of the healing rate the specimens must be taken out of the healing environment. This can be a source of error in the obtained results. In the literature typically 1, 3, 7, 14, 28 days are used to monitor changes of the self-healing rate in terms of average surface crack width changes. 115 However, surface crack width measurements by nature lack 3D information of the crack closing and as a matter of fact visually healed specimens are not necessarily watertight. 57 Respectively, Roig-Flores et al. 26 showed that permeability experiments are the most reliable healing indicators, while crack width measurements show rather good accuracy. Crack area and pixel analysis can show high dispersion. Additionally, polarized, reflected light and electron microscopy can be applied to determine the healing products and the extent of healing. 116 Electron microscopy can TA B L E 8 Overview of the advantages and disadvantages concerning measurements of the surface crack healing as an evaluation method of the efficiency of autogenous self-healing • Spatial information of the crack healing.
• No sample preparation.
• Can easily be conducted on construction site.
• No mineralogical and chemical information of the healing products.
• No information about the watertightness.
• Experiments must be interrupted to determine self-healing rates. Photography* • See digital microscopy.
• Documentation of large areas.
• See digital microscopy.
Polarized and reflected light microscopy* • Direct determination of the crack width in terms of image analysis.
• Spatial information of the crack healing.
• No chemical information.
• Need of destructive sampling and preparation.
• No information about the watertightness. Stereo-microscopy* • See digital microscopy.
• See digital microscopy.
Electron microscopy* • Direct determination of the crack width in terms of image analysis.
• Spatial information of the crack healing.
• Need of destructive sampling and preparation.
• No information about the watertightness.
• Evaporation of OH-Groups from hydrates due to vacuum and high energy electron beam.
provide chemical information by point measurements, profiles or by mapping entire areas. Typically, energy dispersive x-ray spectroscopy (EDX) or wavelength dispersive x-ray spectroscopy (WDX) allow a chemical characterization, whereas WDX systems have a higher accuracy. With the back scattered electron (BSE) mode heavy atoms can be distinguished from light atoms by the signal intensity as the back scattering effect depends on the atomic number. The secondary electron (SE) mode allows a detailed view on the surface structure and can be particularly useful to investigate crystal shapes and so forth. Transmission electron microscopes (TEM) further provide the possibility to investigate the crystal structure by electron diffraction, which is similar to x-ray diffraction (XRD). However, TEM measurements require thin sections of a few nanometers thickness. In general, electron microscopic methods measurements are time-consuming and need a destructive sample preparation such as prepared thin sections, a polished surface and/or a gold or carbon sputtering to allow for conductivity. Moreover, special precautions must be taken to avoid hydroxides present in concrete and healing products from evaporation in the low vacuum of the investigation chamber and due to the high energy of the electron beam. Therefore, low vacuum techniques such as the environmental scanning electron microscopy (ESEM) are typically used. Concluding, electron microscopical methods provide a powerful tool to investigate the chemical mechanisms and causes of autogenous self-healing within the aforementioned limitations. In contrast, digital-, and stereo-microscopy as well as photography can be carried out without extensive preparation and precautions. Moreover, it is possible to scan large areas of the sample surface in the lab as well as on site, while crack width is determined in terms of image analysis. As of today, accurate digital hand microscopes are available that are propound for application on construction site and were also applied in a study by Roig-Flores et al. 83 As a concluding remark it must be addressed that to obtain a complete picture of the autogenous self-healing efficiency a combination of methods is recommendable. A comprehensive overview of different methods that can be applied for surface crack width measurement is given by Ferrara et al. 117

Internal crack healing
Most measurements of the extent of internal crack healing are destructive as the sample must be cut or the crack surfaces broken apart to allow an investigation. Therefore, changes of the crack geometry and destruction of a healed intersection might occur. Furthermore, the sample cannot be used for further experiments. As of today, the qualitative assessment of internal crack healing on site is only possible by taking cores (see ultrasound section for a possible future outlook). Measurements are usually done by the same methods applied for surface crack width measurements with the aforementioned pros and cons (compare Section 5.2). A nondestructive way to assess the extent of autogenous self-healing is given by neutron and x-ray radiography and/or tomography (Table 9). See Snoeck et al. 115 for a comprehensive overview. Neutron and x-ray radiographic methods were recently applied to investigate the efficiency of intrinsic or engineered healing approaches of cementitious materials. 41,55,56,79,105,106,118 Neutrons interact with the nucleus of the probed matter and are scattered depending on the atomic number of the elements. The scattering probability is higher for nuclei with low atomic numbers such as hydrogen. Therefore, neutron imaging techniques are a perfectly suited tool to assess the water distribution, uptake or permeation in the interior of a sample, while the cement stone and aggregates are almost unaffected by this type of radiation. However, neutron capture can lead to the formation of unstable isotopes that decay and emit radiation. Therefore, specimens subjected to neutron radiation must be checked for radioactivity before further experiments or investigations are carried out. In contrast, x-rays mainly interact with the electrons of an atom, while the attenuation of the radiation increases with increasing atomic number. Concerning the Bouguer-Lambert-Beer equation the attenuation depends on the thickness of the material, the initial intensity of the radiation source and the absorption coefficient of the probed material. 119 Thus, voids, pores, and cracks can easily be distinguished from the cement stone and aggregates due to the low absorption coefficient of air. However, the high absorption coefficient of steel, respectively, of rebars is problematic as it shields the radiation. Increasing the intensity would lead to an overexposure of the cement stone, aggregates and crack. Therefore, plain concrete specimens should be used in x-ray radiographic investigations. Comparing the attenuation characteristics of neutrons and x-rays it is important to remark that the attenuation coefficients differ due to the different interaction of the radiation with matter. Both have in common that to obtain a 3D model of a specimen through computed tomography (CT), it must be rotated by 360 • around a vertical axis during the measurement. The samples should be round in order to avoid edge artifacts. 106 From the different angles cross sections are reconstructed and combined to a 3D model by computational methods. 106 Modern software then allows to extract the crack from the model, calculate the volume or the average width of the crack. However, mayor disadvantages are the high costs of laboratory CTs, long exposure times, the lack of direct mineralogical and chemical information and the restriction to small sample sizes in order to achieve a sufficient resolution for self-healing analysis concerning cracks in the range of 100 to 300 μm. Most common laboratory CTs use divergent radiation beams with the consequence that the resolution decreases with increasing sample size, respectively, distance from the radiation source. Therefore, samples are normally only a few cm in height and diameter. An approximation of the resolution of commonly available laboratory x-ray CTs is given by Akhavan et al. 96 with 1/1000 of the sample dimension. Accordingly, the resolution of a 400 mm thick sample is 0.4 mm, which is huge with respect to the crack sizes of interest. However, one solution to the problem could be to fill a crack with epoxy for fixation and then take a core of an area of interest from the sample, which can further be cut to pieces of a few cm in height. Thus, self-healing could take place in samples with realistic dimensions and then be investigated bit by bit through high resolution CT. Finally, it must again be addressed that to obtain a whole picture of the extent of internal self-healing and the corresponding phases and applying chemical processes different methods must be combined.
Ultrasonic testing provides a further nondestructive possibility to obtain information about the extent of internal autogenous self-healing without subjecting small specimens to a time consuming and expensive CT scan (Table 9). Moreover, ultrasound methods are suitable for application on site, generally fast and easy to conduct and can also be applied in a continuous way to monitor changes of the crack interior during self-healing experiments. Commonly applied are impulse based and echo-based techniques. With the latter typically the thickness of concrete components, concrete cover, rebar position and so forth are determined. Impulse ultrasound techniques such as ultrasonic pulse velocity (UPV), surface transmission, diffuse ultrasound, and coda wave interferometry (CWI) are suitable to verify the extent of self-healing or TA B L E 9 Overview of the advantages and disadvantages concerning measurements of the internal crack healing as an evaluation method of the efficiency of autogenous self-healing

Self-healing characteristics Methods Advantages Disadvantages
Internal crack healing compare Table 8 • Compare Table 8 • Practicability.
• Can be applied on construction site.
• No chemical and mineralogical information of healing products.
• No information about the causes of self-healing.
• No information about the exact crack width reduction.
• No information about the watertightness.
• Sensitive to the measurement conditions but lack of standardized testing.
the determination of crack depth. 115 In the following focus is laid on UPV. Ultrasound waves are mechanical waves typically in the frequency range of 20 kHz to 10 MHz that are scattered, reflected and partially transmitted at the crack walls of a specimen under investigation. With change of the crack, for example, in depth, width, or length the transmitted signal of the elastic wave changes. However, it is important that the crack lays between the transducers in order to record any changes of the signal. For UPV the sensors typically are placed in a straight line on one side or on opposite sides of the sample with the crack laying in-between. At point A the signal is generated and transmitted through the sample. At point B a transducer records the arrival of the wave. Thus, the arrival time, amplitude and attenuation of the waveform in time domain can be recorded. Fast Fourier transformation (FFT) of the time domain allows the transformation to the frequency domain, which can also be useful. 115 Generally, the velocity of ultrasound waves in concrete is approx. 3500 m*s −1 and decreases to approx. 343 m*s −1 when the wave travels through air, respectively, through a crack. 21 Therefore, the pulse velocity decreases as the ultra-sonic signal crosses a crack. As healing takes place the UPV increases again, while the extent of healing correlates with the regain of pulse velocity. 21,33,120,121 However, Experiments of Yuan et al. 21 among others revealed that the initial UPV is not completely restored after a healing experiment which is due to an incomplete and discontinuous closure of the crack with healing products. To quantify the extent of self-healing with respect to the UPV the healing rate S(UPV) [%] (Equation 8) was defined by the latter authors. It includes the UPV V 1 of the cured and uncracked sample, the UPV V 2 of the cracked, and the UPV V 3 of the healed sample. A similar approach was proposed by Tomczak et al. 120 It is important to address that ultra-sonic velocity variation in concrete can have various reasons such as pores, cracks, crack geometry, and size as well as composition, temperature, humidity, and curing conditions. 115,120,122 Therefore, the exact UPV signal is specimen specific and should be measured before crack initiation to allow an assessment of the extent of self-healing. This might be an obstacle for applying the method on construction sites. Moreover, the testing conditions such as the used sensors, cables, sensor position and so forth impact the obtained data and should be held constant during a test series. It is also crucial to keep the wavelength of the ultrasound wave bigger than the diameter of the coarsest aggregates to avoid scattering and dissipation of the signal, which is achieved through frequency adjustment. 115 Unfortunately, as of today there is no standardization of the UPV method which makes it difficult to compare data of different publications. Similarly, to the aforementioned UPV measurements waveform and frequency analysis can be applied. 21 The ultrasound signal recorded at point B shows a rapid increase of the amplitude a few μs after a wave impulse is emitted at point A. Then the signal oscillates around the passive state and is attenuated over time by energy conversion. For cracked samples the amplitude is much smaller, while self-healing leads to a restoration of the amplitude. Applying FFT the ultra-sonic signal over time can be transformed to a frequency domain. For uncracked samples the FFT signal shows the highest peak at the excitation frequency of the ultra-sonic source. For cracked specimens the amplitude decreases, and the signal exhibits a shape that is comparable to a noise signal. However, as self-healing takes place the excitation frequency becomes visible in the signal again, while the amplitude correlates with the extent of healing. For both waveform and frequency analysis a self-healing ratio can be formulated as done for the UPV by using the maximum amplitude of the signal or the maximum amplitude of the excitation frequency. All ultra-sonic methods have in common that the extent of self-healing is approximated by restoration of the original signal. However, it is not possible to evaluate the watertightness, the chemical and mineralogical composition of self-healing products or the exact crack width closing the internal healing. Therefore, a combination of methods should be applied. A comprehensive overview of ultrasound testing is given by Snoeck et al. 115 Finally, it must again be addressed that to obtain a whole picture of the efficiency of autogenous self-healing, the corresponding phases, and applying chemical processes different analytical methods must be combined.

Regain of strength
Regain of strength measurements aim at an indirect assessment of the extent of autogenous self-healing after a specimen was subjected to a healing period. The idea is that strength is reduced due to cracking and restored with healing, whereas the extent of healing is supposed to correlate with the extent of healing or crack closure. However, measurements were found to be independent from calcite precipitation and mainly influenced by the formation of CSH phases. 35,36,39,114 Results of Suleiman et al. 123 agree with these findings and show that the regain of strength is most pronounced for samples incorporating fly ash due to the ongoing pozzolanic reaction. A similar behavior of latent hydraulic cements is expected by the latter authors. In addition, cracked concrete specimens that heal under seawater exposure can show a further decrease in strength due to the cation exchange of Ca 2+ with Mg 2+ in CSH phases and the formation of magnesium-silicate-hydrate (MSH). 24,25,124 Thus, regain of strength measurements depend on the healing conditions, the cement type and might only be applicable for microcracks or compressed cracks healed by continued hydration (compare Section 2.2). Further disadvantages lay in the lack of mineralogical and chemical information as well as the locality of crack healing and the complete deterioration of the sample. It can be concluded that regain of strength measurements are not applicable for evaluating autogenous self-healing of through cracked concrete restricted by Eurocode 1992-3. 14 The pros and cons of this method are summarized in Table 10.
TA B L E 10 Overview of the advantages and disadvantages concerning regain of strength measurements as an evaluation method of the efficiency of autogenous self-healing

Self-healing characteristics Methods Advantages Disadvantages
Regain of strength Compression /bending /and so forth.
• Information about the mechanical properties of healed samples.
• Destructive. • Depends on the composition and healing conditions.
• No chemical or mineralogical information.
• No information about the watertightness.
• Self-healing rates cannot be determined.

Mineralogical and chemical assessment of autogenous self-healing
Many studies lack comprehensive chemical and mineralogical investigations. Sometimes it can even be observed that certain healing causes are assumed without showing mineralogical or chemical evidence. However, it is desirable that healing phases are qualitatively determined and quantified concerning a comprehensive understanding of the autogenous self-healing process and applying mechanisms. Only then the impact of variables such as the water or concrete composition can be clarified in detail. Generally, raw materials and unaffected reference concrete specimens should be investigated as well as samples subjected to a healing period to allow for a comparison of microstructural and chemical changes. 79 Commonly applied investigation methods are among others microscopy, XRD, electron microscopy, RAMAN spectrometry, Fourier-transform infrared spectroscopy (FTIR), TG/DTA. A detailed discussion of the methods is out of the scope of this study. Reference is set to Ferrara et al. 79 and Snoeck et al. 115

CONCLUSION
Based on the findings of this study, the following conclusions can be drawn: 1. A lot of research has been carried out on autogenous self-healing of cracked concrete in the last decades. The influence of crack width, roughness, and tortuosity, the presence of liquid water, water pressure, water chemistry, and temperature, as well as the aggregate size, gradation curve, W/C ratio and cement content are examples of well-established influencing factors on the healing efficiency of cracked concrete. Calcite precipitation has been identified as the main cause of autogenous self-healing in freshwater environments under atmospheric conditions that could seal cracks up to 200 μm in width. 2. Studies on the influence of the cement type or Ca 2+ availability on the healing efficiency come to contradictory results.
Some studies reported that the amount of portlandite and CSH affects the amount of CaCO 3 formed during the experiments and hence the healing efficiency, while other studies reported no effect. This indicates a need for further research regarding the diffusion of relevant ions from the concrete into the permeating water and the precipitation reactions at the crack-water interface as a function of composition and time. Reliable diffusion data could lead to a comprehensive chemical and transport-based modeling of autogenous self-healing, for example, with the PHREEQC modeling tool. In addition, a fingerprint of the change in water chemistry during specific phases of the autogenous self-healing process could be generated. 3. Seawater has been identified to impact the chemical causes and the healing efficiency of autogenous self-healing.
Typically, brucite precipitates first and is overlayed by aragonite. However, the extend of healing and the influence of the cement type remains controversial and should be investigated in future studies. Instead of using synthetic seawater, experiments with real seawater are desirable. 4. The lack of standardized testing makes it difficult to compare literature data. Improvements are proposed at several points within this study. For instance, special care should be taken to conserve the crack geometry when permeability experiments are planned.