You are presented with multiple paper abstracts, alongside the associated literature review and chapter titles. Given the provided information, you are going to do a literature review. Please generate a coherent literature review that synthesizes the content, draws connections between different works, highlights major findings, and identifies any gaps in the existing research.

Literature Review Title: Experimental characterization of the self-healing capacity of cement based materials: an overview 
Chapter Title:  Definition of Healing-Related Indices of Performance Recovery 
1. Abstract of Cited Paper (BIB001):  Abstract The aim of this study is analyzing the self-healing effect of a crystalline admixture in four types of environmental exposure comparing with a reference concrete. Healing was studied by means of permeability tests on cracked specimens and physical closing of the crack was observed by optic microscope and quantified through crack geometrical parameters. The studied crack openings were under 300 μm and the time set for healing was 42 days. The results show a different healing behavior depending on the exposure and the presence of the crystalline admixture, demonstrating that the presence of water is necessary for the healing reactions. 
2. Abstract of Cited Paper (BIB002):  Superabsorbent polymers (SAPs) have potential to be used as healing agent in self-healing concrete due to their property to attract moisture from the environment and their capacity to promote autogenous healing. A possible drawback, however, is their uptake of mixing water during concrete manufacturing, resulting in an increased volume of macro-pores in the hardened concrete. To limit this drawback, newly developed SAPs with a high swelling and pH-sensitiveness were developed and tested within the FP7 project HEALCON. Evaluation of their self-sealing performance occurred through a water permeability test via water flow, a test method also developed within HEALCON. Three different sizes of the newly developed SAP were compared with a commercial SAP. Swelling tests in cement filtrate solution indicated that the commercial and in-house synthesized SAPs performed quite similar, but the difference between the swelling capacity at pH 9 and pH 13 is more pronounced for the self-synthesized SAPs. Moreover, in comparison to the commercial SAPs, less macro-pores are formed in the cement matrix of mixes with self-synthesized SAPs and the effect on the mechanical properties is lower, but not negligible, when using high amounts of SAPs. Although the immediate sealing effect of cracks in mortar was the highest for the commercial SAPs, the in-house made SAPs with a particle size between 400 and 600 μm performed the best with regard to crack closure (mainly CaCO3 precipitation) and self-sealing efficiency, after exposing the specimens to 28 wet–dry cycles. Some specimens could even withstand a water pressure of 2 bar. 
3. Abstract of Cited Paper (BIB003):  Abstract This paper analyzes the self-healing properties of early-age concretes, engineered using a crystalline admixture (4% by the weight of cement), by measuring the permeability of cracked specimens and their crack width. Two concrete classes (C30/37 and C45/55) and three healing exposure conditions have been investigated: water immersion at 15 °C, at 30 °C and wet/dry cycles. Specimens were pre-cracked at 2 days, to values of crack width in the range of 0.10–0.40 mm. The results show almost perfect healing capability for specimens healed under water at 30 °C, better than for specimens healed under water at 15 °C, while insufficient for the wet/dry exposure.

Literature Review:
Results garnered through the experimental methodologies summarized in the previous section need then to be "synthesized" into some kind of healing-related indices of performance recovery in order to, e.g., comparatively assess the efficiency of different healing techniques but with the aim of incorporating healing concept and beneficial outcomes into "to be formulated" design approaches. At a first instance, the quantification of crack-sealing through optical microscopy and image processing can lead to the definition of an Index of Crack Sealing (ICS), defined as: which will obviously depend on the multifold set of variables affecting and governing the healing mechanisms, and where w denotes the crack width, as measured at the different stages of the experimental evaluation procedure. Commonly to all the other indices which will be hereafter reviewed, its values range between 0 (no-healing; wpost-healing = wpre-cracking) and 1 (complete healing; wpost-healing = 0). It is worth here remarking that this index will only account for the closure visible at the surface of the crack, whereas internal reconstruction of the through crack material continuity, which will govern as well the recovery of the material performance can only be assessed by means of methods such as X-ray or neutron radiography and tomography, microcomputer-tomography scan and electrical methods  . These methods, though employed in a number of healing related studies, have hardly led so far to any quantification of crack sealing through index such as in Equation (1). In the evaluation of self-healing by means of permeability tests, two main options have been proposed for the definition of an Index of Self-Healing (ISH). Equation (2), proposed in HealCON project BIB003 , uses data from companion unhealed specimen as reference, while equation 3, proposed by Roig-Flores et al. BIB002 BIB004 uses the same specimen and compares the water flow through it before and after healing: ISHpermeability,2 = where Wunhealed,t is the amount of water passing through the specimen's unhealed crack at time t, Whealed,t is the amount of water passing through the specimen's healed crack at time t, Winitial is the amount of water passing through the target specimen before healing and Wfinal, after healing. Gruyaert et al. BIB003 provided extensive explanation on the use of the aforementioned equations in the case of healing engineered through the use of superabsorbent polymers. Similarly, the following expression has been proposed to calculate a healing index from sorptivity tests: where Sunhealed, Shealed and Suncracked are the sorptivity indices for the cracked and unhealed specimen, for the cracked and healed specimen and for the uncracked reference specimen respectively. The definition of healing indices representative of the recovery of mechanical properties requires comparing the pre-cracking response of the material with the post-healing one, as measured on the same specimen, e.g., in terms of nominal stress vs. crack opening. An Index of Strength Recovery (ISR) can be defined, with reference to notation shown in Figure  1 , as: which fits for plain concrete, ordinary FRC and strain softening HPFRCC, whereas for strain/deflection hardening HPFRCC, if pre-cracked in the pre-peak regime, different expressions have to be considered, in order to distinguish the effects of healing from the pre-peak hardening inborn in the material response. Indices of ductility recovery have also been proposed   .  Ferrara et al.   have compared the strength and damage recovery, as from Equations (5) and BIB004 to the index of crack sealing, as from Equation (1). They observed that a "surface crack sealing" of at least 60% is necessary before a significant mechanical healing can be observed. As a K reloading, post-conditioning K unloading, pre-cracking K loading, pre-cracking matter of fact, a higher surface crack sealing, which is reflected in the Index of Crack Sealing, likely corresponds to a more complete internal crack sealing, thus justifying the results. Comparing the pre-cracking and post-conditioning nominal bending stress vs. crack opening displacement (COD) curves a method to indirectly estimate the crack sealing was proposed BIB001 . It consists in operating a "backward" shifting along the COD axis, of the stress-COD post-conditioning curve, until the curve measured in the pre-cracking test on the virgin undamaged sample is met. The new value of the "origin" COD can be estimated by drawing, from the aforementioned point on the pre-cracking curve, an unloading branch parallel to the last unloading previously measured on the virgin sample itself (Figure 2) . Moreover, by performing, during the pre-cracking and postconditioning tests, repeated loading-unloading cycles (Figure 1b) , the evolution of damage (stiffness decay) as a function of the crack opening could be estimated, and damage vs. crack opening curves could be built. By identifying the points representative of damage-COD state in the post-conditioning test and operating a "backward shifting" along the COD axis until the fitted damage-COD evolution curve of the virgin specimen is met, the amount of this backward shifting can be assumed as an indicator of the crack closure effect produced by the self-healing phenomena (Figure 2 ).