## 1 Introduction
Laboratory investigations of three types of stress-absorption layer have been carried out by fatigue experiments. The results showed that the fatigue property of the rubber asphalt stress absorption layer (RASAL) was the best, and the service life of the pavement could be improved significantly by the material; however, the crack resistance of the stress-absorption layer is not very clear [22]. The abovementioned research shows that the stress absorption-layer is good at crack resistance. However, the analyses of the effects of the stress-absorption layer on the crack propagation process and the propagation trend of different crack types were not enough. It is important to study the influence of anti-crack additives, different crack modes, and test configurations on the crack propagation process and the propagation trend. Much research has been done on this. The mixed mode I/III fracture toughness of asphalt concrete materials was determined using the Edge Notched Disc Bend specimen [23]. Mixed mode I/II fracture toughness of five modified asphalt mixtures containing poly phosphoric acid (PPA), Styrene Butadiene Styrene (SBS), anti-stripping agent, crumb rubber (CR), and F-T paraffin wax (Sasobit), and an unmodified one (with no additive), were investigated experimentally using a large number of cracked semi-circular bend (SCB) specimens [24]. Two circular shape test specimens were designed and examined for the experimental determination of mode I fracture toughness in different modified hot mix asphalt materials [25]. The effects of carbon nanotubes as a binder modifier on the fatigue and fracture performance of asphalt mixtures were investigated [26]. Asphalt characteristic effects on its mixed mode I/II low temperature fracture toughness have also been investigated experimentally [27]. One study showed that for top-down cracking when the pavement was under repeated loading, shear damage occurred first in the asphalt layer, and then the damage extended horizontally, resulting in a shear-damaged layer. The damaged layer then led to a higher tensile strain in the upper mixture, which caused tension cracks, that finally propagated upwards to the pavement surface [28]. In this study, laboratory investigations of the anti-crack performance of the high viscous asphalt sand stress absorption layer (HVASAAL) and the RASAL, and the propagation mechanism of different types of cracks, were carried out by force-controlled fatigue crack propagation tests, for which three types of overlay structure with three types of pre-crack were designed. The tests were conducted at room temperature and at the same loading rate, with the cyclic loading applied at the middle of the specimen. The three types of pre-crack were the middle crack, the side crack, and the 45\({}^{\circ}\) inclined crack. The fatigue crack propagation, fatigue life, crack propagation rate, and crack propagation mechanism of the three types of overlay structure were compared and analyzed. The crack propagation process of the three types of overlay with the same type of crack, and the three types of crack with the same type of overlay, were compared and analyzed as well. Considering the dispersion of the data of the crack propagations, a random probability model (\(p-\frac{\mathrm{d}a}{\mathrm{d}N}-\Delta K\) model) based on the reliability theory was established to describe the propagation of the fatigue cracks. Using the least-square method, the relationships between the crack length \(a\) and the fatigue number \(N\) of the three types of crack were obtained by fitting the polynomials. The crack growth rates during the stable growth period of the three structures, and then the anti-crack performance of the structures, were compared. The curves of the three types of crack were analyzed. The variations of the intercept \(\mathrm{lgC}\) and the slope \(n\) with the reliability \(p\) were discussed.