Machine learning (ML) has powerful nonlinear processing and multivariate learning capabilities, so it has been widely utilised in the fatigue field. However, most ML methods are inexplicable black-box models that are difficult to apply in engineering practice. Symbolic regression (SR) is an interpretable machine learning method for determining the optimal fitting equation for datasets. In this study, domain knowledge-guided SR was used to determine a new fatigue crack growth (FCG) rate model. Three terms of the variable subtree of Δ K , R -ratio, and Δ K _th were obtained by analysing eight traditional semi-empirical FCG rate models. Based on the FCG rate test data from other literature, the SR model was constructed using Al-7055-T7511. It was subsequently extended to other alloys (Ti-10V-2Fe-3Al, Ti-6Al-4V, Cr-Mo-V, LC9cs, Al-6013-T651, and Al-2324-T3) using multiple linear regression. Compared with the three semi-empirical FCG rate models, the SR model yielded higher prediction accuracy. This result demonstrates the potential of domain knowledge-guided SR for building the FCG rate model.

Understanding the relationship between the moisture content of unsaturated soil and the instability and dynamic response of slope under the action of seismic load can bring convenience to the field of slope safety assessment. The effect of moisture content of the unsaturated soil on the failure mode and dynamic response of slope under seismic loading was investigated using shaking table tests. In this regard, three different moisture contents of 5%, 8.1%, and 12.5% were considered. The experimental results show that the amplification factor of acceleration (AFA) on the slope surface increases with the increase in both relative elevation and excitation amplitude of acceleration (EAA). As the moisture content of unsaturated soil increases, AFA tends to decrease. An empirical correlation describing the relationship among AFA, relative elevation, dimensionless EAA, and moisture content of unsaturated soil was proposed. The excitation frequency of acceleration (EFA) has a significant impact on the AFA at the middle and upper parts of the slope. The deformation of slope surface is able to reflect the failure mode of slope, which can be used in slope monitoring work. The slope with different moisture contents of unsaturated soil has different instability modes. With the increase in soil moisture content, the slope needs more energy to reach the unstable state under seismic loading. There are three typical regions of principal stress field in the slope exposed to seismic loading, which control the evolution of initial slip plane inside the slope.