Two types of grounding systems are recommended for use in the international standard IEC 62305-3, Part 3: Physical damage to structures and life hazard. One of these is a radial-based grounding system (type-A), which is used in soil resistivities of up to 3000 Omega m and is considered in this paper. It is a well-known fact that during lightning strikes, only a part of the grounding wire contributes to dissipating the lightning current into the surrounding soil. This effective part of the grounding system depends on several features, such as soil resistivity, burial depth, and rise time of the dissipated lightning current. The effect of all of these features on the effective length of the type-A grounding system is explored in this paper. A suitable supervised machine learning regression model is developed, which will enable readers to accurately approximate the effective length of the type-A grounding system for realistic values of input features. The trained model in the paper yielded an R2 value of 0.99998 on the test set. In addition, two simple mathematical formulas are also provided, which produce similar but less accurate results (R2 values of 0.989883 and 0.998557, respectively).

A new numerical-based fragility relation for cast iron (CI) pipelines with lead-caulked joints subjected to seismic body-wave propagation is proposed in this article. Two-dimensional 1600-m-length finite element models for pipelines buried in sand are developed in OpenSees. Parametric analysis is performed to investigate the influence of various parameters on the damage estimates of the buried pipelines. Numerical analyses are conducted to estimate the repair rates (RR) for CI pipelines subjected to wave propagation. The predictive model for RR is thus developed based on the numerical results and the Gaussian Process Regression approach. The model developed employs four predictor variables, namely, the peak particle velocity and wave propagation velocity along axial direction, the maximum soil shear force per unit length, and the outer diameter of pipelines, exhibiting desirable performance in terms of predictive efficiency and generalization. The performance of the developed relation is compared to several existing fragility relations. The new fragility relation can be used to estimate RR for CI pipelines with lead-caulked joints with outer diameters ranging from 169 to 1554 mm subjected to seismic body-wave propagation.