Bedrock-soil layer slopes (BSLSs) are widely distributed in nature. The existence of the interface between bedrock and soil layer (IBSL) affects the failure modes of the BSLSs, and the seismic action makes the failure modes more complex. In order to accurately evaluate the safety and its corresponding main failure modes of BSLSs under seismic action, a system reliability method combined with the upper bound limit analysis method and Monte Carlo simulation (MCS) is proposed. Four types of failure modes and their corresponding factors of safety (Fs) were calculated by MATLAB program coding and validated with case in existing literature. The results show that overburden layer soil's strength, the IBSL's strength and geometric characteristic, and seismic action have significant effects on BSLSs' system reliability, failure modes and failure ranges. In addition, as the cohesion of the inclination angle of the IBSL and the horizontal seismic action increase, the failure range of the BSLS gradually approaches the IBSL, which means that the damage range becomes larger. However, with the increase of overburden layer soil's friction angle, IBSL's depth and strength, and vertical seismic actions, the failure range gradually approaches the surface of the BSLS, which means that the failure range becomes smaller.

Lightning strikes can cause equipment damage and power outages, so the distribution system's reliability in withstanding lightning strikes is crucial. This research paper presents a model that aims to optimise the configuration of a lightning protection system (LPS) in the power distribution system and minimise the System Average Interruption Frequency Index (SAIFI), a measure of reliability, and the associated cost investment. The proposed lightning electromagnetic transient model considers LPS factors such as feeder shielding, grounding design, and soil types, which affect critical current, flashover rates, SAIFI, and cost. A metaheuristic algorithm, PSOGSA, is used to obtain the optimal solution. The paper's main contribution is exploring grounding schemes and soil resistivity's impact on SAIFI. Using 4 grounding rods arranged in a straight line under the soil with 10 Omega m resistivity reduces grounding resistance and decreases SAIFI from 3.783 int./yr (no LPS) to 0.146 int./yr. Unshielded LPS has no significant effect on critical current for soil resistivity. Four test cases with different cost investments are considered, and numerical simulations are conducted. Shielded LPSs are more sensitive to grounding topologies and soil resistivities, wherein higher investment, with 10 Omega m soil resistivity, SAIFI decreases the most by 73.34%. In contrast, SAIFIs for 1 klm and 10 klm soil resistivities show minor decreases compared to SAIFIs with no LPS. The study emphasises the importance of considering soil resistivity and investment cost when selecting the optimal LPS configuration for distribution systems, as well as the significance of LPS selection in reducing interruptions to customers.