Landslides caused by the progressive failure of sensitive clay slopes may cause substantial economic losses and environmental pollution to pipelines. This study utilizes the Karhunen-Loève (K-L) expansion method, the coupled Eulerian-Lagrangian (CEL) method, and the Monte Carlo method to model the large deformation behaviour of slopes with spatial variability. The proposed RCEL-MC framework for joint analysis of extensive deformation-probability statistics of landslide impact on pipelines confirms that the spatial variability clay slope instability failure mechanism, considering the soil softening effect under earthquake action, aligns more closely with real-world scenarios. Furthermore, based on the statistical failure probability of pipelines impacted by landslides, a sensitive clay slope pipeline safety design method is suggested. The research highlights that the random field parameters significantly influence the load-bearing characteristics of pipelines affected by spatially variable slope progressive failure landslides. The uncertainty surrounding the maximum impact force on pipelines notably increases with the rise of the horizontal correlation length and variability coefficient. When accounting for spatial variability, the maximum impact force on landslide pipelines surpasses the deterministic model analysis results by 28-69 %. It is emphasized that the deterministic model analysis, which neglects the spatial variability of soil and the soil softening effect, may seriously underestimate landslide risk. Based on the criteria for pipeline buckling failure and yield failure, it is advised that the safe design parameters for pipelines in practical projects should fall within the intersection of the secure regions defined by the two failure criteria.