An empirical model for bending capacity of defected pipe combined with axial load

Highlights: • Various FE models including the differences in material models and failure criteria have been investigated. • An extensive FE database with 772 samples generated for predicting Moment capacity of the defected pipe. • Accounting to the effect of bidirectional bending moment, axial forces in the bending pipe, the effects of out-of-bending plane defects are observed along with other inputs. • Development of engineering applicable empirical model with R² up to 0.9929. Buried pipes suffer from various natural and human-related phenomena leading to the bending forces on such structures. The analytical models face obstacles such as the complications in modeling material behavior and the local stress concentration due to the appearance of defects are combined. This causes the accumulative over and under-estimation of pipe capacity due to the idealizations of full plastic stress distribution and location of defects at the most dangerous area, respectively. Consequently, such models are not appropriate in the case that defects are not located on the bending plane. The Finite Element, FE, approach is used to overcome these difficulties with the appearance of defects is randomly propagated around the pipe. Additionally, the bilinear material model is also applied accounting for the shape of actual stress-strain curves in a simplified manner. Various Finite Element Analyses are conducted consequently to have an extensive FE database with 772 samples labeled by the bending capacity of the corresponding pipe. To avoid the difficulties for users due to the requirement of coding skill, statistics, and advanced mathematics knowledge, and the implicit appearance of the conventional data-driven models, an empirical model, which can be explicitly expressed, has been developed. The main process of developing such a model is to optimize the design variables in the reduction factors. The objective function is chosen as the Mean Absolute Error of the predicted versus simulated reduction factor. The proposed model has been validated with the high accuracy of R-square at 0.9929 on the test set reveals an improvement compared to other available models.