## 1 Introduction  
Mechanical damage like cracks, scratches, and gouges often occur inside dents in pipelines. The combined defects are considered more injurious to pipeline integrity than plain defects [1; 2; 3; 4; 5; 6]. An example of combined defects found in pipelines is a crack inside a dent, also known as a dent-crack defect [2; 3; 4]. [PERSON] et al. [7] showed that gauge depths greater than 50% of wall thickness cause stresses higher than yield strength of pipe material and cracks are likely to initiate at the tip of such gouges under normal operating pressure. The dent magnifies the maximum principal stresses developed in the gouge, increasing susceptibly to cracking. [PERSON] et al. [8] also showed that hoop stresses are higher in a pipeline with combined dent and gouge defects than in a pipeline with plain gouges and concluded that dent-gouge defects significantly lower the burst strength of pipelines. Very few full-scale experimental studies on dent-crack defects in pipelines have been accomplished [2; 3; 4; 5], mainly because of the difficulty in creating artificial cracks for experiments. Usually, the cracks are represented by notches and gouges [9] with a small fatigue crack at the tip. Currently, there are no analytical models for assessing the integrity of a pipeline with dent-crack defects. The pipeline defect assessment manual [10; 11] recommends the use of dent-gouge fracture models to assess dent-crack, without taking the difference between the stress environments at the tip of cracks and gouges into consideration. [PERSON] et al. [12] proposed a model for assessing dent-crack defects based on the stress distribution in a dent with an axial crack lodged at its deepest point by treating the dent as a source of geometric nonlinearity. Bending stresses through the crack caused by the geometric nonlinearity were added to the stresses caused by the internal pressure and the sum used to calculate the stress intensity factor used to analyze crack propagation. The model is considered conservative because it does not account for the effect of re-rounding of dents under internal pressure on the bending stresses through the crack. [PERSON] et al. [13] used a notch in an infinitely long dent to represent a dent-crack defect and then modified the plastic collapse stress of the pipe material to account for deterioration in the material properties due to the mechanical damage during defect formation and the effect of notch shape. They considered the modified collapse stress as the burst stress of the pipe, and a fraction of it was used to compute burst pressure. The main limitation of their approach is that they used a notch instead of a crack. In the absence of analytical models, the finite element method (FEA) has been successfully used to evaluate burst pressures of pipelines with dent-crack defects [2; 3; 4]. But, it lacks an in-built criterion for determining burst pressure. The software user must choose one out of several that have been suggested in literature. [PERSON] et al. [14] used a threshold for equivalent plastic strain in the defect area to analyze fatigue fracture. [PERSON] and [PERSON] [15] used 20% maximum principal strain as the critical strain for safe excavation of defective pipes in a rock ditch, considering material fails at 20% strain. [PERSON] and [PERSON] [16] used an equivalent stress criterion to assess burst strength of pipes with dent-scratch defect, considering failure to occur when the equivalent stress equals the true tensile strength of the pipe material. Other studies [2; 3; 4; 17] used the J-integral concept, assuming failure occurred when the J-integral at any integration point in the model equaled a critical value \(J_{1c}\) of the material. All the above FEA failure criteria use material properties and geometry of pipe, which are altered by denting and rebound action of dents [18], further introducing uncertainty in the results. The extended finite element method (XFEM) uses damage parameters determined through calibration and input in the model as material properties.