## 1 Introduction  
Cracks in nuclear power plant (NPP) structures can develop due to residual stress, cyclic loading, and corrosion [1, 2]. In-service inspections are carried out to detect these cracks. If the detected crack size does not exceed the allowable crack size specified in ASME Section XI [3], the NPP can continue to operate without requiring maintenance or replacement. However, if the crack size exceeds the allowable crack size, the detected crack is assumed to be an idealized semi-elliptical or circular shape, and structural integrity is assessed using fracture mechanics parameters, including the elastic stress intensity factor (SIF) and the elastic-plastic \(J\)-integral [4]. This evaluation determines the maintenance and replacement cycle of NPP structures by comparing the findings with the critical crack size specified in ASME Section XI. For multiple cracks, various studies [5, 6, 7, 8, 9] have revealed that interaction effects vary depending on factors such as the distance between cracks, geometric configuration, and loading conditions. These interaction effects alter the trends of fracture mechanics parameters due to the influence between adjacent cracks. Moreover, as adjacent cracks grow and coalesce into a single crack, the crack shape can diverge from the idealized semi-elliptical or circular form. The variability in fracture mechanics parameters due to these interaction effects, along with the changes in crack shape caused by multiple crack coalescence, makes it challenging to accurately assess structural integrity under multiple crack conditions. To address these challenges, existing codes such as ASME Section XI, API 579 [10], BS 7910 [11], and British Energy R6 [12] provide criteria for coalescence distance and shape to account for crack interaction in crack evaluation. These coalescence criteria propose that, when the distance between adjacent cracks meets a specific coalescence distance criterion, the multiple cracks should be treated as a single, idealized semi-elliptical crack. However, this approach may lead to overly conservative predictions of coalescence timing, potentially treating non-cracked areas as cracks and resulting in an excessively conservative structural integrity assessment. Such evaluations can prematurely advance the maintenance and replacement cycles of NPP structures, potentially incurring unnecessary costs. Extensive studies utilizing 3D finite element analysis (FEA) have been conducted to evaluate the conservatism of the coalescence criteria considering interaction effects proposed in these codes [13; 14; 15]. [PERSON] et al. [13] conducted a quantitative analysis of the interaction effects on the SIF under membrane and bending stresses to validate the suitability of the newly proposed coalescence criterion, which aims to reduce the conservatism of the existing ASME Section XI criteria. The study confirmed that the new coalescence criterion is less conservative than the ASME Section XI and is more suitable for evaluating multiple cracks. [PERSON] et al. [14] quantitatively analyzed the impact of distance and aspect ratio between multiple cracks located in the same plane of a plate structure on interaction effects using SIF and /-integral values. They compared the interaction effects observed under various distance conditions with the coalescence distance criteria specified in ASME Section XI, API 579, and BS 7910 to evaluate conservatism and discuss potential improvements to the existing coalescence criteria. [PERSON] et al. [15] analyzed the interaction effects of non-coplanar multiple cracks in plate structures, considering the distance between cracks and the offset distance between planes under limited loading conditions, to propose an alternative to the offset distance criteria presented in ASME Section XI by examining changes in the SIF and the /-integral.