## 1 Introduction  
With the increasing number of high-rise buildings, the tightening of construction land, and the growing complexity of construction conditions, the requirements for pile foundation construction technology have become increasingly stringent [1, 2, 3, 4, 5]. Planted pile is a composite foundation type formed by pouring concrete or cement mortar into pre-drilled holes and then inserting precast pipe piles into the concrete or mortar; currently, piling technology is relatively mature, with sufficient theoretical and practical references available [6, 7, 8]. As construction land becomes scarcer and related projects such as land reclamation and rock dumping emerge, the prevalence of isolated stones within the soil layer has significantly increased, greatly impacting engineering projects. To prevent the occurrence of an isolated stone within the designed length area of the project's pile foundation, past measures often included avoidance, excavation, blasting, and the consolidation of multiple piles [9; 10; 11]. However, isolated stones are characterized by widespread distribution, density, and random shapes; thus, implementing these measures not only fails to resolve the problem completely, but also consumes a substantial number of resources and amount of time. To address these issues, composite piles have been widely used, with researchers both domestically and internationally conducting multifaceted theoretical and experimental studies on the load-bearing capacity of composite piles, exploring their bearing performance [12; 13; 14], load transfer mechanisms [15; 16; 17], failure modes, and settlement characteristics [18; 19]. [PERSON] et al. [20] conducted an in-depth study on the construction techniques of composite piles formed by bamboo and concrete piles, suggesting that an expanded drilling method can be applied to the lower half of the pile body to increase the cross-sectional area of the concrete pile, thereby enhancing the load-bearing capacity of the composite pile. [PERSON] et al. [21], in their study of T-shaped deep cement mixing piles, developed calculation methods for reinforcing ground consolidation settlement and its consolidation process. Through theoretical and parameter analyses compared with existing solutions, they found that enlarging the pile cap leads to a faster dissipation of excess pore water pressure while increasing the height and area replacement ratio of the pile cap significantly reduces ground consolidation settlement. [PERSON] et al. [22] utilized numerical simulations to analyze the horizontal and vertical bearing performance of composite piles, investigating the effects of different core pile areas and insertion depths on the load-bearing capacity of concrete-deep mixing composite piles (DCM piles). They concluded that the destruction simulation of pile foundations is influenced by the insertion depth of the core pile, with varying insertion depths leading to different failure modes of the DCM pile. [PERSON] et al. [23] conducted large-scale field tests to investigate the impact of core pile area and pile length on the ultimate load-bearing capacity of composite piles. They found that as the area of the core pile and the length of the core pile increase, the ultimate load-bearing capacity of the composite pile also improves, with the increase in core pile length contributing more significantly to this enhancement. [PERSON] et al. [24] compared the compressive load-bearing capacities of static drilling planted piles and bored concrete piles through field static load tests and numerical simulations, concluding that static drilling piles exhibit greater load-bearing capacity than bored concrete piles, with the load of composite piles primarily borne by the core pile. Similar composite pile foundations have been extensively studied domestically; however, they remain unsuitable for large isolated stones and stone clusters, which still require manual removal.