基于球孔扩张理论的软黏土中载体桩桩端挤密加固效应

载体桩是近年来出现的一种新桩型，其主要利用柱锤对深层土体进行填料夯实，形成桩端扩大载体，从而大大提高桩体竖向承载力。虽然载体桩在实际工程中广泛应用，但目前仍缺乏较为严格的理论分析，特别在关于评价载体的加固范围和载体对土体的挤密效应方面，仍然研究较少，这大大制约了载体桩的推广和发展。针对该问题，将柱锤对填料夯实的过程简化为球孔扩张力学模型，软黏土采用修正剑桥模型的本构关系来模拟，建立球孔扩张偏微分控制方程组，通过相似变换的求解技术将偏微分方程转化为常微分方程组，利用微分方程数值求解技术获得常微分方程组的数值解。开展参数分析，探讨球孔扩张过程中孔周土体强度和刚度的变化、孔周土体挤密区的范围等，从理论角度揭示载体桩载体成形过程中的加固机理，为建立考虑桩端挤密效应的载体桩竖向承载力计算方法提供理论基础。

Compaction and reinforcement effect at the pile end of carrier pile in soft clay based on spherical cavity expansion method

Carrier pile is newly developed in recent years. It utilizes a column hammer to tamp the filling in the deep soil, which forms an expanded carried at the pile end. This will greatly increase the vertical pile bearing capacity. Although the carrier pile has been widely used in practice, rare theoretical analysis has been conducted to check the size of the reinforced area and the compaction effect. This greatly restricts the popularization and development of the carrier pile. Under this condition, the process of the tamping through a column hammer is simplified as the spherical cavity expansion model. The soft clay is described by the MCC model. Then, a series of partial differential equations (PDEs) for spherical cavity expansion is constructed. Similarity solution technique is used to transform the PDEs to ordinary differential equations (ODEs), which can be numerically solved through the ODE solver. Subsequently, a series of parametric analyses were conducted to investigate the variation of the soil strength and stiffness after spherical cavity expansion and the size of the compaction zone. This reveals the reinforced mechanism of the formation of the carried part of the pile from the theoretical viewpoint and provides a theoretical basis for constructing the theoretical calculation methods for the vertical bearing capacity of the carrier pile considering the compaction effect.