Analytical approach for vertical dynamic responses of stiffened deep cement mixing pile in unsaturated ground

Stiffened deep cement mixing (SDCM) piles present excellent engineering performance compared with conventional pipe piles and thus are often applied to the structure foundation in coastal soft-soil area. This study intends to explore the vertical dynamic behavior of a SDCM pile in unsaturated soil by developing an analytical approach. In the proposed approach, the SDCM pile divides into two parts. The first part is considered as a composite pile formed by a prestressed high-strength concrete (PHC) pipe pile and a cement mixing pile through high-strength bonding, and the second part formed by the PHC pipe pile and an unsaturated soil column. The closed-form solution for the dynamic impedance of the SDCM pile has been determined and then verified by contrasting with the existing solutions, where the dynamic impedance is mainly characterized by dynamic stiffness and dynamic damping at SDCM pile head in the vertical direction. Numerical discussions are finally implemented to analysis the dependence of physical parameters of cement mixing pile, PHC pipe pile, and unsaturated soil on the vertical dynamic impedance of SDCM pile. It can be concluded that increasing the depth, radius and elastic modulus of the cement mixing pile at relatively low load excitation frequencies is beneficial for enhancing the vertical vibration resistance of the SDCM pile, while the reverse is true at higher load excitation frequencies. Quantitatively, under relatively low load excitation frequencies, the reinforcement depth of the cement mixing pile should not exceed 2/3 of the length of the PHC pipe pile, while its elastic modulus should be 5 ‰ to 2 % of the elastic modulus of the PHC pipe pile.