(1. College of Urban Planning，Zhejiang Shuren University，Hangzhou，Zhejiang 310015，China；2. MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering，Zhejiang University，Hangzhou，Zhejiang 310058，China；3. Department of Civil Engineering，Zhejiang Ocean University，Zhoushan，Zhejiang 316004，China)
Abstract：Based on Biot¢s dynamic consolidation theory，the torsional vibration of radially inhomogeneous saturated soil surrounding a pile is theoretically investigated. At first，the radially inhomogeneous soil is divided into inner annular disturbed and outer semi-infinite undisturbed regions，and the inner disturbed region is divided into many thin concentric annular zones. Then，the dynamic governing equation of saturated soil undergoing axisymmetric torsional deformations is derived in cylindrical coordinates. By utilizing the properties of modified Bessel function，the vibration displacement solution with undetermined constants of the soil layer is obtained and the solution holds for each thin concentric annular zone. Under the boundary and continuity conditions of the radially inhomogeneous soil layers，the torsional impedance of saturated soil is derived by means of transfer of shearing rigidity. Finally，the influence of changes of soil parameters caused by pile construction effect on torsional impedance of the soil is analyzed within the low frequency range；and several available solutions are compared with the present solution. The results show that：(1) The greater the hardening extent of the soil is，the higher the real stiffness and damping of the soil are；(2) The greater the softening extent of the soil is，the lower the real stiffness and damping of the soil are；(3) Within the two times of the radius of the pile，the larger the width of the inner region is，the higher the real stiffness of the hardening soil is and the lower the real stiffness of the softening soil is；(4) When the excitation frequency is relatively low，the material damping of inner region has negligible influence on the real stiffness of the soil.
