Flexible support of a pile embedded in unsaturated soil under Rayleigh waves

Abstract

Under the action of Rayleigh waves, pile head is easy to rotate with a concrete pile cap, and pure fixed-head condition is rarely achieved, which is a common phenomenon for it usually occurs on the precast piles with insufficient anchorage. In addition, the propagation characteristics of Rayleigh wave have been changed significantly due to the existence of capillary pressure and the coupling between phases in unsaturated soil, which significantly affects the pile-soil interaction. In order to study the above problems, a coupled vibration model of unsaturated soil-pile system subjected to Rayleigh waves is established on the basis that the pile cap is equivalent to a rigid mass block. Meanwhile, the soil constitution is simplified to linear-elastic and small deformations are assumed to occur during the vibration phase of soil-pile system. Then, the horizontal dynamic response of a homogeneous free-field unsaturated soil caused by propagating Rayleigh waves is obtained by using operator decomposition theory and variable separation method. The dynamic equilibrium equation of a pile is established by using the dynamic Winkler model and the Timoshenko beam theory, and the analytical solutions of the horizontal displacement, rotation angle, bending moment and shear force of pile body are derived according to the boundary conditions of flexible constraint of pile top. Based on the present solutions, the rationality of the proposed model is verified by comparing with the previous research results. Through parametric study, the influence of rotational stiffness and yield bending moment of pile top on the horizontal dynamic characteristics of Rayleigh waves induced pile is investigated in detailed. The analysis results can be utilized for the seismic design of pile foundation under Rayleigh waves.

An analytical solution for the horizontal vibration behavior of a cylindrical rigid foundation in poroelastic soil layer

“…[1][2][3] However, most of research objects are aimed at the flexible rod or beam subjected to harmonic external force. [4][5][6][7] Due to the importance of large size cylindrical foundations (mainly refer to the anchorage open caisson and large-span bridges), the dynamic characteristics of the embedded foundation should also be paid attention. Based on the dynamic Winker foundation beam model, Kaldjian, 8 Urlich and Kuhlemeyer, 9 and Apsel and Luco 10 derived the displacement function of a cylindrical rigid foundation embedded in an elastic half-space media under harmonic excitation.…”

“…The interactions of structure foundations with their surrounding soil play an important role in many practical applications, such as pile dynamics problem, design of bridge piers and sub‐structural method 1–3 . However, most of research objects are aimed at the flexible rod or beam subjected to harmonic external force 4–7 . Due to the importance of large size cylindrical foundations (mainly refer to the anchorage open caisson and large‐span bridges), the dynamic characteristics of the embedded foundation should also be paid attention.…”

“…However, soils in general are two-phase medium consisting of a lot of solid skeletons and pores filled with fluid, especially in the ocean area, capillary saturation zone of soil and depth below the water table of soil. [4][5][6] To overcome this deficiency, Senjuntichai et al 13 used the Biot's poroelastic theory and established the governing equations of the cylindrical rigid foundation in poroelastic half-space subjected to vertical loads, where the dual integral equations were solved by iterative approach. Similarly, Cai and his coworkers [14][15][16][17] provided a simplified analytical frame to obtain the compliance coefficient of a rigid foundation partially embedded in soil, which can be used for the vertical and rocking vibrations of foundation problem.…”

“…It is worth noting that the mentioned studies are commonly confined to the assumption of single‐phase soil. However, soils in general are two‐phase medium consisting of a lot of solid skeletons and pores filled with fluid, especially in the ocean area, capillary saturation zone of soil and depth below the water table of soil 4–6 . To overcome this deficiency, Senjuntichai et al 13 .…”

Horizontal motions of a rigid disk placed on a poroelastic soil layer of finite thickness

“…In the increasing construction of high-arch dams, offshore platforms, and port pier projects, the structure foundations often have to withstand horizontal loads such as wind and earthquake waves. [1][2][3] With the rapid development of economic globalization, the foundations have been required to sustain their working condition, dynamic stability and minimize settlement for the safe operation and maintenance of superstructures. 4,5 Therefore, the problem corresponding to horizontal dynamic interaction between the foundation and soil is complicated and important in geotechnical engineering, and these calculation results can be conveniently applied to the dynamic analysis of soil-structure interaction (SSI) based on the substructure method.…”