Vertical vibration of a rigid strip footing on viscoelastic half-space

This paper presents an analytical method for modeling the dynamic response of a rigid strip footing subjected to vertical-only loads. The footing is assumed to rest on the surface of a viscoelastic half-space; therefore, effects of hysteretic soil damping on the impedance of the foundation and the generated ground vibrations are considered in the solution. To solve the mixed boundary value problem, we use the Fourier transform to cast a pair of dual integral equations providing contact stresses, which are solved by means of Jacobi orthogonal polynomials. The resulting soil and footing displacements and stresses are obtained by means of the Fourier inverse transform. The solution provides more realistic estimates of footing impedance, compared to existing solutions for elastic soil, as well as of the attenuation of ground vibrations with distance of the footing. The latter is important for the estimation of machine vibration effects on nearby structures and installations.     

Development of a coupled pile-to-pile interaction model for the dynamic analysis of pile groups subjected to vertical loads

Acta Geotechnica - This paper presents a new analytical model for calculating the dynamic performance of pile groups subjected to vertical loads. The derived solution allows considering the robust...     

Horizontal dynamic response of a large-diameter pipe pile considering the second-order effect of axial force

The second-order effect of axial force on horizontal vibrating characteristics of a large-diameter pipe pile is theoretically investigated. Governing equations of the pile-soil system are established based on elastodynamics. Three-dimensional wave equations of soil are decoupled through differential transformation and variable separation. Consequently, expressions of soil displacements and horizontal resistances can be obtained. An analytical solution of the pile is derived based on continuity conditions between the pile and soil, subsequently from which expressions of the complex impedances are deduced. Analyses are carried out to examine the second-order effect of axial force on the horizontal vibrating behavior of the pipe pile. Some conclusions can be summarized as follows: stiffness and damping factors are decreased with the application of axial force on the pile head; distributions of the pile horizontal displacement and rotation angle are regenerated due to the second-order effect of the applied axial force; and redistributions of the bending moment and shearing force occur due to the second-order effect of the applied axial force.     

A new dynamic interaction factor for the analysis of pile groups subjected to vertical dynamic loads

Τhis paper presents an analytical method for calculating the steady-state impedance factors of pile groups of arbitrary configuration subjected to harmonic vertical loads. The derived solution allows considering the effect of the actual pile geometry on the contribution of pile-soil-pile interaction to the response of the group, via the introduction of a new dynamic interaction factor, defined on the basis of soil resistance instead of pile displacements. The solution is first validated against a published solution for single piles that accounts for the effect of pile geometry on the generated ground vibrations. Accordingly, we show that the derived soil attenuation factor agrees well with existing solutions for pile groups in the high frequency range, but considerable differences are observed in both the stiffness and damping components of the computed impedance when the relative spacing between piles decreases. Numerical results obtained for typical problem parameters suggest that ignoring pile geometry effects while estimating the contribution of pile-soil-pile interaction in the response may lead to inaccurate results, even for relative large pile group spacings.

     

Kinematic response of pipe piles subjected to vertically propagating seismic P-waves

This paper presents an analytical solution for determining the time-harmonic response of single open-ended pipe piles subjected to vertically propagating seismic P-waves. Following the presentation of the formulation, we employ the solution to derive closed-form expressions of seismic pipe pile displacements, as well as robust expressions to determine the depth- and frequency-dependent parameters of complex Winkler springs, for use with beam-on-dynamic-Winkler-foundation models. Finally, the importance of considering the contribution of the inner soil in the seismic analysis of pipe piles is quantified via a parametric sensitivity analysis.

     

Simplified three-dimensional analysis of horizontally vibrating floating and fixed-end pile groups

This note presents an approximate analytical solution for estimating the time-harmonic impedance of pile groups subjected to horizontal dynamic loads, for different boundary conditions at pile tip (free and fixed). The derived solution considers waves due to pile vibrations propagating in both horizontal and vertical directions, unlike earlier solutions based on the plane-strain model, which ignores vertically propagating waves. This allows accounting for pile boundary conditions on the soil attenuation function, as well as modeling the response of the pipe group-soil system near the first natural frequency of the soil layer, where solutions based on the plane-strain model fail to account for resonance phenomena.     

Dynamic analysis of an axially loaded pile embedded in elastic-poroelasitc layered soil of finite thickness

This paper presents an analytical solution for determining the dynamic characteristics of axially loaded piles embedded in elastic-poroelastic layered soil of finite thickness. The interface between the elastic and poroelastic soil coincides with the groundwater table level, which is explicitly taken into account in the solution. The pile is modelled as elastic one-dimensional rod to account for the effect of its dynamic characteristics on the response of the soil-pile system. The solution is based on Biot's poroelastodynamic theory and the classical elastodynamic theory, which we use to establish the governing equations of the soil and pile. Accordingly, the pile base resistance, shaft reaction, and the complex impedance of soil-pile system are obtained using the method of Hankel integral transformation. Following the validation of the derived solution, we identify the main parameters affecting the vertical dynamic impedance of the pile via a parametric study. The presented method poses as an efficient alternative for quickly estimating the dynamic characteristics of axially loaded piles, without having to resort to complex numerical analyses.     

Vertical dynamic response of a pile embedded in a poroelastic soil layer overlying rigid base

Acta Geotechnica - This paper presents an analytical solution to investigate the vertical dynamic response of an elastic pile embedded in poroelastic soil overlying a rigid base. The pile top is...     

Development of a three-dimensional soil model for the dynamic analysis of end-bearing pile groups subjected to vertical loads

This paper presents a new analytical model for calculating the steady-state impedance of pile groups subjected to vertical dynamic loads. The derived solution allows considering effects of radially but also vertically propagating soil waves on the soil attenuation function, pile interaction factor, and pile group impedance. The proposed model provides accurate estimates of the soil stress field and of the response of the pile group in the low as well as in the high-frequency range, unlike earlier solutions based on the plane-strain model to describe the soil surrounding the piles, which ignores the vertical soil stress gradient. The latter assumption results in underestimating pile group impedance and overestimating radiation damping for frequencies lower than the cutoff frequencies of the system, which are explicitly captured with the proposed solution.