An elastic analysis is presented for the horizontal displacement and rotation of a laterally loaded pile group and the distribution of horizontal forces within the group. The interaction between two identical equally loaded piles is analyzed first, and the increases in displacement and rotation of the piles, in relation to the single pile values, are expressed in terms of interaction factors. Using these interaction factors, a method for calculating the displacement and rotation of a general pile group, based on the principle of superposition, is described. An examination of the behavior of square groups of piles reveals that the displacement, rotation, and load distribution in the group is largely influenced by the length-to-diameter ratio of the piles and the relative pile flexibility. It is also found that the displacement depends on the breadth of the group rather than the number of piles in the group. A reasonable measure of agreement is found between a limited number of reported measurements and theoretical predictions of group displacements.

Closure to “Behavior of Laterally Loaded Piles: II-Pile Groups”

SUMMARY
This paper is devoted to the analysis of elastodynamic problems in 3D-layered systems which are unbounded in the horizontal direction. For this purpose, a finite element model of the near field is coupled to a scaled boundary finite element model (SBFEM) of the far field. The SBFEM is originally based on describing the geometry of a half-space or full-space domain by scaling the geometry of the near field / far field interface using a radial coordinate. A modified form of the SBFEM for waves in a 2D layer is also available. None of these existing formulations can be used to describe a 3D-layered medium.

In this paper, a modified SBFEM for the analysis of 3D-layered continua is derived. Based on the use of a scaling line instead of a scaling centre, a suitable scaled boundary transformation is proposed. The derivation of the corresponding scaled boundary finite element (SBFE) equations in displacement and stiffness is presented in detail. The latter is a nonlinear differential equation with respect to the radial coordinate, which has to be solved numerically for each excitation frequency considered in the analysis.

Various numerical examples demonstrate the accuracy of the new method and its correct implementation. These include rigid circular and square foundations embedded in or resting on the surface of layered homogeneous or inhomogeneous 3D soil deposits over rigid bedrock. Hysteretic damping is assumed in some cases. The dynamic stiffness coefficients calculated using the proposed method are compared with analytical solutions or existing highly accurate numerical results. Copyright © 2011 John Wiley & Sons, Ltd.

A modified scaled boundary finite element method for three‐dimensional dynamic soil‐structure interaction in layered soil

The effect of interface friction angle $(\delta)$ between the footing and underlying soil mass on the bearing capacity factor $N_\gamma$ was examined by using the upper bound limit analysis, finite elements, and linear programming. The analysis was carried out by employing velocity discontinuities along all the interfaces of the chosen triangular elements. The development of the plastic strains within elements was incorporated by using an associated flow rule. It was clearly noted that an increase in leads to a continuous increase in $N_\gamma$. With $\delta=\phi$, the magnitude of $N_\gamma$ becomes almost the same as that for a perfectly rough foundation, that is, when no slippage takes place between the footing and underlying soil mass. The size of the plastic zones increases with increase in $\delta$ and $\phi$. The obtained values of $N_\gamma$, for perfectly smooth and perfectly rough footings, compare quite favorably with those reported in literature. The study demonstrates that in the case when $\delta$ is smaller than $\phi$, the assumption of a perfectly rough footing will lead to an unsafe prediction of the ultimate bearing capacity.

Effect of Footing Roughness on Bearing Capacity Factor $N_ \gamma$

A new approach for longitudinal vibration of a large-diameter floating pipe pile in visco-elastic soil considering the three-dimensional wave effects

Continuous monitoring of soil properties using an instrumented roller compactor requires models that can capture the essential features observed during drum/soil vibration. This paper presents the results of lumped parameter modeling of the drum/soil system together with data from complex nonlinear behavior observed experimentally during operation on sandy soil. Model parameters and response were developed using experimental data collected over a wide range of operating frequencies. Three and four-degree-of-freedom (DOF) models with linear and nonlinear soil elements were investigated. The results showed that a 3DOF model incorporating the soil, drum, and frame of the roller was successful in capturing behavior during coupled drum/soil vibration and during decoupling (i.e., loss of contact between drum and soil). Modeling the drum/soil decoupling accounted for most of the experimentally observed nonlinearity. The addition of nonlinear soil stiffness due to the curved drum effect and due to strain hardening soil behavior accounted for additional nonlinearity observed experimentally. Experimentally observed drum rocking during coupled drum/soil vibration was successfully modeled with a 4DOF drum-frame model. The analysis also revealed that commonly observed heterogeneous soil conditions give rise to a transient response that can have a significant influence on vibration behavior.

Capturing Nonlinear Vibratory Roller Compactor Behavior through Lumped Parameter Modeling

Dynamic nonlinear response of pile foundations under vertical vibration—Theory versus experiment

This paper presents the results of vertical vibration tests on two full-scale single piles. The diameter of pile and embedded depth were 0.45 and 22 m, respectively. The soil samples were collected from three boreholes located at the site of investigation and it was explored to a depth up to 30.45 m below the ground level. The vertical vibration tests were conducted for different eccentricities to determine the frequency-amplitude response of the pile. Static load tests were also carried out on two single piles. A simple axisymmetric two-dimensional finite-element model was developed to predict the dynamic pile response. Novak’s plane strain model was also used for the prediction of the dynamic response of single pile. It was observed that the finite-element model predicted the natural frequency and peak displacement amplitude of pile reasonably well. However, prediction of dynamic response of the pile was found unsatisfactory by Novak’s plane strain model. Possible reasons for unsatisfactory performance ...

Vertical Vibration of Full-Scale Pile―Analytical and Experimental Study

This paper presents an investigation of the dynamic response of foundations resting on a layered soil underlain by a rigid layer. Model block vibration test results are used for the investigation. For the analysis, two different methods, namely, the equivalent spring-mass-dashpot model and the cone model, are used. A simple method to estimate the equivalent stiffness of the foundations resting on any multilayered soil system is presented. Obtaining stiffness from the proposed method and using different values of the damping factor ranging between 1.5 and 10.0%, the dynamic response of a foundation resting on a layered soil system is computed. One-dimensional wave propagation in an elastic cone for the analysis of foundations resting on the elastic homogeneous half-space or layered soil is also used to compute dynamic responses of the foundations resting on different layered soil. Finally, results obtained from two analytical methods are compared with the test results. It has been observed from the comparison that the results obtained by the equivalent spring-mass-dashpot model with a damping factor of 1.5% matched well with the experimental results for all cases. Results obtained by the cone model match well with experimental results for the cases where the top layer is softer than the bottom layer.

Investigation of Foundation Vibrations Resting on a Layered Soil System

Dynamic response of foundations resting on layered soil by cone model

Influence of layering and presence of rigid boundary in the soil mass on natural frequency and resonant amplitude are studied experimentally by conducting model block vibration tests in vertical mode. Tests are conducted on different layered beds prepared in a tank using a model footing. A Lazan type mechanical oscillator is used for inducing vibration and two different materials (sand and sawdust) are used to form a layered system. In total, 180 tests are conducted in different layering combinations and different static and dynamic loading combinations, and several important observations are reported. Damping factors are found to be within 6.5% for the entire test series, which indicates that radiation damping is insignificant in the test system. It is also found that layering including layer position and thickness has significant effect on natural frequency. Observed natural frequencies are also compared with the predicted one based on static equivalent stiffness; encouraging agreement between observed and predicted values are found.

Dilip Kumar Baidya

Papers

Dynamic nonlinear response of pile foundations under vertical vibration—Theory versus experiment

Vertical Vibration of Full-Scale Pile―Analytical and Experimental Study

Investigation of Foundation Vibrations Resting on a Layered Soil System

Dynamic response of foundations resting on layered soil by cone model

Investigation of Resonant Frequency and Amplitude of Vibrating Footing Resting on a Layered Soil System