On the Applicability of Transfer Function Models for SSI Embedment Effects

Soil-structure interaction (SSI) effects are typically neglected for relatively lightweight buildings that are less than two-three storeys high with a limited footprint area and resting on shallow foundations (i.e., not featuring a basement). However, when the above conditions are not satisfied, and in particular when large basements are present, important kinematic SSI may develop, causing the foundation-level motion to deviate from the free-field one due to embedment effects. In the literature, transfer function models that estimate the filtering effect induced by rigid massless embedded foundations are available to “transform” foundation-level recordings into free-field ones, and vice-versa. This work describes therefore a numerical study aimed at assessing potential limits of the applicability of such transfer functions through the employment of a 3D nonlinear soil-block model representing a layered soil, recently developed and validated by the authors, and featuring on top a large heavy building with basement. A number of finite element site response analyses were carried out for different seismic input signals, soil profiles and embedment depths of the building’s basement. The numerically obtained transfer functions were compared with the curves derived using two analytical models. It was observed that the latter are able to reliably predict the embedment effects in “idealised” soil/input conditions under which they have been developed. However, in real conditions, namely when a non-homogeneous profile with nonlinear behaviour under a given seismic excitation is considered, especially in presence of a basement that is more than one storey high, they may fail in capturing some features, such as the frequency-dependent amplification of the motion at the basement level of a building with respect to the free-field one.

Evaluation Methods of Vertical Subgrade Reaction Modulus and Rotational Resistance Moment for Seismic Design of Embedded Foundations

In a seismic design of embedded foundations, the vertical Subgrade Reaction (SR) acting on a foundation bottom surface and the Rotational Resistance Moment (RRM) generated by the SR are calculated using an SR Modulus (SRM). The SRM and RRM depend on both ground rigidity and Foundation Width (FW). However, the SRM and RRM calculation methods adopted in design codes might not properly consider their FW dependency. In this study, SRM and RRM evaluation methods for embedded foundations subjected to a seismic load were examined by conducting a two-dimensional finite element analysis under the condition where ground rigidity and FW were changed considering the nonlinearity of the ground. The results show that when the seismic load is large and the nonlinearity of the ground appears, the SR distribution is different from the assumption in the design code. The FW dependency of the SRM was lower than the assumption of the design code. Furthermore, methods to calculate the SRM and RRM in accordance with the FW and ground rigidity are proposed.

Simplified frequency-independent model for vertical vibrations of surface circular foundations

Purpose This paper aims to simplify a new frequency-independent model to calculate vertical vibration of rigid circular foundation resting on homogenous half-space and subjected to vertical harmonic excitation is presented in this paper. Design/methodology/approach The proposed model is an oscillator of single degree of freedom, which comprises a mass, a spring and a dashpot. In addition, a fictitious mass is added to the foundation. All coefficients are frequency-independent. The spring is equal to the static stiffness. Damping coefficient and fictitious mass are first calculated at resonance frequency where the response is maximal. Then, using a curve fitting technique the general formulas of damping and fictitious mass frequency-independent are established. Findings The validity of the proposed method is checked by comparing the predicted response with those obtained by the half-space theory. The dynamic responses of the new simplified model are also compared with those obtained by some existing lumped-parameter models. Originality/value Using this new method, to calculate the dynamic response of foundations, the engineer only needs the geometrical and mechanical characteristics of the foundation (mass and radius) and the soil (density, shear modulus and the Poisson’s ratio) using just a simple calculator. Impedance functions will no longer be needed in this new simplified method. The methodology used for the development of the new simplified model can be applied for the resolution of other problems in dynamics of soil and foundation (superficial and embedded foundations of arbitrary shape, other modes of vibration and foundations resting on non-homogeneous soil).

CALCULATION OF THE NATURAL VIBRATIONAL FREQUENCY OF THE PULSE-LOADED EMBEDDED FOUNDATION

Applicability of formulas obtained within the framework of wave model and Russian design code SP 26.13330.2012 were considered to determine the dynamic stiffness in respect to vertical and horizontal vibrations of shallow and pile embedded foundations. The target is to calculate the system’s varying natural vibrational frequencies regarding the deepening. Obtained results are compared with experimental data of a series of pulse dynamic loadings under half-full-scale conditions on foundation models. Values of transversal wave velocities are found directly on test section from test results. It is found that deepening results in natural vibrational frequencies growth, both in case of pile and shallow foundations. Full deepening of more than 1.6 times increases frequencies at horizontal vibrations, and up to 1.4 times at vertical vibrations; the effect is stronger for shallow foundations. Benefit of the results obtained by wave model against the SP 26.13330.2012 method is demonstrated, as well as the good agreement between calculation and experimental results, which permits finding reliable amplitude-frequency characteristics of the foundations. Results obtained in accordance with SP 26.13330.2012 show lower values of natural vibrational frequencies and do not completely regard the deepening effect. Maximal discrepancy with experimental data is 33% for vertical vibrations on shallow and pile foundations. In case of horizontal vibrations, the maximal discrepancy is from 20% for shallow foundation to 27% for shallow and pile foundation.

Dynamic Behavior of an Embedded Foundation under Horizontal Vibration in a Poroelastic Half-Space

More and more huge embedded foundations are used in large-span bridges, such as caisson foundations and anchorage open caisson foundations. Most of the embedded foundations are undergoing horizontal vibration forces, that is, wind and wave forces or other types of dynamic forces. The embedded foundations are regarded as rigid due to its high stiffness and small deformation during the forcing process. The performance of a rigid, massive, cylindrical foundation embedded in a poroelastic half-space is investigated by an analytical method developed in this paper. The mixed boundary problem is solved by reducing the dual integral equations to a pair of Fredholm integral equations of the second kind. The numerical results are compared with existing solutions in order to assess the accuracy of the presented method. To further demonstrate the applicability of this method, parametric studies are performed to evaluate the dynamic response of the embedded foundation under horizontal vibration. The horizontal dynamic impedance and response factor of the embedded foundation are examined based on different embedment ratio, foundation mass ratio, relative stiffness, and poroelastic material properties versus nondimensional frequency. The results of this study can be adapted to investigate the horizontal vibration responses of a foundation embedded in poroelastic half-space.