Footing Response to Horizontal Vibration

Nagendra, M. V.; Sridharan, A.

doi:10.1061/(asce)0733-9399(1984)110:4(648)

Cited by 5 publications

(2 citation statements)

References 8 publications

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“…In Reissner’s study, the soil was homogeneous elastic half-space; the stress under the foundation was assumed to be uniformly distributed. Based on this classical and important solution, many investigators such as Sung (1953), Quinlan (1953), Bycroft (1956), Richart et al (1970), Luco and Westmann (1971) and Nagendra and Sridharan (1984) have studied the different modes of vibrations with various contact stress distributions.…”

Section: Introductionmentioning

confidence: 99%

Lumped parameter model for vertical vibrations of surface circular foundations on nonhomogeneous soil

Zahafi

Hadid

Bencharif³

2023

WJE

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Purpose A newly developed frequency-independent lumped parameter model (LPM) is the purpose of the present paper. This new model’s direct outcome ensures high efficiency and a straightforward calculation of foundations’ vertical vibrations. A rigid circular foundation shape resting on a nonhomogeneous half-space subjected to a vertical time-harmonic excitation is considered. Design/methodology/approach A simple model representing the soil–foundation system consists of a single degree of freedom (SDOF) system incorporating a lumped mass linked to a frequency-independent spring and dashpot. Besides that, an additional fictitious mass is incorporated into the SDOF system. Several numerical methods and mathematical techniques are used to identify each SDOF’s parameter: (1) the vertical component of the static and dynamic foundation impedance function is calculated. This dynamic interaction problem is solved by using a formulation combining the boundary element method and the thin layer method, which allows the simulation of any complex nonhomogeneous half-space configuration. After, one determines the static stiffness’s expression of the circular foundation resting on a nonhomogeneous half-space. (2) The system’s parameters (dashpot coefficient and fictitious mass) are calculated at the resonance frequency; and (3) using a curve fitting technique, the general formulas of the frequency-independent dashpot coefficients and additional fictitious mass are established. Findings Comparisons with other results from a rigorous formulation were made to verify the developed model’s accuracy; these are exceptional cases of the more general problems that can be addressed (problems like shallow or embedded foundations of arbitrary shape, other vibration modes, etc.). Originality/value In this new LPM, the impedance functions will no longer be needed. The engineer only needs a limited number of input parameters (geometrical and mechanical characteristics of the foundation and the soil). Moreover, a simple calculator is required (i.e. we do not need any sophisticated software).

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Section: Introductionmentioning

confidence: 99%

Lumped parameter model for vertical vibrations of surface circular foundations on nonhomogeneous soil

Zahafi

Hadid

Bencharif³

2023

WJE

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“…In 1963, Reissner developed the analytical solution for a vertically loaded cylindrical disk on elastic half-space assuming uniform stress distribution under the foundation. Later, extending Reissner’s solution, many investigators (Sung, 1953; Quinlan, 1953; Bycroft, 1956; Richart et al , 1970; Luco and Westmann, 1971; Nagendra and Sridharan, 1984) studied different modes of vibrations with different contact stress distributions.…”

Section: Introductionmentioning

confidence: 99%

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

Zahafi

Hadid

2019

WJE

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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).

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