Influence of foundation on motion of blocks

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Introduction

Practically all the research work done in the field of Engineering Seismology is based on the assumption that the effect of an earthquake is the same as that of a shaking table. There is strong theoretical evidence that this conception is erroneous and that the building is more likely to behave like a ship floating in stormy waters. If this is true, the elastic properties of the structure cannot be entirely dissociated from those of the ground and both must be studied simultaneously in order to predict the dynamical properties of the system.

The problem is extremely complex because it involves a complete knowledge of the propagation and properties of the seismic waves in the strongly heterogeneous surface layers of the earth, as well as their diffraction and reflection by objects built on the surface. Instead of tackling this problem in its full complexity, it must rather be expected that a solution will arise gradually from the careful analysis of simplified cases in which the influence of each individual factor is clearly brought to light and checked critically against observation.

In the present investigation, we have attempted to answer the following questions: What is the influence of the elasticity of the ground on the rocking motion of a building? How resistant is the surrounding soil to the rocking displacement of a foundation. What are the factors influencing this rigidity, and can we expect this effect to have a practical influence in the action of earthquakes on buildings? The problem is simplified by neglecting the radiation of elastic waves due to the rocking.

Section snippets

Rocking rigidity of a soil

Considering a semi-infinite elastic body representing the soil, it is well known that a concentrated force P applied vertically to the surface produces a deflection w at a distance r from the load according to the formula [1]w=P(1-ν2)πEr.

E denotes Young's modulus and ν the Poisson ratio of the soil.

Take the “coordinate” axes xy to lie on the surface of the soil and a positive load P per unit length to be concentrated on the line x=ξ, while a negative load P per unit length is concentrated on

Elastic constants of soil

Elastic properties of soils were obtained from dynamical tests by Ishimoto and Iida [2]. Samples taken from the underground of several regions of Tokyo at depths ranging from 2 to 20 m and made into the form of rectangular prisms were submitted to vibration tests. Values for Young's modulus E were derived, and some of the results are given in Table 1. Samples of Rubber and Agar Agar were also tested for comparison.

Values of the Poisson ratio were also derived by comparing the velocities of

Influence of the soil on the response of buildings to earthquakes

It has been established that one of the essential factors in the response of structures to earthquakes is their fundamental period of oscillation [6]. It is therefore appropriate to discuss the influence of the soil on the natural period of a structure.

Consider a rigid structure of mass M whose center of gravity is at a height h above the ground and that rests on a foundation of width 2l. Assuming the axis of rotation to be located at the surface of the soil, the frequency of the rocking motion

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References (6)

  • Timoshenko

    Theory of Elasticity

    (1934)
  • M. Ishimoto et al.

    Determination of elastic constants of soils by means of vibration methods

    Part I. The Bulletin of the Earthquake Research Institute

    (1936)
    M. Ishimoto et al.

    Determination of elastic constants of soils by means of vibration methods

    Part II. The Bulletin of the Earthquake Research Institute

    (1937)
  • D.P. Krynine

    Soil mechanics

    (1941)
There are more references available in the full text version of this article.

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  • Guest editor's note

    2007, ISET Journal of Earthquake Technology

Paper communicated posthumously by M.D. Trifunac.

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