A SIMPLE METHOD FOR EVALUATING STATIC SOIL SPRINGS OF FOOTINGS ON THE SURFACE OF A LAYERED ELASTIC HALF SPACE

Abstract

 The soil springs of a rigid foundation with isolated footings are often evaluated by a superposition of analytical solutions, such as Mindlin’s solution (Mindlin 1936) or Steinbrenner’s method (Steinbrenner 1934), or by finite element methods. However, these methods are unsuitable in practical design. They are computationally expensive, and it is difficult to understand the causal relationship between the design parameters of the foundation and the soil spring values. Therefore, with these methods, it is difficult to reflect the designer’s intention in the foundation design.

 In this study, we proposed a simple method for evaluating static soil springs of a rigid foundation with isolated footings on the surface of a layered elastic half space, and we verified the applicability of the proposed method. Specifically, we proposed a method of approximating the static soil spring by a combination of soil springs of a spread footing foundation. We compared the results of our proposed method with static solutions of the generalized reflection and transition (R/T) coefficient method obtained by Hisada’s procedure (Luco and Apsel, 1983; Hisada, 1994). The R/T coefficient method is well known as a highly accurate method of calculating Green’s function of a multi-layered elastic half space satisfying conditions of displacements and stresses at the layer boundaries.

 As a result of the comparison, the following conclusions were obtained.

 1) The results of the proposed method were in good agreement with the results of the R/T method.

 2) The results of the proposed method were consistent with theoretical values, both when footings were in contact with each other and when the spacing between footings was infinite. This fact ensure the accuracy of the results of the proposed method when the spacing between footings is sufficiently narrow or sufficiently wide.

 3) If the shear modulus of the second layer is higher than that of the first layer, then the interaction factor of an elastic half space gives the lower bound for the interaction factor of a layered half space. Otherwise, the interaction factor of an elastic half space gives the upper bound for the interaction factor of a layered elastic half space. It is considered that the interaction factor of an elastic half space can be applied to a layered elastic half space, if the lower or upper bound for the interaction factor is to be used for an evaluation on the safe side.

 In the future we will study the interaction between footings arranged irregularly, and the interactions between different types of foundations.