A SIMPLE METHOD FOR EVALUATING A STATIC SOIL SPRING OF FOOTINGS ON THE SURFACE OF AN ELASTIC HALF SPACE

Abstract

 Static soil springs of a spread foundation is often evaluated by finite element method, Mindlin's solution, Steinbrenner method, Cerruti's solution, and so on. However, both of these methods have disadvantages that calculation cost is high, and it is difficult to make a prospect of calculation results. This kind of difficulty to evaluate static soil springs is considered to be an obstacle for reasonable design of spread foundations.
 In this paper, the authors propose a simple method for evaluating a static soil spring of footings on the surface of elastic half space. The method is to multiply a soil spring of a single footing by a interaction factor. This interaction factor is given by: ξ = 1/(1 + (n − 1)B/Δr) (where, n: the square root of the total number of footings, B: a width of a footing, Δr: the distance between footings).
 The proposed interaction factor derived from 2 assumptions and 1 condition. One assumption is that the interaction factor is the same regardless of whether the loading condition of footings is a constant stress distribution or a constant displacement distribution. The other assumption is that the displacement around a loaded footing decreases in inverse proportion to the distance from the footing. Combining these 2 assumptions, it leads that the interaction factor is expressed as a closed - form function given by: ξ = 1/(1 + eB/Δr) (where, e: the undetermined coefficient). The undetermined coefficient e can be determined by using 1 condition that is led by the equivalence of 2 systems, single footing with a width of nB and n × n contacted footings with each width of B. That is, e = n − 1. From the above, the proposed interaction factor is derived.
 And as a result of comparing the proposed interaction factor and a interaction factor evaluated by using analytical solution (superposition of Mindlin's solution), the following conclusions is obtained.
 1. With square arrangement of footings, the proposed method agrees well with the analytical solution.
 2. With rectangle arrangement of footings, in the case where the long side / short side ratio is about 1.8 or less, the proposed method generally agrees with analytical solution.
 3. If the ground contact pressure distribution of a single footing is already known, approximate load distribution of footings can be calculated by using the proposed interaction factor.