Abstract

The phenomenon of upthrow of rigid blocks, excited into motion by horizontal impulses, is examined in this study. A simple foundation model is used, consisting of two sets of springs and dashpots; one set near each corner of the block. Each set consists of vertical and horizontal elements. The vertical springs are not permitted to take tensile forces, so separation of the block from the ground is allowed. The associated horizontal spring separates along with the vertical spring. The response can be separated into three regimes, namely, full contact, partial uplift, and complete separation. Analytical expressions for the response are given for the first two cases; the third case is simply rigid body motion. The overall response is nonlinear and analytical criteria for upthrow were not found. The minimum value of the impulse required for complete separation, expressed as a normalized initial velocity, was determined numerically and a parametric investigation performed. Although the irregularity of the results does not allow many general conclusions to be drawn, it was found that for short blocks, a decrease in the stiffness of the horizontal foundation springs required larger impulses for separation. These effects had mixed results for tall blocks.

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