Abstract
Theoretical analysis of shaking table experiments, simulating earthquake response of a dry sand layer, is presented. The aim of such experiments is to study seismic-induced compaction of soil and resulting settlements. In order to determine the soil compaction, the cyclic stresses and strains should be calculated first. These stresses are caused by the cyclic horizontal acceleration at the base of soil layer, so it is important to determine the stress field as function of the base acceleration. It is particularly important for a proper interpretation of shaking table tests, where the base acceleration is controlled but the stresses are hard to measure, and they can only be deduced. Preliminary experiments have shown that small accelerations do not lead to essential settlements, whilst large accelerations cause some phenomena typical for limit states, including a visible appearance of slip lines. All these problems should be well understood for rational planning of experiments. The analysis of these problems is presented in this paper. First, some heuristic considerations about the dynamics of experimental system are presented. Then, the analysis of boundary conditions, expressed as resultants of respective stresses is shown. A particular form of boundary conditions has been chosen, which satisfies the macroscopic boundary conditions and the equilibrium equations. Then, some considerations are presented in order to obtain statically admissible stress field, which does not exceed the Coulomb-Mohr yield conditions. Such an approach leads to determination of the limit base accelerations, which do not cause the plastic state in soil. It was shown that larger accelerations lead to increase of the lateral stresses, and the respective method, which may replace complex plasticity analyses, is proposed. It is shown that it is the lateral stress coefficient K0 that controls the statically admissible stress field during the shaking table experiments.