Complementary Shear Stresses in Dynamic Centrifuge Modelling

Dynamic centrifuge modelling offers the geotechnical engineer an opportunity of testing reduced scale models at correct prototype stresses and strains while subjecting them to earthquake-like vibrations. In testing of such models the boundary effects require special consideration. A technique of using an absorbing ‘duxseal’ boundary was developed at the Princeton University and was extensively used at the Cambridge University. It was proved that at least 65% of the incident stress waves are absorbed by such a duxseal boundary. In addition to the absorption of incident stress waves an ideal boundary must carry the complementary shear stresses generated on every vertical plane in the far field. A natural semi-infinite soil stratum carries these complementary shear stresses when it is subjected to earthquake vibrations. If the artificial boundary in the centrifuge model is unable to carry these complementary shear stresses, the fact that the centre of mass of the soil body lies above the base plane at which shear waves are applied leads to generation of a dynamic ‘rocking’ moment which will result in the variation of the vertical stress along the base plane of the soil body. These are incorrect model conditions. In this paper a new correct boundary scheme was developed with a thin, vertical, inextensible durai sheet placed between the duxseal block and the soil body. This sheet was designed to impose the complementary shear stresses at the ‘far-field’ boundary interface during the earthquake loading. A series of dynamic centrifuge tests were conducted on a horizontal sand bed with the new boundary scheme. Stroud cells were used to measure the vertical and shear stresses along the base of the model. The thin, inextensible complementary shear sheet was strain gauged at three levels to measure the shear stresses along the vertical boundaries at either end. The results from these centrifuge tests are presented. The signals generated from the strain gauges were superposed with line noise. A frequency windowing technique was used to obtain the correct complementary shear stress traces. A simple De Alembert's type of calculation was made to estimate the performance of this boundary scheme. Based on this calculation it appears that two-thirds of the required complementary shear stress will be applied by the present boundary scheme. The other one-third will result in the generation of pressure waves in the model. The vertical stresses recorded by the Stroud cells placed on either side of the centroid were 180° out of phase suggesting the presence of a dynamic moment. When the complementary shear stress is completely borne by the boundary then this dynamic moment will vanish. Based on this study a series of centrifuge tests which will be conducted in future are discussed.