Dynamic Similarity Analysis Of Dynamic Compaction For Collapsible Loess

A dynamic stress analysis model for dynamic compaction for collapsible loess is put forward based on the assumption of microstructural un-stability. The new similar indexes used in the design of dynamic compaction model test for collapsible loess are obtained.The stress wave theory is applied to deduce the equilibrium equations for stresses, the continuity equations for particle velocities, and the conservation laws of momentums on the wave front for the nodes of the idealized spatial structure. The equations describing the changes of the incident waves, the transmitted waves, and the reflected waves at the nodes are obtained. With the aid of MATLAB, the model used to compute the stresses of partial structural elements in short time for the collapsible loess under dynamic compaction is set up.The key quantities used to describe the changes of the stress in collapsible loess under dynamic compaction are derived. The theory of similarity and the dimensional analysis method are applied to obtain new similar indexes.The dynamic stress analysis model for collapsible loess under dynamic compaction can be used to compute the changes of the stresses of partial structural elements happened in a short time. The program represents that the stress waves propagate from the near to the distant with the reduction of the magnitudes of the stresses, and the stresses in the elements increase and decrease while the load and unload wave propagates through the elements, and the stresses are superimposed when the stress waves meet. The key quantities used to describe the changes of the stresses in collapsible loess under dynamic compaction are the stresses of arbitrary point, the coordinates of arbitrary point, the falling distance of the hammer, the mass of the hammer, the density of the hammer, the Young's modulus of the hammer, the radius of the undersurface of the hammer, the Young's modulus of the bar elements of the structural model, the density of the bar elements, the angles between the relative bar elements, the void ratio of collapsible loess, the lateral force of friction between the loess and the hammer, time, and the gravitational acceleration. When the model and prototype tests are carried out under the same gravitational condition, the new similar indexes are still not easy to satisfy.