A Method of Determination of Dominant Vibration Periods Values for Nonhomogeneous Multilayer Ground Sites

摘要

This paper is presenting development of a method for determination of dominating periods (frequencies) of vibrations of heterogeneous, multilayer foundations. By the method of wave mechanics precise complex transcendent equations of frequencies have been obtained for a foundation of two, three and four layers. To obtain such equations for a foundation having more than four layers is practically impossible. To avoid obtaining such complex frequency equations and to solve such equations using special computer programs a simplified method has been developed in this paper. The main point of the presented method is in successive reduction of a multilayer foundation to two-layer one for which depending upon ratios of amplitudes and periods of vibrations of layers, were computed roots of transcendent equations for more than 5000 combinations of these ratios have been tabulated, extrapolation formula has been derived. The procedure designed for determining values of T₀₁ periods of vibrations for any thickness of n layers is performed in the following sequence. First on the basis of data obtained during well-boring or by other geotechnical methods, according to values of H_k thickness, shear waves v_sk velocities, shear moduli G_k, and densities ρ_k of layers are calculated all periods of each layer (as of homogeneous) by the formula T_k=4H_k/v_sk. Next it is regarded that the foundation consists of only two upper layers with their H₁, H₂ and T₁ and T₂. By a special table and a formula the vibration period src=image/14600643_001.png> is calculated. Then two upper layers are regarded as one layer of H₁+H₂ thickness and src=image/14600643_001.png> period, and it considered with the third layer of H₃ thickness and T₃ period. In similar manner by ratio values H₁+H₂ and H₃ and src=image/14600643_001.png> and T₃ a the period of conditional sandwich thickness. This process proceeds for all layers. The obtained at the last stage the value of the period src=image/14600643_002.png> is assumed as a sought value of dominated period of the entire thickness of n layers. The method is illustrated be examples and estimation of its error is given.