Theoretical analysis for isolation effect of an open trench on plane longitudinal waves

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Journal of Vibration and Shock ›› 2017, Vol. 36 ›› Issue (5) : 67-71.

XU Ping

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Abstract

An open trench with finite length was transformed to a unit circle with the conformal mapping method of complex functions,the boundaries of the trench were considered as free,theoretical solutions to isolation problems of longitudinal waves (P waves) and shear waves (SV waves) with an open trench were obtained based the wave function expansion method.The normalized displacement amplitudes were introduced,they were the ratios of displacement amplitudes of soil behind a barrier caused by both incident P or SV waves and scattering P and SV waves to those only by incident P or SV waves.Only incident P waves were taken as examples,and 4 trenches with a width of 0.4 m and lengths of 3.0 m,4.0 m,5.0 m and 6.0 m were analyzed.The results showed that the isolation effect and effective isolation zones increase obviously when the trench length increases from 3.0 m to 6.0 m,and the isolation effect exceeds 70% behind the trench when its length is 6.0 m,it reaches the in-situ test results of an open trench to isolate the impact loads.Finally,the isolation effect of an open trench and that of a discontinuous barrier composed of a row of cylindrical cavities were compared,and the results showed that because wave diffracting and trasmitting occur in a row of cylindrical cavities while only wave diffracting occurs in a trench,so the isolation effect of a trench with length of 6.0 m is equivalent to that of a row of 8 cylindrical cavities with a radius of 1.0 m,and so an open trench is the first and the best choice for the vibration isolation under the permission of field and operation conditions.

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open trench / plane longitudinal waves / isolation effect / conformal mapping method / vibration isolation design

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XU Ping. Theoretical analysis for isolation effect of an open trench on plane longitudinal waves[J]. Journal of Vibration and Shock, 2017, 36(5): 67-71

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