Isolation of plane P waves by discontinuous barriers composed of a row of elastic hollow pipe piles

The ratio of length to diameter of a pile is so large that the vibration isolation of incident plane P waves by discontinuous barriers composed of a row of elastic hollow pipe piles can be simplified as a two-dimensional plane problem. The stresses and displacements at the interfaces between piles and soils are considered as continuous, while the inner walls of piles are assumed stress free. The theoretical solutions for vibration isolation are obtained through the expansion method of wave functions and the Grafts addition theorem. The effects of pile thickness, modulus ratio of pile to soil, span between piles and sum number of piles on vibration isolation are studied in detail. A few important conclusions are drawn out from analysis, and they are: (1) the isolation effects increase with decrease in pile thickness and pile span, (2) the isolation effects increase with increase in the modulus ratio of piles to soils in the initial stage, and then, gradually approach constant after the ratio exceeds 500, which illustrates the piles can be regarded as rigid at that time, (3) as the sum number of piles increase, the best isolation areas increase and the position with best isolation effects moves forward, which provide theoretical basis for the design on discontinuous barrier for vibration isolation.