Periodic Barriers For Surface Wave Isolation

The research effort towards ambient vibration isolation has received much attention these years.Previous studies have shown that a reasonable arrangement of multi rows of barriers(such as infilled trenches or row piles)can achieve a good vibration isolation effect.Multi rows of wave barriers often exhibit periodicity in spatial distribution,which has not only visual beauty but has deep physical connotations.Based on studies in solidstate physics,band gaps(or attenuation zones)exist in a periodic structure,which implies that elastic waves in the frequency band gap cannot propagate through the periodic structure.Inspired by this novel feature,applying the Bloch theory of periodic structures to investigate the dynamic characteristics of multi rows of wave barriers has received increasing attention in recent years.In the field of using periodic barriers to reduce ground vibrations,the main research interest was body waves(uniform plane waves)in the past,while studies involving surface waves were limited,mainly due to the complexity of the problem itself,i.e.,surface wave is a kind of non-uniform plane wave.Its energy is mainly concentrated near the free surface.Ambient vibrations,however,mainly propagate in the form of surface waves(Rayleigh waves).Therefore,investigating the surface-wave attenuation mechanism using periodic wave barriers has important theoretical significance and engineering application value.Within this context,this thesis carries out theoretical,numerical and experimental studies on periodic infilled trench barriers and periodic pile barriers,and achieved some useful results.The main contents and conclusions are drawn as follows:(1)This thesis establishes a physical model and method for the real dispersion relation(real band structure)of surface waves in periodic infilled trench and soil systems.The influence of geometrical parameters of infilled trenches on the vibration isolation effect is further revealed.Results show that the EPS geofoam material commonly used in engineering could yield surface-wave band gaps that cover the main frequency of the measured ambient vibration completely.Besides,numerical results show that the frequency range of vibration attenuation agrees well with the band gap predicted by the present method,which validates the present model and methodology.These contents are the summary of chapter 2.(2)So far,almost all studies on the dynamic characteristics of surface waves in periodic barriers are from the perspective of real dispersion relation.This method has obvious shortcomings although it has many advantages.For example,it fails to deal with material damping and to predicts attenuation coefficients of surface waves.Therefore,this thesis provides two new methods,the coefficient-type differential equation method and the weak-form integral equation method to investigate the complex dispersion relation(complex band structure)of surface waves.The obtained complex dispersion curve,in turn,reveals the effects of geometric parameters,soil parameters,and material damping on band gaps and the isolation efficiency of periodic barriers.Results show that in addition to the surface-wave band gap,there exist pseudo surface waves in periodic barriers.Both surface waves in band gaps and pseudo-surface waves belong to evanescent waves,because they decay exponentially along with propagation direction.The attenuation coefficients of evanescent waves agree well with the theoretical predictions.In addition,the buried depth of periodic barriers is recommended to be twice the period constant,which is equivalent to the suggested value(one Rayleigh wavelength)of previous studies that can be proved easily using the Bloch theory.Moreover,damping has less influence on attenuation coefficients of surface waves in band gaps,but outside band gaps the effect is dominant.This means that in the band gap caused by periodicity,the attenuation induced by wave scattering plays a key role,while outside the band gap,damping plays a major role due to energy dissipation.These contents are the summary of chapters 3 and 6.(3)Layered soil is common in practical engineering.However,there are few reports on the dynamic characteristics of periodic barriers in layered media based on the Bloch theory.The method established in this thesis can effectively analyze the surface-wave isolation by periodic piles in layered soil.The result reveals the effect of geometrical parameters like pile radius,pile spacing and pile length on band gaps and the isolation efficiency.Results show that there are not only Rayleigh wave band gaps in the periodic pile and layered soil systems but also Love wave band gaps.This means that periodic piles can effectively isolate the two types of surface waves.Second,the filling rate of piles is the main factor affecting the band gap width.The larger the filling rate,the wider the band gap.Third,pile spacing is the key factor governing the lower and upper frequency of band gap.The larger the pile spacing,the smaller the lower frequency,but the gap width is also reduced.Therefore,the low-frequency and broadband surface-wave gaps can be obtained by tuning the pile spacing and radius simultaneously.These contents are the summary of chapter 4.(4)Combined with Biot's theory,the above method is extended to the study of periodic piles in saturated soil.The effects of parameters such as pile configuration,pile radius,pile spacing,and pile length on the band gap and vibration isolation effect are revealed.Due to the existence of the groundwater table,the soil is often saturated in engineering.However,most of the current work is based on the assumption of singlephase media,and few of them consider two-phase media.The present method can not only investigate two-phase media,but also reduce to single-phase media.Results show that there is only one type of surface wave,Rayleigh wave band gap in homogeneous saturated soil and pile systems under the condition of the permeable free surface.Compared with the triangular and quadrilateral lattice,the honeycomb lattice can yield a complete band gap at a lower frequency without increasing the pile diameter.Thus,it can be used to isolate omnidirectional incident surface waves and has great application potentials.Besides,this thesis also gives the design flow chart of periodic wave barriers.These contents are the summary of chapter 5.(5)Based on the above theoretical analysis and numerical calculation results,this thesis carries out experimental studies on surface wave isolation using periodic infilled trenches and periodic pile barriers.It is found that the experimental results are in good agreement with the theoretical attenuation zones.Therefore,the feasibility of periodic wave barriers for surface wave isolation is verified.These contents are the summary of chapter 6.