Vertical Impedance Research Articles

Experimental investigation of the sound absorption characteristics of unconsolidated granular materials

In the context of a wider research project investigating the use of Granular Material (GM) within floor and wall structures to increase their sound insulation, this study presents the sound absorption coefficient (SAC) measurements of different thicknesses for a range of GM. A primary aim has been to extend the understanding of the behaviour of GM layers in absorbing the propagated incident sound wave. Equally important has been an assessment of what GM could be sourced from waste and be acceptable for use in buildings from the point of view of fire insulation, handleability, economy, etc. Samples of GM were placed in an 88mm diameter vertical impedance tube and SACs measured up to 2kHz. The results show the effect GM's different structure (size and shape), bulk volume, and mechanical characteristics have on the range and value of the SAC. These determine the extent to which GM could be a replacement for traditional sound absorption materials.

Analytical approach for vertical dynamic responses of stiffened deep cement mixing pile in unsaturated ground

Stiffened deep cement mixing (SDCM) piles present excellent engineering performance compared with conventional pipe piles and thus are often applied to the structure foundation in coastal soft-soil area. This study intends to explore the vertical dynamic behavior of a SDCM pile in unsaturated soil by developing an analytical approach. In the proposed approach, the SDCM pile divides into two parts. The first part is considered as a composite pile formed by a prestressed high-strength concrete (PHC) pipe pile and a cement mixing pile through high-strength bonding, and the second part formed by the PHC pipe pile and an unsaturated soil column. The closed-form solution for the dynamic impedance of the SDCM pile has been determined and then verified by contrasting with the existing solutions, where the dynamic impedance is mainly characterized by dynamic stiffness and dynamic damping at SDCM pile head in the vertical direction. Numerical discussions are finally implemented to analysis the dependence of physical parameters of cement mixing pile, PHC pipe pile, and unsaturated soil on the vertical dynamic impedance of SDCM pile. It can be concluded that increasing the depth, radius and elastic modulus of the cement mixing pile at relatively low load excitation frequencies is beneficial for enhancing the vertical vibration resistance of the SDCM pile, while the reverse is true at higher load excitation frequencies. Quantitatively, under relatively low load excitation frequencies, the reinforcement depth of the cement mixing pile should not exceed 2/3 of the length of the PHC pipe pile, while its elastic modulus should be 5 ‰ to 2 % of the elastic modulus of the PHC pipe pile.

Modelling of railway ballast as a poro-elastic medium and its effects on sleeper sound radiation

Conventional railway track is laid in a layer of coarse stones known as ballast. Due to the gaps between the stones, the railway ballast behaves as a porous acoustic material, with absorptive properties that are important for the noise produced by the railway system. Sound radiated by the bottom of the sleepers may also be transmitted through the ballast. Moreover, during a train pass-by the ballast can vibrate, which may contribute to the radiated noise. To consider all three effects simultaneously, the ballast is treated here as a poro-elastic medium. To obtain the properties of the ballast as a porous medium, transfer function measurements are performed in a vertical impedance tube to determine the surface impedance and absorption coefficient of different depths of reduced scale ballast. The complex wavenumber is also determined through transfer function measurements within the ballast in the vertical tube. Porosity and flow resistivity are determined by non-acoustic measurements, and the Johnson-Champoux-Allard model for porous materials is then fitted to the measured wavenumbers, allowing the remaining parameters to be determined. Comparison is made with the measured impedance and normal incidence absorption coefficient. The model is then used to predict the diffuse field absorption coefficients of both the reduced scale ballast and full-size ballast, which are compared with measurements, showing acceptable agreement. Finally, the effects on the sleeper radiation of introducing the poro-elastic ballast model are estimated and the sensitivity of the results to a practical range of ballast properties is assessed. The ballast vibration increases the sleeper radiation at low frequency, and especially between 120 and 280 Hz. This is caused by the structural vibration of the ballast driven by the sleepers, which has a resonance around 250 Hz. The acoustic velocity within the ballast is 180° out of phase with the structural velocity, and this leads to a small reduction in the sound radiation around 100 Hz. These effects could not be predicted using a surface impedance model for the ballast. Compared with the effect of the ballast vibration and sound transmission, the absorption of the ballast has a much smaller influence on the sleeper radiation.

Vertical dynamic impedance of pile groups embedded in soils considering the groundwater level

Vertical dynamic impedance of pile groups embedded in soils considering the groundwater level

Seismic amplitude inversion based on a new PP-wave reflection coefficient approximation equation for vertical transversely isotropic media

We develop a method for the simultaneous amplitude-variation-with-offset or -angle inversion of anisotropic parameters for transversely isotropic media with vertical axis of symmetry (VTI media). First, we introduce a nonlinear PP-wave reflection coefficient approximation equation in terms of only P- and S-wave impedances for isotropic elastic media. Then, by replacing the isotropic part of Rüger’s equation with this equation, we obtain a new PP-wave reflection coefficient approximation equation called the ASI Rüger equation for VTI media. To invert the parameters for VTI media based on the ASI Rüger equation, we adopt the Bayesian generalized linear inversion (GLI) method, a combination of GLI and Bayesian linear inversion, in which the noise and model perturbation are assumed to conform to the zero-mean Gaussian distribution. Compared with Rüger’s equation, the ASI Rüger equation decreases the trade-off between the parameters and reduces the ill-posedness of the inverse problem. The synthetic and field data tests demonstrate the feasibility of our method for inverting VTI media parameters (the vertical P-wave impedance, the vertical S-wave impedance, and Thomsen’s parameters [Formula: see text] and [Formula: see text]).

Transmission loss measurement of recycled granular material using wave decomposition by impulse response extraction based on deconvolution

A simplified method for measuring transmission loss with a single fixed microphone inside an impedance tube is proposed. The separation of the incident wave from the reflected wave is achieved by deconvolving the loudspeaker driver voltage signal with the microphone signal to extract the impulse response. Random noise and a sinusoidal sweep signal were used as excitation signals for extraction of the impulse response, and two deconvolution methods were employed: linear deconvolution based on the adaptive LMS algorithm and simple spectral division. To avoid the overlap of incident and reflected pulses, a long impedance tube was used. Using a long impedance tube eliminates the need for an anechoic tube termination and the need to calibrate microphones. It is found that a reflective tube termination provides more accurate results compared to an approximately anechoic termination. The approximately anechoic termination shortens the available time window of the reflected pulse because it reflects some of the low-frequency sound. The standard deviation of the results and the dynamic range of the proposed method were determined experimentally. The applicability of the new method was tested on samples of unconsolidated granular material recycled from construction sites. The measured transmission losses of the different granular fractions were compared with a theoretical model for transmission losses at low frequencies. Samples consisting of smaller granule fractions were found to have surprisingly high transmission loss values. The design of the extended vertical impedance tube in combination with the proposed method is cost effective, speeds up the measurement procedure and provides reliable results.

Vertical impedance functions of pile groups under low-to-high loading amplitudes: numerical simulations and experimental validation

Vertical impedance functions of pile groups under low-to-high loading amplitudes: numerical simulations and experimental validation

Scour effects on the vertical dynamic response of single piles in transversely isotropic soils

Pile foundations in ocean engineering are often simultaneously subjected to dynamic loads and scour activity. A coupled finite element method (FEM) - analytical layer element method (ALEM) is provided in this paper for investigating the vertical dynamic impedances of piles in layered soils under scour conditions. The pile modeled as a one-dimensional vibration bar is solved using the FEM. The dynamic responses for a layered soil are derived from the ALEM. Based on the force equilibrium and the displacement compatibility at the pile-soil interface, the pile-soil interaction equations under scour conditions are established and solved. Finally, several numerical examples are performed to verify the correctness of the proposed method, and to explore the effects of scour type, scour depth and slenderness ratio on the vertical impedances of single piles, which show that these factors significantly affect the vertical pile-head impedances, and the optimal pile slenderness ratio is mainly associated with the excitation frequency.

A Simple Approach for the Dynamic Analysis of a Circular Tapered Pile under Axial Harmonic Vibration

The tapered pile offers sustainable use of construction materials due to its higher axial and lateral capacity and better performance owing to its geometry. This paper develops a semi-analytical solution of the vertical dynamic impedance of the tapered pile based on the dynamic Winkler theory and transfer matrix method. The accuracy and reliability of the proposed approach are verified by comparing the impedance functions of cylindrical and tapered piles obtained from the analytical solution and finite element analysis. A parametric study is performed to investigate the influence of the taper angle on the vertical dynamic impedance and resonant frequency. The results reveal that the taper angle has a significant influence on the vertical dynamic impedance, while it does not affect the oscillation period of the dynamic impedance and the resonant frequency. Besides, the vibration performance of the tapered pile is better than that of a cylindrical pile with the same volume. For a fixed-volume tapered pile, varying the pile length while keeping the pile tip diameter constant yields a better dynamic impedance than varying the pile tip diameter while keeping the pile length constant. Finally, the vertical displacement amplitude of the tapered pile decreases as the taper angle increases, especially for high-frequency excitation.

Vertical and horizontal dynamic response of suction caisson foundations

Abstract In this article, the dynamic response of suction caisson foundations is studied using a three-dimensional finite element model with an absorbing boundary. The adopted formulation is based on the substructuring method. This formulation has been applied to analyze the effect of soil–structure interaction on the dynamic response of the suction foundation as a function of the kind of load. The suction caisson foundations are embedded in viscoelastic homogenous soils and subjected to external harmonic forces. For each frequency, the dynamic impedance connects the applied forces to the resulting displacement. The constitutive elements of the system are modeled using the finite element volumes and shell elements. The numerical results for the dynamic response of the suction foundations are presented in terms of vertical and horizontal displacements as well as vertical and horizontal dynamic impedances. The results indicated that the overall dynamic response is highly affected by the suction caisson diameter, the soil stiffness variation, and the suction caisson length.

Inversion of shallow seabed structure and geoacoustic parameters with waveguide characteristic impedance based on Bayesian approach

Underwater acoustic technology is essential for ocean observation, exploration and exploitation, and its development is based on an accurate predication of underwater acoustic wave propagation. In shallow sea environments, the geoacoustic parameters, such as the seabed structure, the sound speeds, the densities, and the sound speed attenuations in seabed layers, would significantly affect the acoustic wave propagation characteristics. To obtain more accurate inversion results for these parameters, this study presents an inversion method using the waveguide characteristic impedance based on the Bayesian approach. In the inversion, the vertical waveguide characteristic impedance, which is the ratio of the pressure over the vertical particle velocity, is set as the matching object. The nonlinear Bayesian theory is used to invert the above geoacoustic parameters and analysis the uncertainty of the inversion results. The numerical studies and the sea experiment processing haven shown the validity of this inversion method. The numerical studies also proved that the vertical waveguide characteristic impedance is more sensitive to the geoacoustic parameters than that of single acoustic pressure or single vertical particle velocity, and the error of simulation inversion is within 3%. The sea experiment processing showed that the seabed layered structure and geoacoustic parameters can be accurately determined by this method. The root mean square between the vertical waveguide characteristic impedance and the measured impedance is 0.38dB, and the inversion results accurately represent the seabed characteristics in the experimental sea area.

Vertical dynamic response of pipe pile embedded in unsaturated soil based on fractional‐order standard linear solid model and Rayleigh‐Love rod model

AbstractConsidering the flow‐independent viscosity of soil skeleton and the lateral inertia effect of pipe pile, the vertical dynamic behavior of a pipe pile embedded in unsaturated soil is investigated in this work when the pipe pile is subjected to the vertical dynamic loading. In order to model this problem, the fractional‐order standard linear solid (FSLS) model is introduced to characterize the flow‐independent viscosity of the soil skeleton, the Rayleigh‐Love rod model is employed to specify the lateral inertia effect of pipe pile, while both vertical and radial soil displacement are entirely considered. The analytical solution of the pipe pile complex impedance is obtained through the rigorous theoretical derivation. Numerical results with known analytical solution are finally presented to discuss the influence of the model parameters for the FSLS model, lateral inertia effect and geometrical characteristic for the pipe pile, and saturation degree and intrinsic permeability for the unsaturated soil on the vertical complex impedance of the pipe pile. The main results indicate that enlarging the fractional‐order index, raising the strain relaxation time, or shortening the stress relaxation time will reduce the oscillation amplitude and natural frequency for the dynamic stiffness and damping of the pipe pile but will improve their mean value. The lateral inertia effect of pipe pile has effect on its complex impedance only in the high‐frequency region. The outer and inner radii of pipe pile, pile length, soil saturation degree, and soil intrinsic permeability are highly correlated with the pipe pile complex impedance.

Vertical dynamic impedance of a sand-filled nodular pile in saturated soil

A new type of composite pile called a sand-filled nodular (SFN) pile has been increasingly used as a foundation element in the southeast coastal region of China. This paper derives an analytical solution of the vertical dynamic impedance of a SFN pile in saturated soil. The accuracy of the derived solution was verified by degenerating the SFN pile into a general pipe pile. The feasibility of incorporating the thin-layer assumption in Biot theory was then examined and the results suggested that for soft soils with shear modulus less than 5 MPa, the thin-layer solution is sufficiently accurate to estimate the vertical dynamic impedance of a pile in saturated soil. A parametric study was further conducted to provide insight into the influences of pile geometries and sand fill properties on the vertical dynamic impedance of the pile. The results indicated that the pile geometries have considerable influence on the vertical dynamic impedance of SFN piles where pile rib length plays a most significant role.

Dynamic response of driven end-bearing piles and a pile group in soft clay: an experimental validation study

This paper presents novel measurement data on the dynamic soil–structure interaction of an end-bearing pile foundation. The purpose is to assess the ability to predict the foundation impedances based on the small-strain properties of the soil obtained from site investigations. Measurements were performed in two stages of construction, allowing to assess interaction between the piles through the soil. First, single pile impedances and interaction factors between the piles were experimentally obtained for the four piles when they were free to move at the surface. Second, the impedances of the square pile group were measured after casting a concrete pile cap. The piles were additionally instrumented with accelerometers at depth along the centerline of each pile, allowing to illustrate the global behaviour of the piles within the soil. Numerical predictions based solely on information of the small-strain soil properties obtained from extensive site investigations are compared to the experimental results. The impedances of the individual piles are overestimated compared to the measurements, while the interaction factors show a better agreement. The pile group impedances are better captured than the individual ones, using the same soil model. The pile–soil–pile interaction is clearly manifested in the experimental results by pronounced peaks in the pile group vertical impedance, validating results from previous numerical studies.

Impedance functions of rigid rectangular foundations bonded on layered transversely isotropic elastic/poroelastic half-space

This paper explores a complete set of impedance functions including vertical, torsional, horizontal, rocking, and coupling impedances for a surface rigid rectangular foundation bonded on a multilayered transversely isotropic half-space composed of alternatively elastic and poroelastic layers with the use of boundary element method. The slow convergence issue of Green's functions in numerical evaluation is remedied by a simple asymptotic approach presented in this paper. To evaluate the impedances accurately and efficiently, new finite elements namely exponentially-gradient elements are employed to consider the singular behavior of tractions that happens at the edges and corners of the foundation. The validity and accuracy of the solutions are verified by comparing the results with some simpler existing cases. The impedance functions are presented for different aspect ratios of the foundation to be applicable for a variety of structures. The effects of anisotropy, inhomogeneity, layer thickness, underground water level, and soil damping are assessed.

Vertical Dynamic Impedance of a Viscoelastic Pile in Arbitrarily Layered Soil Based on the Fictitious Soil Pile Model

The vertical vibration of a viscoelastic pile immersed in arbitrarily layered soil is investigated by taking the interaction among pile, pile surrounding soil (PSS) and pile end soil (PES) into account. Firstly, considering both the stratification and stress wave effect of soil, a mathematical model of the pile–soil system is established based on the fictitious soil pile (FSP) model. Then, utilizing the impedance function transfer method and Laplace transform technique, the analytical solutions of the vertical dynamic impedance of pile are derived in the frequency domain. The analytical solutions are validated by comparing them with other existing solutions. Finally, a parametric study is put forward to investigate the properties of PES on the vertical dynamic impedance of pile. The results reveal that the properties of PES have a significant effect on the vertical dynamic impedance of pile, but there is a critical influence thickness for this effect. For the cases of the PES thickness exceeding the critical influence thickness, further increase of PES thickness will not affect the dynamic behavior of the pile–soil system.

Comparing ventilation modes by electrical impedance segmentography in ventilated children

Electrical impedance segmentography offers a new radiation-free possibility of continuous bedside ventilation monitoring. The aim of this study was to evaluate the efficacy and reproducibility of this bedside tool by comparing synchronized intermittent mandatory ventilation (SIMV) with neurally adjusted ventilatory assist (NAVA) in critically-ill children. In this prospective randomized case–control crossover trial in a pediatric intensive care unit of a tertiary center, including eight mechanically-ventilated children, four sequences of two different ventilation modes were consecutively applied. All children were randomized into two groups; starting on NAVA or SIMV. During ventilation, electric impedance segmentography measurements were recorded. The relative difference of vertical impedance between both ventilatory modes was measured (median 0.52, IQR 0–0.87). These differences in left apical lung segments were present during the first (median 0.58, IQR 0–0.89, p = 0.04) and second crossover (median 0.50, IQR 0–0.88, p = 0.05) as well as across total impedance (0.52 IQR 0–0.87; p = 0.002). During NAVA children showed a shift of impedance towards caudal lung segments, compared to SIMV. Electrical impedance segmentography enables dynamic monitoring of transthoracic impedance. The immediate benefit of personalized ventilatory strategies can be seen when using this simple-to-apply bedside tool for measuring lung impedance.

Tune shift due to the quadrupolar resistive-wall impedance of an elliptical beam pipe

For a beam pipe with an elliptical cross section, the quadrupolar impedance will be produced. During multibunch operation in a circular accelerator, the complex mode frequency shift is sensitive to the long range wake, which will be further enhanced by the quadrupolar component. In order to get more accurate estimation of the quadrupolar impedance and its induced tune shift, materials outside the beam pipe should be considered and impedance model for multilayer elliptical beam pipe is required. In this paper, the horizontal and vertical quadrupolar impedances, as well as the form factors, are derived for an elliptical beam pipe of infinite thickness. The impedances of a multilayer elliptical beam pipe are expressed as the product of the form factors and the impedances of the multilayer cylindrical beam pipe, in which both the conductivity and the permeability of different layers with finite thickness are considered. On the other hand, the complex incoherent frequency shift due to the quadrupolar impedance is derived from beam oscillation equations, which shows that the direct current (DC) value of the quadrupolar impedance dominates the frequency shift. Numerical studies indicate that the incoherent tune shift due to the quadrupolar resistive-wall impedance is sensitive to the permeability of the magnetic material surrounding the beam pipe. In addition, the occupation of the magnets around the accelerator should be considered when evaluating the incoherent tune shifts. Meanwhile, the metallic coating with constant conductivity on the inner surface of the beam pipe tends to have negligible contribution to the tune shift, in contrary to the distinct contribution found to the coherent tune shift.

Vertical dynamic impedance of end‐bearing pile groups embedded in homogeneous unsaturated soils

AbstractAlthough soil is typically an unsaturated (three‐phase) medium, previous studies on the dynamic impedance of pile groups primarily considered the piles embedded in either the single‐phase or fully saturated (two‐phase) soils. In this work, the dynamic impedance of end‐bearing pile groups embedded in homogeneous unsaturated soil subject to a vertical time‐harmonic load is analytically obtained. The soil is modeled as a three‐dimensional axisymmetric continuum, and both the radial and vertical displacements as well as the influence of the saturation degree on the soil's dynamic shear modulus are considered. The governing equations of vibrating unsaturated soil are uncoupled by virtue of the potential function and operator decomposition methods. The attenuation function of soil displacement, surrounding soil resistance factor, and vertical dynamic impedance of a single pile are derived from the pile−soil compatibility conditions. Pile‐to‐pile dynamic interaction factors are then derived and used, along with the superposition principle, to find the vertical dynamic impedance of end‐bearing pile groups in the frequency domain. The proposed analytical solution is verified by comparison with two benchmark solutions. Finally, the influence of various parameters on the dynamic response of end‐bearing pile groups is determined.

The dynamic contact of a viscoelastic coated half-plane under a rigid flat punch

This paper investigates the dynamic contact response of a viscoelastic coated half-plane under a forced rigid punch. This punch, acting on the coating surface, is subjected to a concentrated vertical harmonic force. The coating and half-plane are assumed as viscoelastic materials which can be described by the linear hysteretic damping model. Using the Fourier integral transform technique and the asymptotic method, the dynamic contact problem is reduced to a Cauchy singular integral equation. By using appropriate numerical method, the dynamic contact stress and vertical impedance for the flat punch are calculated. It is found that the dynamic contact behaviors are not only affected by the external excitation frequency but also dependent on the material properties of the coated half-plane.