Predictions of the modified Biot-Attenborough model for the dependence of phase velocity on porosity in cancellous bone

The modified Biot–Attenborough (MBA) model for acoustic wave propagation in porous media has been found useful to predict wave properties in cancellous bone. The present study is aimed at applying the MBA model to predict the dependence of phase velocity on porosity in cancellous bone. The MBA model predicts a phase velocity that decreases nonlinearly with porosity. The optimum values for input parameters of the MBA model, such as compressional speed c_m of solid bone and phase velocity parameter s₂, were determined by comparing the predictions with previously published measurements in human calcaneus and bovine cancellous bone. The value of the phase velocity parameter s₂ = 1.23 was obtained by curve fitting to the experimental data for 53 human calcaneus samples only, assuming a compressional speed c_m = 2500 m/s of solid bone. The root-mean-square error (RMSE) of the curve fit was 15.3 m/s. The optimized value of s₂ for all 75 cancellous bone samples including 22 bovine samples was 1.42 with a value of 55 m/s for the RMSE of the curve fit. The latter fit was obtained by using of a value of c_m = 3200 m/s. Although the MBA model relies on the empirical parameters determined from experimental data, it is expected that the model can be usefully employed as a practical tool in the field of clinical ultrasonic bone assessment.     

无限流体中孔隙介质圆柱周向导波的传播特性

为研究无限大流体约束的孔隙圆柱中周向导波的传播规律,分析孔隙参数对导波传播特性的影响,建立了无限流体中孔隙介质圆柱的理论模型,利用孔隙介质弹性波动理论,建立了周向导波频散方程,通过数值模拟计算得到无限流体中孔隙介质圆柱的频散曲线,探讨了圆柱半径和孔隙参数对导波传播特性的影响,并对导波的衰减特性进行了分析;通过数值计算,得到了周向导波的时域波形,讨论了孔隙参数对波形的影响.结果表明,孔隙介质圆柱半径的改变影响圆柱尺度,孔隙度的改变影响孔隙介质中体声波的波速,都对周向导波频散曲线产生一定的影响,所得到的频散曲线特征及衰减曲线与时域波形吻合.研究结果对开展无限流体中孔隙介质圆柱的超声无损评价提供了一定的理论参考.     

用非饱和三相孔弹模型研究浅层土壤中地震波的传播特性

研究浅层土壤中声波耦合的地震波的传播特性, 用于声波探雷技术的机理分析. 根据浅层土壤具有孔隙度和可压缩性的特点, 利用非饱和三相孔隙介质中的地震波模型, 研究了土壤孔隙度、含水饱和度等参数对地震波传播特性的影响. 计算结果显示: 在给定的参数条件下, 地震波的传播速度和衰减系数均随频率的增加而增加; 纵波的传播速度随孔隙度的增加而减小, 横波的传播速度随孔隙度的增加而增加; 地震波的传播特性随含水饱和度的增加变化比较复杂. 通过对计算结果与已发表实验结果的比较分析, 讨论了解析方法的可行性, 为声-地震耦合机理及其在声波探雷研究中的应用提供了一定的理论基础. 关键词： 声-地震耦合 地震波 孔隙度 声波探雷     

基于动电效应的震电测井方法研究进展*

与双电层和孔隙流体渗流有关的声波-电磁场耦合效应(动电耦合波)在油气储层勘探、地震电磁场等领域有着潜在应用价值。该文简述动电耦合波在理论模型以及井孔动电耦合波的实验测量、模拟计算方面的研究进展,并对油气储层测井领域进一步的动电耦合波研究进行了展望。基于动电信号的探测方法同时接收声波和电磁场两类信号,可避免单一类别信号方法的不足。实验获得了岩心的动电耦合系数,但其表征的孔隙岩石物理性质还有待进一步认识。基于耦合控制方程,开展了震电波场的计算和分析。结果表明,声源激发后,可接收到伴随声波的电磁信号和早于声波的电磁首波。这两类信号都既对影响声波特性的岩石模量、孔隙度和渗透率等参数敏感,又与电导率等岩石电学性质密切相关。非饱和岩石动电耦合波理论和基于动电耦合波的参数反演方法等问题有待进一步研究。     

多孔介质中卡森流体的分形分析

研究了非牛顿流体中的卡森流体在多孔介质中的流动特性.基于服从分形分布的弯曲毛细管束模型,运用分形几何理论推导出了该流体在多孔介质中流动的流量、流速、启动压力梯度和有效渗透率的分形解析解.模型中的每一个参数都有明确的物理意义,它将卡森流体在多孔介质中的流动特性与多孔介质的微结构参数有机联系起来.文中给出了卡森流体的流速、启动压力梯度和有效渗透率随着各影响因素的变化趋势,并进行了讨论.所得分形模型可以更深刻地理解卡森流体在多孔介质中流动的内在物理机理. 关键词： 多孔介质 卡森流体 分形     

海底沉积物压缩波速度与切变波速度的关系

基于连续介质假设,根据无吸收各向同性弹性介质通用方程分析沉积物声波传播关系,提出应用弹性结构分布因子表达的声速通用模型(GMSS,General Model of Sound Speed)分析海底沉积物的声速特性;通过研究Willey时间平均模型、Wood方程、Gassmann方程、Buckingham模型、Biot-Stoll模型和EDFM模型,可以表述成GMSS通用模型中的弹性结构分布因子的具体表达形式,得出GMSS通用模型在解释压缩波速度和切变波速度特性上具有一致性的特点。GMSS通用模型具有弹性结构分布因子、孔隙度、孔隙海水的等效密度和等效弹性模量、固相颗粒的等效密度、固相颗粒的等效体积弹性模量和等效切变弹性模量共7个参数,为研究海底沉积物压缩波和切变波速度提供了一种模型简单、参数少、通用性强的方法。但也需要从物理结构上以及应力应变关系上开展更为深入的分析和探寻GMSS模型的物理意义和参数测量的方法。      

A new empirical model for the acoustic properties of loose granular media

This paper examines physical parameters of loose granular mixes and their empirical relations to the acoustic performance of these mixes. In this work a new classification of granular media has been proposed which is related to the characteristic particle dimension and the specific density of the grain base. It has been shown that this classification is a useful characteristic for rapid evaluation of the acoustic performance of loose granular mixes. The characteristic impedance and propagation constant have been measured for a representative selection of grain mixes and used to develop a new empirical model. This model relates the above acoustic characteristics to the characteristic particle dimension, porosity, tortuosity and specific density of the grain base, which are routinely measurable parameters. A very good agreement with the experimental data is illustrated in the frequency range of 250-4000 Hz for materials with the grain base of 0.4-3.5 mm and specific densities between 200 and 1200 kg/m³. Unlike many theoretical models for the prediction of the acoustic properties of porous media, the proposed expressions do not involve any special functions of complex argument, empirical shape factors or sophisticated characteristics of porous structure. These are practical enough to be of interest to acoustic and noise control engineers and material manufacturers.     

梯度穿缝型双孔隙率多孔材料的吸声性能

在传统单一孔隙率多孔材料中引入宏观尺度的周期性梯度穿缝结构设计,构造出梯度穿缝型双孔隙率多孔材料,其包含多孔材料基体微孔尺度与穿缝尺度两个尺度。采用分层等效的理论建模方法,将复杂梯度渐变问题变为多层均匀等效层叠加问题。针对不同特征尺寸的多孔材料薄层,分别采用低、高两种渗透率对比度双孔隙率理论,给出了其等效密度和动态压缩系数,再应用传递矩阵方法得到了相邻薄层之间的声压和质点速度传递关系并求得其表面声阻抗,从而建立了梯度穿缝型双孔隙率多孔材料的吸声理论模型。发展了多尺度材料声学有限元数值模型,在所考虑的100~3000 Hz频段范围内数值模拟结果完全吻合理论模型结果。理论与模拟分析了多尺度结构参数对双孔隙率多孔材料吸声性能的影响,结果表明引入多尺度梯度结构设计能够显著提高单一孔隙率多孔材料的吸声性能,且穿缝尺度比穿缝梯度影响更为显著;精细数值模拟获得的声压和能量密度分布云图揭示了多尺度结构设计的吸声增强机制。该工作可用于指导双孔隙率多孔材料的多尺度结构设计,从而提高多孔材料的中低频吸声性能。      

含少量气泡流体饱和孔隙介质中的弹性波

考虑孔隙流体中含有少量气泡,且气泡在声波作用下线性振动,研究声波在这种孔隙介质中的传播特性.本文先由流体质量守恒方程和孔隙度微分与流体压力微分的关系推导出了含有气泡形式的渗流连续性方程;在处理渗流连续性方程中的气体体积分数时间导数时,应用Commander气泡线性振动理论导出气体体积分数时间导数与流体压强时间导数的关系,进而得到了修正的Biot形式的渗流连续性方程;最后结合Biot动力学方程求得了含气泡形式的位移场方程,便可得到两类纵波及一类横波的声学特性.通过对快、慢纵波的频散、衰减及两类波引起的流体位移与固体位移关系的考察,发现少量气泡的存在对快纵波和慢纵波的传播特性影响较大.     

二维多孔热密封材料的有效导热系数模拟

本文对于二维多孔热密封材料的有效导热系数模拟提出一种简单有效的方法,它可以模拟介于固相连续和固相不连续之间的任何形式的孔隙分布结构,通过类比多孔渗流模型得出一种相关系数,再根据热阻串并联的关系计算四种可计算模型的有效导热系数,通过相关系数得到具体模型的有效导热系数。本文的模拟方法可以控制孔隙率、孔径、孔隙分布、温度等影响有效导热系数的重要参数,考虑了辐射的影响,而且模拟简单,计算快速,模拟结果与文献中实验的结果相比较能很好的吻合,验证了本文方法的正确性。     

Multi-levels inverse identification of physical parameters of porous materials

The identification of the physical parameters of porous materials presents an important field of research, in which many identification methods are developed. One of those methods is presented in this paper. In fact, a multi-levels inverse identification method is developed in order to estimate these physical parameters. The proposed method is based on the minimization of the difference between a reference acoustic absorption coefficient of a porous material and the computed values. The minimization is done according three levels, in each level an acoustic model of porous material is used to evaluate one or two parameters. Finally, the five physical parameters of the porous materials are deduced. The proposed method is applied to Polyurethane foam material. The obtained results are satisfying with small values of errors and with estimated acoustic absorption coefficient reaching the reference one.     

Sound absorption of cellular metals with semiopen cells

A combined experimental and theoretical study is presented for the feasibility of using aluminum foams with semiopen cells for sound-absorption applications. The foams are processed via negative-pressure infiltration, using a preform consisting of water-soluble spherical particles. An analytical model is developed to quantify the dependence of pore connectivity on processing parameters, including infiltration pressure, particle size, wetting angle, and surface tension of molten alloy. Normal sound-absorption coefficient and static flow resistance are measured for samples having different porosity, pore size, and pore opening. A theory is developed for idealized semiopen metallic foams, with a regular hexagonal hollow prism having one circular aperture on each of its eight surfaces as the unit cell. The theory is built upon the acoustic impedance of the circular apertures (orifices) and cylindrical cavities due to viscous effects, and the principle of electroacoustic analogy. The predicted sound-absorption coefficients are compared with those measured. To help select processing parameters for producing semiopen metallic foams with desirable sound-absorbing properties, emphasis is placed on revealing the correlation between sound absorption and morphological parameters such as pore size, pore opening, and porosity.     

Elastic waves in non-Newtonian (Maxwell) fluid-saturated porous media

This paper studies the elastic waves in non-Newtonian (Maxwell) fluid-saturated porous media with the nonzero boundary slip velocity for pore size distribution. The coefficient bF_m(ω) that measures the deviation from Poiseuille flow friction in such media is presented. Based on this coefficient, we investigate the properties of elastic waves by calculating their phase velocities and attenuation coefficients as functions of frequency and the behaviour of the dynamic permeability. The study shows that the pore size distribution removes oscillations in all physical quantities in the non-Newtonian regime. Consideration of the nonzero boundary slip effect in non-Newtonian (Maxwell) fluid-saturated porous media results in (a) an overall increase of the dynamic permeability, (b) an increase of phase velocities of fast Biot waves and shear waves except in the low frequency domain and an overall increase of phase velocity of slow Biot waves and (c) an overall increase of the attenuation of three Biot waves in the intermediate frequency domain except in the deeply non-Newtonian regime. The study also shows that the attenuation coefficient of slow Biot waves is small in the deeply non-Newtonian regime at higher frequency, which encourages us to detect slow Biot waves in oil-saturated porous rock.     

Experimental measurements of acoustical properties of snow and inverse characterization of its geometrical parameters

Snow is a sound absorbing porous sintered material composed of solid matrix of ice skeleton with air (+water vapour) saturated pores. Investigation of snow acoustic properties is useful to understand the interaction between snow structure and sound waves, which can be further used to devise non-destructive way for exploring physical (non-acoustic) properties of snow. The present paper discusses the experimental measurements of various acoustical properties of snow such as acoustic absorption coefficient, surface impedance and transmission losses across different snow samples, followed by inverse characterization of different geometrical parameters of snow. The snow samples were extracted from a natural snowpack and transported to a nearby controlled environmental facility at Patsio, located in the Great Himalayan range of India. An impedance tube system (ITS), working in the frequency range 63–6300 Hz, was used for acoustic measurements of these snow samples. The acoustic behaviour of snow was observed strongly dependent upon the incident acoustic frequency; for frequencies smaller than 1 kHz, the average acoustic absorption coefficient was found below than 0.4, however, for the frequencies more than 1 kHz it was found to be 0.85. The average acoustic transmission loss was observed from 1.45 dB cm⁻¹ to 3.77 dB cm⁻¹ for the entire frequency range. The real and imaginary components of normalized surface impedance of snow samples varied from 0.02 to 7.77 and −6.05 to 5.69, respectively. Further, the measured acoustic properties of snow were used for inverse characterization of non-acoustic geometrical parameters such as porosity, flow resistivity, tortuosity, viscous and thermal characteristic lengths using the equivalent fluid model proposed by Johnson, Champoux and Allard (JCA). Acoustically derived porosity and flow resistivity were also compared with experimentally measured values and good agreement was observed between them.     

Elastic waves in non-Newtonian (Maxwell) fluid-saturated porous media

Abstract

This paper studies the elastic waves in non-Newtonian (Maxwell) fluid-saturated porous media with the nonzero boundary slip velocity for pore size distribution. The coefficient bF _m (ω) that measures the deviation from Poiseuille flow friction in such media is presented. Based on this coefficient, we investigate the properties of elastic waves by calculating their phase velocities and attenuation coefficients as functions of frequency and the behaviour of the dynamic permeability. The study shows that the pore size distribution removes oscillations in all physical quantities in the non-Newtonian regime. Consideration of the nonzero boundary slip effect in non-Newtonian (Maxwell) fluid-saturated porous media results in (a) an overall increase of the dynamic permeability, (b) an increase of phase velocities of fast Biot waves and shear waves except in the low frequency domain and an overall increase of phase velocity of slow Biot waves and (c) an overall increase of the attenuation of three Biot waves in the intermediate frequency domain except in the deeply non-Newtonian regime. The study also shows that the attenuation coefficient of slow Biot waves is small in the deeply non-Newtonian regime at higher frequency, which encourages us to detect slow Biot waves in oil-saturated porous rock.     

超声纵波在孔隙砂岩中的传播特性实验*

为了深入研究不同入射频率下超声波纵波在砂岩中的传播特性,以灰、红、褐砂岩为研究对象,开展了基于50 k Hz、100 kHz、200 kHz、500 kHz和1000 kHz入射频率的超声波纵波测试。提取纵波波速、幅值衰减系数、主频幅值、波形能量这些声学参数,结合入射频率和砂岩孔隙率进行传播特性的相关性分析。结果表明,在3种砂岩中,纵波波速随入射频率增大呈非线性增长趋势,砂岩种类不同,波速增长规律也不同;波形能量和主频幅值随入射频率呈指数关系降低;灰、红砂岩纵波波速随孔隙率越大,下降速率越大,褐砂岩在同级孔隙率下波速差异性明显。建立了基于3种砂岩的入射频率和幅值衰减系数的回归方程;基于200 kHz的入射频率,建立了砂岩孔隙率于波形能量的回归方程,实际测试中建议采用200 kHz作为入射频率,可较好兼顾检测的灵敏度和探测距离。研究成果为建立声学参数与砂岩抗压强度之间的内在联系提供了更多数据支撑,为实际物探测试中超声波入射频率的选择提供参考。     

The sound speed and attenuation in loose and consolidated granular formulations of high alumina cements

Clinkers of high alumina cements are separated into three granular formulations with particle sizes in the range 0.6-0.71 mm, 0.71-1.18 mm and greater than 1.18 mm. These are used to manufacture consolidated samples of porous concrete in an autoclave. The acoustic and microscopic properties of loose and consolidated porous samples of concrete are investigated using both experimental methods and mathematical modelling. Values of porosity, flow resistivity, tortuosity and parameters of the pore size distribution are determined and used to predict closely the sound speed, acoustic attenuation and normal incidence absorption coefficient of these materials. It is shown that high alumina cements do not require additional binders for consolidation and that the structural bonds in these cements are developed quickly between individual clinkers in the presence of water. The hydration product build-up during the consolidation process is insignificant which ensures good acoustic performance of the consolidated samples resulting from a sufficient proportion of the open pores. The value of porosity in the consolidated samples was found to be around 40%, which is close to that measured in some commercial acoustic absorbers. This work provides a foundation for the development of acoustically efficient and structurally robust materials, which can be integrated in environmentally sustainable concrete and masonry structures.     

Theoretical and experimental study of the ultrasonic attenuation in bovine cancellous bone

In this study a theoretical approach for the estimation of ultrasonic attenuation is proposed. The approach combines two models which take into account both absorption and scattering. Attenuation due to absorption is studied by using the Biot’s analytical model whereas that due to scattering is described by means of a generalized weak scattering model which is formulated for binary mixtures. The scattering model takes account of the density fluctuation of the porous medium in addition to the propagation velocity fluctuation. For the calculation of the attenuation coefficient due to absorption, experimental values have been used to link size of pores to porosity. The theoretical results have been compared with experimental data obtained on bovine cancellous bone samples filled with water. Using an immersion acoustic transmission method, the ultrasonic attenuation has been measured at a frequency range between 0.1 and 1.0 MHz for 12 bovine cancellous bone samples with a porosity range between 40% and 70%. The prediction of attenuation with this model appears to correspond more closely to its experimentally observed behavior. This study indicates that scattering is the predominant mechanism which is responsible for attenuation in trabecular bone. Furthermore, it shows that the density fluctuations contribute significantly to the phenomenon of attenuation and cannot thus be neglected.     

含三聚氰胺多孔材料分层复合介质吸声特性*

三聚氰胺泡沫材料是一种具有高开孔率的多孔材料,具备优良的吸音、防火隔热及环保性能,可以作为吸声材料与弹性板、空腔介质形成复合结构,在建筑、航空、交通工具等工程领域有广泛的应用。该文基于Biot理论和分层介质在交界面处的不同边界条件,建立非均匀复合介质背衬刚性壁面结构的理论声学模型,详细分析了多孔材料布局对复合结构吸声特性的影响。该文理论模型计算的结果与阻抗实验得到的垂直入射吸声系数基本一致,验证了理论模型的正确性。结果表明:在多孔材料前面增加空气层可以改善高频吸声特性;在多孔材料后面增加空气层可以改善复合结构低频吸声特性。通过合理配置多孔材料,可以在应用需求频段上达到满意的吸声效果。     

二维孔隙裂隙双重介质逾渗规律研究

在孔隙介质逾渗理论的基础上，将另外一个非常重要的渗透通道——裂隙引入到介质的逾渗研究中，提出了更为普遍的孔隙裂隙双重介质的逾渗研究方法.通过对二维平面孔隙裂隙双重介质的数值计算，得到了孔隙裂隙双重介质三个重要参数：孔隙率，裂隙分形维数、裂隙数量分布初值与逾渗概率的关系，给出了孔隙裂隙双重介质逾渗阈值的数学表达式，揭示了孔隙裂隙双重介质的逾渗规律. 关键词： 孔隙 裂隙 双重介质 逾渗 逾渗阈值