振动场中散体的动力效应与分形特征研究
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摘要
论文对振动场中散体的动力效应和分形特征展开了系统的研究。研究工作结合国家自然科学基金资助项目“基于散体媒介的弹性波传播和作用机理研究”，以振动作用下散体的动力效应(尤其是波动效应)为线索，对散体的动力特性、液化特征、波动规律、振动助流、振动减阻、振动助滤、分形特征等展开详细全面的研究。论文的主要研究工作如下：
(1)利用DSA-1型振动直剪仪，对散体的动态参数(动抗剪强度τ，黏聚力C，内摩擦角φ)进行测试：并试验研究了振幅、振频、水分、激振方式、振动速度、颗粒尺寸、散体的流动性等对动抗剪强度的影响。
(2)在试验的基础上，对散体的动力特性展开研究。
分析了散体在动荷载作用下的动应力-应变关系，并对散体动强度的有关性质及与循环次数的关系进行详细阐述。建立散体的黏滞阻尼力学模型来研究激励响应。并在此基础上给出了散体激励响应的运动方程和简谐激励作用下的振型-位移近似表达式和坐标响应的稳态效应解。利用逐步积分算法求解了散体激励响应的位移、速度和加速度的递推关系矩阵，并给出了计算流程图和算例。
(3)利用波动理论，对波在弹性、黏弹性及流动散体介质中的传播和耗散规律进行了分析，并给出了振动助流机理。
1) 当应变值ε＜10~(-4)时，认为散体介质的变形为弹性变形。分析给出了各向同性散体介质中弹性波的波动方程、传播速度和波动能量的表达式，和横观各向同性介质中的弹性波的波动方程和能量透过系数表达式，并试验验证了能量衰减与分层介质密度有关。此外，分析了瑞利波及勒夫波的传播特性。
2) 从黏弹性角度来分析松散岩土介质中波的相关规律，给出了三种黏弹性模型及其本构方程：Maxwell模型、Kelvin模型及标准线性固体模型。分析并给出了小变形条件下黏弹性介质中的波动方程、传播向量和衰减向量的复数形式表达式、以及纵波和横波的衰减系数复数形式表达式。
3) 首次利用波动理论解释了流动场中散体的振动助流机理。视流动中的散体为弱横观各向同性介质，给出了P波、SH波和SV波的相速度表达式，分析了它们在流动散体介质中的传播特点。由波的传播特点得出：在振幅和频率较小的情况下，振波对散体的流动性影响不大；当振幅和频率逐渐增加时，椭球体的偏心率减小，散体间的黏性阻力和内摩擦力降低，散体的松散系数增加，抗剪强度降低，使散体具有更好的流动性。试验结果也印证了此结论的正确性。
(4) 对饱和散体的振动液化进行了研究。
首先对散体振动液化的力学机理进行了详细的分析和阐述。然后详细研究了饱和散体中的波的传播规律，分析给出波在无耗散情况下的势矢量方程和三种体波的速度表达式，以及具有耗散情形的势矢量的普遍方程式和P波与S波的衰减系数。并利用波动理论和试验结果，详细分析了振动过程中饱和散体介质的二种体波的传播对孔隙水和颗粒的作用情况，首次用波动理论揭示了孔隙水压力迅速升高的原因和饱和散体液化的机理。此外，还对散体液化后的密实现象、液化的影响因素和液化势的判断进行了分析研究。
(5)利用液固两相流理论和波动理论，对高浓度浆体的振动减阻机理进行研究。
分析了高浓度浆体中应力波的反射与透射规律，并利用多重网格法分析了振动波对层流流态转捩的影响。认为应力波在管道垂直方向上传播时逐渐衰减且对层流附面层有较大影响，使边壁浆体的速度梯度减小，并导致边壁剪切应力的降低：同时使附面层的厚度加大，中性稳定雷诺数增加，阻止流态的转捩。应力波的作用以及附面层的改变，最终导致输送阻力的降低。创造性地解释了高浓度浆体管道的振动减阻机理。
(6)通过试验对高湿度细粒散体振动助滤进行了详细研究，并探讨振动助滤的机理。
1)通过真空施振助滤与真空过滤的对比试验，以及加压施振助滤与加压过滤的对比试验可以看出，对于高湿度细粒散体，加振都具有较大的助滤效果，可以降低平均含湿率为5～9％。而散体浓度、振动频率
博士学位论文
和振动方式对试验结果影响很小，而且，同种情况下加压比真空的过滤效果也会稍好一些。此外，寻求合
适浓度的絮凝剂也是可以适当降低含湿率的。
2)由于振动作用的影响，导致散体颗粒的移动和活化，以及散体介质的液化，使固体颗粒将向滤饼表
面移动，使紧缩活动减弱，孔隙率增大，滤饼比阻减小。因此使液体更容易被挤压出来，从而达到助滤的
目的。而絮凝剂的作用是通过吸附和架桥作用，将不稳定状态的颗粒群或己经凝结的小絮团结合成表观直
径较大的絮团，以利于固液分离。
(7)利用分形几何学，对散粒、孔隙的分形行为、渗流的分形行为、散体振动时的分形行为、散体堆
的自组织行为和饱和散体液化的自组织临界性作系统研究。并利用VisualC一(6.0版本)对这些分形行为
进行计算机模拟。
1)首次完整系统地将分形理论引入到散体动力学的研究之中，分析得出散体粒度的分布、孔隙的分布
和颗粒比表面积都具有分形特征，服从标度律。振动过程中，时间序列、功率谱密度、振动脉冲积分分布，
时间序列的自相关函数均服从幂律关系，具有分形特征。用元胞自动机来模拟一维散体堆的
In this Ph D dissertation, the granular dynamic effect and fractal characteristic under vibration are studied systematically. The research work is supported by the National Natural Science Foundation of China. The principal item is to study on the propagation and mechanism of elastic wave in the granular media. This dissertation focuses on the granular dynamic effect under vibration, especially, the wave effect. The granular dynamic characteristic, liquefaction property, wave law, vibrating aided flow, vibrating drag reduction, vibrating aided filtration and fractal behavior are studied in detail and in depth. The following are the main research findings:
(1) Utilizing the DSA-1 type vibration direct shearing apparatus, the granular dynamic parameters, such as the dynamic shearing strength τ, the cohesion C, and the angle of internal friction ψ have been identified. Moreover, the experimental researches on the factors that will affect the granular dynamic shearing strength, such as the amplitude, the frequency, the moisture content, the excitation method, the vibration velocity, the granular size and the granular flowability, are well experimented.
(2) Based on the experiments, the granular dynamic characteristic is studied.
The granular dynamic stress-strain relation under the dynamic load is analyzed. The related properties of the granular dynamic strength and the relation between the dynamic strength and cyclical index are described in detail. A granular mechanical model of viscosity and damping is given. On the basis of it the motion equation of the excited response of the granules is established, and an approximate expression of vibrating-displacement by harmonic excitation and the steady effect solution of the coordinate response is deduced. By the stepwise integration method, the recursion relation matrix of the displacement, the velocity and the acceleration of the excited response of the granules are resolved, and a calculating flow chart and a calculating example are also given.
(3) By the use of the wave theory, the characteristics of the wave propagation and their dissipation in the elastic granules, the viscoelastic granules and the flowing granules are analyzed. Then the mechanism of the vibrating aided flow is given.
1) The deformation of granular materials would be the elastic deformation when the strain number e < 10-4.
The expressions of wave equation, propagation velocity and wave energy in the elastic homogenous and anisotropic media have been analyzed. At the same time, an expression of energy passing coefficient was deduced, and the conducted experiment has proved that the attenuation of wave has a relation to the density of layered media. The propagation characteristics of Rayleigh and Love waves are also analyzed.
2) In terms of viscoelasticity the related theory in the granular media is analyzed. Three kinds of viscoelasticity models were given: Maxwell model, Kelvin model and standard linear model of solid. The wave equation, the complex number expressions of propagation and attenuation vectors, and the attenuation coefficient
III
expressions of longitudinal and transverse waves under the conditions of small distortion have been deduced.
3) The flowing granular media is regarded as a weak transverse isotropic media, and the phase velocity expressions of waves P, SH and SV are deduced. The propagation specialties of waves in the flowing granular media have been analyzed. It is the first time that the mechanism of the vibrating aided flow is explained creatively as depicted in this Ph D dissertation.
(4) The vibrating liquefaction of saturated granules is studied.
Firstly, the mechanism of liquefaction is described in detail. Then, the characteristic of wave propagation in saturated granular media is studied in depth. The potential vector equation and the velocity expressions of three kinds of body waves under the conditions of no dissipation, as well as the general equation of potential vector and the attenuation coefficients of waves P and S under the conditions of dissip
(1)利用DSA-1型振动直剪仪，对散体的动态参数(动抗剪强度τ，黏聚力C，内摩擦角φ)进行测试：并试验研究了振幅、振频、水分、激振方式、振动速度、颗粒尺寸、散体的流动性等对动抗剪强度的影响。
(2)在试验的基础上，对散体的动力特性展开研究。
分析了散体在动荷载作用下的动应力-应变关系，并对散体动强度的有关性质及与循环次数的关系进行详细阐述。建立散体的黏滞阻尼力学模型来研究激励响应。并在此基础上给出了散体激励响应的运动方程和简谐激励作用下的振型-位移近似表达式和坐标响应的稳态效应解。利用逐步积分算法求解了散体激励响应的位移、速度和加速度的递推关系矩阵，并给出了计算流程图和算例。
(3)利用波动理论，对波在弹性、黏弹性及流动散体介质中的传播和耗散规律进行了分析，并给出了振动助流机理。
1) 当应变值ε＜10~(-4)时，认为散体介质的变形为弹性变形。分析给出了各向同性散体介质中弹性波的波动方程、传播速度和波动能量的表达式，和横观各向同性介质中的弹性波的波动方程和能量透过系数表达式，并试验验证了能量衰减与分层介质密度有关。此外，分析了瑞利波及勒夫波的传播特性。
2) 从黏弹性角度来分析松散岩土介质中波的相关规律，给出了三种黏弹性模型及其本构方程：Maxwell模型、Kelvin模型及标准线性固体模型。分析并给出了小变形条件下黏弹性介质中的波动方程、传播向量和衰减向量的复数形式表达式、以及纵波和横波的衰减系数复数形式表达式。
3) 首次利用波动理论解释了流动场中散体的振动助流机理。视流动中的散体为弱横观各向同性介质，给出了P波、SH波和SV波的相速度表达式，分析了它们在流动散体介质中的传播特点。由波的传播特点得出：在振幅和频率较小的情况下，振波对散体的流动性影响不大；当振幅和频率逐渐增加时，椭球体的偏心率减小，散体间的黏性阻力和内摩擦力降低，散体的松散系数增加，抗剪强度降低，使散体具有更好的流动性。试验结果也印证了此结论的正确性。
(4) 对饱和散体的振动液化进行了研究。
首先对散体振动液化的力学机理进行了详细的分析和阐述。然后详细研究了饱和散体中的波的传播规律，分析给出波在无耗散情况下的势矢量方程和三种体波的速度表达式，以及具有耗散情形的势矢量的普遍方程式和P波与S波的衰减系数。并利用波动理论和试验结果，详细分析了振动过程中饱和散体介质的二种体波的传播对孔隙水和颗粒的作用情况，首次用波动理论揭示了孔隙水压力迅速升高的原因和饱和散体液化的机理。此外，还对散体液化后的密实现象、液化的影响因素和液化势的判断进行了分析研究。
(5)利用液固两相流理论和波动理论，对高浓度浆体的振动减阻机理进行研究。
分析了高浓度浆体中应力波的反射与透射规律，并利用多重网格法分析了振动波对层流流态转捩的影响。认为应力波在管道垂直方向上传播时逐渐衰减且对层流附面层有较大影响，使边壁浆体的速度梯度减小，并导致边壁剪切应力的降低：同时使附面层的厚度加大，中性稳定雷诺数增加，阻止流态的转捩。应力波的作用以及附面层的改变，最终导致输送阻力的降低。创造性地解释了高浓度浆体管道的振动减阻机理。
(6)通过试验对高湿度细粒散体振动助滤进行了详细研究，并探讨振动助滤的机理。
1)通过真空施振助滤与真空过滤的对比试验，以及加压施振助滤与加压过滤的对比试验可以看出，对于高湿度细粒散体，加振都具有较大的助滤效果，可以降低平均含湿率为5～9％。而散体浓度、振动频率
博士学位论文
和振动方式对试验结果影响很小，而且，同种情况下加压比真空的过滤效果也会稍好一些。此外，寻求合
适浓度的絮凝剂也是可以适当降低含湿率的。
2)由于振动作用的影响，导致散体颗粒的移动和活化，以及散体介质的液化，使固体颗粒将向滤饼表
面移动，使紧缩活动减弱，孔隙率增大，滤饼比阻减小。因此使液体更容易被挤压出来，从而达到助滤的
目的。而絮凝剂的作用是通过吸附和架桥作用，将不稳定状态的颗粒群或己经凝结的小絮团结合成表观直
径较大的絮团，以利于固液分离。
(7)利用分形几何学，对散粒、孔隙的分形行为、渗流的分形行为、散体振动时的分形行为、散体堆
的自组织行为和饱和散体液化的自组织临界性作系统研究。并利用VisualC一(6.0版本)对这些分形行为
进行计算机模拟。
1)首次完整系统地将分形理论引入到散体动力学的研究之中，分析得出散体粒度的分布、孔隙的分布
和颗粒比表面积都具有分形特征，服从标度律。振动过程中，时间序列、功率谱密度、振动脉冲积分分布，
时间序列的自相关函数均服从幂律关系，具有分形特征。用元胞自动机来模拟一维散体堆的
In this Ph D dissertation, the granular dynamic effect and fractal characteristic under vibration are studied systematically. The research work is supported by the National Natural Science Foundation of China. The principal item is to study on the propagation and mechanism of elastic wave in the granular media. This dissertation focuses on the granular dynamic effect under vibration, especially, the wave effect. The granular dynamic characteristic, liquefaction property, wave law, vibrating aided flow, vibrating drag reduction, vibrating aided filtration and fractal behavior are studied in detail and in depth. The following are the main research findings:
(1) Utilizing the DSA-1 type vibration direct shearing apparatus, the granular dynamic parameters, such as the dynamic shearing strength τ, the cohesion C, and the angle of internal friction ψ have been identified. Moreover, the experimental researches on the factors that will affect the granular dynamic shearing strength, such as the amplitude, the frequency, the moisture content, the excitation method, the vibration velocity, the granular size and the granular flowability, are well experimented.
(2) Based on the experiments, the granular dynamic characteristic is studied.
The granular dynamic stress-strain relation under the dynamic load is analyzed. The related properties of the granular dynamic strength and the relation between the dynamic strength and cyclical index are described in detail. A granular mechanical model of viscosity and damping is given. On the basis of it the motion equation of the excited response of the granules is established, and an approximate expression of vibrating-displacement by harmonic excitation and the steady effect solution of the coordinate response is deduced. By the stepwise integration method, the recursion relation matrix of the displacement, the velocity and the acceleration of the excited response of the granules are resolved, and a calculating flow chart and a calculating example are also given.
(3) By the use of the wave theory, the characteristics of the wave propagation and their dissipation in the elastic granules, the viscoelastic granules and the flowing granules are analyzed. Then the mechanism of the vibrating aided flow is given.
1) The deformation of granular materials would be the elastic deformation when the strain number e < 10-4.
The expressions of wave equation, propagation velocity and wave energy in the elastic homogenous and anisotropic media have been analyzed. At the same time, an expression of energy passing coefficient was deduced, and the conducted experiment has proved that the attenuation of wave has a relation to the density of layered media. The propagation characteristics of Rayleigh and Love waves are also analyzed.
2) In terms of viscoelasticity the related theory in the granular media is analyzed. Three kinds of viscoelasticity models were given: Maxwell model, Kelvin model and standard linear model of solid. The wave equation, the complex number expressions of propagation and attenuation vectors, and the attenuation coefficient
III
expressions of longitudinal and transverse waves under the conditions of small distortion have been deduced.
3) The flowing granular media is regarded as a weak transverse isotropic media, and the phase velocity expressions of waves P, SH and SV are deduced. The propagation specialties of waves in the flowing granular media have been analyzed. It is the first time that the mechanism of the vibrating aided flow is explained creatively as depicted in this Ph D dissertation.
(4) The vibrating liquefaction of saturated granules is studied.
Firstly, the mechanism of liquefaction is described in detail. Then, the characteristic of wave propagation in saturated granular media is studied in depth. The potential vector equation and the velocity expressions of three kinds of body waves under the conditions of no dissipation, as well as the general equation of potential vector and the attenuation coefficients of waves P and S under the conditions of dissip
引文
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