SMA粗集料骨架结构的细观力学模型研究
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摘要
沥青混合料由离散刚体和连续粘性胶结介质组成，为典型的多相复合体材料。从宏观角度看，沥青混合料对外荷载的响应呈非线性，为固体与粘弹塑性体的联合响应，而且沥青胶结体的粘弹塑性对温度非常敏感，所以该复合材料的性质十分复杂。从微观角度看，沥青混合料以粗细集料颗粒作为刚性固体、沥青材料为胶结体，并且集料体积约占沥青混合料总体积的90％。集料颗粒之间会产生嵌挤、摩擦作用。因此集料各组分的物理力学性质、几何形态、它们之间的相互作用及混合料各体积组成必然对沥青混合料的力学性质有很大影响。
沥青混合料内部的粗集料结构既不是完全的有序也不是完全的随机排列。鉴于此，本文提出了基于蒙特卡罗法的集料空间分布模型，即由蒙特卡罗法随机产生集料粒子，考虑集料下落、滚动等堆积过程和稳定性准则等，按相容条件进行集成。SMA粗集料骨架集成的应用实践表明，该模型能根据给定的级配曲线和边界条件很好地集成混合料内部集料的空间分布形态，经计算机成像处理能清晰看出混合料级配设计的实际效果，为可视化级配设计奠定了基础。
针对集料颗粒间摩擦、接触和嵌挤等复杂的相互作用机制，提出以集料空间分布模型确定单元的划分，进而采用离散元模拟的数值计算方法，建立了适用于离散集料微观模拟的细观力学离散单元模型，并在VC++平台上开发了相应的计算分析程序。经以单一粒径球体以及两种粒径球体组成的结构框架情况进行数值实验验证，证实所开发的程序能很好地模拟集料颗粒体在重力场内的堆积重构。基于传统窗口法的邻近元搜索算法难以适应沥青混合料集料粒径分布范围宽、单元位移大的特点，据此，本文在对窗口合理大小的选取进行了改进的基础上，提出适宜的邻近元二次搜索算法。该接触搜索算法极大地提高了计算效率，使离散单元法与随机堆积模拟的耦合计算方法能在SMA粗集料重力场内的堆积重构得以实际应用。
本文数值模型的另一特色是针对振动堆积实验过程中复杂的振动特性，引入膨胀机制模拟物理实验中的振动作用。振动模拟驱使颗粒体进一步发生重排、空隙进一步被充填、结构更为致密。经检验，该模型能很好地再现振动堆积物理实验。
为深入研究SMA粗集料骨架结构，开展了单一分组粒径和SMA16上限、中值及下限三种级配的粗集料干插捣堆积密度和空隙率实验，结果发现：单一分组粒径集料骨架间隙率VCA_(DRC)相差不大；SMA16三种典型级配的粗集料骨架间隙率VCA_(DRC)也比较接近；由于多组集料之间的相互充填，三种级配粗集料骨架间隙率较单一分组粒径集料的骨架间隙率小。
在实验研究的基础上，利用本文的计算分析程序从微观层面开展单一分组粒径和SMA16三种级配的粗集料骨架结构的数值实验。从粗集料骨架间隙率VCA_(DRC)这一宏观静态指标的分析结果看，数值模拟与上述室内实验结果相吻合。同时，本文还统计分析了目前物理实验很难测得的微观结构参数——配位数，发现：(1)各分组粗集料骨架结构内部集料的配位数分布相差不大，由于单一分组粒径集料之间相互充填，与等粒径粗集料骨架结构相比，配位数分布向增大方向移动，其平均配位数相对较大；(2)相对于单一分组粒径集料骨架结构而言，SMA粗集料骨架内部集料的配位数分布范围相当宽，最大值可达23；(3)SMA混合料骨架内部集料配位数等于3的比例较高，说明由于大粒径集料颗粒的屏蔽，混合料内部较多的小集料颗粒仅起填充作用，不直接支撑其他集料颗粒，这也是SMA内部应力传递形式极为复杂的重要原因，从而在理论上证实：SMA试件其力学性能指标的测试，应考虑骨架结构的不均匀性，采用与集料组成相适应的试件尺寸。
Asphalt mixture is viewed as a composite material of multi-phases consisting of rigid solids separated by continuum of viscous cement. Due to mechanical properties of viscoelastic plasticity of asphalt binders, response of the mixtures to load is basically nonlinear and very sensitive to the temperature. On the other hand, the mechanical property of the asphalt mixture depends also upon the interlock of the particles characterized by the shape and gradation of the aggregates used in the mixture. Importance of the aggregate composition can not be overemphasized since the volume fraction of aggregates is normally around 90% of the total volume of the mixture in practice.
Arrangement of the skeleton of the coarse aggregate of the asphalt mixture is neither completely in order nor absolutely in random. The model for the description of aggregate distribution in asphalt mixture should have random attribute thereby. Based on Monte-Carlo method, the model for the simulation of aggregates distribution is developed in this paper. While the aggregates can be positioned randomly within the mixture in this model, relocation process under gravitational stability criterion is carried out. To build the skeleton, the coarse aggregates generated by Monte-Carlo method are filled in the given space governed by the rule of compatibility. Following this procedure, skeleton of SMA16 is simulated and analyzed. The simulation results confirmed that the model is applicable to describe the location of the aggregates in the mixture according to the given grading curve and boundary restrictions. Also in this work, the computer image process is employed in the dissertation to visualize micro structure of the simulated mix.
Mechanism of the grinding, contacting and wedging among aggregates is very complex. A mapped distribution model of aggregates mixtures have been studied using discrete element method. A micromechanical model which can be applied to discrete particles is proposed and a computer program is developed on the platform of VC++ accordingly. Numerical experiments on packing of mono-sized and binary mixtures of spherical particles confirm the applicability of the code. To solve the problem of computing time consuming in particle contact search, a novel algorithm is incorporated in the program using the technique of "irregular search window method". This paves way for practical simulation for aggregate skeleton of the asphalt mixture since the mixture normally has a wide particle size distribution which is very difficult to be handled by the traditional algorithm of neighboring element search of "regular window method". Coupled with random packing algorithm, the program achieved the goal of re-locating aggregates of SMA in gravity field.
Another feature about the simulation philosophy in this dissertation is the use of taping mechanism to reflect vibration during packing. Particles are relocated during artificial vibration so that the mix gets denser due to the void fillings among particles. Comparing it with physical and numerical experiments, it is found that results obtained from this method match reasonably well with packing experiments.
The packing experiments pounding with a pestle of a single group of aggregates and three grades (upper limit, median and lower limit grade of SMA16) of aggregates have been carried out. Experiment results show that VCA_(drc) formed by the single group of aggregates have little discrepancy. VCA_(drc) formed by the three grades are almost the same. Because of filling among several groups, VCA_(drc) formed by each grade of aggregates are all lower than VCA_(drc) formed by each single group of aggregates.
Micro-structure of a single group of aggregates and SMA16 (three grades) are simulated using the program after the packing experiments. VCA_(drc) measured by experiment is close to VCA_(Drc) calculated by the program. Moreover, coordination number which is an important micro-structure parameter and impracticable to measure in the tests have been analyzed statistically. The following conclusions can be drawn from analyses: (1). There is little discrepancy in coordination numbers formed by the four groups of aggregates. Compared with mono-sized aggregates, curve of distributed coordination number of a single group of aggregates shifts to the larger direction because of filling among aggregates. The mean coordination number increases also. (2). Distribution of the coordination number formed by coarse aggregates skeleton of SMA covers much wider than that made up of single group of aggregates. The coordination number in SMA could be as high as 23. (3). Frequency of the coordination number equal to 3 in the coarse aggregates skeleton of SMA is relatively high. This shows that there is significant number of small particles in the mix that are not the component of the mix skeleton but the void fillings under the shelter of big aggregates. This illustrates again the complicity of load transmission within the frame of SMA. Property of in-homogeneity of SMA in lab tests should therefore be accounted for cautiously and the tested samples of the mixtures should be fabricated in proper sizes to be compatible to the composition of the aggregates.
沥青混合料内部的粗集料结构既不是完全的有序也不是完全的随机排列。鉴于此，本文提出了基于蒙特卡罗法的集料空间分布模型，即由蒙特卡罗法随机产生集料粒子，考虑集料下落、滚动等堆积过程和稳定性准则等，按相容条件进行集成。SMA粗集料骨架集成的应用实践表明，该模型能根据给定的级配曲线和边界条件很好地集成混合料内部集料的空间分布形态，经计算机成像处理能清晰看出混合料级配设计的实际效果，为可视化级配设计奠定了基础。
针对集料颗粒间摩擦、接触和嵌挤等复杂的相互作用机制，提出以集料空间分布模型确定单元的划分，进而采用离散元模拟的数值计算方法，建立了适用于离散集料微观模拟的细观力学离散单元模型，并在VC++平台上开发了相应的计算分析程序。经以单一粒径球体以及两种粒径球体组成的结构框架情况进行数值实验验证，证实所开发的程序能很好地模拟集料颗粒体在重力场内的堆积重构。基于传统窗口法的邻近元搜索算法难以适应沥青混合料集料粒径分布范围宽、单元位移大的特点，据此，本文在对窗口合理大小的选取进行了改进的基础上，提出适宜的邻近元二次搜索算法。该接触搜索算法极大地提高了计算效率，使离散单元法与随机堆积模拟的耦合计算方法能在SMA粗集料重力场内的堆积重构得以实际应用。
本文数值模型的另一特色是针对振动堆积实验过程中复杂的振动特性，引入膨胀机制模拟物理实验中的振动作用。振动模拟驱使颗粒体进一步发生重排、空隙进一步被充填、结构更为致密。经检验，该模型能很好地再现振动堆积物理实验。
为深入研究SMA粗集料骨架结构，开展了单一分组粒径和SMA16上限、中值及下限三种级配的粗集料干插捣堆积密度和空隙率实验，结果发现：单一分组粒径集料骨架间隙率VCA_(DRC)相差不大；SMA16三种典型级配的粗集料骨架间隙率VCA_(DRC)也比较接近；由于多组集料之间的相互充填，三种级配粗集料骨架间隙率较单一分组粒径集料的骨架间隙率小。
在实验研究的基础上，利用本文的计算分析程序从微观层面开展单一分组粒径和SMA16三种级配的粗集料骨架结构的数值实验。从粗集料骨架间隙率VCA_(DRC)这一宏观静态指标的分析结果看，数值模拟与上述室内实验结果相吻合。同时，本文还统计分析了目前物理实验很难测得的微观结构参数——配位数，发现：(1)各分组粗集料骨架结构内部集料的配位数分布相差不大，由于单一分组粒径集料之间相互充填，与等粒径粗集料骨架结构相比，配位数分布向增大方向移动，其平均配位数相对较大；(2)相对于单一分组粒径集料骨架结构而言，SMA粗集料骨架内部集料的配位数分布范围相当宽，最大值可达23；(3)SMA混合料骨架内部集料配位数等于3的比例较高，说明由于大粒径集料颗粒的屏蔽，混合料内部较多的小集料颗粒仅起填充作用，不直接支撑其他集料颗粒，这也是SMA内部应力传递形式极为复杂的重要原因，从而在理论上证实：SMA试件其力学性能指标的测试，应考虑骨架结构的不均匀性，采用与集料组成相适应的试件尺寸。
Asphalt mixture is viewed as a composite material of multi-phases consisting of rigid solids separated by continuum of viscous cement. Due to mechanical properties of viscoelastic plasticity of asphalt binders, response of the mixtures to load is basically nonlinear and very sensitive to the temperature. On the other hand, the mechanical property of the asphalt mixture depends also upon the interlock of the particles characterized by the shape and gradation of the aggregates used in the mixture. Importance of the aggregate composition can not be overemphasized since the volume fraction of aggregates is normally around 90% of the total volume of the mixture in practice.
Arrangement of the skeleton of the coarse aggregate of the asphalt mixture is neither completely in order nor absolutely in random. The model for the description of aggregate distribution in asphalt mixture should have random attribute thereby. Based on Monte-Carlo method, the model for the simulation of aggregates distribution is developed in this paper. While the aggregates can be positioned randomly within the mixture in this model, relocation process under gravitational stability criterion is carried out. To build the skeleton, the coarse aggregates generated by Monte-Carlo method are filled in the given space governed by the rule of compatibility. Following this procedure, skeleton of SMA16 is simulated and analyzed. The simulation results confirmed that the model is applicable to describe the location of the aggregates in the mixture according to the given grading curve and boundary restrictions. Also in this work, the computer image process is employed in the dissertation to visualize micro structure of the simulated mix.
Mechanism of the grinding, contacting and wedging among aggregates is very complex. A mapped distribution model of aggregates mixtures have been studied using discrete element method. A micromechanical model which can be applied to discrete particles is proposed and a computer program is developed on the platform of VC++ accordingly. Numerical experiments on packing of mono-sized and binary mixtures of spherical particles confirm the applicability of the code. To solve the problem of computing time consuming in particle contact search, a novel algorithm is incorporated in the program using the technique of "irregular search window method". This paves way for practical simulation for aggregate skeleton of the asphalt mixture since the mixture normally has a wide particle size distribution which is very difficult to be handled by the traditional algorithm of neighboring element search of "regular window method". Coupled with random packing algorithm, the program achieved the goal of re-locating aggregates of SMA in gravity field.
Another feature about the simulation philosophy in this dissertation is the use of taping mechanism to reflect vibration during packing. Particles are relocated during artificial vibration so that the mix gets denser due to the void fillings among particles. Comparing it with physical and numerical experiments, it is found that results obtained from this method match reasonably well with packing experiments.
The packing experiments pounding with a pestle of a single group of aggregates and three grades (upper limit, median and lower limit grade of SMA16) of aggregates have been carried out. Experiment results show that VCA_(drc) formed by the single group of aggregates have little discrepancy. VCA_(drc) formed by the three grades are almost the same. Because of filling among several groups, VCA_(drc) formed by each grade of aggregates are all lower than VCA_(drc) formed by each single group of aggregates.
Micro-structure of a single group of aggregates and SMA16 (three grades) are simulated using the program after the packing experiments. VCA_(drc) measured by experiment is close to VCA_(Drc) calculated by the program. Moreover, coordination number which is an important micro-structure parameter and impracticable to measure in the tests have been analyzed statistically. The following conclusions can be drawn from analyses: (1). There is little discrepancy in coordination numbers formed by the four groups of aggregates. Compared with mono-sized aggregates, curve of distributed coordination number of a single group of aggregates shifts to the larger direction because of filling among aggregates. The mean coordination number increases also. (2). Distribution of the coordination number formed by coarse aggregates skeleton of SMA covers much wider than that made up of single group of aggregates. The coordination number in SMA could be as high as 23. (3). Frequency of the coordination number equal to 3 in the coarse aggregates skeleton of SMA is relatively high. This shows that there is significant number of small particles in the mix that are not the component of the mix skeleton but the void fillings under the shelter of big aggregates. This illustrates again the complicity of load transmission within the frame of SMA. Property of in-homogeneity of SMA in lab tests should therefore be accounted for cautiously and the tested samples of the mixtures should be fabricated in proper sizes to be compatible to the composition of the aggregates.
引文
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