沙堆演化动态特性及自组织临界现象研究
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摘要
目前人们猜想，自组织临界性同时由系统的尺寸和组织原则确定，前者的依据是Held的沙堆实验，后者还没有实验证据，有关理论解释基本上还是空白。国内外所进行的沙堆模型实验(包括计算机沙堆模拟实验和真实沙堆实验)没有考虑颗粒大小的不均匀性对自组织临界性的影响，并且，都是首先建立一个处于临界状态的沙堆，然后从临界状态开始进行连续加沙实验，没有进行从亚临界状态到临界状态的沙堆演化实验，也没有进行每次都处于完全相同的临界状态的不连续沙堆实验。在我们进行的水下沙堆实验中，首次发现自组织临界性与颗粒大小的非均匀性有关。以此为突破口，着重从上述几个方面进行沙堆模型实验，深入分析沙堆演化的动态机制，并对一些自组织临界现象展开研究。主要工作及结论如下：
1．沙堆模型实验发现，沙堆从亚临界状态向临界状态演化的过程中，雪崩的规模也服从幂律分布，并且沙堆在临界状态下具有不确定性。
2．采用非均匀性不同的沙粒，一共进行了86组、近万次水下沙堆实验和单面坡干沙堆实验，证实颗粒大小的非均匀性影响自组织临界性。
3．采用均匀沙(粒径2.5～5 mm)和非均匀沙(非均匀系数为2.85)，分别进行了从亚临界状态到临界状态、在临界状态下、以及从临界状态开始的三种类型的对比实验；分析沙堆演化的动态特性、临界状态的不确定性和复杂性；在此基础上进行临界状态下大规模雪崩的可预报性研究。获得如下认识：
(1)在小的扰动条件下，两种沙堆自发地向临界状态演化，但是表现出两种不同的动态特性：均匀沙沙堆大规模雪崩服从准周期分布，非均匀沙沙堆所有规模的雪崩服从幂律分布。并用重构相空间分析方法证实了这两种动态特性的存在。
(2)这两种动态特性是由于临界状态下大规模雪崩具有两种不同类型——维持在临界状态的大规模雪崩、偏离临界状态的大规模雪崩产生的。与这两种动态特性相对应，临界状态具有两种不同的吸引子类型：非分形动力学吸引子和分形动力学吸引子。
(3)用沙堆的二元结构(散粒层和摩阻层)模型对这两种动态特性进行了解释。认为非均匀沙沙堆大规模雪崩只发生在散粒层，沙堆始终维持在
第日页
西南交通大学博士研究生学位论文
临界状态，雪崩的规模服从幂律分布;而均匀沙沙堆大规模雪崩发生在摩阻
层，沙堆偏离了临界状态达到亚临界状态，然后又向临界状态演化，在临界
状态发生大规模雪崩，在亚临界状态发生小规模的雪崩，因此大规模雪崩呈
现准周期分布。用大型粗颗粒实验系统，测定不同非均匀系数沙石材料的相
对密度和直剪特性，发现非均匀沙沙堆比均匀沙沙堆密实，内摩擦角大，在
我们的实验条件下，只发生散粒层雪崩，沙堆的整体稳定性不被破坏，始终
维持在临界状态。从而大型粗颗粒实验证实了二元结构模型的合理性。
(4)计算了两个沙堆在临界状态的信息嫡和复杂度，发现信息嫡都较
大，信息嫡是系统不确定性的量度，这种不确定性是沙粒移动的连锁反应产
生的，由于还没有掌握连锁反应的内在机制，因此目前不能够对临界状态的
大规模雪崩进行准确预报。但是均匀沙沙堆由于复杂度低、大规模雪崩呈现
准周期分布，因此对临界状态下的大规模雪崩进行相对准确的预测是可行
的。而非均匀沙沙堆由于复杂度高、雪崩规模呈现幂律分布，对临界状态下
的大规模雪崩进行相对准确的预测也存在很大的困难。采用侧S方法计算了
两个沙堆从临界状态开始实验的雪崩时间序列的H值，并根据H值的大
小，进一步阐述了上述预测观点的合理性。
4.进行了变扰动的沙堆实验，提出影响沙堆自组织临界性的因素有沙
堆规模、结构以及外界扰动的强弱，并对影响沙堆自组织临界性的因素进行
了解释。认为，沙堆维持在临界状态必须同时具备两种动力学特征，敏感性
和鲁棒性，敏感性主要是通过沙堆散粒层沙粒的移动来体现的，而鲁棒性是
通过摩阻层来维持的;如果在临界状态下发生摩阻层雪崩，鲁棒性遭到破
坏，不能维持在临界状态，就不会出现自组织临界性;因而影响连锁反应的
沙堆规模、结构以及外界扰动的强弱就成为影响自组织临界性的因素。
5.采用刃S方法证明，幂律统计方法在自组织临界性研究中存在局限
性。对自组织临界性的幂律分布判断标准进行了改进，在此基础上提出了自
组织临界性的判断标准。
6.对自组织临界性的应用研究进展进行了评述，并对一些自组织临界
现象进行了研究。得到如下一些认识:
一些滑坡、泥石流和森林火灾尽管没有持续的物质或能量供给，却周期
性地达到临界状态，而其他时候没有达到临界状态。在外界周期性的扰动
下，这种周期性波动与系统的结构发生周期性的变化密切相关，并且这种周
期性地达到临界状态的现象也具有普适性，因此，我们认为这是自发地向临
界状态演化的一种新形式。
—一遭鱼塑叁越鱼丝全鲤鱼L一一一
从地壳地质结构出发，依据沙堆演化的动态特性，提出，稳定地块一般
不能够达到临界状态，不会发生破坏性的大地震;在深大断裂带和板块边
缘，对破坏性的大地震进行中长期相对准确的预报是可行的，由于临界状态
的不确定性，大地震的短临预报，尤其是临震预报存在很?
It is guessed that the emergence of self-organization criticality is depended on the size and structure principle of the system, the former foundation being experiments performed by Held, the latter still having not experimental evidence, and its theory explanation is still the blank space. The influence on self-organized criticality of the non-uniform of granular size is not taken into account in sand-pile experiments completed in the home and abroad, including computer simulation and real sand-pile experiment, and those experiments have been carried out only from the critical state, neither from the sub- critical state towards the critical state, nor in the critical state. It is discovered that self-organization criticality is related to the non-uniform coefficient of granular size in our water sand-pile experiments. Taking this as the gap, it is emphasized those respect work in our sand-pile model experiments, the dynamic characteristic of sand-pile evolution is analyzed, and some self-organization critical phenomena are researched as well.Main work and findings as follows:1 It is discovered in our sand-pile model experiments that, avalanches also obey to power-law distribution in the course of evaluation from the sub-critical state to the critical state, and sand-pile possesses the uncertainty in the critical state.2. Adopting the non- uniform difference sand,86 series in all, close to ten thousand wet sand-pile and dry sand-pile with one slope tests finished, it is confirmed the non- uniform of granular size affects the self-organization criticality.3. Adopting 2.5 -5 mm uniform sand and non- uniform sand of the non-uniform factor2.85, three kinds of compared experiments are carried out, including from the sub-critical state towards the critical state, in the critical state, and starting from the critical state as more;The dynamic characteristic of sand-pile evolvement, and the uncertainty and the complexity in critical state, are thoroughly analyzed; The forecast of large-scale avalanche in critical state is researched based on it. The understandings is obtained as follows:
(l)Under little perturbation, two sand-pile spontaneously evolve towards the critical condition, yet presents two kinds of difference dynamics characteristic: large scale avalanche obeying quasi-cycle distributions for 2.5 - 5 mm sand-pile.and all scales avalanches obeying power-law distribution for the non- uniform factor 2.85 sand-pile. These two kinds of dynamics characteristic are confirmed with the phase space analysis means .(2)The reason of the two kinds of dynamics characteristic is that there are is two kinds of distinct forms of large-scale of avalanches in the critical state, keeping or diverging the critical state. Corresponding to these two kinds of dynamics characteristic, the critical state has two kinds of difference attractor types: fractal kinetics attractor and non-fractal kinetics attractor.(3) The two kinds of dynamic behavior are interpreted with the binary composition (the granular layer and the friction-resistance layer) model of sand-pile. It is thought that large-scale avalanches happen only in the granular layer in the critical state, keeping in the critical state, and all scale of avalanches obeying power-law distribution for the non-uniform factor 2.85 sand-pile. Whereas for 2.5-5 mm sand-pile, large-scale avalanches happen in the friction-resistance layer, diverging from the critical state ,then spontaneously evolve towards the critical state, large-scale avalanches happening in the critical state ,and small-scale avalanches in the sub-critical state, hence, large scale avalanche obeying quasi-cycle distributions. The relative density and direct shear characteristics are measured with the large-scale coarse grained soil test system, and it is discovered sand-pile of the non-uniform factor 2.85 much more close-grained ,and internal friction angle larger than2.5~5 mm sand-pile, hence the entire stability of the sand-pile can not been destroyed in the condition of our test, avalanches taking place
1．沙堆模型实验发现，沙堆从亚临界状态向临界状态演化的过程中，雪崩的规模也服从幂律分布，并且沙堆在临界状态下具有不确定性。
2．采用非均匀性不同的沙粒，一共进行了86组、近万次水下沙堆实验和单面坡干沙堆实验，证实颗粒大小的非均匀性影响自组织临界性。
3．采用均匀沙(粒径2.5～5 mm)和非均匀沙(非均匀系数为2.85)，分别进行了从亚临界状态到临界状态、在临界状态下、以及从临界状态开始的三种类型的对比实验；分析沙堆演化的动态特性、临界状态的不确定性和复杂性；在此基础上进行临界状态下大规模雪崩的可预报性研究。获得如下认识：
(1)在小的扰动条件下，两种沙堆自发地向临界状态演化，但是表现出两种不同的动态特性：均匀沙沙堆大规模雪崩服从准周期分布，非均匀沙沙堆所有规模的雪崩服从幂律分布。并用重构相空间分析方法证实了这两种动态特性的存在。
(2)这两种动态特性是由于临界状态下大规模雪崩具有两种不同类型——维持在临界状态的大规模雪崩、偏离临界状态的大规模雪崩产生的。与这两种动态特性相对应，临界状态具有两种不同的吸引子类型：非分形动力学吸引子和分形动力学吸引子。
(3)用沙堆的二元结构(散粒层和摩阻层)模型对这两种动态特性进行了解释。认为非均匀沙沙堆大规模雪崩只发生在散粒层，沙堆始终维持在
第日页
西南交通大学博士研究生学位论文
临界状态，雪崩的规模服从幂律分布;而均匀沙沙堆大规模雪崩发生在摩阻
层，沙堆偏离了临界状态达到亚临界状态，然后又向临界状态演化，在临界
状态发生大规模雪崩，在亚临界状态发生小规模的雪崩，因此大规模雪崩呈
现准周期分布。用大型粗颗粒实验系统，测定不同非均匀系数沙石材料的相
对密度和直剪特性，发现非均匀沙沙堆比均匀沙沙堆密实，内摩擦角大，在
我们的实验条件下，只发生散粒层雪崩，沙堆的整体稳定性不被破坏，始终
维持在临界状态。从而大型粗颗粒实验证实了二元结构模型的合理性。
(4)计算了两个沙堆在临界状态的信息嫡和复杂度，发现信息嫡都较
大，信息嫡是系统不确定性的量度，这种不确定性是沙粒移动的连锁反应产
生的，由于还没有掌握连锁反应的内在机制，因此目前不能够对临界状态的
大规模雪崩进行准确预报。但是均匀沙沙堆由于复杂度低、大规模雪崩呈现
准周期分布，因此对临界状态下的大规模雪崩进行相对准确的预测是可行
的。而非均匀沙沙堆由于复杂度高、雪崩规模呈现幂律分布，对临界状态下
的大规模雪崩进行相对准确的预测也存在很大的困难。采用侧S方法计算了
两个沙堆从临界状态开始实验的雪崩时间序列的H值，并根据H值的大
小，进一步阐述了上述预测观点的合理性。
4.进行了变扰动的沙堆实验，提出影响沙堆自组织临界性的因素有沙
堆规模、结构以及外界扰动的强弱，并对影响沙堆自组织临界性的因素进行
了解释。认为，沙堆维持在临界状态必须同时具备两种动力学特征，敏感性
和鲁棒性，敏感性主要是通过沙堆散粒层沙粒的移动来体现的，而鲁棒性是
通过摩阻层来维持的;如果在临界状态下发生摩阻层雪崩，鲁棒性遭到破
坏，不能维持在临界状态，就不会出现自组织临界性;因而影响连锁反应的
沙堆规模、结构以及外界扰动的强弱就成为影响自组织临界性的因素。
5.采用刃S方法证明，幂律统计方法在自组织临界性研究中存在局限
性。对自组织临界性的幂律分布判断标准进行了改进，在此基础上提出了自
组织临界性的判断标准。
6.对自组织临界性的应用研究进展进行了评述，并对一些自组织临界
现象进行了研究。得到如下一些认识:
一些滑坡、泥石流和森林火灾尽管没有持续的物质或能量供给，却周期
性地达到临界状态，而其他时候没有达到临界状态。在外界周期性的扰动
下，这种周期性波动与系统的结构发生周期性的变化密切相关，并且这种周
期性地达到临界状态的现象也具有普适性，因此，我们认为这是自发地向临
界状态演化的一种新形式。
—一遭鱼塑叁越鱼丝全鲤鱼L一一一
从地壳地质结构出发，依据沙堆演化的动态特性，提出，稳定地块一般
不能够达到临界状态，不会发生破坏性的大地震;在深大断裂带和板块边
缘，对破坏性的大地震进行中长期相对准确的预报是可行的，由于临界状态
的不确定性，大地震的短临预报，尤其是临震预报存在很?
It is guessed that the emergence of self-organization criticality is depended on the size and structure principle of the system, the former foundation being experiments performed by Held, the latter still having not experimental evidence, and its theory explanation is still the blank space. The influence on self-organized criticality of the non-uniform of granular size is not taken into account in sand-pile experiments completed in the home and abroad, including computer simulation and real sand-pile experiment, and those experiments have been carried out only from the critical state, neither from the sub- critical state towards the critical state, nor in the critical state. It is discovered that self-organization criticality is related to the non-uniform coefficient of granular size in our water sand-pile experiments. Taking this as the gap, it is emphasized those respect work in our sand-pile model experiments, the dynamic characteristic of sand-pile evolution is analyzed, and some self-organization critical phenomena are researched as well.Main work and findings as follows:1 It is discovered in our sand-pile model experiments that, avalanches also obey to power-law distribution in the course of evaluation from the sub-critical state to the critical state, and sand-pile possesses the uncertainty in the critical state.2. Adopting the non- uniform difference sand,86 series in all, close to ten thousand wet sand-pile and dry sand-pile with one slope tests finished, it is confirmed the non- uniform of granular size affects the self-organization criticality.3. Adopting 2.5 -5 mm uniform sand and non- uniform sand of the non-uniform factor2.85, three kinds of compared experiments are carried out, including from the sub-critical state towards the critical state, in the critical state, and starting from the critical state as more;The dynamic characteristic of sand-pile evolvement, and the uncertainty and the complexity in critical state, are thoroughly analyzed; The forecast of large-scale avalanche in critical state is researched based on it. The understandings is obtained as follows:
(l)Under little perturbation, two sand-pile spontaneously evolve towards the critical condition, yet presents two kinds of difference dynamics characteristic: large scale avalanche obeying quasi-cycle distributions for 2.5 - 5 mm sand-pile.and all scales avalanches obeying power-law distribution for the non- uniform factor 2.85 sand-pile. These two kinds of dynamics characteristic are confirmed with the phase space analysis means .(2)The reason of the two kinds of dynamics characteristic is that there are is two kinds of distinct forms of large-scale of avalanches in the critical state, keeping or diverging the critical state. Corresponding to these two kinds of dynamics characteristic, the critical state has two kinds of difference attractor types: fractal kinetics attractor and non-fractal kinetics attractor.(3) The two kinds of dynamic behavior are interpreted with the binary composition (the granular layer and the friction-resistance layer) model of sand-pile. It is thought that large-scale avalanches happen only in the granular layer in the critical state, keeping in the critical state, and all scale of avalanches obeying power-law distribution for the non-uniform factor 2.85 sand-pile. Whereas for 2.5-5 mm sand-pile, large-scale avalanches happen in the friction-resistance layer, diverging from the critical state ,then spontaneously evolve towards the critical state, large-scale avalanches happening in the critical state ,and small-scale avalanches in the sub-critical state, hence, large scale avalanche obeying quasi-cycle distributions. The relative density and direct shear characteristics are measured with the large-scale coarse grained soil test system, and it is discovered sand-pile of the non-uniform factor 2.85 much more close-grained ,and internal friction angle larger than2.5~5 mm sand-pile, hence the entire stability of the sand-pile can not been destroyed in the condition of our test, avalanches taking place
引文
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