Stochastic analysis of contact force between geomembrane and particle underlayer based on principle of maximum entropy
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摘要: 土石坝坝面防渗土工膜与其下的垫层颗粒间接触状态存在较大的随机性和无序性,一直是定量分析土石坝面膜防渗结构可靠性的一个难点。基于最大熵原理对土工膜与垫层颗粒之间接触力随机状态进行了分析演绎,提出了一种研究不同垫层颗粒状态（粒径级配、尖锐程度等）、不同压力条件下土工膜与垫层颗粒间接触力大小分布的数学方法,利用该方法分别从理论上推导出了土工膜与均一圆球颗粒垫层之间接触力大小概率密度分布函数以及土工膜与级配圆球颗粒垫层之间的接触力大小概率密度分布函数,理论推导表明在垫层颗粒随机排布的条件下,土工膜与垫层颗粒间接触力大小分布满足以压力和单位面积接触点数为参数的指数分布规律,最后通过室内试验,利用压敏纸测量了上述两种垫层颗粒与土工膜之间的接触力大小,统计每个接触点上接触力后发现与理论推导的结果基本一致。Abstract: In order to quantitatively analyze the reliability of geomembrane surface barrier on rockfill dam, a stochastic method based on the principle of the maximum entropy is employed to analyze the random contact between geomembrane and particle underlayer. The distribution of contact force between geomembrane and particle underlayers with different particle sizes and sharpnesses under different pressures can be obtained theoretically using this method. Two simple cases are also given to show the detailed process of mathematical derivation of this method. The distribution of contact force is exponential according to the proposed method, and the particle size and pressure are the most two important factors to affect the distribution of contact force. The proposed method is then verified by a series of laboratory experiments using the pressure-sensitive film, and it is a reliable tool to measure the contact force at each contact point. The results show that the distribution of contact force from the proposed method is in good agreement with the test data.
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Keywords:
- geomembrane /
- particle underlayer /
- contact force /
- stochastic analysis
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