基于分数导数的非线性爬行损害模型的研究
Guanghe Li1, Hongjun Jia2,3
1College of Mining, Liaoning Technical University, Fuxin, 123000, China. li_7118@126.com.
Scientific reports
|February 19, 2025
概括
这项研究引入了分数非线性爬行损伤模型,以模拟不同含水量下的岩石行为. 该模型准确地预测了岩石爬行特征,为斜坡稳定性分析提供了洞察力.
科学领域:
- 地质技术工程 地质技术工程
- 材料科学 材料科学 材料科学
- 应用数学 应用数学 应用数学
背景情况:
- 分数计算为机械建模提供了先进的方法,特别是对于具有固体和流体之间的中间性质的材料.
- 了解不同条件下的岩石爬行行为对于地质工程和斜坡稳定性至关重要.
- 现有的模型可能无法完全捕捉岩石中复杂的非线性爬行和损伤过程.
研究的目的:
- 开发和验证一个分数非线性爬行损伤模型来模拟岩石爬行.
- 为了研究含水量对岩石爬行特征的影响,使用分数计算.
- 为软岩斜坡的稳定性分析和防灾提供理论基础.
主要方法:
- 里曼-利乌维尔分数运算符的应用,用于模拟粘性和粘性塑性元素.
- 建立分数级粘性元素,非线性粘性元素和粘性塑料体的序列连接.
- 构建分数非线性爬行损伤模型的构成方程.
- 使用最小平方原理识别参数,并根据实验数据进行验证.
主要成果:
- 开发的分数非线性爬行损伤模型与实验数据显示出高相关性 (>0.98).
- 该模型有效地模拟了不同含水量条件下的岩石爬行非线性梯度过程.
- 对模型参数的分析揭示了它们对变形的影响,提高了模型验证和适用性.
结论:
- 分数非线性爬行损伤模型为模拟岩石爬行行为的准确和有效工具.
- 这项研究为评估软岩斜坡的稳定性和预防灾害提供了宝贵的理论见解.
- 该模型对各种压力环境的适应性提高了其在地质工程中的实用性.
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