| 粗粒土的分数阶应变率及其与分形维度的关系 |
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| 引用本文： | 孙逸飞,沈扬,刘汉龙.粗粒土的分数阶应变率及其与分形维度的关系[J].岩土力学,2018,39(Z1):297-302. |
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| 作者姓名： | 孙逸飞 沈扬 刘汉龙 |
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| 作者单位： | 1. 河海大学 教育部岩土力学与堤坝工程教育部重点实验室，南京 210098；2. 重庆大学 土木工程学院，重庆 400044 |
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| 基金项目： | 中央高校基本科研业务费（No. 2017B05214）；博士后面上基金项目（No. 2017M621607）。 |
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| 摘 要： | 在波浪荷载、潮汐作用下砂土等粗粒土常常经受长期动力变形。运用分数阶微积分理论，分析了5种不同粗粒土在不同加载条件下的累积变形特性及粗粒土的分数阶应变率，传统的整数阶应变率随着加载次数的变化而变化，而粗粒土的分数阶应变率在同一加载条件下保持为常数。通过粗粒土颗粒破碎的分形理论，尝试建立分数阶应变率与土颗粒分布的分形维度之间的关系，分析土体分形维度对分数阶应变率大小的影响，发现随着分形维度的增加，分数阶应变率的数值降低。
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| 关 键 词： | 粗粒料 分数阶微积分 边界面 临界状态 本构模型 |
| 收稿时间： | 2017-05-18 |
Fractional strain rate and its relation with fractal dimension of granular soils |
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| SUN Yi-fei,SHEN Yang,LIU Han-long.Fractional strain rate and its relation with fractal dimension of granular soils[J].Rock and Soil Mechanics,2018,39(Z1):297-302. |
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| Authors: | SUN Yi-fei SHEN Yang LIU Han-long |
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| Institution: | 1. Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing, Jiangsu 210098, China; 2. College of Civil Engineering, Chongqing University, Chongqing 400044, China |
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| Abstract: | Due to the wave-load and tidal load, granular soils, such as sand, often suffers from long-term cyclic deformation. Cumulative strains of five different granular soils under different loading conditions are analyzed by using the fractional calculus, and its there exists a fractional strain rate for granular soils subjected to repeated loads. Unlike the traditional integral strain rate which is varying with the load cycles, the fractional strain rate remains constant for a given loading condition. To investigate the physical origin of the fractional approach, fractal breakage theory of granular soils is used. It is found that the fractional strain rate has a strong connection with the corresponding fractal dimension of a given granular soil. It decreases with the increase of the fractal dimension. |
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| Keywords: | granular aggregates fractional calculus bounding surface critical state constitutive model |
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