分形介质土力学理论

徐永福

doi:10.11779/CJGE2015S1004

分形介质土力学理论 English Version

徐永福

1. 上海交通大土木工程系,上海 200030; 2. 河海大学文天学院岩土工程研究所,马鞍山 243000

基金项目: 国家自然科学基金项目（41272318,41472251）

详细信息

作者简介:
徐永福(1967- ),男,教授,博士生导师,从事分形介质力学、非饱和（特殊）土土力学和地基处理研究。

计量
- 文章访问数: 312
- HTML全文浏览量: 3
- PDF下载量: 362
出版历程
- 收稿日期: 2015-03-25
- 发布日期: 2015-07-24

Fractals in soil mechanics

XU Yong-fu

1. Department of Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China; 2 Wentian College of Hohai University, Maanshan 243000, China

摘要

摘要: 根据粗粒土颗粒破碎的分形模型,导出粗粒土颗粒破碎强度的尺寸效应,修正颗粒破碎几率的Weibull模型和粗粒土的剪切强度公式;根据黏土颗粒表面的分形模型,导出黏土的膨胀变形和压缩变形的统一表达式,建立分形介质土力学的理论框架。
- 分形 /
- 颗粒破碎 /
- 表面分维 /
- 压缩变形 /
- 膨胀变形
Abstract: The tensile strength, crushing probability and shear strength are deduced from the fractal model for particle breakage of coarse soils. The swelling deformation and compression are derived fron the surface fractal model for cohesive soils. The soil-water characteristic curve, effective stress and shear strength are derived from the surface fractal model for pore-size distribution of unsaturated soils.
- fractal /
- particle breakage /
- surface fractal dimension /
- compressive deformation /
- swelling deformation

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参考文献(23)

[1]	XU Y F, SUN D A. Correlation of surface fractal dimension to frictional angle at critical state[J]. Géotechnique, 2005, 55(9): 691-696.
[2]	XU Y F. Fractal approach to unsaturated shear strength[J]. Journal of Geotechnical & Geoenvironmental Engineering, ASCE, 2004, 3: 264-274
[3]	XU Y F. Surface irregularity of solids in molecular domain[J]. Chaos, Solitons & Fractals, 2004, 21(2): 435-444.
[4]	XU Y F, SUN D A. A fractal model for soil pores and its application to determination of water permeability[J]. Physica A, 2002, 316(1/2/3/4): 56-64
[5]	XU Y F. Fractal model for compression of swelling clays[J]. Mechanics Research Communication, 2006, 2: 206-216.
[6]	XU Y F. Calculation of unsaturated hydraulic conductivity using a fractal model for the pore-size distribution[J]. Computer and Geotechnics, 2004, 31(7): 549-557
[7]	XU Y F. Explanation of scaling phenomenon based on fractal fragmentation[J]. Mechanics Research Communication, 2005, 32: 209-220.
[8]	KING G C P, SAMMIS C G. The mechanisms of finite brittle strain[J]. Pure and Applied Geophysics, 1992, 238: 611-640.
[9]	SAMMIS C, KING G, BIEGEL R, The kinematics of gouge deformation[J]. Pure and Applied Geophysics, 1987, 125: 777-812.
[10]	XU Y F, XU J P, WANG J H. F. Fractal model for size effect on ice failure strength[J]. Cold Regions Science and Technology, 2004, 40: 135-144.
[11]	STEACY S J, SAMMIS C G. An automation for fractal patterns of fragmentation[J]. Nature, 1991, 353: 250-251.
[12]	MANDELBROT B B. The fractal geometry of nature[M]. San Francisco: WH Freeman and Company, 1982.
[13]	WEIBULL W. A statistical distribution function of wide applicability[J]. Journal of Applied Mechanics, 1951, 18: 293-297.
[14]	MCDOWELL G R, BOLTON M D, ROBERTSON D. The fractal crushing of granular materials[J]. Journal of the Mechanics and Physics of Solids, 1996, 44: 2079-2102.
[15]	MO YF, TURNER KT, SZLUFARSKA I. Friction laws at the nanoscale[J]. Nature, 2009, 457: 1116-1118.
[16]	XU Y F, XI Y, CHU F F. Method for shear strength of coarse granular materials based on fractal grain crushing[C]// IS-Cambridge. Cambridge, 2014.
[17]	AVNIR D, JARONIEC M. An isotherm equation for adsorption on fractal surfaces of heterogeneous porous materials[J]. Langmuir, 1989, 5: 1431-1433.
[18]	KAHR G, KRAEHENBUEHL F, STOECKLI H F. Study of the water-bentonite system by vapour adsorption[J]. Immersion Colorimetry and X-ray Technique. Clay Minerals, 1990, 25: 499-506
[19]	XU Y F, MATSUOKA H, SUN D A. Swelling characteristics of fractal-textured bentonite and its mixtures[J]. Applied Clay Science, 2003, 22(4): 197-209
[20]	徐永福, 项国圣, 褚飞飞, 等. 膨润土膨胀变形的分形模型[J]. 工程地质学报, 2014, 22(5): 785-791. (XU Yong-fu, XIANG Guo-sheng, CHU Fei-fei. Fractal model for swelling deformation of bentonite[J]. Journal of Engineering Geology, 2014, 22(5): 785-791. (in Chinese))
[21]	BOLT G H. Physico-chemical analysis of the compressi- bility of pure clay[J]. Géotechnique, 1956, 6(2): 86-93.
[22]	LIU L, NERETNIEKS I. Homo-interaction between parallel plates at constant charge[J]. Colloids and Surfaces A: Physico chemical and Engineering Aspects, 2008, 317(1): 636-642.
[23]	XU Y F, JIANG H, CHU F F, et al. Fractal model for surface erosion of cohesive sediments[J]. Fractals, 2014. doi: 10.1142/S0218348X14400064.