基于分形理论的饱和土孔隙水压力计算模型
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摘要
孔隙水压力是一种作用于土体孔隙间的应力,其定量分析对于探究土体的抗剪强度等力学性能有着至关重要的作用。传统的孔隙水压力计算方法忽略土体内部孔隙中流体流动及流量变化对孔隙水压力的影响,导致计算结果偏小。为修正此计算误差,基于孔隙数目-尺寸分形模型,推导出土颗粒材料孔隙度与分形维数之间的演化公式,并结合孔隙水流动方程及压力方程推导出饱和土孔隙水压力与分形维数、孔隙水压缩模量及孔隙间流量变化之间的函数关系。并使用此孔隙水压力计算公式对饱和黏土边坡进行数值分析验证公式准确性及实用性。所得公式可用于饱和土体的有效应力及抗剪强度计算修正,并可应用于饱和土体宏观-微观的多尺度液相-固相耦合渗流分析。
Quantifying pore water pressure, a stress acting on the space among soil particles, is of essential significance for investigating the shear strength and other mechanical properties of soil. Traditional calculation method for pore water pressure neglects the influence of fluid flow and flow rate change on pore water pressure in soil, which results in a small calculation result. In view of this, a formula between pore size and fractal dimension of soil granular material is derived based on number-size fractal model of soil to correct the error, and the functional relationship between pore water pressure and fractal dimension, pore water compression modulus and pore flow change of saturated soil is further deduced based on pore water flow equation and pressure equation. A saturated clayey soil slope is taken for numerical analysis to verify the accuracy and practicality of the proposed calculation formula. Result demonstrates that the formula can be used to calculate and revise the effective stress and shear strength of saturated soils, and to analyze the macro-micro multi-scale liquid-solid coupling seepage of saturated soils.
Quantifying pore water pressure, a stress acting on the space among soil particles, is of essential significance for investigating the shear strength and other mechanical properties of soil. Traditional calculation method for pore water pressure neglects the influence of fluid flow and flow rate change on pore water pressure in soil, which results in a small calculation result. In view of this, a formula between pore size and fractal dimension of soil granular material is derived based on number-size fractal model of soil to correct the error, and the functional relationship between pore water pressure and fractal dimension, pore water compression modulus and pore flow change of saturated soil is further deduced based on pore water flow equation and pressure equation. A saturated clayey soil slope is taken for numerical analysis to verify the accuracy and practicality of the proposed calculation formula. Result demonstrates that the formula can be used to calculate and revise the effective stress and shear strength of saturated soils, and to analyze the macro-micro multi-scale liquid-solid coupling seepage of saturated soils.
引文
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[7] MANDELBROT B B,WHEELER J A.The Fractal Geometry of Nature[J].Journal of the Royal Statistical Society,1982,147(4):468.
[8] 郑瑛,周英彪,郑楚光.多孔CaO孔隙结构的分形描述[J].华中科技大学学报,2001,29(3):82-8.
[9] OKADA Y,OCHIAI H.Coupling Pore-water Pressure with Distinct Element Method and Steady State Strengths in Numerical Triaxial Compression Tests under Undrained Conditions[J].Landslides,2007,4(4):357-369.
[10] 蔡建超,胡祥云.多孔介质分形理论与应用[M] .北京:科学出版社,2015.
[11] 宋子亨,杨强,刘耀儒.考虑孔隙水压力作用的岩土体弹塑性模型及其有限元实现[J].岩土力学,2016,37(增刊1):500-508.
[2] 邓英尔.岩石的渗透率与孔隙体积及迂曲度分形分析[C]// 中国岩石力学与工程学会第八次全国岩石力学与工程学术大会论文集.北京:中国岩石力学与工程学会,2004:5.
[3] NEIMARK A.Multiscale Percolation Systems[J].Soviet Physics,1989,69(4):1386-1396.
[4] PERRIER E.Structure Géométrique et Fonctionnement Hydrique des Sols:Simulations Exploratoires[J].British Journal of Psychiatry the Journal of Mental Science,1994,162(1):99-108.
[5] PERRIER E,BIRD N,RIEU M.Generalizing the Fractal Model of Soil Structure:The Pore-Solid Fractal Approach[J].Developments in Soil Science,2000,27:47-74.
[6] 周宏伟,谢和平.多孔介质孔隙度与比表面积的分形描述[J].西安矿业学院学报,1997,(2):2-7.
[7] MANDELBROT B B,WHEELER J A.The Fractal Geometry of Nature[J].Journal of the Royal Statistical Society,1982,147(4):468.
[8] 郑瑛,周英彪,郑楚光.多孔CaO孔隙结构的分形描述[J].华中科技大学学报,2001,29(3):82-8.
[9] OKADA Y,OCHIAI H.Coupling Pore-water Pressure with Distinct Element Method and Steady State Strengths in Numerical Triaxial Compression Tests under Undrained Conditions[J].Landslides,2007,4(4):357-369.
[10] 蔡建超,胡祥云.多孔介质分形理论与应用[M] .北京:科学出版社,2015.
[11] 宋子亨,杨强,刘耀儒.考虑孔隙水压力作用的岩土体弹塑性模型及其有限元实现[J].岩土力学,2016,37(增刊1):500-508.