基于对数几率回归模型的粗颗粒土颗粒破碎过程演化研究
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摘要
掌握粗颗粒土颗粒破碎过程演化具有重要的现实意义,但已有研究未能对颗粒级配的演化中间过程进行预测。为弥补粗颗粒土颗粒破碎演化中间过程预测研究的不足,引入存活概率与破碎概率比值,采用对数几率回归方法,建立了基于对数几率回归的颗粒级配曲线演化模型,分析了模型参数的敏感性。基于所建立的演化模型,推导了相对颗粒破碎指标的数学计算公式,并讨论了土体颗粒破碎的有界性。最后,基于已有试验数据进行了模型的应用分析。应用结果显示:模型预测值与实测值吻合,论证了基于对数几率回归预测模型与相对破碎率预测值公式的合理性。该研究成果将有助于对粗颗粒土材料颗粒破碎演化中间过程的理解。
It is of great practical value to know the degradation process of coarse-grained soil particles, but the research on predicting the process of particle gradation has not been sufficiently executed yet. To compensate this insufficiency, the study on predicting model for coarse-grained soil particle breakage process was carried out using logarithmic probability regression mathematic method.Based on the probability theory, a logarithmic probability regression method was first set up to simulate the particle gradation process of coarse-grained soil in integral distribution curve frame. And then, a ratio of survival probability to death probability(also called breakage probability) was introduced into this setup logarithmic probability regression method to develop a prediction model for the coarse-grained soil particle degradation. The sensitivity analysis of the predicting model parameters was presented, and the degradation imitation for coarse-grained soil was discussed in the frame system of integral distribution curves. After that, a new formula to calculate the Hardin relative particle breakage index was presented to replace traditional formula for Hardin relative particle breakage index. The new model was applied to predict the coarse-grained soil particle breakage process of several experimental data reported by other authors. Application results show that the model-predicted integral distribution curves were very close to the experimental integral distribution curves. The good agreement between the predicted particle breakage process and the tested particle breakage process verifies the feasibility of this predicting model for coarse-grained soil particle breakage process. The results of this study are helpful for the understanding of particle evolution of coarse-grained soil with intermediate process.
It is of great practical value to know the degradation process of coarse-grained soil particles, but the research on predicting the process of particle gradation has not been sufficiently executed yet. To compensate this insufficiency, the study on predicting model for coarse-grained soil particle breakage process was carried out using logarithmic probability regression mathematic method.Based on the probability theory, a logarithmic probability regression method was first set up to simulate the particle gradation process of coarse-grained soil in integral distribution curve frame. And then, a ratio of survival probability to death probability(also called breakage probability) was introduced into this setup logarithmic probability regression method to develop a prediction model for the coarse-grained soil particle degradation. The sensitivity analysis of the predicting model parameters was presented, and the degradation imitation for coarse-grained soil was discussed in the frame system of integral distribution curves. After that, a new formula to calculate the Hardin relative particle breakage index was presented to replace traditional formula for Hardin relative particle breakage index. The new model was applied to predict the coarse-grained soil particle breakage process of several experimental data reported by other authors. Application results show that the model-predicted integral distribution curves were very close to the experimental integral distribution curves. The good agreement between the predicted particle breakage process and the tested particle breakage process verifies the feasibility of this predicting model for coarse-grained soil particle breakage process. The results of this study are helpful for the understanding of particle evolution of coarse-grained soil with intermediate process.
引文
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[15]张季如,祝杰,黄文竞.侧限压缩下石英砂砾的颗粒破碎特性及其分形描述[J].岩土工程学报,2008,30(6):783-789.ZHANG Ji-ru,ZHU Jie,HUANG Wen-jing.Crushing and fractal behaviors of quartz sand-gravel particles under confined compression[J].Chinese Journal of Geotechnical Engineering,2008,30(6):783-789.
[16]石修松,程展林.堆石料颗粒破碎的分形特性[J].岩石力学与工程学报,2010,29(增刊2):3852-3857.SHI Xiu-song,CHENG Zhan-lin.Fractal behavior in crushing of rockfill material[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(Suppl.2):3852-3857.
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[19]XIAO Y,LIU H L,CHEN Q S,et al.Evolution of particle breakage and volumetric deformation of binary granular soils under impact load[J].Granular Matter,2017,19(4):71.
[20]DAS A,BAJPAI P K.A hypo-plastic approach for evaluating railway ballast degradation[J].Acta Geotechnica,2018,13(5):1085-1102.
[21]CHEN X B,ZHANG J S.Effect of load duration on particle breakage and dilative behavior of residual soil[J].Journal of Geotechnical and Geoenvironmental Engineering,2016,142(9):06016008.
[22]杜俊,侯克鹏,梁维,等.粗粒土压实特性及颗粒破碎分形特征试验研究[J].岩土力学,2013,34(增刊1):155-161.DU Jun,HOU Ke-peng,LIANG Wei,et al.Experimental study of compaction characteristics and fractal feature in crushing of coarse-grained soils[J].Rock and Soil Mechanics,2013,34(Suppl.1):155-161.
[23]程中兴.社会统计分析中的悖论与变换问题[J].统计与决策,2011(6):24-25.CHENG Zhong-xing.Paradox and transformation in social statistical analysis[J].Statistics and Decision,2011(6):24-25.
[24]HAGERTY M M,HITE D R,ULLRICH C R,et al.One-dimensional high-pressure compression of granular media[J].Journal of Geotechnical Engineering,1993,119(1):1-18.
[25]张季如,张弼文,胡泳,等.粒状岩土材料颗粒破碎演化规律的模型预测研究[J].岩石力学与工程学报,2016,35(9):1898-1905.ZHANG Ji-ru,ZHANG Bi-wen,HU Yong,et al.Predicting the particle breakage of granular geomaterials[J].Chinese Journal of Rock Mechanics and Engineering,2016,35(9):1898-1905.
[2]LEE K L,FARHOOMAND I.Compressibility and crushing of granular soils in anisotropic triaxial compression[J].Canadian Geotechnical Journal,1967,4(1):68-86.
[3]HARDIN B O.Crushing of soil particles[J].Journal of Geotechnical Engineering,1985,111(10):1177-1192.
[4]KONRAD J M,SALAMI Y.Particle breakage in granular materials:a conceptual framework[J].Canadian Geotechnical Journal,2017,55(5):1-44.
[5]YU F W.Characteristics of particle breakage of sand in triaxial shear[J].Powder Technology,2017,320:656-667.
[6]BAGARIA P,ZHANG J Q,MASHUGA C.Effect of dust dispersion on particle breakage and size distribution in the minimum ignition energy apparatus[J].Journal of Loss Prevention in the Process Industries,2018,56:518-523.
[7]CHEN X B,ZHANG J S.Effect of clay invasion on shear behavior and dilatancy of unbound aggregate subbase[J].Transportation Geotechnics,2016,6:16-25.
[8]SUN Y F,ZHENG C J.Breakage and shape analysis of ballast aggregates with different size distributions[J].Particuology,2017,35:84-92.
[9]EINAV I.Breakage mechanics-Part I:theory[J].Journal of the Mechanics and Physics of Solids,2007,55(6):1274-1297.
[10]徐日庆,畅帅,李雪刚,等.基于裂离参量的粒状土颗粒破碎量化方法[J].岩土工程学报,2013,35(12):2179-2185.XU Ri-qing,CHANG Shuai,LI Xue-gang,et al.Quantitative method for crushing of granular soils based on discarding parameters[J].Chinese Journal of Geotechnical Engineering,2013,35(12):2179-2185.
[11]MCDOWELL G R.On the yielding and plastic compression of sand[J].Soils and Foundations,2002,42(1):139-145.
[12]童晨曦,张升,李希,等.单一粒径组颗粒材料破碎规律及破碎极限研究[J].岩土力学,2015,36(增刊1):260-264.TONG Chen-xi,ZHANG Sheng,LI Xi,et al.Evolution and ultimate state of breakage for uniformly graded granular materials[J].Rock and Soil Mechanics,2015,36(Suppl.1):260-264.
[13]BARD E.Comportement des matériaux granulaires secs etàliant hydrocarbone[D].Paris:Ecole Centrale de Paris,1993.BARD E.Behavior of dry and hydrocarbon binder granular materials[D].Paris:Ecole Centrale de Paris,1993.
[14]蔡正银,李小梅,关云飞,等.堆石料的颗粒破碎规律研究[J].岩土工程学报,2016,38(5):923-929.CAI Zheng-yin,LI Xiao-mei,GUAN Yun-fei,et al.Particle breakage rules of rockfill materials[J].Chinese Journal of Geotechnical Engineering,2016,38(5):923-929.
[15]张季如,祝杰,黄文竞.侧限压缩下石英砂砾的颗粒破碎特性及其分形描述[J].岩土工程学报,2008,30(6):783-789.ZHANG Ji-ru,ZHU Jie,HUANG Wen-jing.Crushing and fractal behaviors of quartz sand-gravel particles under confined compression[J].Chinese Journal of Geotechnical Engineering,2008,30(6):783-789.
[16]石修松,程展林.堆石料颗粒破碎的分形特性[J].岩石力学与工程学报,2010,29(增刊2):3852-3857.SHI Xiu-song,CHENG Zhan-lin.Fractal behavior in crushing of rockfill material[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(Suppl.2):3852-3857.
[17]OZKAN G,ORTOLEVA P J.Evolution of the gouge particle size distribution:a Markov model[J].Pure and Applied Geophysics,2000,157(3):449-468.
[18]COOP M R,SORENSEN K K,FREITAS T B,et al.Particle breakage during shearing of a carbonate sand[J].Géotechnique,2004,54(3):157-163.
[19]XIAO Y,LIU H L,CHEN Q S,et al.Evolution of particle breakage and volumetric deformation of binary granular soils under impact load[J].Granular Matter,2017,19(4):71.
[20]DAS A,BAJPAI P K.A hypo-plastic approach for evaluating railway ballast degradation[J].Acta Geotechnica,2018,13(5):1085-1102.
[21]CHEN X B,ZHANG J S.Effect of load duration on particle breakage and dilative behavior of residual soil[J].Journal of Geotechnical and Geoenvironmental Engineering,2016,142(9):06016008.
[22]杜俊,侯克鹏,梁维,等.粗粒土压实特性及颗粒破碎分形特征试验研究[J].岩土力学,2013,34(增刊1):155-161.DU Jun,HOU Ke-peng,LIANG Wei,et al.Experimental study of compaction characteristics and fractal feature in crushing of coarse-grained soils[J].Rock and Soil Mechanics,2013,34(Suppl.1):155-161.
[23]程中兴.社会统计分析中的悖论与变换问题[J].统计与决策,2011(6):24-25.CHENG Zhong-xing.Paradox and transformation in social statistical analysis[J].Statistics and Decision,2011(6):24-25.
[24]HAGERTY M M,HITE D R,ULLRICH C R,et al.One-dimensional high-pressure compression of granular media[J].Journal of Geotechnical Engineering,1993,119(1):1-18.
[25]张季如,张弼文,胡泳,等.粒状岩土材料颗粒破碎演化规律的模型预测研究[J].岩石力学与工程学报,2016,35(9):1898-1905.ZHANG Ji-ru,ZHANG Bi-wen,HU Yong,et al.Predicting the particle breakage of granular geomaterials[J].Chinese Journal of Rock Mechanics and Engineering,2016,35(9):1898-1905.
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