黏土一维剪切流变的等效时间线模型
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摘要
为揭示变剪应力作用下黏土的流变特性,建立了一维剪切弹黏塑性模型。参照Yin等提出的等效时间流变模型的建模思路,将剪切应变速率分为弹性剪切应变速率和黏塑性剪切应变速率。弹性剪切应变速率与加载路径无关,用非线性函数模拟。而对于黏塑性剪切应变速率,首先基于Singh等提出的常剪应力作用下的蠕变速率经验公式推导黏塑性剪切应变、等效时间与剪应力之间的函数关系式;然后参照Yin等提出的等效时间法,把该关系式通过等效时间代入蠕变速率经验公式,获得以剪应力和剪应变为变量的黏塑性剪切应变速率式。弹性剪切应变速率式与黏塑性剪切应变速率式之和即为一维剪切流变的等效时间线本构关系式,再通过淤泥质黏土的分级加载试验和黄土的加卸载试验与该本构关系式剪切应变表达式之间的比较,验证该模型在变剪应力加载下的适用性。研究结果表明:所构建模型的预测曲线和分级加载试验曲线、加卸载试验曲线吻合较好,这说明该模型在变剪应力加载下具有较好的适用性;模型良好的预测性也说明其建模过程中用到的等效时间法不仅适用于一维压缩流变,还适用于一维剪切流变,拓展了等效时间法的应用范围。
In order to reveal the rheological characteristics for clay under variable shear stress,an elastic viscoplastic model of one-dimensional shear rheology was established.The shear strain rate was divided into elastic shear strain rate and viscoplastic shear strain rate by dint of the modeling ideas of equivalent time rheological model proposed by Yin and Graham.The elastic shear strain rate had no relation with loading path and was simulated by a non-linear function.As to the viscoplastic shear strain rate,the fundamental equation of viscoplastic shear strain,equivalent time and shear stress was deduced on the basis of Singh-Mitchell empirical formula of the creep rate under the action of constant shear stress.In terms of equivalent time method proposed by Yin,et al,the relational expression was put into the empirical formula of the creep rate.Subsequently,the viscoplastic shear strain rate was obtained,taking shear stress and shear strain as variables.The sum of elastic shear strain rate and viscoplastic shear strain rate formulated the equivalent time lines constitutive relation of one-dimensional shear rheology.The comparison was drawn among the multi-stage loading test of silt clay,the loading-unloading testof loess and the shear strain expressions of this constitutive relationship correspondingly to verify the applicability of this model under variable shear stress.The research results show that the prediction curves obtained by this model are in good agreement with the test curves of the multistage loading test and loading-unloading test,which indicate that the model has good applicability under variable shear stress loading.The good predictability of the model also shows that the equivalent time method used in this model is not only suitable for one-dimensional compressional rheology,but also applicable to one-dimensional shear rheology,which expands applied range of the equivalent time method.
In order to reveal the rheological characteristics for clay under variable shear stress,an elastic viscoplastic model of one-dimensional shear rheology was established.The shear strain rate was divided into elastic shear strain rate and viscoplastic shear strain rate by dint of the modeling ideas of equivalent time rheological model proposed by Yin and Graham.The elastic shear strain rate had no relation with loading path and was simulated by a non-linear function.As to the viscoplastic shear strain rate,the fundamental equation of viscoplastic shear strain,equivalent time and shear stress was deduced on the basis of Singh-Mitchell empirical formula of the creep rate under the action of constant shear stress.In terms of equivalent time method proposed by Yin,et al,the relational expression was put into the empirical formula of the creep rate.Subsequently,the viscoplastic shear strain rate was obtained,taking shear stress and shear strain as variables.The sum of elastic shear strain rate and viscoplastic shear strain rate formulated the equivalent time lines constitutive relation of one-dimensional shear rheology.The comparison was drawn among the multi-stage loading test of silt clay,the loading-unloading testof loess and the shear strain expressions of this constitutive relationship correspondingly to verify the applicability of this model under variable shear stress.The research results show that the prediction curves obtained by this model are in good agreement with the test curves of the multistage loading test and loading-unloading test,which indicate that the model has good applicability under variable shear stress loading.The good predictability of the model also shows that the equivalent time method used in this model is not only suitable for one-dimensional compressional rheology,but also applicable to one-dimensional shear rheology,which expands applied range of the equivalent time method.
引文
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[2]胡亚元,杨平,余启致.超固结土次固结系数的时间效应[J].中国公路学报,2016,29(9):29-37.HU Ya-yuan,YANG Ping,YU Qi-zhi.Time Effect of Secondary Consolidation Coefficient of Over-consolidated Soil[J].China Journal of Highway and Transport,2016,29(9):29-37.
[3]祝艳波,余宏明.巴东组碎屑土夹层的非饱和蠕变经验模型[J].中国公路学报,2016,29(4):22-29.ZHU Yan-bo,YU Hong-ming.Empirical Unsaturated Creep Models for Weak Intercalated Soils of Badong Formation[J].China Journal of Highway and Transport,2016,29(4):22-29.
[4]殷宗泽.土工原理[M].北京:中国水利水电出版社,2007.YIN Zong-ze.Geotechnical Principles[M].Beijing:China Water&Power Press,2007.
[5]维亚洛夫C C.土力学的流变原理[M].杜余培,译.北京:科学出版社,1987.VYALOV C C.Rheological Principle of Soil Mechanics[M].Translated by DU Yu-pei.Beijing:Science Press,1987.
[6]唐海明,曹会,朱金生,等.天津地区某工程深基坑失稳的原因分析及其思考[J].工程勘察,2010(增1):299-302.TANG Hai-ming,CAO Hui,ZHU Jin-sheng,et al.Cause Analysis and Thinking of Instability of a Deep Excavation in Tianjin Area[J].Geotechnical Investigation&Surveying,2010(S1):299-302.
[7]王常明,王清,张淑华.滨海软土蠕变特性及蠕变模型[J].岩石力学与工程学报,2004,23(2):227-230.WANG Chang-ming,WANG Qing,ZHANG Shuhua.Creep Characteristics and Creep Model of Marine Soft Soils[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(2):227-230.
[8]徐进,张家生,赵同顺,等.软弱路基土体三轴蠕变试验及蠕变模型研究[J].中南大学学报:自然科学版,2011,42(10):3136-3142.XU Jin,ZHANG Jia-sheng,ZHAO Tong-shun,et al.Creep Triaxial Tests and Constitutive Model of Embankment Foundation Soil[J].Journal of Central South University:Science and Technology,2011,42(10):3136-3142.
[9]孔令伟,张先伟,郭爱国,等.湛江强结构性黏土的三轴排水蠕变特征[J].岩石力学与工程学报,2011,30(2):365-372.KONG Ling-wei,ZHANG Xian-wei,GUO Ai-guo,et al.Creep Behaviour of Zhanjiang Strong Structured Clay by Drained Triaxial Test[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(2):365-372.
[10]谢新宇,李金柱,王文军,等.宁波软土流变试验及经验模型[J].浙江大学学报:工学版,2012,46(1):64-71.XIE Xin-yu,LI Jin-zhu,WANG Wen-jun,et al.Rheological Test and Empirical Model of Ningbo Soft Soil[J].Journal of Zhejiang University:Engineering Science,2012,46(1):64-71.
[11]SINGH A,MITCHELL J K.General Stress-straintime Function for Soils[J].Journal of the Soil Mechanics and Foundations Division,1968,94:21-46.
[12]MESRI G,FEBRES-CORDERO E,SHIELDS D R,et al.Shear Stress-strain-time Behavior of Clays[J].Géotechnique,1981,31(4):537-552.
[13]KONDNER R L.Hyperbolic Stress-strain Response:Cohesive Soils[J].Journal of Soil Mechanics and Foundation Division,1964,89(SM1):126-127.
[14]朱鸿鹄,陈晓平,程小俊,等.考虑排水条件的软土蠕变特性及模型研究[J].岩土力学,2006,27(5):694-698.ZHU Hong-hu,CHEN Xiao-ping,CHENG Xiao-jun,et al.Study on Creep Characteristics and Model of Soft Soil Considering Drainage Condition[J].Rock and Soil Mechanics,2006,27(5):694-698.
[15]李军世,林咏梅.上海淤泥质粉质黏土的SinghMitchell蠕变模型[J].岩土力学,2000,21(4):363-366.LI Jun-shi,LIN Yong-mei.Singh-Mitchell Creep Model of Shanghai Very Soft Silt Clay[J].Rock and Soil Mechanics,2000,21(4):363-366.
[16]王琛,张永丽,刘浩吾.三峡泄滩滑坡滑动带土的改进Singh-Mitchell蠕变方程[J].岩土力学,2005,26(3):415-418.WANG Chen,ZHANG Yong-li,LIU Hao-wu.A Modified Singh-Mitchell's Creep Function of Sliding Zone Soils of Xietan Landslide in Three Gorges[J].Rock and Soil Mechanics,2005,26(3):415-418.
[17]卢萍珍,曾静,盛谦.软黏土蠕变试验及其经验模型研究[J].岩土力学,2008,29(4):1041-1044,1052.LU Ping-zhen,ZENG Jing,SHENG Qian.Creep Tests on Soft Clay and Its Empirical Models[J].Rock and Soil Mechanics,2008,29(4):1041-1044,1052.
[18]刘业科,邓志斌,曹平,等.软黏土的三轴蠕变试验与修正的Singh-Mitchell蠕变模型[J].中南大学学报:自然科学版,2012,43(4):1440-1446.LIU Ye-ke,DENG Zhi-bin,CAO Ping,et al.Triaxial Creep Test and Modified Singh-Mitchell Creep Model of Soft Clay[J].Journal of Central South University:Science and Technology,2012,43(4):1440-1446.
[19]王鹏程,骆亚生,胡连信,等.重塑黄土三轴蠕变特性研究及模型分析[J].岩土力学,2015,36(6):1627-1632.WANG Peng-cheng,LUO Ya-sheng,HU Lian-xin,et al.Research on Triaxial Creep Characteristics and Models of Remolded Loess[J].Rock and Soil Mechanics,2015,36(6):1627-1632.
[20]王鹏程,骆亚生,张希栋,等.分级加卸载条件下Q3黄土三轴蠕变特性研究[J].地下空间与工程学报,2014,10(6):1237-1242.WANG Peng-cheng,LUO Ya-sheng,ZHANG Xidong,et al.Research on the Triaxial Creep Characteristics of Q3 Loess Under Loading and Unloading by Steps[J].Chinese Journal of Underground Space and Engineering,2014,10(6):1273-1242.
[21]YIN J H,GRAHAM J.Viscous-elastic-plastic Modelling of One-dimensional Time-dependent Behavior of Clays[J].Canadian Geotechnical Journal,1989,26(2):199-209.
[22]YIN J H,GRAHAM J.Equivalent Times and One-dimensional Elastic Viscoplastic Modelling of Time-dependent Stress-strain Behavior of Clays[J].Canadian Geotechnique Journal,1993,31(1):42-52.
[23]殷建华,朱俊高.软土弹粘塑性固结模拟[J].岩土工程学报,1999,21(3):360-365.YIN Jian-hua,ZHU Jun-gao.Elastic Visco-plastic Consolidation Modelling of Soft Clay[J].Chinese Journal of Geotechnical Engineering,1999,21(3):360-365.
[24]朱鸿鹄,陈晓平,殷建华.公路软基蠕变-固结耦合有限元分析[J].工程勘察,2009(11):23-27.ZHU Hong-hu,CHEN Xiao-ping,YIN Jian-hua.Creep-consolidation Coupled Finite Element Analysis of a Highway Embankment on Soft Ground[J].Geotechnical Investigation and Surveying,2009(11):23-27.
[25]ZHU G F,YIN J H.Elastic Visco-plastic Consolidation Modelling of Clay Foundation at Berthierville Test Embankment[J].International Journal for Numerical and Analytical Methods in Geomechanics,2000,24(5):491-508.
[26]胡亚元.黏土的一维非平行等效时间线流变模型[J].土木建筑与环境工程,2012,34(2):32-38.HU Ya-yuan.A 1-D Nonparallel Equivalent-time-lines Rheological Model for Clay[J].Journal of Civil,Architectural&Environmental Engineering,2012,34(2):32-38.
[27]周秋娟,陈晓平.软土蠕变特性试验研究[J].岩土工程学报,2006,28(5):626-630.ZHOU Qiu-juan,CHEN Xiao-ping.Experimental Study on Creep Characteristics of Soft Soils[J].Chinese Journal of Geotechnical Engineering,2006,28(5):626-630.
[2]胡亚元,杨平,余启致.超固结土次固结系数的时间效应[J].中国公路学报,2016,29(9):29-37.HU Ya-yuan,YANG Ping,YU Qi-zhi.Time Effect of Secondary Consolidation Coefficient of Over-consolidated Soil[J].China Journal of Highway and Transport,2016,29(9):29-37.
[3]祝艳波,余宏明.巴东组碎屑土夹层的非饱和蠕变经验模型[J].中国公路学报,2016,29(4):22-29.ZHU Yan-bo,YU Hong-ming.Empirical Unsaturated Creep Models for Weak Intercalated Soils of Badong Formation[J].China Journal of Highway and Transport,2016,29(4):22-29.
[4]殷宗泽.土工原理[M].北京:中国水利水电出版社,2007.YIN Zong-ze.Geotechnical Principles[M].Beijing:China Water&Power Press,2007.
[5]维亚洛夫C C.土力学的流变原理[M].杜余培,译.北京:科学出版社,1987.VYALOV C C.Rheological Principle of Soil Mechanics[M].Translated by DU Yu-pei.Beijing:Science Press,1987.
[6]唐海明,曹会,朱金生,等.天津地区某工程深基坑失稳的原因分析及其思考[J].工程勘察,2010(增1):299-302.TANG Hai-ming,CAO Hui,ZHU Jin-sheng,et al.Cause Analysis and Thinking of Instability of a Deep Excavation in Tianjin Area[J].Geotechnical Investigation&Surveying,2010(S1):299-302.
[7]王常明,王清,张淑华.滨海软土蠕变特性及蠕变模型[J].岩石力学与工程学报,2004,23(2):227-230.WANG Chang-ming,WANG Qing,ZHANG Shuhua.Creep Characteristics and Creep Model of Marine Soft Soils[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(2):227-230.
[8]徐进,张家生,赵同顺,等.软弱路基土体三轴蠕变试验及蠕变模型研究[J].中南大学学报:自然科学版,2011,42(10):3136-3142.XU Jin,ZHANG Jia-sheng,ZHAO Tong-shun,et al.Creep Triaxial Tests and Constitutive Model of Embankment Foundation Soil[J].Journal of Central South University:Science and Technology,2011,42(10):3136-3142.
[9]孔令伟,张先伟,郭爱国,等.湛江强结构性黏土的三轴排水蠕变特征[J].岩石力学与工程学报,2011,30(2):365-372.KONG Ling-wei,ZHANG Xian-wei,GUO Ai-guo,et al.Creep Behaviour of Zhanjiang Strong Structured Clay by Drained Triaxial Test[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(2):365-372.
[10]谢新宇,李金柱,王文军,等.宁波软土流变试验及经验模型[J].浙江大学学报:工学版,2012,46(1):64-71.XIE Xin-yu,LI Jin-zhu,WANG Wen-jun,et al.Rheological Test and Empirical Model of Ningbo Soft Soil[J].Journal of Zhejiang University:Engineering Science,2012,46(1):64-71.
[11]SINGH A,MITCHELL J K.General Stress-straintime Function for Soils[J].Journal of the Soil Mechanics and Foundations Division,1968,94:21-46.
[12]MESRI G,FEBRES-CORDERO E,SHIELDS D R,et al.Shear Stress-strain-time Behavior of Clays[J].Géotechnique,1981,31(4):537-552.
[13]KONDNER R L.Hyperbolic Stress-strain Response:Cohesive Soils[J].Journal of Soil Mechanics and Foundation Division,1964,89(SM1):126-127.
[14]朱鸿鹄,陈晓平,程小俊,等.考虑排水条件的软土蠕变特性及模型研究[J].岩土力学,2006,27(5):694-698.ZHU Hong-hu,CHEN Xiao-ping,CHENG Xiao-jun,et al.Study on Creep Characteristics and Model of Soft Soil Considering Drainage Condition[J].Rock and Soil Mechanics,2006,27(5):694-698.
[15]李军世,林咏梅.上海淤泥质粉质黏土的SinghMitchell蠕变模型[J].岩土力学,2000,21(4):363-366.LI Jun-shi,LIN Yong-mei.Singh-Mitchell Creep Model of Shanghai Very Soft Silt Clay[J].Rock and Soil Mechanics,2000,21(4):363-366.
[16]王琛,张永丽,刘浩吾.三峡泄滩滑坡滑动带土的改进Singh-Mitchell蠕变方程[J].岩土力学,2005,26(3):415-418.WANG Chen,ZHANG Yong-li,LIU Hao-wu.A Modified Singh-Mitchell's Creep Function of Sliding Zone Soils of Xietan Landslide in Three Gorges[J].Rock and Soil Mechanics,2005,26(3):415-418.
[17]卢萍珍,曾静,盛谦.软黏土蠕变试验及其经验模型研究[J].岩土力学,2008,29(4):1041-1044,1052.LU Ping-zhen,ZENG Jing,SHENG Qian.Creep Tests on Soft Clay and Its Empirical Models[J].Rock and Soil Mechanics,2008,29(4):1041-1044,1052.
[18]刘业科,邓志斌,曹平,等.软黏土的三轴蠕变试验与修正的Singh-Mitchell蠕变模型[J].中南大学学报:自然科学版,2012,43(4):1440-1446.LIU Ye-ke,DENG Zhi-bin,CAO Ping,et al.Triaxial Creep Test and Modified Singh-Mitchell Creep Model of Soft Clay[J].Journal of Central South University:Science and Technology,2012,43(4):1440-1446.
[19]王鹏程,骆亚生,胡连信,等.重塑黄土三轴蠕变特性研究及模型分析[J].岩土力学,2015,36(6):1627-1632.WANG Peng-cheng,LUO Ya-sheng,HU Lian-xin,et al.Research on Triaxial Creep Characteristics and Models of Remolded Loess[J].Rock and Soil Mechanics,2015,36(6):1627-1632.
[20]王鹏程,骆亚生,张希栋,等.分级加卸载条件下Q3黄土三轴蠕变特性研究[J].地下空间与工程学报,2014,10(6):1237-1242.WANG Peng-cheng,LUO Ya-sheng,ZHANG Xidong,et al.Research on the Triaxial Creep Characteristics of Q3 Loess Under Loading and Unloading by Steps[J].Chinese Journal of Underground Space and Engineering,2014,10(6):1273-1242.
[21]YIN J H,GRAHAM J.Viscous-elastic-plastic Modelling of One-dimensional Time-dependent Behavior of Clays[J].Canadian Geotechnical Journal,1989,26(2):199-209.
[22]YIN J H,GRAHAM J.Equivalent Times and One-dimensional Elastic Viscoplastic Modelling of Time-dependent Stress-strain Behavior of Clays[J].Canadian Geotechnique Journal,1993,31(1):42-52.
[23]殷建华,朱俊高.软土弹粘塑性固结模拟[J].岩土工程学报,1999,21(3):360-365.YIN Jian-hua,ZHU Jun-gao.Elastic Visco-plastic Consolidation Modelling of Soft Clay[J].Chinese Journal of Geotechnical Engineering,1999,21(3):360-365.
[24]朱鸿鹄,陈晓平,殷建华.公路软基蠕变-固结耦合有限元分析[J].工程勘察,2009(11):23-27.ZHU Hong-hu,CHEN Xiao-ping,YIN Jian-hua.Creep-consolidation Coupled Finite Element Analysis of a Highway Embankment on Soft Ground[J].Geotechnical Investigation and Surveying,2009(11):23-27.
[25]ZHU G F,YIN J H.Elastic Visco-plastic Consolidation Modelling of Clay Foundation at Berthierville Test Embankment[J].International Journal for Numerical and Analytical Methods in Geomechanics,2000,24(5):491-508.
[26]胡亚元.黏土的一维非平行等效时间线流变模型[J].土木建筑与环境工程,2012,34(2):32-38.HU Ya-yuan.A 1-D Nonparallel Equivalent-time-lines Rheological Model for Clay[J].Journal of Civil,Architectural&Environmental Engineering,2012,34(2):32-38.
[27]周秋娟,陈晓平.软土蠕变特性试验研究[J].岩土工程学报,2006,28(5):626-630.ZHOU Qiu-juan,CHEN Xiao-ping.Experimental Study on Creep Characteristics of Soft Soils[J].Chinese Journal of Geotechnical Engineering,2006,28(5):626-630.