非饱和原状黄土弹塑性损伤流固耦合模型及其初步应用
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摘要
非饱和原状黄土具有显著的结构性,结构性对其力学变形特征有着较大影响,但鲜有报道将结构性引入到非饱和黄土地基湿陷变形的多场耦合响应分析中,该领域亟待进一步深入研究。以已建立的非饱和原状黄土弹塑性损伤本构模型为基础,将其纳入到非饱和土流固理论中,结合非饱和原状黄土水气运移规律,建立考虑结构性的非饱和原状黄土弹塑性损伤流固耦合模型。对新建流固耦合模型的控制方程在时间域和空间域上进行离散,得到单元模量矩阵各元素的具体表达式,并编写多场耦合分析有限元程序ULEDSC。利用新编程序对黄土地区的大型现场浸水试验进行数值计算,得到浸水和停水阶段的孔压场、位移场以及损伤场等关键变化特征,以初步揭示湿陷性黄土地基浸水沉降变形过程中的多场耦合响应机制。研究成果可为黄土地区的工程实践提供一定参考,新编程序也能为初步解决黄土地基的湿陷性问题提供可能。
The unsaturated intact loess has obvious structural characteristics which significantly affect its mechanical behaviors. However, introducing structural characteristics into multi-field coupled analysis of collapse deformation for unsaturated loess foundation has not been widely reported, and further research is urgently needed in this field. Based on the established elastoplastic damage constitutive model for unsaturated intact loess combining water – gas migration law of unsaturated loess, a new elastoplastic damage seepage-consolidation coupled model is presented in this paper, which considers the influence of structural damage. The concrete expressions of the governing equations of the new coupled model in the two-dimensional coordinates are derived, and the governing equations are discretized in time domain and space domain by Galerkin method, respectively. At the same time, the concrete expressions of each element of the modulus matrix are obtained, and a multi-field coupling finite element program named after ULEDSC is compiled. Large field immersion test of loess foundation is simulated by this new program(taking in-situ soaking test of the self weight collapsible loess site in Heping town, Lanzhou city, Gansu province as an example). The pore pressure, displacement and damage fields during wetting and subsequent drying processes are obtained in this paper, which reveals the multifield coupling response of self weight collapsible loess foundation because of the action of water and self-weight of loess. The research results in this paper can give scientific basis for the project design of loess area, and the new compiled finite element program is a powerful tool to solve the problem of loess collapsibility.
The unsaturated intact loess has obvious structural characteristics which significantly affect its mechanical behaviors. However, introducing structural characteristics into multi-field coupled analysis of collapse deformation for unsaturated loess foundation has not been widely reported, and further research is urgently needed in this field. Based on the established elastoplastic damage constitutive model for unsaturated intact loess combining water – gas migration law of unsaturated loess, a new elastoplastic damage seepage-consolidation coupled model is presented in this paper, which considers the influence of structural damage. The concrete expressions of the governing equations of the new coupled model in the two-dimensional coordinates are derived, and the governing equations are discretized in time domain and space domain by Galerkin method, respectively. At the same time, the concrete expressions of each element of the modulus matrix are obtained, and a multi-field coupling finite element program named after ULEDSC is compiled. Large field immersion test of loess foundation is simulated by this new program(taking in-situ soaking test of the self weight collapsible loess site in Heping town, Lanzhou city, Gansu province as an example). The pore pressure, displacement and damage fields during wetting and subsequent drying processes are obtained in this paper, which reveals the multifield coupling response of self weight collapsible loess foundation because of the action of water and self-weight of loess. The research results in this paper can give scientific basis for the project design of loess area, and the new compiled finite element program is a powerful tool to solve the problem of loess collapsibility.
引文
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[7]COSTA L M,PONTES I D S,GUIMAR?ES L J N,et al.Numerical modelling of hydro-mechanical behaviour of collapsible soils[J].International Journal for Numerical Methods in Biomedical Engineering,2008,24(12):1839-1852.
[8]HAERI S M.Hydro-mechanical behavior of collapsible soils in unsaturated soil mechanics context[J].Japanese Geotechnical Society Special Publication,2016,2(1):25-40.
[9]ROTISCIANI G M,SCIARRA G,CASINI F,et al.Hydro-mechanical response of collapsible soils under different infiltration events[J].International Journal for Numerical and Analytical Methods in Geomechanics,2015,39(11):1212-1234.
[10]姚志华,陈正汉,黄雪峰,等.非饱和原状和重塑Q3黄土渗水特性研究[J].岩土工程学报,2012,34(6):1020-1027.YAO Zhi-hua,CHEN Zheng-han,HUANG Xue-feng,et al.Hydraulic conductivity of unsaturated undisturbed and remolded Q3 loess[J].Chinese Journal Geotechnical Engineering,2012,34(6):1020-1027.
[11]姚志华,陈正汉,黄雪峰,等.非饱和Q3黄土渗气特性研究[J].岩石力学与工程学报,2012,31(6):1264-1273.YAO Zhi-hua,CHEN Zheng-han,HUANG Xue-feng,et al.Experimental research on gas permeability of unsaturated Q3 loess[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(6):1264-1273.
[12]姚志华,连杰,陈正汉,等.考虑细观结构演化的非饱和Q3原状黄土弹塑性本构模型[J].岩土力学,2018,39(5):1153-1163.YAO Zhi-hua,LIAN Jie,CHEN Zheng-han,et al.An elastic-plastic constitutive model for unsaturated Q3undisturbed loess considering meso-structured evolution[J].Rock and Soil Mechanics,2018,39(5):1153-1163.
[13]CHEN ZHENGHAN,HUANG HAI,LU ZAIHUA.Nonlinear and elasto-plasticity consolidation models of unsaturated soil and applications[J].Applied Mathematics and Mechanics,2001,22(1):105-117.
[14]LU ZAIHUA,CHEN ZHENGHAN,FANG XIANGWEI,et al.Structural damage model of unsaturated expansive soil and its application in multi-field couple analysis on expansive soil slope[J].Applied Mathematics and Mechanics,2006,27(7):891-900.
[15]GENUCHTEN M T V.A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[J].Soil Science Society of America Journal,1980,44(5):892-898.
[16]姚志华,陈正汉,黄雪峰.自重湿陷性黄土的水气运移及力学变形特征[M].北京:人民交通出版社,2018:214-219.YAO Zhi-hua,CHEN Zheng-han,HUANG Xue-feng.Water-air migration and mechanical deformation of self-weight collapse loess[M].Beijing:China Communication Press Co.,Ltd.,2018:214-219.
[17]方祥位,陈正汉,申春妮,等.剪切对非饱和土土-水特征曲线影响的探讨[J].岩土力学,2004,25(9):1451-1454.FANG Xiang-wei,CHEN Zheng-han,SHEN Chun-ni,et al.A study on effect of shear on soil-water characteristic curve[J].Rock and Soil Mechanics,2004,25(9):1451-1454.
[18]姚志华.大厚度自重湿陷性黄土的水气运移和力学特性及地基湿陷变形规律研究[D].重庆:后勤工程学院,2012.YAO Zhi-hua.Water-air migration,mechanical characteristics and foundation collapse deformation of self-weight collapse loess with heavy section[D].Chongqing:Logistic Engineering University,2012.
[19]XU H F,WANG W J,ZHA Z X.Consolidation of unsaturated soils due to dissipation of pore-air pressure[J].Applied Mechanics&Materials,2014(580-583):160-164.
[20]姚志华,陈正汉,李加贵,等.基于CT技术的原状黄土细观结构动态演化特征[J].农业工程学报,2017,33(13):134-142.YAO Zhi-hua,CHEN Zheng-han,LI Jia-gui,et al.Microcosmic structure dynamic evolution characteristic of undisturbed loess based on CT technology[J].Transactions of the CSAE,2012,28(7):150-154.
[21]朱元青,陈正汉.研究黄土湿陷性的新方法[J].岩土工程学报,2008,30(4):524-528.ZHU Yuan-qing,CHEN Zheng-han.A new method of studying collapsibility of loess[J].Chinese Journal of Geotechnical Engineering,2008,30(4):524-528.
[2]沈珠江.土体结构性的数学模型--21世纪土力学的核心问题[J].岩土工程学报,1996,18(1):95-97.SHEN Zhu-jiang.Mathematical model for soil structural characteristics-core issues of soil mechanics in the 21st century[J].Chinese Journal of Geotechnical Engineering,1996,18(1):95-97.
[3]黄雪峰,陈正汉,哈双,等.大厚度自重湿陷性黄土场地湿陷变形特征的大型现场浸水试验研究[J].岩土工程学报,2006,28(3):382-389.HUANG Xue-feng,CHEN Zheng-han,HA Shuang,et al.Large area field immersion test on characteristics of deformation of self-weight collapse loess under overburden pressure[J].Chinese Journal of Geotechnical Engineering,2006,28(3):382-389.
[4]姚志华,黄雪峰,陈正汉,等.兰州地区大厚度自重湿陷性黄土场地浸水试验综合观测研究[J].岩土工程学报,2012,34(1):65-74.YAO Zhi-hua,HUANG Xue-feng,CHEN Zheng-han,et al.Comprehensive soaking tests on self-weight collapse loess with heavy section in Lanzhou region[J].Chinese Journal of Geotechnical Engineering,2012,34(1):65-74.
[5]沈珠江,章为民.损伤力学在土力学中的应用[C]//全国岩土力学数值分析与解析方法讨论会.北京:中国建筑工业出版社,1988:595-610.SHEN Zhu-jiang,ZHANG Wei-min.Application of damage mechanics in soil mechanics[C]//Proceedings of Third Conference on Analytical Method for Numerical Analysis of Rock and Soil Mechanics.Beijing:China Architecture&Building Press,1988:595-610.
[6]JIANG M J,LI T,HU H J,et al.DEM analyses of one-dimensional compression and collapse behaviour of unsaturated structural loess[J].Computers&Geotechnics,2014,60(1):47-60.
[7]COSTA L M,PONTES I D S,GUIMAR?ES L J N,et al.Numerical modelling of hydro-mechanical behaviour of collapsible soils[J].International Journal for Numerical Methods in Biomedical Engineering,2008,24(12):1839-1852.
[8]HAERI S M.Hydro-mechanical behavior of collapsible soils in unsaturated soil mechanics context[J].Japanese Geotechnical Society Special Publication,2016,2(1):25-40.
[9]ROTISCIANI G M,SCIARRA G,CASINI F,et al.Hydro-mechanical response of collapsible soils under different infiltration events[J].International Journal for Numerical and Analytical Methods in Geomechanics,2015,39(11):1212-1234.
[10]姚志华,陈正汉,黄雪峰,等.非饱和原状和重塑Q3黄土渗水特性研究[J].岩土工程学报,2012,34(6):1020-1027.YAO Zhi-hua,CHEN Zheng-han,HUANG Xue-feng,et al.Hydraulic conductivity of unsaturated undisturbed and remolded Q3 loess[J].Chinese Journal Geotechnical Engineering,2012,34(6):1020-1027.
[11]姚志华,陈正汉,黄雪峰,等.非饱和Q3黄土渗气特性研究[J].岩石力学与工程学报,2012,31(6):1264-1273.YAO Zhi-hua,CHEN Zheng-han,HUANG Xue-feng,et al.Experimental research on gas permeability of unsaturated Q3 loess[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(6):1264-1273.
[12]姚志华,连杰,陈正汉,等.考虑细观结构演化的非饱和Q3原状黄土弹塑性本构模型[J].岩土力学,2018,39(5):1153-1163.YAO Zhi-hua,LIAN Jie,CHEN Zheng-han,et al.An elastic-plastic constitutive model for unsaturated Q3undisturbed loess considering meso-structured evolution[J].Rock and Soil Mechanics,2018,39(5):1153-1163.
[13]CHEN ZHENGHAN,HUANG HAI,LU ZAIHUA.Nonlinear and elasto-plasticity consolidation models of unsaturated soil and applications[J].Applied Mathematics and Mechanics,2001,22(1):105-117.
[14]LU ZAIHUA,CHEN ZHENGHAN,FANG XIANGWEI,et al.Structural damage model of unsaturated expansive soil and its application in multi-field couple analysis on expansive soil slope[J].Applied Mathematics and Mechanics,2006,27(7):891-900.
[15]GENUCHTEN M T V.A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[J].Soil Science Society of America Journal,1980,44(5):892-898.
[16]姚志华,陈正汉,黄雪峰.自重湿陷性黄土的水气运移及力学变形特征[M].北京:人民交通出版社,2018:214-219.YAO Zhi-hua,CHEN Zheng-han,HUANG Xue-feng.Water-air migration and mechanical deformation of self-weight collapse loess[M].Beijing:China Communication Press Co.,Ltd.,2018:214-219.
[17]方祥位,陈正汉,申春妮,等.剪切对非饱和土土-水特征曲线影响的探讨[J].岩土力学,2004,25(9):1451-1454.FANG Xiang-wei,CHEN Zheng-han,SHEN Chun-ni,et al.A study on effect of shear on soil-water characteristic curve[J].Rock and Soil Mechanics,2004,25(9):1451-1454.
[18]姚志华.大厚度自重湿陷性黄土的水气运移和力学特性及地基湿陷变形规律研究[D].重庆:后勤工程学院,2012.YAO Zhi-hua.Water-air migration,mechanical characteristics and foundation collapse deformation of self-weight collapse loess with heavy section[D].Chongqing:Logistic Engineering University,2012.
[19]XU H F,WANG W J,ZHA Z X.Consolidation of unsaturated soils due to dissipation of pore-air pressure[J].Applied Mechanics&Materials,2014(580-583):160-164.
[20]姚志华,陈正汉,李加贵,等.基于CT技术的原状黄土细观结构动态演化特征[J].农业工程学报,2017,33(13):134-142.YAO Zhi-hua,CHEN Zheng-han,LI Jia-gui,et al.Microcosmic structure dynamic evolution characteristic of undisturbed loess based on CT technology[J].Transactions of the CSAE,2012,28(7):150-154.
[21]朱元青,陈正汉.研究黄土湿陷性的新方法[J].岩土工程学报,2008,30(4):524-528.ZHU Yuan-qing,CHEN Zheng-han.A new method of studying collapsibility of loess[J].Chinese Journal of Geotechnical Engineering,2008,30(4):524-528.