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标题 基于空间滑动面理论的LadeDuncan模型改进
范文 邢国起等
摘要:应用空间滑动面原理改进了LadeDuncan弹塑性模型的屈服准则及破坏准则,建立了基于非关联流动法则的改进LadeDuncan弹塑性模型,模型参数可通过常规三轴试验获取。利用潍坊中南部平原地区某深基坑持力层的粉土UU三轴试验结果,验证了改进LadeDuncan模型对粉土试样的适应性。改进模型较LadeDuncan弹塑性模型能够更好地反映持力层粉土的关系,以及应力路径的相关性与剪胀等特性。改进弹塑性模型可为该地区高层及超高层建筑粉土地基变形计算创造有利条件。
关键词:关键词:空间滑动面理论;LadeDuncan模型;粉土;屈服准则;破坏准则
中图分类号:TV45 文献标志码:A 文章编号:
16721683(2014)05001804
Modified LadeDuncan model based on the theory of spatial mobilized plane
XING Guoqi1,2,XIAO Hongtian1,LI Dayong1
(1.Shandong Province Key Laboratory of Geotechnical and Structural Engineering,Shandong University of Science and Technology,Qingdao 266590,China;
2.College of architectural engineering,Weifang University,Weifang 261061,China)
Abstract:The theory of spatial mobilized plane was used to improve the yield criterion and failure criterion of LadeDuncan elastoplastic model,and then the modified LadeDuncan model was established based on the nonassociated flow rule.Model parameters can be determined by the traditional triaxial test.The adaptability to the modified LadeDuncan model for silt was verified based on the triaxial UU test results of the silt samples collected in the deep foundation pit of the southcentral plain area in Weifang.The modified model can better reflect the relationship between (σ1-σ3)and ε1 of supporting layer of silt,and the relativity and shear dilatancy properties of stress paths.The modified model can provide reference for the calculation of silt foundation deformation of the highrise buildings and ultratall buildings.
Key words:theory of spatial mobilized plane;LadeDuncan elastoplastic model;silt;yield criterion;failure criterion
近年来高层及超高层建筑的发展推动了土的本构关系研究日益广泛和深入,成为岩土工程的重要研究领域之一。土的弹塑性模型能够反映土的非线性、弹塑性、剪胀性以及各向异性等特点,在高层及超高层建筑的地基沉降计算中得到了广泛的应用并且取到了较好的效果。土的弹塑性模型建立在增量塑性理论基础上,弹性应变增量可用弹性理论求解,塑性应变增量可用增量塑性理论计算。Roscoe等[1]在塑性力学加工硬化理论基础上,对正常固结重塑黏土建立了第一个土的弹塑性帽子模型,即剑桥模型(CamClay)。英国剑桥大学的Burland[2](1965)采用了一种新的能量方程形式,得到了修正剑桥模型。魏汝龙(1981)[34]提出了不同于剑桥模型与修正剑桥模型的新的能量方程式,把弹性剪应变考虑进去,功能的假定更全面,比修正的剑桥模型适用性更广。黄文熙[57](1979)通过进行土的等向固结试验和常规三轴压缩试验,建立了土的弹塑性模型(清华弹塑性模型)。濮家骝[8]、李广信[9]根据平面应变和真三轴试验资料和p、vσ及q三维应力空间的流动法则的推导,进一步建立了三维弹塑性模型。沈珠江[1011]提出了双重屈服面模型以及三重屈服面模型。Lade和Duncan[1213]根据真三轴仪上砂土试验成果,建立了一个适应三维空间的弹塑性应力应变模型。随后Lade[14]又针对LadeDuncan弹塑性模型不能反映土在各向等压的应力下不产生屈服的现象,将原来的直线屈服轨迹改为弯曲的并增加了“帽子”屈服面,以反映比例加载条件、应变软化和强度随围压变化等因素。LadeDuncan弹塑性模型采用非关联流动法则的砂土本构模型,但是塑性势函数却是基于传统塑性力学理论提出的,试验假定的塑性势函数与所采用的屈服函数具有相似的形式,理论不严密。在松岗元等基于空间滑动面理论提出[1516]的空间滑动面模型(SMP)中,屈服准则考虑了三个应力张量不变量的影响。
本文将空间滑动面模型中的屈服函数作为LadeDuncan弹塑性模型中的屈服函数,塑性势函数形式不变,破坏准则采用松冈元-中井准则,建立基于非关联流动法则的改进LadeDuncan弹塑性模型,并以潍坊中南部地区持力层粉土为试样验证改进弹塑性模型对粉土类材料的可行性,为本地区高层及超高层建筑地基变形计算提供支持。
1
空间滑动面模型与LadeDuncan弹塑性模型
参数α随围压σ3增大呈减小趋势;土性参数β随围压σ3增大而增大。
(4)针对试验粉土试样,改进模型的精度优于LadeDuncan弹塑性模型,改进模型可为本地区高层及超高层建筑地基变形计算创造更有利条件。
本次试验以潍坊中南部地区某深基坑持力层粉土重塑试样进行了常规UU三轴试验,验证了改进模型适用于高层及超高层粉土地基变形的可行性,但改进模型是否适用于CU及CD三轴试验,还有待于进一步研究。
参考文献(References):
[1]
Roscoe K H,Schofield A N,Thurairajah A.Yielding of clay in states wetter than critical[J].Geotechnique,1963,13(3):211240.
[2] Roscoe K H,Burland J B.On the Generalized Stressstrain Behavior of “Wet” Clay[J].Journal of Terramechanics,1970,7(2):107108.
[3] 魏汝龙.正常压密粘土的塑性势[J].水利学报,1964,(6):921(WEI Rulong.The plastic potential of normally consolidated clays[J].Journal of Hydraulic Engineering,1964,(6):921.(in chinese))
[4] 魏汝龙.正常压密粘土的本构定律[J].岩土工程学报,1981,3(3):1018(WEI Rulong.Constitutive laws for normally consolidated clay[J].Chinese Jounal of Geotechnical Engineering,1981,3(3):1018.(in chinese))
[5] 黄文熙.土的弹塑性应力一应变模型理论[J].清华大学学报,1979,19(1):120(HUANG Wenxi.Theory of elastoplastic stressstrain models for soils[J].Journal of Tsinghua University,1979,19(1):120.(in chinese))
[6] 黄文熙.硬化规律对土的弹塑性应力应变模型影响的研究[J].岩士工程学报,1980,2(1):111(HUANG Wenxi.The influence of the hardening law on the formulation of the elastoplastic model of soil[J].Chinese Journal of Geotechnical Engineering,1980,2(1):111.(in chinese))
[7] Huang Wenxi.Effect of work hardening rules on the elastoplastic matrix[A].Soils under Cyclic and Transient Loading/Swansea[C].1980,1:711.
[8] 濮家骝,李广信,孙岳嵩.砂土复杂应力状态试验及三维弹塑性数学模型研究[A].第4届土力学及基础工程学术会议论文集[C].北京:中国建筑工业出版社,1986:156163.(PU Jialiu,LI Guangxin,SUN Yuesong.Tests on sands under complicated stress states and study of a three dimensional elastoplastic model for the sands[A].Proceedings of the 4th National Conference on Soil Mechanics and Foundation Engineering[C].Beijing:China Building Industry Press,1986:156163.(in chinese))
[9] 李广信.土的三维本构关系的探讨与模型验证[D].北京:清华大学,1985:7889.(LI Guangxin.A study of threedimensional constitutive relationship of soils and an examination of various models[D].Beijing:Tsinghua University,1985:7889.(in chinese))
[10] 沈珠江.土的弹塑性应力应变关系的合理形式[J].岩土工程学报,1980,2(2):1119.(SHEN Zhujiang.The rational form of stressstrain relationship of soils based on elasloplasticity theory[J].Chinese Journal of Geotechnical Engineering,1980,2(2):1119.(in chinese)).
[11] 沈珠江.土的三重屈服面应力应变模式[J].固体力学学报,1982(2):163174.(SHEN Zhujiang.A stressstrain model for soils with three yield surface[J].Acta Mechanica Solida Sinica,1982(2):163174.(in Chinese))
[12] Lade,P.V.and Duncan,J.M.Elastoplastic.Stressstrain Theory for Cohesionless Soil[J].Geotechnical Engineering Division,1975,101(10):10371053.
[13] Lade P V,Duncan J M.Stresspath dependent behavior of cohesionless soi1[J].Journal of Geotechnical Engineering Division,ASCE,1976,102(GT1):4248.
[14] Lade P V.Elastoplastic.Stressstrain theory for cohesionless with curved yield surfaces[J].Solids and Struc,1977,13(11):10191035.
[15] Matsuoka H,Yao Y P,Aun D A.The camclay models revised by SMP criterion[J].Soils and Foundations,1999,39(1):8195.
[16] Matsuoka H,Nakai T.Stressdeformation and strength characteristics of soil under three different principal stresses[A].Proceedings of Japan Society of Civil Engineers[C].Tokyo:[s.n.],1974,232:5970.
1
空间滑动面模型与LadeDuncan弹塑性模型
参数α随围压σ3增大呈减小趋势;土性参数β随围压σ3增大而增大。
(4)针对试验粉土试样,改进模型的精度优于LadeDuncan弹塑性模型,改进模型可为本地区高层及超高层建筑地基变形计算创造更有利条件。
本次试验以潍坊中南部地区某深基坑持力层粉土重塑试样进行了常规UU三轴试验,验证了改进模型适用于高层及超高层粉土地基变形的可行性,但改进模型是否适用于CU及CD三轴试验,还有待于进一步研究。
参考文献(References):
[1]
Roscoe K H,Schofield A N,Thurairajah A.Yielding of clay in states wetter than critical[J].Geotechnique,1963,13(3):211240.
[2] Roscoe K H,Burland J B.On the Generalized Stressstrain Behavior of “Wet” Clay[J].Journal of Terramechanics,1970,7(2):107108.
[3] 魏汝龙.正常压密粘土的塑性势[J].水利学报,1964,(6):921(WEI Rulong.The plastic potential of normally consolidated clays[J].Journal of Hydraulic Engineering,1964,(6):921.(in chinese))
[4] 魏汝龙.正常压密粘土的本构定律[J].岩土工程学报,1981,3(3):1018(WEI Rulong.Constitutive laws for normally consolidated clay[J].Chinese Jounal of Geotechnical Engineering,1981,3(3):1018.(in chinese))
[5] 黄文熙.土的弹塑性应力一应变模型理论[J].清华大学学报,1979,19(1):120(HUANG Wenxi.Theory of elastoplastic stressstrain models for soils[J].Journal of Tsinghua University,1979,19(1):120.(in chinese))
[6] 黄文熙.硬化规律对土的弹塑性应力应变模型影响的研究[J].岩士工程学报,1980,2(1):111(HUANG Wenxi.The influence of the hardening law on the formulation of the elastoplastic model of soil[J].Chinese Journal of Geotechnical Engineering,1980,2(1):111.(in chinese))
[7] Huang Wenxi.Effect of work hardening rules on the elastoplastic matrix[A].Soils under Cyclic and Transient Loading/Swansea[C].1980,1:711.
[8] 濮家骝,李广信,孙岳嵩.砂土复杂应力状态试验及三维弹塑性数学模型研究[A].第4届土力学及基础工程学术会议论文集[C].北京:中国建筑工业出版社,1986:156163.(PU Jialiu,LI Guangxin,SUN Yuesong.Tests on sands under complicated stress states and study of a three dimensional elastoplastic model for the sands[A].Proceedings of the 4th National Conference on Soil Mechanics and Foundation Engineering[C].Beijing:China Building Industry Press,1986:156163.(in chinese))
[9] 李广信.土的三维本构关系的探讨与模型验证[D].北京:清华大学,1985:7889.(LI Guangxin.A study of threedimensional constitutive relationship of soils and an examination of various models[D].Beijing:Tsinghua University,1985:7889.(in chinese))
[10] 沈珠江.土的弹塑性应力应变关系的合理形式[J].岩土工程学报,1980,2(2):1119.(SHEN Zhujiang.The rational form of stressstrain relationship of soils based on elasloplasticity theory[J].Chinese Journal of Geotechnical Engineering,1980,2(2):1119.(in chinese)).
[11] 沈珠江.土的三重屈服面应力应变模式[J].固体力学学报,1982(2):163174.(SHEN Zhujiang.A stressstrain model for soils with three yield surface[J].Acta Mechanica Solida Sinica,1982(2):163174.(in Chinese))
[12] Lade,P.V.and Duncan,J.M.Elastoplastic.Stressstrain Theory for Cohesionless Soil[J].Geotechnical Engineering Division,1975,101(10):10371053.
[13] Lade P V,Duncan J M.Stresspath dependent behavior of cohesionless soi1[J].Journal of Geotechnical Engineering Division,ASCE,1976,102(GT1):4248.
[14] Lade P V.Elastoplastic.Stressstrain theory for cohesionless with curved yield surfaces[J].Solids and Struc,1977,13(11):10191035.
[15] Matsuoka H,Yao Y P,Aun D A.The camclay models revised by SMP criterion[J].Soils and Foundations,1999,39(1):8195.
[16] Matsuoka H,Nakai T.Stressdeformation and strength characteristics of soil under three different principal stresses[A].Proceedings of Japan Society of Civil Engineers[C].Tokyo:[s.n.],1974,232:5970.
1
空间滑动面模型与LadeDuncan弹塑性模型
参数α随围压σ3增大呈减小趋势;土性参数β随围压σ3增大而增大。
(4)针对试验粉土试样,改进模型的精度优于LadeDuncan弹塑性模型,改进模型可为本地区高层及超高层建筑地基变形计算创造更有利条件。
本次试验以潍坊中南部地区某深基坑持力层粉土重塑试样进行了常规UU三轴试验,验证了改进模型适用于高层及超高层粉土地基变形的可行性,但改进模型是否适用于CU及CD三轴试验,还有待于进一步研究。
参考文献(References):
[1]
Roscoe K H,Schofield A N,Thurairajah A.Yielding of clay in states wetter than critical[J].Geotechnique,1963,13(3):211240.
[2] Roscoe K H,Burland J B.On the Generalized Stressstrain Behavior of “Wet” Clay[J].Journal of Terramechanics,1970,7(2):107108.
[3] 魏汝龙.正常压密粘土的塑性势[J].水利学报,1964,(6):921(WEI Rulong.The plastic potential of normally consolidated clays[J].Journal of Hydraulic Engineering,1964,(6):921.(in chinese))
[4] 魏汝龙.正常压密粘土的本构定律[J].岩土工程学报,1981,3(3):1018(WEI Rulong.Constitutive laws for normally consolidated clay[J].Chinese Jounal of Geotechnical Engineering,1981,3(3):1018.(in chinese))
[5] 黄文熙.土的弹塑性应力一应变模型理论[J].清华大学学报,1979,19(1):120(HUANG Wenxi.Theory of elastoplastic stressstrain models for soils[J].Journal of Tsinghua University,1979,19(1):120.(in chinese))
[6] 黄文熙.硬化规律对土的弹塑性应力应变模型影响的研究[J].岩士工程学报,1980,2(1):111(HUANG Wenxi.The influence of the hardening law on the formulation of the elastoplastic model of soil[J].Chinese Journal of Geotechnical Engineering,1980,2(1):111.(in chinese))
[7] Huang Wenxi.Effect of work hardening rules on the elastoplastic matrix[A].Soils under Cyclic and Transient Loading/Swansea[C].1980,1:711.
[8] 濮家骝,李广信,孙岳嵩.砂土复杂应力状态试验及三维弹塑性数学模型研究[A].第4届土力学及基础工程学术会议论文集[C].北京:中国建筑工业出版社,1986:156163.(PU Jialiu,LI Guangxin,SUN Yuesong.Tests on sands under complicated stress states and study of a three dimensional elastoplastic model for the sands[A].Proceedings of the 4th National Conference on Soil Mechanics and Foundation Engineering[C].Beijing:China Building Industry Press,1986:156163.(in chinese))
[9] 李广信.土的三维本构关系的探讨与模型验证[D].北京:清华大学,1985:7889.(LI Guangxin.A study of threedimensional constitutive relationship of soils and an examination of various models[D].Beijing:Tsinghua University,1985:7889.(in chinese))
[10] 沈珠江.土的弹塑性应力应变关系的合理形式[J].岩土工程学报,1980,2(2):1119.(SHEN Zhujiang.The rational form of stressstrain relationship of soils based on elasloplasticity theory[J].Chinese Journal of Geotechnical Engineering,1980,2(2):1119.(in chinese)).
[11] 沈珠江.土的三重屈服面应力应变模式[J].固体力学学报,1982(2):163174.(SHEN Zhujiang.A stressstrain model for soils with three yield surface[J].Acta Mechanica Solida Sinica,1982(2):163174.(in Chinese))
[12] Lade,P.V.and Duncan,J.M.Elastoplastic.Stressstrain Theory for Cohesionless Soil[J].Geotechnical Engineering Division,1975,101(10):10371053.
[13] Lade P V,Duncan J M.Stresspath dependent behavior of cohesionless soi1[J].Journal of Geotechnical Engineering Division,ASCE,1976,102(GT1):4248.
[14] Lade P V.Elastoplastic.Stressstrain theory for cohesionless with curved yield surfaces[J].Solids and Struc,1977,13(11):10191035.
[15] Matsuoka H,Yao Y P,Aun D A.The camclay models revised by SMP criterion[J].Soils and Foundations,1999,39(1):8195.
[16] Matsuoka H,Nakai T.Stressdeformation and strength characteristics of soil under three different principal stresses[A].Proceedings of Japan Society of Civil Engineers[C].Tokyo:[s.n.],1974,232:5970.
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