复杂加载条件下的砂土本构模型

万征; 孟达

doi:10.6052/0459-1879-18-047

复杂加载条件下的砂土本构模型

doi: 10.6052/0459-1879-18-047

万征^*, ,,
孟达

中国建筑科学研究院地基基础研究所,北京 100013

基金项目: 国家自然科学基金资助项目(11402260).

详细信息

作者简介:
^*万征,副研究员,主要研究方向：地下结构与土相互作用,混凝土及土的本构关系. E-mail：zhengw111@126.com

通讯作者:
万征

中图分类号: TU43;
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出版历程
- 收稿日期: 2018-03-01
- 刊出日期: 2018-07-18

A CONSTITUTIVE MODEL FOR SAND UNDER COMPLEX LOADING CONDITIONS

Wan Zheng^{*
, ,},
Meng Da

Foundation Engineering Research Institute,China Academy of Building Research, Beijing 100013,China

摘要

摘要: 试验表明,饱和砂土的应力应变关系具有显著的密度以及压力依存性,上述两点构成了描述砂土静力加载下变形特性无法忽视的因素. 此外,在循环加载等复杂加载作用下,砂土还会表现出明显的应力诱导各向异性以及相变转换特性. 基于在 $e$ -- $p$ 空间中存在唯一的临界状态线这一基本假定,通过在 $e$ -- $p$ 空间中引入当前状态点与临界状态线的距离 $R$ 来作为反映密度与压力依存特性的状态参量, 将变相应力比以及峰值应力比表达为状态参量的指数函数,将上述应力比参量引入到统一硬化参量中可准确地反映初始状态下围压、密度对于单调加载下应力应变关系的影响规律,能描述砂土剪缩、剪胀,应变软化、硬化等特性. 采用非相关联流动法则, $p$ -- $q$ 空间中采用水滴型屈服面,塑性势面为椭圆面,松砂在单调加载下的静态液化现象也可描述. 为反映循环加载下塑性体积应变的累积特性以及塑形偏应变的滞回特性,在循环加载下将状态参量 $R$ 表达为应力比参量,并在硬化参数中引入描述应力诱导各向异性特性的旋转硬化部分,所提模型可有效地描述循环加载下剪切模量的衰减特性、刚度衰化性质、强度减小特性,在不排水约束作用下,则会产生往返活动性现象. 通过一系列的模型模拟与试验结果对比,验证了本构模型的有效性及适用性.
- 密度与压力依存特性 /
- 液化 /
- 往返活动性 /
- 本构模型 /
- 循环加载
Abstract: Abstract The test shows that stress-strain relationship of saturated sand has significant dependence on density and confining pressure. The above two factors can not be ignored to describe the deformation behavior of sand under static load conditions. In addition, saturated sand also exhibits obvious stress-induced anisotropy and phase transformation behaviors under complex loading, such as cyclic loading conditions. The distance $R$ between the current stress state and its corresponding point in critical state line (CSL) can be treated as a state parameter is introduced into the proposed model to reflect the density and confining pressure dependent behaviors based on the assumption that there is a unique CSL in $e$ -- $p$ space. The influence principle to stress-strain relationship under monotonic loading condition due to density and confining pressure is accurately described by using unified hardening parameter introduced by phase changing stress ratio and peak stress ratio expressed by exponential functions of state parameter. The shear volume compression, dilatancy, strain softening and hardening are all described for sand. By using non-associated flow rule, a water drop shape yield surface and an ellipse shape plastic potential surface are adopted in $p$ -- $q$ space. The liquefaction phenomenon under monotonic loading condition are also be described. To reflect the accumulation of plastic volume strain and hysteresis loops of deviatoric plastic strain under cyclic loading condition, the state parameter $R$ can be expressed as stress ratio parameter and the rotational hardening part can be adopted to describe the stress-induced anisotropy are introduced into the hardening parameter. The attenuation of shear modulus, stiffness weaken and strength decreasing behaviors are described effectively by using the proposed model. The cyclic mobility phenomenon is predicted under undrained cyclic loading conditions. The effectiveness and applicability of the proposed constitutive model is verified by the comparison of a series of simulation and test results.
- density and confining pressure dependent behaviors /
- liquefaction /
- cyclic mobility /
- constitutive model /
- cyclic loading

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参考文献(1)

[1]	Hashiguchi K, Chen ZP.Elastoplastic constitutive equation of soils with the subloading surface and the rotational hardening.International Journal for Numerical and Analytical Methods in Geomechanics, 2015, 22(3): 197-227
[2]	Roscoe KH, Schofield AN, Thurairajah A.Yielding of clays in state wetter than critical.Geotechnique, 1963, 13(3): 211-240
[3]	Been K, Jefferies MG.A state parameter for sands.Geotechnique, 1985,35(2): 99-112
[4]	Cai ZY, Li XS.Deformation characteristics and critical state of sand.Chinese Journal of Geotechnical Engineering, 2004, 26(5): 697-701
[5]	Zhang JM, Wang G.A constitutive model for evaluating small to large cyclic strains of saturated sand during liquefaction process.Chinese Journal of Geotechnical Engineering, 2004, 26(4): 546-552
[6]	Taiebat M, Dafalias YF.Sanisand: Simple anisotropic and plasticity model.International Journal for Numerical and Analytical Methods in Geomechanics, 2008, 32(8): 915-948
[7]	Gao ZW, Zhao JD.Constitutive modeling of anisotropic sand behavior in monotonic and cyclic loading.Journal of Engineering Mechanics, 2015(8): 04105017
[8]	Li XS, Dafalias YF.A constitutive framework for anisotropic sand including nonproportional loading.Geotechnique, 2004, 54(1): 41-55
[9]	栾茂田,许成顺,何杨等. 主应力方向对饱和松砂不排水单调剪切特性影响的试验研究. 岩土工程学报, 2006, 28(9): 1085-1089
[9]	(Luan Maotian, Xu Chengshun, He Yang, et al.Experimental study on effect of orientation of the principal stress on undrained behavior of saturated loose sand under monotonic shearing.Chinese Journal of Geotechnical Engineering, 2006, 28(9): 1085-1089 (in Chinese))
[10]	刘汉龙, 周云东, 高玉峰. 砂土地震液化后大变形特性试验研究. 岩土工程学报, 2002, 24(2): 142-146
[10]	(Liu Hanlong, Zhou Yundong, Gao Yufeng.Study on the behavior of large ground displacement of sand due to seismic liquefaction.Chinese Journal of Geotechnical Engineering, 2002, 24(2): 142-146 (in Chinese))
[11]	黄茂松, 李学丰, 贾苍琴. 基于材料状态相关临界状态理论的砂土双屈服面模型. 岩土工程学报, 2010, 32(11): 1764-1771
[11]	(Huang Maosong, Li Xuefeng, Jia Cangqin.A double yield surface constitutive model for sand based on state-dependent critical state theory.Chinese Journal of Geotechnical Engineering, 2010, 32(11): 1764-1771 (in Chinese))
[12]	董晓丽, 赵成刚, 张卫华. 考虑相变状态的较密实饱和砂土弹塑性模型. 工程力学, 2017, 34(1): 51-57
[12]	(Dong Xiaoli, Zhao Chenggang, Zhang Weihua.The saturated dense sand elastic-plastic model considering phase transition state.Engineering Mechanics, 2017, 34(1): 51-57 (in Chinese))
[13]	董全杨, 蔡袁强, 王军等. 松散砂土不稳定性试验研究. 岩石力学与工程学报, 2014, 33(3): 623-630
[13]	(Dong Quanyang, Cai Yuanqiang, Wang Jun, et al.Experimental study of instability of loose sand.Chinese Journal of Rock Mechanics and Engineering, 2014, 33(3): 623-630 (in Chinese))
[14]	许成顺, 高英, 杜修力等. 双向耦合剪切条件下饱和砂土动强度特性试验研究. 岩土工程学报, 2014, 36(12): 2335-2340
[14]	(Xu Chengshun, Gao Ying, Du Xiuli, et al.Dynamic strength of saturated sand under bi-directional cyclic loading.Chinese Journal of Geotechnical Engineering, 2014, 36(12): 2335-2340 (in Chinese))
[15]	陈国兴, 庄海洋. 基于Davidenkov骨架曲线的土体动力本构关系及其参数研究. 岩土工程学报, 2005, 27(8): 860-864
[15]	(Chen Guoxing, Zhuang Haiyang.Developed nonlinear dynamic constitutive relations of soils based on Davidenkov skeleton curve.Chinese Journal of Geotechnical Engineering, 2005, 27(8): 860-864 (in Chinese))
[16]	耿大将, Peijun Guo, 周顺华. 结构性软土弹塑性模型的隐式算法实现. 力学学报, 2018, 50(1): 78-86
[16]	(Gen Dajiang, Peijun Guo, Zhou Shunhua.Implicit numerical integration of an elasto-plastic constitutive model for structured clays.Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(1): 78-86 (in Chinese))
[17]	林皋. 地下结构地震响应的计算模型. 力学学报, 2017, 49(3): 528-542
[17]	(Lin Gao.A computational model for seismic response analysis of underground structures.Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 528-542 (in Chinese))
[18]	周健, 史旦达, 吴峰等. 基于数字图像技术的砂土液化可视化动三轴试验研究. 岩土工程学报, 2011, 33(1): 81-87
[18]	(Zhou Jian, Shi Danda, Wu Feng, et al.Visualized cyclic triaxial tests on sand liquefaction using digital imaging technique.Chinese Journal of Geotechnical Engineering, 2011, 33(1): 81-87 (in Chinese))
[19]	陈育民, 刘汉龙, 邵国建等. 砂土液化及液化后流动特性试验研究. 岩土工程学报, 2009, 31(9): 1408-1413
[19]	(Chen Yumin, Liu Hanlong, Shao Guojian, et al.Laboratory tests on flow characteristics of liquefied and post-liquefied sand.Chinese Journal of Geotechnical Engineering, 2009, 31(9): 1408-1413 (in Chinese))
[20]	王星华, 周海林. 砂土液化动稳态强度分析. 岩石力学与工程学报, 2003, 22(1): 96-102
[20]	(Wang Xinghua, Zhou Hailin.Study on dynamic steady state strength of sand soil liquefaction.Chinese Journal of Rock Mechanics and Engineering, 2003, 22(1): 96-102 (in Chinese))
[21]	迟明杰, 赵成刚, 李小军. 砂土剪胀机理的研究. 土木工程学报, 2009, 42(3): 99-104
[21]	(Chi Mingjie, Zhao Chenggang, Li Xiaojun.Stress-dilation mechanism of sands.China Civil Engineering Journal, 2009, 42(3): 99-104 (in Chinese))
[22]	Verdugo R, Ishihara K.The steady state of sandy soils.Soils and Foundations, 1996, 36(2): 81-91
[23]	Yao YP, Sun DA, Matsuoka H.A unified constitutive model for both clay and sand with hardening parameter independent on stress path.Computers and Geotechnics, 2008, 35: 210-222
[24]	Yao YP, Sun DA, Luo T.A critical state model for sands dependent on stress and density.International Journal for Numerical and Analytical Methods in Geomechanics, 2004, 28: 323-337
[25]	Yao YP, Hou W, Zhou AN.UH model: Three-dimensional unified hardening model for overconsolidated clays.Geotechnique, 2009, 59(5): 451-469
[26]	Yao YP, Matsuoka H, Sun DA. A unified elastoplastic model for clay and sand with the SMP criterion//Proc., 8th Australia New Zealand Conf. on Geomechanics, Hobart, 1999,Vol.Ⅱ: 997-1003
[27]	姚仰平, 侯伟, 周安楠. 基于Hvorslev面的超固结土本构模型. 中国科学:技术科学, 2007, 37(11): 1417-1429
[27]	(Yao Yangping, Hou Wei, Zhou Annan.Constitutive model for overconsolidated clays.Science China-Technological Sciences, 2007, 37(11): 1417-1429 (in Chinese))
[28]	姚仰平, 余亚妮. 基于统一硬化参数的砂土临界状态本构模型. 岩土工程学报, 2011, 33(12): 1827-1832
[28]	(Yao Yangping, Yu Yani.Extended critical state constitutive model for sand based on unified hardening parameter.Chinese Journal of Geotechnical Engineering, 2011, 33(12): 1827-1832 (in Chinese))
[29]	Seed HB, Martin PP, Lysmer J.Pore pressure changes during soil liquefaction.Journal of Geotechnical Engineering Division, ASCE, 1976, 102(4): 323-346
[30]	Lee KL, Seed HB.Drained strength characteristics of sands.Journal of the Soil Mechanics and Foundations Division. Proceedings of the American Society of Civil Engineers, 1967, 93(SM6): 117-141
[31]	Yao YP, Lu DC, Zhou AN, et al.Generalized non-linear strength theory and transformed stress space.Science in China Ser. E, 2004, 47(6): 691-709
[32]	Gao ZW, Zhao JD, Yao YP.A generalized anisotropic failure criterion for geomaterials.International Journal of Solids and Structures, 2010, 47(22-23): 3166-3185
[33]	Matsuoka H, Yao YP, Sun DA.The Cam-clay models revised by the SMP criterion.Soils and Foundations, 1999, 39(1): 81-95
[34]	Yao YP, Wang ND.Transformed stress method for generalizing soil constitutive models.Journal of Engineering Mechanics, 2014, 140(3): 614-629
[35]	Nakai T, Matsuoka H.Shear behaviors of sand and clay under three-dimensional stress condition.Soils and Foundations, 1983, 23(2): 26-42
[36]	Matsuoka H, Nakai T.Stress-deformation and strength characteristics of soil under three difference principal stresses.Proceedings fo the Japan Society of Civil Engineers, 1974, 232: 59-70
[37]	Yao YP, Sun DA.Application of Lade’s criterion to Cam-Clay model.Journal of Engineering Mechanics ASCE, 2000, 126(1): 112-119
[38]	Yao YP, Zhou AN, Lu DC.Extended transformed stress space for geomaterials and its application.Journal of Engineering Mechanics ASCE, 2007, 133(10): 1115-1123
[39]	Yao YP, Hou W, Zhou AN.UH model: Three-dimensional unified hardening model for overconsolidated clays.Geotechnique, 2009, 59(5): 451-469
[40]	Yao YP, Niu L, Cui WJ.Unified hardening (UH) model for overconsolidated unsaturated soils.Canadian Geotechnical Journal, 2014, 51(7): 810-821
[41]	Yao YP, Cui WJ, Wang ND.Three-dimensional dissipative stress space considering yield behavior in deviatoric plane.Science China-Technological Sciences, 2013, 56(8): 1999-2009
[42]	万征, 姚仰平, 孟达. 复杂加载下混凝土的弹塑性本构模型. 力学学报, 2016, 48(5): 1159-1171
[42]	(Wan Zheng, Yao Yangping, Meng Da.An elastoplastic constitutive model of concrete under complicated load.Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(5): 1159-1171 (in Chinese))
[43]	万征, 秋仁东, 郭金雪. 岩土的一种强度准则及其变换应立法. 力学学报, 2017, 49(3): 726-740
[43]	(Wan Zheng, Qiu Rendong, Guo Jinxue.A kind of strength and yield criterion for geomaterials and its transformation stress method.Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 726-740 (in Chinese))
[44]	Ishihara K, Tatsuoka F, Yasuda S.Undrained deformation and liquefaction of sand under cyclic stresses.Soils and Foundations, 1975, 15(1): 29-44
[45]	Pradhan TBS, Tatsouka F, Sato Y.Experimental stress-dilatancy relations of sand subjected to cyclic loading.Soils and Foundations, 1989, 29(1): 45-64