Abstract：In order to explore the deformation of soil due to the rotation of principal stress axes，the following ideas are adopted to establish a model. (1) The results of single shear test on two dimensional aluminum rods are analyzed. The relationship of the ratio of the shear stress to the normal stress(shear stress ratio) with the shear strain is similar to the hyperbolic curve. The Weibull function is adopted to describe the relationship of shear stress ratio and shear strain which describes both the strain hardening and softening. (2) An implicit function about the shear strain is established by combining the shear stress ratio equation in Mohr?s circle and Weibull function. There are three factors influencing the shear strain，including the mean stress p under isotropic or deviatoric compressions， the mobilized friction angle corresponding to the general deviatoric stress state and the half of angle between the shear stress and larger principal stress axe. (3) An incremental equation about the shear strain and shear stress ratio is established by differentiating the above implicit equation. A two dimensional incremental constitutive equation is established by combining the above stress ratio equation and Rowe dilatancy equation. A three-dimensional incremental constitutive equation is derived by expanding the above model adopted by SMP criterion. The compression hardening，shear shrinkage，shear dilation，hardening and softening are reflected in the proposed model(WB). A general stress-strain relationship considering the rotation of principal stress axes is thus derived. The applicability and rationality of the proposed model are verified by comparison of the experimental and calculated results.
万 征，秋仁东，赵晓光 . 考虑主应力轴旋转作用的一个增量模型[J]. 岩石力学与工程学报, 2017, 36(9): 2275-2287.
WAN Zheng，QIU Rendong，ZHAO Xiaoguang. An incremental model considering the effect of rotation of principal stress axes. , 2017, 36(9): 2275-2287.
[1] ARTHUR J R F，CHUA K S，DUNSTAN T. Dense sand weakened by continuous principal stress direction rotation[J]. Geotechnique，1979，29(1)：91–96.
[2] JOER H A，LANIER J，FAHEY M. Deformation of granular materials due to rotation of principal axes[J]. Geotechnique，1998，48(5)：605–619.
[3] ISHIHARA K，TOWHATA I. Sand response to cyclic rotation of principal stress directions as induced by wave loads[J]. Soils and Foundations，1983，23(4)：11–26.
[4] TOWHATA I，ISHIHARA K. Undrained strength of sand undergoing cyclic rotation of principal stress axes[J]. Soils and Foundations，1985，25(2)：135–147.
[5] SIVATHAYALAN S，VAID Y P. Influence of generalized initial state and principal stress rotation on the undrained response of sands[J]. Canadian Geotechnical Journal，2002，39(1)：63–76.
[6] ZDRAVKOVIC L，JARDINE R J. The effect on anisotropy of rotating the principal stress axes during consolidation[J]. Geotechnique，2001，51(1)：69–83.
[7] 郭 莹，栾茂田，许成顺，等. 主应力方向变化对松砂不排水动强度特性的影响[J]. 岩土工程学报，2003，25(6)：666–670.(GUO Ying，LUAN Maotian，XU Chengshun，et al. Effect of variation of principal stress orientation on undrained dynamic strength behavior of loose sand[J]. Chinese Journal of Geotechnical Engineering，2003，25(6)：666–670.(in Chinese))
[8] 郭 莹，栾茂田，何 杨，等. 复杂应力条件下饱和松砂孔隙水压力增长特性的试验研究[J]. 地震工程与工程振动，2004，24(3)：139–144.(GUO Ying，LUAN Maotian，HE Yang，et al. Experimental study on development pattern of shaking-induced pore water pressure of saturated loose sand under complex loading[J]. Earthquake Engineering and Engineering Vibration，2004，24(3)：139–144.(in Chinese))
[9] 付 磊，王洪瑾，周景星. 主应力偏转角对砂砾料动力特性影响的试验研究[J]. 岩土工程学报，2000，22(4)：435–440.(FU Lei，WANG Hongjin，ZHOU Jingxing. Effect of the initial rotation angle of principal stress on the dynamic properties of soil[J]. Chinese Journal of Geotechnical Engineering，2000，22(4)：435–440.(in Chinese))
[10] LADE P V，KIRKGARD M M. Effects of stress rotation and changes of b-values on cross-anisotropic behavior of natural K0-consolidated soft clay[J]. Soils and Foundations，2000，40(6)：93–105.
[11] 严佳佳，周 建，龚晓南，等. 主应力轴纯旋转条件下原状黏土变形特性研究[J]. 岩土工程学报，2014，36(3)：474–481.(YAN Jiajia，ZHOU Jian，GONG Xiaonan，et al. Deformation behavior of intact clay under pure principal stress rotation[J]. Chinese Journal of Geotechnical Engineering，2014，36(3)：474–481.(in Chinese))
[12] 李广信. 高等土力学[J]. 北京：清华大学出版社，2004：2.(LI Guangxin. Advanced soil mechanics[J]. Beijing：Tsinghua University，2004：2.(in Chinese))
[13] 黄茂松，杨 超，崔玉军. 循环荷载下非饱和结构性土的边界面模型[J]. 岩土工程学报，2009，31(6)：817–823.(HUANG Maosong，YANG Chao，CUI Yujun. Elasto-plastic bounding surface model for unsaturated soils under cyclic loading[J]. Chinese Journal of Geotechnical Engineering，2009，31(6)：817–823.(in Chinese))
[14] 姚仰平，万 征，秦振华. 动力UH模型及其有限元应用[J]. 力学学报，2012，44(1)：132–139.(YAO Yangping，WAN Zheng，QIN Zhenhua. Dynamic UH model for sands and its application in FEM[J]. Chinese Journal of Theoretical and Applied Mechanics，2012，44(1)：132–139.(in Chinese))
[15] 王 磊，朱 斌，来向华. 砂土循环累积变形规律与显式计算模型研究[J]. 岩土工程学报，2015，37(11)：2 024–2 029.(WANG Lei，ZHU Bin，LAI Xianghua. Cyclic accumulative deformation of sand and its explicit model[J]. Chinese Journal of Geotechnical Engineering，2015，37(11)：2 024–2 029.(in Chinese))
[16] 李吴刚，杨 庆，刘文化，等. 基于SFG模型的非饱和膨胀土本构模型研究[J]. 岩土工程学报，2015，37(8)：1 449–1 453.(LI Wugang，YANG Qing，LIU Wenhua，et al. Constitutive model for unsaturated expansive clays based on SFG model[J]. Chinese Journal of Geotechnical Engineering，2015，37(8)：1 449–1 453.(in Chinese))
[17] 宋世雄，张建民. 砂土流变行为的热力学本构模型研究[J]. 岩土工程学报，2015，37(增1)：129–133. (SONG Shixiong，ZHANG Jianmin. Thermodynamic constitutive model for rheological behavior of sand[J]. Chinese Journal of Geotechnical Engineering，2015，37(Supp.1)：129–133.(in Chinese))
[18] 孔令明，姚仰平. 考虑时间效应的K0各向异性UH模型[J]. 岩土工程学报，2015，37(5)：812–820.(KONG Lingming，YAO Yangping. K0-anisotropic UH model considering time effects[J]. Chinese Journal of Geotechnical Engineering，2015，37(5)：812–820.(in Chinese))
[19] 杜修力，马 超，路德春. 正常固结黏土的三维弹塑性本构模型[J]. 岩土工程学报，2015，37(2)：235–241.(DU Xiuli，MA Chao，LU Dechun. Three-dimensional elastoplastic constitutive model for normal consolidated clays[J]. Chinese Journal of Geotechnical Engineering，2015，37(2)：235–241.(in Chinese))
[20] 朱 晟，魏匡民，林道通. 筑坝土石料的统一广义塑性本构模型[J]. 岩土工程学报，2014，36(8)：1 394–1 399.(ZHU Sheng，WEI Kuangmin，LIN Daotong. Generalized plasticity model for soil and coarse-grained dam materials[J]. Chinese Journal of Geotechnical Engineering，2014，36(8)：1 394–1 399.(in Chinese))
[21] 李校兵，谷 川，蔡袁强. 循环偏应力和循环围压耦合应力路径下饱和软黏土动模量衰减规律研究[J]. 岩土工程学报，2014，36(7)：1 218–1 226.(LI Xiaobing，GU Chuan，CAI Yuanqiang. Dynamic modulus degradation for soft saturated clay under coupling stress paths of cyclic deviatoric stress and cyclic confining pressure[J]. Chinese Journal of Geotechnical Engineering，2014，36(7)：1 218–1 226.(in Chinese))
[22] TAIEBAT M，DAFALIAS Y F. SANISAND：Simple anisotropic and plasticity model[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2008，32(8)：915–948.
[23] DAFALIAS Y F，TAIEBAT M，PAPADIMITRIOU A G. SANICLAY： simple anisotropic clay plasticity model[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2006，30(12)：1 231–1 257.
[24] 陈生水，沈珠江，郦能惠. 复杂应力路径下无粘性土的弹塑性数值模拟[J]. 岩土工程学报，1995，17(2)：20–28.(CHEN Shengshui，SHEN Zhujiang，LI Nenghui. A elastoplastic model for cohesionless soils under complex stress paths[J]. Chinese Journal of Geotechnical Engineering，1995，17(2)：20–28.(in Chinese))
[25] 刘元雪，郑颖人，陈正汉. 含主应力轴旋转的土体一般应力–应变关系[J]. 应用数学和力学，1998，19(5)：407–413.(LIU Yuanxue，ZHENG Yingren，CHEN Zhenghan. The general stress strain relation of soils involving the rotation of principal stress axes[J]. Applied Mathematics and Mechanics，1998，19(5)：407–413.(in Chinese))
[26] 董 彤，刘元雪，郑颖人. 考虑主应力轴旋转的土体本构关系研究进展[J]. 应用数学和力学，2013，34(4)：327–335.(DONG Tong，LIU Yuanxue，ZHENG Yingren. Research progress of the soil constitutive relation considering principal stress axes rotation[J]. Applied Mathematics and Mechanics，2013，34(4)：327–335.(in Chinese))
[27] MATSUOKA H，SAKAKIBARA K. A constitutive model for sands and clays evaluating principal stress rotation[J]. Soils and Foundations. 1987，27(4)：73–88.
[28] HASHIGUCHI K，TSUTSUMI S. Elastoplastic constitutive equation with tangential stress rate effect[J]. International Journal of Plasticity. 2001，17(1)：117–145.
[29] KHOJASTEHPOUR M，HASHIGUCHI K. Axisymmetric bifurcation analysis in soils by the tangential-subloading surface model[J]. Journal of the Mechanics and Physics of Solids，2004，52(10)：2 235–2 262.
[30] KHOJASTEHPOUR M，MURAKAMI Y，HASHIGUCHI K. Antisymmetric bifurcation in a circular cylinder with tangential plasticity[J]. Mechanics of Materials，2006，38(11)：1 061–1 071.
[31] KHOJASTEHPOUR M，HASHIGUCHI K. The plane strain bifurcation analysis of soils by the tangential-subloading surface model[J]. International Journal of Solids and Structures，2004，41(20)：5 541–5 563.
[32] HASHIGUCHI K. General description of elastoplastic deformation/ sliding phenomena of solids in high accuracy and numerical efficiency：subloading surface[J]. Archives of Computational Methods in Engineering，2013，20(4)：361–417.
[33] MATSUOKA H，NAKAI T. Stress-deformation and strength characteristics of soil under three different principle stresses[C]// Proceedings of JSCE，[S. l.]：[s. n.]，1974，232：59–70.
[34] ROWE P W. The stress-dilatancy relation for static equilibrium of an assembly of particles in contact[C]// Proceedings of Royal Society A.，[S. l.]：[s. n.]，1962，269(1339)：500–527.
[35] LEE K L，SEED H B. Drained strength characteristics of sands[J]. Journal of the Soil Mechanics and Foundations Division 1967，93(SM6)：117–141.
[36] LEE K L，FARHOOMAND I. Compressibility and crushing of granular soil in anisotropic triaxial compression[J]. Canadian Geotechnical Journal，2011，4(1)：68–86
[37] LADE P V，BOPP P A . Relative density effects on drained sand behavior at high pressures. Soils and Foundations，2005，45(1)：1–13.
2017, Vol. 36 
