土体软化条件下条形基础地基承载力数值模拟
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摘要
为克服材料软化导致的有限元网格敏感性难题,提出了一个压力相关隐式梯度塑性模型来模拟土体软化条件下条形基础地基承载力。通过引入微应变作为附加运动学变量,推导了包含高阶广义应力的微力平衡和经典动量方程,并基于热力学第二定律,将附加的微力平衡转化为宏观等效塑性应变与微应变耦合的Helmholtz方程。进一步建立能耦合位移和微变量的有限元算法,并通过软化材料双轴压缩试验模拟,验证了该算法在应变局部化数值模拟中的适用性。将建立的方法用于条形基础地基承载力特性模拟,并通过与理想弹塑性模型计算结果对比表明,土体软化将导致地基承载能力降低,破坏模式表现为失稳区域变小且塑性应变幅值增大。
To overcome the mesh sensitivity induced by strain softening, an implicit gradient plasticity model is put forward to simulate the bearing capacity of a rigid strip foundation on strain-softening soil. A micro-variable is introduced to serve as the additional kinematic variable, and a micro-force balance containing higher-order generalized stresses together and the classical balance of momentum equation are derived. Based on the second law of thermodynamics, the additional micro-force balance is converted into a Helmholtz equation that couples the effective plastic strain and micro-strain. Furthermore, a finite element procedure coupling both displacements and micro-strain is implemented. The applicability of the proposed methodology to capture strain localization is verified by the plane strain compression tests. Finally, the established methodology is used to simulate the bearing capacity of a rigid strip foundation on strain-softening soil, and compared to the calculations from perfectly plasticity model. The simulations show that the strain softening induces a decreasing bearing capacity. The resulted failure mode shows a smaller instability range and a larger maximum deformation magnitude.
To overcome the mesh sensitivity induced by strain softening, an implicit gradient plasticity model is put forward to simulate the bearing capacity of a rigid strip foundation on strain-softening soil. A micro-variable is introduced to serve as the additional kinematic variable, and a micro-force balance containing higher-order generalized stresses together and the classical balance of momentum equation are derived. Based on the second law of thermodynamics, the additional micro-force balance is converted into a Helmholtz equation that couples the effective plastic strain and micro-strain. Furthermore, a finite element procedure coupling both displacements and micro-strain is implemented. The applicability of the proposed methodology to capture strain localization is verified by the plane strain compression tests. Finally, the established methodology is used to simulate the bearing capacity of a rigid strip foundation on strain-softening soil, and compared to the calculations from perfectly plasticity model. The simulations show that the strain softening induces a decreasing bearing capacity. The resulted failure mode shows a smaller instability range and a larger maximum deformation magnitude.
引文
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[7]ETEZAD M,HANNA A M,KHALIFA M.Bearing capacity of a group of stone columns in soft soil subjected to local or punching shear failures[J].International Journal of Geomechanics,2018,18(12):04018169.
[8]LEE J K,S.LEE J S.Undrained bearing capacity factors for ring footings in heterogeneous soil[J].Computers and Geotechnics,2016,75:103-111.
[9]LU X L,XUE D W,HUANG M S,et al.A shear hardening plasticity model with nonlinear shear strength criterion for municipal solid waste[J].Computers and Geotechnics,2018,104:204-215.
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[2]HUANG M S,QU X,LU X L.Numerical modeling of the progressive failure of soil with nonlocal regularized strain softening plasticity[J].Computational Mechanics,2017,doi:10.1007/s00466-017-1500-6.
[3]杜修力,侯世伟,路德春,等.梯度塑性理论的计算方法与应用[J].岩土工程学报,2012,34(6):1094-1101.(DUXiu-li,HOU Shi-wei,LU De-chun,et al.Application of gradient plastic theory based on FEPG platform[J].Chinese Journal of Geotechnical Engineering,2012,34(6):1094-1101.(in Chinese))
[4]AIFANTIS E C.The physics of plastic deformation[J].International Journal of Plasticity,1987,3:211-247.
[5]ENGLEN R A B,GEERS M G D,BAAIJENS F P T.Nonlocal implicit gradient-enhanced elasto-plasticity for the modelling of softening behavior[J].International Journal of Plasticity,2003,19:403-433.
[6]PEERLINGS R H J.On the role of moving elastic-plastic boundaries in strain gradient plasticity[J].Modelling and Simulation in Materials Science and Engineering,2007,15:109-120.
[7]ETEZAD M,HANNA A M,KHALIFA M.Bearing capacity of a group of stone columns in soft soil subjected to local or punching shear failures[J].International Journal of Geomechanics,2018,18(12):04018169.
[8]LEE J K,S.LEE J S.Undrained bearing capacity factors for ring footings in heterogeneous soil[J].Computers and Geotechnics,2016,75:103-111.
[9]LU X L,XUE D W,HUANG M S,et al.A shear hardening plasticity model with nonlinear shear strength criterion for municipal solid waste[J].Computers and Geotechnics,2018,104:204-215.
[10]FOREST S.Micromorphic approach for gradient elasticity,viscoplasticity,and damage[J].J Eng Mech,2009,135(3):117-131.