﻿ 应力主轴旋转下砂土力学特性的数值模拟分析
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Discrete element simulation of mechanical characteristics of sands under principal stress axes rotation
TONG Zhaoxia , WANG Bo , ZUO Zhaokun , YAO Yangping
School of Transportation Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract:The mechanical behavior of sands and other granular materials subjected to rotation of principal stress axes is significantly dependent on the micro fabric properties and their evolution. The discrete element simulation for sands under cyclic rotation of principal stress axes was validated by comparing the numerical simulation and laboratory test results on the development of two normal strains, the relationship between shear stress and shear strain, the evolution of the volumetric strain, and the effects of initial void ratio and stress ratio. Four variables characterized by the spatial distribution features of particle major axis orientation and inter-particle contact normal directions were used to describe the fabric properties of granular materials. The evolution of the four fabric variables in a single cycle was studied for granular materials subjected to cyclic rotation of principal stress axes. The effects of initial void ratio and stress ratio on the evolution of fabric variables were also investigated in detail.
Key words: principal stress axes rotation     discrete element numerical simulation     sand     mechanical characteristics     micro fabric properties

1 离散元数值模拟

 图 1 应力主轴旋转边界应力的施加方式说明Fig. 1 Illustration of applied mode of boundary stress under rotation of principal stress axes

 初始孔隙比e0 施加的应力比R=(σ1-σ3)/(σ1+σ3) 球应力p/kPa 0.275 0.05/0.10/0.15/0.20/0.25/0.30 200 0.251 0.10/0.15/0.20/0.25/0.30/0.35 0.235 0.30 0.210 0.30
2 数值模拟有效性验证

 图 2 数值模拟实现的应力路径Fig. 2 Achieved stress path for numerical simulation

 图 3 正应变分量与循环周数的关系曲线Fig. 3 Relation curve of normal strain components changing with cycle number

 图 4 剪应力-剪应变关系Fig. 4 Relationship between shear stress and strain

 图 5 应力比对体应变发展的影响(e0=0.251)Fig. 5 Effects of stress ratio on development of volumetric strain (e0=0.251)

 图 6 初始孔隙比对体应变发展的影响(R=0.3)Fig. 6 Effects of initial void ratio on development of volumetric strain (R=0.3)
3 细观组构演化规律分析

αp:颗粒长轴定向组构张量(Fp)两主值的差,用于反映颗粒定向分布的各向异性程度.该值变化范围在0~1之间,αp=0表示颗粒长轴定向为各向同性,αp越大则颗粒长轴定向各向异性程度越强.

θp:颗粒长轴定向组构张量(Fp)的主方向,可认为是所有颗粒的平均定向角.

αc:粒间接触法线组构张量(Fc)两主值的差,用于反映颗粒接触分布的各向异性程度.与αp类似.

θc:粒间接触法线组构张量(Fc)的主方向,可认为是所有颗粒间接触法线的平均定向角.

 图 7 颗粒组构特征在一个周期内的变化规律Fig. 7 Evolution of fabric properties of granules in a single cycle

 图 8 配位数在一个周期内的变化规律Fig. 8 Evolution of coordination number in a single cycle

 图 9 应力比对αc和θc的影响(e0=0.251)Fig. 9 Effects of stress ratio on αc and θc(e0=0.251)

 图 10 初始孔隙比对αc和θc的影响(R=0.3)Fig. 10 Effects of initial void ratio on αc and θc(R=0.3)

4 结 论

1) 颗粒长轴定向组构在应力主轴循环旋转过程中基本无变化,这表明颗粒长轴定向引起的试样固有各向异性对应力主轴旋转条件下的力学特性有重要影响.

2) 粒间接触法线分布的各向异性程度在单个循环周内呈余弦式变化规律,其变化幅度随循环周数增加有增大的趋势.

3) 粒间接触法线角度θc在单个循环周内呈正弦式变化;随循环周数增加,θc的变化幅度呈递减趋势,但远小于应力主轴旋转幅度.

4) 粒间接触法线分布的各向异性程度及法线角度θc均随应力比的增大而增加.在应力比相同的条件下,试样初始孔隙比主要对前几个循环周次的粒间接触法线组构有影响;随循环周数的增加,初始孔隙比不同的试样趋近于达到相同的粒间接触法线组构.

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文章信息

TONG Zhaoxia, WANG Bo, ZUO Zhaokun, YAO Yangping

Discrete element simulation of mechanical characteristics of sands under principal stress axes rotation

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(6): 976-981.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0434