工程地质学报  2018, Vol. 26 Issue (6): 1409-1414   (2807 KB)
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XU Yongfu. 2018. PFC2D simulation of rockfill shear strength based on particle fragmentation[J]. Journal of Engineering Geology, 26(6): 1409-1414. doi: 10.13544/j.cnki.jeg.2017-432.

① 上海交通大学土木工程系 上海 200240;
② 河海大学文天学院 马鞍山 243000

PFC2D SIMULATION OF ROCKFILL SHEAR STRENGTH BASED ON PARTICLE FRAGMENTATION
XU Yongfu①②
① Department of Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240;
② Wentian College of Hohai University, Maanshan 243000
Abstract: PFC2D code is used to simulate the direct shear tests of rockfills, taking into consideration of the particle crushing. The methods to establish the model of the rockfill sample and conduct the tests are given. The results obtained from the numerical simulation are analyzed from several aspects, such as the characteristics of stress-strain relationship, volume strain and shear strength. The effect of the contact-bond strength between basic particles, the porosity of the single rock particle and the porosity of the rockfill material on the shear strength of the rockfills are also discussed.
Key words: Rockfill    Direct shear test    Shear strength    Particle breakage    Fractals    PFC2D simulation

0 引言

1 离散单元模拟方法
1.1 离散单元模型

 图 1 颗粒接触本构模型 Fig. 1 Particle contact constitutive models

 ${{k}_{p}}=2{{E}_{p}}t$ (1)

 ${{F}^{n}}={{K}^{n}}{{U}^{n}}$ (2)

 {{U}^{n}}=\text{ }\left\{ \begin{align} &{{R}_{A}}+{{R}_{B}}-d\ \ \ \ \ \ \left({颗粒间接触} \right) \\ &{{R}_{C}}-d\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left({颗粒与墙接触} \right) \\ \end{align} \right. (3)

 $\Delta {F^s} = - {K^s}\Delta {U^s}$ (4)

 $F_{(2)}^s = F_{(1)}^s\Delta {F^s}$ (5)

 图 2 直剪试样的制备方法 Fig. 2 Model for rockfill sample

(1) 当接触处法向拉力超过Fcn，接触黏结破坏，接触处法向力和切向力会消失。

(2) 当接触处法向压力超过Fcn或者切向作用力超过Fcs，接触黏结破坏，若切向作用力没有超过最大摩擦力(μ|Fn|)，接触处法向力和切向力仍然保持原来大小；若切向作用力超过最大摩擦力，接触处法向力不变，切向力等于最大摩擦力，发生侧向滑移。

1.2 计算参数

2 直剪试验的模拟结果

 图 3 直剪试验中的颗粒位移分布 Fig. 3 Particle displacement in direct shear test

 图 4 直剪试验结果 Fig. 4 Relationship of shear stress-shear displacement

 图 5 剪胀孔隙率与竖向应力的关系 Fig. 5 Porosity of dilatancy and vertical stress

 图 6 剪切强度包络线 Fig. 6 Envelope of shear strength

3 剪切强度

 ${\tau _f} = a\sigma _n^b$ (1)

Xu et al.(2015a)根据颗粒破碎的分形模型给出参数b与颗粒破碎分维D的关系：

 $b = \frac{D}{3}$ (2)

 图 7 颗粒分布曲线 Fig. 7 Particle-size distribution curve

 $P \propto {d^{3 - D}}$ (3)

 图 8 剪切强度与竖向应力的关系 Fig. 8 Relationship between shear strength and normal stress

4 结论

(1) 粗粒土的直剪试验中存在颗粒破碎现象，颗粒破碎程度越高，粗粒土的剪胀变形越小；颗粒不破碎的试样在直剪试验中剪胀现象更明显。

(2) 颗粒不破碎的试样的剪切强度符合Mohr-Coulomb准则；颗粒破碎的试样的强度包络线符合幂函数关系，幂函数的指数与颗粒破碎的分维有关。

(3) 颗粒不破碎的试样的内摩擦角比颗粒不破碎的试样的内摩擦角小；颗粒破碎程度越高，粗粒土的内摩擦角越小。

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