离散单元法 在岩土力学中的应用研究

1. 离散单元法在岩土力学中的应用研究 河海大学 刘斯宏

2. 离散单元法(Distinct Element Method, DEM) A numerical technique 连续体 DEM：颗粒与空隙 Meso Macro Micro 颗粒介质的考虑方法

6. Hertz弹性接触模型与计算公式

7. Contact models of two rigid disks in DEM (Cundall & Strack 1979 )

9. Start Time step loop Initial state (t=t+⊿t) Calculating contact forces, body forces body force m, I Calculating accelerations, velocities and displacement increments contact force Calculating resultant forces (F,M) acting on particle centers F M Calculating new co-ordinates of particle centres End

10. Relative Displacements at Contact

11. Determination of Contact Forces The modeling of the contact between two discs by elastic springs and viscous dashpots leads to two components of the contact forces: one due to the relative displacement increments, corresponding to the elastic springs, and the other due to the relative velocities, corresponding to the viscous dashpots.

12. Normal contact force between two discs Over a very small time step ⊿t At any time t, the components of the normal contact force between two discs due to elastic springs and viscous dashpots are, therefore, obtained: If , then The total normal contact force between two discs at any time t is then given as:

13. Tangential contact force between two discs where ks and ηs are the tangential stiffness and damping, respectively. At any time t, the components of the tangential contact force due to elastic springs and viscous dashpots are then obtainedas If then If then The total tangential contact force between two discs at any time t

14. Governing Equations of Static Equilibrium

16. 1. Simulating direct shear box test • Liu, S.H.: Simulating direct shear test by DEM, Canadian Geotechnical Journal, Vol.43 (2), 155-168, 2006. • Liu, S.H. and Matsuoka, H.: Microscopic interpretation on a stress-dilatancy relationship of granular materials, Soils and Foundations, Vol.43, No.3, pp.73-84, 2003.

19. Quasi-simple shear deformation σz=49kPa

20. Dense sample Loose sample Particle Instantaneous velocity field: (a) Dense sample; (b)Loose sample.

22. 为粒子接点力的分布函数

23. 粒子接点角分布 平均接点力分布 总结点力分布 可见，粒状材料发挥的内摩擦角与颗粒的组构、平均接点力大小及其沿剪切方向倾斜的程度有关，而与通常认为的颗粒间摩擦无直接关系（后再述）

24. N(θ): Frequency distribution of interparticle contact angles, θ.

26. 剪切滑动面上应力应变宏观量与微观量关系 滑动面上宏观应力应变量与细观结构量间的关系

28. 剑桥模型中用到的应力剪胀方程 q/p M (Modified) 1 1 (Original)

29. A A (after Lee and Seed, 1967) τ=σtanφμ Commonly, it is considered that shear strength is essentially originated from the friction between soil particles.

30. Influence of φμ on stress-dilatancy relationship

31. ▼千種砂 (FU=0.755) • ■　鬼ヶ城 礫( FU=0.827) ◆ 砕砂 (FU=0.654) ▼木曽川地点E（FU=0.611） ▲木曽川地点D（FU=0.664） ◆木曽川地点C（FU=0.691） △正三角錐(FU=0.605) □立方体(FU=0.785) ○球(FU=1.0) ■木曽川地点B（FU=0.729）　　 ◎豊浦砂（FU=0.747）　　 ●木曽川地点A（FU=0.758） T－K地点 アウターロック J－IN地点 粗粒材 T－K地点 インナーロック K－O地点 ロックフィル材 ◇Glass Beads(FU=0.881)

32. 2. Simulating the Collapse of Unsaturated Soil • Liu, S.H. and Sun, D.A.: Simulating the collapse of unsaturated soil by DEM, International Journal for Numerical and Analysis Methods in Geomechanics, Vol.26 (6), pp.633-646, 2002. • Liu, S.H., Sun, D.A. and Y.S. Wang: Numerical study of soil collapse behaviors by discrete element modeling, International Journal of Computers and Geotechnics, Vol.30, pp.399-408,2003.

33. Suction and interparticle adhesive force water attachment in an assembly of wet circular aluminum rods

34. DEM incorporating with Ps The components of the resultant forces in x and y directions as well as the resultant moment acting on particle i due to Psij are given The force components due to the interparticle adhesive force Psij are added to the forces based on the overlap of the bodies at the contact and the stiffness of the springs yielding a final resultant force which is then used to compute the acceleration of the body according to Newton’s laws of motion.

35. Collapse behavior during isotropic compaction Experimental results of compacted Kaolin-clay DEM simulation results

36. Collapse behavior during shearing Experimental results of compacted Kaolin-clay DEM simulation results

37. Microscopic view of collapse Variation of (a) contact normals and (b) contact force ratios when Ps released from 20N to 0N at p=100kPa Distributions of contact normals for the specimen with Ps deduced from 5N to 0N and for the specimen with Ps=5N at the same shear strains

38. Comments from one reviewer The proposed model of unsaturated soil is rather simple because the interaction due to capillarity suction is only modelled by constant forces in all contacts. This rather rough model nevertheless allows interesting qualitative results to be shown from numerical simulations.

39. 3. Study on the failure mechanism of granular slope • H.(Joanna) Chen and S.H. Liu :Failure Characteristics and Stabilization Methods, Canadian Geotechnical Journal, Volume 44, Number 4, pp.377-391, 2007. • Liu, S.H. and Bauer, E.: A microscopic study of rainfall-induced granular slope failure. Proc. of 3rd Asian Conf. on unsaturated soils, Nanjing, China, pp.379-383, 2007.

41. Numerical simulations of the dry granular slope at failure

42. Variation of contact angles on planes parallel to the slope surface during the tilting of the box until failure occurs: solid line  before titling, dashed line  tilting to the slope angle of 25° Particle contact information of disappearance and generation on the planes parallel to the slope surface

43. 25 Ps=0.2N 25 25 Ps=0.1N Ps=0 Ps decreases from 0.2 N to 0 with the interval of 0.05 N to simulate the variation of the capillary suction in unsaturated soils

44. 4. Study on soilbags by DEM

45. 地面 建筑基础减震隔振 土工袋基础减振隔震概念图 （专利号:CN101914922A；CN201010239164.1） (1)承载特性;(2)隔震特性;(3)阻尼消能特性

46. Under cyclic loading