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### 离散单元法在岩土力学中的应用研究

河海大学 刘斯宏

Hertz弹性接触模型与计算公式

Start 1979

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

Determination of Contact Forces 1979

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.

Normal contact force between two discs 1979

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:

Tangential contact force between two discs 1979

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

1. Simulating direct shear box test 1979

- 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.

Quasi-simple shear deformation 1979

σz=49kPa

D 1979ense sample Loose sample

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

为粒子接点力的分布函数 1979

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）

剪切滑动面上应力应变宏观量与微观量关系 angles, θ.

滑动面上宏观应力应变量与细观结构量间的关系

A angles, θ.

A

(after Lee and Seed, 1967)

τ=σtanφμ

Commonly, it is considered that shear strength is essentially originated from the friction between soil particles.

Influence of φ angles, θ. μ on stress-dilatancy relationship

▼ angles, θ. 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)

2. Simulating the Collapse of Unsaturated Soil angles, θ.

- 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.

Suction and interparticle adhesive force angles, θ.

water attachment in an assembly of wet circular aluminum rods

DEM incorporating with P angles, θ. s

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.

Collapse behavior during isotropic compaction angles, θ.

Experimental results of compacted Kaolin-clay

DEM simulation results

Collapse behavior during shearing angles, θ.

Experimental results of compacted Kaolin-clay

DEM simulation results

Microscopic view of collapse angles, θ.

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

Comments from one reviewer angles, θ.

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.

3. Study on the failure mechanism of granular slope angles, θ.

- 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.

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

25 surface during the tilting of the box until failure occurs: solid line

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

4. Study on soilbags by DEM surface during the tilting of the box until failure occurs: solid line

地面 surface during the tilting of the box until failure occurs: solid line

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

Under cyclic loading surface during the tilting of the box until failure occurs: solid line

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