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# 离散单元法 在岩土力学中的应用研究 PowerPoint PPT Presentation

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## 离散单元法在岩土力学中的应用研究

A numerical technique

DEM：颗粒与空隙

Meso

Macro

Micro

Hertz弹性接触模型与计算公式

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

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

Relative Displacements at Contact

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.

### 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:

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

Governing Equations of Static Equilibrium

### 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.

Quasi-simple shear deformation

σz=49kPa

Dense sample Loose sample

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

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

### 剑桥模型中用到的应力剪胀方程

q/p

M

(Modified)

1

1

(Original)

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.

Influence of φμ on stress-dilatancy relationship

▼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

T－K地点

インナーロック

K－O地点

ロックフィル材

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.

water attachment in an assembly of wet circular aluminum rods

### 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.

### Collapse behavior during isotropic compaction

Experimental results of compacted Kaolin-clay

DEM simulation results

### Collapse behavior during shearing

Experimental results of compacted Kaolin-clay

DEM simulation results

### 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

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

• 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.

Numerical simulations of the dry granular slope at failure

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

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

### 建筑基础减震隔振

（专利号:CN101914922A；CN201010239164.1）

(1)承载特性;(2)隔震特性;(3)阻尼消能特性