Have a personal or library account? Click to login
3D DEM simulations of basic geotechnical tests with early detection of shear localization Cover

3D DEM simulations of basic geotechnical tests with early detection of shear localization

Studia Geotechnica et Mechanica
Volume 43 (2021): Issue 1 (April 2021)
By: Aleksander Grabowski and  Michał Nitka  
Open Access
|Dec 2020

Figures & Tables

Figure 1

Two spheres in contact with forces and momentum acting on them ( F→n{\vec F_n} - normal contact force, F→s{\vec F_s} – tangential contact force, M→n{\vec M_n} - contact moment force and n→\vec n - contact normal vector) [48].
Two spheres in contact with forces and momentum acting on them ( F→n{\vec F_n} - normal contact force, F→s{\vec F_s} – tangential contact force, M→n{\vec M_n} - contact moment force and n→\vec n - contact normal vector) [48].

Figure 2

Mechanical response of (a) tangential (b) normal and (c) rolling contact model laws [45].
Mechanical response of (a) tangential (b) normal and (c) rolling contact model laws [45].

Figure 3

Model set-up for numerical simulations of triaxial test.
Model set-up for numerical simulations of triaxial test.

Figure 4

Discrete simulations of homogeneous triaxial compression test compared to experiments by Wu [1]: A) vertical normal stress σ1 and B) volumetric strain ɛv versus vertical normal strain ɛ1 from a) numerical results and b) experimental results (e0 = 0.53, d50 = 5.0 mm, σ0 = 50, 200 and 500 kPa).
Discrete simulations of homogeneous triaxial compression test compared to experiments by Wu [1]: A) vertical normal stress σ1 and B) volumetric strain ɛv versus vertical normal strain ɛ1 from a) numerical results and b) experimental results (e0 = 0.53, d50 = 5.0 mm, σ0 = 50, 200 and 500 kPa).

Figure 5

Vertical normal stress σ1 versus vertical normal strain ɛ1 from discrete simulations of homogeneous triaxial compression test for different initial void ratios e0: a) e0 = 0.53, b) e0 = 0.60 and c) e0 = 0.75 (σ0 = 200 kPa, d50 = 5.0 mm).
Vertical normal stress σ1 versus vertical normal strain ɛ1 from discrete simulations of homogeneous triaxial compression test for different initial void ratios e0: a) e0 = 0.53, b) e0 = 0.60 and c) e0 = 0.75 (σ0 = 200 kPa, d50 = 5.0 mm).

Figure 6

Volumetric strain ɛv versus vertical normal strain ɛ1 from discrete simulations of homogeneous triaxial compression test for different initial void ratios e0: a) e0 = 0.53, b) e0 = 0.60 and c) e0 = 0.75 (σ0 = 200 kPa, d50 = 5.0 mm).
Volumetric strain ɛv versus vertical normal strain ɛ1 from discrete simulations of homogeneous triaxial compression test for different initial void ratios e0: a) e0 = 0.53, b) e0 = 0.60 and c) e0 = 0.75 (σ0 = 200 kPa, d50 = 5.0 mm).

Figure 7

Void ratio e versus vertical normal strain ɛ1 from discrete simulations of homogeneous triaxial compression test for different initial void ratios e0: a) e0 = 0.53, b) e0 = 0.60 and c) e0 = 0.75 (σ0 = 200 kPa, d50 = 5.0 mm).
Void ratio e versus vertical normal strain ɛ1 from discrete simulations of homogeneous triaxial compression test for different initial void ratios e0: a) e0 = 0.53, b) e0 = 0.60 and c) e0 = 0.75 (σ0 = 200 kPa, d50 = 5.0 mm).

Figure 8

Internal friction angle ϕw versus vertical normal strain ɛ1 from discrete simulations of homogeneous triaxial compression test for different initial confining stress: a) σ0 = 50 kPa, b) σ0 = 200 kPa and c) σ0 = 500 kPa (e0 = 0.60, d50 = 5.0 mm).
Internal friction angle ϕw versus vertical normal strain ɛ1 from discrete simulations of homogeneous triaxial compression test for different initial confining stress: a) σ0 = 50 kPa, b) σ0 = 200 kPa and c) σ0 = 500 kPa (e0 = 0.60, d50 = 5.0 mm).

Figure 9

Volumetric strain ɛv versus vertical normal strain ɛ1 from discrete simulations of homogeneous triaxial compression test for different initial confining stress: a) σ0 = 50 kPa, b) σ0 = 200 kPa and c) σ0 = 500 kPa (e0 = 0.60, d50 = 5.0 mm).
Volumetric strain ɛv versus vertical normal strain ɛ1 from discrete simulations of homogeneous triaxial compression test for different initial confining stress: a) σ0 = 50 kPa, b) σ0 = 200 kPa and c) σ0 = 500 kPa (e0 = 0.60, d50 = 5.0 mm).

Figure 10

Model set-up for numerical simulations of direct shear test.
Model set-up for numerical simulations of direct shear test.

Figure 11

Internal friction angle ϕw versus horizontal displacement ux from discrete simulations of direct shear test for different initial void ratios: a) e0 = 0.53, b) e0 = 0.60 and c) e0 = 0.75 (σ0 = 200 kPa, d50 = 0.5 mm).
Internal friction angle ϕw versus horizontal displacement ux from discrete simulations of direct shear test for different initial void ratios: a) e0 = 0.53, b) e0 = 0.60 and c) e0 = 0.75 (σ0 = 200 kPa, d50 = 0.5 mm).

Figure 12

Volumetric strain ɛv versus horizontal displacement ux from discrete simulations of direct shear test for different initial void ratios: a) e0 = 0.53, b) e0 = 0.60 and c) e0 = 0.75 (σ0 = 200 kPa, d50 = 0.5 mm).
Volumetric strain ɛv versus horizontal displacement ux from discrete simulations of direct shear test for different initial void ratios: a) e0 = 0.53, b) e0 = 0.60 and c) e0 = 0.75 (σ0 = 200 kPa, d50 = 0.5 mm).

Figure 13

Front view of the specimen at the final state for different initial void ratios: a) e0 = 0.53, b) e0 = 0.60 and c) e0 = 0.75 (σ0 = 200 kPa, d50 = 0.5 mm) (the dark/light grey stripes were perfectly vertical at the beginning of the tests).
Front view of the specimen at the final state for different initial void ratios: a) e0 = 0.53, b) e0 = 0.60 and c) e0 = 0.75 (σ0 = 200 kPa, d50 = 0.5 mm) (the dark/light grey stripes were perfectly vertical at the beginning of the tests).

Figure 14

Distribution of sphere rotations at the final state of the test for different initial void ratios: a) e0 = 0.53, b) e0 = 0.60 and c) e0 = 0.75 (σ0 = 200 kPa, d50 = 0.5 mm) (red colour – clockwise rotations, blue colour – anti-clockwise rotations) (colour online)
Distribution of sphere rotations at the final state of the test for different initial void ratios: a) e0 = 0.53, b) e0 = 0.60 and c) e0 = 0.75 (σ0 = 200 kPa, d50 = 0.5 mm) (red colour – clockwise rotations, blue colour – anti-clockwise rotations) (colour online)

Figure 15

Internal friction angle ϕw versus horizontal displacement ux from discrete simulations of direct shear test for different vertical load: a) σ0 = 50 kPa, b) σ0 = 200 kPa and c) σ0 = 500 kPa (e0 = 0.60, d50 = 0.5 mm).
Internal friction angle ϕw versus horizontal displacement ux from discrete simulations of direct shear test for different vertical load: a) σ0 = 50 kPa, b) σ0 = 200 kPa and c) σ0 = 500 kPa (e0 = 0.60, d50 = 0.5 mm).

Figure 16

Volumetric strain ɛv versus horizontal displacement ux from discrete simulations of direct shear test for different vertical load: a) σ0 = 50 kPa, b) σ0 = 200 kPa and c) σ0 = 500 kPa (e0 = 0.60, d50 = 0.5 mm).
Volumetric strain ɛv versus horizontal displacement ux from discrete simulations of direct shear test for different vertical load: a) σ0 = 50 kPa, b) σ0 = 200 kPa and c) σ0 = 500 kPa (e0 = 0.60, d50 = 0.5 mm).

Figure 17

Void ratio e0 versus horizontal displacement ux from discrete simulations of direct shear test for different vertical load: a) σ0 = 50 kPa, b) σ0 = 200 kPa and c) σ0 = 500 kPa (e0 = 0.60, d50 = 0.5 mm).
Void ratio e0 versus horizontal displacement ux from discrete simulations of direct shear test for different vertical load: a) σ0 = 50 kPa, b) σ0 = 200 kPa and c) σ0 = 500 kPa (e0 = 0.60, d50 = 0.5 mm).

Figure 18

Distribution of sphere rotations at the final state of the test for different vertical load: a) σ0 = 50 kPa, b) σ0 = 200 kPa and c) σ0 = 500 kPa (e0 = 0.60, d50 = 0.5 mm) (red colour – clockwise rotations, blue colour – anti-clockwise rotations) (colour online).
Distribution of sphere rotations at the final state of the test for different vertical load: a) σ0 = 50 kPa, b) σ0 = 200 kPa and c) σ0 = 500 kPa (e0 = 0.60, d50 = 0.5 mm) (red colour – clockwise rotations, blue colour – anti-clockwise rotations) (colour online).

Figure 19

Distribution of horizontal sphere displacement u’x across the normalized specimen height h/d50 at the specimen centre for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (dark vertical line demonstrates 5% limit).
Distribution of horizontal sphere displacement u’x across the normalized specimen height h/d50 at the specimen centre for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (dark vertical line demonstrates 5% limit).

Figure 20

Distribution of vertical sphere displacement u’y across the normalized specimen height h/d50 at the specimen centre for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (dark vertical line demonstrates 5% limit).
Distribution of vertical sphere displacement u’y across the normalized specimen height h/d50 at the specimen centre for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (dark vertical line demonstrates 5% limit).

Figure 21

Distribution of sphere rotations ω across the normalized specimen height h/d50 at the specimen centre for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (negative value corresponds to the clockwise rotation; dark vertical line demonstrates 5% limit).
Distribution of sphere rotations ω across the normalized specimen height h/d50 at the specimen centre for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (negative value corresponds to the clockwise rotation; dark vertical line demonstrates 5% limit).

Figure 22

Distribution of void ratio e across the normalized specimen height h/d50 at the specimen centre for: a) ux = 0.25mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (dark vertical line demonstrates 5% limit).
Distribution of void ratio e across the normalized specimen height h/d50 at the specimen centre for: a) ux = 0.25mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (dark vertical line demonstrates 5% limit).

Figure 23

Distribution of coordination number n across the normalized specimen height h/d50 at the specimen centre for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (dark vertical line demonstrates 5% limit).
Distribution of coordination number n across the normalized specimen height h/d50 at the specimen centre for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (dark vertical line demonstrates 5% limit).

Figure 24

Evolution of displacements fluctuations ( (u→i−u→i,avg)\left( {{{\vec{u}}}_{i}}-{{{\vec{u}}}_{i,avg}} \right) ) in the entire specimen for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (the arrows are multiple by 10 due to readability; red lines show the estimated localization shape).
Evolution of displacements fluctuations ( (u→i−u→i,avg)\left( {{{\vec{u}}}_{i}}-{{{\vec{u}}}_{i,avg}} \right) ) in the entire specimen for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (the arrows are multiple by 10 due to readability; red lines show the estimated localization shape).

Figure 25

Force chain distribution in the entire specimen for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (red colour corresponds to the force chain above the mean value) (colour online)
Force chain distribution in the entire specimen for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (red colour corresponds to the force chain above the mean value) (colour online)

Figure 26

Distribution of the normal forces fx acting on spheres across the normalized specimen height h/d50 at the specimen centre for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (dark vertical line demonstrates 5% limit).
Distribution of the normal forces fx acting on spheres across the normalized specimen height h/d50 at the specimen centre for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (dark vertical line demonstrates 5% limit).

Figure 27

Distribution of the normal forces fy acting on spheres across the normalized specimen height h/d50 at the specimen centre for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm).
Distribution of the normal forces fy acting on spheres across the normalized specimen height h/d50 at the specimen centre for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm).

Figure 28

Distribution of the maximal normal forces fx,max acting on spheres, in the averaging cell, across the normalized specimen height h/d50 at the specimen centre for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (dark vertical line demonstrates 5% limit).
Distribution of the maximal normal forces fx,max acting on spheres, in the averaging cell, across the normalized specimen height h/d50 at the specimen centre for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (dark vertical line demonstrates 5% limit).

Figure 29

Distribution of the maximal normal forces fy,max acting on spheres, in the averaging cell, across the normalized specimen height h/d50 at the specimen centre for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (dark vertical line demonstrates 5% limit).
Distribution of the maximal normal forces fy,max acting on spheres, in the averaging cell, across the normalized specimen height h/d50 at the specimen centre for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (dark vertical line demonstrates 5% limit).

Figure 30

Distribution of the resultant moment m acting on spheres across the normalized specimen height h/d50 at the specimen centre for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (dark vertical line demonstrates 5% limit).
Distribution of the resultant moment m acting on spheres across the normalized specimen height h/d50 at the specimen centre for: a) ux = 0.25 mm, b) ux = 0.50 mm, c) ux = 0.75 mm, d) ux = 1.00 mm, e) ux = 1.25 mm, f) ux = 1.50 mm, g) ux = 1.75 mm, h) ux = 2.00 mm and i) ux = 10.00 mm (e0 = 0.60, σ0 = 200 kPa, d50 = 0.5 mm) (dark vertical line demonstrates 5% limit).

Early predictor summation_

Predictorux (mm)ts (mm)
Horizontal displacement ux0.7520 × d50
Vertical displacement uy0.7520 × d50
Rotations ω1.5019 × d50
Void ratio e2.0025 × d50
Coordination number n0.75-
Displacement fluctuations1.756 × d50
Normal force fx0.75-
Normal force fy--
Maximal force fx,max1.00-
Maximal force fy,max0.7525 × d50
Moments m0.5030 × d50

Material micro-parameters for discrete simulations_

Material micro-parametersValue
Modulus of elasticity of grain contact Ec (MPa)300
Normal/tangential stiffness ratio of grain contact vc (−)0.3
Inter-particle friction angle μ (°)18
Rolling stiffness coefficient β (−)0.7
Moment limit coefficient η (−)0.4
DOI: https://doi.org/10.2478/sgem-2020-0010 | Journal eISSN: 2083-831X | Journal ISSN: 0137-6365
Journal RSS Feed
Language: English
Page range: 48 - 64
Submitted on: Jun 23, 2020
|
Accepted on: Oct 16, 2020
|
Published on: Dec 4, 2020
Published by: Wroclaw University of Science and Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
direct shear,
granular material,
discrete element method,
localization,
grain level
Related subjects:
Geosciences,
Geosciences, other,
Materials sciences,
Composites,
Porous materials,
Physics,
Mechanics and fluid dynamics

© 2020 Aleksander Grabowski, Michał Nitka, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Previous articleVolume 43 (2021): Issue 1 (April 2021)