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

Aleksander Grabowski; Michał Nitka

doi:10.2478/sgem-2020-0010

.blurhash-client-img { display: none !important; }

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

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

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

Model set-up for numerical simulations of triaxial test.

Discrete simulations of homogeneous triaxial compression test compared to experiments by Wu [1]: A) vertical normal stress σ₁ and B) volumetric strain ɛ_v 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).

Table 1

Material micro-parameters for discrete simulations.

Material micro-parameters	Value
Modulus of elasticity of grain contact E_c (MPa)	300
Normal/tangential stiffness ratio of grain contact v_c (−)	0.3
Inter-particle friction angle μ (°)	18
Rolling stiffness coefficient β (−)	0.7
Moment limit coefficient η (−)	0.4

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).

Volumetric strain ɛ_v 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).

Internal friction angle ϕ_w 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).

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

Internal friction angle ϕ_w versus horizontal displacement u_x 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 ɛ_v versus horizontal displacement u_x 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).

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).

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)

Internal friction angle ϕ_w versus horizontal displacement u_x 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 ɛ_v versus horizontal displacement u_x 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 u_x 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).

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

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

Evolution of displacements fluctuations ( $({\vec{u}}_{i} - {\vec{u}}_{i, avg})$ ) in the entire specimen for: a) u_x = 0.25 mm, b) u_x = 0.50 mm, c) u_x = 0.75 mm, d) u_x = 1.00 mm, e) u_x = 1.25 mm, f) u_x = 1.50 mm, g) u_x = 1.75 mm, h) u_x = 2.00 mm and i) u_x = 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).

Force chain distribution in the entire specimen for: a) u_x = 0.25 mm, b) u_x = 0.50 mm, c) u_x = 0.75 mm, d) u_x = 1.00 mm, e) u_x = 1.25 mm, f) u_x = 1.50 mm, g) u_x = 1.75 mm, h) u_x = 2.00 mm and i) u_x = 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)

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

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

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

Table 2

Early predictor summation.

Predictor	ux (mm)	ts (mm)
Horizontal displacement u_x	0.75	20 × d₅₀
Vertical displacement u_y	0.75	20 × d₅₀
Rotations ω	1.50	19 × d₅₀
Void ratio e	2.00	25 × d₅₀
Coordination number n	0.75	-
Displacement fluctuations	1.75	6 × d₅₀
Normal force f_x	0.75	-
Normal force f_y	-	-
Maximal force f_x,_max	1.00	-
Maximal force f_y,_max	0.75	25 × d₅₀
Moments m	0.50	30 × d₅₀

References

Authors

Metrics

Articles in this issue

DOI: https://doi.org/10.2478/sgem-2020-0010 | Journal eISSN: 2083-831X (formerly 0137-124X) | 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

Keywords:

direct shear,

granular material,

discrete element method,

Related subjects:

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.

Volume 43 (2021): Issue 1 (April 2021)

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

Figures & Tables

Figure 1

Figure 2

Figure 3

Figure 4

Table 1

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Figure 14

Figure 15

Figure 16

Figure 17

Figure 18

Figure 19

Figure 20

Figure 21

Figure 22

Figure 23

Figure 24

Figure 25

Figure 26

Figure 27

Figure 28

Figure 29

Figure 30

Table 2

Paradigm

My account