Deformations and stability of granular soils: Classical triaxial tests and numerical results from an incremental model

Justyna Sławińska-Budzich; Jacek Mierczyński

Open Access

Deformations and stability of granular soils: Classical triaxial tests and numerical results from an incremental model

Justyna Sławińska-Budzich

and

Jacek Mierczyński

| Jun 30, 2020

Studia Geotechnica et Mechanica

Volume 42 (2020): Issue 2 (June 2020)

About this article

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Published Online: Jun 30, 2020

Page range: 137 - 150

Received: Jul 05, 2019

Accepted: Jan 10, 2020

DOI: https://doi.org/10.2478/sgem-2019-0039

Keywords
constitutive equations, granular soils, deformations, instability, stability

© 2020 Justyna Sławińska-Budzich et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Sand sample preparation for testing with gauges installed (photo by W. Świdziński).

The stress plane p′ − q with a grey zone in which the definitions of deviatoric loading and unloading are unclear.

The meaning of the variable η and the sign of dη.

Stress paths η = const used for the calibration of the incremental model.

Experimental results and an approximation curve for volumetric strain that develops during anisotropic consolidation of contractive sand.

Experimental results and an approximation curve for volumetric strain that develops in contractive sand for various stress paths η = const when dp′ < 0.

Experimental results and an approximation of deviatoric strain that develops in contractive sand for stress paths η = const when dp′ > 0.

Relationship Aq (η): experimental results and their analytical approximation for deviatoric strain that develops in contractive sand for stress paths η = const when dp′ > 0.

Experimental results for deviatoric strain that develops in contractive for stress paths η = const when dp′ < 0.

Relationship Aq (η): experimental results and their analytical approximation for deviatoric strain that develops in dilative sand for stress paths η = const when dp′ > 0.

Experimental results for pure shearing of dilative sand presented in the form of a single ‘common’ curve.

Diagram illustrating the application of subsequent incremental equations.

Spherical unloading for different initial deviator stress levels.

Volumetric strains corresponding to different stress paths.

Static liquefaction: experimental and numerical results.

The behaviour of dilative sand under undrained conditions: experimental and numerical results.

Series of experiments performed to calibrate the model for contractive sand.

Test	η = const	First phase: dp′ > 0

		$I_{D}^{0}$ I_D^0	A_q
LH75d	η = 0.64	0.077	2.94
LH77d	η = 0.97	0.146	6
LH79d	η = 0.44	0.23	1.3
LH80d	η = 1.12	0.113	9.76
LH81d	η = 1.27	0.082	28.3
LH81dd	η = 1.22	0.057	20.2
LH82d	η = 0.23	0.094	0.21
LH84d	η = 0	0.056	−2.63

Functions needed to build the incremental model.

	Function		Average values of coeflcients

	Contractive	Dilative	Contractive	Dilative
M^l	$A_{v} / 2 \sqrt{p^{'}}$ A_v /2\sqrt {p^\prime}		A_v = 9.33	A_v = 3.48
P^l	$(a + b η^{4}) / 2 \sqrt{p^{'}}$ \left( {a + b\eta ^4 } \right)/2\sqrt {p^\prime}		a = −0.68	a = 0
P^l			b = 9.74	b = 1.62
N^l	$4 c_{1} η^{3} \sqrt{P^{'}} (2 a_{1} a_{2} \exp {(a_{2} η)}^{2} + 3 a_{3} η^{2}) \sqrt{p^{'}}$ 4c_1 \eta ^3 \sqrt {P^\prime} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\left( {2a_1 a_2 {\it exp} \left( {a_2 \eta } \right)^2 + 3a_3 \eta ^2 } \right)\sqrt {p^\prime}		c₁ = 2.97	a₁ = −0.74 * 10⁻⁴
				a₂ = 6.39
				a₃ = 0.848
Q^l	$b_{1} b_{2} (\exp b_{2} η) \sqrt{p^{'}}$ b_1 b_2 ({\it exp}\; b_2 \eta )\sqrt {p^\prime}		b₁ = 0.023	b₁ = 3.5 × 10⁻⁴
Q^l			b₂ = 6.245	b₂ = 6.648
M^u		$A_{v}^{u} / 2 \sqrt{p^{'}}$ A_v^u /2\sqrt {p^\prime}	$A_{u}^{v} = 4.59$ A_u^v = 4.59	$A_{u}^{v} = 3$ A_u^v = 3
P^u		0	-	-
N^u		$a_{v} \sqrt{p^{'}}$ a_v \sqrt {p^\prime}	a_v = −0.87	a_v = −0.39
Q^u		$b_{q} \sqrt{p^{'}}$ b_q \sqrt {p^\prime}	b_q = 0.76	b_q = 0.4

List of experiments performed on contractive sand samples and the corresponding results for a single spherical loading–unloading loop.

Test	η = const	First phase:			Second phase: dp′ < 0

		$I_{D}^{0}$ I_D^0	A_v	A_q	$I_{D}^{0}$ I_D^0	$A_{v}^{u}$ A_v^u
SH73d	η = 0.96	0.702	3.3	1	0.749	2.59
SH75d	η = 1.23	0.701	3.28	2.22	0.749	3.04
SH76d	η = 0.64	0.669	3.72	0.52	0.722	3.04
SH77d	η = 0.34	0.703	3.52	0.62	0.753	2.9
SH78d	η = 0	0.701	3.45	0	0.750	2.96
SH80d	η = 1.35	0.632	3.27	6.5	0.678	3.35

eISSN:: 2083-831X
Language:: English

Publication timeframe:: 4 times per year
Journal Subjects:: Geosciences, other, Materials Sciences, Composites, Porous Materials, Physics, Mechanics and Fluid Dynamics

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Deformations and stability of granular soils: Classical triaxial tests and numerical results from an incremental model

Article Category: Research Article

Published Online: Jun 30, 2020

Page range: 137 - 150

Received: Jul 05, 2019

Accepted: Jan 10, 2020

DOI: https://doi.org/10.2478/sgem-2019-0039

Keywords
constitutive equations, granular soils, deformations, instability, stability

© 2020 Justyna Sławińska-Budzich et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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Series of experiments performed to calibrate the model for contractive sand.

Functions needed to build the incremental model.

List of experiments performed on contractive sand samples and the corresponding results for a single spherical loading–unloading loop.

Deformations and stability of granular soils: Classical triaxial tests and numerical results from an incremental model

Article Category: Research Article

Published Online: Jun 30, 2020

Page range: 137 - 150

Received: Jul 05, 2019

Accepted: Jan 10, 2020

DOI: https://doi.org/10.2478/sgem-2019-0039

Keywordsconstitutive equations, granular soils, deformations, instability, stability

© 2020 Justyna Sławińska-Budzich et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Figure 14

Figure 15

Figure 16

Series of experiments performed to calibrate the model for contractive sand.

Functions needed to build the incremental model.

List of experiments performed on contractive sand samples and the corresponding results for a single spherical loading–unloading loop.

Keywords
constitutive equations, granular soils, deformations, instability, stability