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

Justyna Sławińska-Budzich; Jacek Mierczyński

doi:10.2478/sgem-2019-0039

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

Studia Geotechnica et Mechanica

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

By: Justyna Sławińska-Budzich and Jacek Mierczyński

Open Access

|Jun 2020

Figures & Tables

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.

Table 1

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

Test	η = const	dp′ > 0		dp′ < 0

		$I_{D}^{0}$	$A_{v}^{u}$	$I_{D}^{0}$	$A_{v}^{u}$
LH75d	η = 0.64	0.077	10.75	0.239	5.10
LH77d	η = 0.97	0.146	8.82	0.280	4.15
LH79d	η = 0.44	0.23	8.69	0.356	5.07
LH80d	η = 1.12	0.113	9.02	0.248	4.17
LH81d	η = 1.27	0.082	10.26	0.204	4.49
LH81dd	η = 1.22	0.057	10.42	0.201	4.45
LH82d	η = 0.23	0.094	8.3	0.181	4.54
LH84d	η = 0	0.056	8.4	0.178	4.72

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

Table 2

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

Test	η = const	First phase: dp′ > 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

Relationship A_q (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.

Table 3

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

		$I_{D}^{0}$	A_v	A_q	$I_{D}^{0}$	$A_{v}^{u}$
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

Relationship A_q (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.

Table 4

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

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.

References

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DOI: https://doi.org/10.2478/sgem-2019-0039 | Journal eISSN: 2083-831X (formerly 0137-124X) | Journal ISSN: 0137-6365

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Language: English

Page range: 137 - 150

Submitted on: Jul 5, 2019

Accepted on: Jan 10, 2020

Published on: Jun 30, 2020

Published by: Wroclaw University of Science and Technology

In partnership with: Paradigm Publishing Services

Keywords:

constitutive equations,

Related subjects:

Physics,

Mechanics and fluid dynamics

© 2020 Justyna Sławińska-Budzich, Jacek Mierczyński, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

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

Figures & Tables

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Table 1

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Table 3

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Table 4

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