Characteristic parameters of soil failure criteria for plane strain conditions – experimental and semi-theoretical study

Justyna Sławińska-Budzich

doi:10.2478/sgem-2021-0015

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Characteristic parameters of soil failure criteria for plane strain conditions – experimental and semi-theoretical study

Studia Geotechnica et Mechanica

Volume 43 (2021): Issue 3 (September 2021)

By: Justyna Sławińska-Budzich

Open Access

|Sep 2021

Figures & Tables

Two-dimensional and three-dimensional soil stress states: a) cylindrical sample in axisymmetric stress conditions, σ₂ = σ₃ and b) rectangular sample in true triaxial conditions, σ₁ ≠ σ₂ ≠ σ₃.

The principal stress and axial strain curves for the selected test in plane strain conditions: a) q(ɛ₁) and b) σ₁(ɛ₁), σ₂(ɛ₁) and σ₃(ɛ₁).

Comparison of the results from drained triaxial and plane strain tests on sand [18] and true-triaxial tests on Skarpa sand.

Failure surfaces in the deviatoric plane, see Georgiadis et al. (2004). In plane strain conditions, Lode angle varies roughly from θ = 10° to θ = 20°.

Table 1

Parameters of Skarpa sand.

Specific density [kg/m³]	2650
Mean particle size [mm]	D₅₀ - 0.42
Uniformity coefficient [ − ]	U = 2.5
Minimum void ratio [ − ]	e_min = 0.432
Maximum void ratio [ − ]	e_max = 0.677

Layout of the soil sample under plane strain conditions in EMTTA.

a) The GDS EMTTA chamber with a sample prepared for the test. The role of the side plates is to prevent soil deformations in the x₂direction, b) proximity transducer on the doors of the measurement cell (test chamber).

Results of the experimental tests listed in Table 1: deviator stress as a function of the axial strain q(ɛ₁).

Results of the experimental tests listed in Table 1: maximum principal stress as a function of the axial strain σ₁(ɛ₁).

Results of the experimental tests listed in Table 1: principal stress in the direction of fixed strain (ɛ₂ = 0) as a function of the axial strain σ₂(ɛ₁).

Results of the experimental tests listed in Table 1: volumetric strain as a function of the axial strain ɛ_v(ɛ₁).

Table 2

Initial test conditions.

Test	e	*I_D*	σ^c₃[kPa]	*e^c*	$I_{D}^{c}$	*n^c*
009_17_MC_5	0.585	0.376	391	0.563	0.465	0.36
033_17_MC_14	0.559	0.482	293	0.548	0.527	0.354
012_18_MC_21	0.541	0.555	292	0.532	0.592	0.347
013_18_MC_22	0.519	0.645	146	0.514	0.665	0.339
010_18_MC_19	0.517	0.653	195	0.508	0.690	0.337
001_18_MC_15	0.521	0.637	191	0.499	0.727	0.333
010_15_MC_1	0.496	0.739	278	0.490	0.763	0.329
009_18_MC_18	0.488	0.771	292	0.480	0.804	0.324
008_18_MC_17	0.489	0.767	295	0.476	0.820	0.322
028_17_MC_12	0.467	0.857	52	0.462	0.878	0.316
031_17_MC_13	0.469	0.849	99	0.462	0.878	0.316

Table 3

Characteristics of peak strength state for the tested samples.

Test	σ₁^max [kPa]	σ₂ [kPa]	σ₃ [kPa]	p [kPa]	q [kPa]	b [ − ]	θ [ ° ]
009_17_MC_5	1402	653	391	815	909	0.26	14.46
033_17_MC_14	1072	479	293	615	705	0.24	13.21
012_18_MC_21	1184	459	292	645	821	0.19	10.14
013_18_MC_22	678	262	146	362	485	0.22	11.97
010_18_MC_19	902	355	195	484	642	0.23	12.46
001_18_MC_15	870	332	191	464	621	0.21	11.35
010_15_MC_1	1291	529	278	699	914	0.25	13.76
009_18_MC_18	1483	528	292	768	1092	0.20	10.78
008_18_MC_17	1396	506	295	732	1012	0.19	10.40
028_17_MC_12	287	109	52	149	212	0.24	13.44
031_17_MC_13	508	191	99	266	372	0.22	12.38

Relations between principal stress components, corresponding to peak soil strength: σ₁^max (σ₃) and σ₂(σ₃).

Relation between Lode angle θ and intermediate stress σ₂.

Table 4

Characteristic parameters of Drucker–Prager, Matsuoka–Nakai and Lade–Duncan soil failure criteria, obtained from direct stress measurements (A) and the associated flow rule assuming plane strain conditions (B).

Test	A. Direct stress measurements Eqs. (15)–(18)				B. Flow rule and plane strain condition Eqs. (25)–(27)
	ϕ_ps	$κ_{D - P}^{\exp}$	$κ_{M - N}^{\exp}$	$κ_{L - D}^{\exp}$	$σ_{2}^{D-P}$	$σ_{2}^{M-N}$	$σ_{2}^{L-D}$	$κ_{D - P}^{f low rule}$	$κ_{M - N}^{f low rule}$	$κ_{L - D}^{f low rule}$
009_17_MC_5	34.3°	0.21	11.7	40.9	1181.5	740.4	896.5	0.179	11.7	39.6
033_17_MC_14	34.8°	0.22	11.9	41.7	904.8	560.4	682.5	0.181	11.8	40.0
012_18_MC_21	37.2°	0.25	12.5	45.7	1007.5	588.0	738	0.190	12.3	42.5
013_18_MC_22	40.2°	0.26	13.2	49.4	583.8	314.6	412	0.202	13.1	46.3
010_18_MC_19	40.1°	0.26	13.1	49.0	776.3	419.3	548.5	0.201	13.1	46.2
001_18_MC_15	39.8°	0.26	13.1	49.0	747.8	407.6	530.5	0.200	13.0	45.7
010_15_MC_1	40.2°	0.25	13.1	48.6	1111.5	599.1	784.5	0.202	13.1	46.3
009_18_MC_18	42.1°	0.27	13.8	53.4	1287.1	658.1	887.5	0.209	13.7	49.1
008_18_MC_17	40.6°	0.27	13.4	50.9	1203.9	641.7	745.5	0.203	13.2	46.9
028_17_MC_12	43.9°	0.27	14.3	55.3	251.0	122.1	169.5	0.215	14.3	52.0
031_17_MC_13	42.4°	0.27	13.8	52.9	441.3	224.3	303.5	0.209	13.7	46.5

The intermediate stress σ₂, obtained for Drucker–Prager (D-P), Matsuoka–Nakai (M-N) and Lade–Duncan (L-D) failure criteria, assuming plane strain condition and the associated flow rule, as function of the measured σ₂ (Table 3): (a) σ₂^calc (σ₂^exp) and (b) R(σ₂^exp), where R = σ₂^calc/σ₂^exp.

Dependence of the intermediate stress σ₂ (Tables 3 and 4) on the initial relative density of Skarpa sand.

Dependence of the ratio of intermediate stress σ₂ to confining pressure σ₃ (Table 4) on the initial relative density of Skarpa sand.

Parameters of Mohr–Coulomb (M-C), Drucker–Prager (D-C), Matsuoka–Nakai (M-N) and Lade–Duncan (L-D) failure criteria depending on soil relative density: (a) friction angle ϕ, (b)–(d) comparison of κ_D-P, κ_L-D and κ_M-N, obtained by Eqs. (16)–(18) (full stress state measurement) and Eqs. (25)–(27) (plane strain condition – Vikash and Prashant approach).

Table 5

The linear fits $κ^{\exp} (I_{D}^{c})$ and the corresponding Pearson's correlation coefficients.

	Linear fit	Pearson's coefficient r
Drucker–Prager	$κ_{D - P}^{\exp} = 0.16 I_{D}^{c} + 0.13$	r_D-P = 0.94
Lade–Duncan	$κ_{L - D}^{\exp} = 26.33 I_{D}^{c} + 31.64$	r_L-D = 0.96
Matsuoka–Nakai	$κ_{M - N}^{\exp} = 9.20 I_{D}^{c} + 5.48$	r_M-N = 0.96

Table 6

The linear fits κ^exp(ϕ_ps)and the corresponding statistics Pearson's correlation coefficients.

	Linear fit	Pearson's coefficient r
Drucker–Prager	$κ_{D - P}^{\exp} = 0.006353 φ_{ps} + 0.001497$	r_D-P = 0.970
Lade–Duncan	$κ_{L - D}^{\exp} = 1.5 φ_{ps} - 10.613$	r_L-D = 0.993
Matsuoka–Nakai	$κ_{M - N}^{\exp} = 0.2605 φ_{ps} + 2.767$	r_M-N = 0.997

Table 7

Average relative difference of parameters κ and intermediate principal stress σ₂, determined by the two approaches: full set of principal stresses and Vikash and Prashant proposal, for Drucker–Prager, Lade–Duncan and Matsuoka–Nakai failure criteria.

	*v_κ*	v_σ₂
Drucker–Prager	$ν_{κ}^{D - P} = 21.21 %$	$ν_{σ_{2}}^{D - P} = 119.0 %$
Lade–Duncan	$ν_{κ}^{L - D} = 5.99 %$	$ν_{σ_{2}}^{L - D} = 55.5 %$
Matsuoka–Nakai	$ν_{κ}^{M - N} = 0.66 %$	$ν_{σ_{2}}^{M - N} = 19.4 %$

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DOI: https://doi.org/10.2478/sgem-2021-0015 | Journal eISSN: 2083-831X (formerly 0137-124X) | Journal ISSN: 0137-6365

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Language: English

Page range: 237 - 254

Submitted on: Jan 12, 2021

Accepted on: Apr 29, 2021

Published on: Sep 30, 2021

Published by: Wroclaw University of Science and Technology

In partnership with: Paradigm Publishing Services

Keywords:

soil failure criteria,

soil peak strength,

plane strain conditions,

true triaxial apparatus,

Related subjects:

Physics,

Mechanics and fluid dynamics

© 2021 Justyna Sławińska-Budzich, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 43 (2021): Issue 3 (September 2021)

Characteristic parameters of soil failure criteria for plane strain conditions – experimental and semi-theoretical study

Figures & Tables

Figure 1

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Figure 4

Table 1

Figure 5

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Figure 7

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Figure 11

Table 2

Table 3

Figure 12

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Table 4

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Figure 16

Figure 17

Table 5

Table 6

Table 7

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