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

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

Figure 1

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.
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.

Figure 2

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).
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).

Figure 3

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

Figure 4

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°.
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°.

Figure 5

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

Figure 6

Components of EMTTA, used in the study.
Components of EMTTA, used in the study.

Figure 7

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).
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).

Figure 8

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: deviator stress as a function of the axial strain q(ɛ1).

Figure 9

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: maximum principal stress as a function of the axial strain σ1(ɛ1).

Figure 10

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: principal stress in the direction of fixed strain (ɛ2 = 0) as a function of the axial strain σ2(ɛ1).

Figure 11

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

Figure 12

Relations between principal stress components, corresponding to peak soil strength: σ1max (σ3) and σ2(σ3).
Relations between principal stress components, corresponding to peak soil strength: σ1max (σ3) and σ2(σ3).

Figure 13

Relation between Lode angle θ and intermediate stress σ2.
Relation between Lode angle θ and intermediate stress σ2.

Figure 14

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) σ2calc (σ2exp) and (b) R(σ2exp), where R = σ2calc/σ2exp.
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) σ2calc (σ2exp) and (b) R(σ2exp), where R = σ2calc/σ2exp.

Figure 15

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

Figure 16

Dependence of the ratio of intermediate stress σ2 to confining pressure σ3 (Table 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.

Figure 17

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 κD-P, κL-D and κM-N, obtained by Eqs. (16)–(18) (full stress state measurement) and Eqs. (25)–(27) (plane strain condition – Vikash and Prashant approach).
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 κD-P, κL-D and κM-N, obtained by Eqs. (16)–(18) (full stress state measurement) and Eqs. (25)–(27) (plane strain condition – Vikash and Prashant approach).

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_

vκvσ2
Drucker–Prager νκD−P=21.21 % \nu _\kappa ^{{\rm{D}} - {\rm{P}}} = 21.21\,\% νσ2D−P=119.0 % \nu _{{\sigma _2}}^{{\rm{D}} - {\rm{P}}} = 119.0\,\%
Lade–Duncan νκL−D=5.99 % \nu _\kappa ^{{\rm{L}} - {\rm{D}}} = 5.99\,\% νσ2L−D=55.5 % \nu _{{\sigma _2}}^{{\rm{L}} - {\rm{D}}} = 55.5\,\%
Matsuoka–Nakai νκM−N=0.66 % \nu _\kappa ^{{\rm{M}} - {\rm{N}}} = 0.66\,\% νσ2M−N=19.4 % \nu _{{\sigma _2}}^{{\rm{M}} - {\rm{N}}} = 19.4\,\%

The linear fits κexp(ϕps)and the corresponding statistics Pearson's correlation coefficients_

Linear fitPearson's coefficient r
Drucker–Prager κD−Pexp=0.006353 φps+0.001497 \kappa _{{\rm{D}} - {\rm{P}}}^{\exp } = 0.006353\,{\varphi _{{\rm{ps}}}} + 0.001497 rD-P = 0.970
Lade–Duncan κL−Dexp=1.5 φps−10.613 \kappa _{{\rm{L}} - {\rm{D}}}^{\exp } = 1.5\,{\varphi _{{\rm{ps}}}} - 10.613 rL-D = 0.993
Matsuoka–Nakai κM−Nexp=0.2605 φps+2.767 \kappa _{{\rm{M}} - {\rm{N}}}^{\exp } = 0.2605\,{\varphi _{{\rm{ps}}}} + 2.767 rM-N = 0.997

Characteristics of peak strength state for the tested samples_

Testσ1max [kPa]σ2 [kPa]σ3 [kPa]p [kPa]q [kPa]b [ − ]θ [ ° ]
009_17_MC_514026533918159090.2614.46
033_17_MC_1410724792936157050.2413.21
012_18_MC_2111844592926458210.1910.14
013_18_MC_226782621463624850.2211.97
010_18_MC_199023551954846420.2312.46
001_18_MC_158703321914646210.2111.35
010_15_MC_112915292786999140.2513.76
009_18_MC_18148352829276810920.2010.78
008_18_MC_17139650629573210120.1910.40
028_17_MC_12287109521492120.2413.44
031_17_MC_13508191992663720.2212.38

Initial test conditions_

TesteIDσc3[kPa]ec IDc {\boldsymbol {I}}_{\boldsymbol {D}}^{\boldsymbol {c}} nc
009_17_MC_50.5850.3763910.5630.4650.36
033_17_MC_140.5590.4822930.5480.5270.354
012_18_MC_210.5410.5552920.5320.5920.347
013_18_MC_220.5190.6451460.5140.6650.339
010_18_MC_190.5170.6531950.5080.6900.337
001_18_MC_150.5210.6371910.4990.7270.333
010_15_MC_10.4960.7392780.4900.7630.329
009_18_MC_180.4880.7712920.4800.8040.324
008_18_MC_170.4890.7672950.4760.8200.322
028_17_MC_120.4670.857520.4620.8780.316
031_17_MC_130.4690.849990.4620.8780.316

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)_

TestA. Direct stress measurements Eqs. (15)–(18)B. Flow rule and plane strain condition Eqs. (25)–(27)
ϕps κD−Pexp \kappa _{{\rm{D}} - {\rm{P}}}^{\exp } κM−Nexp \kappa _{{\rm{M}} - {\rm{N}}}^{\exp } κL−Dexp \kappa _{{\rm{L}} - {\rm{D}}}^{\exp } σ2D-P \sigma _2^{{\rm{D - P}}} σ2M-N \sigma _2^{{\rm{M - N}}} σ2L-D \sigma _2^{{\rm{L - D}}} κD-Pflow rule \kappa _{D{\rm{ - }}P}^{f{\rm{low}}\,{\rm{rule}}} κM-Nflow rule \kappa _{M{\rm{ - }}N}^{f{\rm{low}}\,{\rm{rule}}} κL-Dflow rule \kappa _{L{\rm{ - }}D}^{f{\rm{low}}\,{\rm{rule}}}
009_17_MC_534.3°0.2111.740.91181.5740.4896.50.17911.739.6
033_17_MC_1434.8°0.2211.941.7904.8560.4682.50.18111.840.0
012_18_MC_2137.2°0.2512.545.71007.5588.07380.19012.342.5
013_18_MC_2240.2°0.2613.249.4583.8314.64120.20213.146.3
010_18_MC_1940.1°0.2613.149.0776.3419.3548.50.20113.146.2
001_18_MC_1539.8°0.2613.149.0747.8407.6530.50.20013.045.7
010_15_MC_140.2°0.2513.148.61111.5599.1784.50.20213.146.3
009_18_MC_1842.1°0.2713.853.41287.1658.1887.50.20913.749.1
008_18_MC_1740.6°0.2713.450.91203.9641.7745.50.20313.246.9
028_17_MC_1243.9°0.2714.355.3251.0122.1169.50.21514.352.0
031_17_MC_1342.4°0.2713.852.9441.3224.3303.50.20913.746.5

The linear fits κexp(IDc) {\kappa ^{\exp }}\left( {I_D^c} \right) and the corresponding Pearson's correlation coefficients_

Linear fitPearson's coefficient r
Drucker–Prager κD−Pexp=0.16IDc+0.13 \kappa _{{\rm{D}} - {\rm{P}}}^{\exp } = 0.16I_D^c + 0.13 rD-P = 0.94
Lade–Duncan κL−Dexp=26.33IDc+31.64 \kappa _{{\rm{L}} - {\rm{D}}}^{\exp } = 26.33I_D^c + 31.64 rL-D = 0.96
Matsuoka–Nakai κM−Nexp=9.20IDc+5.48 \kappa _{{\rm{M}} - {\rm{N}}}^{\exp } = 9.20I_D^c + 5.48 rM-N = 0.96

Parameters of Skarpa sand_

Specific density [kg/m3]2650
Mean particle size [mm]D50 - 0.42
Uniformity coefficient [ − ]U = 2.5
Minimum void ratio [ − ]emin = 0.432
Maximum void ratio [ − ]emax = 0.677
DOI: https://doi.org/10.2478/sgem-2021-0015 | Journal eISSN: 2083-831X | 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
Publication frequency: 4 issues per year
Keywords:
soil failure criteria,
soil peak strength,
plane strain conditions,
true triaxial apparatus,
plastic flow rule
Related subjects:
Geosciences,
Geosciences, other,
Materials sciences,
Composites,
Porous materials,
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.

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