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An elastoplastic constitutive model for assessing ground settlements induced by deep excavations

Hiba El-Arja
Hiba El-Arja
, 
Sébastien Burlon
Sébastien Burlon
 oraz 
Emmanuel Bourgeois
Emmanuel Bourgeois
   | 21 wrz 2023
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Article Category: Original Study
Data publikacji: 21 wrz 2023
Zakres stron: 231 - 245
Otrzymano: 16 sty 2023
Przyjęty: 13 maj 2023
DOI: https://doi.org/10.2478/sgem-2023-0011
Słowa kluczowe
© 2023 Hiba El-Arja et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1:

Yield surface in the principal stress space.
Yield surface in the principal stress space.

Figure 2:

Section of the yield surface in the deviatoric plane.
Section of the yield surface in the deviatoric plane.

Figure 3:

Calibration of the HCD model on tests B1, B2, and B3.
Calibration of the HCD model on tests B1, B2, and B3.

Figure 4:

Calibration of the HCD model on tests C2 and C3.
Calibration of the HCD model on tests C2 and C3.

Figure 5:

Calibration of the HCD model on tests E1, E2, and E3.
Calibration of the HCD model on tests E1, E2, and E3.

Figure 6:

Calibration of the HCD model on the monotonic drained triaxial test on alluvial material.
Calibration of the HCD model on the monotonic drained triaxial test on alluvial material.

Figure 7:

Calibration of the HCD model on the drained triaxial test with unloading cycles on alluvial material.
Calibration of the HCD model on the drained triaxial test with unloading cycles on alluvial material.

Figure 8:

Experimental setup (a) front view, (b) top view.
Experimental setup (a) front view, (b) top view.

Figure 9:

Mesh used for the simulations.
Mesh used for the simulations.

Figure 10:

Results of the calibration of the Hardening Soil Model parameters.
Results of the calibration of the Hardening Soil Model parameters.

Figure 11:

Results of the calibration of the HCD model parameters.
Results of the calibration of the HCD model parameters.

Figure 12:

Comparison of the horizontal displacements (last three stages).
Comparison of the horizontal displacements (last three stages).

Figure 13:

Comparison of the settlements behind the wall (last two stages).
Comparison of the settlements behind the wall (last two stages).

Figure 14:

Comparison of the forces in the struts (for four stages: excavation down to 3, 4, and 5 m, and surcharge).
Comparison of the forces in the struts (for four stages: excavation down to 3, 4, and 5 m, and surcharge).

Figure 15:

Comparison of the settlements behind the wall (last two stages) with a friction angle of 20° for the sand–wall interface.
Comparison of the settlements behind the wall (last two stages) with a friction angle of 20° for the sand–wall interface.

Reference parameters (calibrated on the triaxial tests) for the Hochstetten sand.

HSM Eurref=63 MPa, E50ref=21 MPa, ν=0.1, m=0.5, pref=100 kPa, c=5 kPa, φ=43°, ψ=14°, Rf=0.9
HCD model E=75 MPa, ν=0.3, Ro=0, pc=2 kPa, φult=43°, φc=29°, αo=3, b=0.0025

HCD model parameters.

E v φo pc φult αo φc b
MPa ° kPa deg deg
Monotonic test (confining pressure 175 kPa) 57 0.4 φmin 0 37 8 27 0.001
Cyclic test (confining pressure 157 kPa) 57 0.4 φmin 0 37 20 31 0.003

Parameters of the reaction wall and the sheet pile wall.

Wall E(MPa) I(cm4/m) A(cm2/m) Eeq (MPa) teq (cm)
Reaction wall 210,000 968 106 24,400 10
Sheet pile wall 210,000 11,610 116 6800 35

Results obtained with HSM (displacements in mm).

Measures HSM (ref.) HSM (adj.)
Max horizontal displacement – 4 m 1.83 1.34 (−27%) 0.91 (−50%)
Max horizontal displacement – 5 m 2.95 4.49 (+52%) 2.56 (−13%)
Max horizontal displacement –surcharge 3.36 5.80 (+73%) 3.28 (−2%)
Settlement 1 m behind the wall – 5 m 2.17 1.21 (−44%) 0.80 (−63%)
Settlement 1 m behind the wall – surcharge 2.80 4.18 (+49%) 2.26 (−19%)

Summary of the triaxial tests considered in this study.

Test Depth Type of soil Type of test
B 6.5–7 Very fine silty sand Consolidated drained CD
C 8.5–9.5 Slightly sandy pebbles and gravel Consolidated drained CD
E 13.7–14 Silty clay Consolidated drained CD

Parameters of the HCD model for tests B, C, and E (σc denotes the confining pressure).

σc E v φo pc φult αo φc b
kPa MPa - ° kPa ° - ° -
Test B 1 150 45 0.2 7 10 35 1 31 0.005
2 250 70 0.2 7 10 35 1 32 0.008
Test C 3 400 107 0.2 7 10 35 1 33 0.009
2 200 133 0.1 15 15 41 1 38 0.002
3 350 233 0.127 15 15 41 1 39 0.005
Test E 1 200 16 0.12 1.2 60 23 1 20 0.004
2 350 45 0.12 2.2 60 23 1 20 0.005
3 550 112 0.14 4.2 60 23 1 21 0.015

Results obtained with the HCD model (displacements in mm).

Measures HCD (ref.) HCD (adj.)
Max. horizontal displacement – 4 m 1.83 0.86 (−53%) 1.37 (−25%)
Max. horizontal displacement – 5 m 2.95 2.53 (−14%) 2.99 (+1%)
Max. horizontal displacement – surcharge 3.36 2.86 (−14%) 3.51 (+4%)
Settlement 1 m behind the wall – 5 m 2.17 1.81 (−17%) 1.81 (−17%)
Settlement 1 m behind the wall – surcharge 2.80 2.65 (−5%) 3.04 (+8%)
eISSN:
2083-831X
Język:
Angielski
Częstotliwość wydawania:
4 razy w roku
Dziedziny czasopisma:
Geosciences, other, Materials Sciences, Composites, Porous Materials, Physics, Mechanics and Fluid Dynamics
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