Figure 1:
Yield surface in the principal stress space.
Figure 2:
Section of the yield surface in the deviatoric plane.
Table 1:
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 |
Figure 3:
Calibration of the HCD model on tests B1, B2, and B3.
Figure 4:
Calibration of the HCD model on tests C2 and C3.
Figure 5:
Calibration of the HCD model on tests E1, E2, and E3.
Table 2:
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 |
Figure 6:
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.
Table 3:
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 |
Figure 8:
Experimental setup (a) front view, (b) top view.
Figure 9:
Mesh used for the simulations.
Table 4:
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 |
Figure 10:
Results of the calibration of the Hardening Soil Model parameters.
Figure 11:
Results of the calibration of the HCD model parameters.
Table 5:
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 |
Table 6:
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%) |
Table 7:
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%) |
Figure 12:
Comparison of the horizontal displacements (last three stages).
Figure 13:
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).
Figure 15:
Comparison of the settlements behind the wall (last two stages) with a friction angle of 20° for the sand–wall interface.