Group 1: Benchmarks from literature (exact solution)
This section describes a number of benchmarks for which an exact analytical solution can be found in the literature.
1.1. Study Case described in "Technisch Rapport Voorland Zettingsvloeiing"
Description
The example given in "Annex A - Case Study" of the Deltares report 1200503-001-GEO-0004 "Concept Technisch Rapport Voorland Zettingsvloeiing" of G.A. van den Ham & Co is used.
In this example, both global and detailed checks are completed on the basis of a (fictitious) dike section, which with regard to geometry and soil structure is typical of the Southwest Delta.
The dike has a height of NAP+5 m, a crest width of 3 m and a slope of 1:3.
The foreshore begins to imaginary toe of the dike at an elevation of NAP and is 60 m wide. The toe of the trench is NAP-15 m and has a slope of 1:6. The dike section is 800 m long. The phreatic level is at NAP-2 m.
The soil profile is as follows:
- from NAP+3.5 m to NAP+1 m: peat
- from NAP+1 m to NAP-5 m: silty clay
- from NAP-5 m to NAP-18 m: moderately to loosely compacted sand (Calais)
- from NAP-18 m to NAP-30 m: densely compacted sand
Benchmarks results
The details of the calculation can be found in annex A of the report. The main results are given in the table below. The global check fails but the detailed check passes.
D-Flow Slide results
Results of benchmark 1-1 for the Global Check
| Unit | Benchmark | D-FLOW SLIDE | Relative error |
|---|---|---|---|---|
Marge | [m] | 35 | 35 | 0.00% |
X coordinate of the observation profile (Xsign) | [m] | -35 | -35 | 0.00% |
X coordinate of the liquefaction point (XZV) | [m] | 30 | 30 | 0.00% |
Question 1 : Would flow slide lead to damage on levee? |
| Yes | Yes | OK |
| Question 2: Criterion on slope protection met (<1:2,5)? | - | - | ||
Question 3: Artificially underwater installed and non-compacted sandy foreland? |
| No | No | OK |
Question 4: Flow slide possible based on geometry only? |
| Yes | Yes | OK |
| Question 5: Is liquefaction possible? | - | Yes | ||
Question 6: Are there any sensitive to liquefaction layers present? |
| Yes | Yes | OK |
| Question 7: Is breaching possible? | - | Yes | ||
Result of the Global check |
| Failed | Failed | OK |
Results of benchmark 1-1 for the Detailed Check
| Unit | Benchmark | D-FLOW SLIDE | Relative error |
|---|---|---|---|---|
Fictive channel depth (Hr) | [m] | 21.571 | 21.571 | 0.00 % |
Fictive slope (cotan αr) | [-] | 10.500 | 10.500 | 0.00 % |
Probability of liquefaction | [-] | Not checked | ||
β | [-] | 3.749 | 3.749 | 0.00 % |
P(L > Lallowable) | [-] | Not checked | ||
Probability of failure | [-] | Not checked | ||
Allowable probability of failure | [-] | 2.50 × 1E-06 | 2.50 × 1E-06 | 0.00 % |
Result of Detailed Check |
| Not checked | ||
1.2. Determination of the steepest possible breaching profile (step 7 of the Global check)
Description
The local critical profile given in Table A.4.2a from CUR113b is modeled in D-Flow Slide for both type of sand (not too fine and fairly coarse).
Different cases are considered:
| Case | Type of sand | Number of flat berm | Description | Expected result for breaching |
|---|---|---|---|---|
| A | not too fine sand | 0 | The surface line coincides with the critical (local) profile given in Table A.4.2a from CUR113b | Fail |
| B | 0 | The surface line is steeper than the critical (local) profile given in Table A.4.2a from CUR113b (local slope are 1:X-0.1m instead of 1:X) | Fail | |
| C | 0 | The surface line is softer than the critical (local) profile given in Table A.4.2a from CUR113b (local slope are 1:X+0.1m instead of 1:X) | Pass | |
| D | 0 | The surface line is softer than the critical (local) profile given in Table A.4.2a from CUR113b, but is steeper than the critical average profiles | Fail | |
| E | fairly coarse sand | 0 | The surface line coincides with the critical (local) profile given in Table A.4.2a from CUR113b | Fail |
| F | 0 | The surface line is steeper than the critical (local) profile given in Table A.4.2a from CUR113b (local slope are 1:X-0.1m instead of 1:X) | Fail | |
| G | 0 | The surface line is softer than the critical (local) profile given in Table A.4.2a from CUR113b (local slope are 1:X+0.1m instead of 1:X) | Pass | |
| H | 0 | The surface line is softer than the critical (local) profile given in Table A.4.2a from CUR113b, but is steeper than the critical average profiles | Fail | |
| I | not too fine sand | 0 | The surface line is softer than the critical (local) profile given in Table A.4.2a from CUR113b (local slope are 1:X+0.1m instead of 1:X), but the channel is deeper than 40m. | Fail |
Benchmarks results
The values of the slope is given in xxx.
D-Flow Slide results
Results of benchmark 1-2 for the Global Check - Step 7 (Breaching)
Question 7: Is unstable breaching possible? | Benchmark | D-FLOW SLIDE | Error |
|---|---|---|---|
case A | Yes (Fail) | Yes (Fail) | OK |
case B | Yes (Fail) | Yes (Fail) | OK |
case C | No (Pass) | No (Pass) | OK |
case D | Yes (Fail) | Yes (Fail) | OK |
case E | Yes (Fail) | Yes (Fail) | OK |
| case F | Yes (Fail) | Yes (Fail) | OK |
case G | No (Pass) | No (Pass) | OK |
case H | Yes (Fail) | Yes (Fail) | OK |
case I | Yes (Fail) | Yes (Fail) | OK |
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