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
For the Detailed check, the following input is used:
- Required probability of failure of the dike: 1:4000 year
- Percentage probability of failure by liquefaction: 1 %
- Maximum allowable retrogression length: Lallowable = 60 m (length of the foreland)
- Considered dike length: 800 m
- Mean value of the area ratio (c = A2/A1): 1.4
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
D-Flow Slide needs extra input parameters compared to the Study Case:
- Ψ5m = -0.03 for sand layers and Ψ5m = -0.06 for other layers (used in Global step 1)
- Ψ5m = -0.03 (used in Global step 5 and Detailed checks)
- D50 = 180 μm and D15 = 130 μm for Calais sand
- D50 = 160 μm and D15 = 110 μm for Compacted sand
- Cohesive layers factor = 0.2
- Migration velocity = 0.0001 mm/year
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 inputted channel slope is given in the tables below per case, and compared with the allowed slope (from CUR table) for the breaching step 7 of the Global check.
Case A:
The surface line coincides with the critical (local) profile given in Table A.4.2a from CUR113b as can be seen in the table below.
The soil has grain diameters of D50 = 200.1 μm and D15 = 100.1 μm, which corresponds to "Not too fine sand" soil type.
The local and average checks for all the points along the channel slope fail, so the Global check for Step 7 - Breaching fails.
Inputted profile along channel slope | Critical profile from CUR table A.4.2a | Result Global check - step 7 per point | |||||
---|---|---|---|---|---|---|---|
X [m] | Z [m +GL] | Local slope [1:xxx] | Average slope [1:xxx] | Local slope [1:xxx] | Average slope [1:xxx] | Local check | Average check |
260 | 0 | ||||||
254 | -3 | 2 | 2 | 2 | 2 | Fail | Fail |
250 | -5 | 2 | 2 | 2 | 2 | Fail | Fail |
239.5 | -8.5 | 3 | 2.4118 | 3 | 2.5 | Fail | Fail |
235 | -10 | 3 | 2.5 | 3 | 2.5 | Fail | Fail |
219 | -14 | 4 | 2.9286 | 4 | 3 | Fail | Fail |
215 | -15 | 4 | 3 | 4 | 3 | Fail | Fail |
190 | -20 | 5 | 3.5 | 5 | 3.5 | Fail | Fail |
160 | -25 | 6 | 4 | 6 | 4 | Fail | Fail |
120 | -30 | 8 | 4.6667 | 8 | 4.67 | Fail | Fail |
70 | -35 | 10 | 5.4286 | 10 | 5.43 | Fail | Fail |
20 | -40 | 10 | 6 | 10 | 6 | Fail | Fail |
Case B:
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).
The soil has grain diameters of D50 = 200.1 μm and D15 = 100.1 μm, which corresponds to "Not too fine sand" soil type.
The local and average checks for all the points along the channel slope fail, so the Global check for Step 7 - Breaching fails.
Inputted profile along channel slope | Critical profile from CUR table A.4.2a | Result Global check - step 7 per point | |||||
---|---|---|---|---|---|---|---|
X [m] | Z [m +GL] | Local slope [1:xxx] | Average slope [1:xxx] | Local slope [1:xxx] | Average slope [1:xxx] | Local check | Average check |
256 | 0 | ||||||
250.3 | -3 | 1.9 | 1.9 | 2 | 2 | Fail | Fail |
246.5 | -5 | 1.9 | 1.9 | 2 | 2 | Fail | Fail |
236.35 | -8.5 | 2.9 | 2.3118 | 3 | 2.5 | Fail | Fail |
232 | -10 | 2.9 | 2.4 | 3 | 2.5 | Fail | Fail |
216.4 | -14 | 3.9 | 2.8286 | 4 | 3 | Fail | Fail |
212.5 | -15 | 3.9 | 2.9 | 4 | 3 | Fail | Fail |
188 | -20 | 4.9 | 3.4 | 5 | 3.5 | Fail | Fail |
158.5 | -25 | 5.9 | 3.9 | 6 | 4 | Fail | Fail |
119 | -30 | 7.9 | 4.5667 | 8 | 4.67 | Fail | Fail |
69.5 | -35 | 9.9 | 5.3286 | 10 | 5.43 | Fail | Fail |
20 | -40 | 9.9 | 5.9 | 10 | 6 | Fail | Fail |
Case C:
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).
The soil has grain diameters of D50 = 200.1 μm and D15 = 100.1 μm, which corresponds to "Not too fine sand" soil type.
The local and average checks for all the points along the channel slope fail, so the Global check for Step 7 - Breaching fails.
Inputted profile along channel slope | Critical profile from CUR table A.4.2a | Result Global check - step 7 per point | |||||
---|---|---|---|---|---|---|---|
X [m] | Z [m +GL] | Local slope [1:xxx] | Average slope [1:xxx] | Local slope [1:xxx] | Average slope [1:xxx] | Local check | Average check |
264 | 0 | ||||||
257.7 | -3 | 2 | 2.1 | 2.1 | 2 | Pass | Pass |
253.5 | -5 | 2 | 2.1 | 2.1 | 2 | Pass | Pass |
242.65 | -8.5 | 3 | 2.5118 | 3.1 | 2.5 | Pass | Pass |
238 | -10 | 3 | 2.6 | 3.1 | 2.5 | Pass | Pass |
221.6 | -14 | 4 | 3.0286 | 4.1 | 3 | Pass | Pass |
217.5 | -15 | 4 | 3.1 | 4.1 | 3 | Pass | Pass |
192 | -20 | 5 | 3.6 | 5.1 | 3.5 | Pass | Pass |
161.5 | -25 | 6 | 4.1 | 6.1 | 4 | Pass | Pass |
121 | -30 | 8 | 4.7667 | 8.1 | 4.67 | Pass | Pass |
70.5 | -35 | 10 | 5.5286 | 10.1 | 5.43 | Pass | Pass |
20 | -40 | 10 | 6.1 | 10.1 | 6 | Pass | Pass |
Case I:
Inputted profile along channel slope | Critical profile from CUR table A.4.2a | Result Global check - step 7 per point | |||||
---|---|---|---|---|---|---|---|
X [m] | Z [m +GL] | Local slope [1:xxx] | Average slope [1:xxx] | Local slope [1:xxx] | Average slope [1:xxx] | Local check | Average check |
274.1 | 0 | ||||||
267.8 | -3 | 2.1 | 2.1 | 2 | 2 | Pass | Pass |
263.6 | -5 | 2.1 | 2.1 | 2 | 2 | Pass | Pass |
252.75 | -8.5 | 3.1 | 2.5118 | 3 | 2.5 | Pass | Pass |
248.1 | -10 | 3.1 | 2.6 | 3 | 2.5 | Pass | Pass |
231.7 | -14 | 4.1 | 3.0286 | 4 | 3 | Pass | Pass |
227.6 | -15 | 4.1 | 3.1 | 4 | 3 | Pass | Pass |
202.1 | -20 | 5.1 | 3.6 | 5 | 3.5 | Pass | Pass |
171.6 | -25 | 6.1 | 4.1 | 6 | 4 | Pass | Pass |
131.1 | -30 | 8.1 | 4.7667 | 8 | 4.67 | Pass | Pass |
80.6 | -35 | 10.1 | 5.5286 | 10 | 5.43 | Pass | Pass |
20 | -41 | 10.1 | 6.1976 | 10 | 6 | Pass | Pass |
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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