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 profile at one point only | 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+0.35m 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 profile | 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 for "Not too fine sand" | 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 for "Not too fine sand" | 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 pass, so the Global check for Step 7 - Breaching passes.
Inputted profile along channel slope | Critical profile from CUR table A.4.2a for "Not too fine sand" | 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 | 2.1 | 2.1 | 2 | 2 | Pass | Pass |
253.5 | -5 | 2.1 | 2.1 | 2 | 2 | Pass | Pass |
242.65 | -8.5 | 3.1 | 2.5118 | 3 | 2.5 | Pass | Pass |
238 | -10 | 3.1 | 2.6 | 3 | 2.5 | Pass | Pass |
221.6 | -14 | 4.1 | 3.0286 | 4 | 3 | Pass | Pass |
217.5 | -15 | 4.1 | 3.1 | 4 | 3 | Pass | Pass |
192 | -20 | 5.1 | 3.6 | 5 | 3.5 | Pass | Pass |
161.5 | -25 | 6.1 | 4.1 | 6 | 4 | Pass | Pass |
121 | -30 | 8.1 | 4.7667 | 8 | 4.67 | Pass | Pass |
70.5 | -35 | 10.1 | 5.5286 | 10 | 5.43 | Pass | Pass |
20 | -40 | 10.1 | 6.1 | 10 | 6 | Pass | Pass |
Case D:
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 profile at one point.
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 pass except for one point for which the average check fails, so the Global check for Step 7 - Breaching fails.
Inputted profile along channel slope | Critical profile from CUR table A.4.2a for "Not too fine sand" | 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 |
263.83 | 0 | ||||||
257.53 | -3 | 2.1 | 2.1 | 2 | 2 | Pass | Pass |
253.33 | -5 | 2.1 | 2.1 | 2 | 2 | Pass | Pass |
242.65 | -8.5 | 3.05 | 2.4912 | 3 | 2.5 | Pass | Fail |
238 | -10 | 3.1 | 2.5825 | 3 | 2.5 | Pass | Pass |
221.6 | -14 | 4.1 | 3.0161 | 4 | 3 | Pass | Pass |
217.5 | -15 | 4.1 | 3.0883 | 4 | 3 | Pass | Pass |
192 | -20 | 5.1 | 3.5913 | 5 | 3.5 | Pass | Pass |
161.5 | -25 | 6.1 | 4.093 | 6 | 4 | Pass | Pass |
121 | -30 | 8.1 | 4.7608 | 8 | 4.67 | Pass | Pass |
70.5 | -35 | 10.1 | 5.5236 | 10 | 5.43 | Pass | Pass |
20 | -40 | 10.1 | 6.0956 | 10 | 6 | Pass | Pass |
Case E:
The surface line coincides with the critical (local) profile given in Table A.4.2a from CUR113b .
The soil has grain diameters of D50 = 500.1 μm and D15 = 250.1 μm, which corresponds to "Fairly coarse sand" soil type.
The local check for all the points along the channel slope fails, so the Global check for Step 7 - Breaching fails.
Inputted profile along channel slope | Critical profile from CUR table A.4.2a for "Fairly coarse sand" | 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 |
170 | 0 | ||||||
164 | -3 | 2 | 2 | 2 | 2 | Fail | Fail |
160 | -5 | 2 | 2 | 2 | 2 | Fail | Fail |
153 | -8.5 | 2 | 2 | 2 | 2 | Fail | Fail |
150 | -10 | 2 | 2 | 2 | 2 | Fail | Fail |
138 | -14 | 3 | 2.2857 | 3 | 2.3333 | Fail | Fail |
135 | -15 | 3 | 2.3333 | 3 | 2.3333 | Fail | Pass |
120 | -20 | 3 | 2.5 | 3 | 2.5 | Fail | Fail |
100 | -25 | 4 | 2.8 | 4 | 2.8 | Fail | Fail |
80 | -30 | 4 | 3 | 4 | 3 | Fail | Fail |
50 | -35 | 6 | 3.4286 | 6 | 3.43 | Fail | Fail |
20 | -40 | 6 | 3.75 | 6 | 3.75 | Fail | Fail |
Case F:
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 = 500.1 μm and D15 = 250.1 μm, which corresponds to "Fairly coarse 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 for "Fairly coarse sand" | 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 |
166 | 0 | ||||||
160.3 | -3 | 1.9 | 1.9 | 2 | 2 | Fail | Fail |
156.5 | -5 | 1.9 | 1.9 | 2 | 2 | Fail | Fail |
149.85 | -8.5 | 1.9 | 1.9 | 2 | 2 | Fail | Fail |
147 | -10 | 1.9 | 1.9 | 2 | 2 | Fail | Fail |
135.4 | -14 | 2.9 | 2.1857 | 3 | 2.3333 | Fail | Fail |
132.5 | -15 | 2.9 | 2.2333 | 3 | 2.3333 | Fail | Fail |
118 | -20 | 2.9 | 2.4 | 3 | 2.5 | Fail | Fail |
98.5 | -25 | 3.9 | 2.7 | 4 | 2.8 | Fail | Fail |
79 | -30 | 3.9 | 2.9 | 4 | 3 | Fail | Fail |
49.5 | -35 | 5.9 | 3.3286 | 6 | 3.43 | Fail | Fail |
20 | -40 | 5.9 | 3.65 | 6 | 3.75 | Fail | Fail |
Case G:
The surface line is softer than the critical (local) profile given in Table A.4.2a from CUR113b (local slope are 1:X+0.35m instead of 1:X).
The soil has grain diameters of D50 = 500.1 μm and D15 = 250.1 μm, which corresponds to "Fairly coarse sand" soil type.
The local and average checks for all the points along the channel slope pass, so the Global check for Step 7 - Breaching passes.
Inputted profile along channel slope | Critical profile from CUR table A.4.2a for "Fairly coarse sand" | 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 |
184 | 0 | ||||||
176.95 | -3 | 2.35 | 2.35 | 2 | 2 | Pass | Pass |
172.25 | -5 | 2.35 | 2.35 | 2 | 2 | Pass | Pass |
164.03 | -8.5 | 2.35 | 2.35 | 2 | 2 | Pass | Pass |
160.5 | -10 | 2.35 | 2.35 | 2 | 2 | Pass | Pass |
147.1 | -14 | 3.35 | 2.6557 | 3 | 2.3333 | Pass | Pass |
143.75 | -15 | 3.35 | 2.6833 | 3 | 2.3333 | Pass | Pass |
127 | -20 | 3.35 | 2.85 | 3 | 2.5 | Pass | Pass |
105.25 | -25 | 4.35 | 3.15 | 4 | 2.8 | Pass | Pass |
83.5 | -30 | 4.35 | 3.35 | 4 | 3 | Pass | Pass |
51.75 | -35 | 6.35 | 3.7786 | 6 | 3.43 | Pass | Pass |
20 | -40 | 6.35 | 4.1 | 6 | 3.75 | Pass | Pass |
Case H:
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 profile.
The soil has grain diameters of D50 = 500.1 μm and D15 = 250.1 μm, which corresponds to "Fairly coarse sand" soil type.
The local and average checks for all the points along the channel slope pass except for one point for which the average check fails, so the Global check for Step 7 - Breaching fails.
Inputted profile along channel slope | Critical profile from CUR table A.4.2a for "Fairly coarse sand" | 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 |
171.84 | 0 | ||||||
165.69 | -3 | 2.05 | 2.05 | 2 | 2 | Pass | Pass |
161.59 | -5 | 2.05 | 2.05 | 2 | 2 | Pass | Pass |
154.42 | -8.5 | 2.05 | 2.05 | 2 | 2 | Pass | Pass |
151.34 | -10 | 2.05 | 2.05 | 2 | 2 | Pass | Pass |
139.3 | -14 | 3.01 | 2.3243 | 3 | 2.3333 | Pass | Fail |
136.25 | -15 | 3.05 | 2.3727 | 3 | 2.3333 | Pass | Pass |
121 | -20 | 3.05 | 2.542 | 3 | 2.5 | Pass | Pass |
100.75 | -25 | 4.05 | 2.8436 | 4 | 2.8 | Pass | Pass |
80.5 | -30 | 4.05 | 3.0447 | 4 | 3 | Pass | Pass |
50.25 | -35 | 6.05 | 3.474 | 6 | 3.43 | Pass | Pass |
20 | -40 | 6.05 | 3.796 | 6 | 3.75 | Pass | Pass |
Case I:
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.
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 pass but the channel is deeper than 40m (which is not covered by the CUR table), so the Global check for Step 7 - Breaching fails.
Inputted profile along channel slope | Critical profile from CUR table A.4.2a for "Not too fine sand" | 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 |