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
|
Benchmark |
D-FLOW SLIDE |
Relative error |
---|---|---|---|
Marge |
xxx |
xxx |
xxx |
X coordinate of the observation profile (Xsign) |
xxx |
xxx |
xxx |
X coordinate of the liquefaction point (XZV) |
xxx |
xxx |
xxx |
Step 1: Is liquefaction damaging on basis of geometry? |
Yes |
Yes |
|
Step 2: Artificially underwater installed and non-compacted sandy foreshore? |
No |
No |
|
Step 4: Is liquefaction possible on the basis of the geometry? |
Yes |
Yes |
|
Step 5: Are there any sensitive to liquefaction layers present? |
Yes |
Yes |
|
Result of the Global Check |
Failed |
Failed |
|
Results of benchmark 1-1 for the Detailed Check
|
|
Benchmark |
D-FLOW SLIDE |
Relative error |
---|---|---|---|---|
Fictive channel depht (Hr) |
[m] |
|
21.571 |
|
Fictive slope (cotan αr) |
[-] |
|
10.500 |
|
Probability of liquefaction |
[-] |
|
2.93 × 10-3 |
|
Representative probability of failure |
[-] |
|
3.52 × 10-3 |
|
β |
[-] |
|
3.749 |
|
P(L > Lallowable) |
[-] |
|
8.86 × 10-5 |
|
Probability of failure |
[-] |
|
3.12 × 10-7 |
|
Allowable probability of failure |
[-] |
|
2.50 × 10-6 |
|
Result of Detailed Check |
|
|
Succeeded |
|