Detailed check

 

The detailed check is a probabilistic check on section level ("vakniveau"). The way in which dike sections are defined are described in the Schematiseringshandleiding zettingsvloeiing. Per dike section the following steps have to be passed through subsequently, see also Rekenregels voor gedetailleerde toets:

 

Step 1             Determine the probability of occurrence per subsurface scenario Si: P(ZV|Si)

Step 2             Determine the probability of occurrence for all subsurface scenario's: P(ZV|Si)P(Si)  (not supported by D-FlowSlide)

Step 3             Determine the probability of exceedance of the maximum allowable retrogression length (inscharingslengte) given the occurrence of a flow slide: P(L > Ltoelaatbaar|ZV).

Step 4             Determine the probability of exceedance of the maximum allowable retrogression length (inscharingslengte) of the dike section: P(L > Ltoelaatbaar)vak.

Step 5             Check if P(L > Ltoelaatbaar)vak is less than the allowable probability Peis,vak. (not supported by D-FlowSlide)

 

Step 2 is not supported by D-FlowSlide. In case of more than one subsurface scenario, for each scenario (P(L > Ltoelaatbaar)vak)P(Si) can be calculated and then combined in (P(L > Ltoelaatbaar)vak). In fact step 2 is done after step 4.

Also Step 5 is not supported by D-FlowSlide and should be done by hand.

Step 1

Determine the probability of occurrence per subsurface scenario P(ZV|Si)

First per subsurface scenario the frequency F(ZV|Si) is calculated:

 

(1)

 

The frequency is transformed into a probability with:

 

 

(2)

 

A detailed description how the parameters in the equations above should be determined is given in the schematiseringshandleiding. Below a brief description is given, by subdividing the parameters referring to slope geometry, soil properties/state and dynamics of the geometry respectively:

 

Geometry (see figure below):

The geometry of the fictitious under water slope (rekentalud), resulting in highest probability of failure during the assessment period (e.g. 12 years) is characterized by the fictitious slope height HR [m] slope angle αR [graden]:

(3)

with

(4)

in which:

Hgeul     channel depth [m]

Δhonder  height of the slope above the water level during extremely low tide: “niveau van geulrand” – “niveau LLWS/OLW/OLR” [m]

hdijk       crest height of the dike above the outer dike toe [m]

B          distance between outer dike toe and top of the top of the channel bank ("geulrand"). In case of a "schaardijk": B = 0 [m]

αR         angle the (schematized) under water slope [degrees]

αboven    angle of the outer slope of the dike [degrees]

α’boven   fictitious slope angle of a line running from the top of the channel bank to the crest of a fictitious dike with a height equal to two times the actual dike height [degrees]. In case of a "schaardijk" α’boven = αboven

 

Other parameters in the figure (Dutch)

 

LLWS meerjarig gemiddelde van het laagste springlaagwater ten opzichte van NAP, geldig in het kustgebied en de estuaria.

OLW    Overeengekomen Laag Water ten opzichte van NAP, geldig in het benedenrivierengebied (in Waal stroomafwaarts van Tiel).

OLR     Overeengekomen Lage Rivierstand ten opzichte van NAP, geldig in het boven­rivierengebied (in Waal stroomopwaarts van Tiel), hetgeen overeen­komt met de Overeengekomen Lage Afvoer bij Lobith.

 

A detailed description how various bends (characteristic points) are determined is given in the schematiseringshandleiding.

 

 

 

 

Material parameters:

ψ5m,kar            characteristic value of ψ5m [-]. ψ5m is the value of the state parameter ψ averaged over a total (cumulative) thickness of 5 m of sand layers in which the state parameter is the highest (most liquefiable) and which are between the ground water level and a depth of 0,5 HR below the channel bottom.

d50,gemiddeld,kar   characteristic value of d50,gemiddeld [m]. d50,gemiddeld is the average value of d50 in all sand layers between the top of the channel bank and the channel bottom.

Fcohesivelayers     is a parameter expressing the influence of thin clay and peat layers (between 0.5 m and 5 m thickness) within the sand layers [-]. See table below

 

 

(0,5m < thickness of cohesive layer < 5m)

Fcohesivelayers

almost no clay of peat layers

1/3

limited number of clay of peat layers (comparable with "average" sand in Zeeland)

1

large number of clay of peat layers

3

 

 

Dynamics of the under water slope:

  • Vlokaal is a measure for the dynamics of the under water slope. This parameter is the largest value of:

–         velocity of backward or forward displacement of the waterline,

–         velocity of backward or forward displacement of the average under water slope

–         velocity of deepening of the channel bottom multiplied with cotαR.

The minimum value of Vlokaal is 0,001 m/year

  • VZeeland is the average value of Vlokaal of the under water slopes in Zeeland, that form the basis of the equation of the probability of occurrence of flow sliding.  VZeeland = 1 m/year

Step 2 (not supported by D-FlowSlide )

The probabilities of occurrence per subsurface scenario are combined with:

(5)

in which P(Si) is the probability of occurrence of a subsurface scenario Si. Furthermore: .

Step 3

The method to predict the retrogression length of a flow slide is based on analysis of the pre- and post failure geometries of a large number of flow slides in Zeeland. The figure below gives the variables that D-FlowSlide uses to calculate the retrogression length.

In top-view most flow slides show a hourglass shape: a shelf-shaped scar around the erosion area, a narrow flow channel and a wide, cone-shaped sedimentation area. If schematized in 2D cross section through the centerline of the flow slide the surface area of part in which soil is removed (Area 1 in figure below) is in average approximately 1.4 times larger than the deposition area (Area 2). Generally the resulting profile roughly consists of two parts: a very gentle lower part and a much steeper upper part, see figure below.

 

Figuur: Inscharingslengte (L) na zettingsvloeiing


The variables in the figure above are uncertain. Based on statistical analysis of ca 140 flow slides in Zeeland for each variable the expected values, standard deviation and distribution type were derived, see table below.

The standard deviation of parameters c en cotan(a) are not based on observations and were estimated.

 

 

 

 

Underlying normal distribution

X

E(X)

σ(X)

Type of distribution

μ(X)

σ(X)

cotan(γ)

16,8

7,1

Lognormal

2,82

0,38

cotan(β)

2,9

1,7

Lognormal

1,05

0,47

D/H

0,43

0,06

Normal

 

 

c

1,4

0,1

Normal

 

 

cotan(α)

 

0,05·μ(X)

Normal

 

 

Conversion of expected value and standard deviation from average and stand deviation of the underlying normal distribution:  en

 

To determine the probability that the retrogression length L is larger than the maximum allowable retrogression length Ltoelaatbaar the following reliability function (z-function) should be solved:

 

(6)

 

In D-FlowSlide the equation is solved using a FORM analysis. The probabilistic parameters are D/H, c, cotan γ and cotan β. The balance between c.Area 1 and Area 2 is solved numerically. This means that in case of a narrow channel, the retrogression length will smaller compared with a wide channel.

 

Note: During the different steps of the FORM analysis, the values of the four probabilistic parameters (D/H, c, cotan γ and cotan β) can lead to a damage profile outside the geometry limits. That's why the program extrapolates the geometry at both left and right sides by extending the surface line with an horizontal line (length is 1000 m) starting at the point situated at geometry limit as illustrated in figure below.


 

  • No labels

Disclaimer