SOIL AND GROUNDWATER - Introduction to Soft Soil Geotechnique: Content, Context and Application - page 59

levee, which grows from the downstream side to the upstream side. Continued
erosion may finally lead to instability and failure of the levee.

Figure 4.6 Start of retrograde erosion piping and a full-scale piping test

A few design rules are available to estimate the probability of piping, such as the
empirical model of Bligh and the semi-analytical model of Sellmeijer

Bligh (1910) H < L / C (4.18a)

Sellmeijer (1989) H < abcL ( 0.68 0.10ln( b )) (4.18b)

0 28

w sin( )

2

( Z / L ) 1

L ) 1/3 , c =

with a = ( Z/L ) , b = D 70 /(

s w

cos

H is the hydraulic drop, L the minimum seepage length, C an empirical
factor (18 for fine, 15 for medium, 12 for coarse sand, 7 for gravel), a is a
geometry factor, b a sand scaling factor, c a sand grain equilibrium factor,

Here,

the

rolling resistance angle of the sand grains, the slope of the pipe, a drag force

factor (coefficient of White), the intrinsic permeability of the sand layer, D 70 the

70% value of the grain distribution, and Z the thickness of the sand layer. Some
large-scale tests on one type of sand have been conducted for validation. The
suggested model (4.18b) has been validated on the base of extensive physical tests
and it is incorporated in a practical numerical FEM design tool. Full-scale
experiments have shown that piping failure is time-dependent. Dike breach may
occur within several hours after pipes reach the upstream side (Fig 4.6).
For a particular geological situation (Fig 4.7a), the variation in geometry has
been elaborated by an artificial neural-network (ANN), a self-learning approach.
The chosen network contained 5 input nodes ( Z i / L and the permeability ratio), 50
hidden nodes and 1 output node ( F ). After 18674 calculations (90% training, 10%
check) the trained network prediction for the check showed an excellent match (Fig
4.7b). The result is a simple formula