Feed-Back on Five Years of Industrialization of Erosion
Tests in Europe
Patrick Pinettes and Rémi Béguin1
Jean-Robert Courivaud & Jean-Jacques Fry2
INTRODUCTION
Erosion mechanisms have long been known to be the main cause of breaches in earthen hydraulic
structures, like embankment dams and/or dykes (Foster et al., 2000). Yet, the way the level of risk to this
pathology was up to recently assessed was, in practise, limited to standard identifications, which just give
qualitative information about the actual resistance to erosion of the soil which constitutes the structure.
In order to provide dam or dyke owners with quantitative information about erosion, various erosion tests
were imagined and designed during the last decades : the Jet Erosion Test (JET) for overtopping (Hanson
and Robinson, 1993), the Hole Erosion Test (HET) for piping erosion (Lefebvre et al., 1985), the Contact
Erosion Test (CET) for contact erosion (ICOLD, International Commission on Large Dams (2013),
Bulletin on the Internal Erosion of Dams, Dikes and their Foundations, to be published), and the
Suffusion Test (ST) for suffusion.
geophyConsult introduced, for the first time in Europe, the USDA JET in 2009 (Hanson and Cook, 2004),
the IRSTEA HET in 2013 (Bonelli et al., 2006), and the LTHE-EDF-CNR-geophyConsult CET in 2014
(Béguin, 2014, Personal communication). The present paper discusses the experiences and lessons learned
from these introductions (in fact mainly the introduction of the Jet Erosion Test), based on 286 tests
carried out in 4.5 years.
After a brief description of the Jet Erosion test, we will describe the market and show that it is dominated
by 2 main applications.
We will then describe the main improvements brought by geophyConsult to fulfil the local market specific
requests, and end with the improvements which are presently under development.
THE JET EROSION TEST OF GREG HANSON
The « Jet Erosion Test » attempts to quantify the resistance to erosion of a sample of rather cohesive a soil
that (1) does not contain gravels of size greater than a given characteristic length determined by the
apparatus characteristics (in practice 4.75 mm) and (2) is assumed to be subject to erosion phenomena
that can be described by the following equation
̇=
×( −
),
where ̇ represents the rate of erosion, expressed in ms-1,  the effective hydraulic stress, expressed in Pa,
c the critical stress of the soil, expressed in Pa, and D the erodibility or detachment coefficient of the soil,
expressed in m2skg-1.
The test is described in details in the ASTM D5852. The modifications introduced later in order to
increase the convenience and the flexibility of the test are presented in Hanson and Cook (2004).
geophyConsult carries out its tests with the latest version of Mr. Hanson’s apparatus.
1
2
geophyConsult SAS – 159, quai des Allobroges – 73 000 Chambéry – France – [email protected]
EDF-CIH – Savoie Technolac – 73 373 Le Bourget du Lac – France
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The test consists in submerging a sample of soil below 4 to 10 cm of water, and to impact it with a vertical
water jet of approximately 6.35 mm in diameter and pressure of less than 400 mbar (see Figure 1 and
Picture 1). The depth h(t) of the scour formed by the jet is measured over time, and D and c are derived
from the experimental h(t) curve following the procedures presented in Hanson and Cook (2004).
Water inlet
Overflow outlet
Figure 1. The JET erodimeter principle.
H ≈ 50 cm to 4 m
Ruler
 ≈ 6,35 mm
Impacting jet
Water outlet
≈ 25 cm
Tested sample
( ≈ 10 cm, h ≈ 12 cm)
Eroded surface
 ≈ 50 cm
Picture 1. Pictures
of the apparatus,
used in the lab (to
the left) and in the
field (to the right).
The soil must be cut to 4.75 mm and it can be either a core taken in the field and possibly reworked (then
the recommended size of the core is 10.16 cm in diameter and 11.64 cm in height), or the actual soil,
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tested on site. In situ, it is recommended to scrub the ground cover away over a flat surface of about 40 cm
in diameter.
The results provided with the test are traditionally provided in a (D, c) « Hanson’s soil classification diagram »
(see Figure 2).
Results given in the Hanson's soils classification diagram
Domain of critical stresses that can, in practise, be applied to the samples
surfaces
1,00E+ 03 cm^3/ N/ s
Very erodible
d [cm3×N-1×s -1]
1,00E+ 02 cm^3/ N/ s
1,00E+ 01 cm^3/ N/ s
1,00E+ 00 cm^3/ N/ s
Erodible
Moderatly
resistant
1,00E-01 cm^3/ N/ s
Resistant
1,00E-02 cm^3/ N/ s
1,00E-01 Pa
1,00E+ 00 Pa
1,00E+ 01 Pa
Extremely
resistant
1,00E+ 02 Pa
1,00E+ 03 Pa
c [Pa]
Figure 2. Hanson’s soil classification diagram, in which the results are traditionally provided.
MAIN CHARACTERISTICS OF THE FRENCH MARKET
Although the French law does not formally urge dam or dyke owners to regularly assess the resistance to
erosion of their structure, it states that, when the structure is of a given importance (i.e. when significant
human or economic interests are at stake downwards), the owner must regularly assess the « kinetics of
potential accidents » likely to affect.
Market segmentation
Control of
reinforcement
28%
Type of ordered test
In situ
5%
Sedimentation
2%
Survey
70%
Lab
95%
Figure 3. Main characteristics of the French market, after 5 years of commercialisation of the
tests and achievement of 286 tests.
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Therefore, when security surveys show that erosion is a potential mode of failure of the structure, owners
need to quantify the resistance to erosion of the a priori most vulnerable to erosion layers, which leads them
to order erosion tests.
Three applications drive the demand for such tests : first the determination of the resistance to erosion of
the structure in the framework of security surveys, second the determination of the resistance to erosion
for reinforced soils, in the framework of post-achievement quality controls, and third sedimentation
studies. Figure 3 shows how these application segment the market, and whether laboratory tests are more
frequent that in situ tests. Clearly, security surveys are the main cause for demanding erosion tests, and
most of the orders are for the laboratory.
IMPROVEMENTS BROUGHTS BY GEOPHYCONSULT
The introduction of the « Jet Erosion Test » in Europe has led to refinements requested by the specificity of
the local demand, with respect to the American demand, initially targeted by the apparatus.
New method for fitting the experimental data
With the notations of Figure 4, the Torricelli formula states that
=
2 ×∆
where UO is the jet velocity at the jet outlet and H is the applied hydraulic head. The mass conservation
states for its part that
×
=
×
where
=
×
where d0 is the nozzle diameter and Cd is the jet diffusion constant (which is equal to 6.35 mm and 6.2 in
the case of the apparatus of Hanson and Cook, 2004).
Figure 4. Schematic of
circular submerged jet
with definitions and
stress distribution, from
Hanson and Cook, 2004.
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Considering in addition that
̇=
= κ × τ-τ
it can be shown that
=
×
×
×
×
ℎ
−A
×
×
ℎ
×
−
×
×
×
×∆ ×(
×∆ ×(
×∆ ×(
)
×
×
)
×
)
×
×
× ( − ).
Hence modelling the experimental data can be achieved by calculating, for a given set of a priori plausible
values of (D, C), all the
deduced from the above equation, estimating the
,
error ∆(
,
)=
∑
−
,
,
for each set of a priori plausible values of (D, C), and
selecting the values of (D, C) which minimize the error ∆(
,
).
Figure 5. Example of an actual test illustrating the difference between the Hanson and geophyConsult
modelling : in blue the raw experimental data, in orange the best geophyConsult fit and in red the Hanson
fit.
geophyConsult developed an algorithm based on this method and a random Monte Carlo simulation of the
(D, C) space. It delivers in about 5 minutes a very robust result which turns out, in practice, to be better
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than the results generated by the Hanson algorithm in about 75% of the tested cases, sometimes
significantly better (particularly for the extremely erodible soils) and in no case worse. Figure 5 illustrates
the differences between both modelling methods.
The discrepancy between the results of the Hanson fit and the geophyConsult inversion can be easily
explained. Both modelling methods are based on exactly the same physical hypothesis and equations,
however, while the geophyConsult method does not add any assumption to the equations presented before,
the Hanson modelling implicitly assumes that D slightly depends on C. Therefore, the geophyConsult
algorithm explores more possible values for (DC) than the Hanson algorithm, so that its fit is
mathematically more exact.
New estimate of the uncertainty associated with the mathematical modelling
In parallel to the growth of the demand for erosion tests, a demand for a quantitative estimate of the
uncertainty associated with the mathematical modelling progressively emerged, in order to better constrain
the uncertainty associated with the erosion tests.
geophyConsult tried to meet this demand by developing a method aimed at describing the shape of the
surface ∆( , ) around the nominal values D andC delivered by the initial modelling. The idea was to
find a mathematical estimate of the range over which the minimum remains flat and the error does not
significantly vary.
Figure 6. Example of an actual test illustrating the estimate of the mathematical uncertainty
associated with the delivered results now systematically offered by geophyConsult : in blue the
raw experimental data, in orange the best geophyConsult fit, and in purple and in red the
modelling results that border the experimental data.
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In order to achieve this goal, geophyConsult proposed to explore the error surface around its minimum
∆
according to a threshold value of the relative error
error ∆(
,
)
=
,
∆
∆
,
above which the
,
is considered as having to be rejected. Then, it analyzes the sensitivity of this result relative
to the arbitrary parameter ϵ, before delivering a reasonable uncertainty associated with the delivered values
of D and C – see Figure 6.
The Hanson’s « Jet Erosion Test » apparatus of 2004 is not capable of testing soils with a hydraulic head
smaller than 50 cm, which corresponds in the best case to an initial jet velocity of the order of 1.5 m×s-1,
i.e. an initial stress of the order of 3 Pa. The intrinsic physical resolution on critical stress is therefore of the
order of 0.5 Pa. Results of modelling which lead to critical stresses lower than 0.5 Pa hence have to be
rejected as physically unrealistic.
Each time geophyConsult faced up to this problem, the evaluation of the mathematical uncertainties
revealed that the error ∆( , ) was almost constant below 0.5 Pa, which confirmed that the result was not
sensitive to critical stresses below 0.5 Pa.
IMPROVEMENTS UNDER DEVELOPMENT
geophyConsult recently found a new way of measuring the scour versus time – via the introduction of a
sensor that will replace the limnimetric man-made measurement. The test is therefore expected to be soon
automated, leading to running costs reduction, better accuracy and repeatability, as well as wider
applications.
The incoming pressure will in addition soon be controlled by a patented pump association that will enable
to generate, at very affordable a price, stable to at least a few percent flow rates ranging from about
0.2 m3×h-1 (corresponding to the flow generated with a hydraulic head of 10 cm flowing in a 6.35 mm
diameter hole, which is adapted to very erodible sands) to about 70 m3×h-1 (corresponding to the flow
generated with a hydraulic head of 5 m flowing in a 5 cm diameter hole, which is adapted to extremely
resistive soils possibly containing centimetric gravels).
Electrically rotating
axis
Flow and/or Pressure
measurement
Acoustic
measurement
Turbidity
measurement
Figure 7.
Design of
the future
new JET
Additional sensors will at last be installed at
various positions in the apparatus, including a
turbidity sensor located in the submergence
tank, a flowmeter and a pressure gage
positioned in the impeging jet. The
submergence tank will besides be overflowing
in a secondary tank so as not to brake the axis
symmetry of the flow in the submergence tank
(see Figure 7).
These improvements will enable to quantify
the resistance to erosion of reinforced soils,
which most of the time cannot be eroded by
the Hanson and Cook (2004) apparatus.
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CONCLUSION
The introduction of the « Jet Erosion Test » in France showed that the test meets an actual demand, which is
pushed by new regulations that urge dams, dikes or levees owners to quantify the kinetics of the rupture
modes that are likely to affect their structure. It however needed methodological refinements, that
geophyConsult carried out easily or is about to carry out.
REFERENCES
Bonelli S., Brivois O., Borghi R. and Benahmed N. (2006), On the modelling of piping erosion, Comptes
Rendus de Mécanique, 8-9(334):555-559.
Foster M., Fell, R. abd Spannagalen M. (2000). “The statistics of embankment dam failures and accidents”,
Canadian Geotechnical Journal, 37, 1000-1024.
Hanson, G. J. and Cook, K. R. (2004). “Apparatus, test procedures and analytical methods to measure soil
erodibility in situ”, Applied engineering in agriculture, 20 (4), 455-462.
Hanson G. J., Robinson K. M. and Temple D. M. (2000), Pressure and Stress Distributions Due to a
Submerged Impinging Jet, Res. Hydr. Engr. USDA.
Lefebvre G., Rohan K. and Douville S. (1985), Erosivity of natural intact structured clay: evaluation,
Canadian Geotechical Journal 22:508-517.
Standard D5852. Annual Book of ASTM Standards, Section 4: Construction, Vol. 04.08. Philadelphia,
Penn.: American Society for Testing and Materials.
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