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A to Evaluate the Internal Stability of Grain Structrures

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ICSE6 Paris - August 27-31, 2012 Etzer, Auﬂeger, Muckenthaler
ICSE6-112
A Software Tool to evaluate the Internal Stability of GrainStructures
Thomas ETZER
1
, Markus AUFLEGER
1
, Peter MUCKENTHALER
2
1, Unit of hydraulic engineering, University of Innsbruck, Technikerstrasse 13a A-6020 Innsbruck, Austria, +43 512 507 2912, markus.auﬂeger@uibk.ac.at 2, Ingenieurbüro Dr. Muckenthaler, Dr.-August-Einsele-Ring 12 D-82418 Murnau, Germany, ib.dm@t-online.de
Abstract:
Many of the available criteria for the assessment of internal erosion require extensive calculationsand are therefore prone to arithmetic errors. A free software tool developed at the University of Innsbruck provides a user-friendly possibility for the application of established methods to estimate the internal stabilityof grain structures. A simpliﬁed pore model based on geometrical considerations is also included. The paper deals with the range of functions of this instrument. The on-site conditions of a conducted dyke project areused as a case study to illustrate its practicability.
Key words:
seepage, software, erosion criteria, pore model
1 Introduction
Common criteria for the evaluation of the internal stability in grain structures have been derived either em-pirically by laboratory tests or theoretically by geometrical considerations. Despite the remarkable number of different ﬁndings, only a few rules are recommended in reference books and used in practice. In many casesthe applied criterion is not the one, which is ﬁtted best to the problem, but the easiest to use. A reason for thismay be the fact that some procedures require more calculation effort than others.For research on internal erosion processes, a software tool named
Prolix
was developed at the
University of Innsbruck
to apply and compare different approaches. It was written in the widely-used programming languageMATLAB, which is marketed by
MathWorks Inc
. The structure has a modular concept to allow a quick adaptionof existing parts and the easy implementation of new thoughts. The basic idea was to provide a simple graphicalinterface for the user which controls a couple of expandable functions. These functions are realized as so called
Script-Files
and may be adapted individually. Some of them are presented and discussed below.The usual starting point for most approaches is the particle size distribution (PSD) of the observed soil. It canbe easily received by standardized methods and is therefore a suitable base for an objective examination. Torun an analysis in
Prolix
, the used sieve sizes and the corresponding percentage passing by weight are required.The data can be transferred into the software interactively for several soils at once from an Excel table with adeﬁned structure.
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ICSE6 Paris - August 27-31, 2012 Etzer, Auﬂeger, Muckenthaler
2 Basic Functions
The software stores the name of each soil and it’s PSD in a temporary ﬁle. Additionally, each PSD is stored in avector of uniform size as given in equation 1. Therefore, the corresponding grain diameters are interpolated log-linear from mass percentage 0 to 100 with spacing of 1 %. As usual, the characteristic diameter
d
x
,
i
representsthe grain size, which is not exceeded by
x
weight percent of the particles in soil specimen number
i
. This stepsimpliﬁes the handling of samples which are gathered with unequal sets of sieves.
PSD
i
= [
d
0
,
i
d
1
,
i
d
2
,
i
...
d
100
,
i
]
(1)It is possible, to classify the soils as a ﬁlter or base material in an additional column in the data source. This in-formation is also written in the temporary ﬁle and allows the application of standard recommendations for ﬁlterdesign. The actual version of
Prolix
contains the criteria of Terzaghi, the United States Bureau of Reclama-tion and the United States Department of Agriculture [Terzaghi & Peck, 1948], [USBR, 1987], [USDA, 1994].Herein, these functions will not be treated further. All the results as well as the PSD of each soil can be plottedautomatically in standard graphs by the software. Export to common ﬁle formats is provided.
3 Implemented Criteria
3.1 Criterion of Burenkova
The criterion of Burenkova is based on experiments carried out on wide-graded, non-cohesive sand-gravel soilswith a maximum grain size of 100 mm [Burenkova, 1993]. The basic assumption is that transport processesof internal erosion may only occur, if ﬁne soil particles are able to pass through the constrictions between thecoarser grains. This approach divides the material in a supporting soil skeleton and a potentially mobile ﬁlling.Initially, the tested soils were divided into fractions with grains of about the same size and the volume of thecoarsest size fraction was measured. Stepwise, at a time the next ﬁner size fraction was added and the volumeof the mixture was measured again. If the volume of the mixture increased after the addition of a ﬁner fraction,this ﬁner fraction was considered to belong to the soil skeleton. Otherwise it was believed to consist of particles,which are loose and able to move though the specimen. Burenkova used two factors of uniformity to describethe soils. Their deﬁnition is given in equation 2 and 3.
h
=
d
90
/
d
60
(2)
h
=
d
90
/
d
15
(3)According to Burenkova a sample is classiﬁed as a “Non-suffusive Soil”, if it satisﬁes equation 4.0
.
76
·
log
(
h
)+
1
≤
h
≤
1
.
86
·
log
(
h
)+
1 (4)Figure 1 shows a plot of
h
against log
(
h
)
and the boundaries between “Suffusive Soils” and “Non-suffusiveSoils”. The Zones
I
and
III
represent soils which are vulnerable to suffusion, and Zone
IV
is an area of artiﬁcialsoils. The materials which are stable against the effects of suffusion are located in Zone
II
.The evaluation of this criterion is done pretty simple in the software. The program reads the characteristic graindiameters out of the temporary ﬁle and calculates the factors of uniformity
h
and
h
. The output is done in agraph similar to ﬁgure 1 and additionally in written text.
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ICSE6 Paris - August 27-31, 2012 Etzer, Auﬂeger, Muckenthaler
3 5 10 20 30 50 100 20012345
d
90
/d
15
d
9 0
/ d
6 0
IIIIIIIV
Figure 1: Diagram for the classiﬁcation of soils after Burenkova
3.2 Criterion of Kenney & Lau
The diameter of pores left between equally sized grains is in average about a fourth of their size. Kenney & Laustated that a particle with size
d
can not be washed out of a soil, if there are enough grains with a size between
d
and 4
·
d
. They carried out seepage tests on non-cohesive sand-gravel soil samples with a maximum grain sizeof 100 mm [Kenney & Lau, 1985].For the evaluation of their results, Kenney & Lau plotted the mass percentage
F
(
d
)
passing a sieve with anopening width of
d
against the auxiliary number
H
.
H
represents the proportion of grains that will preventparticles of size
d
from moving and is calculated according to equation 5.
H
=
F
(
4
·
d
)
−
F
(
d
)
(5)Soils that were unstable in the experiment had according to Kenney & Lau at least a part of the shape curveplotted below the borderline represented by
H
=
1
.
3
·
F
. The percentage of possible movable grains, andtherefore the end of the limit range in the H-F diagram was deﬁned with 30 %. In widely-graded soils with anuniformity coefﬁcient
C
u
>
3, only the smallest 20 % of the grains are suspected to be washed out. Figure 2shows the H-F diagrams for narrow and for widely-graded soils and an example for a stable and an unstablespecimen.
00.20.40.60.8100.20.40.60.81
F
(
d
)
H
=
F
( 4
d
)
−
F
(
d
)
unstable sample
00.20.40.60.8100.20.40.60.81
F
(
d
)
H
=
F
( 4
d
)
−
F
(
d
)
stable sample
Figure 2: H-F diagrams for narrow (left) and for widely-graded (right) soils after Kenney & Lau
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ICSE6 Paris - August 27-31, 2012 Etzer, Auﬂeger, Muckenthaler
Based on additional tests the borderline was later lowered to
H
=
1
.
0
·
F
. The area between the ﬁrst and therevised threshold is referred to as “transition zone”.To rate a soil sample using this criterion, the
Prolix
Software calculates in the ﬁrst step a log-linear interpolationof the mass percentages corresponding to the 4-times multiples of all characteristic diameters. This allowsthe evaluation of equation 5 to determine
H
. The length of the borderline is selected due to the uniformitycoefﬁcient
C
u
. Then it is checked, whether or not
H
is smaller than 1
.
3 or 1
.
0
·
F
in this interval. The result isdelivered in written text. Also, the
H
−
F
diagram for the examined soil sample is plotted.
3.3 Criterion of Wan & Fell
Wan & Fell carried out seepage tests in the laboratory and applied various existing criteria on the used soils tocompare the results [Wan & Fell, 2004]. In their investigation, they identiﬁed the already mentioned methodsof Kenney & Lau and Burenkova as most accurate. The criterion of Kenney & Lau seemed to be more con-servative and identiﬁed a couple of soils as unstable, which really showed no sign of internal erosion duringthe experiments. According to the authors, the method of Burenkova was more accurate in identifying unstablesoils, but also predicted some collapsing samples as reliable.Based on their results, Wan & Fell suggested to combine these methods, as they seem to successfully supple-ment each other. The scheme for assessing the likelihood of internal instability is given in table 1. The softwareTable 1: Scheme for the criterion of WAN & FELLLikelihood of internal instability KENNEY & LAU (1985, 1986)
H
<
F F
≤
H
<
1
,
3
F H
≥
1
,
3
F h
≤
0
,
76
·
log
(
h
)+
1 Likely - Neutral - VeryBURENKOVA Very likely Likely unlikely(1993)
h
>
0
,
76
·
log
(
h
)+
1 Unlikely Very unlikely - VeryUnlikely unlikelysimply carries out the steps which are required for the methods of Kenney & Lau and Burenkova and unites theresults. The classiﬁcation of the observed sample is done in form of a chart similar to table 1.
4 Pore model
Another approach to evaluate the internal stability of granular materials is based on the geometry of the voidconstrictions. A soil can be considered as internal stable, if the voids between the coarser grains are narrowenough to prevent the ﬁnes from moving through this interstitial volume. Therefore, a couple of authors havetried in the past to determine the pore structure to describe the liability of a soil to processes of internal erosion.Unfortunately, there is an inﬁnite number of possible combinations, because the particles in a natural soil differwidely in size and shape. Therefore, the use of spherical shaped grains is a prevalent simpliﬁcation for this kindof calculations. In a soil with the densest packing, a void is built by three grains. The narrow point is within theplane going through the center of these spheres, as pictured in the left side of ﬁgure 3. The biggest grain whichwould be able to pass this void can be drawn as a circle, which is tangent to the outer three. Its diameter
d
p
canbe calculated with simple, trigonometric considerations. This model was established by Silveira, who publishedthe void diameters for all possible combinations of ﬁve different grain sizes in form of a table [Silveira, 1965].The use of four connected grains as limit for the void is a common assumption for the loosest state of packingin a soil. The biggest possible pore is composed, if the centers of all spheres are within the same plane. Again,the pore size can be found as the solution of an 2D-problem. It is shown on the right side of ﬁgure 3. Silveiradescribed the area of the pore
A
p
dependent on the aperture angle
α
. This function has a maximum which canbe found by solving the corresponding extremum problem [Silveira et al., 1975].
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