lyx ,^.->.yt-/, -V- ^ -«- *^ VÜJ u
lAHR 1961 Belgrade
INVESTIGATION OF EXCESS WATER-PRESSURE UNDER
1 THE ASPHALT FACING OF SAND-CORED DYKES
BY
Ir. W.C. Bischoff van Heemskerck
"Rijkswaterstaat" - Netherlands
Paper lAHR I96I Belgrade
INVESTIGATION OF EXCESS WATER-PRESSURE UNDER THE ASPHALT FACING OF SAND-CORED DYKES
by: Ir. B.C. Bischoff van Heemskerck, "Rijkswaterstaat" -Netherlands
Summary.
The excess pressures anticipated underneath the asphalt facing of a number of sea dykes were determined with the aid of plate-shaped electrical conductors and alternating current.
As these excess pressures are influenced by factors
varying from place to place in the prototype, a series of tests were carried out in which one or more of these factors v/ere varied.
With the help of some examples the following subjects will be dealt with:
the influence of permeability and its inhomogenity; the influence of various forms of drainage in the toes of the dykes;
the consequences of air being imprisoned between the facing and the surface of the ground water.
Memoire lAHR I96I Belgrado.
Recherches sur la sous-pression au-dessous du revetement bitumineux d'un nombre de digues avec un corps en sable. par Ir. W.C. Bischoff van Heemskerck
"Rijkswaterstaat" Pays Bas.
Résumé:
Les sous-pressions anticipées de l'eau sous Ie
revetement bitumineux d'un certain nombre de digues maritimes ont été déterminées a l'aide de conducteurs electridues plats et d'un courant alternatif.
Etant donné que ces sous-pressions sont influencées par des elements, variant de place en place dans la prototype, une série d'essais a été effectuee avec un ou plusieurs de ces elements variables.
A l'aide de queiques exemples, les sujets suivants ont été traites:
L'incidence de la perméabilité et de son manque d'homogénéité.
l'incidence des différentes formes de drainage au pied des digues.
Les consequences de l'air, emprisonné entre Ie revetement et la nappe a qui fére.
Figures
1. Example of a modern dyke in the Netherlands. 2. Factors determining design.
3. Electrical circuit diagram for analogous model.
k. Analysis of boundary conditions.
5. Grain distribution diagram. 6. Boundary condition example 1. 7. Construction of example 1.
8. Rise in metres in relation to top of facing expressed as a function of permeability coefficient K.
9. Construction of example 2.
10. Maximum potentials in example 2. 11. Construction of example
3-12. Maximum thickness of asphalt required expressed as a function of the length y of the layer of loam (fig.11). 13* Systems of open drainage.
^k. Construction of open drainage in example k.
15' Resistance of the drainage shov/n in fig. 14 expressed as a function of silting up.
16. Boundary condition example k.
17- Maximum potentials in example k for various resistances
(degrees of silting up) based on fig.15. 18. Construction of example
5-19' Maximum potentials in example 5*
20. Curve showing maximum air pressure along dyke facing with ventilation at crown of dyke (example 6 ) .
21. Diagram example
Figures.
1. Exemple d'une digue maritime de conception moderne aux Pays Bas.
2. Critères de base.
5. Schema électrique d'un modèle d'analogie.
k. Composition de conditions marginales.
5. Courbes granulométriques.
6. Condition marginale de 1'exemple 1. 7. Construction de 1'exemple 1.
8. Elevation du niveau de I'eau en metres au-dessus de la surface supérieure du revetement en fonction du coefficient de perméabilité K.
9. Construction de I'exemple 2. 10. Elevations maxima de I'exemple 2. 11. La construction de I'exemple
5-12. L'epaisseur maximum du revetement d'après le critère de flottaison en fonction de la longueur (y) de la couche d'argile dans la figure 11.
13. Methodes pour un drainage ouvert.
1^. Construction d'un drainage ouvert (exemple 4 ) .
15. Resistance du drainage représenté dans la figure k en
fonction de 1'ensablement.
16. Condition margi.nale de I'exemple k.
17. Elevations maxima de I'exemple k pour de différentes
resistances (ensablements) d'après la figure 15* 18. Construction de I'exemple
5-19* Elevations maxima de I'exemple 5 sans drainage, avec drainage ouvert et avec drainage a sens unique
20. Courbe de la pression de I'air maximum le long du revetement en cas d'aeration dans la crête de la digue (exemple 6 ) . 21. Schema de I'exemple
7-22. Courbes de la pression de I'air et de la pression de I'eau de I'exemple 7 en fonction du temps.
Foto's
1. Cylinder for measuring the apparent water-retaining capacity.
2. Analogous electrical model. 3. Boundary condition apparatus.
Photo's.
1. Cylindre pour la mesure de la capacite apparente de I'eau emmagasiree.
2. Modèle d'analogie électrique.
Introduction.
The sea dykes now being constructed in the Netherlands consist of a core of poured sand faced with asphaltic concrete. In order to keep down the loss of sand resulting from current and wave action while the dam is being constructed retaining embankments of other material are sometimes used near the inside and outside toes (Fig.l).
Since asphaltic concrete is much more impervious to water than the underlying materials, hydraulic stresses may build up under the facing, which will reduce the maximum friction between this facing and the material to which it has been applied.
Consequently, after a certain moment, as the water pressure rises an ever-increasing part of the component of the weight of the facing itself parallel to the slope will be absorbed by the facing itself. This may give rise to inadmissible deformations in the long run because of the viscosity of asphaltic concrete.
To discover the extent of these deformations it would be necessary to know the stress and deformation conditions in the facing under the influence of the weight of the facing itself and the ever-changing hydraulic stresses. So far, no satisfactory method of obtaining this information has been devised, so that
for the time being a comparatively arbitrary standard has to be adopted which must be met to cope with viscous deformation, viz., that under frequently recurring circumstances such as normal spring tides the component of the weight of the facing itself parallel to the slope shall never exceed the maximum friction between the facing and the underlying material (Fig.2).
Moreover, a different standard must be observed for rarely occurring circumstances. Then the requirement is that nowhere shall the excess pressure be greater than the component of the weight of the facing itself perpendicular to the slope.
So in an extreme case the facing would "float" on the hlope in places (Fig.2). The component of the weight of the facing parallel to the slope is then entirely absorbed by the facing itself. This is considered acceptable under extreme conditions, because the viscous deformations are expected to remain within reasonable limits owing to the short duration of those conditions.
11,
RETAINING EMBANKMFMT
N A P - . 13 5 0 m t r s NAP» i 5 0 m t r s F L O O D / T I
N A P « 2 m t r s HIGH TIDE
FIG 1 EXAMPLE OF A MODERN DYKE IN THE NETHERLANDS
ƒ>> . Ya t a n • - ton C
' \ ^ Vu, t o n * P S d ™5 cos a
FOR FREQUENTLY RECURRING CIRCUMSTANCES FOR EXTREME SITUATIONS F I G 2 FACTORS DETERMINING DESIGN
^\ — 1 I I ^ 1 I V I 1 r
-1 >^ i i
i^i
1 ^
V Ï P L A T E - S H A P E D CONDiJCTOB
'•\_, SOURCE OF ALTERNATING CURRENT
• > .
^ \
i CONDENSER 1
2
-It must be pointed out, however, that in such cases the grain pressures in the material immediately underneath the facing will be reduced to zero, thus increasing the risk of deformation of the slope underneath the facing.
Swell and wind waves, which in view of their high frequency are usually ignored when calculating excess pressures, may also cause such deformation of the slope. Not only do they constitute a varying load applied externally to the slope, but they
result in the excess pressures not having the calculated values changing with the tide, but fluctuating with a frequency equal to that of the wave motion.
The above standards may be expressed in draft formulae as follows.
For frequently recurring circumstances:
, , /« tg tf-tgcx p ^ a.-— .coscx. —r r —
For extreme s i t u a t i o n s :
p 4 d.ifL cos«
i n which
P = water pressure underneath the asphalt facing in metres for j-w =1
d = thickness of the asphalt facing in metres
(J"^ = specific gravity of the asphalt facing in tons per cub.metre
tj:^ = specific gravity of the water in tons per cub. metre
(X = angle of inclination of the slope
f = angle of friction between the facing and the underlying
material or the angle of the internal friction of the underlying material itself.
In order to determine the thickness d of the asphalt by means of these tentative formulae the potential curves must be known, both for frequently recurring circumstances and for
3
-2. Method of investigation.
The distribution of potential in the body of a dyke can be found by calculation if the boundary conditions are known and the mass of soil through which the water runs can be reduced to simple terms. In this particular problem the latter has turned out to be impossible to achieve as a rule without seriously sacrificing accuracy.
In view of the high expense of the asphalt facing on the one hand and the sensitivity of the thickness of facing required on the other hand, such inaccuracy was regarded as unacceptable and other methods of investigation were considered.
Water stresses in the body of a dyke are determined by a great number of factors. A niimber of these factors are known to be liable to great variations, for example, the permeability
may differ considerably at one spot compared with another. Neither can the tidal boundary conditions and the v/ind effect to be
superimposed on them be regarded as constant quantities. In most cases it will moreover be desirable to investigate a great number of alternative designs. It must therefore be possible to vary these and other factors during the experiments.
In order to fulfil these requirements it seemed to be advisable to choose a method in which use is made of the well-known analogy between a stream of liquid passing through porous substances and an electric current passing through resistances and capacities. In principle this can be done in different ways. An analogous model composed of a network of resistances and capacities would in many respects have been preferable for the solution of the present problem. Such a model, however, would have to contain a very great number of sections, all the
resistances and capacities of which v/ould have to be adjustable in view of the variations referred to above.
In order to gain the insight necessary for designing such a comprehensive model, preliminary experiments were carried out with plate-shaped electrical conductors (Photograph 2 ) . These conformed to the shape of the water-bearing soil-mass, the upper edge of the model being located at a height equal to the capillary elevation above the phreatic plane formed if the water levels
PHOTO 1
CYLINDER FOR MEASURING
THE APPARENT
WATER-RETAINING CAPACITY
PHOTO 2
ANALOGOUS ELECTRICAL
MODEL
PHOTO 3
BOUNDARY CONDITION
APPARATUS
PHOTO 3
k
-on either side of the dyke are held stati-onary at their average level.
Along this edge short electrodes are fixed, all of which are connected to an earthed condenser (Fig.3)« These condensers represent analogously the water-retaining capacity. The boundary conditions are applied as alternating current. In order to
make the latter follow the desired shape of curve use is made of a special boundary condition apparatus (Photograph 3 ) • By this means a great number of periodic tidal curves can be obtained from a few harmonics, while a flood tide can be imitated by superimposing a wind effect on the tidal curve thus obtained (Fig.4).
This ï/ind effect, the curve of which can also be varied at will, occurs in the model every 64 tides. The effect of the previous flood tide has then largely disappeared by the time
the next flood tide appears.
If there is a horizontal or practically horizontal beach in front of the dyke, the part of the tidal curve below beach level will not be expressed in the ground water potential in front of the dyke. This is represented in the model by means of a special device which prevents the current applied from decreasing below a certain predetermined value corresponding to the level of the beach. Part of the tidal curve is thus lopped off, as it were (Fig.'t).
Another device switches the condensers off wherever the free water level reaches the under surface of the asphalt facing.
The frequency of the boundary condition of the tide can be varied between 200 Hz and 5OOO Hz. Since a change in frequency has the same effect as a change in permeability or as a change in the water-retaining capacity of the soil, variations in these can easily be investigated.
Alterations in the shape of the water-bearing soil-mass can quickly be made, while anisotropy and inhomogeneity of the
permeability can easily be reproduced. It also takes very little time to measure the distribution of potential in the model, so
4 a ,
n
NORMAL TIDAL MOVEMENT
BOUNDARY C O N D I T I O N
FIG 4 ANALYSIS OF BOUNDARY CONDITIONS
O i 1 ' i I i ' • ! I I *~ 1 p-O p-O o p-O p-O p-O ^ p-O . l . l p-O r f ï ' ^ p-O p-O ." o o o N 0<^'~r^€ycioOtt~COti <n e*
- d o o d ó o o o o b ö ó ó ö ó Ö 6 6 DIAMETER IN m m »•
FIG. 5 GRAIN DISTRIBUTION DIAGRAM a = SAND SAMPLE FROM HYDRAULICALLY DEPOSITED
DYKE
b = S A N D , T H E APPARENT WATER - RETAINING PROPERTIES OF WHICH HAD B E E N DETERMINED
c = A V E R A G E OF SAND SAMPLES TAKEN FROM THE UPPERMOST 6 METRES OF THE SUBSOIL
5* 4* 2' NAP .fc z I
^y
->r^.
I?'
/,/\J
— / / ui
—"S
/ — — V . \ / — /\ ^^\ \i \ ^ \ \ ' L E V E L OF J LANDWARD SIDE •^BOUNDARY — ^CONDITIONFIG 6 BOUNDARY CONDITION EXAMPLE 1 irijliijj
N A P * 0 . 5 0 m t r NAP+1.00 m t r
NAP-2.gQrntr».
5
-that the influence of a great number of variables can be investigated with little delay. A few results of the tests carried out so far are discussed below.
3. The influence of water-retaining capacity and permeability. As the phreatic level moves up and dovm, complicated
phenomena are observed in the capillary zone and in the zone above it, which is partly saturated with water. These phenomena can hardly be taken into account directly.
So experiments are carried out for the types of soil to be considered in a cylinder v/ith a diameter of 0.20 mtr and a height of 2.10 mtrs (Photograph 1 ) . In this cylinder the upward and downward movement of the phreatic level is imitated to a time scale of 1 to 1, the current and potential being measured at the bottom of the cylinder, so that the relation between the current working perpendicularly on the phreatic level and the rise in potential can be determined. This relation, which has been found empirically, is taken to be the water-retaining capacity. The value of this apparent water-retaining capacity fluctuates during the up-and-down movement. In the majority of cases, however, it is possible to take for this an equivalent constant value. For the
types of sand encountered in the coastal area of the Netherlands an apparent water-retaining capacity of 20% was found in this way.
The apparent water-retaining capacity is one of the factors the value of which may differ in one and the same dyke. In principle such variations must therefore also be included in the investigation. As a rule, however, this is not done, since variation in the water-retaining capacity has the same effect as a variation in permeability. The range of variation in permeability anticipated is so much greater than that in the water-retaining capacity that in most cases the investigation may be carried out vi?ith a single value for the apparent water-retaining capacity. Both from measurements on the spot and
laboratory experiments it was concluded that the permeability factor K from Darcy's formula (v=-Kgrad.(fi) for the sand found in the Netherlands coastal areas might vary from 5x10 ^ mtrs per s e c to 5x10~^ mtrs per se& Grain distribution curves for this sand are shown in Fig.5'
6
-Both the dyke body and the subsoil are composed of such sand. This sand mass almost everywhere reaches a depth of 30-^0 metres below average sea level (= N.A.P.) where it rests on an unbroken stratum of clay. In places clay lenses may occur in higher deposits, but these too are often so deep that they hardly affect the current pattern in the toe of the dyke.
The variation in permeability referred to above, however, is always a factor that must be carefully reckoned•with. One example is the case the boundary condition and construction of which are shown in Figs. 6 and 7 respectively.
The tidal boundary condition is built up from the components
M2 = 1.00 c o s ( n t - 8 2 ° ) , M^ = 0.28 COS ( 2 nt - 1 5 6 ° ) a n d Mg = 0 . 0 8 5 c o s ( 3 n t - 9 0 ° ) .
The wind effect superimposed on this tide had a maximum rise
of k metreSu it was spread over k tides and had a decline of 0.25
metres per s^aeaié. This wind effect was superimposed on the spring
tide in such a way that the greatest excess pressures could be found. This was achieved by sliding the wind effect along the time axis. The landward side boundary condition was fixed at N.A.P. + 0.^0 mtr.
The permeability factor K was in this case varied between 10~5 and 10~5 mtrs/sec. The results are shown in Fig.8, in which the rise in respect to the top of the facing is plotted against permeability. Since the greatest excess pressure at any measuring point occurs at the moment when the outside v/ater level has fallen
to measuring-point level, only the potential at that moment was read off. Consequently, the values shown in Fig. 8 «rere not reached simultaneously at the different measuring points.
The figure also shows that the most unfavourable value of the permeability factor K is different at every point on the slope. These most unfavourable values are in the toe of the dyke, where the greatest excess pressures occur, just within the range of permeability variation anticipated in actual practice. Since this
coincidence appears to occur in most cases, the design is based on the most unfavourable value of K for each point on the slope. This appears to be of great importance,especially for low-lying toe constructions.
During experiments in which only the M2 tide represented the spring tide in the boundary condition, excess pressures were found
X=Omlr XM 1.00 mtr X.1.7Ö mtrs X=4.13 mtrs X.C.47 mtrs X =0.00 mtrs NAP*- 300 mtrj^ F I G . 9 CONSTRUCTION OF EXAMPLE 2 K (sond ) K ( rubble ) — _ _ ^ 10" * mlrs/sec 10"^ ö 10"-*mtrs/s«c , ^ _ l O " * mtrs/wc I0"*mirs(scc 1 0 " * mtrsls«c O 10 n 12
FIG. 8 RISE IN METRES IN RELATION FIG 10 MAXIMUM POTENTIALS IN EXAMPLE 2 TO TOP OF FACING EXPRESSED AS A
FUNCTION OF PERMEABILITY COEFFICIENT K NAP.I.aOmu-s NAP.0.00 mlfs I S m i r ! . _ ^ NAP+4.15 m t r s
7
-which were 0.05 - 0.10 mtr lower. Halving the length of the sheet piling appeared to result in differences lying within the same range.
The influence of inhomogeneities of permeability. The importance of the influence of inhomogeneity of permeability appears from the investigation of the toe construction shown in Fig.9.
The whole dyke is shown in Fig.l.
In contrast with the previous case this exeimple was one of a dyke in which a retaining embankment of rubble had been
included. The permeability of rubble is much greater than that of sand. The possibility of the sand impregnating the rubble during the pouring operation, however, was taken into account. Therefore experiments v/ere carried out in which the retairting embankment of rubble was made both less permeable than, equally permeable as and more permeable than the sand in the dyke. The boundary condition on the tidal side is shown in Fig.4. The inside water level was N.A.P. + 0.^0 mtr.
The results are shown in Fig.10, in which the maximum
potentials are joined by an enveloping line. Consequently these curves do not shov/ the potential line at one particular moment, but the maximum values of the potential which were reached at different moments.
It was found that a retaining embankment of rubble, which is very permeable compared with sand, caused the greatest excess pressures. Since there was no guarantee that the embankment would actually become impregnated with sand, the facing was designed accordingly.
Layers containing clay lenses or unbroken layers of clay are of particular importance when the bottom of the sheet piling ends in or just above them and when the landward-side water level is high.
Figure 11 shows such a case. In this instance the length of
the layer of clay y was varied while the boundary conditions were
fixed at the levels shown. The results are given in Fig.12. In the case of a homogeneous dyke and subsoil, an asphalt thickness of 0.90 mtr. appears to be necessary in the toe of the dyke. When a layer of clay is present, the thickness required will be considerably greater. Greater permeability in a horizontal direction than in
7a.
HOMOGENEOUS
KChorizortal direction)^ QxKCvertical K(dyke) = 10xKUubsoil) direct ion) HOMOGENEOUS WITH DRAIN (FIG. 14)
FIG 12 MAXIMUM THICKNESS OF ASPHALT REQUIRED EXPRESSED AS A FUNCTION OF THE LENGTH Y OF THE LAYER OF LOAM (FIG 11)
S AP • ' , 5 0 n-t-S
FIG 13 SYSTEMS OF OPEN DRAINAGE
F I N E SAND COARSE SAND FINE GRAVEL
COARSE GRAVEL C O N C R E T E
FIG. 14 CONSTRUCTION OF OPEN DRAINAGE IN EXAMPLE 4 6 0 * 4
RESlS-ANCE TC DRAINAGE —
D
FIG 15 RESISTANCE OF THE DRAINAGE SHOWN IN FIG. 14 EXPRESSED AS A FUNCTION OF SILTING UP
- 8
when there is no layer of clay. Greater permeability of the sand in the dyke body has the same effect. As it was uncertain
that there was sufficient space everywhere between the bottom of the sheet piling and the top of the layers of clay, drainage was provided for in the toe of the dyke. In view of the unfavourable results mentioned above the toe of the dyke was made 0-50 mtr higher.
The effect of drainage of the toe of the dyke.
The toe of the dyke can be drained in different ways. In general natural drainage is preferred, because it is undesirable to rely on pumps, which not only consume energy, but may also fail at inconvenient moments.
So a gravel drain was devised connected v/ith the tidal water in the toe of the dyke. The gravel drain may be located just behind the sheet piling or extended for a certain distance under the
facing (Fig.13)•
The latter expedient is not as a rule resorted to, because if silting up of the lower part occurs, hydrostatic pressure is set up. The former design was therefore also chosen for the case referred
to above, in which the sheet piling reached dovm into the layer of clay and the landward-side water level was high. (Figs.11 and 12, but now with the toe at N.A.P. + 1.50 mtrs.)
This design is shown in Fig.l4, the sand-filled concrete trough being used as a mud catcher. If there is any silting up with mud or clay a greater excess pressure occurs, so that in the end the sand in the trough will start to "boil up". Experiments have shown that the mud will disappear again, so that in this respect the mud catcher is self-cleaning.*
* This construction was designed by Mr. G. Boomstra of Messrs. Zanen & Verstoep, contractors, The Hague.
_ 9
-Silting-up with sand is a greater source of danger in such a design.
Therefore the hydraulic resistance of the filter construction was calculated for different types of silting-up, as shown in Fig.15* Further experim.ents v/ere carried out with the boundary conditions shown in Fig.l6.on the tidal side and the landward-side water level referred to before. In these experiments the effect of, different types of silting up was investigated. The results of these tests are shown in Fig.171 showing again the enveloping lines of the potential curves appearing in succession.
In this case the drain only relieves the bottom part of the slope, consequently its efficiency is limited. If silting up occurs even this limited efficiency is largely lost. Nevertheless the drain with mud-catcher was used because the sheet piling might extend down into the layer of clay mentioned above. Moreover, immediately after a violent flood tide the sand can be expected to be swept away again. In the meantime it appeared that this drainage was a practically indispensable device in view of the difficulties accompanying the pouring of asphalt below high-water mark.
In other cases a one-way valve system had to be used. It v/as used for the first time on an existing dyke, the asphalt facing of which was repeatedly damaged. On investigation it appeared that this dyke had a very permeable retaining embankment which has been referred to above as having an unfavourable effect. Moreover the slope was so steep (1 in 3i) that but for the one-way valve system it would have been impossible to satisfy the standard for frequently occurring conditions referred to earlier. The construct-ion of the toe of this dyke is shown in Fig.lS. Since the dyke in question was situated at a spot exposed to violent waves and strong currents, there was no fear of its silting up.
Fig.19 shows the effect of open drainage and of a one-way valve. From this figure it is clear that an open drainage system may spoil conditions for the upper part of the slope.
A sinusoidal tide with an amplitude of 2 mtrs was applied as a boundary condition. The wind effect superimposed on it had a maximum rise of 3 mtrs and an overall duration of 3? tides. The decline in this wind effect was again 0.25 mtrs per hour.
r
9 a .
FIG. 17 MAXIMUM POTENTIALS IN EXAMPLE 4 FOR VARIOUS RESISTANCES (DEGREES OF SILTING UP ) BASED ON FIG. 15
NO DRAINAGE OPEN DRAINAGE ONE-WAY VALVE SYSTEM
I MATTRESS
FIG. 18 CONSTRUCTION OF E X A M P L E S
5 S 7 DISTANCE IN m t r s
FIG, 19 MAXIMUM POTENTIALS IN EXAMPLE 5
8 0 DISTANCE IN m l r s
2 0 CURVE SHOWING MAXIMUM AIR PRESSURE ALONG DYKE FACING WITH VENTILATION AT CROWN OF DYKE ( E X A M P L E 6 )
SHEET PILING
F I G . 21 DIAGRAM EXAMPLE 7
BOUNDARY CONDITION
CURVE SHOWING POTENTIAL IN GROUNDWATER FOR AN ANALOGOUS WATER-RETAINING CAPACITY POTENTIAL IN GROUND WATER FOR ACTUAL WATER- RETAINING CAPACITY
FIG. 22 AIR AND WATER .PRESSURES OF E X A M P L E 7 PLOTTED AGAINST TIME
10
-^. The effect of air being trapped between the facing and the free water surface.
Air can be imprisoned between the asphalt facing and the ground water surface, the volume of this air changing as a consequence of tidal movement.
This change in volume V is accompanied by a change in air pressure P following the law PxV = constant.
Varying air pressure not only affects the water movement in the dyke body, but it may also threaten the stability of the facing. Therefore most sand dykes in the Netherlands are provided with a ventilation system in the crown, consisting basically of a continuous trough of gravel connected at intervals with the open air by means of a vent pipe with inverted orifice.
Originally it was thought that the outflowing air would meet v/ith increasing resistance as it approached the narrow gravel trough.
This was investigated for the case shown in Figs. 6 - 8 . The maximum water currents in a direction perpendicular to the phreatic plane were measured in the model at different places along that plane. These currents were then used as boundary conditions in a model of the top of the dyke. The results are shown in Fig.20. From this
figure it is.clear that there is no question of the head concentrating around the trough of gravel, since the change in water level and
consequently the displacement of air occurs mainly near the toe of the dyke, where there is also a narrow profile acting as a choke. In most cases, therefore, the gravel trough need not be larger than is
necessary for easy construction. In this instance it was sufficient to have a gravel trough with a cross-sectional area of 0.25 sq.mtrs.
For the case illustrated in Figs. 1,^,9 and 10 the fluctuation in air pressure near the toe of the dam was investigated, because
the original design had provided for sheet piling up to the level of the flat (Fig.21). The purpose of this sheet piling was to
prevent the sand in the dyke from running away if the asphalt facing should give way, thus restricting any damage to the retaining
embankment only.
No separate model for the air flow was used for this investigation, the air pressure being imitated in the existing model for the ground-water flow by introducing an imaginary ground-water-retaining capacity n saaller than the water-retaining capacity of 20% mentioned above.
11
-The potentials found are shown in Fig.22. It may now be assumed that -rp- of these potentials were caused by actual
ground-water flow and ~ö?r" °^ them by fluctuation in air pressure.
If the correct value is chosen for n, the air pressure curve thus obtained must be equal to the air pressure curve which can be calculated from the actual ground-water movement and the formula PxV = constant.
Consequently the correct value of n can be found empirically. In this instance it appeared to lie between 1% and 5%> For values of n within this range it turned out that the air-pressures reached unacceptably high values. So it was decided not to use sheet piling here.
