Fluidisation and deformation of submerged soil due to fluctuating water level
Fluidisation et d´eformations des sols submerg´es produites par les fluctuations du niveau de l’eau
H.-J. K¨ohler
Federal Waterways Engineering and Research Institute (BAW), Karlsruhe, Germany H. Spies, O. Beringer & H. Haußecker
Interdisciplinary Centre for Scientific Computing, University of Heidelberg, Germany
Keywords: fluidisation, oscillating waves, image processing, pore water pressure
ABSTRACT: One of the reasons why river or sea beds change their morphological surface continu- ously is the transportation of soil particles caused by water flow normal and parallel to the soil-water interface. This erosion process may be linked to the expansion and shrinkage of gas bubbles in the pore fluid due to pressure changes. Thus delayed pore water pressure responses occur by fluctuating water levels, especially such with short frequencies. These periods of pressure changes initiate par- ticle motion and transient water flow cycles inside the pores of the soil. This contribution presents results from measurements of the resulting soil structure changes obtained with an endoscope tech- nique. It can be shown that fluidisation of the soil can directly be observed with the method described in this paper, if the changing velocity of the water head is greater than the permeability of the soil.
R ´ESUME: Une des raisons du changement de la morphologie du fond des rivie`eres ou de la mer est le transport continu des particules du sol produit par l’´ecoulement de l’eau perpendiculairement et par- all´element a la surface du lit. Cette ´erosion peut ˆetre li´ee a l’expansion ou r´etre´ecissement des boules d’air contenues dans le fluide, provoques par les changements de pression. La r´eponse retard´ee de la pression interstitielle se r´ealise dans le cas des fluctuations du niveau de l´eau, sp´ecialement pour les fluctuatins a haute fr´equence. Ces p´eriodes de changement de pression d´eclenchent des mouvements des particules et des courants d’´ecoulement d’eau dans les pores du sol. On pr´esent les r´esultats des mesures du changement de la strucutre du sol obtenues a l’aide d’un technique endoscopique. On met en ´evidence le fait que la fluidisation du sol peut ˆetre observ´ee par la m´ethode d´ecrite dans cet article si la vitesse du changement du niveau de l’eau est plus grande que la perm´eabilit´e du sol.
1 INTRODUCTION
Oscillating water levels induce counter directional changes in pore water pressure u(z, t) inside the submerged soil. Transient pore water flow will be initiated causing soil particle fluid flow transport, especially at the soil-water boundary. Material transport and dangerous soil deformations may occur.
The temporal development of the transient excess pore water pressure distribution over the soil depth due to the event of water level lowering or rising can be described by a simple exponential function:
∆u(z, t) = γwdh(1− a(t)e−b(t)z) . (1) The parameters a(t) and b(t) change their values during the elapsed time t for different soil and load characteristics. The pressure distribution of the induced excess pore water pressure below the river or canal bed perpendicular to the bed surface is directly dependent on the draw down value dh and the specific weight γw of the water medium. It is measured over increasing soil depth z, K¨ohler (1993).
Figure 1: Example image sequence, the enlarged area is shown for three time steps, ∆t = 1.2 sec.
2 EXPERIMENTAL SET-UP
Experiments were carried out using a purpose build large pressure tank located at the Federal Water- ways Engineering and Research Institute in Karlsruhe, Germany. The tank is about 2 m long, 80 cm high and 80 cm wide. This unique device allows to apply pressure gradients in all directions superim- posed by steady and transient water flow in a pressure environment of up to three bar. Through sev- eral endoscope inlets all critical areas within the sediment may be observed. During the measurement campaign reported here, the tank was filled with uniform sand of a mean diameter = 0.2 mm, cov- ered by a 10 cm granular filter. Stabilisation against the load of oscillating water levels was achieved by applying variable top loads. The different load levels are provided artificially by four controlled pressure pistons acting on a distributing metal grid.
3 IMAGE PROCESSING
In previous investigations a method based on image sequence analysis to determine the amount of mo- tion that occurs at sand-gravel boundaries under changing pressure conditions was presented, K¨ohler et al. (1996). The project described here is an extension that also captures the accompanying velocity fields. Due to space limitations only a brief description of the image processing algorithm is given here, more details can be found in Spies et al. (1999).
From the image sequences the local displacement vector fields are found by means of the structure tensor technique outlined in J¨ahne et al. (1998). The algorithm analyses the spatio-temporal greyvalue structure in each local neighbourhood to compute the displacement vector. From the thus computed velocity fields local structure changes can be detected. This is done through the calculation of their divergence and vorticity values. Those values indicate inhomogeneous movements, i.e. structural changes within the soil. Furthermore mean velocity values can be obtained which can in turn be compared to the simultaneously captured pressure distributions.
4 OBSERVATIONS
The images are gathered with a sampling rate of 25 Hz. The images taken are of size 512 by 512 pixels corresponding to a viewing area of 6 by 6 mm.
In our primary experiment the endoscope was placed in such a way that the gravel-sand boundary was visible and greyvalue images were taken. One example image is shown in Figure 1. The outlined area is enlarged for three successive time steps (∆t = 1.2 sec). In these images the lifting and settling of the complete sediment structure can be observed. Apart from sediment particles a moving bubble embedded in the soil can clearly be seen. The enlarged area is approximately 2 by 2 mm. Thus the gas bubble shown here is of the same size as the larger sand particles, i.e. a diameter of about 0.3 mm.
Observed velocity magnitudes vary greatly with the initial water level, the top load and the draw
0 10 20 30 40 360
380 400 420 440
t Gravel (+5 cm)
Boundary Sand (-10 cm) Sand (-15 cm) Sand (-20 cm) Sand (-25 cm) Sand (-35 cm) Sand (-45 cm)
Hydraulic head change [cm WH]
t [sec]
a)
-0.2 [1/s] 0.2
0 10 20 30 40
120 140 160 180 200 220
240 t Gravel (+5 cm)
Boundary Sand (-10 cm) Sand (-15 cm) Sand (-20 cm) Sand (-25 cm) Sand (-35 cm) Sand (-45 cm)
Hydraulic head change [cm WH]
t [sec]
b)
-0.2 [1/s] 0.2
0 10 20 30 40
120 140 160 180 200 220
240 t Gravel (+5 cm)
Boundary Sand (-10 cm) Sand (-15 cm) Sand (-20 cm) Sand (-25 cm) Sand (-35 cm) Sand (-45 cm)
Hydraulic head change [cm WH]
t [sec]
c)
-0.2 [1/s] 0.2
0 10 20 30 40
120 160 200 240 280
320 t Gravel (+5 cm)
Boundary Sand (-10 cm) Sand (-15 cm) Sand (-20 cm) Sand (-25 cm) Sand (-35 cm) Sand (-45 cm)
Hydraulic head change [cm WH]
t [sec]
d)
-0.2 [1/s] 0.2
Figure 2: Comparing the amount of motion under varying hydraulic conditions, top loads including gravel filter layer (simulating revetment weight) applied were: a) 2.8kNm2, b) 8.5kNm2, c) 2.8kNm2 and d) 1.3 kNm2. On the left: hydraulic head change, middle: velocity fields at times t (during draw down), right: divergence image revealing regions with structural changes.
0 5 10 15 20 25 30 0
1 2 3 4 5 6
t
a) b) c) d)
Hydraulic gradient [ - ]
t [sec]
water head (start) [m]
pressure change [m]
draw down time [s]
lowering speed [m/s]
hydr. gradient [ - ] top load [kN/m^2]
parameter b [1/m]
a) b) c) d)
4.2 0.65
5 0.14
7.5 3.2 2.8
2.3 0.92
7.5 0.12
7.0 5.5 8.5
2.2 0.95
9 0.11
6.0 4.4 2.8
3.2 1.75
14 0.12
2.0 3.1 1.3
Figure 3: Hydraulic gradients due to fluctuating water levels and derived parameters for the examples given.
We refer to typical situations in a navigable inland canal of about 4 m water head.
• a) In the first situation the relatively high initial water level of about 4.2 m describes the hy- draulic condition at the depth of the canal bed. For the applied pressure change of about 65 cm in 4.5 s the top load of 2.8kNm2 is sufficient to protect the soil against fluidisation. Only heaving effects due to small elastic deformations are to be found. As a result the complete sediment is slowly lifting and settling and hardly any structural changes occur during the entire load cycle.
• b) and c) Here the initial water level is reduced to 2 m and thus represents the condition of an embankment at medium water depths. Both examples show the onset of fluidisation effects occurring locally due to the expansion of air bubbles embedded in the pore water of the sub- merged soil. Here some inhomogeneous movements can be observed which results in regions with higher divergence. Even the high top load of 8.5kNm2 in case b) can not prevent some struc- tural changes to occur in the sediment. A similar situation can be observed in case c) where a much smaller top load of 2.8kNm2 has been applied. Only the draw down velocities are different with a slightly higher value achieved in case b).
• d) Fluidisation occurs for a top load of 1.3kNm2. Even though the draw down speed of the water level change equals that of case b), far greater movements and accompanying structural changes took place. Thus both lifting and mixing of particles describe the typical situation in a hydraulically induced unstable (boiling) soil.
In summary the observed results demonstrate clearly the influence of all parameters mentioned before.
In Figure 3 the induced hydraulic gradients during water level lowering phases are plotted over the elapsed time t. The critical hydraulic gradient icrit = 1 for sandy soil is exceeded up to five times indicating that fluidisation may easily occur, especially on unprotected soil beds. As can be seen from Figure 3 as soon as fluidisation occurs this critical condition extends remarkably long, see cases a) and d). Figure 3 also gives the characteristic values for each of the considered pressure load changes.
The parameter b, Eq. 1, indicates expected smaller excess pore water pressure during fluidisation.
4.1 Fluidisation
In another set-up two layers of differently coloured sand were placed just beneath the boundary and viewed with an endoscope. Figure 4 shows some example images where the green particles are shown brighter than the red ones. In these images the increasing mixing of the submerged soil particles due to fluidisation can nicely be seen. The images were taken at different days during a measurement campaign, which means that roughly 35 water level draw downs lie between each of them. Thus the
Figure 4: Fluidisation phases over a period of about 35 load changes, between each image, of roughly the same size (≈ 60-180 cm) starting from different water heads (between 2 and 10 m water height).
Differently coloured sand of the same grain size is packed into two horizontal layers, green sand above red sand. For illustration green sand particles are shown brighter than red ones. The left image shows the layers at the beginning and the right one after altogether 70 load changes.
Figure 5: Measured and anticipated velocities: a) stable set-up and b) non-stable situation. Please note the different scales.
4.2 Heaving and settling due to pressure changes
As described in K¨ohler et al. (1996) the moving area of a gas bubble in the pore fluid can be found from a first order Taylor expansion of the ideal gas equation. If we take the radius change as the expected velocity the following formula describes the anticipated mean velocity:
v(t) = dr(t)
dt =−( c
36π)13 P−34 dP (t)
dt . (2)
Here P denotes the pressure and c is a constant that captures the gas content in the sediment. If bubble expansion is the only cause of motion Equation 2 should qualitatively describe the measured velocities. Figure 5 compares measured and expected velocity. While the theoretical and measured velocities coincide well for stable situations this is clearly not the case with less top load stabilising the sediment. In the latter case structural changes introduce far greater movements which are not accounted for by Equation 2, but are governed by the induced fluidisation process.
a) 7cm
Endoscope
b)
Figure 6: Observation of the water flow inside a pore volume: a) Endoscope placed in an artificial pore and b) observed Eulerian and Lagrangian flow.
5 FUTURE WORK
Future investigations will be concerned with the flow that can be observed inside a pore volume. In a first step a flexible endoscope is placed in an artificial pore as illustrated in Figure 6a. In the ongoing project it is anticipated to reduce the gravel grain size to a diameter of roughly 10 mm. The flow measured in the preliminary experiment is reported in Figure 6b.
6 CONCLUSION
A novel measurement technique based on digital image sequence analysis of images captured with specifically designed endoscope set-ups was reported. Combined analysis of the calculated displace- ment vector fields and the simultaneously acquired pressure values reveal excess pore water pressure to be the primary cause of motion under changing hydraulic load conditions. A simple model for the occurring movements in a stable environment was shown to agree well with the measured data.
Furthermore the occurrence of large chances in the soil structure could be observed at lower water levels if insufficient top load was placed on the soil bed. The phenomenon of gas-water mixtures inside the pore fluid causes soil deformations under hydraulic pressure variations. This even occurs in a situation when high top loads are applied.
REFERENCES
J¨ahne, B., Haußecker, H., Spies, H., Schmundt, D. & Schurr, U. 1998. Study of Dynamical Processes with Tensor-Based Spatiotemporal Image Processing Techniques. In Computer Vision - ECCV
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K¨ohler, H. J. 1993. The influence of hydraulic head and hydraulic gradient on the filtration process.
In Brauns, Heibaum & Schuler (eds), Filters in Geotechnical and Hydraulic Engineering; Proc.
Geofilters’92, Karlsruhe. Rotterdam:Balkema.
K¨ohler, H.-J., Haußecker, H. & J¨ahne, B 1996. Detection of Particle Movements at Soil Interfaces due to Changing Hydraulic Load Conditions, Localised by a Digital Image Processing Technique.
In J. Lafleur, A. L. Rollin (eds), Proc. Geofilters 96, Montreal. ´Ecole Polytechnique Montreal.
Spies, H., Beringer, O., Gr¨oning, H. & Haußecker, H. 1999. Analyzing Particle Movements at Soil Interfaces. In J¨ahne, B., Haußecker, H. & Geißler, P. (eds), Handbook on Computer Vision and Applications. Academic Press.
