At present no methodology exists to evaluate the failure mode of a caisson breakwater subjected to a tsunami attack. The present paper investigates the sliding ...
Laboratory Experiments on the Sliding Failure of a Caisson Breakwater Subjected to Solitary Wave Attack Miguel Esteban United Nations University, Institute of Advanced Studies Yokohama, Japan
Nguyen Danh Thao Ho Chi Minh City University of Technology Ho Chi Minh City, Vietnam
Hiroshi Takagi Yokohama National University, Department of Civil Engineering Yokohama, Japan
Tomoya Shibayama Yokohama National University, Department of Civil Engineering Yokohama, Japan
ABSTRACT At present no methodology exists to evaluate the failure mode of a caisson breakwater subjected to a tsunami attack. The present paper investigates the sliding and tilting failure of a caisson breakwater subjected to a solitary wave attack, and establishes a relationship between the sliding and vertical movement. The vertical movement of the caisson is evaluated using the method of Esteban and Shibayama (2006), originally was developed for wind waves. The method was verified by carrying out laboratory experiments using solitary waves and comparing the results to those obtained using the new methodology. The sliding failure will be discussed and a general expression for an upper bound limit to the sliding will be proposed. KEY WORDS: Tsunami; sliding; reliability; risk assessment; tilting; deformation; rubble mound.
INTRODUCTION In order to correctly design structures to withstand tsunami attack it is necessary to evaluate how reliable they would be against a range of tsunami wave types and heights. The development of these countermeasures is of paramount importance in order to prevent the loss of life and property that might occur as a result of these waves. Researchers such as Shibayama et al, (2006), Sasaki (2006) and Jayaratne et al. (2006) have noted how various types of coastal terrain can attenuate or magnify the damage due to tsunami attack. However the degree of protection that the various natural or artificial coastal structures offer against tsunami attack is not yet properly understood. The 2004 Banda Aceh tsunami has highlighted how coastal forests are
Paper No. PO8-T24
Esteban
not always as effective against tsunamis as previously thought. At present it is therefore not entirely clear which is the best method to protect against tsunami attack and what degree or risk is related to the different counter-measures available. For the case of Japan, sea dikes have been built along the coast to protect against tsunamis, high waves and storm surges, and numerous studies (e.g. Naksuksakul 2006) can be found of the construction of such counter-measures. However, expected tsunami heights are often higher than the existing defences, and hence the potential damage due to a tsunami of a given height should be evaluated in order to formulate a correct disaster prevention policy. The sliding/tilting failure induced by the wave force, along with the scouring of breakwaters foundations, are two of the major factors relating to the failure of coastal dikes. The force exerted by the tsunami would depend strongly on the shape of the wave, which in term depends on the depth of water and other factors. Tanimoto et al. (1984) performed large-scale experiments on a vertical breakwater by using a sine wave and developed a formula for the calculation of the wave pressure. Ikeno et al (2001) conducted model experiments on bore type tsunamis and modified Tanimoto’s formula by introducing an extra coefficient for wave breaking. Subsequently Ikeno et al (2003) improved the formula to include larger pressures around the still water level, where the largest wave pressure was observed to occur. Mizutani and Imamura (2002) also conducted model experiments on a bore overflowing a dike on a level bed and proposed a set of formulae to calculate the maximum wave pressure behind a dike.
8 pages
For the case of tsunami protection, however, it is of paramount importance to understand the failure mechanism of the structure. This allows the engineer to determine the level of risk of the protected area against a variety of tsunami scenarios. In the case of caisson breakwaters, it is necessary to understand what kind of deformations can be expected in the rubble mound due to a given tsunami wave height. This deformation can be decomposed into two separate movements, one horizontal (sliding) and one vertical. The present paper will describe a method to calculate the vertical deformation and based on this vertical deformation an empirical upper bound limit of the sliding will also be proposed. The methodology to estimate the vertical displacement is based on the method of Esteban and Shibayama (2006), and it allows to estimate the upper bound displacements that are likely due to a caisson breakwater subjected to a solitary wave attack. Currently there are no other models that can simulate this displacement.
LABORATORY EXPERIMENTS
Laboratory experiments were carried to measure the displacements, pressure exerted onto the vertical face of the caisson breakwater, and load transmitted to the heel of the caisson. The wave flume used measured 15.3m long x 0.6m wide x 0.55m deep and was located at the Hydraulics laboratory of Yokohama National University in Japan. Fig. 1 shows a schematic representation of the wave tank and apparatus used, which was modelled using a 1:100 scale. The experiments were conducted for a range of water depths between h=15 and 20cm. At one end of the wave tank a wooden gate was placed to create a water reservoir (2.25m long x 0.6m wide x 0.55m deep) behind it. At the other end of the tank a wave absorption beach was placed in order to dissipate the energy of the waves created by the overtopping of the caisson. Drop-down Displ. Gage
Gate
Gravel Rubble Mound
Sand
H1 H2
3m
Fig.1. Experimental Set-Up
7cm
8cm
Pressure gages 24cm 7 Load cell 1:2
Gravel Rubble Mound D50=1cm
1:2
Fig.2. Experimental set up and location of measuring devices at the breakwater model
Apparatus
Wave Height Gage
B=14cm
1:1 1:10
3.7
0.2
The dimensions of the model caisson can be seen in Fig. 2. The mean diameter of the underlayer particles used was 10mm. The caisson units were made of an outer shell of glass which were then filled with a mixture of iron sand and normal sand to ensure that the final density was similar to that of a real life concrete caisson (ρc=2.0 tons/m3). The dimensions of the model caisson studied were 24cm tall x 14 cm long x 20 cm wide. To the side of the caisson studied a number of other caissons were placed in order to ensure that the experiment was carried out under two-dimensional conditions. A clearance of 2mm was kept between the model and the dummy caissons so that friction on either side did not occur during the experiments. No toe armour was placed on top of the rubble mound gravel, and although some limited scouring took place due to the solitary wave attack it was clear that this was not the predominant mode of failure. Nevertheless, the exclusion of armour allowed for the potential damage due to scouring to be assessed and so it was felt that valuable information could be gained from its exclusion. Two wave gages were placed, one around the middle of the tank and one before the caisson. This allowed for the change in the shape of the wave as it moved along the tank to be evaluated, and also to measure the incident wave height. The wave gages were connected to a PC, which recorded the waves as voltage signals that were later analysed to obtain the wave profiles. A drop-down displacement gage was mounted on rails above the tank to measure the vertical and horizontal displacement of the caisson. The method of Esteban and Shibayama (2007) highlights how the load at the heel of the caisson is the critical load for determining the vertical displacement. Hence, a single load cell was placed at the top of the foundations, with the measuring head of the device situated 1.5cm from the back heel of the caisson. A total of 3 pressure gages were placed, one at the water mark and the other two 1.5 and 3 cm higher than the first one, all of which were connected to a second PC to record the signals. A high resolution digital camera was placed in front of the caisson to film the wave attack and identify the failure mechanism.
Classification
T1
15
15
1
bore type
T2
16
15
6
bore type/breaking on caisson
T3
17
15
7
bore type/breaking on caisson
T4
18
15
8
almost breaking on caisson
T5
19
15
5
almost breaking on caisson
T6
20
15
5
non-breaking
T7
16
20
2
bore type/breaking on caisson
T8
17
20
3
Caisson failure
At the beginning of each experiment the rubble mound was slightly compacted to reproduce the compaction process that would be applied to the foundations during the construction of a breakwater. This created a level foundation on top of which the caisson was placed. The location of the caisson was determined at the beginning and end of the experiment by means of the drop-down gage.
6 5 4 3 2
Experimental Conditions
There was a clear limitation to the number of experimental conditions that could be carried out in the wave tank available. A number of different conditions outside the ones outlined in Table 1 were tried, but resulted in either almost no pressure acting on the breakwater (for h20cm or when h>17 with a step of 20cm). Generally speaking for the higher h the incident wave looked like a standing wave, but as h decreased the arriving wave front was more eccentric and eventually looked like a breaking wave (for conditions T2 and T3 for example). For conditions T1-T3 many of the waves broke in the mid-section of the tank and the incident wave looked like a bore-type tsunami.
Experimental Results
19 .3 19 .5 6 19 .8 2 20 .0 8 20 .3 4 20 .6 20 .8 6 21 .1 2 21 .3 8 21 .6 4
0
Time (seconds)
Fig. 3. Time series of pressure at face of caisson and load at back of foundations (Condition T2) Wave Time Series 20 18 16 14 12 10 8 6 4 2 0
Mid-tank wave gage Incident Wave Gage
2 2.36 2.72
The waves created in this manner had a celerity of between 3.9 and 4.16 m/s, a typical height of 7-10 cm at the first wave gage which increased due to shoaling to 17-20 cm as they hit the caisson.
1
Wave Height (cm)
The experiment was repeated for a number of different experimental conditions in order to create a variety of solitary wave types, as shown in Table 1. The reservoir situated at one extreme of the tank was filled to create the required water step according to the conditions set in Table 1. It was then rapidly opened manually by two people to create a solitary wave. Care was taken to try to raise the gate in the same way each time. However, slightly lower or higher rising times did produce waves of slightly different characteristics.
Pressure Gage 2 (KPa) Pressure Gage 3 (KPa) Load Cell 4 (kgf)
3.0 8 3.44 3 .8 4.1 6 4.52 4.88 5.2 4 5 .6 5.96 6.3 2 6.68 7.04 7 .4 7.76
Water Water No. Step Condition level h (H2-H1) Repetitions (cm) cm
wave acts as if it was formed of a number of “mini-waves” which act on top of the hydrostatic pressure that builds up as the mass of water piles up next to the caisson. Essentially, the first part of the wave appears to have a churchroof shape, characteristic of wind waves, but it is then followed by subsequent peaks of slightly lower magnitude. These oscillations in the load are though to be caused by the various parts of the mass of water hitting the caisson in sequence. This type of loading time series was essentially observed for all the non-bore type waves. The bore type waves did not appear to create this oscillatory movement, and essentially just applied a hydrostatic force on the caisson.
Load/Pressure
Table 1. Experimental Conditions
Time (sec)
Fig. 4. Wave Profile (Condition T2) Fig. 3 shows a sample time series of the pressure at the face of the caisson and the load at the back of the foundation for a typical solitary wave (corresponding to Condition T2). Fig. 4. shows the wave profile (for each of the two wave gages shown in Fig. 1) corresponding to the results shown in Fig. 3. The video analysis of the failure mode shows an intense rocking movement of the caisson. It appears that the solitary
Classification of Waves
P foundation From the analysis of the video recordings the incident solitary wave can be broadly categorized as follows: • Non Breaking: this occurs mainly when the h=20cm. The incident wave is similar to a sinusoidal wave and as it hits the caisson there will be a little overtopping. The first part of the wave mass to hit the caisson acts in a way similar to a wind wave and is followed by the main mass of water hitting the caisson. If the overtopping is large (when h>20cm then the caisson was washed away) • Almost breaking: as the incident wave approaches the caisson it starts to deform prior to impact. The load profile is similar to the non-breaking part but with a higher initial peak and smaller subsequent oscillations. • Breaking wave: the front of the solitary wave appears similar to a breaking wind wave, though the period of the wave is much longer and hence it differs due to the large amount of water at the back . • Bore type: the wave breaks before it arrives at the breakwater. The wave front that arrives is characterised by a high turbulence, though due to this turbulence the impact component of the wave force is completely lost and thus mostly hydrostatic pressure is applied to the caisson. In most of the recorded cases almost no load is placed on the foundations by these waves, which would imply that caisson breakwaters should be relatively safe against this type of wave attack.
The methodology to estimate the deformation in the rubble mound foundation of a caisson breakwater subjected to wind waves (Esteban et al. (2007) was adapted to the case of solitary waves.
Equation of Motion in the Vertical Direction To evaluate the vertical displacement at the back of the caisson a similar principle to that used by Esteban and Shibayama (2007) for a caisson breakwater subjected to wind waves was employed. The original methodology of Esteban and Shibayama (2007) uses the force exerted by the wave on the face of the caisson to evaluate the load at its heel. However, in the present case the load cell situated at the back of the caisson provided the necessary data. These loads were used as the starting point of the calculation, as the present methodology aims to predict the deformation of the rubble mound once the loading exerted by the caisson is known. It is assumed that the solitary wave acting on the caisson induces a triangular distribution of pressure underneath the breakwater, as can be seen in Fig. 5. Taking into account this triangular distribution, the total pressure applied to the whole of the foundation is given by the formula:
s
=
B ⋅ P foundation
s . max
=
2 ⋅ P foundation
s
(2)
B
The total pressure acting on the last section (a strip of length s) of the breakwater foundation will be given by:
Plast sec tion ≈
(
2 ⋅ P foundation
s
B
+
W water B
)⋅ s
(3)
B
Wwat
s s Pfoundations.max Plastsection
Fig.5. Diagram of Vertical Movement Parameters
ANALYSIS OF THE RESULTS
P foundation
s . max
(1)
2
where B is the breadth of the caisson, Pfoundations is the total pressure applied to the foundation, and Pfoundations.max is the maximum pressure applied to any one point of the foundation (which corresponds to the value measured by the shoreside load cell placed under the caisson). Hence,
Where Wwater is the weight of the caisson in water. In order to obtain the motion inducing force acting on this strip of soil, the resistance forces (in this case the bearing capacity of the ground) need to be deducted from the pressure applied. The equation of movement in the vertical direction according to Newton’s Law of Motion can be expressed as:
2 ⋅ Pfoundation s + W water W .. + M a x E = B g
s − qU ⋅ s
(4)
..
where x E is the acceleration at the edge of the caisson, W the caisson weight in the air, Ma is the added mass, and qU the bearing capacity of the soil. Or,
2 ⋅ P foundation s + W water W .. + M a x E = − qU B g
s
(5)
From this equation the vertical movement of the caisson can be calculated by integrating the acceleration twice with respect to time.
Bearing Capacity Esteban et al. (2007) highlight how the choice of an adequate value for qU is quite difficult, as this value is thought to change throughout the life of the caisson, with the progressive deformation of the caisson increasing the compaction of the foundation material under it. Table 2 gives some presumed bearing capacity values according to British Standard (BS) 8004: 1986. This table shows how the bearing capacity of the foundation is greatly affected by the degree of
compaction in the foundation material. An initial bearing capacity of 200 kN/m2 (corresponding to the lower bound of medium-dense gravel as described in BS 8004:1986, as shown in Table 2) was chosen, which is believed to be on the lower end of what could be expected for a caisson which has been through a few storms during its life.
Bearing value (kN/m2)
Dense gravel or dense sand and gravel Medium-dense gravel or medium-dense sand and gravel
>600 200-600
Loose gravel or loose sand and gravel
300
Medium-dense sand Loose sand
100-300
Remarks
0.55 0.5 0.4 0.3 0
200000
400000
600000
800000
Compaction energy (KJ/m3)
Fig.6. Void ratios vs. Compaction Energy
300KN/m2.
40
T1 (h=15cm)
35
T2 (H=16cm)
30
T3 (h=17cm)
25
T4 (h=18cm)
20 15
T5 (h=19cm)
10 T6 (h=20cm)
5 0
T7 (h=16cm, 0
5
10
15
20
Laboratory Experiments (mm)
Fig. 7. Experimental Relationship between vertical deformation and sliding
Discussion The ability of the model proposed to correctly estimate the sliding distance thus lies in being able to correctly predict the vertical deformation. Fig. 8 shows an example of the calculation of the vertical movement of an almost breaking wave type, with the experimental recording of the load cell resulting in the computation of a displacement at the back. This shows how the “peaks” are responsible for most of the vertical deformation, and indeed the video analysis also shows how the sliding motion also follows the same pattern as the vertical movement. Generally the results compare well, though the simulation sometimes overestimates the displacement, by up to a factor of 2 for some events. The reason for this probably lies in part in the difficulties in measuring the load exerted on the foundation. The load measured by the load cell does not always return to 0 at the end of the wave. This possibly indicates that displacements in the rubble mound are subjecting the load cell to a higher pressure than it was originally withstanding. It is quite difficult to know from what point the instrument started to over-estimate the pressure which is applied by the wave. Also, there is the possibility that the instrument was overrecording during part of the wave and the returned to its original condition due to further deformation in the rubble mound. Each experiment was clearly analysed, and some experiments where the load cell clearly did not function properly were removed from the final graph. Nevertheless it is possible that some of the points in Fig. 9 could also be slightly inaccurate. By analysing load time history graphs it is believed that the load values subsequent to the first peak could have an error of up to 20%. This error is probably not present in the first measured peak in the time history as prior to this time there has been no deformation in the rubble mound. This can thus result in a certain deviation from the observed results and could explain to some extent the scattering of values shown in Fig. 9.
Displacement (mm) Load Cell 4
21 .7 22 .46 23 .2 23 2 .9 24 8 .74 25 .5 26 .26 27 .02
-2
Load (kNx10 ) / Displacement (mm)
6 5 4 3 2 1 0
Time (s) Fig. 8. Time Series of load and vertical displacement at the heel of the caisson (Condition T5)
Comparison of Predicted and Observed Vertical Displacements T1 (h=15cm)
10
T2 (H=16cm)
8
T3 (h=17cm)
6
T4 (h=18cm)
4
T5 (h=19cm)
2
T6 (h=20cm)
Simulation (mm)
12
T7 (h=16cm, step=20cm)
0 0
2
4
6
Laboratory Experiments (mm)
Fig. 9. Comparison simulated and observed displacements
Comparison of Predicted and Observed Sliding T1 (h=15cm) C alculated (m m )
40
T2 (H=16cm)
30
T3 (h=17cm)
20
T4 (h=18cm)
10 T5 (h=19cm) 0 0
5
10
15
Laboratory Experiments (mm)
20
T6 (h=20cm) T7 (h=16cm,
Fig.10 Comparison between estimated and observed displacements
Another source of error is the choice of the initial gravel parameters. These are based on an “engineering” guess, though in the case of high loads the choice of a low initial bearing capacity value will result in a very large acceleration of the caisson into the ground. The original model of Esteban and Shibayama (2006) dealt with a large number of consecutive wind waves, and hence it is unlikely that the highest waves will occur at the beginning of the storm, thus allowing the simulation to slowly compact the ground due to smaller waves. However in the present simulation no such computational procedure takes place, and hence a wave which exerts a high initial load into the ground can somewhat confound the results. Furthermore, it is likely that in many of the experimental cases the ground had a bearing capacity greater than the 200 kN/m2 used in the simulation, which would result in lower deformations that those predicted by the model. The classification of the waves shown in Table 1 was carried out by analysing slow-motion videos of the waves as they hit the breakwater. This classification however was sometimes not easy, and for example, the difference in shape between the “almost breaking type (T5)” and “not-breaking type (T6)” is often very small. This visual classification was not able to determine why some of the results in Fig. 10 showed no vertical movement but only sliding. Analysis of the wave time history showed wave profiles similar in magnitude to other waves, but without the initial high-peak church shape. It appears possible that in this case the wave “breaks” fractions of a second before it hits the breakwater. This would result in much lower initial impact strengths, which could be the main reason for tilting to occur. It is possible that due to the limitations of the camera used, it was not able to capture these events in detail. At this point it would be possible to venture that a bore-type wave would thus cause sliding only, while a breaking or non-breaking wave would cause both sliding and tilting. Another interesting find of the experiment was the difference in load exerted between types T4 and T5. Although the shapes of the waves were very similar and the authors expected higher pressures for type T4, these were not present. The authors believe that the two most crucial factors that affect the pressure of the solitary wave on the caisson are the depth of water in front of the caisson and the effect of the breaking wave (impulse pressures). Thus, for the cases were h is high or the wave breaks on the breakwater a high load is recorded, though for case T4 it is possible that none of these two effects are present. Limitations in the laboratory equipment prevented a more thorough investigation of this phenomenon. The present experiments showed how the water surface elevation in front of the caisson breakwater has a critical effect on the stability against solitary wave attack. The experiments were conducted for two different water profiles (h, as shown on table 1). Any experiments carried out for h< 10 cm resulted in the solitary wave becoming a bore that exerted very little pressure on the caisson. As the objective of the present paper was to attempt to analyse the failure of caissons under tsunami attack further experiments on bores were not performed. On the other hand, the caisson’s vulnerability appeared to increase generally with an increase in h, and one of the highest recorded pressures at the back of the caisson were generally found at the highest ranges of h. Some trials were also conducted for h>20 cm, but these resulted in the caisson being washed away. Thus, the most dangerous type of wave highlighted in the experiments is the one that overtops the breakwater, as it can overturn it and wash it away completely. The range of application of the model presented in the previous section is thus relatively limited. More specifically, the deformations against a bore that occurs in relatively higher h were not investigated, as this
wave could not be reproduced under the laboratory conditions available. Although it would be expected that this type of wave would still not produce a church-roof shape initial impact, it would nevertheless produce higher forces (possibly mainly hydrostatic) on the breakwater, and as such could potentially cause the caisson to move. Also, for waves that do not produce a high-impact the model is able to reproduce the vertical deformation (none) but fails to give an upper bound limit for the sliding. Hence it could be concluded that the model is only valid for non-breaking or breaking waves solitary waves that act on the caisson, for generally the range of Conditions detailed in Table. 1. This is one a limitation of the model described in this paper. Another limitation of the present experiments is the limited scale (1:100) on which they were carried out. Unfortunately due to laboratory limitations it was not possible to carry out these experiments on a bigger scale, and it is clear that scale effects could somewhat confound the application of the method shown in this paper into real life design. The type of scaling that should be used is also not clear, as PROVERBS suggests that the “church-roof” impact part of a breaking wave should be scaled using Cauchy scaling and the non-breaking using Froude scaling. However, the results of PROVERBS apply to wind-waves and the results shown on the present paper relate to solitary waves. It is not clear if the impact pressure part of a breaking solitary wave should be scaled using the Cauchy relationship or not. Some future analysis of this is necessary before any conclusion can be made. Future work should also focus on clarifying the effect of solitary wave overtopping of caissons and also on determining the reason why sometimes the caisson only slides without tilting. To do so it is recommended that a high-speed camera is used, and that the experiments are carried out at a higher scale. The limit at which the caisson is washed away should also be established, although a method should be put in place to avoid the laboratory apparatus (or indeed the wave tank itself) from suffering damage.
CONCLUSIONS The present paper outlined a method that is able to provide engineers with an approximate idea of the movements that can be expected of a caisson breakwater that is subjected to solitary wave attack. By adapting the methodology of Esteban et al. (2007) an idea of the vertical displacement at the back of the caisson can be obtained, and by assuming that these displacements are proportional to the sliding movement then an upper bound limit of the sliding displacement can also be obtained. The methodology proposed, however, does not appear to be valid for the case of wave just after breaking, which would cause only sliding and not tilting of the caisson, or for overtopping waves (that appear likely to wash away the caisson). Waves that become bores long before reaching the breakwater subject it to comparatively much lower forces, and as such are not dangerous for the caisson provided that the depth of water in front of it is low. Hence, the model is limited in its application, and more exhaustive tests should be carried out to ascertain its validity and to check it against a more exhaustive selection of solitary wave types. Nevertheless, at present no other model is able to calculate these displacements, and thus it is valuable to carry out a risk assessment of a breakwater against a type of solitary wave attack similar to the ones shown.
ACKNOWLEDGEMENTS The author's would like to thank the Japanese Society for the Promotion of Science (JSPS) for the grants without which this research could not have been possible.
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