Analysis of shore line protection works in tsunami hit areas of east coast of India.

Babu, G.L. Sivakumar ; Srivastava, Amit

Evaluation and design of shore protection works in the case of tsunamis assumes considerable importance in view of the impact it had in the recent tsunami of 26th December 2004 in India and other countries in Asia. The fact that there are no proper guidelines have made in the matters worse and resulted in the magnitude of damage that occurred. Survey of the damages indicated that the scour as a result of high velocities is one of the prime reasons for damages in the case of simple structures. It is revealed that sea walls in some cases have been helpful to minimize the damages. The objective of this paper is to suggest that design of shore line protection systems using expected wave heights that get generated and use of flexible systems such as geocells is likely to give a better protection. The protection systems can be designed to withstand the wave forces that corresponding to different probabilities of incidence. A design approach of geocells protection system is suggested and illustrated with reference to the data of wave heights in the east coast of India.

INTRODUCTION

The terminal effects of tsunami are observed in terms of damage to coastal areas including structural damages, flooding, scour, and deposition of both sediments and floating debris. Due to lack of awareness and the proper implementation of protective measures, the recent tsunami on 26th December 2004 caused enormous damage to the economic and social life of the people in India and other countries of Indian Ocean [BAPPENAS, (2005)]. It has also prompted various researchers and practitioners in the world to provide suitable protective measures and design guidelines for the protection of seashore area from such events in future. In the present study, the authors have proposed the use of flexible structure like reinforced earth retaining structure using geocells that will be able to meet all the design requirements in terms of its stability and strength to resist the static and the dynamic loads as well as wave forces from the sea water.

DESIGN REQUIREMENTS

Unlike wind generated waves [figure (1)], tsunamis are generated due to underwater displacement of tectonic plates, volcanic eruption or landslide and travel unnoticed across the open sea with amplitude of only few centimeters and a velocity as high as 800 km/hr. However, as they approach sea shore, they gradually build up and in areas where the topography of the seabed is especially suited they will reach heights of 10+ meters with a speed of 10 to 80 km/hr.

[FIGURE 1 OMITTED]

As tsunami propagates shoreward, large turbulent bores rush inland and cause significant damage to the coastal area. In general, the problems related to tsunami waves are studied in terms of its development, shape and propagation characteristics, run up at the shore [Whitman (1958), Keller et al. (1960), Yeh et al. (1989)] and its interaction with the structures that are constructed near the shore or that are built as barrier [Ramsden and Raichlen (1990), Ramsden (1996)]. In the present study, only the last part i.e., the tsunami-structure interaction is studied in terms of estimation of hydrodynamic forces on the structure built as a barrier and the design and safety of proposed geocells structure is studied considering the effect of dead load, live load, earthquake load in addition to the hydrodynamic effect of the water wave generated due to tsunami.

CHARACTERISTICS OF TSUNAMI (WAVE VELOCITY, WAVE LENGTH AND WAVE PERIOD)

The tsunami waves are treated as long wave (shallow water waves) and the phase velocity (c) and group velocity ([c.sub.g]) are dependent on depth of sea floor (h) which is obtained using the Eq. (1).

c = [c.sub.g] [approximately equal to] [square root of gh](1)

The estimation of design wave height and wave period need the statistical analysis of the past records. The significant wave height (H) is defined as the average height of the highest one-third of the waves in a wave train. In the similar way, [H.sub.10] and [H.sub.1] can be defined as the average of the 10 % and 1% of the highest waves in a wave train respectively. Assuming a Rayleigh distribution for the wave heights in a wave train, the values of [H.sub.10] and [H.sub.1] will be approximately 1.27 H and 1.67 H.

The different wave periods are defined as the period of the peak energy density of the spectrum ([T.sub.p]), average wave period ([T.sub.z]) and significant wave period ([T.sub.s]). In the design, an appropriate choice of design wave height (H) and wave period (T) depends on the designer choice or the recommendations given by the codes or design manuals. For the known value of wave period (T) and depth of sea floor below the SWL (h), the estimation of wave length ([lambda]) can be made using the Eq. (2) given by Eckart (1952).

[lambda] = [g][T.sup.2]/2[pi] [square root of (4[[pi].sup.2]h/[T.sup.2]g)] (2)

DESIGN OF VERTICAL BARRIER

The Height ([H.sub.s]) of the structure

The total height of the structure above the still sea water level, as shown in Figure (2), is the sum of design wave height (H) plus extra allowance given for the wave run up, anticipated settlement of the structure and additional freeboard to avoid overtopping.

[FIGURE 2 OMITTED]

The height of wave run up (R) on the vertical wall can be estimated using Eq. (3).

R g/[c.sup.2] = 1.467 [(H/h).sup.-0.0504](3)

Estimation of wave force

In the literature analytical, experimental and numerical solutions (using finite difference codes) are available for estimating the hydrodynamic force on the wall due to tsunami waves (Cross 1967, Wiegel 1970, Ramsden and Raichlen 1990, Ramsden 1996, Hamzah 2000). Ramsden (1996) gave the empirical relationships for finding the hydrodynamic Force (F) and moment (M) on the vertical wall type barrier.

F/[F.sub.1] = 1.325 + 0.325 (H/h) + 1/58.5 [(H/h).sup.2] + 1/7160 [(H/h).sup.3] (4)

[F.sub.1] = 1/2 [gamma] b[(2H + [h.sub.w]).sup.2] (5)

M/[M.sub.t] = 1.923 + 0.454 (H/h) + 1/8.21 + [(H/h).sup.2] + 1/808 [(H/h).sup.3] (6)

[M.sub.t] = 1/6[gamma] b[(2H + [h.sub.w]).sup.3] (7)

The values of F1 and M1 are calculated assuming hydrostatic distribution for value of the wave run up height (R) equal to two times the wave height (H). The table (1) shows the calculation for the wave length ([lambda]), run up (R) and forces.

For the design of vertical reinforced soil wall under static and dynamic conditions, the procedure given in IS: 1893-1984 is followed. As shown in table (2), the external stability of the wall is checked against sliding, overturning and bearing failure both under static and dynamic conditions. Based on the analysis, the proposed base width is 15.0 m. The internal stability of the wall is checked against tension failure and pull out failure. Table (3) and (4) shows the calculations for tension failure under static and dynamic conditions respectively. From the pull out failure criterion, the maximum tension ([T.sub.i]) in the reinforcement is obtained as 20.5 kN and 24.52 kN under static and dynamic conditions respectively. The results of the analysis shows that the wall is safe and stable (internally and externally) for the forces coming on it from the backfill and surcharge load.

TOE PROTECTION

The toe of the structure should be protected from the scouring and undercutting due to passage of waves in order to make the structure stable. Figure (3) shows the arrangement for the toe protection. The total weight of the toe stone can be calculated using the following Eq. (16) given by Brebner and Donnelly (1962).

[FIGURE 3 OMITTED]

W = [gamma] [sub.t][H.sup.3]/[N.sup.3.sub.s] [([S.sub.t] - 1).sup.3] (8)

Where Ns is the minimum design stability number obtained from the curve provided in figure (5). [[gamma].sub.t] and [S.sub.t] are the unit weight and specific gravity of the stone material. H is the design wave height taken between [H.sub.1] and [H.sub.10]. Using friction circle method, the passive resistance of the backfill material is obtained as 1354.21 kN which is approximately 2.0 times more than the expected hydrodynamic force due to tsunami waves.

CONCLUDING REMARKS

In the present study, a vertical reinforced retaining wall using geocells is proposed for protecting the sea shore area in the event like tsunami. In the analysis and design, the discussions are restricted to geotechnical and hydrological aspects only. The procedures are given to find the hydrodynamic force expected to act on the structure and to check the external stability of the structure from different modes of failure. The advantage of using reinforced earth retaining wall can be said in terms of the economy and the flexibility of the structure. Being flexible, it has the capability of absorbing some part of kinetic energy of the water waves coming on it but the quantification of the same could be an active area of research in this field. In addition, the use of numerical tools and model testing will give extra inputs in studying the behavior of structure. In addition to these engineering barriers, development of effective tsunami warning system and general awareness program conducted by the local government will definitely help in saving the life of people living in the coastal region.

REFERENCES

BAPPENAS (2005). Indonesia: Preliminary damage and loss assessment, the December 26 2004 natural disaster. A technical report prepared by BAPPENAS and the international donor community.

Brebner, A., and Donnelly, P. (1962). "Laboratory study of rubble foundations for vertical breakwaters," Engineer Report No. 23, Queen's University at Kingston, Ontario.

Cross, R. H. (1967). "Tsunami surge forces", Journal of waterways and harbor division ASCE, vol. 93, No. 4, 201-231.

Cumberbatch, E. (1960). "The impact of a water wedge on a wall", Journal of fluid mechanics, Vol. 7, No. 3, 353-373.

Eskart, C. (1952). "The propagation of gravity waves from deep to shallow water", Natl. bur. Standards, Circular 521, Washington, DC, 165-173.

Hamzah, M.A., Mase, H., and Takayama, T. (2000). "Simulation and experiment of hydrodynamic pressure on a tsunami barrier", Coast. Engrg., 1501-1507.

Hoyt, J. W. and Sellin, R. H. (1989). "Hydraulic jumps as a 'mixing layers'", Journal of hydraulic engineering division, ASCE, Vol. 115, No. 12, 1607-1614.

IS 1893 : 1984. "Criteria for earthquake resistant design of structures", Bureau of Indian standards.

Kamel, A.M. (1970). "Laboratory study for design of tsunami barrier", J. Waterway. Horbor and Coastal Engrg. Division, Vol. 96, No. WW4, 767-779.

Keller, H. B., Levine, D. A. and Whitham, G. B. (1960). "Motion of a bore over a sloping beach",. Journal of fluid mechanics, Vol. 7, No. 2, 302-316.

Ramsden, J. D. (1996). "Forces on a vertical wall due to long waves, bores, and dry-bed surges", Journal of waterway, port, coastal, and ocean engineering, ASCE, Vol. 122, No. 3, 134-141

Ramsden, J. D. and Raichlen, F. (1990). "Forces on vertical wall caused by incident bores". Journal of waterway, port, coastal, and ocean engineering, ASCE, Vol. 116, No. 5, 592-613

Shen, M.C. and Meyer, R.E. (1963). "Climb of a bore on a beach Part 3: Run-up". Journal of fluid mechanics, Vol. 16, No. 1, 113-125.

Titov, V. V. and Synolakis, C. E. (1995). "Modeling of breaking and nonbreaking long-wave evolution and runup using VTCS-2", Journal of waterway, port, coastal, and ocean engineering, ASCE, Vol .121, No.6, 308-316.

Whitham, G.B. (1958). "On the propagation of shock waves through regions of non-uniform area of flow", Journal of fluid mechanics, Vol. 4, No. 4, 337-360.

Yeh, H.H., Ghazali, A. and Marton, I. (1989). "Experimental study of bore runup". Journal of fluid mechanics, Vol. 206, 563-578.

G. L. SIVAKUMAR BABU

Dept. of civil Engg., IISc, Bangalore, 560012, India

AMIT SRIVASTAVA

Dept. of civil Engg., IISc, Bangalore, 560012, India

Table 1. Estimation of wave run up and forces on the wall

Depth of sea water at the 1.50 m
wall ([h.sub.w])

Wave height (H) 3.50 m

Time period (T) 1000.00 sec

Celerity (C) 3.84 m/sec (13.8 km/hr)

Wave length ([gamma]) 3836.01 wave length of tsunami
 = 3.8 km

Run up on the wall ([lambda]) 2.12 m

Free board 2.00 m

Total height of the 9.12 height of structure 9.15 m
structure ([H.sub.s])

unit weight of water 9.79 kN/[m.sup.3]
([[gamma].sub.w])

Unit weight of the reinforced 22.00 kN/[m.sup.3]
soil ([gamma].sub.s])

slope (1: m) 20.00

Estimation of hydrostatic force (F)

Estimation of hydrostatic 353.56 kN
force ([F.sub.1])

H/h 1.47

F/[F.sub.1] 1.87

Hydrodvnamic force on the 662.54 kN
structure

Estimation of Moment (M) on the wall

Estimation of Moment [M.sub.t] 1001.74 KN-m

M/[M.sub.t] (using equation 11) 2.86

Moment M 2865.52 KN-m

Table 2. External stability analysis of the wall uder static and
dynamic loading

Stability Analysis of the reinforced soil wall

Soil properties for wall fill ([c.sub.1] = 0, [pi][N.sub.1] = 30,
[[pi].sub.1] = 18 kN/m3, [[pi].sub.1] = 20,
[pi][N.sub.s1] = 22 kN/m3 and [[pi].sub.b1] = 12 kN/m3)

Soil properties for wall fill ([c.sub.2] = 0,[pi][N.sub.2] = 27,
[[pi].sub.2] = 17 kN/m3, [[pi].sub.2] = 18,
[pi][N.sub.s2] = 20 kN/m3 and [[pi].sub.b2] = 10 kN/m3)

Surchagre load on the wall = 10 kN/m2

External stability Analysis

The coefficient of active earth pressure (Ka) in static case above
the water table = 0.326

The coefficient of active earth pressure (K'a) in static case below
the water table = 0.349

The total static earth pressure (PT) = 438.73 kN/ m width of wall
The total Moment of static pressure about the base (MT) = 3905.86 kN-m

Dynamic Increment

The horizontal ([pi]h) and vertical seismic coefficient ([pi]v)= 0.08
and 0.04 respectively
The coefficient of active earth pressure for the soil above the water
level in dynamic case = 0.404
The value of lateral dynamic increment in active case
(Pa[pi]i)= 96.96 kN/m width of the wall
The value of additional dynamic increment due to uniform surcharge
(Paqi) = 13.94 kN/ m width of the wall
The moment of dynamic increment about the base of the wall
(Ma[pi]i) in active case = 628.62 kN-m
The moment of dynamic increment about the base of the wall
(Maqi) in active case due to surcharge q=115.05 kN-m
Assuming the base width of the wall = L
The weight of the wall (Ww) = 235.8 L
The effective weight of the wall (W'w) = 190.8 L
The moment of weight of wall about toe (Mw) = 117.9 [L.sup.2]
The surcharge force on the wall (Q) = 10 L
The moment of surcharge force about toe (Mq) = 5 [L.sup.2]

Seismic force on the weight of the wall

In horizontal direction = 18.86 L
In vertical direction = 9.43 L
The moment of seismic forces acting on the weight of the wall
(Msw) = 292.06 L [+ or -] 4.716 [L.sup.2]
Seismic forces acting on the wall due to surcharge load
Horizontal seismic force = 0.8 L
Vertical seismic force = 0.4 L
The moment of seismic forces due to the surcharge acting on the
wall about toe (Msq) = 9.68L [+ or -] 0.2 [L.sup.[pi]]
The Factor of safety against sliding = 2.0
Static condition: The length L is obtained as 13.44 m
Dynamic condition: The length L is obtained as 14.87 m
Factor of safety against overturning = 2.0
Static condition: The length L is obtained as 9.15 m
Dynamic condition: The length L is obtained as 11.8 m

From the above analysis, the base width of the wall
(L) is provided as 15 m

Check for tilting/bearing failure
Static condition: qmax = 241.00 kpa and qmin = 160.45 kPa
Dynamic condition: qmax = 357.03 kPa and qmin = 340.96 kPa

Table 3. Checking the internal stability ofthe wall against tension
failure (Static condition)

Tension Failure (Static condition)

[h.sub.i] [M.sub.1] [[sigma].sub.vi] Ti [M.sub.a[gamma]]

0.50 9.88 19.09 2.86
1.00 39.96 28.38 4.33
1.50 90.96 37.87 5.87
2.00 163.55 47.57 7.49
2.50 258.44 57.38 9.20
3.00 376.31 67.61 10.99
3.50 517.86 77.97 12.87
3.00 683.79 88.56 14.83
4.50 874.76 99.40 16.90
5.00 1091.50 110.48 19.06
5.50 1334.69 121.81 21.32
6.00 1605.02 133.41 23.68
6.50 1903.19 145.27 26.15
7.00 2229.89 157.41 28.73
7.50 2585.81 169.82 31.42
9.00 473.81
8.50 571.85
9.00 684.72
9.50 913.30
10.00 959.45
10.50 1121.06
11.00 1301.99
11.50 1502.11
12.00 1722.30

Tension Failure (Static condition)

[h.sub.i] [M.sub.aq] [M.sub.2] [[sigma].sub.vi] [T.sub.i]

0.50
1.00
1.50
2.00
2.50
3.00
3.50
3.00
4.50
5.00
5.50
6.00
6.50
7.00
7.50
9.00 17.99 491.80 158.72 29.76
8.50 31.76 603.61 168.79 32.07
9.00 46.41 731.13 179.02 34.46
9.50 61.92 975.22 189.40 36.93
10.00 78.31 1030.77 199.95 39.49
10.50 95.59 1216.64 210.68 42.14
11.00 113.71 1415.70 221.59 44.87
11.50 133.72 1634.83 232.69 47.70
12.00 152.60 1874.90 244.00 50.63

Table 4. Checking the internal stability of the wall against tension
failure (Dynamic condition)

Tension Failure (seismic condition)

[h.sub.i] [M.sub.3] [M.sub.Tni] [M.sub.Tni]

0.50 0.08 0.20 24.65
1.00 1.33 0.78 80.07
1.50 6.71 1.76 169.93
2.00 21.22 3.12 299.89
2.50 51.80 4.88 477.61
3.00 107.41 7.02 712.73
3.50 198.98 9.56 1016.89
4.00 339.46 12.48 1403.71
4.50 543.74 15.80 1888.80
5.00 828.75 19.50 2489.75
5.50 1213.37 23.60 3226.16
6.00 1718.50 28.08 4119.60
6.50 2366.99 32.96 5193.64
7.00 3183.73 38.22 6473.84
7.50 4195.55 43.88 7987.73
8.00
8.50
9.00
9.50
10.00
10.50
11.00
11.50
12.00

[h.sub.i] [[sigma].sub.vi+] [[sigma].sub.vi-] [T.sub.i+]

0.50 20.76 17.72 3.11
1.00 31.01 26.53 4.73
1.50 41.59 35.67 6.45
2.00 52.56 45.20 8.28
2.50 63.99 55.19 10.24
3.00 75.96 65.72 12.34
3.50 88.60 76.92 14.62
4.00 102.04 88.92 17.09
4.50 116.41 101.85 19.79
5.00 131.90 115.90 22.75
5.50 148.69 131.25 26.02
6.00 166.99 148.11 29.64
6.50 187.02 166.70 33.66
7.00 209.03 187.27 38.15
7.50 233.28 210.08 43.16
8.00
8.50
9.00
9.50
10.00
10.50
11.00
11.50
12.00

 [h.sub.i]
[h.sub.i] [T.sub.i-] (H-[H.sub.w]) [M.sub.5] [M.sub.6]

0.50 2.66
1.00 4.05
1.50 5.53
2.00 7.12
2.50 8.83
3.00 10.68
3.50 12.69
4.00 14.89
4.50 17.31
5.00 19.99
5.50 22.97
6.00 26.29
6.50 30.01
7.00 34.18
7.50 38.87
8.00 0.40 171.97 49.92
8.50 0.90 229.68 56.35
9.00 1.40 342.13 63.15
9.50 1.90 540.86 70.33
10.00 2.40 859.79 77.88
10.50 2.90 1335.17 85.79
11.00 3.40 2005.60 94.06
11.50 3.90 2911.97 102.69
12.00 4.40 4097.49 111.68

[h.sub.i] [T.sub.Tni] [[sigma].sub.vi+] [[sigma].sub.vi-]

0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
6.50
7.00
7.50
8.00 714.68 152.81 152.11
8.50 890.64 165.94 164.36
9.00 1137.41 179.75 177.29
9.50 1487.41 194.55 191.21
10.00 1975.43 210.68 206.45
10.50 2638.59 228.48 223.38
11.00 3516.35 248.35 242.35
11.50 4650.49 270.68 270.68
12.00 6085.08 295.89 295.89

[h.sub.i] [T.sub.i+] [T.sub.i-]

0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
6.50
7.00
7.50
8.00 28.65 28.52
8.50 31.53 31.23
9.00 34.60 34.13
9.50 37.94 37.29
10.00 41.61 40.77
10.50 45.70 44.68
11.00 50.29 49.08
11.50 55.49 54.08
12.00 61.40 59.79