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Experimental study on tsunami wave load acting on storage tank in coastal area
Journal of Loss Prevention in the Process Industries xxx (2016) 1e8
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Journal of Loss Prevention in the Process Industries journal homepage: www.elsevier.com/locate/jlp
Experimental study on tsunami wave load acting on storage tank in coastal area Susumu Araki a, *, Wataru Kunimatsu a, Shinji Nishiyama b, Tomohiro Furuse c, Shin-ichi Aoki a, Yasuo Kotake c a b c
Department of Civil Engineering, Osaka University, Japan West Japan Railway Company, Japan Toyo Construction Co., Ltd., Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 June 2016 Received in revised form 5 September 2016 Accepted 11 October 2016 Available online xxx
Damage to storage tanks in coastal area due to tsunamis can cause extensive fires. In order to prevent damage to storage tanks, tsunami wave loads acting on a storage tank have to be investigated. This study aims at investigating the features of the tsunami wave loads and the method for estimating them. In a wave basin, the tsunami wave load acting on a storage tank is measured under both conditions of the presence of the surrounding tanks and of no surrounding tanks. Inundation depth and horizontal velocity on the storage site are also measured under the condition of no surrounding tanks, which are used for estimating the tsunami wave load. The vertical component of the tsunami wave load is estimated by buoyancy based on the static pressure calculated from the inundation depth. The horizontal component of the tsunami wave load is estimated by Morison equation. The analysis shows that Morison equation estimates the measured impulsive force at the beginning of the inundation. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Tsunami Wave load Tank Inundation depth Velocity
1. Introduction Damage to storage tanks in large industrial complexes can lead to a spill of gas or oil, which is one of the main causes of extensive fires. Fires in large industrial complexes can last long and spread out surrounding areas because a large amount of gas and oil is stored. A massive tsunami struck the northeastern coast of Japan in 2011. The tsunami caused serious damage to large industrial complexes facing the sea. In several industrial complexes, there were extensive fires. A huge tsunami generated at Nankai trough located south of Japan is predicted to strike Japan in the near future. That means that the Nankai trough tsunami will strike large industrial complexes located along coastlines. Therefore, we need to take countermeasures against tsunami striking in large industrial complexes. In order to prevent damage to storage tanks in large industrial complexes, tsunami wave loads acting on them have to be investigated and estimated. Tsunami wave loads acting on structures have been conducted by many researchers.
* Corresponding author. E-mail address: [email protected] (S. Araki).
Cross (1967) investigated the tsunami impact forces acting on vertical walls. Ramsden and Raichlen (1990) measured the fluid force and the pressure acting on vertical walls due to bore. Recently, tsunami wave load acting on three dimensional structures has been conducted. Asakura et al. (2002) measured the fluid force acting on structures on land by tsunami overflowing into the land. The Federal Emergency Management Agency FEMA (2008) indicated a procedure for estimating tsunami wave load. Arnason et al. (2009) measured the tsunami wave load acting on vertical columns and the water particle velocity around the columns in detail. Fire and Disaster Management Agency of Japan FDMA (2009) proposed an equation for estimating tsunami wave load acting on a storage tank. Fujima et al. (2009) measured a pressure distribution on a model building on land due to tsunami inundation flow. Nouri et al. (2010) measured the fluid load and pressure due to bore acting on both cylindrical and square structures placed on a dry bed. Arimitsu et al. (2012) measured tsunami wave load acting on vertical columns and proposed an equation for estimating the tsunami wave load. Wei et al. (2015) computed tsunami bore load acting on bridge piers using SPH. Shafiei et al. (2016) measured the tsunami wave load and pressure acting on a square prism structure. However, few studies have been conducted in which tsunami wave load acting on cylindrical storage tanks were investigated. In addition, the
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Please cite this article in press as: Araki, S., et al., Experimental study on tsunami wave load acting on storage tank in coastal area, Journal of Loss Prevention in the Process Industries (2016), http://dx.doi.org/10.1016/j.jlp.2016.10.004
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influence of the presence of surrounding storage tanks on tsunami wave load acting on a tank has not been investigated. In this study, tsunami wave loads acting on model storage tanks were measured under both conditions of the presence of the surrounding storage tanks and of no surrounding tanks. The target storage tank is a relatively smaller tank whose volume is less than 2000 kl. The reason for it is that a large number of storage tanks with the volume of less than 2000 kl are placed in coastal zones of Osaka Bay, Japan, which is one of the areas that the Nankai trough tsunami will strike. The experiment was conducted in a wave basin, in which horizontally two-dimensional fluid motion is generated. From the measured tsunami wave load, the features and the estimation of the tsunami wave load acting on the storage tanks were discussed. 2. Hydraulic experiment 2.1. Experimental setup The hydraulic experiment was conducted in a wave basin at Technical Research Institute, Naruo, Toyo Construction Co., Ltd. The wave basin is 30 m long, 19 m wide and 1.5 m deep. Tsunami waves like solitary waves were generated in the wave basin by piston type wave maker which has the maximum stroke of 1.5 m. A model harbor was constructed in the wave basin shown in Fig. 1. A model storage site on which model cylindrical storage tanks were placed was located in the model harbor. The blue rectangle in the figure is the storage site, which is 1.8 m long and 2.9 m wide. Yellow slender structures in the figure are breakwaters. In the model storage site, 12 cylindrical storage tanks can be placed in total. Tsunami waves were obliquely incident on the storage site. The model cylindrical storage tanks were made of acrylic plastic and were 15 cm in diameter and 10 cm in height. Fig. 2 shows a plan view of the storage site. The cylindrical storage tanks are numbered as shown in the figure (1eF, 1eM, 1eB and so on). Fig. 3 shows a photograph of the model cylindrical storage tanks placed on the model storage site. The storage site was surrounded by walls against oil spill. The walls were 1.0 cm high. The model scale was assumed to be 1:100. The diameter and height of the cylindrical storage tank used in this experiment are 15 m and 10 m in prototype, respectively. This is not a huge tank but a relatively smaller tank. However, this is our target storage tank as mentioned before. The water surface elevation was measured offshore (in front of the wave maker). The inundation depth on the storage site was measured at each point where cylindrical storage tanks were placed by capacitance-type wave gauge. The horizontal water particle velocity 1.0 cm above the surface of the storage site was
Fig. 1. Wave basin and model harbor.
Fig. 2. Plan view of storage site.
measured at each point of cylindrical storage tanks by electromagnetic velocity meter installed on the surface of the storage site. The horizontal and vertical tsunami wave loads acting on the cylindrical storage tanks were measured by three-component force transducer installed under the surface of the storage site. Fig. 4 shows a rough sketch of the cross section of the force measuring device. There was a gap of 2 mm between the cylindrical storage tank and the surface of the storage site in order to measure the tsunami wave load. Therefore, the inundated tsunami also flowed under the cylindrical tanks. The water surface elevation, the inundation depth on the storage site, the horizontal water particle velocity and the tsunami wave load were recorded at the sampling rate of 1000 Hz. All the recorded data were analyzed without using any filter. 2.2. Procedure for measurement Two kinds of incident wave were generated in the wave basin. The one (Wave 1) is a wave like a solitary wave with the maximum rise in the water surface of 6.9 cm at the offshore measuring point. The other (Wave 2) is that of 9.7 cm at the offshore measuring point. Wave 1 has the maximum rise in the water surface which is equivalent to a typical tsunami height striking the southern coast of
Fig. 3. Cylindrical storage tanks placed in industrial complex.
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under the condition of Fr < 1.6. They suggested that the coefficient a of 3.0 gave the estimation on the safe side. FDMA (Fire and Disaster Management Agency of Japan) (2009) proposed equations for estimating the horizontal and vertical components of the maximum tsunami wave loads acting on a cylindrical storage tank. The equation is based on the static pressure of which spatial distribution around the cylindrical storage tank was taken into account. The equation is expressed as follows: For the horizontal component of the maximum tsunami wave load Fhmax
Fhmax ¼
Fig. 4. Cross section of force measuring device.
Japan once in hundreds of years. Wave 2 has the maximum rise in the water surface which is larger than Wave 1. In this experiment, a wave like a solitary wave was generated by piston type wave maker which has been already installed. However, the storage site was inundated for a long time as shown in figures later. First, the water surface elevation was measured at the points where the cylindrical storage tanks were placed under the condition of no storage tank on the storage site. Second, the horizontal water particle velocity was measured at the same points. Next, the horizontal and vertical tsunami wave loads acting on the storage tank were measured. However, no other storage tank than the tank for measuring the tsunami wave load was placed on the storage site. The tsunami wave load was measured for the cylindrical storage tanks of 1eM, 2eF, 2eB, 3eM, 4eF and 4eB shown as red circles in Fig. 2. Finally, the tsunami wave load acting on a cylindrical storage tank was measured under the condition that all the 12 storage tanks were placed on the storage site. The water surface elevation (and also the water particle velocity) at the points of the storage tank and the tsunami wave load acting on the storage tank were not measured simultaneously. Therefore, the water surface elevation (and the water particle velocity) was synchronized with the tsunami wave load by using the water surface elevation measured at the offshore measuring point. 3. Equation for estimating tsunami wave load Asakura et al. (2002) proposed an equation for estimating the maximum tsunami wave pressure acting on a vertical wall and a prism on land. The equation is based on the static pressure and is expressed as follows:
pmax ðzÞ ¼ rgðahmax zÞ
(1)
a ¼ 1:2Fr þ 1:0
(2)
where hmax is the maximum inundation depth at the structure measured under the condition that the structure is not placed, z is the vertical coordinate from the bed, Fr is Froude number, r is the fluid density and g is the gravitational acceleration. In the equations proposed by Asakura et al. (2002), Froude number Fr is defined as follows:
uhmax Fr ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi g hmax
(3)
where hmax is the maximum inundation depth under the condition that any structure is not placed, uhmax is the horizontal velocity at the moment when the inundation depth h reaches the maximum. Asakura et al. (2002) conducted their hydraulic experiment
Zp
1 2
rg½hhmax ðqÞ2 R cos q dq
(4)
p
3 X
hhmax ðqÞ ¼ ahmax
pm cos mq
(5)
m¼0
a¼
hs;hmax hmax
(6)
For the vertical component of the maximum tsunami wave load Fzmax
Zp Fzmax ¼ 2
rghzmax ðqÞR2 sin2 q dq
(7)
0
3 X
hzmax ðqÞ ¼ bhmax
qm cos mq
(8)
m¼0
b¼
hs;zmax hmax
(9)
where R is the radius of the cylindrical storage tank, q is the rotated coordinates along the arc of the cylinder, hmax is the maximum inundation depth at the structure measured under the condition that the structure is not placed, hs,hmax and hs, zmax are the maximum inundation depths just in front of the storage tank at the moment when the horizontal and vertical tsunami wave loads reach the maximum under the condition that the storage tank is placed, respectively, and pm and qm are constants; p0 ¼ 0.680, p1 ¼ 0.340, p2 ¼ 0.015 and p3 ¼ 0.035; q0 ¼ 0.720, q1 ¼ 0.308, q2 ¼ 0.014 and q3 ¼ 0.042. Fig. 5 shows the spatial distribution of the pressure taken into account in the equation. FDMA (2009) also proposed the equations for estimating the coefficients a and b as follows:
8 < 1:8 a ¼ 2:0Fr 0:8 : 1:0 8 < 1:2 b ¼ 0:5Fr þ 0:55 : 1:0
1:3 < Fr 0:9 < Fr < 1:3 Fr < 0:9 1:3 < Fr 0:9 < Fr < 1:3 Fr < 0:9
(10)
(11)
where Fr is Froude number. In the equation proposed by FDMA, Froude number Fr is defined as follows:
Please cite this article in press as: Araki, S., et al., Experimental study on tsunami wave load acting on storage tank in coastal area, Journal of Loss Prevention in the Process Industries (2016), http://dx.doi.org/10.1016/j.jlp.2016.10.004
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Fig. 5. Spatial distribution of pressure around cylindrical storage tank in equation proposed by FDMA (2009).
umax Fr ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi ghmax
(12)
where umax is the maximum horizontal velocity above the storage site and hmax is the maximum inundation depth. umax and hmax are not necessarily measured at the same moment. However, their experiment showed that there was not so much difference between the moments when umax was measured and when hmax was measured. Arimitsu et al. (2012) proposed an equation for estimating tsunami wave pressure acting on a vertical wall and a prism on land. The equation is composed of the term of the static pressure and the term of momentum of fluid. The equation is as follows:
pðz; tÞ ¼ rg½hs ðtÞ z þ rus ðtÞ2
(13)
where p(z, t) is the pressure distribution, z is the vertical coordinate from the surface of the storage site, t is time and hs(t) and us(t) is the inundation depth on the surface of the storage site and the horizontal water particle velocity just in front of the structure under the condition that the structure is placed, respectively. An equation for estimating fluid force as drag force or Morison equation (the sum of drag and inertia forces) are often used for estimating tsunami wave load acting on structures. Morison equation for the horizontal component is as follows:
1 vu Fh ¼ CD rujujA þ CM r V 2 vt
(14)
where CD and CM are the drag and inertia coefficients, u is the horizontal water particle velocity, A is the submerged area of the structure projected in the direction of the tsunami flow and V is the submerged volume of the structure.
4. Experimental result 4.1. Wave load without surrounding storage tanks Fig. 6 shows an example of the time series of the inundation depth h, the horizontal water particle velocity above the bed of the storage site u and the horizontal and vertical components of the tsunami wave load Fh and Fz without the surrounding storage tanks measured at 1eM under Wave 2. As mentioned before, the inundation depth h and the horizontal water particle velocity u were measured under the condition that the cylindrical storage tank was not placed at 1eM. In the figures, the origin of the horizontal axis “t ¼ 0 s” is the time when the water surface elevation at the offshore measuring point reached the peak.
Fig. 6. Time series of h, u, Fh and Fz without surrounding storage tanks at 1eM under Wave 2.
The inundation depth h rapidly rises and keeps the depth approximately more than 2.0 cm. The horizontal water particle velocity u sharply reaches the maximum of more than 100 cm/s at the beginning of the inundation. After the maximum, the velocity decreases and fluctuates at a small amplitude even when the inundation depth increases between t ¼ 20 s and 35 s. The horizontal component of the tsunami wave load Fh shows the impulsive load at the beginning of the inundation. After the impulsive load, the horizontal tsunami wave load Fh decreases. The variation is slightly large between t ¼ 20 s and 35 s when the inundation depth increases. The features of the variation in the horizontal component of the tsunami wave load is more similar to that in the water particle velocity u than that in the inundation depth h because the time series of the inundation depth does not have a sharp peak at the beginning. The vertical component of the tsunami wave load Fz has no sharp peak at the beginning of the inundation. The features of the variation in the vertical component of the tsunami wave load is quite similar to that in the inundation depth h. Fig. 7 shows another example of h, u and Fh and Fz without the surrounding storage tanks measured at 4eF under Wave 2. The features of them are similar to those measured at 1eM shown in Fig. 5. However, the time series of the inundation depth h has a sharp peak at the beginning of the inundation. Although the vertical component of the tsunami wave load Fz does not have a sharp peak at the beginning, the features of the rest of the variation in the vertical component of the tsunami wave load looks similar to that in the inundation depth.
Please cite this article in press as: Araki, S., et al., Experimental study on tsunami wave load acting on storage tank in coastal area, Journal of Loss Prevention in the Process Industries (2016), http://dx.doi.org/10.1016/j.jlp.2016.10.004
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without the surrounding storage tank measured at 1eM under Wave 2 shown in Fig. 6. The reason is that the water particle velocity caused by tsunami is smaller than those without storage tank due to sheltering effect of the presence of the surrounding storage tanks. On the other hands, the vertical component of the tsunami wave load Fz with the surrounding storage tank is slightly smaller than that without storage tank. As discussed later, buoyancy is predominant in the vertical component of the tsunami wave load. Although the water particle velocity is reduced by the presence of the surrounding storage tanks, the inundation depth is not reduced so much. Therefore, the vertical component of the tsunami wave load with the surrounding storage tanks is not reduced so much, compared with that without the surrounding storage tank. Fig. 9 shows the time series of Fh and Fz with the surrounding storage tanks measured at 4eF under Wave 2. The horizontal component of the tsunami wave load Fh with the surrounding storage tanks is smaller than that without the surrounding storage tank at 4eF under Wave 2 shown in Fig. 7 because of the sheltering effect. The vertical component of the tsunami wave load Fz with the surrounding storage tanks is slightly smaller than that without the surrounding storage tank due to the same reason as mentioned in Fig. 8. 5. Discussion 5.1. Comparison between wave loads with and without surrounding storage tanks
Fig. 7. Time series of h, u, Fh and Fz at 4eF without surrounding storage tanks under Wave 2.
4.2. Wave load with surrounding storage tanks Fig. 8 shows the time series of Fh and Fz with the surrounding storage tanks measured at 1eM under Wave 2. The horizontal component of the tsunami wave load Fh is smaller than that
Fig. 8. Time series of Fh and Fz at 1eM with surrounding storage tanks under Wave 2.
The maximum tsunami wave loads measured with the surrounding storage tanks are smaller than those measured without the surrounding storage tank. Figs. 10(a) and (b) show the comparisons between the maximum horizontal and vertical components of the tsunami wave loads with and without the surrounding storage tanks, respectively. The horizontal axis shows the position of the storage tanks. The blue and red circles show the maximum tsunami wave loads with and without the surrounding storage tanks, respectively. In most of the positions of the storage tanks, the maximum tsunami wave loads measured with the surrounding storage tanks are smaller than those measured without the surrounding storage tank. However, the tsunami wave loads measured with the surrounding storage tanks at 2eF and 3eM has the same magnitude as those without the surrounding storage tank. The presence of the surrounding storage tanks may cause the increase in the tsunami wave load under several conditions. In this
Fig. 9. Time series of Fh and Fz at 4-F with surrounding storage tanks under Wave 2.
Please cite this article in press as: Araki, S., et al., Experimental study on tsunami wave load acting on storage tank in coastal area, Journal of Loss Prevention in the Process Industries (2016), http://dx.doi.org/10.1016/j.jlp.2016.10.004
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Fig. 10. Comparison of maximum wave load under Wave 1.
experiment, the distance between the cylindrical storage tanks was relatively large. The influence of the surrounding storage tanks should be discussed together with the distance between the storage tanks. 5.2. Vertical component of tsunami wave load The estimation of the tsunami wave load acting on a storage tank is discussed under the condition of no surrounding storage tank because the inundation flow is complicated under the condition of the presence of the surrounding storage tanks. The features of the variation in the vertical tsunami wave load Fz is similar to that in the inundation depth. This suggests that the buoyancy calculated based on the static pressure has a great influence on the measured vertical tsunami wave load. Fig. 11 shows the correlation coefficient between the measured vertical component of the tsunami wave load Fz and the inundation depth h. The vertical and horizontal axes show the correlation coefficient and
Fig. 11. Correlation coefficient between measured vertical tsunami wave load and measured water surface elevation.
the position where the wave load was measured, respectively. The red and blue circles show the correlation coefficients for Wave 1 and Wave 2, respectively. In all the positions, the correlation coefficients are more than 0.90, which indicates a strong positive linear correlation between the vertical component of the tsunami wave load and the inundation depth. Fig. 12 shows the time series of the buoyancy estimated from the inundation depth which was measured under the condition that the storage tank was not placed. Figs. 12(a) and (b) show the time series at 1eM under Wave 2 and at 4eF under Wave 2, respectively. Although the buoyancy overestimates the measured vertical component of the tsunami wave load, the features of the variation in the calculated buoyancy is in good agreement with that in the measured tsunami wave load. The time series of the measured tsunami wave load does not have short period variations. It might result from the dynamic pressure acting on the bottom of the cylindrical storage tank or the difference between the inundation depths under the cylindrical storage tank was placed or not. The measured maximum vertical tsunami wave load was estimated by the equation proposed by FDMA (2009) (Eqs. (7)e(9), (11)), which is based on the static pressure. Fig. 13 shows the comparison between the maximum vertical wave loads estimated by FDMA equation and measured in the experiment. The vertical and horizontal axes show the maximum vertical wave load and the position where the wave load was measured, respectively. In the equation proposed by FDMA, the maximum vertical wave load was estimated by using the maximum value in the time series of Froude number, which corresponds to the viewpoint of FDMA. The figure shows that the equation proposed by FDMA (2009) approximately estimated the measured maximum vertical wave load acting on the cylindrical storage tank. However, the difference between the measured and the estimated wave loads is large under several conditions. The values of the constants in the equations need to be investigated further. 5.3. Horizontal component of tsunami wave load The features of the variation in the horizontal component of the tsunami wave load is more similar to that in the water particle velocity u than that in the inundation depth h. Therefore, the
Fig. 12. Estimation of vertical wave load by static pressure.
Please cite this article in press as: Araki, S., et al., Experimental study on tsunami wave load acting on storage tank in coastal area, Journal of Loss Prevention in the Process Industries (2016), http://dx.doi.org/10.1016/j.jlp.2016.10.004
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Fig. 15. Correlation coefficient between measured and estimated horizontal tsunami wave loads.
Fig. 13. Estimation of vertical maximum tsunami wave load by FDMA's equation.
horizontal component of the tsunami wave load is expected to be estimated by the equation proposed by Arimitsu et al. (2012) (Eq. (13)) and Morison equation (Eq. (14)). In the equation proposed by Arimitsu et al. (2012), hs (t) and us (t) are the inundation depth and the velocity measured or estimated under the condition that the structure is placed, respectively, which were not measured in the present experiment. Therefore, the horizontal component of the tsunami wave load was compared with only Morison equation.
Fig. 14. Estimation of horizontal wave load by Morison equation.
Figs. 14(a) and (b) show the time series of the horizontal tsunami wave loads estimated by Morison equation at 1eM under Wave 2 and at 4eF under Wave 2, respectively. The drag and inertia coefficients in Morison equation were set at CD ¼ 1.2 and CM ¼ 2.0, respectively. The measured impulsive force at the beginning of the inundation is estimated because Morison equation has a term including the velocity. The variation after the impulsive force at the beginning was also approximately estimated. Fig. 15 shows the correlation coefficient between the horizontal tsunami wave loads measured in the experiment and estimated by Morison equation. The vertical and horizontal axes show the correlation coefficient and the position where the wave load was measured. The correlation coefficient for Wave 2 is higher than that for Wave 1. The reason is that the static force as well as the drag and inertia forces may have an influence on the horizontal wave load. Since the horizontal velocity in Wave 1 is smaller than that in Wave 2, the static force has relatively more influence on the horizontal wave load. 6. Conclusions The horizontal and vertical components of the tsunami wave load acting on the cylindrical storage tanks were measured with and without the surrounding tanks. In most of the positions of the storage tanks, the maximum tsunami wave loads measured with the surrounding storage tanks were smaller than those measured without the surrounding storage tank. However, the presence of the surrounding storage tanks caused the increase in the tsunami wave load under several conditions. The measured tsunami wave load was estimated by several methods. In the measured vertical component of the tsunami wave load, the buoyancy was predominant. Therefore, the measured vertical tsunami wave load was approximately estimated by the buoyancy based on the static pressure calculated from the inundation depth. The maximum measured vertical tsunami wave load was also approximately estimated by the equation proposed by FDMA because the equation is based on the static pressure. The measured horizontal component of the tsunami wave load was compared with the wave load calculated by Morison equation. The correlation between the horizontal tsunami wave load measured in the experiment and estimated by Morison equation for Wave 2 was higher than that for Wave 1 which had a smaller wave height. Other component of wave force besides the drag and inertia forces in Wave 1 was maybe relatively larger than that in Wave 2 because the horizontal velocity in Wave 1 was smaller than that in Wave 2. In this study, the horizontal wave load was not compared with the estimation by Arimitsu equation because the inundation depth and the horizontal velocity on the storage site was not measured under the condition that the storage tank was placed. The discussion of the applicability of Arimitsu equation is a future task.
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References Arimitsu, T., Ooe, K., Kawasaki, K., 2012. Hydraulic experiment on evaluation method tsunami wave pressure using inundation depth and velocity in front of land structure. J. Jpn. Soc. Civ. Eng. Ser. B2 Coast. Eng. 68 (No. 2), 776e780 (in Japanese). Arnason, H., Petroff, C., Yeh, H., 2009. Tsunami bore impingement onto a vertical column. J. Disaster Res. 4 (No. 6), 391e403. Asakura, R., Iwase, K., Ikeya, T., Takao, M., Kaneto, T., Fujii, N., Ohmori, M., 2002. Tsunami wave force acting on land structures. In: Proceedings of International Conference on Coastal Engineering, No. 28, pp. 1191e1202. Cross, R.H., 1967. Tsunami surge forces. J. Waterw. Harb. Div. ASCE 93 (No. 4), 201e231. FDMA, 2009. The Report of Research and Examination Regarding the Countermeasures of Tsunami and Inundation for Facilities of Hazardous Material. Fire
and Disaster Management Agency of Japan (in Japanese). FEMA, 2008. Guidelines for Design of Structures for Vertical Evacuation from Tsunamis (FEMA P646). Fujima, K., Achmad, F., Shigihara, Y., Mizutani, N., 2009. Estimation of tsunami force acting on rectangular structures. J. Disaster Res. 4 (No. 6), 404e409. Nouri, Y., Nistor, I., Palermo, D., 2010. Experimental investigation of tsunami impact on free standing structures. Coast. Eng. J. 52 (No. 1), 43e70. Ramsden, J.D., Raichlen, F., 1990. Forces on vertical wall caused by incident bores. J. Waterw. Port Coast. Ocean Eng. ASCE 116 (No. 5), 592e613. Shafiei, S., Melville, B.W., Shamseldin, A.Y., 2016. Experimental investigation of tsunami bore impact force and pressure on a square prism. Coast. Eng. 110, 1e16. rault, A., Bilotta, G., Rustico, E., Yeh, H., 2015. SPH Wei, Z., Dalrymple, R.A., He modeling of dynamic impact of tsunami bore on bridge piers. Coast. Eng. 104, 26e42.
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Journal of Loss Prevention in the Process Industries journal homepage: www.elsevier.com/locate/jlp
Experimental study on tsunami wave load acting on storage tank in coastal area Susumu Araki a, *, Wataru Kunimatsu a, Shinji Nishiyama b, Tomohiro Furuse c, Shin-ichi Aoki a, Yasuo Kotake c a b c
Department of Civil Engineering, Osaka University, Japan West Japan Railway Company, Japan Toyo Construction Co., Ltd., Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 June 2016 Received in revised form 5 September 2016 Accepted 11 October 2016 Available online xxx
Damage to storage tanks in coastal area due to tsunamis can cause extensive fires. In order to prevent damage to storage tanks, tsunami wave loads acting on a storage tank have to be investigated. This study aims at investigating the features of the tsunami wave loads and the method for estimating them. In a wave basin, the tsunami wave load acting on a storage tank is measured under both conditions of the presence of the surrounding tanks and of no surrounding tanks. Inundation depth and horizontal velocity on the storage site are also measured under the condition of no surrounding tanks, which are used for estimating the tsunami wave load. The vertical component of the tsunami wave load is estimated by buoyancy based on the static pressure calculated from the inundation depth. The horizontal component of the tsunami wave load is estimated by Morison equation. The analysis shows that Morison equation estimates the measured impulsive force at the beginning of the inundation. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Tsunami Wave load Tank Inundation depth Velocity
1. Introduction Damage to storage tanks in large industrial complexes can lead to a spill of gas or oil, which is one of the main causes of extensive fires. Fires in large industrial complexes can last long and spread out surrounding areas because a large amount of gas and oil is stored. A massive tsunami struck the northeastern coast of Japan in 2011. The tsunami caused serious damage to large industrial complexes facing the sea. In several industrial complexes, there were extensive fires. A huge tsunami generated at Nankai trough located south of Japan is predicted to strike Japan in the near future. That means that the Nankai trough tsunami will strike large industrial complexes located along coastlines. Therefore, we need to take countermeasures against tsunami striking in large industrial complexes. In order to prevent damage to storage tanks in large industrial complexes, tsunami wave loads acting on them have to be investigated and estimated. Tsunami wave loads acting on structures have been conducted by many researchers.
* Corresponding author. E-mail address: [email protected] (S. Araki).
Cross (1967) investigated the tsunami impact forces acting on vertical walls. Ramsden and Raichlen (1990) measured the fluid force and the pressure acting on vertical walls due to bore. Recently, tsunami wave load acting on three dimensional structures has been conducted. Asakura et al. (2002) measured the fluid force acting on structures on land by tsunami overflowing into the land. The Federal Emergency Management Agency FEMA (2008) indicated a procedure for estimating tsunami wave load. Arnason et al. (2009) measured the tsunami wave load acting on vertical columns and the water particle velocity around the columns in detail. Fire and Disaster Management Agency of Japan FDMA (2009) proposed an equation for estimating tsunami wave load acting on a storage tank. Fujima et al. (2009) measured a pressure distribution on a model building on land due to tsunami inundation flow. Nouri et al. (2010) measured the fluid load and pressure due to bore acting on both cylindrical and square structures placed on a dry bed. Arimitsu et al. (2012) measured tsunami wave load acting on vertical columns and proposed an equation for estimating the tsunami wave load. Wei et al. (2015) computed tsunami bore load acting on bridge piers using SPH. Shafiei et al. (2016) measured the tsunami wave load and pressure acting on a square prism structure. However, few studies have been conducted in which tsunami wave load acting on cylindrical storage tanks were investigated. In addition, the
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Please cite this article in press as: Araki, S., et al., Experimental study on tsunami wave load acting on storage tank in coastal area, Journal of Loss Prevention in the Process Industries (2016), http://dx.doi.org/10.1016/j.jlp.2016.10.004
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influence of the presence of surrounding storage tanks on tsunami wave load acting on a tank has not been investigated. In this study, tsunami wave loads acting on model storage tanks were measured under both conditions of the presence of the surrounding storage tanks and of no surrounding tanks. The target storage tank is a relatively smaller tank whose volume is less than 2000 kl. The reason for it is that a large number of storage tanks with the volume of less than 2000 kl are placed in coastal zones of Osaka Bay, Japan, which is one of the areas that the Nankai trough tsunami will strike. The experiment was conducted in a wave basin, in which horizontally two-dimensional fluid motion is generated. From the measured tsunami wave load, the features and the estimation of the tsunami wave load acting on the storage tanks were discussed. 2. Hydraulic experiment 2.1. Experimental setup The hydraulic experiment was conducted in a wave basin at Technical Research Institute, Naruo, Toyo Construction Co., Ltd. The wave basin is 30 m long, 19 m wide and 1.5 m deep. Tsunami waves like solitary waves were generated in the wave basin by piston type wave maker which has the maximum stroke of 1.5 m. A model harbor was constructed in the wave basin shown in Fig. 1. A model storage site on which model cylindrical storage tanks were placed was located in the model harbor. The blue rectangle in the figure is the storage site, which is 1.8 m long and 2.9 m wide. Yellow slender structures in the figure are breakwaters. In the model storage site, 12 cylindrical storage tanks can be placed in total. Tsunami waves were obliquely incident on the storage site. The model cylindrical storage tanks were made of acrylic plastic and were 15 cm in diameter and 10 cm in height. Fig. 2 shows a plan view of the storage site. The cylindrical storage tanks are numbered as shown in the figure (1eF, 1eM, 1eB and so on). Fig. 3 shows a photograph of the model cylindrical storage tanks placed on the model storage site. The storage site was surrounded by walls against oil spill. The walls were 1.0 cm high. The model scale was assumed to be 1:100. The diameter and height of the cylindrical storage tank used in this experiment are 15 m and 10 m in prototype, respectively. This is not a huge tank but a relatively smaller tank. However, this is our target storage tank as mentioned before. The water surface elevation was measured offshore (in front of the wave maker). The inundation depth on the storage site was measured at each point where cylindrical storage tanks were placed by capacitance-type wave gauge. The horizontal water particle velocity 1.0 cm above the surface of the storage site was
Fig. 1. Wave basin and model harbor.
Fig. 2. Plan view of storage site.
measured at each point of cylindrical storage tanks by electromagnetic velocity meter installed on the surface of the storage site. The horizontal and vertical tsunami wave loads acting on the cylindrical storage tanks were measured by three-component force transducer installed under the surface of the storage site. Fig. 4 shows a rough sketch of the cross section of the force measuring device. There was a gap of 2 mm between the cylindrical storage tank and the surface of the storage site in order to measure the tsunami wave load. Therefore, the inundated tsunami also flowed under the cylindrical tanks. The water surface elevation, the inundation depth on the storage site, the horizontal water particle velocity and the tsunami wave load were recorded at the sampling rate of 1000 Hz. All the recorded data were analyzed without using any filter. 2.2. Procedure for measurement Two kinds of incident wave were generated in the wave basin. The one (Wave 1) is a wave like a solitary wave with the maximum rise in the water surface of 6.9 cm at the offshore measuring point. The other (Wave 2) is that of 9.7 cm at the offshore measuring point. Wave 1 has the maximum rise in the water surface which is equivalent to a typical tsunami height striking the southern coast of
Fig. 3. Cylindrical storage tanks placed in industrial complex.
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under the condition of Fr < 1.6. They suggested that the coefficient a of 3.0 gave the estimation on the safe side. FDMA (Fire and Disaster Management Agency of Japan) (2009) proposed equations for estimating the horizontal and vertical components of the maximum tsunami wave loads acting on a cylindrical storage tank. The equation is based on the static pressure of which spatial distribution around the cylindrical storage tank was taken into account. The equation is expressed as follows: For the horizontal component of the maximum tsunami wave load Fhmax
Fhmax ¼
Fig. 4. Cross section of force measuring device.
Japan once in hundreds of years. Wave 2 has the maximum rise in the water surface which is larger than Wave 1. In this experiment, a wave like a solitary wave was generated by piston type wave maker which has been already installed. However, the storage site was inundated for a long time as shown in figures later. First, the water surface elevation was measured at the points where the cylindrical storage tanks were placed under the condition of no storage tank on the storage site. Second, the horizontal water particle velocity was measured at the same points. Next, the horizontal and vertical tsunami wave loads acting on the storage tank were measured. However, no other storage tank than the tank for measuring the tsunami wave load was placed on the storage site. The tsunami wave load was measured for the cylindrical storage tanks of 1eM, 2eF, 2eB, 3eM, 4eF and 4eB shown as red circles in Fig. 2. Finally, the tsunami wave load acting on a cylindrical storage tank was measured under the condition that all the 12 storage tanks were placed on the storage site. The water surface elevation (and also the water particle velocity) at the points of the storage tank and the tsunami wave load acting on the storage tank were not measured simultaneously. Therefore, the water surface elevation (and the water particle velocity) was synchronized with the tsunami wave load by using the water surface elevation measured at the offshore measuring point. 3. Equation for estimating tsunami wave load Asakura et al. (2002) proposed an equation for estimating the maximum tsunami wave pressure acting on a vertical wall and a prism on land. The equation is based on the static pressure and is expressed as follows:
pmax ðzÞ ¼ rgðahmax zÞ
(1)
a ¼ 1:2Fr þ 1:0
(2)
where hmax is the maximum inundation depth at the structure measured under the condition that the structure is not placed, z is the vertical coordinate from the bed, Fr is Froude number, r is the fluid density and g is the gravitational acceleration. In the equations proposed by Asakura et al. (2002), Froude number Fr is defined as follows:
uhmax Fr ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi g hmax
(3)
where hmax is the maximum inundation depth under the condition that any structure is not placed, uhmax is the horizontal velocity at the moment when the inundation depth h reaches the maximum. Asakura et al. (2002) conducted their hydraulic experiment
Zp
1 2
rg½hhmax ðqÞ2 R cos q dq
(4)
p
3 X
hhmax ðqÞ ¼ ahmax
pm cos mq
(5)
m¼0
a¼
hs;hmax hmax
(6)
For the vertical component of the maximum tsunami wave load Fzmax
Zp Fzmax ¼ 2
rghzmax ðqÞR2 sin2 q dq
(7)
0
3 X
hzmax ðqÞ ¼ bhmax
qm cos mq
(8)
m¼0
b¼
hs;zmax hmax
(9)
where R is the radius of the cylindrical storage tank, q is the rotated coordinates along the arc of the cylinder, hmax is the maximum inundation depth at the structure measured under the condition that the structure is not placed, hs,hmax and hs, zmax are the maximum inundation depths just in front of the storage tank at the moment when the horizontal and vertical tsunami wave loads reach the maximum under the condition that the storage tank is placed, respectively, and pm and qm are constants; p0 ¼ 0.680, p1 ¼ 0.340, p2 ¼ 0.015 and p3 ¼ 0.035; q0 ¼ 0.720, q1 ¼ 0.308, q2 ¼ 0.014 and q3 ¼ 0.042. Fig. 5 shows the spatial distribution of the pressure taken into account in the equation. FDMA (2009) also proposed the equations for estimating the coefficients a and b as follows:
8 < 1:8 a ¼ 2:0Fr 0:8 : 1:0 8 < 1:2 b ¼ 0:5Fr þ 0:55 : 1:0
1:3 < Fr 0:9 < Fr < 1:3 Fr < 0:9 1:3 < Fr 0:9 < Fr < 1:3 Fr < 0:9
(10)
(11)
where Fr is Froude number. In the equation proposed by FDMA, Froude number Fr is defined as follows:
Please cite this article in press as: Araki, S., et al., Experimental study on tsunami wave load acting on storage tank in coastal area, Journal of Loss Prevention in the Process Industries (2016), http://dx.doi.org/10.1016/j.jlp.2016.10.004
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Fig. 5. Spatial distribution of pressure around cylindrical storage tank in equation proposed by FDMA (2009).
umax Fr ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi ghmax
(12)
where umax is the maximum horizontal velocity above the storage site and hmax is the maximum inundation depth. umax and hmax are not necessarily measured at the same moment. However, their experiment showed that there was not so much difference between the moments when umax was measured and when hmax was measured. Arimitsu et al. (2012) proposed an equation for estimating tsunami wave pressure acting on a vertical wall and a prism on land. The equation is composed of the term of the static pressure and the term of momentum of fluid. The equation is as follows:
pðz; tÞ ¼ rg½hs ðtÞ z þ rus ðtÞ2
(13)
where p(z, t) is the pressure distribution, z is the vertical coordinate from the surface of the storage site, t is time and hs(t) and us(t) is the inundation depth on the surface of the storage site and the horizontal water particle velocity just in front of the structure under the condition that the structure is placed, respectively. An equation for estimating fluid force as drag force or Morison equation (the sum of drag and inertia forces) are often used for estimating tsunami wave load acting on structures. Morison equation for the horizontal component is as follows:
1 vu Fh ¼ CD rujujA þ CM r V 2 vt
(14)
where CD and CM are the drag and inertia coefficients, u is the horizontal water particle velocity, A is the submerged area of the structure projected in the direction of the tsunami flow and V is the submerged volume of the structure.
4. Experimental result 4.1. Wave load without surrounding storage tanks Fig. 6 shows an example of the time series of the inundation depth h, the horizontal water particle velocity above the bed of the storage site u and the horizontal and vertical components of the tsunami wave load Fh and Fz without the surrounding storage tanks measured at 1eM under Wave 2. As mentioned before, the inundation depth h and the horizontal water particle velocity u were measured under the condition that the cylindrical storage tank was not placed at 1eM. In the figures, the origin of the horizontal axis “t ¼ 0 s” is the time when the water surface elevation at the offshore measuring point reached the peak.
Fig. 6. Time series of h, u, Fh and Fz without surrounding storage tanks at 1eM under Wave 2.
The inundation depth h rapidly rises and keeps the depth approximately more than 2.0 cm. The horizontal water particle velocity u sharply reaches the maximum of more than 100 cm/s at the beginning of the inundation. After the maximum, the velocity decreases and fluctuates at a small amplitude even when the inundation depth increases between t ¼ 20 s and 35 s. The horizontal component of the tsunami wave load Fh shows the impulsive load at the beginning of the inundation. After the impulsive load, the horizontal tsunami wave load Fh decreases. The variation is slightly large between t ¼ 20 s and 35 s when the inundation depth increases. The features of the variation in the horizontal component of the tsunami wave load is more similar to that in the water particle velocity u than that in the inundation depth h because the time series of the inundation depth does not have a sharp peak at the beginning. The vertical component of the tsunami wave load Fz has no sharp peak at the beginning of the inundation. The features of the variation in the vertical component of the tsunami wave load is quite similar to that in the inundation depth h. Fig. 7 shows another example of h, u and Fh and Fz without the surrounding storage tanks measured at 4eF under Wave 2. The features of them are similar to those measured at 1eM shown in Fig. 5. However, the time series of the inundation depth h has a sharp peak at the beginning of the inundation. Although the vertical component of the tsunami wave load Fz does not have a sharp peak at the beginning, the features of the rest of the variation in the vertical component of the tsunami wave load looks similar to that in the inundation depth.
Please cite this article in press as: Araki, S., et al., Experimental study on tsunami wave load acting on storage tank in coastal area, Journal of Loss Prevention in the Process Industries (2016), http://dx.doi.org/10.1016/j.jlp.2016.10.004
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without the surrounding storage tank measured at 1eM under Wave 2 shown in Fig. 6. The reason is that the water particle velocity caused by tsunami is smaller than those without storage tank due to sheltering effect of the presence of the surrounding storage tanks. On the other hands, the vertical component of the tsunami wave load Fz with the surrounding storage tank is slightly smaller than that without storage tank. As discussed later, buoyancy is predominant in the vertical component of the tsunami wave load. Although the water particle velocity is reduced by the presence of the surrounding storage tanks, the inundation depth is not reduced so much. Therefore, the vertical component of the tsunami wave load with the surrounding storage tanks is not reduced so much, compared with that without the surrounding storage tank. Fig. 9 shows the time series of Fh and Fz with the surrounding storage tanks measured at 4eF under Wave 2. The horizontal component of the tsunami wave load Fh with the surrounding storage tanks is smaller than that without the surrounding storage tank at 4eF under Wave 2 shown in Fig. 7 because of the sheltering effect. The vertical component of the tsunami wave load Fz with the surrounding storage tanks is slightly smaller than that without the surrounding storage tank due to the same reason as mentioned in Fig. 8. 5. Discussion 5.1. Comparison between wave loads with and without surrounding storage tanks
Fig. 7. Time series of h, u, Fh and Fz at 4eF without surrounding storage tanks under Wave 2.
4.2. Wave load with surrounding storage tanks Fig. 8 shows the time series of Fh and Fz with the surrounding storage tanks measured at 1eM under Wave 2. The horizontal component of the tsunami wave load Fh is smaller than that
Fig. 8. Time series of Fh and Fz at 1eM with surrounding storage tanks under Wave 2.
The maximum tsunami wave loads measured with the surrounding storage tanks are smaller than those measured without the surrounding storage tank. Figs. 10(a) and (b) show the comparisons between the maximum horizontal and vertical components of the tsunami wave loads with and without the surrounding storage tanks, respectively. The horizontal axis shows the position of the storage tanks. The blue and red circles show the maximum tsunami wave loads with and without the surrounding storage tanks, respectively. In most of the positions of the storage tanks, the maximum tsunami wave loads measured with the surrounding storage tanks are smaller than those measured without the surrounding storage tank. However, the tsunami wave loads measured with the surrounding storage tanks at 2eF and 3eM has the same magnitude as those without the surrounding storage tank. The presence of the surrounding storage tanks may cause the increase in the tsunami wave load under several conditions. In this
Fig. 9. Time series of Fh and Fz at 4-F with surrounding storage tanks under Wave 2.
Please cite this article in press as: Araki, S., et al., Experimental study on tsunami wave load acting on storage tank in coastal area, Journal of Loss Prevention in the Process Industries (2016), http://dx.doi.org/10.1016/j.jlp.2016.10.004
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Fig. 10. Comparison of maximum wave load under Wave 1.
experiment, the distance between the cylindrical storage tanks was relatively large. The influence of the surrounding storage tanks should be discussed together with the distance between the storage tanks. 5.2. Vertical component of tsunami wave load The estimation of the tsunami wave load acting on a storage tank is discussed under the condition of no surrounding storage tank because the inundation flow is complicated under the condition of the presence of the surrounding storage tanks. The features of the variation in the vertical tsunami wave load Fz is similar to that in the inundation depth. This suggests that the buoyancy calculated based on the static pressure has a great influence on the measured vertical tsunami wave load. Fig. 11 shows the correlation coefficient between the measured vertical component of the tsunami wave load Fz and the inundation depth h. The vertical and horizontal axes show the correlation coefficient and
Fig. 11. Correlation coefficient between measured vertical tsunami wave load and measured water surface elevation.
the position where the wave load was measured, respectively. The red and blue circles show the correlation coefficients for Wave 1 and Wave 2, respectively. In all the positions, the correlation coefficients are more than 0.90, which indicates a strong positive linear correlation between the vertical component of the tsunami wave load and the inundation depth. Fig. 12 shows the time series of the buoyancy estimated from the inundation depth which was measured under the condition that the storage tank was not placed. Figs. 12(a) and (b) show the time series at 1eM under Wave 2 and at 4eF under Wave 2, respectively. Although the buoyancy overestimates the measured vertical component of the tsunami wave load, the features of the variation in the calculated buoyancy is in good agreement with that in the measured tsunami wave load. The time series of the measured tsunami wave load does not have short period variations. It might result from the dynamic pressure acting on the bottom of the cylindrical storage tank or the difference between the inundation depths under the cylindrical storage tank was placed or not. The measured maximum vertical tsunami wave load was estimated by the equation proposed by FDMA (2009) (Eqs. (7)e(9), (11)), which is based on the static pressure. Fig. 13 shows the comparison between the maximum vertical wave loads estimated by FDMA equation and measured in the experiment. The vertical and horizontal axes show the maximum vertical wave load and the position where the wave load was measured, respectively. In the equation proposed by FDMA, the maximum vertical wave load was estimated by using the maximum value in the time series of Froude number, which corresponds to the viewpoint of FDMA. The figure shows that the equation proposed by FDMA (2009) approximately estimated the measured maximum vertical wave load acting on the cylindrical storage tank. However, the difference between the measured and the estimated wave loads is large under several conditions. The values of the constants in the equations need to be investigated further. 5.3. Horizontal component of tsunami wave load The features of the variation in the horizontal component of the tsunami wave load is more similar to that in the water particle velocity u than that in the inundation depth h. Therefore, the
Fig. 12. Estimation of vertical wave load by static pressure.
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Fig. 15. Correlation coefficient between measured and estimated horizontal tsunami wave loads.
Fig. 13. Estimation of vertical maximum tsunami wave load by FDMA's equation.
horizontal component of the tsunami wave load is expected to be estimated by the equation proposed by Arimitsu et al. (2012) (Eq. (13)) and Morison equation (Eq. (14)). In the equation proposed by Arimitsu et al. (2012), hs (t) and us (t) are the inundation depth and the velocity measured or estimated under the condition that the structure is placed, respectively, which were not measured in the present experiment. Therefore, the horizontal component of the tsunami wave load was compared with only Morison equation.
Fig. 14. Estimation of horizontal wave load by Morison equation.
Figs. 14(a) and (b) show the time series of the horizontal tsunami wave loads estimated by Morison equation at 1eM under Wave 2 and at 4eF under Wave 2, respectively. The drag and inertia coefficients in Morison equation were set at CD ¼ 1.2 and CM ¼ 2.0, respectively. The measured impulsive force at the beginning of the inundation is estimated because Morison equation has a term including the velocity. The variation after the impulsive force at the beginning was also approximately estimated. Fig. 15 shows the correlation coefficient between the horizontal tsunami wave loads measured in the experiment and estimated by Morison equation. The vertical and horizontal axes show the correlation coefficient and the position where the wave load was measured. The correlation coefficient for Wave 2 is higher than that for Wave 1. The reason is that the static force as well as the drag and inertia forces may have an influence on the horizontal wave load. Since the horizontal velocity in Wave 1 is smaller than that in Wave 2, the static force has relatively more influence on the horizontal wave load. 6. Conclusions The horizontal and vertical components of the tsunami wave load acting on the cylindrical storage tanks were measured with and without the surrounding tanks. In most of the positions of the storage tanks, the maximum tsunami wave loads measured with the surrounding storage tanks were smaller than those measured without the surrounding storage tank. However, the presence of the surrounding storage tanks caused the increase in the tsunami wave load under several conditions. The measured tsunami wave load was estimated by several methods. In the measured vertical component of the tsunami wave load, the buoyancy was predominant. Therefore, the measured vertical tsunami wave load was approximately estimated by the buoyancy based on the static pressure calculated from the inundation depth. The maximum measured vertical tsunami wave load was also approximately estimated by the equation proposed by FDMA because the equation is based on the static pressure. The measured horizontal component of the tsunami wave load was compared with the wave load calculated by Morison equation. The correlation between the horizontal tsunami wave load measured in the experiment and estimated by Morison equation for Wave 2 was higher than that for Wave 1 which had a smaller wave height. Other component of wave force besides the drag and inertia forces in Wave 1 was maybe relatively larger than that in Wave 2 because the horizontal velocity in Wave 1 was smaller than that in Wave 2. In this study, the horizontal wave load was not compared with the estimation by Arimitsu equation because the inundation depth and the horizontal velocity on the storage site was not measured under the condition that the storage tank was placed. The discussion of the applicability of Arimitsu equation is a future task.
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Please cite this article in press as: Araki, S., et al., Experimental study on tsunami wave load acting on storage tank in coastal area, Journal of Loss Prevention in the Process Industries (2016), http://dx.doi.org/10.1016/j.jlp.2016.10.004