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Liquid-solid Interaction Seismic Response of an Isolated Overground Rectangular Reinforced-concrete Liquid-storage Structure

Liquid-solid Interaction Seismic Response of an Isolated Overground Rectangular... In this paper, the liquid-solid interaction dynamic finite element integral models of a reinforced-concrete rectangular liquid-storage structure are established to obtain the liquid-solid interaction seismic response of an isolated overground rectangular reinforced-concrete liquid-storage structure. It is assumed that the liquid is incompressible and the influence of gravity wave on the surface of liquid is considered. Some mechanical properties, such as the liquid sloshing height, wallboard displacement and equivalent stress under seismic action and the seismic response under different liquid level of the single cell liquid-storage structure, are discussed, by considering factors of the nonlinear dynamic characteristic, element selection, seismic input, mesh density, convergence and liquid-solid interaction. The results of numerical examples indicate that: the peak displacements of the isolated structure under different earthquake intensities are basically the same, the displacement of the wallboard and stress increase with the increase of seismic intensity, and the lower the level of the liquid is, the less the amount of liquid is and the greater the shaking amplitude is, the greater the stress and displacement of the wallboard are. Keywords: earthquake; seismic isolation; reinforced concrete; rectangular liquid-storage structure; fluid-solid interaction 1. Introduction storage tank with FEM. Liu et al. (2006) studied the Researchers have carried out a long-term and gravitational wave phenomenon in the rectangular unremitting study on the seismic design of reinforced- elastic shell-fluid coupling system. concrete liquid-storage structures from the 1930s. Zienkiewicz and Bettes (1978) presented numerical Although some more mature research results have been treatment under fluid-structure dynamic interaction obtained, many unsolved problems still remain. and wave force. Geer (1971) studied the residual Westergaard (1933) first proposed the liquid-solid potential and approximation methods concerning the coupling vibration problem in his famous essay. three-dimensional fluid-structure interaction problem. Hosking and Jacobsen (1934) analyzed the dynamic Chen and Taylor (1990) studied the displacement water pressure problem of a rigid tank under seismic method for the vibration analysis of coupled fluid- load. Many scholars throughout the world have further structure systems. Jenings et al. (Jenings, 1985; Bathe researched the liquid-solid coupling vibration problem et al., 1995; Bathe et al., 1999; Rugonyi and Bathe, on the basis of Hosking's work, and great achievements 2001) conducted numerical simulations concerning have been made. Housner (1957) thought that the liquid-solid coupling problems. Cheng et al. (Cheng, dynamic liquid effect of a rigid liquid-storage structure 2009; Wall et al., 2007; Du et al., 2008a;, Du et al., was composed of the pulsating component and the 2008b; Wang and Lei, 2011; Cheng and Du, 2011) convective component, and conducted a numerical theoretically studied the vibrating characteristics of simulation of the water sloshing effect with a spring- the liquid-solid coupling problem. Zhu (1991, 2011) mass system (Housner, 1959). Liu and Wang (2005) studied Rayleigh quotients and the orhogonality of wet conducted seismic analysis of a rectangular liquid- modes in coupled vibrations. Shrimali and Jangid (2002a, 2002b) studied non- linear seismic response regarding isolated liquid *Contact Author: Xuansheng Cheng, Professor, storage tanks under bi-directional excitation, but the School of Civil Engineering, Lanzhou University of Technology, structure involved was circular, and the nonlinearity No. 287 Langongping Road, Lanzhou 730050, China of concrete and the influence of the gravity wave Tel: +86-931-2973784 Fax: +86-931-2976327 were not considered. Mustafa (2005) analyzed the E-mail: chengxuansheng@gmail.com sloshing Characteristic in Liquid-Filled Containers ( Received April 3, 2014 ; accepted October 15, 2014 ) Journal of Asian Architecture and Building Engineering/January 2015/180 175 using FEM. Malhotra (1997) proposed a new method 2.2 Selection of Seismic Wave of seismic isolation concerning liquid-storage tanks. The Northridge wave (Shao, 2002; Papazoglou and Chalhoub et al. (Chalhoub and Kelly, 1990; Cho et Elnashai, 1996) is shown in Fig.2. Frequent earthquake al., 2004; Kim and Lee, 1995; Wang et al., 2001; and rare earthquake are considered. F requent Kim et al., 2002) studied the seismic performance of earthquake is the transcendental probability of an base-isolated liquid storage tanks. So in this paper, earthquake intensity value of 63%, and rare earthquake ADINA software is applied to establish the liquid-solid is the transcendental probability of an earthquake interaction dynamic finite element integral models of intensity value of about 2%-3% in a design reference the isolated reinforced-concrete rectangular liquid- period of 50 years. storage structure; by considering the factors of the nonlinear dynamic characteristic, element selection, seismic input, grid density, convergence and liquid- solid interaction, the liquid sloshing height, wallboard displacement and equivalent stress under seismic action, also the seismic response under different levels of liquid of the single cell liquid-storage structure, are discussed. 2. FEM Model Fig.2. Northridge Wave 2.1 Model Diagram Fig. 2 Northridge Wave Assuming that the size of the reinforced-concrete 2.3 Concrete Constitutive Model rectangular liquid-storage structure is a×b×h=4 m x Some modification was carried out by Sargin on the 4 m x 4 m, and the thickness of the wallboard and concrete constitutive model (Lv et al., 1999) suggested bottom board is 0.2 m. The model is shown as Fig.1. by Saenz, namely    FF   2   12    00     kf 3 c 2    12  F  F   12   0  0  where F =E /E , E and E are the tangent modulus 1 0 s 0 s    10 2 and the secant modulus through the coordinate origin, EE  E 1  1   1.04E 3.1 10 N/m    x y c sx c respectively; and are the strain and stress of ε σ    c   concrete respectively; and are the ultimate strain (a) Plan ε σ 0 0 and ultimate stress of concrete respectively; f is the 1  -1 c 10 2 E EE 1.0 3.010 N/m compressive strength of concrete; k is the strength z c c 1  1-  -1 influence coefficient of lateral restraint, and F is the parameter of the decline segment (shown in Fig.3.). For convenience of calculation, an elastic-plastic  z 1-  1- material is used.   c 10 2 GG G 1.0G 1.210 N/m yx xy  c c  G 01  1- 1-    c 1.0 (b) Profile        - F =0.0. 5 2   xy yx c y s c Fig. 1 Model Diagram F =0.5 Fig.1. Model Diagram 2 F =0.0 The density of the reinforced concrete is 2500 kg/ 3  m , and the height of water is 3/4 of the wallboard 1.0 height. The 3D model of the reinforced-concrete rectangular liquid-storage structure is produced with Fig.3. Concrete Constitutive Model Fig. 3 Concrete Constitutive Model the fluid-structure interaction function in ADINA, and the rubber pad, which is an isolation layer, is set at the 2.4 Determination of the Elastic Constants bottom. The rebar of the rectangular liquid-storage structure is usually double layered and in two directions 176 JAABE vol.14 no.1 January 2015 Xuansheng Cheng        DISPLACEMENT MAXIMUM MAGNITUDE Δ 1.205E-05 TIME 17.90 NODE 4392 MINIMUM DISPLACEMENT MAXIMUM * 0.000 MAGNITUDE Δ 1.205E-05 NODE 463 TIME 17.90 NODE 4392 1.170E-05 MINIMUM 9.900E-06 DISPLACEMENT MAXIMUM * 0.000 8.100E-06 MAGNITUDE Δ 1.205E-05 NODE 463 6.300E-06 TIME 17.90 NODE 4392 1.170E-05 4.500E-06 MINIMUM 9.900E-06 DISPLACEMENT MAXIMUM 2.700E-06 * 0.000 according to a certain gap, and is evenly distributed. 8.100E-06 2 MAGNI 9.000E TUDE -07 Δ 1.205E-05 NODE 463 6.300E-06 TIME 17.90 NODE 4392    1.170E-05 f is 30 MPa, and the strength of the rebar is 335 MPa. 4.500E-06 MINIMUM 9.900E-06 FF   2   2.700E-06 12   * 0.000 8.100E-06 The reinforcement ratio in both x- and y-directions is  9.000E-07 NODE 463 00   6.300E-06 1.170E-05   kf 4.500E-06 3 c an economic reinforcement ratio 2 of 1%. The elastic 9.900E-06 2.700E-06    8. a) 100E 7--d 06eg ree of frequent earthquake 9.000E-07 modulus, shear modulus and Poisson's ratio are shown 12  F  F 6.300E-06     4.500E-06  as follows (Cheng and Du, 2006): 0 0   2.700E-06 a) 7-degree of frequent earthquake DISPLACEMENT MAXIMUM 9.000E-07 MAGNITUDE Δ 1.205E-05 TIME 17.90 NODE 4392    E 10 2 MINIMUM a) 7-degree of frequent earthquake EE  E 1  1   1.04E 3.1 10 N/m DISPLACEMENT MAXIMUM   x y c  sx c * 0.000 MAGNITUDE Δ 1.205E-05 a) 7-degree of frequent earthquake   NODE 463  c   TIME 17.90 NODE 4392 1.170E-05 MINIMUM a) 7-degree of frequent earthquake 9.900E-06 DISPLACEMENT MAXIMUM * 0.000 8.100E-06 1  -1 MAGNITUDE Δ 1.205E-05   NODE 463 10 2 6.300E-06 TIME 17.90 NODE 4392 E EE 1.0 3.010 N/m 1.170E-05 z c c 4.500E-06 MINIMUM 9.900E-06 DISPLACEMENT MAXIMUM 1  1-  -1 2.700E-06   * 0.000   8.100E-06 MAGNITUDE Δ 1.205E-05 9.000E-07 NODE 463 6.300E-06 TIME 17.90 NODE 4392 1.170E-05 4.500E-06 MINIMUM 9.900E-06 2.700E-06 * 0.000  G 8.100E-06 9.000E-07 NODE 463 1-  1-  6.300E-06 1.170E-05 G 4.500E-06  c 10 2 9.900E-06 GG G 1.0G 1.210 N/m 2.700E-06 yx xy c c 8.100E-06 9.000E-07  G b) 8-degree of frequent earthquake s 6.300E-06 1  1- 1-   4.500E-06  c 2.700E-06 9.000E-07 b) 8-degree of frequent earthquake DISPLACEMENT MAXIMUM b) 8-degree of frequent earthquake MAGNITUDE Δ 1.205E-05 TIME 17.90 NODE 4392        - 0.2   xy yx c y s c MINIMUM b) 8-degree of frequent earthquake DISPLACEMENT MAXIMUM * 0.000 MAGNITUDE Δ 1.205E-05 NODE 463 TIME 17.90 NODE 4392 where, G and G are shear moduli; E , E and E 1.170E-05 xy yx x y z MINIMUM b9. ) 900E 8-d -06 eg ree of frequent earthquake DISPLACEMENT MAXIMUM * 0.000 are the elastic moduli in the x-, y- and z-directions 8.100E-06 MAGNITUDE Δ 1.205E-05 NODE 463 6.300E-06 TIME 17.90 NODE 4392 1.170E-05 respectively; µ and µ are Poisson ratios; is the 4.500E-06 ρ MINIMUM xy yx 9.900E-06 DISP2. LA 700E CEMEN -06 T MAXIMUM * 0.000 8.100E-06 MAGNI 9.000E TUDE -07 Δ 1.205E-05 reinforcement ratio of the wallboard and bottom plate; NODE 463 6.300E-06 TIME 17.90 NODE 4392 1.170E-05 4.500E-06 MINIMUM E and E are the elastic moduli of concrete and rebar 9.900E-06 c s 2.700E-06 * 0.000 8.100E-06 9.000E-07 NODE 463 6.300E-06 respectively; α = E /E is the ratio of the elastic moduli s c 1.170E-05 4.500E-06 9.900E-06 of rebar and concrete. It is assumed that the liquid is 2.700E-06 8.100E-06 9.000E-07 c) 9-degree of frequent earthquake 6.300E-06 the potential fluid with a bulk modulus of 2.3 x l0 Pa. c) 9-degree of frequent earthquake 4.500E-06 2.700E-06 2.5 Boundary Conditions and Meshing DISPLACEMENT MAXIMUM 9.000E-07 c) 9-degree of frequent earthquake MAGNITUDE Δ 1.205E-05 The bottom is fixed to the isolation layer, and the TIME 17.90 NODE 4392 MINIMUM DISPLACEMENT MAXIMUM influence of the gravity wave on the surface of the c) 9-d* eg 0.000 ree of frequent earthquake MAGNITUDE Δ 1.205E-05 NODE 463 TIME 17.90 NODE 4392 liquid is considered. However, the compressibility 1.170E-05 MINIMUM 9.900E-06 DISPLACEMENT MAXIMUM * 0.000 of the liquid is not considered. The structure and c) 9-degree of frequent earthquake 8.100E-06 MAGNITUDE Δ 1.205E-05 NODE 463 6.300E-06 TIME 17.90 NODE 4392 1.170E-05 the liquid are considered as 3D-solid and 3D-fluid 4.500E-06 MINIMUM 9.900E-06 DISPLACEMENT MAXIMUM 2.700E-06 * 0.000 8.100E-06 elements respectively. MAGNITUDE Δ 1.205E-05 9.000E-07 NODE 463 6.300E-06 TIME 17.90 NODE 4392 1.170E-05 4.500E-06 Meshing of the solid domain and liquid domain MINIMUM 9.900E-06 2.700E-06 * 0.000 8.100E-06 9.000E-07 is uniform. Due to the regular shape, the length of NODE 463 6.300E-06 1.170E-05 4.500E-06 DISPLACEMENT MAXIMUM d) 7-degree of rare earthquake 9.900E-06 the grid in both the horizontal direction and vertical 2.700E-06 MAGNITUDE Δ 1.888E-05 8.100E-06 9.000E-07 TIME 17.90 NODE 980 6.300E-06 direction is 0.2m. The meshing is shown in Fig.4. DISPLACd EMEN ) 7-T MA degr Xee IM U o M f rare earthquake MINIMUM 4.500E-06 MAGNITUDE Δ 1.888E-05 * 0.000 2.700E-06 TIME 17.90 NNODE ODE 980 46 3 9.000E-07 1.733E-05 M INIMUM d) 7-degree of rare earthquake 1.467E-0* 5 0. 000 1.200E-05NODE 463 9. 1.333 733E E--06 05 d) 7-degree of rare earthquake 6. 1.667 467E E--06 05 4. 1.0 200 00E E--06 05 1.333E-07 9.333E-06 6.667E-06 d) 7-degree of rare earthquake 4.000E-06 1.333E-07 e) 8-degree of rare earthquake e) 8-degree of rare earthquake DISPLACEMENT MAXIMUM e) 8-degree of rare earthquake Fig. 4 Schematic Diagram of Grid Division MAGNITUDE Δ 1.888E-05 Fig.4. Schematic Diagram of Grid Division TIME 17.90 NODE 980 MINIMUM DISPLACEMENT MAXIMUM * 0.000 MAGNITUDE Δ 1.888E-05 NODE 463 3. Numerical Simulation TIME 17.90 NODE 980 1.733E-05 MINIMUM 1.467E-05 3.1 Liquid Sloshing Height * 0.000 1.200E-05 NODE 463 9.333E-06 The seismic responses of the reinforced-concrete 1.733E-05 6.667E-06 1.467E-05 4.000E-06 rectangular liquid-storage structure under the 1.200E-05 1.333E-07 9.333E-06 Northridge wave with frequency seismic intensities of 6.667E-06 4.000E-06 7-, 8- and 9-degree of frequent earthquake, as well as 1.333E-07 7-, 8- and 9-degree of rare earthquake, are shown in f) 9-degree of rare earthquake Fig.5. Fig.5. Displacement Graph under the Northridge Wave f) 9-degree of rare earthquake Fig. 5. Displacement Graph under the Northridge Wave f) 9-degree of rare earthquake Fig. 5. Displacement Graph under the Northridge Wave JAABE vol.14 no.1 January 2015 Xuansheng Cheng 177        DISPLACEMENT MAXIMUM M DIA SGNI PLAT CUDE EMEN T MA Δ 6.831 XE IM -0U 6 M T M IA ME GNI 17. T90 UDE NO DΔ E 6. 979 831 (E 6. -85 066E -06) TIME 17.90 N M OINI DE M 979 UM ( 6.856E-06) * M 0. INI 000 M UM * 0. NODE 000 461 6.500E-06NODE 461 5. 6.500 500E E- -0 06 6 4. 5.500 500E E- -0 06 6 3. 4.500 500E E- -06 06 2. 3.500 500E E- -06 06 1. 2.500 500E E- -06 06 5. 1.000 500E E- -07 06 5.000E-07 a) 7-degree of frequent earthquake a) 7-degree of frequent earthquake DISPLACEMENT MAXIMUM DISPLACEMENT MAXIMUM MAGNITUDE Δ7.043E-06 MAGNITUDE Δ7.043E-06 TIME 17.90 NODE 979 (7.029E-06) TIME 17.90 NODE 979 (7.029E-06) MINIMUM MINIMUM * 0.000 * 0. NOD 000 E 46 1 6.300E-06NOD E 461 5. 6.400 300E E- -0 06 6 4. 5.500 400E E- -0 06 6 3. 4.600 500E E- -06 06 2. 3.700 600E E- -06 06 1. 2.800 700E E- -06 06 9. 1.000 800E E- -07 06 9.000E-07 b) 8-degree of frequent earthquake b) 8-degree of frequent earthquake DISPLACEMENT MAXIMUM M DIA SGNI PLAT CUDE EMEN T MA Δ7.815 XE IM -06 U M It can be observed from Fig.5. that the peak liquid T M IA ME GNI 17. T90 UDE NO DΔ E 7.979 815 ( E 7. -0 73 6 6E-06) TIME 17.90 N M OINI DE M 979 UM ( 7.736E-06) sloshing displacement appears in Node 4372 with * M 0. INI 000 M UM * 0. NODE 000 461 frequent seismic intensities of 7-, 8- and 9-degree 7.000E-06NODE 461 6. 7.000 000E E- -0 06 6 of frequent earthquake, as well as 7-degree of rare 5. 6.000 000E E- -0 06 6 4. 5.000 000E E- -06 06 earthquake, and the liquid sloshing height, which is 3. 4.000 000E E- -06 06 -5 2. 3.000 000E E- -06 06 1.205 x 10 m, does not increase with the increase 1. 2.000 000E E- -0 06 6 1.000E-06 of seismic intensity. However, a peak liquid sloshing -5 displacement, which is 1.888 x 10 m, appears in Node 980 with seismic intensity of the rare 9-degree. The c) 9-degree of frequent earthquake c) 9-degree of frequent earthquake extreme liquid sloshing height is shown in Table 1. c) 9-degree of frequent earthquake DISPLACEMENT MAXIMUM Table 1. Displacement of the Liquid Sloshing Height (m) M DIA SGNI PLAT CUDE EMEN T MA Δ9.125 XE IM -06 U M T M IA ME GNI 17. T90 UDE NO DΔ E 9.979 125 E (8. -0 99 6 2E-06) TIME 17.90 N M OINI DE M 979 UM ( 8.992E-06) Frequent Earthquake * M 0. INI 000 M UM * 0. NODE 000 461 7-degree 8-degree 9-degree 8.400E-06NODE 461 7. 8.200 400E E- -0 06 6 -5 -5 -5 6. 7.000 200E E- -0 06 6 1.205 x 10 1.205 x 10 1.205 x 10 4. 6.800 000E E- -06 06 3. 4.600 800E E- -06 06 Rare Earthquake 2. 3.400 600E E- -06 06 1. 2.200 400E E- -0 06 6 1.200E-06 7-degree 8-degree 9-degree -5 -5 -5 1.205 x 10 1.888 x 10 7.733 x 10 d) 7-degree of rare earthquake It can be observed from Table 1. that the extreme DISPLACEMENT MAXIMUM d) 7-degree of rare earthquake MAGNITUDE Δ1.863E-05 d) 7-degree of rare earthquake liquid sloshing heights are basically the same under T DIIME SPLA 17. C90 EMEN NOD T MA E 979 X I(M 1.U 84 M 1E -05) MAGNITUDE Δ1.863E-05 MINIMUM frequent earthquake, and increase with earthquake TIME 17.90 NODE 979 (1.841E-05) * 0.000 MINIMUM NODE 461 intensity under rare earthquake. * 0.000 1.733E-05 NODE 461 1.467E-05 3.2 Wallboard Displacement 1.733E-05 1.200E-05 1.467E-05 9.333E-06 The seismic responses of the reinforced-concrete 1.200E-05 6.667 E-06 9.333E-06 4.000E-06 rectangular liquid-storage structure under the 6.667 E-06 1.333E-06 4.000E-06 Northridge earthquake wave with frequency seismic 1.333E-06 intensities of 7-, 8- and 9-degree of frequent earthquake e) 8-egree of rare earthquake e) 8-egree of rare earthquake as well as 7-, 8- and 9-degree of rare earthquake are e) 8-egree of rare earthquake shown in Fig.6. The extreme wallboard displacements DISPLACEMENT MAXIMUM M DIA SGNI PLAT CUDE EMEN T MA Δ7.698 XIE M -0 U 5 M at x=1.9 m of the isolated liquid-storage structure T M IME AGNI 17. TUDE 90 N O DΔE 7.698 979E (-7. 05 67 5E-05) TIME 17.90 N M OINI DE M 979 UM (7. 675E-05) under the seismic load with 7-, 8- and 9-degree of MINIMUM * 0.000 * 0.000 NODE 461 frequent earthquake, as well as 7-, 8- and 9-degree of NODE 461 7.000E-05 7.000E-05 6.000E-05 rare earthquake are shown in Table 2. 6.000E-05 DISPLACEMENT MAXIMUM 5.000E-05 5.000E-05 MAGNITUDE Δ 6.831E-06 4.000E-06 4.000E-06 TIME 17.90 NODE 979 (6.856E-06) 3.000 E-06 DISPLACEMENT MAXIMUM 3.000 E-06 MINIMUM 2.000E-06 MAGNITUDE Δ 6.831E-06 2.000E-06 * 0.000 1.000E-06 TIME 17.90 NODE 979 (6.856E-06) 1.000E-06 NODE 461 MINIMUM 6.500E-06 * 0.000 5.500E-06 NODE 461 4.500E-06 6.500E-06 f) 9-degree of rare earthquake 3.500E-06 5.500E-06 2.500E-06 f) 9-degree of rare earthquake 4.500E-06 f) 9-degree of rare earthquake 1.500E-06 3.500E-06 Fig.6. Wallboard Displacement Graph at x=1.9 under the 5.000E-07 2.500E-06 FiF g. ig. 6 .6 W . W alal lblo bar oar dd D D isp isp lac lac ee m meen nt t G Grrap aph h at at x x=1 =1..9 u 9 unde nde rr t he the N N oo rtrhr thr idg idg e e W W avav e e 1.500E-06 Northridge Wave 5.000E-07 Table 2. Wallboard Displacement at x=1.9m (m) Frequent Earthquake a) 7-degree of frequent earthquake a) 7-degree of frequent earthquake 7-degree 8-degree 9-degree a) 7-degree of frequent earthquake DISPLACEMENT MAXIMUM -6 -6 -6 6.831 x 10 7.043 x 10 7.815 x 10 MAGNITUDE Δ7.043E-06 TIME 17.90 NODE 979 (7.029E-06) DISPLACEMENT MAXIMUM MINIMUM MAGNITUDE Δ7.043E-06 Rare Earthquake TIME 17.90 N *O 0. D 000 E 979 (7.029E-06) M NOD INIM E 46 UM1 7-degree 8-degree 9-degree 6.300E-0* 6 0. 000 5.400E-06NOD E 461 -6 -6 -6 4. 6.500 300E E- -0 06 6 9.125 x 10 1.865 x 10 7.698 x 10 3. 5.600 400E E- -0 06 6 2. 4.700 500E E- -0 06 6 1. 3.800 600E E- -06 06 It can be observed from Table 2. that the peak 9. 2.000 700E E- -06 07 1.800E-06 wallboard displacement of the isolated liquid-storage 9.000E-07 st ruc t ure i nc re a se s wi t h t he i nc re a se of se i sm i c b) 8-degree of frequent earthquake intensity. b) 8-degree of frequent earthquake b) 8-degree of frequent earthquake DISPLACEMENT MAXIMUM MAGNITUDE Δ7.815E-06 DISPLACEMENT MAXIMUM TIME 17.90 NODE 979 (7.736E-06) MAGNITUDE Δ7.815E-06 MINIMUM TIME 17.90 NODE 979 (7.736E-06) * 0.000 MINIMUM NODE 461 * 0.000 7.000E-06 NODE 461 6.000E-06 7.000E-06 5.000E-06 178 JAABE vol.14 no.1 January 2015 Xuansheng Cheng 6.000E-06 4.000E-06 5.000E-06 3.000E-06 4.000E-06 2.000E-06 3.000E-06 1.000E-06 2.000E-06 1.000E-06 c) 9-degree of frequent earthquake c) 9-degree of frequent earthquake DISPLACEMENT MAXIMUM MAGNITUDE Δ9.125E-06 DISPLACEMENT MAXIMUM TIME 17.90 NODE 979 (8.992E-06) MAGNITUDE Δ9.125E-06 MINIMUM TIME 17.90 NODE 979 (8.992E-06) * 0.000 MINIMUM NODE 461 * 0.000 8.400E-06 NODE 461 7.200E-06 8.400E-06 6.000E-06 7.200E-06 4.800E-06 6.000E-06 3.600E-06 4.800E-06 2.400E-06 3.600E-06 1.200E-06 2.400E-06 1.200E-06 d) 7-degree of rare earthquake d) 7-degree of rare earthquake SMOOTHED MAXIMUM 3.3 Distribution of Equivalent Stress EFFECTIVE The seismic responses of the reinforced-concrete STRESS Δ269975 RST CALC MINIMUM rectangular liquid-storage structure under the TIME 17.90 * 4347 Northridge earthquake wave with 7-, 8- and 9-degree of frequent earthquake as well as 7-, 8- and 9-degree of rare earthquake are shown in Fig.7. SMOOTHED MAXIMUM EFFECTIVE SMOOTHED MAXIMUM STRESS Δ99493 EFFECTIVE RST CALC MINIMUM S ST MOO RESS TH ED MAΔ99493 XIMU M f) 9-degree of rare earthquake f) 9-degree of rare earthquake TIME 17.90 * 203.8 EFFECTIVE RST CALC MINIMUM T ST IME RS EMOO SS 17. 90 TH * EDΔ99493 MA 203.X 8 I MUM 97500 SMOO THED MAXIMUM RST EF CA FLC EC MI TIVE N IMUM Fig. 7. Equivalent Stress under the Northridge Wave Fig.7. Equivalent Stress under the Northridge Wave 82500 EFFEC TIVE TIME S 97500 T 17. RE90 SS * 203. Δ99493 8 67500 STRE SS Δ99493 RST CALC MINIMUM 5R2500 ST C ALC MINIMUM T 67500 97500 IME 17. 90 * 203.8 The equivalent stresses of the isolated liquid-storage 37500 TIME 17.90 * 203.8 37500 67500 97500 under the seismic load with 7-, 8- and 9-degree of 7500 97500 52500 82500 82500 frequent earthquake as well as 7-, 8- and 9-degree of 7500 37500 67500 22500 52500 rare earthquake are shown in Table 3. a) 7-degree of frequent earthquake a) 7-degree of frequent earthquake a) 7-degree of frequent earthquake Table 3. Stress Values SMOOTHED MAXIMUM a) 7-degree of frequent earthquake EFFECTIVE SMOOTHED MAXIMUM Frequent Earthquake STRESS Δ99765 EFFECTIVE a) 7-degree of frequent earthquake RST CALC MINIMUM S ST MOO RESS TH ED MAΔ99765 XIMU M a) 7-degree of frequent earthquake TIME 17.90 * 354.8 7-degree 8-degree 9-degree R EFSF T EC CA TLC IVE MI NIMUM T ST IME RS EMOO SS 17. 90 TH * EDΔ99765 MA 354.X 8 I MUM EF 97500 SMOO FEC T TIH VED E MA XIMUM RST CALC MI NIMUM 99493 99765 100316 82500 EFFEC TIVE TIME S 97500 T 17. RE90 SS * 354. Δ99765 8 R 67500 SSTT RC E SS ALC MI Δ99765 NIMU M Rare Earthquake 52500 RST C ALC MINIMUM T 67500 97500 IME 17. 90 * 354.8 37500 TIME 17.90 * 354.8 52500 82500 7-degree 8-degree 9-degree 37500 67500 97500 750082500 97500 22500 52500 7500 37500 67500 165964 166925 269775 52500 67500 22500b ) 8-degree of frequent earthquake b) 8-degree of frequent earthquake 22500 37500 b) 8-degree of frequent earthquake SMOOTHED MAXIMUM 22500 It can be observed from Fig.7. and Table 3. that the EFFECTIV b E) 8 -degree of frequent earthquake SMOOTHED MAXIMUM STRESS Δ100316 EFFECTIVE equivalent stress of the isolated liquid-storage structure b) 8-degree of frequent earthquake RST CALC MINIMUM SMOOTHED MAXIMUM STRESS Δ100316 b) 8-degree of frequent earthquake TIME 17.90 *761.5 R EFSF T EC CA TLC IVE MI NIMUM increases with the increase of seismic intensity. S TT IME RS EMOO SS 17. 90 TH * EDΔ100316 MA 761.5 X I MUM 97500 SMOO THED MAXIMUM 3.4 Seismic Response of Different Liquid Level R ST EF CA FLC EC MI TI VE N IMUM 82500 EFFEC TIVE TIME ST 17. RE90 SS *761.Δ100316 5 2 A peak value of 0.70m/s is applied in the x-direction 67500 STRE SS Δ100316 R 82500 ST C ALC MI NIMUM 52500 RST C ALC MINIMUM T 97500 IME 17. 90 *761.5 of the reinforced-concrete rectangular liquid-storage 37500 TIME 17.90 *761.5 82500 52500 67500 37500 97500 structure, and a peak value of 0.45m/s is applied in the 7500 97500 52500 22500 82500 37500 67500 y-direction. The results are shown in Table 4. below. 22500 52500 c) 9-degree of frequent earthquake c) 9-degree of frequent earthquake 22500 Table 4. Seismic Responses under Different Liquid Levels SMOOTHED MAXIMUM EFFECTIVE SMOOTHED MAXIMUM c) 9-degree of frequent earthquake STRESS Δ165964 Liquid Wave Wallboard Stress c) 9-degree of frequent earthquake EFFECTIVE RST CALC MINIMUM S ST MOO RESS TH ED MA Δ X 16596 IMUM 4 c) 9-degree of frequent earthquake Level (m) Height (m) Displacement (m) (Pa) TIME 17.90 *5.652E-05 EFFECTIVE c) 9-degree of frequent earthquake RST CALC MINIMUM T ST IME RS EMOO SS 17. 90 TH * ED Δ MA 5. 16596 652E XI4 MU -05 M -5 -6 156000 SMOOT HED MAXIMUM 3 1.249 x 10 6.766 x 10 163017 RST EF CA FLC EC MI TIVE N IMUM 132000 EFFEC TIVE TIME S 156000 T 17. RE90 SS *5.652E Δ16596 -05 4 -5 -6 108000 STRESS Δ165964 RST CALC MI NIMUM 2 1.875 x 10 7.207 x 10 422277 84000 RST C ALC MINIMUM T 108000 156000 IME 17. 90 *5.652E-05 -1 -1 60000 TIME 17.90 *5.652E-05 1 2. 217 x 10 1.277 x 10 2139402 60000 108000 156000 12000 156000 84000 132000 12000 60000 108000 It can be observed from Table 4. that the seismic 36000 84000 12000 60000 response of the isolated liquid-storage structure under d) 7-degree of rare earthquake the same seismic load is influenced by the liquid d) 7-degree of rare earthquake SMOOTHED MAXIMUM level. The lower the level of the liquid and the less the EFFECTIVE SMOOTHED MAXIMUM d) 7-degree of rare earthquake volume of the liquid, the greater the shaking amplitude, STRESS Δ166925 EFFECTIVE RST CALC MINIMUM SMOOTHED MAXIMUM d) 7-degree of rare earthquake STRESS Δ166925 d) 7 -degree of rare earthquake stress, and displacement of the wallboard are. TIME 30 * 5.811E-05 R EFSF T EC CA TLC IVE MI NIMU d) 7 M -degree of rare earthquake STRS EMOO SS THEDΔ166925 MAXI MUM TIME 30 * 5.811E-05 156000 SMOOT HED MAXIMUM RST EF CA FLC EC MI TIVE N IMUM 132000 EFFEC TIVE TIME ST 30 RE SS * 5.81Δ166925 1E-05 4. Conclusions 108000 STRESS Δ166925 R 132000 ST CA LC MINIMUM 84000 RST C ALC MINIMUM T 156000 IME 30 * 5.811E-05 108000 Assuming that the liquid is incompressible, and 60000 TIME 30 * 5.811E-05 84000 132000 108000 156000 considering the influence of gravity wave on the 12000 156000 36000 84000 132000 132000 surface of the liquid, the dynamic finite element 12000 60000 36000 84000 integral model of the isolated reinforced concrete 12000 60000 rectangular liquid-storage structure is established e) 8-degree of rare earthquake using ADINA software. The liquid sloshing height, e) 8-degree of rare earthquake wallboard displacement and equivalent stress under e) 8-degree of rare earthquake earthquake and the seismic response under different e) 8-degree of rare earthquake e) 8-degree of rare earthquake e) 8-degree of rare earthquake JAABE vol.14 no.1 January 2015 Xuansheng Cheng 179 13) Housner, G.W. (1957) Dynamic pressure on accelerated fluid liquid levels of the single cell liquid-storage structure container. Bulletin of the seismological society of America, 47(1), are discussed, the conclusions are as follows: pp.15-35. First, the peak displacements of the isolated liquid- 14) Housner, G.W. (1959). Behavior of structures during earthquake. storage structure under different intensities are Journal of the Engineering Mechanics Division, 85(4), pp.109- basically the same due to the filtering and energy- 129. 15) Jenings, A. (1985) Added mass for fluid-structure vibration consuming function of the isolation cushion. problems. International Journal for Numerical Methods in Second, the wallboard displacement of the isolated Engineering, 5, pp.817-830. liquid-storage structure increases with the increase of 16) Kim, N.S. and Lee, D.G. (1995) Pseudo-dynamic test for seismic intensity. evaluation of seismic performance of base-isolated liquid storage Third, the stress of the isolated liquid-storage tanks. Engineering Structures, 17, pp.198-208. 17) Kim M.K., Lim Y.M., S.Y. Cho, et al. (2002) Seismic analysis of structure increases with the increase of seismic intensity. base-isolated liquid storage tanks using the BE-FE-BE coupling Fourth, the lower the level of the liquid, the greater technique, Soil Dynamics and Earthquake Engineering, 22, the shaking amplitude, stress, and displacement of the pp.1151-1158. wallboard are. 18) Liu, Y.H. and Wang, K.C. (2005) Seismic analysis of liquid storage container. Earthquake Engineering and Engineering Vibration, 25(1), pp.149-154. Acknowledgments 19) Liu, X.J., Zhang, S.X., Liu, G.Y., et al. (2006). The analyses of This paper is a part of the national natural science gravity waves in rectangular elastic fluid-shell coupled system. foundation of China (Grant number: 51368039; Chinese Journal of Theoretical and Applied Mechanics, 38(1), 51478212), and a part of the education ministry pp.106-111. doctoral tutor foundation of China (Grant number: 20) Lv, X.L., Jin, G.F. and Wu, X.H. (1999) Reinforced concrete structural nonlinear finite element theory and application. 20136201110003). Shanghai: Tongji University Press. 21) Malhotra, P.K. (1997) New method for seismic isolation of liquid- References storage tanks. Earthquake Engineering and Structure Dynamics, 1) Bathe, K.J., Zhang, H. and Ji, S. (1999) Finite element analysis of 26, pp.839-847. fluid flows fully coupled with structural interactions. Computers & 22) Mustafa, A. (2005) Finite Element Analysis of Sloshing in Liquid- Structures, 72, pp.1-16. Filled Containers. Journal of Sound and Vibration, 279(2), pp.217- 2) Bathe, K.J., Zhang, H. and Wang, M.H. (1995) Finite element analysis of incompressible and compressible fluid flows with free 23) Papazoglou, A. J. and Elnashai, A. S. (1996) Analytical and field surfaces and structural interactions. Computers & Structures, 56, evidence of the damaging effect of vertical earthquake ground pp.193-213. motion. Earthquake Engineering and Structural Dynamics, 25(10): 3) Chalhoub, M.S and Kelly, J.M. (1990) Shake table test of pp.1109-1137. cylindrical water tanks in base-isolated structures, Journal of 24) Rugonyi, S. and Bathe, K.J. (2001) On finite element analysis of Engineering Mechanics, 116 (7), pp.1451-1472. fluid flows fully coupled with structural interaction. Computational 4) Chen, H.C. and Taylor, R.L. (1990) Vibration analysis of fluid- Modeling in Engineering Science, 2(2), pp.195-212. solid systems using a finite element displacement formulation. 25) Shrimali, M.K. and Jangid, R.S. (2002a) Non-linear seismic International Journal for Numerical Methods in Engineering, 29, response of base-isolated liquid storage tanks to bi-directional pp.683-698. excitation. Nuclear Engineering & Design, 217, pp.1-20. 5) Cheng, X.S. (2009) Liquid-solid coupling vibration of reinforced 26) Shrimali, M.K. and Jangid, R.S. (2002b) Seismic response of concrete rectangular liquid-storage tanks. Journal of China Coal liquid storage tanks isolated by sliding bearings. Engineering Society, 34(3), pp.340-344. Structure, 24, pp.909-921. 6) Cheng, X.S. and Du, Y.F. (2006) Confirm of elasticity coefficient 27) Shao, P.C. (2002) Post-quake condominium reconstruction for about orthotropic plates of reinforced concrete. Sichuan Build Taiwan Chi-Chi earthquake in 1999. Journal of Asian Architecture Science, 32(5), pp.30-33. and Building Engineering, 1(1): 229-236. 7) Cheng, X.S. and Du, Y.F. (2011) Vibration characteristic analysis 28) Wall, W.A., Genkinger, S. and Ramm, E. (2007) A strong coupling of rectangular liquid-storage structures considering liquid-solid partitioned approach for fluid-structure interaction with free coupling on elastic foundation. Engineering Mechanics, 28(2), surfaces. Computers & Fluids, 36, pp.169-183. pp.186-192. 29) Wang, C.C. and Lei, X.G. (2011). Nonlinear seismic response 8) Cho, K.H., Kim, M.K., Lim, Y.M., et al. (2004) Seismic response analysis of liquid storage tanks considering liquid-solid coupling. of base-isolated liquid storage tanks considering fluid-structure- Journal of Institute of Disaster Prevention, 13(1), pp.19-22. soil interaction in time domain. Soil Dynamics and Earthquake 30) Wang, Y.P., Teng, M.C. and Chung K.W. (2001) Seismic isolation Engineering, 24, pp.839-852. of rigid cylindrical tanks using friction pendulum bearings, 9) Du, Y.F., Shi, X.Y. and Cheng, X.S. (2008a) Dynamic analysis Earthquake Engineering and Structure Dynamics, 30, pp.1083- of reinforced concrete rectangular liquid storage structures considering liquid-structure interaction. Northwestern 31) Westergaard, H.M. (1933) Water pressures on dams during Seismological Journal, 3(1), pp.21-26. earthquakes. Transactions of the American Society of Civil 10) Du, Y.F., Shi, X.Y. and Cheng, X.S. (2008b) The liquid-solid Engineers, 98, pp.418-433. coupling frequency domain analysis of the reinforced concrete 32) Zhu, F. (1991) Orthogonality of wet modes in coupled vibration. rectangular liquid-storage structure. Special Structure, 25(3), Journal of sound and Vibration, 146, pp.439-448. pp.65-68. 33) Zhu, F. (1994) Rayleigh quotients for coupled vibrations. Journal 11) Geer, T.L. (1971) Residual potential and approximation methods of Sound and Vibration, 171, pp.64l-649. for three-dimensional fluid-structure interaction problems. The 34) Zienkiewicz, O.C. and Bettes, P. (1978) Fluid-structure dynamic Journal of the Acoustical Society of America, 49, pp.1505-1510. interaction and wave force: An introduction to numerical 12) Hoskin, L.M. and Jacobsen, L.S. (1934) Water pressure in a tank treatment. International Journal for Numerical Methods in caused by a simulated earthquake. Bulletin of the seismological Engineering, 13, pp.1-16. society of America, 24(1), pp.1-32. 180 JAABE vol.14 no.1 January 2015 Xuansheng Cheng http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Asian Architecture and Building Engineering Taylor & Francis

Liquid-solid Interaction Seismic Response of an Isolated Overground Rectangular Reinforced-concrete Liquid-storage Structure

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Abstract

In this paper, the liquid-solid interaction dynamic finite element integral models of a reinforced-concrete rectangular liquid-storage structure are established to obtain the liquid-solid interaction seismic response of an isolated overground rectangular reinforced-concrete liquid-storage structure. It is assumed that the liquid is incompressible and the influence of gravity wave on the surface of liquid is considered. Some mechanical properties, such as the liquid sloshing height, wallboard displacement and equivalent stress under seismic action and the seismic response under different liquid level of the single cell liquid-storage structure, are discussed, by considering factors of the nonlinear dynamic characteristic, element selection, seismic input, mesh density, convergence and liquid-solid interaction. The results of numerical examples indicate that: the peak displacements of the isolated structure under different earthquake intensities are basically the same, the displacement of the wallboard and stress increase with the increase of seismic intensity, and the lower the level of the liquid is, the less the amount of liquid is and the greater the shaking amplitude is, the greater the stress and displacement of the wallboard are. Keywords: earthquake; seismic isolation; reinforced concrete; rectangular liquid-storage structure; fluid-solid interaction 1. Introduction storage tank with FEM. Liu et al. (2006) studied the Researchers have carried out a long-term and gravitational wave phenomenon in the rectangular unremitting study on the seismic design of reinforced- elastic shell-fluid coupling system. concrete liquid-storage structures from the 1930s. Zienkiewicz and Bettes (1978) presented numerical Although some more mature research results have been treatment under fluid-structure dynamic interaction obtained, many unsolved problems still remain. and wave force. Geer (1971) studied the residual Westergaard (1933) first proposed the liquid-solid potential and approximation methods concerning the coupling vibration problem in his famous essay. three-dimensional fluid-structure interaction problem. Hosking and Jacobsen (1934) analyzed the dynamic Chen and Taylor (1990) studied the displacement water pressure problem of a rigid tank under seismic method for the vibration analysis of coupled fluid- load. Many scholars throughout the world have further structure systems. Jenings et al. (Jenings, 1985; Bathe researched the liquid-solid coupling vibration problem et al., 1995; Bathe et al., 1999; Rugonyi and Bathe, on the basis of Hosking's work, and great achievements 2001) conducted numerical simulations concerning have been made. Housner (1957) thought that the liquid-solid coupling problems. Cheng et al. (Cheng, dynamic liquid effect of a rigid liquid-storage structure 2009; Wall et al., 2007; Du et al., 2008a;, Du et al., was composed of the pulsating component and the 2008b; Wang and Lei, 2011; Cheng and Du, 2011) convective component, and conducted a numerical theoretically studied the vibrating characteristics of simulation of the water sloshing effect with a spring- the liquid-solid coupling problem. Zhu (1991, 2011) mass system (Housner, 1959). Liu and Wang (2005) studied Rayleigh quotients and the orhogonality of wet conducted seismic analysis of a rectangular liquid- modes in coupled vibrations. Shrimali and Jangid (2002a, 2002b) studied non- linear seismic response regarding isolated liquid *Contact Author: Xuansheng Cheng, Professor, storage tanks under bi-directional excitation, but the School of Civil Engineering, Lanzhou University of Technology, structure involved was circular, and the nonlinearity No. 287 Langongping Road, Lanzhou 730050, China of concrete and the influence of the gravity wave Tel: +86-931-2973784 Fax: +86-931-2976327 were not considered. Mustafa (2005) analyzed the E-mail: chengxuansheng@gmail.com sloshing Characteristic in Liquid-Filled Containers ( Received April 3, 2014 ; accepted October 15, 2014 ) Journal of Asian Architecture and Building Engineering/January 2015/180 175 using FEM. Malhotra (1997) proposed a new method 2.2 Selection of Seismic Wave of seismic isolation concerning liquid-storage tanks. The Northridge wave (Shao, 2002; Papazoglou and Chalhoub et al. (Chalhoub and Kelly, 1990; Cho et Elnashai, 1996) is shown in Fig.2. Frequent earthquake al., 2004; Kim and Lee, 1995; Wang et al., 2001; and rare earthquake are considered. F requent Kim et al., 2002) studied the seismic performance of earthquake is the transcendental probability of an base-isolated liquid storage tanks. So in this paper, earthquake intensity value of 63%, and rare earthquake ADINA software is applied to establish the liquid-solid is the transcendental probability of an earthquake interaction dynamic finite element integral models of intensity value of about 2%-3% in a design reference the isolated reinforced-concrete rectangular liquid- period of 50 years. storage structure; by considering the factors of the nonlinear dynamic characteristic, element selection, seismic input, grid density, convergence and liquid- solid interaction, the liquid sloshing height, wallboard displacement and equivalent stress under seismic action, also the seismic response under different levels of liquid of the single cell liquid-storage structure, are discussed. 2. FEM Model Fig.2. Northridge Wave 2.1 Model Diagram Fig. 2 Northridge Wave Assuming that the size of the reinforced-concrete 2.3 Concrete Constitutive Model rectangular liquid-storage structure is a×b×h=4 m x Some modification was carried out by Sargin on the 4 m x 4 m, and the thickness of the wallboard and concrete constitutive model (Lv et al., 1999) suggested bottom board is 0.2 m. The model is shown as Fig.1. by Saenz, namely    FF   2   12    00     kf 3 c 2    12  F  F   12   0  0  where F =E /E , E and E are the tangent modulus 1 0 s 0 s    10 2 and the secant modulus through the coordinate origin, EE  E 1  1   1.04E 3.1 10 N/m    x y c sx c respectively; and are the strain and stress of ε σ    c   concrete respectively; and are the ultimate strain (a) Plan ε σ 0 0 and ultimate stress of concrete respectively; f is the 1  -1 c 10 2 E EE 1.0 3.010 N/m compressive strength of concrete; k is the strength z c c 1  1-  -1 influence coefficient of lateral restraint, and F is the parameter of the decline segment (shown in Fig.3.). For convenience of calculation, an elastic-plastic  z 1-  1- material is used.   c 10 2 GG G 1.0G 1.210 N/m yx xy  c c  G 01  1- 1-    c 1.0 (b) Profile        - F =0.0. 5 2   xy yx c y s c Fig. 1 Model Diagram F =0.5 Fig.1. Model Diagram 2 F =0.0 The density of the reinforced concrete is 2500 kg/ 3  m , and the height of water is 3/4 of the wallboard 1.0 height. The 3D model of the reinforced-concrete rectangular liquid-storage structure is produced with Fig.3. Concrete Constitutive Model Fig. 3 Concrete Constitutive Model the fluid-structure interaction function in ADINA, and the rubber pad, which is an isolation layer, is set at the 2.4 Determination of the Elastic Constants bottom. The rebar of the rectangular liquid-storage structure is usually double layered and in two directions 176 JAABE vol.14 no.1 January 2015 Xuansheng Cheng        DISPLACEMENT MAXIMUM MAGNITUDE Δ 1.205E-05 TIME 17.90 NODE 4392 MINIMUM DISPLACEMENT MAXIMUM * 0.000 MAGNITUDE Δ 1.205E-05 NODE 463 TIME 17.90 NODE 4392 1.170E-05 MINIMUM 9.900E-06 DISPLACEMENT MAXIMUM * 0.000 8.100E-06 MAGNITUDE Δ 1.205E-05 NODE 463 6.300E-06 TIME 17.90 NODE 4392 1.170E-05 4.500E-06 MINIMUM 9.900E-06 DISPLACEMENT MAXIMUM 2.700E-06 * 0.000 according to a certain gap, and is evenly distributed. 8.100E-06 2 MAGNI 9.000E TUDE -07 Δ 1.205E-05 NODE 463 6.300E-06 TIME 17.90 NODE 4392    1.170E-05 f is 30 MPa, and the strength of the rebar is 335 MPa. 4.500E-06 MINIMUM 9.900E-06 FF   2   2.700E-06 12   * 0.000 8.100E-06 The reinforcement ratio in both x- and y-directions is  9.000E-07 NODE 463 00   6.300E-06 1.170E-05   kf 4.500E-06 3 c an economic reinforcement ratio 2 of 1%. The elastic 9.900E-06 2.700E-06    8. a) 100E 7--d 06eg ree of frequent earthquake 9.000E-07 modulus, shear modulus and Poisson's ratio are shown 12  F  F 6.300E-06     4.500E-06  as follows (Cheng and Du, 2006): 0 0   2.700E-06 a) 7-degree of frequent earthquake DISPLACEMENT MAXIMUM 9.000E-07 MAGNITUDE Δ 1.205E-05 TIME 17.90 NODE 4392    E 10 2 MINIMUM a) 7-degree of frequent earthquake EE  E 1  1   1.04E 3.1 10 N/m DISPLACEMENT MAXIMUM   x y c  sx c * 0.000 MAGNITUDE Δ 1.205E-05 a) 7-degree of frequent earthquake   NODE 463  c   TIME 17.90 NODE 4392 1.170E-05 MINIMUM a) 7-degree of frequent earthquake 9.900E-06 DISPLACEMENT MAXIMUM * 0.000 8.100E-06 1  -1 MAGNITUDE Δ 1.205E-05   NODE 463 10 2 6.300E-06 TIME 17.90 NODE 4392 E EE 1.0 3.010 N/m 1.170E-05 z c c 4.500E-06 MINIMUM 9.900E-06 DISPLACEMENT MAXIMUM 1  1-  -1 2.700E-06   * 0.000   8.100E-06 MAGNITUDE Δ 1.205E-05 9.000E-07 NODE 463 6.300E-06 TIME 17.90 NODE 4392 1.170E-05 4.500E-06 MINIMUM 9.900E-06 2.700E-06 * 0.000  G 8.100E-06 9.000E-07 NODE 463 1-  1-  6.300E-06 1.170E-05 G 4.500E-06  c 10 2 9.900E-06 GG G 1.0G 1.210 N/m 2.700E-06 yx xy c c 8.100E-06 9.000E-07  G b) 8-degree of frequent earthquake s 6.300E-06 1  1- 1-   4.500E-06  c 2.700E-06 9.000E-07 b) 8-degree of frequent earthquake DISPLACEMENT MAXIMUM b) 8-degree of frequent earthquake MAGNITUDE Δ 1.205E-05 TIME 17.90 NODE 4392        - 0.2   xy yx c y s c MINIMUM b) 8-degree of frequent earthquake DISPLACEMENT MAXIMUM * 0.000 MAGNITUDE Δ 1.205E-05 NODE 463 TIME 17.90 NODE 4392 where, G and G are shear moduli; E , E and E 1.170E-05 xy yx x y z MINIMUM b9. ) 900E 8-d -06 eg ree of frequent earthquake DISPLACEMENT MAXIMUM * 0.000 are the elastic moduli in the x-, y- and z-directions 8.100E-06 MAGNITUDE Δ 1.205E-05 NODE 463 6.300E-06 TIME 17.90 NODE 4392 1.170E-05 respectively; µ and µ are Poisson ratios; is the 4.500E-06 ρ MINIMUM xy yx 9.900E-06 DISP2. LA 700E CEMEN -06 T MAXIMUM * 0.000 8.100E-06 MAGNI 9.000E TUDE -07 Δ 1.205E-05 reinforcement ratio of the wallboard and bottom plate; NODE 463 6.300E-06 TIME 17.90 NODE 4392 1.170E-05 4.500E-06 MINIMUM E and E are the elastic moduli of concrete and rebar 9.900E-06 c s 2.700E-06 * 0.000 8.100E-06 9.000E-07 NODE 463 6.300E-06 respectively; α = E /E is the ratio of the elastic moduli s c 1.170E-05 4.500E-06 9.900E-06 of rebar and concrete. It is assumed that the liquid is 2.700E-06 8.100E-06 9.000E-07 c) 9-degree of frequent earthquake 6.300E-06 the potential fluid with a bulk modulus of 2.3 x l0 Pa. c) 9-degree of frequent earthquake 4.500E-06 2.700E-06 2.5 Boundary Conditions and Meshing DISPLACEMENT MAXIMUM 9.000E-07 c) 9-degree of frequent earthquake MAGNITUDE Δ 1.205E-05 The bottom is fixed to the isolation layer, and the TIME 17.90 NODE 4392 MINIMUM DISPLACEMENT MAXIMUM influence of the gravity wave on the surface of the c) 9-d* eg 0.000 ree of frequent earthquake MAGNITUDE Δ 1.205E-05 NODE 463 TIME 17.90 NODE 4392 liquid is considered. However, the compressibility 1.170E-05 MINIMUM 9.900E-06 DISPLACEMENT MAXIMUM * 0.000 of the liquid is not considered. The structure and c) 9-degree of frequent earthquake 8.100E-06 MAGNITUDE Δ 1.205E-05 NODE 463 6.300E-06 TIME 17.90 NODE 4392 1.170E-05 the liquid are considered as 3D-solid and 3D-fluid 4.500E-06 MINIMUM 9.900E-06 DISPLACEMENT MAXIMUM 2.700E-06 * 0.000 8.100E-06 elements respectively. MAGNITUDE Δ 1.205E-05 9.000E-07 NODE 463 6.300E-06 TIME 17.90 NODE 4392 1.170E-05 4.500E-06 Meshing of the solid domain and liquid domain MINIMUM 9.900E-06 2.700E-06 * 0.000 8.100E-06 9.000E-07 is uniform. Due to the regular shape, the length of NODE 463 6.300E-06 1.170E-05 4.500E-06 DISPLACEMENT MAXIMUM d) 7-degree of rare earthquake 9.900E-06 the grid in both the horizontal direction and vertical 2.700E-06 MAGNITUDE Δ 1.888E-05 8.100E-06 9.000E-07 TIME 17.90 NODE 980 6.300E-06 direction is 0.2m. The meshing is shown in Fig.4. DISPLACd EMEN ) 7-T MA degr Xee IM U o M f rare earthquake MINIMUM 4.500E-06 MAGNITUDE Δ 1.888E-05 * 0.000 2.700E-06 TIME 17.90 NNODE ODE 980 46 3 9.000E-07 1.733E-05 M INIMUM d) 7-degree of rare earthquake 1.467E-0* 5 0. 000 1.200E-05NODE 463 9. 1.333 733E E--06 05 d) 7-degree of rare earthquake 6. 1.667 467E E--06 05 4. 1.0 200 00E E--06 05 1.333E-07 9.333E-06 6.667E-06 d) 7-degree of rare earthquake 4.000E-06 1.333E-07 e) 8-degree of rare earthquake e) 8-degree of rare earthquake DISPLACEMENT MAXIMUM e) 8-degree of rare earthquake Fig. 4 Schematic Diagram of Grid Division MAGNITUDE Δ 1.888E-05 Fig.4. Schematic Diagram of Grid Division TIME 17.90 NODE 980 MINIMUM DISPLACEMENT MAXIMUM * 0.000 MAGNITUDE Δ 1.888E-05 NODE 463 3. Numerical Simulation TIME 17.90 NODE 980 1.733E-05 MINIMUM 1.467E-05 3.1 Liquid Sloshing Height * 0.000 1.200E-05 NODE 463 9.333E-06 The seismic responses of the reinforced-concrete 1.733E-05 6.667E-06 1.467E-05 4.000E-06 rectangular liquid-storage structure under the 1.200E-05 1.333E-07 9.333E-06 Northridge wave with frequency seismic intensities of 6.667E-06 4.000E-06 7-, 8- and 9-degree of frequent earthquake, as well as 1.333E-07 7-, 8- and 9-degree of rare earthquake, are shown in f) 9-degree of rare earthquake Fig.5. Fig.5. Displacement Graph under the Northridge Wave f) 9-degree of rare earthquake Fig. 5. Displacement Graph under the Northridge Wave f) 9-degree of rare earthquake Fig. 5. Displacement Graph under the Northridge Wave JAABE vol.14 no.1 January 2015 Xuansheng Cheng 177        DISPLACEMENT MAXIMUM M DIA SGNI PLAT CUDE EMEN T MA Δ 6.831 XE IM -0U 6 M T M IA ME GNI 17. T90 UDE NO DΔ E 6. 979 831 (E 6. -85 066E -06) TIME 17.90 N M OINI DE M 979 UM ( 6.856E-06) * M 0. INI 000 M UM * 0. NODE 000 461 6.500E-06NODE 461 5. 6.500 500E E- -0 06 6 4. 5.500 500E E- -0 06 6 3. 4.500 500E E- -06 06 2. 3.500 500E E- -06 06 1. 2.500 500E E- -06 06 5. 1.000 500E E- -07 06 5.000E-07 a) 7-degree of frequent earthquake a) 7-degree of frequent earthquake DISPLACEMENT MAXIMUM DISPLACEMENT MAXIMUM MAGNITUDE Δ7.043E-06 MAGNITUDE Δ7.043E-06 TIME 17.90 NODE 979 (7.029E-06) TIME 17.90 NODE 979 (7.029E-06) MINIMUM MINIMUM * 0.000 * 0. NOD 000 E 46 1 6.300E-06NOD E 461 5. 6.400 300E E- -0 06 6 4. 5.500 400E E- -0 06 6 3. 4.600 500E E- -06 06 2. 3.700 600E E- -06 06 1. 2.800 700E E- -06 06 9. 1.000 800E E- -07 06 9.000E-07 b) 8-degree of frequent earthquake b) 8-degree of frequent earthquake DISPLACEMENT MAXIMUM M DIA SGNI PLAT CUDE EMEN T MA Δ7.815 XE IM -06 U M It can be observed from Fig.5. that the peak liquid T M IA ME GNI 17. T90 UDE NO DΔ E 7.979 815 ( E 7. -0 73 6 6E-06) TIME 17.90 N M OINI DE M 979 UM ( 7.736E-06) sloshing displacement appears in Node 4372 with * M 0. INI 000 M UM * 0. NODE 000 461 frequent seismic intensities of 7-, 8- and 9-degree 7.000E-06NODE 461 6. 7.000 000E E- -0 06 6 of frequent earthquake, as well as 7-degree of rare 5. 6.000 000E E- -0 06 6 4. 5.000 000E E- -06 06 earthquake, and the liquid sloshing height, which is 3. 4.000 000E E- -06 06 -5 2. 3.000 000E E- -06 06 1.205 x 10 m, does not increase with the increase 1. 2.000 000E E- -0 06 6 1.000E-06 of seismic intensity. However, a peak liquid sloshing -5 displacement, which is 1.888 x 10 m, appears in Node 980 with seismic intensity of the rare 9-degree. The c) 9-degree of frequent earthquake c) 9-degree of frequent earthquake extreme liquid sloshing height is shown in Table 1. c) 9-degree of frequent earthquake DISPLACEMENT MAXIMUM Table 1. Displacement of the Liquid Sloshing Height (m) M DIA SGNI PLAT CUDE EMEN T MA Δ9.125 XE IM -06 U M T M IA ME GNI 17. T90 UDE NO DΔ E 9.979 125 E (8. -0 99 6 2E-06) TIME 17.90 N M OINI DE M 979 UM ( 8.992E-06) Frequent Earthquake * M 0. INI 000 M UM * 0. NODE 000 461 7-degree 8-degree 9-degree 8.400E-06NODE 461 7. 8.200 400E E- -0 06 6 -5 -5 -5 6. 7.000 200E E- -0 06 6 1.205 x 10 1.205 x 10 1.205 x 10 4. 6.800 000E E- -06 06 3. 4.600 800E E- -06 06 Rare Earthquake 2. 3.400 600E E- -06 06 1. 2.200 400E E- -0 06 6 1.200E-06 7-degree 8-degree 9-degree -5 -5 -5 1.205 x 10 1.888 x 10 7.733 x 10 d) 7-degree of rare earthquake It can be observed from Table 1. that the extreme DISPLACEMENT MAXIMUM d) 7-degree of rare earthquake MAGNITUDE Δ1.863E-05 d) 7-degree of rare earthquake liquid sloshing heights are basically the same under T DIIME SPLA 17. C90 EMEN NOD T MA E 979 X I(M 1.U 84 M 1E -05) MAGNITUDE Δ1.863E-05 MINIMUM frequent earthquake, and increase with earthquake TIME 17.90 NODE 979 (1.841E-05) * 0.000 MINIMUM NODE 461 intensity under rare earthquake. * 0.000 1.733E-05 NODE 461 1.467E-05 3.2 Wallboard Displacement 1.733E-05 1.200E-05 1.467E-05 9.333E-06 The seismic responses of the reinforced-concrete 1.200E-05 6.667 E-06 9.333E-06 4.000E-06 rectangular liquid-storage structure under the 6.667 E-06 1.333E-06 4.000E-06 Northridge earthquake wave with frequency seismic 1.333E-06 intensities of 7-, 8- and 9-degree of frequent earthquake e) 8-egree of rare earthquake e) 8-egree of rare earthquake as well as 7-, 8- and 9-degree of rare earthquake are e) 8-egree of rare earthquake shown in Fig.6. The extreme wallboard displacements DISPLACEMENT MAXIMUM M DIA SGNI PLAT CUDE EMEN T MA Δ7.698 XIE M -0 U 5 M at x=1.9 m of the isolated liquid-storage structure T M IME AGNI 17. TUDE 90 N O DΔE 7.698 979E (-7. 05 67 5E-05) TIME 17.90 N M OINI DE M 979 UM (7. 675E-05) under the seismic load with 7-, 8- and 9-degree of MINIMUM * 0.000 * 0.000 NODE 461 frequent earthquake, as well as 7-, 8- and 9-degree of NODE 461 7.000E-05 7.000E-05 6.000E-05 rare earthquake are shown in Table 2. 6.000E-05 DISPLACEMENT MAXIMUM 5.000E-05 5.000E-05 MAGNITUDE Δ 6.831E-06 4.000E-06 4.000E-06 TIME 17.90 NODE 979 (6.856E-06) 3.000 E-06 DISPLACEMENT MAXIMUM 3.000 E-06 MINIMUM 2.000E-06 MAGNITUDE Δ 6.831E-06 2.000E-06 * 0.000 1.000E-06 TIME 17.90 NODE 979 (6.856E-06) 1.000E-06 NODE 461 MINIMUM 6.500E-06 * 0.000 5.500E-06 NODE 461 4.500E-06 6.500E-06 f) 9-degree of rare earthquake 3.500E-06 5.500E-06 2.500E-06 f) 9-degree of rare earthquake 4.500E-06 f) 9-degree of rare earthquake 1.500E-06 3.500E-06 Fig.6. Wallboard Displacement Graph at x=1.9 under the 5.000E-07 2.500E-06 FiF g. ig. 6 .6 W . W alal lblo bar oar dd D D isp isp lac lac ee m meen nt t G Grrap aph h at at x x=1 =1..9 u 9 unde nde rr t he the N N oo rtrhr thr idg idg e e W W avav e e 1.500E-06 Northridge Wave 5.000E-07 Table 2. Wallboard Displacement at x=1.9m (m) Frequent Earthquake a) 7-degree of frequent earthquake a) 7-degree of frequent earthquake 7-degree 8-degree 9-degree a) 7-degree of frequent earthquake DISPLACEMENT MAXIMUM -6 -6 -6 6.831 x 10 7.043 x 10 7.815 x 10 MAGNITUDE Δ7.043E-06 TIME 17.90 NODE 979 (7.029E-06) DISPLACEMENT MAXIMUM MINIMUM MAGNITUDE Δ7.043E-06 Rare Earthquake TIME 17.90 N *O 0. D 000 E 979 (7.029E-06) M NOD INIM E 46 UM1 7-degree 8-degree 9-degree 6.300E-0* 6 0. 000 5.400E-06NOD E 461 -6 -6 -6 4. 6.500 300E E- -0 06 6 9.125 x 10 1.865 x 10 7.698 x 10 3. 5.600 400E E- -0 06 6 2. 4.700 500E E- -0 06 6 1. 3.800 600E E- -06 06 It can be observed from Table 2. that the peak 9. 2.000 700E E- -06 07 1.800E-06 wallboard displacement of the isolated liquid-storage 9.000E-07 st ruc t ure i nc re a se s wi t h t he i nc re a se of se i sm i c b) 8-degree of frequent earthquake intensity. b) 8-degree of frequent earthquake b) 8-degree of frequent earthquake DISPLACEMENT MAXIMUM MAGNITUDE Δ7.815E-06 DISPLACEMENT MAXIMUM TIME 17.90 NODE 979 (7.736E-06) MAGNITUDE Δ7.815E-06 MINIMUM TIME 17.90 NODE 979 (7.736E-06) * 0.000 MINIMUM NODE 461 * 0.000 7.000E-06 NODE 461 6.000E-06 7.000E-06 5.000E-06 178 JAABE vol.14 no.1 January 2015 Xuansheng Cheng 6.000E-06 4.000E-06 5.000E-06 3.000E-06 4.000E-06 2.000E-06 3.000E-06 1.000E-06 2.000E-06 1.000E-06 c) 9-degree of frequent earthquake c) 9-degree of frequent earthquake DISPLACEMENT MAXIMUM MAGNITUDE Δ9.125E-06 DISPLACEMENT MAXIMUM TIME 17.90 NODE 979 (8.992E-06) MAGNITUDE Δ9.125E-06 MINIMUM TIME 17.90 NODE 979 (8.992E-06) * 0.000 MINIMUM NODE 461 * 0.000 8.400E-06 NODE 461 7.200E-06 8.400E-06 6.000E-06 7.200E-06 4.800E-06 6.000E-06 3.600E-06 4.800E-06 2.400E-06 3.600E-06 1.200E-06 2.400E-06 1.200E-06 d) 7-degree of rare earthquake d) 7-degree of rare earthquake SMOOTHED MAXIMUM 3.3 Distribution of Equivalent Stress EFFECTIVE The seismic responses of the reinforced-concrete STRESS Δ269975 RST CALC MINIMUM rectangular liquid-storage structure under the TIME 17.90 * 4347 Northridge earthquake wave with 7-, 8- and 9-degree of frequent earthquake as well as 7-, 8- and 9-degree of rare earthquake are shown in Fig.7. SMOOTHED MAXIMUM EFFECTIVE SMOOTHED MAXIMUM STRESS Δ99493 EFFECTIVE RST CALC MINIMUM S ST MOO RESS TH ED MAΔ99493 XIMU M f) 9-degree of rare earthquake f) 9-degree of rare earthquake TIME 17.90 * 203.8 EFFECTIVE RST CALC MINIMUM T ST IME RS EMOO SS 17. 90 TH * EDΔ99493 MA 203.X 8 I MUM 97500 SMOO THED MAXIMUM RST EF CA FLC EC MI TIVE N IMUM Fig. 7. Equivalent Stress under the Northridge Wave Fig.7. Equivalent Stress under the Northridge Wave 82500 EFFEC TIVE TIME S 97500 T 17. RE90 SS * 203. Δ99493 8 67500 STRE SS Δ99493 RST CALC MINIMUM 5R2500 ST C ALC MINIMUM T 67500 97500 IME 17. 90 * 203.8 The equivalent stresses of the isolated liquid-storage 37500 TIME 17.90 * 203.8 37500 67500 97500 under the seismic load with 7-, 8- and 9-degree of 7500 97500 52500 82500 82500 frequent earthquake as well as 7-, 8- and 9-degree of 7500 37500 67500 22500 52500 rare earthquake are shown in Table 3. a) 7-degree of frequent earthquake a) 7-degree of frequent earthquake a) 7-degree of frequent earthquake Table 3. Stress Values SMOOTHED MAXIMUM a) 7-degree of frequent earthquake EFFECTIVE SMOOTHED MAXIMUM Frequent Earthquake STRESS Δ99765 EFFECTIVE a) 7-degree of frequent earthquake RST CALC MINIMUM S ST MOO RESS TH ED MAΔ99765 XIMU M a) 7-degree of frequent earthquake TIME 17.90 * 354.8 7-degree 8-degree 9-degree R EFSF T EC CA TLC IVE MI NIMUM T ST IME RS EMOO SS 17. 90 TH * EDΔ99765 MA 354.X 8 I MUM EF 97500 SMOO FEC T TIH VED E MA XIMUM RST CALC MI NIMUM 99493 99765 100316 82500 EFFEC TIVE TIME S 97500 T 17. RE90 SS * 354. Δ99765 8 R 67500 SSTT RC E SS ALC MI Δ99765 NIMU M Rare Earthquake 52500 RST C ALC MINIMUM T 67500 97500 IME 17. 90 * 354.8 37500 TIME 17.90 * 354.8 52500 82500 7-degree 8-degree 9-degree 37500 67500 97500 750082500 97500 22500 52500 7500 37500 67500 165964 166925 269775 52500 67500 22500b ) 8-degree of frequent earthquake b) 8-degree of frequent earthquake 22500 37500 b) 8-degree of frequent earthquake SMOOTHED MAXIMUM 22500 It can be observed from Fig.7. and Table 3. that the EFFECTIV b E) 8 -degree of frequent earthquake SMOOTHED MAXIMUM STRESS Δ100316 EFFECTIVE equivalent stress of the isolated liquid-storage structure b) 8-degree of frequent earthquake RST CALC MINIMUM SMOOTHED MAXIMUM STRESS Δ100316 b) 8-degree of frequent earthquake TIME 17.90 *761.5 R EFSF T EC CA TLC IVE MI NIMUM increases with the increase of seismic intensity. S TT IME RS EMOO SS 17. 90 TH * EDΔ100316 MA 761.5 X I MUM 97500 SMOO THED MAXIMUM 3.4 Seismic Response of Different Liquid Level R ST EF CA FLC EC MI TI VE N IMUM 82500 EFFEC TIVE TIME ST 17. RE90 SS *761.Δ100316 5 2 A peak value of 0.70m/s is applied in the x-direction 67500 STRE SS Δ100316 R 82500 ST C ALC MI NIMUM 52500 RST C ALC MINIMUM T 97500 IME 17. 90 *761.5 of the reinforced-concrete rectangular liquid-storage 37500 TIME 17.90 *761.5 82500 52500 67500 37500 97500 structure, and a peak value of 0.45m/s is applied in the 7500 97500 52500 22500 82500 37500 67500 y-direction. The results are shown in Table 4. below. 22500 52500 c) 9-degree of frequent earthquake c) 9-degree of frequent earthquake 22500 Table 4. Seismic Responses under Different Liquid Levels SMOOTHED MAXIMUM EFFECTIVE SMOOTHED MAXIMUM c) 9-degree of frequent earthquake STRESS Δ165964 Liquid Wave Wallboard Stress c) 9-degree of frequent earthquake EFFECTIVE RST CALC MINIMUM S ST MOO RESS TH ED MA Δ X 16596 IMUM 4 c) 9-degree of frequent earthquake Level (m) Height (m) Displacement (m) (Pa) TIME 17.90 *5.652E-05 EFFECTIVE c) 9-degree of frequent earthquake RST CALC MINIMUM T ST IME RS EMOO SS 17. 90 TH * ED Δ MA 5. 16596 652E XI4 MU -05 M -5 -6 156000 SMOOT HED MAXIMUM 3 1.249 x 10 6.766 x 10 163017 RST EF CA FLC EC MI TIVE N IMUM 132000 EFFEC TIVE TIME S 156000 T 17. RE90 SS *5.652E Δ16596 -05 4 -5 -6 108000 STRESS Δ165964 RST CALC MI NIMUM 2 1.875 x 10 7.207 x 10 422277 84000 RST C ALC MINIMUM T 108000 156000 IME 17. 90 *5.652E-05 -1 -1 60000 TIME 17.90 *5.652E-05 1 2. 217 x 10 1.277 x 10 2139402 60000 108000 156000 12000 156000 84000 132000 12000 60000 108000 It can be observed from Table 4. that the seismic 36000 84000 12000 60000 response of the isolated liquid-storage structure under d) 7-degree of rare earthquake the same seismic load is influenced by the liquid d) 7-degree of rare earthquake SMOOTHED MAXIMUM level. The lower the level of the liquid and the less the EFFECTIVE SMOOTHED MAXIMUM d) 7-degree of rare earthquake volume of the liquid, the greater the shaking amplitude, STRESS Δ166925 EFFECTIVE RST CALC MINIMUM SMOOTHED MAXIMUM d) 7-degree of rare earthquake STRESS Δ166925 d) 7 -degree of rare earthquake stress, and displacement of the wallboard are. TIME 30 * 5.811E-05 R EFSF T EC CA TLC IVE MI NIMU d) 7 M -degree of rare earthquake STRS EMOO SS THEDΔ166925 MAXI MUM TIME 30 * 5.811E-05 156000 SMOOT HED MAXIMUM RST EF CA FLC EC MI TIVE N IMUM 132000 EFFEC TIVE TIME ST 30 RE SS * 5.81Δ166925 1E-05 4. Conclusions 108000 STRESS Δ166925 R 132000 ST CA LC MINIMUM 84000 RST C ALC MINIMUM T 156000 IME 30 * 5.811E-05 108000 Assuming that the liquid is incompressible, and 60000 TIME 30 * 5.811E-05 84000 132000 108000 156000 considering the influence of gravity wave on the 12000 156000 36000 84000 132000 132000 surface of the liquid, the dynamic finite element 12000 60000 36000 84000 integral model of the isolated reinforced concrete 12000 60000 rectangular liquid-storage structure is established e) 8-degree of rare earthquake using ADINA software. The liquid sloshing height, e) 8-degree of rare earthquake wallboard displacement and equivalent stress under e) 8-degree of rare earthquake earthquake and the seismic response under different e) 8-degree of rare earthquake e) 8-degree of rare earthquake e) 8-degree of rare earthquake JAABE vol.14 no.1 January 2015 Xuansheng Cheng 179 13) Housner, G.W. (1957) Dynamic pressure on accelerated fluid liquid levels of the single cell liquid-storage structure container. Bulletin of the seismological society of America, 47(1), are discussed, the conclusions are as follows: pp.15-35. First, the peak displacements of the isolated liquid- 14) Housner, G.W. (1959). Behavior of structures during earthquake. storage structure under different intensities are Journal of the Engineering Mechanics Division, 85(4), pp.109- basically the same due to the filtering and energy- 129. 15) Jenings, A. (1985) Added mass for fluid-structure vibration consuming function of the isolation cushion. problems. International Journal for Numerical Methods in Second, the wallboard displacement of the isolated Engineering, 5, pp.817-830. liquid-storage structure increases with the increase of 16) Kim, N.S. and Lee, D.G. (1995) Pseudo-dynamic test for seismic intensity. evaluation of seismic performance of base-isolated liquid storage Third, the stress of the isolated liquid-storage tanks. Engineering Structures, 17, pp.198-208. 17) Kim M.K., Lim Y.M., S.Y. Cho, et al. (2002) Seismic analysis of structure increases with the increase of seismic intensity. base-isolated liquid storage tanks using the BE-FE-BE coupling Fourth, the lower the level of the liquid, the greater technique, Soil Dynamics and Earthquake Engineering, 22, the shaking amplitude, stress, and displacement of the pp.1151-1158. wallboard are. 18) Liu, Y.H. and Wang, K.C. (2005) Seismic analysis of liquid storage container. Earthquake Engineering and Engineering Vibration, 25(1), pp.149-154. Acknowledgments 19) Liu, X.J., Zhang, S.X., Liu, G.Y., et al. (2006). The analyses of This paper is a part of the national natural science gravity waves in rectangular elastic fluid-shell coupled system. foundation of China (Grant number: 51368039; Chinese Journal of Theoretical and Applied Mechanics, 38(1), 51478212), and a part of the education ministry pp.106-111. doctoral tutor foundation of China (Grant number: 20) Lv, X.L., Jin, G.F. and Wu, X.H. (1999) Reinforced concrete structural nonlinear finite element theory and application. 20136201110003). Shanghai: Tongji University Press. 21) Malhotra, P.K. (1997) New method for seismic isolation of liquid- References storage tanks. Earthquake Engineering and Structure Dynamics, 1) Bathe, K.J., Zhang, H. and Ji, S. (1999) Finite element analysis of 26, pp.839-847. fluid flows fully coupled with structural interactions. Computers & 22) Mustafa, A. (2005) Finite Element Analysis of Sloshing in Liquid- Structures, 72, pp.1-16. Filled Containers. Journal of Sound and Vibration, 279(2), pp.217- 2) Bathe, K.J., Zhang, H. and Wang, M.H. (1995) Finite element analysis of incompressible and compressible fluid flows with free 23) Papazoglou, A. J. and Elnashai, A. S. (1996) Analytical and field surfaces and structural interactions. Computers & Structures, 56, evidence of the damaging effect of vertical earthquake ground pp.193-213. motion. Earthquake Engineering and Structural Dynamics, 25(10): 3) Chalhoub, M.S and Kelly, J.M. (1990) Shake table test of pp.1109-1137. cylindrical water tanks in base-isolated structures, Journal of 24) Rugonyi, S. and Bathe, K.J. (2001) On finite element analysis of Engineering Mechanics, 116 (7), pp.1451-1472. fluid flows fully coupled with structural interaction. Computational 4) Chen, H.C. and Taylor, R.L. (1990) Vibration analysis of fluid- Modeling in Engineering Science, 2(2), pp.195-212. solid systems using a finite element displacement formulation. 25) Shrimali, M.K. and Jangid, R.S. (2002a) Non-linear seismic International Journal for Numerical Methods in Engineering, 29, response of base-isolated liquid storage tanks to bi-directional pp.683-698. excitation. Nuclear Engineering & Design, 217, pp.1-20. 5) Cheng, X.S. (2009) Liquid-solid coupling vibration of reinforced 26) Shrimali, M.K. and Jangid, R.S. (2002b) Seismic response of concrete rectangular liquid-storage tanks. Journal of China Coal liquid storage tanks isolated by sliding bearings. Engineering Society, 34(3), pp.340-344. Structure, 24, pp.909-921. 6) Cheng, X.S. and Du, Y.F. (2006) Confirm of elasticity coefficient 27) Shao, P.C. (2002) Post-quake condominium reconstruction for about orthotropic plates of reinforced concrete. Sichuan Build Taiwan Chi-Chi earthquake in 1999. Journal of Asian Architecture Science, 32(5), pp.30-33. and Building Engineering, 1(1): 229-236. 7) Cheng, X.S. and Du, Y.F. (2011) Vibration characteristic analysis 28) Wall, W.A., Genkinger, S. and Ramm, E. (2007) A strong coupling of rectangular liquid-storage structures considering liquid-solid partitioned approach for fluid-structure interaction with free coupling on elastic foundation. Engineering Mechanics, 28(2), surfaces. Computers & Fluids, 36, pp.169-183. pp.186-192. 29) Wang, C.C. and Lei, X.G. (2011). Nonlinear seismic response 8) Cho, K.H., Kim, M.K., Lim, Y.M., et al. (2004) Seismic response analysis of liquid storage tanks considering liquid-solid coupling. of base-isolated liquid storage tanks considering fluid-structure- Journal of Institute of Disaster Prevention, 13(1), pp.19-22. soil interaction in time domain. Soil Dynamics and Earthquake 30) Wang, Y.P., Teng, M.C. and Chung K.W. (2001) Seismic isolation Engineering, 24, pp.839-852. of rigid cylindrical tanks using friction pendulum bearings, 9) Du, Y.F., Shi, X.Y. and Cheng, X.S. (2008a) Dynamic analysis Earthquake Engineering and Structure Dynamics, 30, pp.1083- of reinforced concrete rectangular liquid storage structures considering liquid-structure interaction. Northwestern 31) Westergaard, H.M. (1933) Water pressures on dams during Seismological Journal, 3(1), pp.21-26. earthquakes. Transactions of the American Society of Civil 10) Du, Y.F., Shi, X.Y. and Cheng, X.S. (2008b) The liquid-solid Engineers, 98, pp.418-433. coupling frequency domain analysis of the reinforced concrete 32) Zhu, F. (1991) Orthogonality of wet modes in coupled vibration. rectangular liquid-storage structure. Special Structure, 25(3), Journal of sound and Vibration, 146, pp.439-448. pp.65-68. 33) Zhu, F. (1994) Rayleigh quotients for coupled vibrations. Journal 11) Geer, T.L. (1971) Residual potential and approximation methods of Sound and Vibration, 171, pp.64l-649. for three-dimensional fluid-structure interaction problems. The 34) Zienkiewicz, O.C. and Bettes, P. (1978) Fluid-structure dynamic Journal of the Acoustical Society of America, 49, pp.1505-1510. interaction and wave force: An introduction to numerical 12) Hoskin, L.M. and Jacobsen, L.S. (1934) Water pressure in a tank treatment. International Journal for Numerical Methods in caused by a simulated earthquake. Bulletin of the seismological Engineering, 13, pp.1-16. society of America, 24(1), pp.1-32. 180 JAABE vol.14 no.1 January 2015 Xuansheng Cheng

Journal

Journal of Asian Architecture and Building Engineering – Taylor & Francis

Published: Jan 1, 2015

Keywords: earthquake; seismic isolation; reinforced concrete; rectangular liquid-storage structure; fluid-solid interaction

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