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Evaluation of seismic ground motion scaling procedures for linear time-history analysis of liquid storage tanks
Engineering Structures 102 (2015) 266–277
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Evaluation of seismic ground motion scaling procedures for linear time-history analysis of liquid storage tanks Miguel Ormeño ⇑, Tam Larkin, Nawawi Chouw Department of Civil and Environmental Engineering, Faculty of Engineering, The University of Auckland, New Zealand
a r t i c l e
i n f o
Article history: Received 12 November 2014 Revised 17 August 2015 Accepted 17 August 2015
Keywords: Storage tanks Seismic standards ASCE/SEI 7-10 NZS 1170.5 Eurocode 8 Time-history analysis Earthquake record scaling
a b s t r a c t Liquid storage tanks are vital life-line structures, especially following destructive seismic events. However, at present there is no accepted procedure to scale ground motions to perform time-history analysis for these very short period structures. Current standards and design codes e.g. ASCE/SEI 7-10, Eurocode 8 and NZS 1170.5, for conventional structures, e.g. buildings and bridges, minimise in a predefined range of periods the difference between the response spectra of chosen records and the target spectrum. This period range has limits related to the fundamental period of the structure in the excitation direction being considered. However, these design specifications have important differences in their scaling procedures and consequently affect the calculated seismic response of the structure. Additionally, these procedures were not formulated for time-history analysis of liquid storage tanks. This is evident in the case of the restriction imposed by NZS 1170.5 for very stiff structures, which includes most tanks. This restriction leads to reduced structural loading giving non-representative results. The research reported here concerns the seismic response of storage tanks, in terms of base shear, overturning moment and wall stresses, when subjected to scaled ground motions using the procedures of three design specifications. It was found that the Eurocode 8 approach produces the highest seismic response on storage tanks. ASCE/SEI 7-10 gives intermediate results in terms of applied load and seismic response compared to the other two specifications. The study also shows that the restriction imposed by NZS 1170.5 for tanks, produces an underestimate of the seismic load on storage tanks. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Storage tanks are essential structures that provide basic supplies such as water and fuel. It is very important that this kind of structure remain operational after a destructive seismic event to facilitate rapid recovery. Because of the importance of these structures many studies have been carried out [e.g. 1–3] and standards and design guides have been established [4–6] and compared [7]. Yet despite the importance of storage tanks, there is no specific widely accepted procedure for time-history analysis to enable an estimation of the behaviour of storage tanks under a specific seismic excitation. Current design practice only provides seismic coefficients based on a pseudo-dynamic method of assessment. Using this design method it is impossible to see the potential for successive plastic incursions of the structural elements of storage tanks (shell and base plate). It has been shown [8] that such plastic behaviour will lower the impact of earthquake loading whilst imposing ⇑ Corresponding author. E-mail addresses: [email protected] (M. Ormeño), [email protected] (T. Larkin), [email protected] (N. Chouw). http://dx.doi.org/10.1016/j.engstruct.2015.08.024 0141-0296/Ó 2015 Elsevier Ltd. All rights reserved.
ductility requirements. Thus, it is essential to have an appropriate selection criteria and scaling procedure of the ground motions. There are two distinctly different sources of obtaining ground motions for time-history analysis [9]. The first is to use recorded ground motions from databases of previous events [10–12]. The second source is to use ground motions stochastically generated using physical or numerical models [e.g. 13,14]. Standards and codes, e.g. NZS 1170.5 [15], ASCE/SEI 7-10 [16] and Eurocode 8 [17], recommend the use of recorded motions from previous events. However, if there is insufficient recorded data the three design specifications above [15–17] allow the use of supplementary simulated ground motions to make up the total number of records required. All three documents agree in the requirements for choosing the records to be used. The ground motions should have compatible seismological characteristics, i.e. magnitude, distance, fault mechanism and soil conditions, to the tectonics of the region and the site of the structure. Studies have been carried out in a number of locations to obtain ground motions that meet the requirements imposed by standards and codes. Oyarzo-Vera et al. [18] provide a list of ground motions to be used in the North Island of New Zealand for time-history analysis. Iervolino et al. [19]
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and Cooper [20] state the criteria for selecting ground motions for using the Eurocode 8 [17] and ASCE/SEI 7-10 [16] procedures, respectively. Contrary to the criteria for selecting records, where there is agreement between the standards and codes, the scaling procedures to apply to the chosen records differ substantially in important ways. The procedures defined in the three design specifications implemented here specify different period ranges of interest. Over these ranges the chosen record should be matched as close as possible to the target spectrum. To the authors’ knowledge a comparison of the application of the three main design specifications to liquid storage tanks has not been reported. The objectives of the work is to evaluate the consequences of the procedures for the analysis of the seismic performance of liquid storage tanks and to reveal the differences and similarities of the outcomes resulting from application of the specifications. The selection of records for time-history analysis is not part of the scope of this study. However, some important points about the criteria for selecting records are provided in the discussion of the results. 2. Method for scaling records A summary of the three design specifications used in this study is presented below. All three design specifications require the computation of a multiplication factor to apply to the chosen time history to ensure a match to the target spectrum in the period range of interest. However, this factor is computed differently depending on the standard or code considered. 2.1. New Zealand Standard (NZS 1170.5) NZS 1170.5 requires the use a family of at least three pairs of horizontal ground motions recorded in seismic events. The vertical component shall be included when the structure analysed is sensitive to the action of vertical acceleration. The selected events shall have similar seismological characteristics (magnitude, fault mechanism, source-to-site distance and near-surface soil profile) to the characteristics of the events that mainly contributed to the seismic hazard at the site over the period range of interest. When there is insufficient suitable recorded ground motions available for a site, simulated ground motion records may be used to complete the family of records. The period range of interest defined by this standard is between 0.4T1 and 1.3T1, where T1 is the fundamental period of the structure in the direction analysed, but may not be less than 0.4 s. In this range, the records should match the target spectrum as closely as possible by using the multiplication factors, k1 and k2. k1 is known as the record scale factor and is different for each record. k2 is known as the family scale factor and is common to all records in the family. k1 is the value that minimises in a least mean square sense the function defined in Eq. (1) in the period range of interest.
log k1 SAcomponent SAtarget
ð1Þ
where SAcomponent: 5% damped spectrum value of the chosen horizontal component of the record; and SAtarget: corresponding target spectrum value at the same period. In this way, k1 is computed for each horizontal component of the record and the smallest value is chosen as the record scale factor. The component that yields the value of k1 for a pair of horizontal ground motion components is called the principal component. The family scale factor k2 is the maximum of 1.0 and the value computed from Eq. (2):
k2 ¼ SAtarget = maxðSAprincipal Þ
ð2Þ
267
where SAprincipal: 5% damped spectrum of the principal component of the record. In this way, the principal component of at least one record spectrum, scaled by its record scale factor k1, exceeds the target spectrum after application of the family factor k2. Additionally, the following restrictions apply to the scale factors:
0:33 < k1 < 3:0 1:0 < k2 < 1:3 It is important to realise that the minimum value for T1 = 0.4 s imposed by this standard will affect the time-history analysis of the storage tanks analysed. Liquid storage tanks generally have very short fundamental periods, only a few tenths of second [21], and, therefore, their periods are most likely less than 0.4 s. 2.2. U.S.A. Standard (ASCE/SEI 7-10) ASCE/SEI 7-10 requires the use of at least three pairs of ground motions. The selected events shall have magnitudes, fault distance, and source mechanisms consistent with the expected maximum earthquake considered in the analysis. Soil profile similarities are not required explicitly by this standard. Appropriate simulated ground motion pairs can be used to make up the total number of ground motions when the required number of recorded ground motions is not available. The square root of the sum of the squares (SRSS) of the 5% damped response spectrum of each ground motion must be computed from the scaled pair that forms the records. The same scale factor shall apply to both horizontal components, i.e., each pair has a unique scale factor. The scale factor is determined by the criterion that the SRSS of the response spectrum of each pair shall not be less than the target spectrum in the period range of interest defined by ASCE/SEI 7-10. The period range is specified as being between 0.2T1 and 1.5T1, where T1 is the fundamental period of the structure in the direction analysed. When seven or more pairs are used to perform the analysis, the average response will be considered for design purposes. If less than seven ground motions are used, then the maximum response will be considered. 2.3. Eurocode 8 This design specification requires the use of a set at least three pairs, regardless of their origin. The records shall consist of both horizontal components and a vertical component when this is required. The records that make up the set shall be consistent with the magnitude and other relevant features of the seismic event considered. The average of the 5% damped elastic spectrum, calculated from all time histories, should not be less than 90% of the target spectrum in the period range of interest. The period range of interest defined by Eurocode 8 is between 0.2T1 and 2T1, where T1 is the fundamental period of the structure in the direction of application of the motion. It should be noted that this procedure, contrary to the previous two, does not provide a specific method to compute the scale factors for the records. The requirement established by Eurocode 8 can be fulfilled in several ways. Even a single unique scale factor for all the records can be used if the average of the 5% damped elastic spectrum of all time histories meets the requirement. Iervolino et al. [19] realised this issue and proposed additional conditions on choosing ground motions to be utilised for time-history analysis. Katsanos et al. [22], present a complete review of the state of art of the selection of records for timehistory analysis. They confirmed that there is a high variability in
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the spectral acceleration when real unscaled records are used following the procedure give by Eurocode 8. In this study, a different scale factor has been computed for each record and the average of the 5% damped elastic spectrum has been computed from both horizontal components. As an additional requirement, the average spectral acceleration, calculated from the individual time histories, at a period essentially equal to zero has to be larger than the value of the target spectrum at the same period. It is recommended that seven or more ground motions be used and the average response taken for design purposes. If less than seven ground motions are used, then the maximum response should be considered.
rffiffiffiffiffiffiffiffiffi
cl
Eg
ð3Þ
where H = liquid height; kh = period coefficient which depends on the ratio of the height of liquid to tank radius (Fig. 2); cl = unit weight of the liquid; E = Young’s modulus of the tank material; and g = gravitational acceleration. The convective period of vibration, Tc, is computed from Eq. (4) given by [4]:
qffiffi
2 p Rg T c ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1:841 tanh 1:841 HR
ki ¼
T 2i
0.07 0.06 0.05 0.04
0
1
2
3
4
Fig. 2. Period coefficient kh for first horizontal tank-liquid mode, from [4]. Where t = tank wall thickness; and R = mean radius of the tank.
Dimensionless ratio shown
0.8
mi/mt
0.6 0.4
mc/mt 0.2 0 0
1
2
3
4
5
Height to radius ratio, H/R Fig. 3. Impulsive and convective mass components, from [4]. Where mt = total mass of the liquid.
kc ¼
4 p2 mc T 2c
ð6Þ
The height of the centre of the impulsive mass, Hi, is computed from Eqs. (7) and (8). For R/H P 0.667:
Hi ¼ 0:375 H
ð7Þ
For R/H < 0.667:
ð4Þ
NZSEE [4] give the relationships shown in Fig. 3 to determine the modal masses of the tank-fluid system. Once the masses and periods of the impulsive and convective modes are determined, the stiffness of both modes is computed using Eqs. (5) and (6) respectively.
4 p2 m i
0.08
1
Current specifications for seismic design of storage tanks are based mainly on the damped spring-mounted mass analogy proposed by Housner [1] (see Fig. 1). This analogy proposes that a tank-liquid system can be represented by two vibration modes [2,3]. The portion of the liquid contents which moves together with the tank shell is known as the impulsive mass mi. The portion of the contents which moves independently of the tank shell and develops a sloshing motion is known as the convective mass mc. The predominant mode of vibration of liquid storage tanks during an earthquake is the impulsive mode [21,23] and its period is very short, generally a few tenths of a second. In this work, the impulsive period of vibration will be considered as the fundamental period in the analyses presented. The analysis method given in NZSEE [4] will be followed here and is outlined below. The impulsive period of vibration, Ti, is computed from Eq. (3) given by [4]:
5:61 p H kh
0.09
Height to radius ratio, H/R
3. Storage tanks analysed
Ti ¼
t/R = 0.001
0.10
Period coefficient, kh
268
ð5Þ
Fig. 1. Spring-mounted mass analogy for storage tanks. Where ki: stiffness of the impulsive mode; kc: stiffness of the convective mode; ci: damping of the impulsive mode; and cc: damping of the convective mode.
2R H Hi ¼ 0:5 0:094 H
ð8Þ
The height of the centre of the convective mass, Hc, is computed from Eq. (9).
Hc ¼
! cosh 3:67H 1 2R H 1:0 3:67H sinh 3:67H 2R 2R
ð9Þ
In this study six different storage tanks will be analysed using the methods described above. The dynamic characteristics of the tanks are shown in Table 1. The liquid is considered to have a unit weight of 10 kN/m3. The material considered was steel grade 450 according to [24]. The yield stress of this steel is equal to 450 MPa and its tensile strength is 520 MPa. The aspect ratios, H/R, considered herein are 0.5, 1.0, 1.5, 2.0, 2.5 and 3.0. Housner’s model [1] is used for the elastic time-history analysis carried out herein. The damping ratios recommended in [4], i.e. 5% for the impulsive mode and 0.5% for the convective mode, are used in this study.
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M. Ormeño et al. / Engineering Structures 102 (2015) 266–277 Table 1 Properties of the storage tanks considered in the study. Tank
H (m)
R (m)
t (mm)
Ti (s)
Tc (s)
mt (103 kg)
mi (103 kg)
mc (103 kg)
Hi (m)
Hc (m)
T1 T2 T3 T4 T5 T6
5 10 15 20 25 30
10 10 10 10 10 10
10 10 16 22 28 34
0.085 0.139 0.157 0.183 0.214 0.250
5.461 4.772 4.672 4.656 4.653 4.653
1571 3142 4713 6284 7855 9426
453 1704 3344 4914 6484 8055
1118 1438 1369 1370 1371 1371
1.875 3.750 5.625 8.120 10.620 13.120
2.662 6.051 10.204 14.821 19.660 24.595
4. Ground motion records and target spectrum A set of eleven different pairs of records are utilised in the timehistory analysis. The earthquakes selected are shown in Table 2. The ground motions were selected according to the recommendations given by [18] and are appropriate for a site in Wellington New Zealand. The New Zealand design guide, NZSEE recommendations [4], will be used to determine the design spectrum for this site. Both horizontal components of each earthquake are used in this study. ASCE/SEI 7-10 and Eurocode 8 require at least seven records to be utilised before the average response can be considered for design purposes. To determine the design spectrum, NZS 1170.5 works in conjunction with NZSEE recommendations, which is the New Zealand design guide for storage tanks (also known as the Red Book). In a similar way to NZS 1170.5, ASCE/SEI 7-10 works in conjunction with API 650 [5] to obtain the seismic load for storage tanks. To enable useful comparison between the design specifications, only one of these three spectra has to be chosen as the target spectrum. The target spectrum selected in this study is given by NZS 1170.5 [15] in conjunction with NZSEE recommendations [4]. The parameters necessary to compute the spectrum were selected for Wellington and site classifications of C and D. The return period of the target spectrum considered is 2500 years. In this study, these two site classifications will be used to compare the design specifications in an effort to have an improved statistical basis. Site subsoil classes C, also known as ‘‘Shallow soil sites”, and D, also known as ‘‘Deep or soft soil sites”, are defined by [15]. NZS 1170.5 [15] requires that one record in three in each set shall have a forward directivity component, whilst the remainder of the set shall be of near-neutral or backwards directivity when the site is near a major fault. The selected site, Wellington, is near a major fault according to NZS 1170.5 [15] and, thus, three in seven
pairs have a forward directivity component for both site classes to fulfil the requirement of this standard. Not all near source records have a forward directivity component. Somerville and Smith [25] report that two conditions have to be met for forward directivity effects: (a) the rupture propagation has to be towards the site and (b) the direction of the slip on the fault has to be aligned with the site. This is the reason why even though most of the pairs shown in Table 2 are from near source earthquakes only three in each site class have a forward directivity component. All the tanks described in Table 1 meet the design requirements imposed by [4,5] for both site classes.
5. Results 5.1. Scale factors All the ground motions records were scaled to the target spectra, defined in the previous section, using the three procedures given by the design specifications described in Section 2. Fig. 4 shows the unscaled 5% damped response spectra of the records and the target spectrum for both site classifications. Both horizontal components are shown in Fig. 4. Figs. 5–7 show the 5% damped response spectra of the records scaled by [15–17] respectively and the target spectrum of the tank T6. Table 3 shows the period ranges of interest computed according to the three design specifications considered. Tables 4 and 5 show a summary of the scale factors computed using the three procedures described above for the six tanks. Table 3 shows that the restriction imposed by NZS 1170.5 regarding the minimum value for T1, i.e. 0.4 s, leads to the same period range of interest for all tanks analysed. Thus, the same scale
Table 2 Earthquake records used from Oyarzo-Vera et al. [18]. Station
Date
Magnitude (Mw)
Di (km)
Depth (km)
PGA (g)
Fault mechanism
FDa
Site classification C EQ1 El Centro, USA EQ2 Tabas, Iran EQ3 Michoacan, Mexico EQ4 Landers, USA EQ5 Kocaeli, Turkey EQ6 Duzce, Turkey EQ7 Hokkaido, Japan
0117 (i) UNIO Lucerne Valley Darica (ii) HKD085
19-05-40 16-09-78 19-09-85 28-06-92 17-08-99 12-11-99 26-09-03
7 7.4 8.1 7.3 7.5 7.2 8.3
6 2 16 1 14 8 43
10 5 15 5 15 10 33
0.348 0.931 0.169 0.813 0.211 0.535 0.282
Strike-Slip Reverse Subduction Strike-Slip Strike-Slip Strike-Slip Subduction
No Yes No Yes Yes No No
Site classification D EQ1 El Centro, USA EQ2 El Centro #6, Imperial Valley EQ3 Michoacan, Mexico EQ4 Kocaeli, Turkey EQ5 Chi-Chi, Taiwan EQ6 Duzce, Turkey EQ7 Hokkaido, Japan
0117 5158 Caleta de Campos YPT (iii) TCU051 (ii) HKD085
19-05-40 15-10-79 19-09-85 17-08-99 20-09-99 12-11-99 26-09-03
7 6.5 8.1 7.5 7.5 7.2 8.3
6 0 16 3 7 8 43
10 10 15 15 – 10 33
0.348 0.437 0.143 0.349 0.234 0.535 0.282
Strike-Slip Reverse Subduction Strike-Slip Reverse Strike-Slip Subduction
No Yes No Yes Yes No No
ID
Event
Di = Distance to the epicentre. (i) Latitude & Longitude: 33.6000, 56.9200; (ii) Available at http://peer.berkeley.edu/nga_files/ath/DUZCE/DZC270.AT2 and DZC180.AT2; (iii) Available at http://peer.berkeley.edu/nga_files/ath/KOCAELI/YPT330.AT2 and YPT060.AT2. a FD = forward directivity component.
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M. Ormeño et al. / Engineering Structures 102 (2015) 266–277
10
10
Spectral Acceleration (g)
Spectral Acceleration (g)
Target Spectra
1
0.1
0.01 0.01
0.1
1
1
0.1
0.01 0.01
10
0.1
1
10
Period (s)
Period (s)
Fig. 4. Target spectra and response spectra of the unscaled ground motion records. Site classification C (left) and site classification D (right).
10
10
Spectral Acceleration (g)
Spectral Acceleration (g)
Target Spectra 1
Range of interest
0.1
0.01 0.01
0.1
1
10
1
0.1
0.01 0.01
Range of interest
0.1
1
10
Period (s)
Period (s)
Fig. 5. Target spectrum and response spectra of the ground motion records scaled by NZS 1170.5 for tank T6. Site classification C (left) and site classification D (right).
10
10
Spectral Acceleration (g)
Spectral Acceleration (g)
Target Spectra
1
0.1 Range of interest
0.01 0.01
0.1
1
10
Period (s)
1
0.1 Range of interest
0.01 0.01
0.1
1
10
Period (s)
Fig. 6. Target spectrum and response spectra of the ground motion records scaled by ASCE/SEI 7-10 for tank T6. Site classification C (left) and site classification D (right).
factors are computed for all earthquake records for the six tanks analysed (Tables 4 and 5). This occurs for both site classifications and, as was mentioned before, is due to storage tanks being very stiff structures with fundamental periods (impulsive) of a few tenths of a second. In this way, the tanks analysed have a period shorter than 0.4 s and, thus, their scale factor is the same for each record. The reason to have an upper limit in the range of interest, 1.3T1, is to cover the possibility that the effective fundamental
period could lengthen into during nonlinear response. In the cases considered this upper limit is irrelevant because elongation of the fundamental period does not occur in a linear time-history analysis. The lower limit, 0.4T1, exists to pick up some of the higher modes of the structure. However, with the restriction of a minimum fundamental period of 0.4 s, those two limits are the same for all the tanks analysed and, thus, the reasons why the limits were imposed do not apply in these cases. Furthermore, the
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M. Ormeño et al. / Engineering Structures 102 (2015) 266–277
10
10
Spectral Acceleration (g)
Spectral Acceleration (g)
Target Spectra
1
0.1
1
0.1 Range of interest
Range of interest
0.01 0.01
0.1
1
10
0.01 0.01
Period (s)
0.1
1
10
Period (s)
Fig. 7. Target spectrum and response spectra of the ground motion records scaled by Eurocode 8 for tank T6. Site classification C (left) and site classification D (right).
Table 3 Period ranges of interest according to the design specifications. Tank
T1 T2 T3 T4 T5 T6
T1 (s)
0.085 0.139 0.157 0.183 0.214 0.250
NZS 1170.5
ASCE/SEI 7–10
Eurocode 8
Lower (s)
Upper (s)
Lower (s)
Upper (s)
Lower (s)
Upper (s)
0.160 0.160 0.160 0.160 0.160 0.160
0.520 0.520 0.520 0.520 0.520 0.520
0.017 0.028 0.031 0.037 0.043 0.050
0.128 0.209 0.236 0.275 0.321 0.375
0.017 0.028 0.031 0.037 0.043 0.050
0.170 0.278 0.314 0.366 0.428 0.500
minimum value of T1 = 0.4 s leads to a period range of interest that does not extend to the fundamental period of tanks T1, T2 and T3. NZS 1170.5 establishes a maximum value of the scale factor of 4.9 (k1k2 6 4.9) to ensure a similar amplitude between the record and the target spectrum. This restriction has not been taken into account in this study to enable the use of the records recommended by Oyarzo et al. [18]. The scale factors computed according to Eurocode 8, shown in Tables 4 and 5, have average values of 3.79 and 4.34 for site classes
C and D, respectively. These records would qualify as moderately scaled records according to Iervolino et al. [26]. Amongst the six classes of records used to match the target spectrum of Eurocode 8 considered by Iervolino et al. [26], two of these groups were real records linearly scaled. The first group is named ‘‘Moderately scaled records” with an average scale factor equal to 5 and the second one is named ‘‘Significantly scaled records” with an average scale factor equal to 12. The variability in the scale factors computed in the example given by Iervolino et al. [26] was very high compared to the results shown herein for this study, e.g., in a set formed by seven events Iervolino et al. [26] report a minimum scale factor equal to 0.229 and a maximum equal to 21.882, with an average value of 5 for the whole set. Thus there is a big difference between NZS 1170.5 results and the results of the study in [26]. As was mentioned above, NZS 1170.5 establishes a maximum value of scale factor of 4.9. A software package called REXEL 2.5 (beta) was used by Iervolino et al. [26] to select the real records used in their study. The use of REXEL is extensively explained in [27]. Iervolino et al. [26] conclude that the use of linearly scaled records is a legitimate practice, showing that there is no systematic bias in the seismic response with respect to the unscaled real records. Watson-Lamprey et al. [28] and Luco and Bazurro [29]
Table 4 Scale factors computed using the three procedures for site classification C. Tank NZS 1170.5 T1 T2 T3 T4 T5 T6
EQ1
EQ2
EQ3
EQ4
EQ5
EQ6
EQ7
Average value
Standard deviation
2.699
0.902
4.349
2.098
6.351
1.790
2.909
3.014
1.82
0.804
4.634
0.803 1.102
5.150
2.220
3.575
2.870 2.913
1.72 1.66
4.474 4.326
1.528 1.701
2.951 2.955
1.57 1.52
5.898
1.320 1.417 1.746 2.172
3.727 3.740 3.788 3.849 3.820 3.801
2.15 2.13 2.08 2.01 1.98 1.96
ASCE/SEI 7-10 T1 2.906 T2 T3 T4 T5 T6 Eurocode 8 T1 T2 T3 T4 T5 T6
3.809
0.801 0.808
1.026 1.029
5.695 5.562
6.642
2.839
4.551
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Table 5 Scale factors computed using the three procedures for site classification D. Tank NZS 1170.5 T1 T2 T3 T4 T5 T6
EQ1
EQ2
EQ3
EQ4
EQ5
EQ6
EQ7
Average value
Standard deviation
3.035
2.780
6.522
3.884
4.725
2.013
3.271
3.747
1.49
1.556 2.198
4.808
3.640
4.296
2.232
3.646
3.307 3.399
1.14 0.99
3.386 3.374
0.97 0.95
4.344 4.353
1.27 1.26
4.339 4.319 4.323
1.24 1.21
ASCE/SEI 7-10 T1 2.975 T2 T3 T4 T5 T6 Eurocode 8 T1 T2 T3 T4 T5 T6
4.715 4.628
3.900
2.735 2.798
6.142
4.637
5.499
2.855
4.640
6.045 5.900 5.932
reported that there is a bias associated with scaling if the records are selected based only on the magnitude, distance and site conditions. However, both studies concluded that when the records are selected based on the properties of the scaled ground motion, which means, similar spectral shape to the target spectrum, the amount of scaling (value of the scale factor) does not introduce bias in the seismic response. Eurocode 8 gives the highest average values of scale factors for both site classifications. 5.2. Seismic response The values of the scale factors are just one aspect of computing the applied load. The other aspect is the records. To analyse the effects of these two aspects combined the tank response has to be studied. Tables 6 and 7 show the average, the standard deviation and the coefficient of variation (COV) of the maximum base
shears obtained from all the ground motions, computed by the three scaling procedures and for all the tanks analysed. Tables 6 and 7 show that Eurocode 8 gives higher average values of base shear than the other two procedures, which is consistent with the scale factors shown in Tables 4 and 5. For both site classes, NZS 1170.5 gives higher values of average base shear than ASCE/SEI 7-10 in most cases. Figs. 8 and 9 show that the maximum values of overturning moment obtained using Eurocode 8 are the highest in most cases. Dashed lines in Figs. 8 and 9 indicate the capacity of the tank. These results are also consistent with those shown in Tables 4–7. The seismic response of a tank for a given record is directly related to the scale factor of the record. Thus the higher values obtained with Eurocode 8 can be explained by the procedure used to compute the scale factors to match the target spectrum. The procedure provided in NZS 1170.5 minimises the difference between the
Table 6 Base shear statistics from all ground motions – Site Class C. Tank
Ground motion records – base shear (MN) NZS 1170.5
T1 T2 T3 T4 T5 T6
ASCE/SEI 7-10
Eurocode 8
Average
Standard deviation
COV (%)
Average
Standard deviation
COV (%)
Average
Standard deviation
COV (%)
7.3 27.2 49.2 70.3 98.6 131.3
3.6 9.8 9.7 13.4 30.4 40.7
48.6 36.0 19.8 19.0 30.8 31.0
6.1 25.1 46.6 70.1 102.5 136.8
0.7 6.8 10.0 27.0 48.7 56.4
11.8 26.9 21.5 38.5 47.5 41.3
8.1 32.2 61.1 93.2 132.5 175.8
1.1 8.7 10.7 30.2 61.0 72.9
13.5 27.0 17.6 32.3 46.1 41.5
Table 7 Base shear statistics from all ground motions – Site Class D. Tank
Ground Motion Records - Base Shear (MN) NZS 1170.5
T1 T2 T3 T4 T5 T6
ASCE/SEI 7–10
Eurocode 8
Average
Standard deviation
COV (%)
Average
Standard deviation
COV (%)
Average
Standard deviation
COV (%)
7.1 25.1 51.5 82.6 128.2 167.5
1.8 4.2 7.4 13.6 32.3 37.8
25.2 16.7 14.4 16.5 25.2 22.5
6.3 23.5 48.1 77.9 121.4 157.7
1.7 5.1 8.4 20.2 41.6 45.0
26.7 21.5 17.4 26.0 34.3 28.6
8.4 30.1 61.6 99.7 155.3 202.2
2.0 6.5 10.7 25.6 53.0 58.2
23.7 21.5 17.4 25.7 34.1 28.8
M. Ormeño et al. / Engineering Structures 102 (2015) 266–277
35 30 25 20 15 10
0
200
150
100
50
EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
0
Ground Motion
Ground Motion
Tank T3
Overturning Moment (MNm)
500
1400
400 300 200 100 0
3500
Tank T4
1200 1000 800 600 400 200
EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
0
Ground Motion
Ground Motion
Tank T5
4000
Tank T6
3500
Overturning Moment (MNm)
3000 2500 2000 1500 1000
3000 2500 2000 1500 1000 500
0
0 EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
500
EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
Overturning Moment (MNm)
Tank T2
5
600
Overturning Moment (MNm)
250
EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
Overturning Moment (MNm)
205 MNm
NZS 1170.5 ASCE/SEI 7-10 Eurocode 8
Overturning Moment (MNm)
Tank T1
273
Ground Motion
Ground Motion
Fig. 8. Maximum overturning moment. Site classification C. Dashed line indicates the capacity of the tank in terms of overturning moment.
response spectrum of the scaled record and the target spectrum, thereby allowing the response spectrum of the scaled record to be below the target spectrum in some zones of the period range of interest. Something similar is the outcome of using the procedure given by ASCE/SEI 7-10. This procedure uses the SRSS criterion to match the scaled record to the target spectrum. Thus the
scaled record will be always below the target spectrum along the whole period range of interest. The procedure given by Eurocode 8 uses the average of the response spectra of the scaled records to match the target spectrum. In this case there is always at least one component of a scaled record above the target spectrum along the whole period range of interest. Even though matching is carried
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M. Ormeño et al. / Engineering Structures 102 (2015) 266–277
Tank T1
Overturning Moment (MNm)
35 30 25 20 15 10
250
Overturning Moment (MNm)
205 MNm
NZS 1170.5 ASCE/SEI 7-10 Eurocode 8
150
100
50
EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
0
Ground Motion
Ground Motion
Tank T3
1400
Overturning Moment (MNm)
600
Overturning Moment (MNm)
200
5 0
500 400 300 200 100
3500
Tank T4
1200 1000 800 600 400 200
EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
0 EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
0
Ground Motion
Ground Motion
Tank T5
4500
Tank T6
4000
3000
Overturning Moment (MNm)
Overturning Moment (MNm)
Tank T2
2500 2000 1500 1000 500
3500 3000 2500 2000 1500 1000 500
0 EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
0
Ground Motion
Ground Motion
Fig. 9. Maximum overturning moment. Site classification D. Dashed line indicates the capacity of the tank in terms of overturning moment.
out to 90% of the target spectrum, the scale factors computed using the procedure provided by Eurocode 8 are the highest amongst the scaling procedures studied herein. From the point of view of structural integrity it is necessary to check the axial compressive stresses in the tank wall. To enable comparison between the three scaling procedures, the NZSEE recommendations [4] will be used to calculate the axial stresses in the tank shell. Two cases of axial stress are considered: buckling in membrane compression and elastic–plastic collapse. Eq. (10) is
the expression given by [4] to compute the stress limit for buckling in membrane compression.
fp fm 6 0:19 þ 0:81 f c1 f c1
ð10Þ
where fm = vertical membrane compression stress for tanks with internal pressure, subject to flexural compression (cantilever mode); fc1 = classical shell buckling stress (see Eq. (11)); and
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fp = modification of classical shell buckling stress which includes the increase due to internal pressure and the reduction due to initial imperfections in buckling stress (see Eq. (12)).
f c1 ¼ 0:6 E
t R
ð12Þ
where p = expression to take into account the internal pressure (Eq. (13)); and f0 = expression that reflects the imperfections of the tank shell (Eqs. (14) and (15)).
pR t f c1
ð13Þ
if k 6 2
k2 f0 ¼ fy 1 4
! ð14Þ
if k > 2
f 0 ¼ r f c1
ð15Þ
where p = internal f c1 Þ; k ¼ f y =ðr
pressure;
fy = material
yield
2 3 !1=2 d 4 2 1þ r¼1w 15 t w dt
stress;
ð16Þ
(d/t) = ratio of maximum imperfection amplitude to wall thickness defined in Eq. (17); and w = 1.24 for membrane compression buckling.
0:06 ðd=tÞ ¼ a
rffiffiffi R t
ð17Þ
where a = 2.5 for very high quality construction [4]. Tanks of high quality construction are considered to compute the ratio of maximum imperfection amplitude to wall thickness (d/t). NZSEE recommendations provide Eq. (18) for computing the stress limit for elastic–plastic collapse.
2
fm
Tank
ð11Þ
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi u 2 !! 2 u f p 0 1 f p ¼ f c1 t 1 1 f c1 5
p¼
Table 9 Number of occasions the elastic limit is exceeded, nex.
# !2 3 " fy s þ 250 pR 5 1 4 1 6 f c1 1 t fy 1:12 þ s1:5 sþ1
ð18Þ
1 where s ¼ Rt 400 . The capacity for vertical membrane compression stress (fm) is the minimum value between Eqs. (10) and (18). Table 8 shows this value for the 6 tanks considered. Table 9 shows the number of cases that the maximum compressive stresses at the bottom of the wall (rc) for all the tanks exceed the values shown in Table 8. It is noticeable that for tanks with aspect ratios equal or lower than 2 (T1–T4), the stresses obtained using NZS 1170.5 and ASCE/SEI 7-10 are lower than the capacity
Table 8 fm for the 6 tank analysed. Tank
fm (MPa)
T1 T2 T3 T4 T5 T6
71.7 76.7 116.4 149.3 185 212.6
T1 T2 T3 T4 T5 T6
Soil C
Soil D
NZS 1170.5
ASCE/SEI 7-10
Eurocode 8
NZS 1170.5
ASCE/SEI 7-10
Eurocode 8
0 0 0 0 2 2
0 0 0 0 2 5
0 0 0 3 3 8
0 0 0 0 3 5
0 0 0 0 2 5
0 0 0 3 6 10
of the tanks in all the cases. However, use of Eurocode 8 predicts 3 cases where rc exceeds fm (defined as nex = 3) for T4 in both site classes. This result is consistent with those shown in Figs. 8 and 9 because the overturning moment is directly related to the axial stresses developed in the tank wall. All the design specifications predict nex P 1 for tanks with aspect ratios equal or higher than 2.5. The Eurocode 8 procedure predicts the highest nex for both site classes. Table 9 shows that NZS 1170.5 predicts the lowest nex. This can be explained by considering the scaling procedure specified in this document, which requires all records to reach at least 90% of the target spectrum in the period range of interest. ASCE/SEI 7-10 requires a 100% match of the target spectrum as a minimum. NZS 1170.5 requires minimisation of a function over the period range of interest (Eq. (1)). On the other hand, ASCE/SEI 7-10 requires that at all periods in the range of interest the requirements of the document are meet. Therefore, the scale factors computed by ASCE/SEI 7-10 are larger than those computed by NZS 1170.5. For site class D, nex is higher than that of site class C. As was stated previously, all tanks meet the design requirements of NZSEE [4] and API 650 [5]. However, site class D controlled the design in all cases, and thus the tanks are overdesigned for site class C. This explains the lower nex for site class C. 5.3. NZS 1170.5 limit for fundamental period NZS 1170.5 imposes a lower limit of 0.4 s to the fundamental period when scaling ground motions, thus influencing the range of interest. The 0.4 s limit was imposed because there is difficulty in estimating the periods of short-period structures, e.g. due to effects such as stiffening from non-structural elements, periodlengthening from soil-structure interaction and selection of appropriate material and section properties for estimating the period. However, storage tanks are very simple structures in geometry and issues such as stiffening from non-structural elements or uncertainty in appropriate material and section properties do not apply to liquid storage tanks to any great extent. Furthermore, in all the cases analysed herein, the periods are shorter than that limit and, for this reason, the selected range of interest does not enclose the fundamental periods of the tanks analysed. For all the reasons explained above the authors of this work are of the opinion that this limit should not apply to storage tanks. In this section the method of NZS 1170.5 is applied but the lower limit on period is disregarded. Table 10 shows the scale factors computed using the method in NZS 1170.5 but modified as above. The values shown in Table 10 are in most cases larger than the values shown in Tables 4 and 5 (which include the lower limit on Period of 0.4 s), respectively. For ease of comparison, the ratio RF of the values shown in Table 10 to those shown in Tables 4 and 5 are plotted in Fig. 10 for all ground motions and tanks, where RF is defined as
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M. Ormeño et al. / Engineering Structures 102 (2015) 266–277
2.0
2.0
1.8
1.8
1.6
1.6
1.4
1.4
1.2
RF
RF
1.2 1.0
1.0 0.8
0.8
0.6
0.6
T1 T3 T5
0.4 0.2 0.0 EQ1
EQ2
EQ3
EQ4
EQ5
T2 T4 T6 EQ6
0.4 0.2 0.0 EQ1 EQ2 EQ3 EQ4 EQ5 EQ6 EQ7
EQ7
Ground motion
Ground motion
Fig. 10. Scale factor ratio, Site classification C (left), Site classification D (right).
Table 10 Scale factors using NZS 1170.5 disregarding lower limit on period. Ground motion
Site class C
EQ1 EQ2 EQ3 EQ4 EQ5 EQ6 EQ7
Site class D
T1
T2
T3
T4
T5
T6
T1
T2
T3
T4
T5
T6
3.595 1.179 6.624 0.841 6.563 2.861 5.413
3.457 0.987 5.682 1.011 5.353 3.138 4.365
3.427 0.943 5.633 1.113 5.038 2.961 4.267
3.363 0.88 5.456 1.238 4.907 2.64 4.032
3.112 0.803 4.987 1.524 4.894 2.394 3.755
3.019 0.833 4.774 1.663 5.213 2.202 3.41
3.833 1.829 6.916 4.753 6.469 3.051 5.773
3.503 2.408 6.34 5.139 5.409 3.18 4.424
3.483 2.595 6.212 5.067 5.142 3.01 4.337
3.431 2.776 6.306 5.021 4.728 2.693 4.114
3.184 2.878 6.495 4.71 4.381 2.45 3.842
3.1 2.842 6.558 4.398 4.404 2.261 3.502
Table 11 nex for site classes C and D. Tank
T1 T2 T3 T4 T5 T6
RF ¼
Site class C
Site class D
NZS 1170.5
NZS 1170.5 (no lower limit)
NZS 1170.5
NZS 1170.5 (no lower limit)
0 0 0 0 2 2
0 0 0 2 2 6
0 0 0 0 3 5
0 0 0 2 5 7
Scale factor without lower limit Scale factor with lower limit
ð19Þ
In most cases the scale factors computed without the restriction on the minimum period are larger than those computed with the restriction. In only 24 of the 84 cases analysed, considering both site classes, are the scale factor ratios lower than 1. Table 11 shows a comparison of nex for both site classes. Table 11 corroborates the previous results of this section, i.e., the restriction of the lower limit for the fundamental period results in an underestimation of the seismic loads acting on the tank. The value of nex increases from 4 to 10 for site class C and from 8 to 14 for site class D, when the tanks are analysed disregarding the lower limit for the fundamental period. Using this modification to the period range NZS 1170.5 predicts a higher nex than ASCE/SEI 7-10. The consequence of the 0.4 s period limit for estimation of the seismic performance of storage tanks is especially relevant because storage tanks are essential structures, pivotal in the recovery process following devastating earthquakes. 6. Conclusions A series of time-history earthquake response analyses have been carried out using 3 different procedures to match an
earthquake record to a target spectrum. Six different liquid storage tanks were considered. The main aim was to evaluate the different scaling procedures given by three internationally used design specifications and to develop an understanding of the different consequences of the scaling procedures for the tank response. Using the ground motions and the target spectrum considered in this study, the investigations reveal: 1. Most liquid storage tanks are not in the period range of interest defined by NZS 1170.5 for scaling earthquake records, and therefore, the frequency range considered over which to scale the records does not match the predominant dynamic properties of liquid storage tanks. 2. Eurocode 8 scaling procedure gives, in most cases, the highest scale factors amongst the design specifications studied in this work. This is due to the scaling procedure to match the target spectrum given by Eurocode 8 which is more stringent than that given by the other two design specifications. 3. Eurocode 8 also gives the highest values of base shear and overturning moment in most cases, predicting the highest number of exceedance of the elastic limit, followed by ASCE/SEI 7-10. 4. NZS 1170.5 is the least conservative document in terms of axial compressive stresses developed in the tank wall. This is due to the requirements of NZS 1170.5 to match the target spectrum being less onerous than those of the other two design specifications. However, this changes substantially when the tanks are analysed disregarding the lower limit for the fundamental period imposed by this standard. Use of NZS 1170.5, under this modification, results in a higher of number of exceedance of the elastic limit than ASCE/SEI 7-10. 5. The authors of this work recommend analysing liquid storage tanks disregarding the lower period restriction imposed by NSZ 1170.5. This recommendation is made because the reasons for establishing the lower limit for the fundamental period do not generally apply to liquid storage tanks.
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Acknowledgements The authors wish to thank the Chilean Government for awarding the first author with the scholarship ‘‘Becas Chile” for his doctoral study at the University of Auckland and the Ministry of Business, Innovation and Employment through the National Hazards Research Platform, award number UoA3703249, for the support of this research and also the reviewers for their constructive comments that have led to an improvement of the clarity of the article. References [1] Housner GW. Dynamic pressures on accelerated fluid containers. Bull Seismol Soc Am 1957;47:15–35. [2] Wozniak RS, Mitchell WW. Basis of seismic design provisions for welded steel oil storage tanks. In: Adv storage tank des API, refin 43rd midyear meet, Toronto, Ontario, Canada; 1978. [3] Veletsos AS. Seismic response and design of liquid storage tanks. Tech counc lifeline earthq eng, New York; 1984, p. 255–370. [4] NZSEE. Seismic design of storage tanks – recommendations of a study group of the New Zealand national society for earthquake engineering (NZSEE); 2009. [5] API 650. Welded steel tanks for oil storage, 11th ed., American Petroleum Institute (API); 2007. [6] Eurocode 8. Design of structures for earthquake resistance – Part 4: Silos, tanks and pipelines, vol. 3. The European Standard EN; 2006. [7] Ormeño M, Larkin T, Chouw N. Comparison between standards for seismic design of liquid storage tanks with respect to soil-foundation-structure interaction and uplift. Bull N Z Soc Earthq Eng 2012;45:40–6. [8] Qin X, Chen Y, Chouw N. Effect of uplift and soil nonlinearity on plastic hinge development and induced vibrations in structures. Adv Struct Eng 2013;16:135–48. [9] Oyarzo-Vera C, Chouw N. Comparison of record scaling methods proposed by standards currently applied in different countries. In: 14th World conf earthq eng, Beijing, China; 2008. [10] COSMOS. Consortium of organizations for strong-motion observation system (COSMOS). COSMOS virtual data center; 1999. [11] EQC-GNS. Earthquake commission New Zealand and GNS science (EQC-GNS). GeoNet strong motion data; 2004.
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[12] PEER. Pacific earthquake engineering research center (PEER). PEER NGA database; 2005. [13] Chouw N, Hao H. Study of SSI and non-uniform ground motion effect on pounding between bridge girders. Soil Dyn Earthq Eng 2005;25:717–28. [14] Boore DM. Simulation of ground motion using the stochastic method. Pure Appl Geophys 2003;160:635–76. [15] NZS 1170.5. Structural design actions Part 5: earthquake actions – New Zealand. New Zealand Standard (NZS); 2004. [16] ASCE. ASCE/SEI 7-10 minimum design loads for buildings and other structures. American Society of Civil Engineers (ASCE); 2010. [17] Eurocode 8. Design of structures for earthquake resistance – Part 1: General rules, seismic actions and rules for buildings, vol. 3. The European Standard EN; 2011. [18] Oyarzo-Vera CA, McVerry GH, Ingham JM. Seismic zonation and default suite of ground-motion records for time-history analysis in the north island of New Zealand. Earthq Spectra 2012;28:667–88. [19] Iervolino I, Maddaloni G, Cosenza E. Eurocode 8 compliant real record sets for seismic analysis of structures. J Earthq Eng 2008;12:54–90. [20] Cooper TW. A study of the performance of petroleum storage tanks during earthquakes, 1933–1995 NIST GCR 97-720; 1997. [21] Larkin T. Seismic response of liquid storage tanks incorporating soil structure interaction. J Geotech Geoenviron Eng 2008;134:1804–14. [22] Katsanos EI, Sextos AG, Manolis GD. Selection of earthquake ground motion records: a state-of-the-art review from a structural engineering perspective. Soil Dyn Earthq Eng 2010;30:157–69. [23] Veletsos AS, Tang Y, Tang HT. Dynamic response of flexibly supported liquidstorage tanks. J Struct Eng 1992;118:264–83. [24] Standard AZ. AS/NZS 3678:2011. Structural steel—Hot-rolled plates, floorplates and slabs; 2011. [25] Somerville P, Smith N. Accounting for near-fault rupture directivity effects in the development of design ground motions. Elev World Conf Earthq Eng 1996. [26] Iervolino I, De Luca F, Cosenza E. Spectral shape-based assessment of SDOF nonlinear response to real, adjusted and artificial accelerograms. Eng Struct 2010;32:2776–92. [27] Iervolino I, Galasso C, Cosenza E. REXEL: computer aided record selection for code-based seismic structural analysis. Bull Earthq Eng 2009;8:339–62. [28] Watson-Lamprey J, Abrahamson N. Selection of ground motion time series and limits on scaling. Soil Dyn Earthq Eng 2006;26:477–82. [29] Luco N, Bazzurro P. Does amplitude scaling of ground motion records result in biased nonlinear structural drift responses? Earthq Eng Struct Dyn 2007;36:1813–35.
Contents lists available at ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Evaluation of seismic ground motion scaling procedures for linear time-history analysis of liquid storage tanks Miguel Ormeño ⇑, Tam Larkin, Nawawi Chouw Department of Civil and Environmental Engineering, Faculty of Engineering, The University of Auckland, New Zealand
a r t i c l e
i n f o
Article history: Received 12 November 2014 Revised 17 August 2015 Accepted 17 August 2015
Keywords: Storage tanks Seismic standards ASCE/SEI 7-10 NZS 1170.5 Eurocode 8 Time-history analysis Earthquake record scaling
a b s t r a c t Liquid storage tanks are vital life-line structures, especially following destructive seismic events. However, at present there is no accepted procedure to scale ground motions to perform time-history analysis for these very short period structures. Current standards and design codes e.g. ASCE/SEI 7-10, Eurocode 8 and NZS 1170.5, for conventional structures, e.g. buildings and bridges, minimise in a predefined range of periods the difference between the response spectra of chosen records and the target spectrum. This period range has limits related to the fundamental period of the structure in the excitation direction being considered. However, these design specifications have important differences in their scaling procedures and consequently affect the calculated seismic response of the structure. Additionally, these procedures were not formulated for time-history analysis of liquid storage tanks. This is evident in the case of the restriction imposed by NZS 1170.5 for very stiff structures, which includes most tanks. This restriction leads to reduced structural loading giving non-representative results. The research reported here concerns the seismic response of storage tanks, in terms of base shear, overturning moment and wall stresses, when subjected to scaled ground motions using the procedures of three design specifications. It was found that the Eurocode 8 approach produces the highest seismic response on storage tanks. ASCE/SEI 7-10 gives intermediate results in terms of applied load and seismic response compared to the other two specifications. The study also shows that the restriction imposed by NZS 1170.5 for tanks, produces an underestimate of the seismic load on storage tanks. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Storage tanks are essential structures that provide basic supplies such as water and fuel. It is very important that this kind of structure remain operational after a destructive seismic event to facilitate rapid recovery. Because of the importance of these structures many studies have been carried out [e.g. 1–3] and standards and design guides have been established [4–6] and compared [7]. Yet despite the importance of storage tanks, there is no specific widely accepted procedure for time-history analysis to enable an estimation of the behaviour of storage tanks under a specific seismic excitation. Current design practice only provides seismic coefficients based on a pseudo-dynamic method of assessment. Using this design method it is impossible to see the potential for successive plastic incursions of the structural elements of storage tanks (shell and base plate). It has been shown [8] that such plastic behaviour will lower the impact of earthquake loading whilst imposing ⇑ Corresponding author. E-mail addresses: [email protected] (M. Ormeño), [email protected] (T. Larkin), [email protected] (N. Chouw). http://dx.doi.org/10.1016/j.engstruct.2015.08.024 0141-0296/Ó 2015 Elsevier Ltd. All rights reserved.
ductility requirements. Thus, it is essential to have an appropriate selection criteria and scaling procedure of the ground motions. There are two distinctly different sources of obtaining ground motions for time-history analysis [9]. The first is to use recorded ground motions from databases of previous events [10–12]. The second source is to use ground motions stochastically generated using physical or numerical models [e.g. 13,14]. Standards and codes, e.g. NZS 1170.5 [15], ASCE/SEI 7-10 [16] and Eurocode 8 [17], recommend the use of recorded motions from previous events. However, if there is insufficient recorded data the three design specifications above [15–17] allow the use of supplementary simulated ground motions to make up the total number of records required. All three documents agree in the requirements for choosing the records to be used. The ground motions should have compatible seismological characteristics, i.e. magnitude, distance, fault mechanism and soil conditions, to the tectonics of the region and the site of the structure. Studies have been carried out in a number of locations to obtain ground motions that meet the requirements imposed by standards and codes. Oyarzo-Vera et al. [18] provide a list of ground motions to be used in the North Island of New Zealand for time-history analysis. Iervolino et al. [19]
M. Ormeño et al. / Engineering Structures 102 (2015) 266–277
and Cooper [20] state the criteria for selecting ground motions for using the Eurocode 8 [17] and ASCE/SEI 7-10 [16] procedures, respectively. Contrary to the criteria for selecting records, where there is agreement between the standards and codes, the scaling procedures to apply to the chosen records differ substantially in important ways. The procedures defined in the three design specifications implemented here specify different period ranges of interest. Over these ranges the chosen record should be matched as close as possible to the target spectrum. To the authors’ knowledge a comparison of the application of the three main design specifications to liquid storage tanks has not been reported. The objectives of the work is to evaluate the consequences of the procedures for the analysis of the seismic performance of liquid storage tanks and to reveal the differences and similarities of the outcomes resulting from application of the specifications. The selection of records for time-history analysis is not part of the scope of this study. However, some important points about the criteria for selecting records are provided in the discussion of the results. 2. Method for scaling records A summary of the three design specifications used in this study is presented below. All three design specifications require the computation of a multiplication factor to apply to the chosen time history to ensure a match to the target spectrum in the period range of interest. However, this factor is computed differently depending on the standard or code considered. 2.1. New Zealand Standard (NZS 1170.5) NZS 1170.5 requires the use a family of at least three pairs of horizontal ground motions recorded in seismic events. The vertical component shall be included when the structure analysed is sensitive to the action of vertical acceleration. The selected events shall have similar seismological characteristics (magnitude, fault mechanism, source-to-site distance and near-surface soil profile) to the characteristics of the events that mainly contributed to the seismic hazard at the site over the period range of interest. When there is insufficient suitable recorded ground motions available for a site, simulated ground motion records may be used to complete the family of records. The period range of interest defined by this standard is between 0.4T1 and 1.3T1, where T1 is the fundamental period of the structure in the direction analysed, but may not be less than 0.4 s. In this range, the records should match the target spectrum as closely as possible by using the multiplication factors, k1 and k2. k1 is known as the record scale factor and is different for each record. k2 is known as the family scale factor and is common to all records in the family. k1 is the value that minimises in a least mean square sense the function defined in Eq. (1) in the period range of interest.
log k1 SAcomponent SAtarget
ð1Þ
where SAcomponent: 5% damped spectrum value of the chosen horizontal component of the record; and SAtarget: corresponding target spectrum value at the same period. In this way, k1 is computed for each horizontal component of the record and the smallest value is chosen as the record scale factor. The component that yields the value of k1 for a pair of horizontal ground motion components is called the principal component. The family scale factor k2 is the maximum of 1.0 and the value computed from Eq. (2):
k2 ¼ SAtarget = maxðSAprincipal Þ
ð2Þ
267
where SAprincipal: 5% damped spectrum of the principal component of the record. In this way, the principal component of at least one record spectrum, scaled by its record scale factor k1, exceeds the target spectrum after application of the family factor k2. Additionally, the following restrictions apply to the scale factors:
0:33 < k1 < 3:0 1:0 < k2 < 1:3 It is important to realise that the minimum value for T1 = 0.4 s imposed by this standard will affect the time-history analysis of the storage tanks analysed. Liquid storage tanks generally have very short fundamental periods, only a few tenths of second [21], and, therefore, their periods are most likely less than 0.4 s. 2.2. U.S.A. Standard (ASCE/SEI 7-10) ASCE/SEI 7-10 requires the use of at least three pairs of ground motions. The selected events shall have magnitudes, fault distance, and source mechanisms consistent with the expected maximum earthquake considered in the analysis. Soil profile similarities are not required explicitly by this standard. Appropriate simulated ground motion pairs can be used to make up the total number of ground motions when the required number of recorded ground motions is not available. The square root of the sum of the squares (SRSS) of the 5% damped response spectrum of each ground motion must be computed from the scaled pair that forms the records. The same scale factor shall apply to both horizontal components, i.e., each pair has a unique scale factor. The scale factor is determined by the criterion that the SRSS of the response spectrum of each pair shall not be less than the target spectrum in the period range of interest defined by ASCE/SEI 7-10. The period range is specified as being between 0.2T1 and 1.5T1, where T1 is the fundamental period of the structure in the direction analysed. When seven or more pairs are used to perform the analysis, the average response will be considered for design purposes. If less than seven ground motions are used, then the maximum response will be considered. 2.3. Eurocode 8 This design specification requires the use of a set at least three pairs, regardless of their origin. The records shall consist of both horizontal components and a vertical component when this is required. The records that make up the set shall be consistent with the magnitude and other relevant features of the seismic event considered. The average of the 5% damped elastic spectrum, calculated from all time histories, should not be less than 90% of the target spectrum in the period range of interest. The period range of interest defined by Eurocode 8 is between 0.2T1 and 2T1, where T1 is the fundamental period of the structure in the direction of application of the motion. It should be noted that this procedure, contrary to the previous two, does not provide a specific method to compute the scale factors for the records. The requirement established by Eurocode 8 can be fulfilled in several ways. Even a single unique scale factor for all the records can be used if the average of the 5% damped elastic spectrum of all time histories meets the requirement. Iervolino et al. [19] realised this issue and proposed additional conditions on choosing ground motions to be utilised for time-history analysis. Katsanos et al. [22], present a complete review of the state of art of the selection of records for timehistory analysis. They confirmed that there is a high variability in
M. Ormeño et al. / Engineering Structures 102 (2015) 266–277
the spectral acceleration when real unscaled records are used following the procedure give by Eurocode 8. In this study, a different scale factor has been computed for each record and the average of the 5% damped elastic spectrum has been computed from both horizontal components. As an additional requirement, the average spectral acceleration, calculated from the individual time histories, at a period essentially equal to zero has to be larger than the value of the target spectrum at the same period. It is recommended that seven or more ground motions be used and the average response taken for design purposes. If less than seven ground motions are used, then the maximum response should be considered.
rffiffiffiffiffiffiffiffiffi
cl
Eg
ð3Þ
where H = liquid height; kh = period coefficient which depends on the ratio of the height of liquid to tank radius (Fig. 2); cl = unit weight of the liquid; E = Young’s modulus of the tank material; and g = gravitational acceleration. The convective period of vibration, Tc, is computed from Eq. (4) given by [4]:
qffiffi
2 p Rg T c ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1:841 tanh 1:841 HR
ki ¼
T 2i
0.07 0.06 0.05 0.04
0
1
2
3
4
Fig. 2. Period coefficient kh for first horizontal tank-liquid mode, from [4]. Where t = tank wall thickness; and R = mean radius of the tank.
Dimensionless ratio shown
0.8
mi/mt
0.6 0.4
mc/mt 0.2 0 0
1
2
3
4
5
Height to radius ratio, H/R Fig. 3. Impulsive and convective mass components, from [4]. Where mt = total mass of the liquid.
kc ¼
4 p2 mc T 2c
ð6Þ
The height of the centre of the impulsive mass, Hi, is computed from Eqs. (7) and (8). For R/H P 0.667:
Hi ¼ 0:375 H
ð7Þ
For R/H < 0.667:
ð4Þ
NZSEE [4] give the relationships shown in Fig. 3 to determine the modal masses of the tank-fluid system. Once the masses and periods of the impulsive and convective modes are determined, the stiffness of both modes is computed using Eqs. (5) and (6) respectively.
4 p2 m i
0.08
1
Current specifications for seismic design of storage tanks are based mainly on the damped spring-mounted mass analogy proposed by Housner [1] (see Fig. 1). This analogy proposes that a tank-liquid system can be represented by two vibration modes [2,3]. The portion of the liquid contents which moves together with the tank shell is known as the impulsive mass mi. The portion of the contents which moves independently of the tank shell and develops a sloshing motion is known as the convective mass mc. The predominant mode of vibration of liquid storage tanks during an earthquake is the impulsive mode [21,23] and its period is very short, generally a few tenths of a second. In this work, the impulsive period of vibration will be considered as the fundamental period in the analyses presented. The analysis method given in NZSEE [4] will be followed here and is outlined below. The impulsive period of vibration, Ti, is computed from Eq. (3) given by [4]:
5:61 p H kh
0.09
Height to radius ratio, H/R
3. Storage tanks analysed
Ti ¼
t/R = 0.001
0.10
Period coefficient, kh
268
ð5Þ
Fig. 1. Spring-mounted mass analogy for storage tanks. Where ki: stiffness of the impulsive mode; kc: stiffness of the convective mode; ci: damping of the impulsive mode; and cc: damping of the convective mode.
2R H Hi ¼ 0:5 0:094 H
ð8Þ
The height of the centre of the convective mass, Hc, is computed from Eq. (9).
Hc ¼
! cosh 3:67H 1 2R H 1:0 3:67H sinh 3:67H 2R 2R
ð9Þ
In this study six different storage tanks will be analysed using the methods described above. The dynamic characteristics of the tanks are shown in Table 1. The liquid is considered to have a unit weight of 10 kN/m3. The material considered was steel grade 450 according to [24]. The yield stress of this steel is equal to 450 MPa and its tensile strength is 520 MPa. The aspect ratios, H/R, considered herein are 0.5, 1.0, 1.5, 2.0, 2.5 and 3.0. Housner’s model [1] is used for the elastic time-history analysis carried out herein. The damping ratios recommended in [4], i.e. 5% for the impulsive mode and 0.5% for the convective mode, are used in this study.
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M. Ormeño et al. / Engineering Structures 102 (2015) 266–277 Table 1 Properties of the storage tanks considered in the study. Tank
H (m)
R (m)
t (mm)
Ti (s)
Tc (s)
mt (103 kg)
mi (103 kg)
mc (103 kg)
Hi (m)
Hc (m)
T1 T2 T3 T4 T5 T6
5 10 15 20 25 30
10 10 10 10 10 10
10 10 16 22 28 34
0.085 0.139 0.157 0.183 0.214 0.250
5.461 4.772 4.672 4.656 4.653 4.653
1571 3142 4713 6284 7855 9426
453 1704 3344 4914 6484 8055
1118 1438 1369 1370 1371 1371
1.875 3.750 5.625 8.120 10.620 13.120
2.662 6.051 10.204 14.821 19.660 24.595
4. Ground motion records and target spectrum A set of eleven different pairs of records are utilised in the timehistory analysis. The earthquakes selected are shown in Table 2. The ground motions were selected according to the recommendations given by [18] and are appropriate for a site in Wellington New Zealand. The New Zealand design guide, NZSEE recommendations [4], will be used to determine the design spectrum for this site. Both horizontal components of each earthquake are used in this study. ASCE/SEI 7-10 and Eurocode 8 require at least seven records to be utilised before the average response can be considered for design purposes. To determine the design spectrum, NZS 1170.5 works in conjunction with NZSEE recommendations, which is the New Zealand design guide for storage tanks (also known as the Red Book). In a similar way to NZS 1170.5, ASCE/SEI 7-10 works in conjunction with API 650 [5] to obtain the seismic load for storage tanks. To enable useful comparison between the design specifications, only one of these three spectra has to be chosen as the target spectrum. The target spectrum selected in this study is given by NZS 1170.5 [15] in conjunction with NZSEE recommendations [4]. The parameters necessary to compute the spectrum were selected for Wellington and site classifications of C and D. The return period of the target spectrum considered is 2500 years. In this study, these two site classifications will be used to compare the design specifications in an effort to have an improved statistical basis. Site subsoil classes C, also known as ‘‘Shallow soil sites”, and D, also known as ‘‘Deep or soft soil sites”, are defined by [15]. NZS 1170.5 [15] requires that one record in three in each set shall have a forward directivity component, whilst the remainder of the set shall be of near-neutral or backwards directivity when the site is near a major fault. The selected site, Wellington, is near a major fault according to NZS 1170.5 [15] and, thus, three in seven
pairs have a forward directivity component for both site classes to fulfil the requirement of this standard. Not all near source records have a forward directivity component. Somerville and Smith [25] report that two conditions have to be met for forward directivity effects: (a) the rupture propagation has to be towards the site and (b) the direction of the slip on the fault has to be aligned with the site. This is the reason why even though most of the pairs shown in Table 2 are from near source earthquakes only three in each site class have a forward directivity component. All the tanks described in Table 1 meet the design requirements imposed by [4,5] for both site classes.
5. Results 5.1. Scale factors All the ground motions records were scaled to the target spectra, defined in the previous section, using the three procedures given by the design specifications described in Section 2. Fig. 4 shows the unscaled 5% damped response spectra of the records and the target spectrum for both site classifications. Both horizontal components are shown in Fig. 4. Figs. 5–7 show the 5% damped response spectra of the records scaled by [15–17] respectively and the target spectrum of the tank T6. Table 3 shows the period ranges of interest computed according to the three design specifications considered. Tables 4 and 5 show a summary of the scale factors computed using the three procedures described above for the six tanks. Table 3 shows that the restriction imposed by NZS 1170.5 regarding the minimum value for T1, i.e. 0.4 s, leads to the same period range of interest for all tanks analysed. Thus, the same scale
Table 2 Earthquake records used from Oyarzo-Vera et al. [18]. Station
Date
Magnitude (Mw)
Di (km)
Depth (km)
PGA (g)
Fault mechanism
FDa
Site classification C EQ1 El Centro, USA EQ2 Tabas, Iran EQ3 Michoacan, Mexico EQ4 Landers, USA EQ5 Kocaeli, Turkey EQ6 Duzce, Turkey EQ7 Hokkaido, Japan
0117 (i) UNIO Lucerne Valley Darica (ii) HKD085
19-05-40 16-09-78 19-09-85 28-06-92 17-08-99 12-11-99 26-09-03
7 7.4 8.1 7.3 7.5 7.2 8.3
6 2 16 1 14 8 43
10 5 15 5 15 10 33
0.348 0.931 0.169 0.813 0.211 0.535 0.282
Strike-Slip Reverse Subduction Strike-Slip Strike-Slip Strike-Slip Subduction
No Yes No Yes Yes No No
Site classification D EQ1 El Centro, USA EQ2 El Centro #6, Imperial Valley EQ3 Michoacan, Mexico EQ4 Kocaeli, Turkey EQ5 Chi-Chi, Taiwan EQ6 Duzce, Turkey EQ7 Hokkaido, Japan
0117 5158 Caleta de Campos YPT (iii) TCU051 (ii) HKD085
19-05-40 15-10-79 19-09-85 17-08-99 20-09-99 12-11-99 26-09-03
7 6.5 8.1 7.5 7.5 7.2 8.3
6 0 16 3 7 8 43
10 10 15 15 – 10 33
0.348 0.437 0.143 0.349 0.234 0.535 0.282
Strike-Slip Reverse Subduction Strike-Slip Reverse Strike-Slip Subduction
No Yes No Yes Yes No No
ID
Event
Di = Distance to the epicentre. (i) Latitude & Longitude: 33.6000, 56.9200; (ii) Available at http://peer.berkeley.edu/nga_files/ath/DUZCE/DZC270.AT2 and DZC180.AT2; (iii) Available at http://peer.berkeley.edu/nga_files/ath/KOCAELI/YPT330.AT2 and YPT060.AT2. a FD = forward directivity component.
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10
10
Spectral Acceleration (g)
Spectral Acceleration (g)
Target Spectra
1
0.1
0.01 0.01
0.1
1
1
0.1
0.01 0.01
10
0.1
1
10
Period (s)
Period (s)
Fig. 4. Target spectra and response spectra of the unscaled ground motion records. Site classification C (left) and site classification D (right).
10
10
Spectral Acceleration (g)
Spectral Acceleration (g)
Target Spectra 1
Range of interest
0.1
0.01 0.01
0.1
1
10
1
0.1
0.01 0.01
Range of interest
0.1
1
10
Period (s)
Period (s)
Fig. 5. Target spectrum and response spectra of the ground motion records scaled by NZS 1170.5 for tank T6. Site classification C (left) and site classification D (right).
10
10
Spectral Acceleration (g)
Spectral Acceleration (g)
Target Spectra
1
0.1 Range of interest
0.01 0.01
0.1
1
10
Period (s)
1
0.1 Range of interest
0.01 0.01
0.1
1
10
Period (s)
Fig. 6. Target spectrum and response spectra of the ground motion records scaled by ASCE/SEI 7-10 for tank T6. Site classification C (left) and site classification D (right).
factors are computed for all earthquake records for the six tanks analysed (Tables 4 and 5). This occurs for both site classifications and, as was mentioned before, is due to storage tanks being very stiff structures with fundamental periods (impulsive) of a few tenths of a second. In this way, the tanks analysed have a period shorter than 0.4 s and, thus, their scale factor is the same for each record. The reason to have an upper limit in the range of interest, 1.3T1, is to cover the possibility that the effective fundamental
period could lengthen into during nonlinear response. In the cases considered this upper limit is irrelevant because elongation of the fundamental period does not occur in a linear time-history analysis. The lower limit, 0.4T1, exists to pick up some of the higher modes of the structure. However, with the restriction of a minimum fundamental period of 0.4 s, those two limits are the same for all the tanks analysed and, thus, the reasons why the limits were imposed do not apply in these cases. Furthermore, the
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10
10
Spectral Acceleration (g)
Spectral Acceleration (g)
Target Spectra
1
0.1
1
0.1 Range of interest
Range of interest
0.01 0.01
0.1
1
10
0.01 0.01
Period (s)
0.1
1
10
Period (s)
Fig. 7. Target spectrum and response spectra of the ground motion records scaled by Eurocode 8 for tank T6. Site classification C (left) and site classification D (right).
Table 3 Period ranges of interest according to the design specifications. Tank
T1 T2 T3 T4 T5 T6
T1 (s)
0.085 0.139 0.157 0.183 0.214 0.250
NZS 1170.5
ASCE/SEI 7–10
Eurocode 8
Lower (s)
Upper (s)
Lower (s)
Upper (s)
Lower (s)
Upper (s)
0.160 0.160 0.160 0.160 0.160 0.160
0.520 0.520 0.520 0.520 0.520 0.520
0.017 0.028 0.031 0.037 0.043 0.050
0.128 0.209 0.236 0.275 0.321 0.375
0.017 0.028 0.031 0.037 0.043 0.050
0.170 0.278 0.314 0.366 0.428 0.500
minimum value of T1 = 0.4 s leads to a period range of interest that does not extend to the fundamental period of tanks T1, T2 and T3. NZS 1170.5 establishes a maximum value of the scale factor of 4.9 (k1k2 6 4.9) to ensure a similar amplitude between the record and the target spectrum. This restriction has not been taken into account in this study to enable the use of the records recommended by Oyarzo et al. [18]. The scale factors computed according to Eurocode 8, shown in Tables 4 and 5, have average values of 3.79 and 4.34 for site classes
C and D, respectively. These records would qualify as moderately scaled records according to Iervolino et al. [26]. Amongst the six classes of records used to match the target spectrum of Eurocode 8 considered by Iervolino et al. [26], two of these groups were real records linearly scaled. The first group is named ‘‘Moderately scaled records” with an average scale factor equal to 5 and the second one is named ‘‘Significantly scaled records” with an average scale factor equal to 12. The variability in the scale factors computed in the example given by Iervolino et al. [26] was very high compared to the results shown herein for this study, e.g., in a set formed by seven events Iervolino et al. [26] report a minimum scale factor equal to 0.229 and a maximum equal to 21.882, with an average value of 5 for the whole set. Thus there is a big difference between NZS 1170.5 results and the results of the study in [26]. As was mentioned above, NZS 1170.5 establishes a maximum value of scale factor of 4.9. A software package called REXEL 2.5 (beta) was used by Iervolino et al. [26] to select the real records used in their study. The use of REXEL is extensively explained in [27]. Iervolino et al. [26] conclude that the use of linearly scaled records is a legitimate practice, showing that there is no systematic bias in the seismic response with respect to the unscaled real records. Watson-Lamprey et al. [28] and Luco and Bazurro [29]
Table 4 Scale factors computed using the three procedures for site classification C. Tank NZS 1170.5 T1 T2 T3 T4 T5 T6
EQ1
EQ2
EQ3
EQ4
EQ5
EQ6
EQ7
Average value
Standard deviation
2.699
0.902
4.349
2.098
6.351
1.790
2.909
3.014
1.82
0.804
4.634
0.803 1.102
5.150
2.220
3.575
2.870 2.913
1.72 1.66
4.474 4.326
1.528 1.701
2.951 2.955
1.57 1.52
5.898
1.320 1.417 1.746 2.172
3.727 3.740 3.788 3.849 3.820 3.801
2.15 2.13 2.08 2.01 1.98 1.96
ASCE/SEI 7-10 T1 2.906 T2 T3 T4 T5 T6 Eurocode 8 T1 T2 T3 T4 T5 T6
3.809
0.801 0.808
1.026 1.029
5.695 5.562
6.642
2.839
4.551
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Table 5 Scale factors computed using the three procedures for site classification D. Tank NZS 1170.5 T1 T2 T3 T4 T5 T6
EQ1
EQ2
EQ3
EQ4
EQ5
EQ6
EQ7
Average value
Standard deviation
3.035
2.780
6.522
3.884
4.725
2.013
3.271
3.747
1.49
1.556 2.198
4.808
3.640
4.296
2.232
3.646
3.307 3.399
1.14 0.99
3.386 3.374
0.97 0.95
4.344 4.353
1.27 1.26
4.339 4.319 4.323
1.24 1.21
ASCE/SEI 7-10 T1 2.975 T2 T3 T4 T5 T6 Eurocode 8 T1 T2 T3 T4 T5 T6
4.715 4.628
3.900
2.735 2.798
6.142
4.637
5.499
2.855
4.640
6.045 5.900 5.932
reported that there is a bias associated with scaling if the records are selected based only on the magnitude, distance and site conditions. However, both studies concluded that when the records are selected based on the properties of the scaled ground motion, which means, similar spectral shape to the target spectrum, the amount of scaling (value of the scale factor) does not introduce bias in the seismic response. Eurocode 8 gives the highest average values of scale factors for both site classifications. 5.2. Seismic response The values of the scale factors are just one aspect of computing the applied load. The other aspect is the records. To analyse the effects of these two aspects combined the tank response has to be studied. Tables 6 and 7 show the average, the standard deviation and the coefficient of variation (COV) of the maximum base
shears obtained from all the ground motions, computed by the three scaling procedures and for all the tanks analysed. Tables 6 and 7 show that Eurocode 8 gives higher average values of base shear than the other two procedures, which is consistent with the scale factors shown in Tables 4 and 5. For both site classes, NZS 1170.5 gives higher values of average base shear than ASCE/SEI 7-10 in most cases. Figs. 8 and 9 show that the maximum values of overturning moment obtained using Eurocode 8 are the highest in most cases. Dashed lines in Figs. 8 and 9 indicate the capacity of the tank. These results are also consistent with those shown in Tables 4–7. The seismic response of a tank for a given record is directly related to the scale factor of the record. Thus the higher values obtained with Eurocode 8 can be explained by the procedure used to compute the scale factors to match the target spectrum. The procedure provided in NZS 1170.5 minimises the difference between the
Table 6 Base shear statistics from all ground motions – Site Class C. Tank
Ground motion records – base shear (MN) NZS 1170.5
T1 T2 T3 T4 T5 T6
ASCE/SEI 7-10
Eurocode 8
Average
Standard deviation
COV (%)
Average
Standard deviation
COV (%)
Average
Standard deviation
COV (%)
7.3 27.2 49.2 70.3 98.6 131.3
3.6 9.8 9.7 13.4 30.4 40.7
48.6 36.0 19.8 19.0 30.8 31.0
6.1 25.1 46.6 70.1 102.5 136.8
0.7 6.8 10.0 27.0 48.7 56.4
11.8 26.9 21.5 38.5 47.5 41.3
8.1 32.2 61.1 93.2 132.5 175.8
1.1 8.7 10.7 30.2 61.0 72.9
13.5 27.0 17.6 32.3 46.1 41.5
Table 7 Base shear statistics from all ground motions – Site Class D. Tank
Ground Motion Records - Base Shear (MN) NZS 1170.5
T1 T2 T3 T4 T5 T6
ASCE/SEI 7–10
Eurocode 8
Average
Standard deviation
COV (%)
Average
Standard deviation
COV (%)
Average
Standard deviation
COV (%)
7.1 25.1 51.5 82.6 128.2 167.5
1.8 4.2 7.4 13.6 32.3 37.8
25.2 16.7 14.4 16.5 25.2 22.5
6.3 23.5 48.1 77.9 121.4 157.7
1.7 5.1 8.4 20.2 41.6 45.0
26.7 21.5 17.4 26.0 34.3 28.6
8.4 30.1 61.6 99.7 155.3 202.2
2.0 6.5 10.7 25.6 53.0 58.2
23.7 21.5 17.4 25.7 34.1 28.8
M. Ormeño et al. / Engineering Structures 102 (2015) 266–277
35 30 25 20 15 10
0
200
150
100
50
EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
0
Ground Motion
Ground Motion
Tank T3
Overturning Moment (MNm)
500
1400
400 300 200 100 0
3500
Tank T4
1200 1000 800 600 400 200
EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
0
Ground Motion
Ground Motion
Tank T5
4000
Tank T6
3500
Overturning Moment (MNm)
3000 2500 2000 1500 1000
3000 2500 2000 1500 1000 500
0
0 EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
500
EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
Overturning Moment (MNm)
Tank T2
5
600
Overturning Moment (MNm)
250
EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
Overturning Moment (MNm)
205 MNm
NZS 1170.5 ASCE/SEI 7-10 Eurocode 8
Overturning Moment (MNm)
Tank T1
273
Ground Motion
Ground Motion
Fig. 8. Maximum overturning moment. Site classification C. Dashed line indicates the capacity of the tank in terms of overturning moment.
response spectrum of the scaled record and the target spectrum, thereby allowing the response spectrum of the scaled record to be below the target spectrum in some zones of the period range of interest. Something similar is the outcome of using the procedure given by ASCE/SEI 7-10. This procedure uses the SRSS criterion to match the scaled record to the target spectrum. Thus the
scaled record will be always below the target spectrum along the whole period range of interest. The procedure given by Eurocode 8 uses the average of the response spectra of the scaled records to match the target spectrum. In this case there is always at least one component of a scaled record above the target spectrum along the whole period range of interest. Even though matching is carried
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M. Ormeño et al. / Engineering Structures 102 (2015) 266–277
Tank T1
Overturning Moment (MNm)
35 30 25 20 15 10
250
Overturning Moment (MNm)
205 MNm
NZS 1170.5 ASCE/SEI 7-10 Eurocode 8
150
100
50
EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
0
Ground Motion
Ground Motion
Tank T3
1400
Overturning Moment (MNm)
600
Overturning Moment (MNm)
200
5 0
500 400 300 200 100
3500
Tank T4
1200 1000 800 600 400 200
EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
0 EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
0
Ground Motion
Ground Motion
Tank T5
4500
Tank T6
4000
3000
Overturning Moment (MNm)
Overturning Moment (MNm)
Tank T2
2500 2000 1500 1000 500
3500 3000 2500 2000 1500 1000 500
0 EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
EQ1A EQ1B EQ2A EQ2B EQ3A EQ3B EQ4A EQ4B EQ5A EQ5B EQ6A EQ6B EQ7A EQ7B
0
Ground Motion
Ground Motion
Fig. 9. Maximum overturning moment. Site classification D. Dashed line indicates the capacity of the tank in terms of overturning moment.
out to 90% of the target spectrum, the scale factors computed using the procedure provided by Eurocode 8 are the highest amongst the scaling procedures studied herein. From the point of view of structural integrity it is necessary to check the axial compressive stresses in the tank wall. To enable comparison between the three scaling procedures, the NZSEE recommendations [4] will be used to calculate the axial stresses in the tank shell. Two cases of axial stress are considered: buckling in membrane compression and elastic–plastic collapse. Eq. (10) is
the expression given by [4] to compute the stress limit for buckling in membrane compression.
fp fm 6 0:19 þ 0:81 f c1 f c1
ð10Þ
where fm = vertical membrane compression stress for tanks with internal pressure, subject to flexural compression (cantilever mode); fc1 = classical shell buckling stress (see Eq. (11)); and
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fp = modification of classical shell buckling stress which includes the increase due to internal pressure and the reduction due to initial imperfections in buckling stress (see Eq. (12)).
f c1 ¼ 0:6 E
t R
ð12Þ
where p = expression to take into account the internal pressure (Eq. (13)); and f0 = expression that reflects the imperfections of the tank shell (Eqs. (14) and (15)).
pR t f c1
ð13Þ
if k 6 2
k2 f0 ¼ fy 1 4
! ð14Þ
if k > 2
f 0 ¼ r f c1
ð15Þ
where p = internal f c1 Þ; k ¼ f y =ðr
pressure;
fy = material
yield
2 3 !1=2 d 4 2 1þ r¼1w 15 t w dt
stress;
ð16Þ
(d/t) = ratio of maximum imperfection amplitude to wall thickness defined in Eq. (17); and w = 1.24 for membrane compression buckling.
0:06 ðd=tÞ ¼ a
rffiffiffi R t
ð17Þ
where a = 2.5 for very high quality construction [4]. Tanks of high quality construction are considered to compute the ratio of maximum imperfection amplitude to wall thickness (d/t). NZSEE recommendations provide Eq. (18) for computing the stress limit for elastic–plastic collapse.
2
fm
Tank
ð11Þ
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi u 2 !! 2 u f p 0 1 f p ¼ f c1 t 1 1 f c1 5
p¼
Table 9 Number of occasions the elastic limit is exceeded, nex.
# !2 3 " fy s þ 250 pR 5 1 4 1 6 f c1 1 t fy 1:12 þ s1:5 sþ1
ð18Þ
1 where s ¼ Rt 400 . The capacity for vertical membrane compression stress (fm) is the minimum value between Eqs. (10) and (18). Table 8 shows this value for the 6 tanks considered. Table 9 shows the number of cases that the maximum compressive stresses at the bottom of the wall (rc) for all the tanks exceed the values shown in Table 8. It is noticeable that for tanks with aspect ratios equal or lower than 2 (T1–T4), the stresses obtained using NZS 1170.5 and ASCE/SEI 7-10 are lower than the capacity
Table 8 fm for the 6 tank analysed. Tank
fm (MPa)
T1 T2 T3 T4 T5 T6
71.7 76.7 116.4 149.3 185 212.6
T1 T2 T3 T4 T5 T6
Soil C
Soil D
NZS 1170.5
ASCE/SEI 7-10
Eurocode 8
NZS 1170.5
ASCE/SEI 7-10
Eurocode 8
0 0 0 0 2 2
0 0 0 0 2 5
0 0 0 3 3 8
0 0 0 0 3 5
0 0 0 0 2 5
0 0 0 3 6 10
of the tanks in all the cases. However, use of Eurocode 8 predicts 3 cases where rc exceeds fm (defined as nex = 3) for T4 in both site classes. This result is consistent with those shown in Figs. 8 and 9 because the overturning moment is directly related to the axial stresses developed in the tank wall. All the design specifications predict nex P 1 for tanks with aspect ratios equal or higher than 2.5. The Eurocode 8 procedure predicts the highest nex for both site classes. Table 9 shows that NZS 1170.5 predicts the lowest nex. This can be explained by considering the scaling procedure specified in this document, which requires all records to reach at least 90% of the target spectrum in the period range of interest. ASCE/SEI 7-10 requires a 100% match of the target spectrum as a minimum. NZS 1170.5 requires minimisation of a function over the period range of interest (Eq. (1)). On the other hand, ASCE/SEI 7-10 requires that at all periods in the range of interest the requirements of the document are meet. Therefore, the scale factors computed by ASCE/SEI 7-10 are larger than those computed by NZS 1170.5. For site class D, nex is higher than that of site class C. As was stated previously, all tanks meet the design requirements of NZSEE [4] and API 650 [5]. However, site class D controlled the design in all cases, and thus the tanks are overdesigned for site class C. This explains the lower nex for site class C. 5.3. NZS 1170.5 limit for fundamental period NZS 1170.5 imposes a lower limit of 0.4 s to the fundamental period when scaling ground motions, thus influencing the range of interest. The 0.4 s limit was imposed because there is difficulty in estimating the periods of short-period structures, e.g. due to effects such as stiffening from non-structural elements, periodlengthening from soil-structure interaction and selection of appropriate material and section properties for estimating the period. However, storage tanks are very simple structures in geometry and issues such as stiffening from non-structural elements or uncertainty in appropriate material and section properties do not apply to liquid storage tanks to any great extent. Furthermore, in all the cases analysed herein, the periods are shorter than that limit and, for this reason, the selected range of interest does not enclose the fundamental periods of the tanks analysed. For all the reasons explained above the authors of this work are of the opinion that this limit should not apply to storage tanks. In this section the method of NZS 1170.5 is applied but the lower limit on period is disregarded. Table 10 shows the scale factors computed using the method in NZS 1170.5 but modified as above. The values shown in Table 10 are in most cases larger than the values shown in Tables 4 and 5 (which include the lower limit on Period of 0.4 s), respectively. For ease of comparison, the ratio RF of the values shown in Table 10 to those shown in Tables 4 and 5 are plotted in Fig. 10 for all ground motions and tanks, where RF is defined as
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2.0
2.0
1.8
1.8
1.6
1.6
1.4
1.4
1.2
RF
RF
1.2 1.0
1.0 0.8
0.8
0.6
0.6
T1 T3 T5
0.4 0.2 0.0 EQ1
EQ2
EQ3
EQ4
EQ5
T2 T4 T6 EQ6
0.4 0.2 0.0 EQ1 EQ2 EQ3 EQ4 EQ5 EQ6 EQ7
EQ7
Ground motion
Ground motion
Fig. 10. Scale factor ratio, Site classification C (left), Site classification D (right).
Table 10 Scale factors using NZS 1170.5 disregarding lower limit on period. Ground motion
Site class C
EQ1 EQ2 EQ3 EQ4 EQ5 EQ6 EQ7
Site class D
T1
T2
T3
T4
T5
T6
T1
T2
T3
T4
T5
T6
3.595 1.179 6.624 0.841 6.563 2.861 5.413
3.457 0.987 5.682 1.011 5.353 3.138 4.365
3.427 0.943 5.633 1.113 5.038 2.961 4.267
3.363 0.88 5.456 1.238 4.907 2.64 4.032
3.112 0.803 4.987 1.524 4.894 2.394 3.755
3.019 0.833 4.774 1.663 5.213 2.202 3.41
3.833 1.829 6.916 4.753 6.469 3.051 5.773
3.503 2.408 6.34 5.139 5.409 3.18 4.424
3.483 2.595 6.212 5.067 5.142 3.01 4.337
3.431 2.776 6.306 5.021 4.728 2.693 4.114
3.184 2.878 6.495 4.71 4.381 2.45 3.842
3.1 2.842 6.558 4.398 4.404 2.261 3.502
Table 11 nex for site classes C and D. Tank
T1 T2 T3 T4 T5 T6
RF ¼
Site class C
Site class D
NZS 1170.5
NZS 1170.5 (no lower limit)
NZS 1170.5
NZS 1170.5 (no lower limit)
0 0 0 0 2 2
0 0 0 2 2 6
0 0 0 0 3 5
0 0 0 2 5 7
Scale factor without lower limit Scale factor with lower limit
ð19Þ
In most cases the scale factors computed without the restriction on the minimum period are larger than those computed with the restriction. In only 24 of the 84 cases analysed, considering both site classes, are the scale factor ratios lower than 1. Table 11 shows a comparison of nex for both site classes. Table 11 corroborates the previous results of this section, i.e., the restriction of the lower limit for the fundamental period results in an underestimation of the seismic loads acting on the tank. The value of nex increases from 4 to 10 for site class C and from 8 to 14 for site class D, when the tanks are analysed disregarding the lower limit for the fundamental period. Using this modification to the period range NZS 1170.5 predicts a higher nex than ASCE/SEI 7-10. The consequence of the 0.4 s period limit for estimation of the seismic performance of storage tanks is especially relevant because storage tanks are essential structures, pivotal in the recovery process following devastating earthquakes. 6. Conclusions A series of time-history earthquake response analyses have been carried out using 3 different procedures to match an
earthquake record to a target spectrum. Six different liquid storage tanks were considered. The main aim was to evaluate the different scaling procedures given by three internationally used design specifications and to develop an understanding of the different consequences of the scaling procedures for the tank response. Using the ground motions and the target spectrum considered in this study, the investigations reveal: 1. Most liquid storage tanks are not in the period range of interest defined by NZS 1170.5 for scaling earthquake records, and therefore, the frequency range considered over which to scale the records does not match the predominant dynamic properties of liquid storage tanks. 2. Eurocode 8 scaling procedure gives, in most cases, the highest scale factors amongst the design specifications studied in this work. This is due to the scaling procedure to match the target spectrum given by Eurocode 8 which is more stringent than that given by the other two design specifications. 3. Eurocode 8 also gives the highest values of base shear and overturning moment in most cases, predicting the highest number of exceedance of the elastic limit, followed by ASCE/SEI 7-10. 4. NZS 1170.5 is the least conservative document in terms of axial compressive stresses developed in the tank wall. This is due to the requirements of NZS 1170.5 to match the target spectrum being less onerous than those of the other two design specifications. However, this changes substantially when the tanks are analysed disregarding the lower limit for the fundamental period imposed by this standard. Use of NZS 1170.5, under this modification, results in a higher of number of exceedance of the elastic limit than ASCE/SEI 7-10. 5. The authors of this work recommend analysing liquid storage tanks disregarding the lower period restriction imposed by NSZ 1170.5. This recommendation is made because the reasons for establishing the lower limit for the fundamental period do not generally apply to liquid storage tanks.
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