Recommendation of New Design Spectra for Iran Using Modi�ed Newmark Method

: 7 The Newmark design spectra are commonly adopted in seismic codes to calculate design spectra, 8 while these spectra generally differ from the statistically driven ones. This study aims to re-9 construct the Iranian design spectra by implementing a modified Newmark method on an extensive 10 database of previous earthquakes in Iran. To this end, three sets of earthquakes recorded at three 11 different sites are considered. The effects of parameters such as source-to-site distance, the 12 magnitude of ground motion, and the shear wave velocity are evaluated. Subsequently, the 13 amplification factors are obtained through a statistical approach, and the spectral bounds are 14 calculated for three site categories and two types of earthquake magnitudes. As a result, for the 15 first time, the coefficients of the site design spectrum of Iran are presented as a function of ground 16 motion’s magnitude for the aforementioned site categories. The calculated coefficients can be used 17 to modify the Newmark spectral values in displacement, velocity, and acceleration-sensitive 18 regions to obtain suitable design spectra. Finally, a comprehensive statistical study is conducted 19 on earthquake parameters to assess the characteristics of the earthquakes in Iran from statistical 20 perspective. The proposed design spectra can address most shortcomings of 4 th edition of the 21 Iranian seismic design code, and it is recommended to include them in the next revision.


Introduction:
It was traditionally believed that spectral ordinates mainly depend on Peak Ground Acceleration (PGA).However, Newmark and Hall [1] found that some spectral ordinates are also affected by Peak Ground Displacement (PGD) and Peak Ground Velocity (PGV).Newmark and Hall [1] and Hall et al. [2] proposed elastic design spectra mainly known as Newmark design spectra, which include three sensitive regions.The first region is the acceleration-sensitive region in the high frequencies.The second and third regions are velocity-and displacement-sensitive regions which are in the intermediate and low frequencies, respectively.
To obtain Newmark design spectra, the amplification factors and earthquake parameters need to be calculated.The amplification factors are generally obtained by using a set of ground motion records.Seismic codes such as ASCE/SEI 7-22 [3], FEMA 356 [4], IBC 2021 [5], and the Iranian seismic code (denoted as Standard No. 2800 [6]) used the idea proposed by Newmark and Hall [1] and Hall et al. [2] for proposing design spectra.However, these codes slightly modified the original Newmark design spectra.For instance, Standard No. 2800 [6] proposes smooth design spectra for four site categories, while none of these spectra have displacement-sensitive regions.Furthermore, Standard No. 2800 [6] neglects some important factors.Firstly, the proposed spectra were constructed merely based on horizontal components of ground motions, and the vertical components were neglected.Secondly, the spectra were constructed only for 5% damping ratio.
Therefore, it seems that the Standard No. 2800 [6] needs substantial revisions.
In one of the early attempts, Hall et al. [1], [2] utilized 87 horizontal and 40 vertical components of earthquake motions to obtain amplification factors.They indicated that in the Western United States, the horizontal design spectra could be taken as 1.5 times greater than vertical design spectra.
The construction of Newmark design spectra requires earthquake parameters such as PGA, PGV, and PGD, symbolized by a, v, and d, respectively.To calculate PGV for a known PGA, they proposed the relations of v/a = 0.124 s and v/a =0.093 s for soil and rock sites, respectively.After calculating PGV, PGD can be calculated using ad/v 2 = 6 for both rock and soil sites.Mohraz [2], [7], [8] studies indicated that the relationships between PGA, PGV, and PGD can significantly affect the Newmark spectral shape and amplitude.Furthermore, Dunbar and Charlwood [9] showed that the aforementioned relationships are functions of ground motion's magnitude.
Therefore, the values proposed by Newmark and Hall [1] and Hall et al. [2] may lead to significant errors in the estimated design spectrum and considerable differences with the statistically driven spectrum [10].
Mohraz [7] improved the accuracy of the Newmark spectrum by categorizing 54 records from 16 earthquakes and calculating the mean of v/a and ad/v 2 ratios.He also estimated the amplification factors for four site categories and proposed site design spectrum coefficients.It should be noted that in Mohraz's [7] study, the sites were categorized according to the alluvium depth located on the bedrock.However, this criterion is not employed in the existing building codes.
A new method of calculating amplification factors was proposed by Malhotra [11].In this method, the earthquake response spectrum is normalized; hence, the need for assuming a constant period range for displacement, velocity, and acceleration sensitive regions is eliminated.Malhotra [11] implemented this method to calculate amplification factors for 63 earthquake records.Furthermore, Malhotra [11] showed that, from a statistical viewpoint, the site condition has a negligible effect on the spectrum amplification factors.In another study, Ghasemi et al. [12] developed design spectra with 51 Iranian near-field records through Malhotra's method [11].They also concluded that site conditions did not considerably affect the calculated amplification factors.
Palermo et al. [13] constructed a displacement design spectrum using data from 177 records.They conducted a statistical analysis and evaluated the correlation of 11 earthquake parameters.They also investigated the spectrum amplification factors.Accordingly, they concluded that PGA, PGV, and PGD could represent the earthquake parameters adequately, while amplification factors are mainly functions of PGV and PGD parameters.In another relevant study, Li et al. [14] developed modified Newmark design spectra using 591 records.They categorized the earthquake records according to site type (B, C, and D) and earthquake magnitude (small and large) and calculated the design spectra for each category.They concluded that, in most categories, the Newmark design spectra were conservative in velocity and displacement sensitive regions and unconservative in acceleration sensitive regions.
In general, different methods such as: performance-based design, energy-based design, and forcebased design can be adopted for the design of structures.Among these methods, the force-based design is the most prevalent one.In this method, the pseudo-acceleration spectra are taken into account in order to define input seismic action.The pseudo-acceleration spectra are also used in the performance-based design method.However, in the energy-based method, the energy spectra are generally utilized.Climent et al. [15] calculated equivalent bilinear energy spectra using the horizontal component of 144 motions in Colombia.These bilinear spectra pass through origin with a mild slope, then they take a constant value in high periods.Ghodrati et al. [16] calculated energy spectra for Iran for four site categories.The calculated energy spectra for soil sites in mid and high periods and also for rock sites in all periods are less than those proposed by Climent et al. [15].Bin Du et al. [17] calculated energy spectra by finding the relationship between energy and pseudoacceleration spectra for a single-degree-of-freedom system.Accordingly, energy spectra were more compatible with the pseudo-acceleration spectra proposed by the existing codes.Although the energy-based design was proven to have several advantageous, it is not a commonly-used approach, and the existing seismic codes are unwilling to use this approach, mainly due to the complexity in their applications [18].
In performance-based design, it is required to specify the target displacement that can be obtained by the displacement spectra.Some investigations were carried out to identify the influential factors on the displacement spectra and attempted to improve their accuracy.The shapes and values of the spectra depend on many factors such as site category, magnitude, source-to-site distance, soilstructure interaction, pulse-like records, kinematic interaction, inertial interaction, fling effect, etc.
Wang et al. [19] evaluated the influence of earthquake magnitude, source-to-site distance, and site category on the displacement spectra.They proposed bilinear displacement spectra for damping ratios ranging from 2% to 30%.Schiappapietra et al. [20] stated that the classical methods for processing records led to eliminating the fling effect (i.e. the effects of permanent tectonic offset) from records and displacement spectra.They proposed a solution to consider this effect through modifying the displacement spectra.To assess the influence of kinematic and inertial interactions on the spectra, Behnamfar et al. [21], [22] modeled a single-degree-of-freedom structure with a foundation on the soil.
Another influential factor affecting the displacement spectra is pulse-like near-field records.These records generally lead to high spectral values and unusual shapes [23], [24].Some response spectra compatible with the pulse-like near filed ground motions were proposed by Chen et al. [25] and Waezi and Balzadeh [26].It is worth noting that due to the lack of sufficient pulse-like near-field records, artificial ground motions were produced in most previous studies [23], [25].
To overcome the aforementioned shortcomings in current Iranian seismic design spectra, in this study, a large number of earthquake records on various site types are considered to develop new design spectra through modifying Newmark spectra.The site types are categorized as B, C, and D according to ASCE/SEI 7-22 [3].Aligned with the current building codes, the average of the shear wave velocity in the depth of 0~30 meters (VS30) is used to classify the sites.The selected records include 617 horizontal and 207 vertical motions with a broad range of magnitudes, collected for the aforementioned categories from the Iran Building and Housing Research Center (BHRC) database [27].Earthquake magnitude is considered as the key parameter in the calculation of the coefficients of the site design spectrum.Accordingly, for the two horizontal and vertical components, the v/a and ad/v 2 ratios and amplification factors are calculated for different classifications.Then, coefficients of the site design spectrum are recommended for each category.
Finally, Statistical analyses are conducted on some important earthquake parameters to reflect their statistical characteristics.

Tripartite response spectrum
For seismic design applications, the pseudo-acceleration, pseudo-velocity, and displacement spectra can be depicted in a single plot denoted as a tripartite response spectrum as shown in Fig. 1.The expression of spectral displacement is expressed as follows: The pseudo spectral velocity is calculated as: The pseudo spectral acceleration can be also written as: In the above equations, ,   , ξ, and g are the natural angular frequency, angular frequency of damped vibration, damping ratio, and ground motion acceleration, respectively.Using these equations, the tripartite response spectrum of an earthquake record can be depicted.As previously mentioned, the response spectrum is divided into three main sections, including acceleration, velocity, and displacement sensitive regions.The amplification factors of PGA, PGV, and PGD are also represented by   ,   , and   (see Fig. 1).

Earthquake selection:
The criteria for selecting the earthquake records in this study are: 1.According to Mohraz [7], PGA=0.05g is considered as the threshold of strong ground motion.Therefore, in this study, the earthquake records with PGA<0.05g are ignored.
2. Only records with sufficient information are selected.This information includes three components of earthquake motions (two horizontal and one vertical motions), shear wave velocity, source-to-site distance and magnitude.The records which lack the aforementioned information are disregarded.
The selected earthquakes were filtered and their baselines were corrected according to Ghodrati et al. [28] study.In their study appropriate frequency ranges for filtering the earthquake records in Iran are proposed for different site conditions and instruments.Table 1 lists the characteristics of the selected records.In this table, M and R represent earthquake magnitude and source-to-site distance, respectively.

Statistical analysis of earthquake parameters:
According to Li et al. [14], the earthquakes are categorized into four groups, including Small Near-field (SN), Small Far-field (SF), Large Near-field (LN), and Large Far-field (LF) earthquakes.In the adopted categorizing system, if the R parameter is less than or equal to 40 km, the earthquake is categorized as near-field.Furthermore, the earthquake is considered large if the M parameter is higher than 6.Referring to Table 2 , it can be found that the effect of the R parameter on v/a and ad/v 2 ratios is less than that of magnitude in most categories, which is in agreement with the results reported by Li et al. [14].On the other hand, these ratios are shown to be highly dependent on the M parameter, which is especially evident for v/a ratio.Accordingly, in this study the maximum values of far-field and near-field for v/a and ad/v 2 ratios based on site classification and earthquake magnitudes are recommended.As it is shown in Table 2, these ratios are relatively high for most selected categories in earthquakes with large magnitude.

Calculation of amplification factors:
To obtain design spectrum in Newmark method, it is required to normalize the response spectra of the earthquakes with respect to PGA, PGV, and PGD parameters in high, intermediate, and low-frequency ranges, respectively.For all spectral values, at each period, it is assumed that the amplification factors are distributed normally for the selected number of earthquakes (Q).For chosen in the acceleration sensitive region [7].The selection of the aforementioned ranges is based on the procedure of constructing the Newmark design spectrum in building codes [14].To calculate the spectrum amplification factors, the method proposed by Newmark and Hall [1] and Hall et al. [2] is adopted.
In this section the procedure for finding the   is briefly presented.It should be noted that the displacement and velocity amplification factors,   and   , can be calculated similarly.The amplification factor for normalized acceleration of j-th record at a frequency of   and for a given damping ratio of ξ  is calculated as: where  A and K are the number of different frequency points and damping ratios, respectively.
For Q records, the average of the amplification factors at a frequency of   and for a given damping ratio of ξ  is calculated as: The variance of the amplification factors at a frequency of   and for a given damping ratio of ξ  is then written as: Then, the mean (or 50% non-exceedance probability) of the amplification factors for a given frequency and damping ratio is calculated as: Subsequently, the mean-plus-one-sigma (or 84.1% non-exceedance probability) of the amplification factors for a given frequency and damping ratio is obtained by: The average of   50% (  ) parameter over acceleration sensitive region is presented as: Similarly, the average of   84.1% (  ) is obtained as: The   50% (  ) and   84.1% (  ) parameters correspond to   damping ratio.A statistical study is then conducted on the amplification factors using the above-mentioned procedure.These amplification factors are calculated for 19 different damping ratios including 0.5%, 1%, 2%, 3%, 4%, 5%, 7%, 10%, 15%, 20%, 25%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, and 100%.Moreover, regression analyses are conducted to predict the amplification factors as a function of damping ratio.The general form of the regression functions is presented as follows: ( ) where  is the percent value of the damping ratio.The a and b factors are calculated for three site categories (B, C, and D according to the BHRC database) and two earthquake magnitude levels (M6 and M>6).The coefficients calculated through regression analysis are presented in Tables 3 to 5. In general, the results indicate that the earthquake magnitude has a significant effect on the amplification factors.It can be also concluded that for a given site category and damping ratio, the amplification factors of M>6 are generally higher than those of M  6.

Calculation of the coefficients of the site design spectrum
To remedy the shortfall of the Newmark design spectrum, Li. et al. [14] proposed a set of coefficients for horizontal component corresponding to different site classifications and earthquake magnitudes as presented in Table 9.The idea of modifying the Newmark design spectrum using site coefficients has been originally proposed by Mohraz (see Table 10) [7].The adjusted spectral bound ratios of vertical components to those of horizontal components of 84.1% are also presented in Table 11.It should be noted that in this study, sites with alluvium layer with the depth less than 9.14 m underlain by rock and sites with 9.14 to 60.9 m of alluvium layer underlain by rock are assumed to be equivalent to site categories C and D, respectively.Moreover, according to Li et al. [14], site category B is considered as rock.
In this section, sites are categorized into two groups including rock sites (site category B) and soil sites (site categories C and D).In Table 12, the ratio of the proposed spectral bounds to those of Newmark for BHRC database are presented for various site types and damping ratios, and for both horizontal and vertical components.As indicated, the aforementioned ratios are relatively constant for a given site category and earthquake magnitude regardless of the selected damping ratio.Accordingly, the average of the ratios for different damping ratios and the recommended values for each category are presented in Tables 13 and 14, respectively.According to Tables 9 to     14, it can be concluded that: • Regardless of the site category, for zones dominated by small earthquakes, the Newmark design spectra are conservative in displacement, velocity and acceleration sensitive regions.This is in agreement with Li et al. [14] presented results for both displacement and velocity-sensitive regions.However, according to Li et al. [14] for sites dominated by small earthquakes, Newmark design spectra is unconservative in acceleration sensitive region.
• Similar to Li et al. [14] study, in zones dominated by large earthquakes, the Newmark design spectra are unconservative for acceleration sensitive region and conservative for displacement and velocity regions.
• The Newmark design spectra in Mohraz [8] provide unconservative values for acceleration-sensitive region and conservative values for velocity and displacement regions for different sites regardless of the selected earthquake magnitude.
• According to Li et al. [14] and this study, Newmark Design spectra in velocity and displacement sensitive regions for sites dominated by small magnitude is much more conservative than sites dominated by large earthquakes.As a result, earthquake magnitude plays a significant role in earthquake record spectra.In these design and response spectra, the PGA, damping ratio, and non-exceedance level are taken as 0.3g, 5%, and 84.1%, respectively.The proposed, Newmark and Hall [1], Mohraz [8] and Li et al. [14] spectral bounds are also presented in Figs.In this section, probable earthquakes denoted as "scenario" earthquakes are taken into account.
The scenario earthquakes are used to check whether or not the recommended values for modifying Newmark design spectra can appropriately construct 50% design spectra.To this end, mean response spectra of 10 random ground motions recorded at different categories are selected.For sites with less than 10 records, all the records are considered.All ground motion records are

Statistical analysis of ground motion parameters
As discussed before, there are three key parameters for determining the earthquake properties including PGA, PGV, and PGD.However, in this section some other important earthquake characteristic parameters are also evaluated as summarized in Table 15 Pearson correlation coefficient between two sets of X and Y is defined as follows: in which   ,   and   are standard deviation of X, the standard deviation of Y, and covariance between X and Y, respectively.The Pearson correlation can vary between -1 and +1.If the Pearson correlation coefficient approaches -1 and +1, it indicates a high correlation.In contrast, if the Pearson correlation approaches 0, it shows a low correlation.To conduct statistical analysis, a group of records with the highest number of records are selected.Accordingly, 301 Horizontal component records of the C sites with small magnitude are used in this section.Table 16 shows the correlation between the earthquake parameters for the aforementioned category.According to Table 16, it is found that: 1.There is a high correlation between PGA and PGV.Furthermore, parameters I c and a rms are highly correlated with PGA.
2. The PGV parameter is highly correlated with the other parameters.
3. The PGD parameter is highly correlated with D rms , V rms and HI parameters.Furthermore, there is a low correlation between PGD and PGA parameters.
4. The correlation coefficient of the PGV and PGD with the other parameters is high, which indicates that the PGV and PGD can be used for predicting the other parameters.
In this section, the probabilistic distributions of each parameter are shown in Fig. 17.As shown, the probability density of the earthquake parameter can be estimated by a lognormal distribution.
Statistical properties of the parameters for each category are given in Tables 17 to 22. Furthermore, the ratio of the median and average of vertical components to those of horizontal components are presented in Table 23.It is evident that the vertical components and small magnitude earthquakes have lower values in comparison with the horizontal components and large magnitude earthquakes, respectively.
In this section, the previous characteristic parameters are estimated through regression analysis, based on PGA, PGV and PGD.The general form of the regression functions is presented as follows: Y(Parameter) = a1 + a2.PGA + a3.PGV + a4.PGD (16) In this function a1, a2, a3 and a4 are the regression coefficients which are tabulated in Tables 24 to 29.The left hand of the Eq.16, can be Arms, Vrms, Drms and HI.As it can be seen, for most categories, R 2 values obtained through regression analysis are relatively high which means that the PGA, PGV and PGD can be used to appropriately estimate the other characteristic parameters.

Conclusion:
In this study, new design spectra were proposed for Iran using the modified Newmark method for both horizontal and vertical components.To this end, 164 horizontal and 58 vertical motions recorded at site class B, 352 horizontal and 120 vertical motions recorded at site class C, and 101 horizontal and 29 vertical motions recorded at site class D (obtained from the Building and Housing Research Center (BHRC) database) were utilized.The selected motions were categorized according to site, source-to-site distance (R) and magnitude (M).The earthquakes with M>6 and R>40 were considered as large magnitude and far-field earthquakes, respectively.In the first step, the effects of the selected classifications on v/a and ad/v 2 ratios were studied.It was found that source-to-site distance was less influential than earthquake magnitude.Accordingly, amplification factors were calculated for different sites and earthquake magnitude levels.Furthermore, coefficients of the site design spectrum for the aforementioned categories were recommended using spectral bounds of 84.1%.Using these coefficients, new design spectra for Iran were recommended.Finally, a statistical study was conducted on the earthquake's characteristic parameters.Based on the results of this study, the following key conclusions are drawn: 1.The newly proposed design spectra fit the statistical spectra fairly well and they are recommended to be used in the next version of the Iranian seismic code.
2. Newmark spectra are generally conservative in velocity and displacement-sensitive regions, especially for small magnitude earthquakes.In contrast, in acceleration sensitive region, Newmark spectra for large magnitude earthquakes are usually unconservative.
3. Probability distribution of the key parameters including PGA, PGV, and PGD can be accurately estimated by a lognormal distribution.It was shown that other earthquake characteristic parameters can be also estimated based on PGA, PGV, and PGD using the proposed regression expressions.
horizontal motions, the frequency ranges of displacement, velocity, and acceleration sensitive regions are [0.1 Hz, 0.3 Hz], [0.3 Hz, 3.0 Hz], and [3.0 Hz, 8.0 Hz], respectively.The frequency ranges of vertical and horizontal motions are considered similar.However, because of the existence of records with high frequencies in vertical motions, the range of [3.0 Hz, 10.0 Hz] is

Fig. 8 Fig. 9 Fig. 8 Fig. 9 Fig. 10 Fig. 11
Fig. 8 Comparison of Newmark, proposed modified Newmark design spectra of B sites with damping ratio of 5% with scenario earthquakes for (a) small and (b) large earthquakes for horizontal component.

Table 1
Number of records in each category in this study.

Table 2
The proposed values for average of v/a and ad/v 2 ratios for B, C, and D sites and SN, SF, LN, and LF earthquakes based on BHRC database.

Table 3
Regression coefficients for B Sites.

Table 4
Regression coefficients for C Sites.

Table 5
[1]ression coefficients for D sites.According to Newmark et al.[1], to calculate the spectral bounds of 84.1% non-exceedance probability Newmark design spectra, the v/a and ad/v 2 ratios and amplification factors of 84.1% are required.With the assumption of a=1g, the v and d parameters can be found through the v/a and ad/v 2 ratios.Finally, the multiplication of a, v, and d parameters and amplification factors of 84.1% will result in spectral bounds.The obtained Newmark design spectral bonds are presented in Table6.Furthermore, using this study's recommended values of v/a and ad/v 2 ratios and the amplification factors of 84.1% for various damping ratios, the spectral bounds are calculated.These spectral bounds are calculated for both vertical and horizontal components, which are presented in Table7and 8, respectively.

Table 6
Newmark spectral bounds with the assumption of a=1g.

Table 7
Spectral bounds of 84.1% for vertical component with the assumption of a=1g in this study.

Table 8
Spectral bounds of 84.1% for horizontal component with the assumption of a=1g in this study.

Table 11
[8]io of vertical component to horizontal component with the non-exceedance level of 84.1% in Mohraz[8].

Table 12
The ratio of proposed spectral bounds to those of Newmark for BHRC database.

Table 13
The mean ratio of proposed spectral bounds to those of Newmark for BHRC database.

Table 14
Recommended site design coefficient for different categories for BHRC database.In the modified Newmark design spectrum, the spectral values are equal to   .(  .),   .(  .), and   .(  .) in acceleration, velocity, and displacement sensitive regions, respectively.  ,   , and   are modification factors for acceleration, velocity and displacement regions, respectively.The proposed modified Newmark design spectra for B, C, and D sites for both horizontal and vertical components are depicted in Figs. 2 to 7, according to the BHRC database.

Table 15
Parameters used in correlation analysis.

Table 16
Pearson correlation between earthquake parameters.

Table 17
Statistical properties of ground motion parameters for vertical component at B sites.

Table 19
Statistical properties of ground motion parameters for vertical component at C sites.

Table 20
Statistical properties of ground motion parameters for horizontal component at C sites.

Table 24
Regression coefficients of ground motion parameters for B sites and vertical component.

Table 25
Regression coefficients of ground motion parameters for B sites and horizontal component.

Table 26
Regression coefficients of ground motion parameters for C sites and vertical component.

Table 27
Regression coefficients of ground motion parameters for C sites and vertical component.

Table 28
Regression coefficients of ground motion parameters for D sites and vertical component.

Table 29
Regression coefficients of ground motion parameters for D sites and horizontal component.