A STUDY ON SENSITIVITY OF SEISMIC SITE AMPLIFICATION FACTORS TO SITE CONDITIONS FOR BRIDGES

Seismic site amplification factors and seismic design spectra for bridges are influenced by site conditions that include geotechnical properties of soil strata as well as the geological setting. All modern seismic design codes recognize this fact and assign design spectral shapes based on site conditions or specify a 2-parameter model with site amplification factors as a function of site class, seismic intensity and vibration period (short and long). Design codes made a number of assumptions related to the site conditions while specifying the values of short (Fa) and long period (Fv) site amplification factors. Making these assumptions was necessary due to vast variation in site properties and limited availability of actual strong motion records on all site conditions and seismic setting in a region. This paper conducted a sensitivity analysis for site amplification factors for site classes C and D in the AASHTO bridge design code by performing a 1-D site response analysis in which values of site parameters like strata depth, travel-time averaged shear wave velocity in the top 30 m strata (Vs30), plasticity index (PI), impedance contrast ratio (ICR) and intensity of seismic ground motion were varied. The results were analyzed to identify the site parameters that impacted Fa and Fv values for site classes C and D. The computed Fa and Fv values were compared with the corresponding values in the AASHTO bridge design code and it was found that the code-based Fa and Fv values were generally underestimated and overestimated respectively.


INTRODUCTION
Influence of site conditions (geological setting and geotechnical properties) on seismic design spectra and site amplification factors is well recognized in modern seismic design codes [1]. The AASHTO bridge design code in the United States [2] caters for the site effects by classifying the site conditions into six classes based on three methods for the top 30 m depth of the strata: (i) travel-time averaged shear wave velocity, s30 (ii) average standard penetration test (SPT) ̅ values and (iii) average undrained shear strength, ̅ . It is to be noted that method (i) i.e. Vs30 is the preferred method for site classification in the US practice. Design spectrum for a bridge site is constructed based on its mapped peak ground acceleration (PGA), short period (0.2 s) spectral acceleration, Ss, and long period (1.0 s) spectral acceleration, S1, along with site amplification factors FPGA, Fa and Fv whose values are determined from pertinent sections of the code. The effect of variation in geotechnical properties like plasticity index (PI), over consolidation ratio (OCR), effective stress ('), depth of soil strata over bedrock and variation in impedance contrast ratio (ICR) between soil strata and bedrock are currently not included in the AASHTO code-based site characterization and design spectrum construction processes. This study examined the influence of these geotechnical and site parameters on site amplification factors (Fa and Fv) used for constructing the seismic design spectrum for bridge design.
Site amplification factors in the AASHTO code are based on site conditions and seismicity representative of the western United States [3]. The effect of variation in seismic setting is somewhat taken into account by assigning higher values of site amplification factors for lower design PGA values [4]. However, the effect of geological setting characterized by depth and properties of the bedrock as well as variation in the index properties of soil are currently not included. A number of investigators had taken note of the discrepancy related to the geological setting for particular areas [5][6][7][8][9][10][11][12][13]. Few studies also attempted to analyze the sensitivity of site amplification factors to variability in soil index properties [14,15]. This study had attempted to conduct an extensive analysis on the sensitivity of site amplification factors (Fa and Fv) to geological variability (strata depth and bedrock properties), geotechnical factors (PI, OCR, ') and intensity of seismic ground motions for site classes C and D in the AASHTO code. The results were analyzed to identify the most influential parameters for various site conditions. The computed site amplification factors were compared with values in the AASHTO bridge design code and potential limitations in the code were identified as the large variability of individual site responses does not appear to be well-captured by a single discrete code value for each site class.

Background
AASHTO code classifies site conditions into six categories (A to F) based on Vs30. Refering to Table 1, these site classes are: (a) rock sites (classes A and B) with Vs30 greater than 1500 m/s and 760 m/s respectively, (b) soil-rock ( class C) with 360 < Vs30 < 760 m/s, (c) stiff soil (class D) having Vs30 between 175 and 360 m/s, (d) soft soil (class E) in which Vs30 is less than 175 m/s and (e) highly organic or highly plastic soft soils (class F) requiring site-specific studies. Table 1 also presents an and those in the European [16], Japanese [17] and Australia -New Zealand [18] design codes. The US and European codes utilize Vs30 for site classification while the Japanese and Australia-New Zealand approximate correspondence between AASHTO site classes codes employ fundamental period of the strata overlying the bedrock in site classification as well.
Seismic design spectrum for a bridge site is constructed in the AASHTO code based on seismic hazard at the site, which is given in terms of PGA, short (0.2 s) and long (1.0 s) period spectral accelerations; Ss and S1 respectively and site amplification factors, Fa and Fv, which correspond to short and medium periods respectively. Fa and Fv in the AASHTO code were developed for geological conditions and seismic setting prevalent in the western United States with the following values: strata depth of 30 -40 m, PI of 15 and Vrock between 760 and 900 m/s [3].
This study attempted to investigate the influence of variability in geological and geotechnical parameters on Fa and Fv by conducting 1-D site response analysis on soil profiles representatives of AASHTO site classes C and D. These site classes were selected because these are the most commonly occurring soil classes which are suitable for both shallow as well as deep foundations and are characterized by a wide variation in Vs30 (175 -760 m/s), PI (0 -60), OCR (1 -10) and ' (20 -1500 kPa or 0.2 -15 atm).

Procedure
Sensitivity of soil amplification factors to variation in Vs30, PI, OCR, ', depth of soil strata and variation in bedrock shear wave velocity (Vrock) was undertaken in this study. Considered values of these parameters are listed in Table 2. The analysis procedure consisted of the following steps:

Selection of Soil Profiles
AASHTO site classes C and D encompass a wide range of Vs30 values (i.e. 175 -760 m/s). In order to delineate the effect of Vs30 on seismic site amplification factors, these site classes were further sub-divided into 5 site classes as listed in Table 3. Soil profiles corresponding to the Vs30 ranges for these five site classes were selected from the literature [21,22] and are depicted in Fig. 1 for 40 m and 110 m deep strata. These physically-realistic soil profiles were generated based on statistical study of 858 real soil profiles from Japan, western North America and France in [21] while [22] used a maximumlikelihood procedure on 557 soil profiles to statistically generate shear wave velocity profiles corresponding to Geomatrix and US Geological Survey (USGS) site classes.
The profiles used in this study are representative of soil strata with gradually increasing shear wave velocity with depth. Other   permutations of soil profiles with sharp differences in layer properties (Vs30, unit weight, PI etc.) were not considered in this study. Mechanical properties, i.e. Vs30, density (), Poisson's ratio (), shear modulus (G) and damping ratio (), of the soil profiles are listed in Table 3. Vs values in some layers of these profiles were scaled to match the target Vs30 for each site class. Refer to [23] for details.

Selection of Bedrock Parameters
In this study, shear wave velocity of the rock mass (Vrock) was chosen as the defining parameter for rock classification. South African Council on Scientific and Industrial Research (CSIR) classification for rocks [24] was used to classify the bedrock into classes I to V as listed in Table 4. According to this classification, quality of rock decreases from class I to V as Vrock decreases from 3353 m/s for class I rock to 600 m/s for class V rock. Mechanical properties, i.e. Vrock, , , G and allowable bearing pressure (qa), of the bedrock are listed in Table 4. Damping ratio of the bedrock (rock) was taken as 1% [25]. correspond to the generally accepted limits for non-plastic (i.e. sand), medium plastic and highly plastic soils [26]. A constant value of OCR (= 1) was adopted for all soil profiles based on the recommendations of [27].  Confining pressure of soil layers increases with depth when density of the strata is assumed to stay constant. However, only two values of effective stress, ', (2 atm for sands and 4 atm for clays) were used in the study. This simplification was based on the work of [27] who compared modulus reduction and damping (MRD) curves proposed by [28 -30] and demonstrated that MRD curves of [28,29] provided better fit for engineering applications than [30]. MRD curves of [29] do not account for the confining pressure effect, while it is captured in curves of [28]. In the current study, confining pressure values that matched the MRD curves of [29] and the median value of curves of [28] were used (i.e. 2 atm for sands and 4 atm for clays). This decision was also supported by the work of [8] who showed that variability in MRD curves did not significantly affect the site response variability in comparison to other factors. Restricting the range of ' to two values in defining the MRD curves thus allowed reduction of the number of variables in the study without significantly affecting the final conclusions.

Selection of Seismic Ground Motions
The selected seismic ground motions were representative of typical far-field records that were recorded more than 10 km away from the epicenter [31]. Seismic ground motions were sorted into three groups based on the median PGA values. Groups 1, 2 and 3 had median PGA values of 0.17g, 0.31g and 0.43g respectively. These seismic ground motion groups approximately correspond to design basis earthquake (DBE), functional evaluation earthquake (FEE) and maximum considered earthquake (MCE) for a site with design PGA of 0.2g.
It is required that in order to use the mean (or median) response as the design value, a ground motion suite consisting of seven or more different records should be used in the analysis for a single hazard level [16,32]. If fewer records are used, then the design value is defined as the maximum observed response and mean value cannot be used. Use of eleven seismic records is recommended by [33] so that the mean response parameters are within 30% and 70% confidence levels. Therefore, a suite of eleven ground motions for each of the three levels of earthquake intensities were selected from the literature [34 -36] to perform one-dimensional non-linear seismic site response analysis. The seismic ground motions were downloaded from PEER strong motion database website [37].  Table 5 lists the salient seismic event details of the used seismic ground motions. Some ground motions were scaled to match the targeted median value and such values are identified in Table 5 with a footnote.
Shear wave velocity of the sites in the selected ground motion set shown in Table 5 varied between 600 m/s and 1428 m/s with an average value of 747 m/s. It is understood that the bedrock Vs used in the study varied between 760 m/s and 3353 m/s and Vs of the used input motions should ideally match these values. However, non-availability of recorded ground motions on very hard rock sites that also satisfy the far-field fault distance criterion (>= 10 km), PGA variation from 0.1g to 0.5g and the required number of the ground motions (minimum 7 and preferably 11 to use the median response value as representative of the actual response with statistical confidence) precluded this effort. Additionally, the author did not want to scale very weak motions recorded on hard rock sites to match PGA values targeted in the study.
This is the reason that the suite of ground motions presented in Table 5 is representative of 'weak to hard rock' motions instead of 'hard rock' conditions (Vs > 760 m/s). Nonetheless, average Vs of the suite of ground motions (747 m/s) is very close to the threshold value of 760 m/s assigned to Vs of seismic bedrock. Therefore, use of the ground motion data set of Table 5 should provide values of the response parameters sufficiently close to the 'real' values corresponding to the data set recorded on 'hard rock'. Additionally, it has been demonstrated that use of input ground motions with different frequency content that resulted from recordings made on soil or rock sites, did not cause significant discrepancy in the response quantities [38].

1-D Seismic Site Response Analysis
More than 3950 1-D seismic site response analysis were carried out for the 33 seismic ground motions, 5 site classes, 3 values of PI, 4 Vrock values and 2 strata depths included in this study. 1-D seismic site response analysis was carried out using the STRATA software [25]. STRATA is capable of performing a 1-D equivalent-linear seismic site response analysis of the soil column in the time domain while utilizing strain dependent nonlinear MRD curves from multiple references. This study used MRD curves of [28] for reasons mentioned earlier. Fig. 3 depicts the used MRD curves for the site classes included in the study (i.e. AASHTO C and D).

Site Amplification Factors and Sensitivity Analysis
Site amplification factors for the short period (Fa) and medium period (Fv) ranges were computed from the ratio of spectral acceleration between the surface and bedrock locations. A detailed analysis was carried out to find impact of variation in PI, soil strata depth above the bedrock and variation in bedrock properties on soil amplification factors for various site classes and EQ intensity levels. These steps are explained in the following sections.

Comparison with AASHTO Code
The computed soil amplification factors (Fa and Fv) were compared with the AASHTO code values and conclusion were drawn in the last section.

COMPUTATION OF SOIL AMPLIFICATION FACTORS
Seismic design spectrum is constructed using 2 soil amplification factors (i.e. Fa and Fv) in the AASHTO code [2]. Fa and Fv and represent soil amplification in the short period (0 -0.4 s) and the medium period (0.5 -2.0 s) ranges respectively. Researchers have proposed a variety of approaches to compute these amplification factors [39 -42]. However, in the current study, the method proposed by [43] and modified by [44] was used to compute Fa and Fv values given by the following expressions: Herein, the term ( ) ( ) represents the median value of acceleration spectral ratio for the suite of eleven seismic ground motions for a particular analysis case at a given earthquake intensity level (i.e. DBE, FEE or MCE). Equations 1 and 2 were numerically integrated to get the values of Fa and Fv. It is to be noted that the Fa and Fv factors in the AASHTO code were computed using the same procedure [45].

Figure 4: Distribution of Fa and Fv values for 40 m deep strata for various soil classes, Vrock, earthquake intensity and PI.
Note: Numbers on the X-axis represent Vrock.  998  1320  2251  3353  830  1320  2251  3353  760  1320  2251  3353  760  1320  2251  3353  350  760  1320   Influence of each of these parameters is discussed in the following section.

SENSITIVITY ANALYSIS FOR SOIL AMPLIFICATION FACTORS
This section analyses the sensitivity of soil amplification factors (Fa and Fv) with respect to: (i) PI, (ii) Vrock, (iii) earthquake intensity, (iv) strata depth and (v) site classification.
In order to conduct this sensitivity analysis, the results shown in Figs The amplification factors are presented side-by-side for two depths of strata for direct comparison. Code based values of Fa and Fv are also marked in these figures. Discussion on sensitivity of soil amplification factors for the above-mentioned parameters is presented below.

Effect of PI
It is well understood that soils with different PI values exhibit significantly varying shear stress-strain and damping behavior with increasing seismic acceleration [28 -30]. However, the AASHTO code considers only Vs30 values while assigning site amplification factors. Therefore, soil index properties are not taken into account while selecting the values of these parameters despite the fact that soils with vastly different index properties can have the same Vs30.
The effect of variation in PI on soil amplification factors (Fa & Fv) is examined by computing the percent difference in these  Observations related to variation in Fv are slightly different than those mentioned for Fa and are depicted in Fig. 8(b). The variation in Fv for site classes C_high and C_avg was more than that observed for Fa but the value was less than 20%. For site classes D_high and D_avg, the maximum difference was slightly more than 20% that was less than half the difference for Fa values. Fv values in site class D_low were affected the most by the PI variation as the maximum difference was more than 60% for both strata depths. However, this difference was almost half that was noted for Fa values. In conclusion, it is noted that Fa values were affected more than Fv values due to variation in PI.

Effect of Vrock
It was observed in Fig. 6 that Fa values showed an increasing trend with increasing value of Vrock for all site classes except D_low. Similar examination of Fig. 7 revealed that Fv values exhibited the same trend for all site classes except C_high. This strong correlation between Vrock and amplification factors (Fa and Fv) has its theoretical background in the elastic wave theory. It has been shown that the maximum amplification corresponding to resonance in shear in a soil layer overlying a rock occurs approximately at the fundamental frequency of the soil layer and is approximately given by the following expression [46]: In this equation, ICR is the impedance contrast ratio defined as: =   , where  is the unit weight, Vs is the shear wave velocity and subscripts R and S refers to parameters of the bedrock and the soil layer above it respectively. Whereas,  is the damping ratio of the soil layer.
For the analysis cases investigated in this study, ICR varied between 1 and 4 for site class C soils and between 1 and 18 for site class D soils for 110 m deep strata, while it was between 1 and 7 for type C soils and between 1 and 16 for type D soils respectively for 40 m soil profiles [23]. Fig. 9 depicts the relationship between ICR and amplification factor (Fa and Fv) for 40 m deep strata. Despite the scatter in the data points, a clear trend of increasing Fa and Fv values can be noted with increasing ICR. The coefficient of determination (R 2 ) had a value of 0.52 and 0.49 for Fa and Fv respectively, whereas, the coefficient of correlation (R) had a value of  0.72 and  0.70 for Fa and Fv respectively. As R-value is in between 0.5 and 0.8, therefore a moderate correlation exist between Fa and Fv with respect to ICR [47]. Amplification given by Eq. (4) for  = 2% and 20% are also plotted in Fig. 9(a) to provide a comparison with the theoretical expression.
The decreasing trend for Fa values for site class D_low in Fig.  6 was due to the dominant period of the soil strata having its peak outside the interval for which Fa was computed. Similarly, Fv values in Fig. 7 showed a weak correlation with Vrock for site class C, which was due to the natural period of the strata being outside the interval over which Fv was computed. However, Fv values for soils D_avg and D_low exhibited a relatively stronger correlation with Vrock as the natural period of the strata was within the interval over which Fv was calculated.   weaker soils due to which high material damping was mobilized, which reduced the amplification factor.

Effect of Earthquake Intensity on Fv
Relationship between earthquake intensity and Fv for various site classes and Vrock values is presented in Fig. 11. Similar to Fa values, Fv values in site class C_high were also unaffected by level of earthquake intensity. Fv values for site class D_avg exhibited a mixed trend of slightly increasing for lower Vrock values and slightly decreasing for higher Vrock values. Contrary to the trend for Fa values, Fv values for site classes C_avg and D_high showed an increasing trend with increasing earthquake intensity. This trend was more pronounced in site class D_high.
Fv values for site class D_low showed a decreasing trend with increasing earthquake intensity which was similar to the Fa values for this site class. However, this decreasing trend reduced with increasing PI values for this site class.

Effect of Strata Depth
The influence of strata depth on the values of amplification factors (Fa and Fv) was examined by plotting the ratio of the values for 110 m and 40 m strata as depicted in Fig. 12. The following observations were made.

Effect of Strata Depth on Fa
Referring to Fig. 12, it was observed that the influence of strata depth on Fa values for site classes C_avg and D_avg is minor as the ratio is within  10% of unity. There is a moderate influence of strata depth on Fa values for site class D_high as the ratio is about +20% above unity. However, there is a strong influence of strata depth on Fa for site classes C_high and D_low as the ratio is more than 20% above and below unity for these site classes respectively. It is to be noted that site class D_low is the only site class in which the ratio is below unity (i.e. values are more for 40 m strata) for all data points. This anomaly could be attributed to the higher ICR values for the 40 m deep strata as compared to the 110 m strata.

Effect of Strata Depth on Fv
Examination of Fig. 12 for Fv revealed that Fv values for all site classes were moderately to strongly influenced by the strata depth. Moderate influence ( +20%) was noted for site class C_high and some cases of C_avg. However, strong positive influence ( > +20%) was noted for site classes D_high and D_avg and a strong negative influence (> -20%) was observed for site class D_low. It was noted that site class D_low was the only site class in which the ratio was below unity (i.e. values were more for 40 m strata) for all data points. This anomaly could be attributed to the higher ICR value for the 40 m deep strata as compared to the 110 m strata.

Effect of Site Class
Effect of site class on amplification factors Fa and Fv for both strata depths was examined in Fig. 13

Effect of Soil Non-linearity on Site Amplification Factors
An equivalent linear 1-D site response analysis was carried out in the presented study. It is understood [48 -50] that use of nonlinear site response analysis may be required under certain situations of site class and seismicity level. It is demonstrated in [50] that the equivalent linear response is essentially the same as the non-linear response for peak soil shear strains () of less than 0.1% and equivalent linear response analysis can be used with high confidence for such cases. For strains between 0.1% and 1%, the equivalent linear response starts to diverge from the non-linear response and equivalent linear response analysis should be used with caution. Whereas, for soil shear strains greater than 1%, use of non-linear response analysis is essential [50].
It was noted in the study presented herein that the median peak soil shear strain () value for site classes C_high and C_avg was less than the lower threshold value of 0.1% for all PI values, ground motions and for both strata depths. Therefore, using equivalent linear response analysis is not expected to cause any discrepancy in the results for these site classes. For site class D_high and D_avg,  exceeded the lower threshold of 0.1% for most of the MCE ground motions in a limited depth (< 6 m at the top) with a maximum median values of 0.16% and 0.3% for site classes D_high and D_avg respectively. However, for site class D_low,  exceeded the lower threshold of 0.1% for all ground motions and registered a maximum value of 0.8% for earthquake ID # 32. This means that a non-linear response analysis may have resulted in different values of amplification factors for only a limited number of site classes under certain earthquake intensities. Therefore, the conclusions reached in this study are still valid despite the use of an equivalent-linear seismic site response analysis.

Summary of the Sensitivity Analysis
Tables 6 and 7 summarize results of the sensitivity analysis for Fa and Fv respectively for various parameters based on the discussion presented earlier in the section. The influence of a parameter on soil amplification factors is quantified as follows:    i-Median values of amplification factor Fa computed in this study were 50% to 160% more than the code values for site classes C_high, C_avg, D_high and D_avg. ii-Median values of Fa computed in this study for site class D_low were 30% to 60% smaller than the code values. iii-Fa values computed for parameters similar to code conditions were within +11 % to +65% of the code values for site classes C_high, C_avg, D_high and D_avg. and -18% to -40% for site class D_low. This implies that the procedure adopted in the study is reliable and the values reported for other cases and the conclusions drawn from the sensitivity analysis are valid. iv-Smaller values of Fa for the weakest site class (D_low) as compared to the code value are also no surprise as others had also reported similar findings [11,13]. Physical explanation for this fact may be the increased soil shear strains and soil non-linearity as noted earlier. Fig. 14

CONCLUSIONS
The following conclusions are drawn from this study, which are applicable only to the site and geotechnical parameters considered in the study. Extrapolation to other site and geotechnical conditions should be done with caution while exercising engineering judgement.
i-It is concluded from the results of more than 3950 1-D site response analysis, computation of soil amplification factors and results of sensitivity analysis that the soil amplification factors for AASHTO site classes C and D showed varying degree of dependence on geological setting and geotechnical properties as well as strata depth and earthquake intensity. ii-Bedrock properties and soil PI were found to be the two most influential parameters affecting soil amplification factors, Fa and Fv. Bedrock properties affected the Fa and Fv values for sites with higher Vs30 while variation in PI influenced these parameters for sites with smaller Vs30. iii-Earthquake intensity did not have an appreciable influence on Fa and Fv values for sites with higher Vs30 but for other sites, Fa values decreased with increasing earthquake intensity. However, earthquake intensity did not affect Fv values for sites with lower Vs30. iv-Strata depth had a low to moderate influence on Fa and Fv values in all site classes except for site classes C_avg and D_avg for which its effect on Fa values could be ignored. However, this conclusion was based on the study conducted on two strata depths (i.e. 40 m and 110 m) only. Additional strata depths should be analysed to fully appreciate the influence of strata depth on Fa and Fv. v-Soil amplification factors computed for conditions similar to the one used for finding these factors in AASHTO code varied between 11 -60% for Fa and -7 --48% for Fv with an average variation of 35% and -27% for Fa and Fv respectively. It is to be noted that the computed Fv values were generally lower than the code values.  vi-There is a need to include a disclaimer in the AASHTO code for use of the specified Fa and Fv values for site conditions not included in the derivation of these factors. Users should be asked to seek alternative soil amplification factors for sites with harder bedrock (Vrock > 900 m/s), strata depth other than 30 -40 m and PI different than 15-30.