Estimation of Time-Averaged Shear Wave Velocity (SWV) to 30 m considering Site SWV Structural Characteristic

+e time-averaged shear wave velocity (SWV) to 30m (VS30) is a site condition parameter that has been widely used to specify the site class in building codes. However, the penetration depth of some building sites is less than 30m, and thus, VS30 cannot be determined based on the velocity profiles. To estimate the site parameter VS30 accurately, we examined the effect of the velocity structural characteristic parameter of site profiles, βH, on VS30 by performing a residual analysis. Further, a method to estimate VS30 was established considering the effect of βH, and the validity of the proposed model was assessed based on site data pertaining to Japan and California (USA). +e results show that the time-averaged shear wave velocity to the depth H (H< 30m), VSH, is weakly correlated with the parameter βH. However, βH has a significant effect on VS30; for the same site VSH, VS30 tended to increase with βH. Compared with the extrapolation method, the proposed model can significantly reduce the standard deviation for the estimation of VS30, while increasing the correlation between the estimated and measured values of VS30. +us, the estimation accuracy can be significantly improved by considering the effect of βH.


Introduction
e local site effects have notable influence on the characteristic of the ground motion.To estimate site effects on ground motion, two general approaches are used [1].e "site-specific" analysis that can be conducted using the numerical seismic response method is usually performed for sensitive buildings and large infrastructure [1].For the site response analysis of soil, static and dynamic site characterizations are crucial points [2][3][4].In order to obtain the geotechnical characteristics, laboratory and in situ investigations are usually carried out to measure material index, constrained modulus, undrained shear strength, horizontal stress, shear wave velocity, shear modulus, damp ratio, etc. [5][6][7][8][9][10]. rough the tests, the special attention is devoted to obtain the shear wave velocity (SWV) of the profiles [3] because it is very important in seismic wave amplification.In addition, the variation of the shear modulus and damping ratio with the shear strain level needs to be determined for the reason that nonlinearity of site response is also one of the major issues in evaluating site effects [3].
Alternatively, generic site factors are used for final design of typical buildings [1].Developing site factors has been done by compiling ground motion data recorded at soil and rock sites during past earthquakes and examining dependence of amplification factor on certain site parameter, also known as site proxy [1].Given that the site shallow SWV is a determining factor of the effect of the local site condition [11][12][13], the most commonly used site proxy is the timeaveraged SWV to 30 m, V S30 .
To accurately determine V S30 , the SWV survey value to a depth of 30 m must be obtained; however, because the drilling depth of some building sites is less than 30 m, it is extremely difficult to measure the SWV at a sufficient depth.To overcome this, a number of scholars have proposed alternatives for the estimation of the site V S30 , e.g., the V S30 estimation model established using the topography, slope [14].In addition, the SWV of the profiles can also be estimated from soil physical properties of the building site through the empirical correlations because the SWV depends significantly on soil physical properties [15][16][17][18][19][20][21][22].e soil physical properties used generally include the cone tip resistance, liquidity index, standard penetration test blow counts, void ratio, etc., which should be determined by static and dynamic penetration tests [16][17][18][19][20][21][22].Kuo et al. examined the estimation accuracy of V S30 using soil physical properties based on actual site data in Taiwan, and the results of this study show that this method is less accurate than the bottom-constant extrapolation method [23].Further, the model using soil physical properties is region-dependent [24].e bottom-constant extrapolation method is used to obtain V S30 using the measurement results of the shallow soil layer SWV, assuming that the magnitude of the SWV from the bottom of the borehole to the subsurface depth of 30 m is constant, and it is equal to the SWV at the bottom of the borehole.
e bottom-constant extrapolation method is one of the first methods used to estimate the site V S30 ; however, the results still involve a few errors because the method does not consider the progressive increase in SWV with the depth.Given this, Boore [25] and Boore et al. [26] proposed the gradient extrapolation method and established an empirical model for the estimation of V S30 using the measured site data in California, Japan, and other areas.Several other scholars also engaged in the research of V S30 based on the subsurface SWV and obtained some meaningful results.Xie et al. [27] established and validated a V S30 estimation model for Beijing plain areas using the gradient extrapolation method.Dai et al. [28] proposed a V S30 estimation method based on the conditional independence property.Wang and Wang [29] and Wang et al. [30] estimated the site V S30 based on a given subsurface velocity, using the interpolation method by assuming the SWV profiles.Of the many V S30 estimation alternatives based on the subsurface velocity, the gradient extrapolation method is the most influential and has been widely used.For example, in the Next Generation Attenuation (NGA) project, the V S30 of some strong motion station sites was determined using this method.
e gradient extrapolation method is used to characterize the correlation between V SH which is the timeaveraged SWV to H (H < 30 m) and V S30 in the shallow layer.Although this method can reflect the common trend that the SWV of the profile increases progressively with the depth, the effect of the complexity of the SWV profile down to H (H < 30 m), especially its variability at depth, on the estimated results of V S30 is not considered.e current work attempts to examine the effect of the structural characteristics of SWV in the shallow soil layer (H < 30 m) on the estimated value of V S30 , in order to propose an alternative method for the estimation of V S30 . is study involves four main phases: introducing the parameter β H , which characterizes the SWV structural characteristics; examining the correlation between β H , V SH , and V S30 using a residual analysis; establishing an estimation model for V S30 , considering the effect of β H ; and assessing the estimation accuracy of the proposed model.e results obtained herein can effectively indicate the effect of the SWV structural characteristics on the estimated value of V S30 , which is of great significance to improving the estimation accuracy of V S30 , so as to determine a reasonable design for the ground motion.

Research Method and Basic Data
To examine the effect of the SWV structural characteristics in the given shallow layer on the estimated value of V S30 , we first introduce the parameter β H , which was first proposed by Regnier et al. [31] to characterize the behavior of the SWV profile with depth.e parameter β H is defined as the slope of the linear regression between the common logarithm of the shear wave propagation velocity and the common logarithm of the depth as shown in the following equation: where V S (H) characterizes the SWV at the depth H ,and β H and c are determined by fitting the relationship between V S (H) and the depth according to equation ( 1). e parameter β H can reflect the rate of increase in the SWV with depth.A lower β H value means low velocity increases with depth; a higher β H value indicates a rapid velocity increases with depth.To better specify the meaning of the parameter β H , three sites from Japan, OKYH03, YMGH09, and AICH05, for which the values of V S30 are 307 m/s, 303 m/s, and 302 m/s, respectively, are selected.e SWV profiles down to 30 m for the sites selected are shown in Figure 1. e stratigraphic sections with the indication of geotechnical layers for the sites selected are shown in Figure 2.Although the three sites have almost the same values of V S30 , the SWV structures show quite different characteristics.e SWV increase of site OKYH03 is more rapid than those of other sites.e fitted curves of the SWV of the sites with depth from equation ( 1) are also given in Figure 1, and the values of β 30 for OKYH03, YMGH09, and AICH05 are 1.02, 0.58, and 0.29, respectively.It is obvious that the differences of the SWV structural characteristics can be reflected by β 30 because the site with larger β 30 shows more rapid velocity increases with depth.
To investigate whether the estimation accuracy of V S30 is improved by introducing β H into the gradient extrapolation method, the correlations between β H and V SH , V S30 were examined based on actual site SWV data.To examine the effect of β H on V S30 , values of V S30 corresponding to actual sites in California and Japan were estimated from V SH using the models proposed by Boore [25] and Boore et al. [26], respectively, with residuals obtained.e effect of β H on V S30 was examined by analyzing the dependence of the residual on β H .
In this thesis, the actual site SWV data were sourced from California and Japan (courtesy of KiK-net).For California, a dataset of SWV profiles compiled by Boore [32] was used.e selected sites were required to have a drilling depth of more than 30 m and definite SWV; the resulting number of selected sites in Japan and California was 646 and 135, respectively.

Correlation between β H and V SH
e correlation between β H and V SH determines whether they can be used to estimate V S30 simultaneously.A strong correlation implies that the accuracy of V S30 estimated using the two parameters is similar to that using one of the two parameters.For the convenience of engineering applications, it 2 Advances in Civil Engineering is enough to use a single parameter to estimate V S30 .To examine the correlation between β H and V SH , the following depths were selected: H � 10, 15, 20, and 25 m.Subsequently, the β H and V SH at each depth were calculated using the actual drilling data to examine the variations of V SH with β H , as shown in Figure 3.As noted from Figure 3, the value of β H corresponds to three cases.If β H is 0, the value of SWV within the depth H is constant.If β H is less than 0, a soft interlayer exists as the depth increases.For Japanese sites, for H between 10 and 25 m, the variations of V SH with β H did not show a welldefined tendency.For sites in California, V SH tended to slightly increase with β H , progressively.In order to quantitatively examine the correlation between V SH and β H , the Pearson correlation coefficients were calculated and are listed in Table 1.
Table 1 shows that for Japanese sites, the correlation coefficient is extremely small, indicating a weak correlation between the two parameters.For California sites, the correlation coefficient is slightly larger.Further analysis of the data  Advances in Civil Engineering noted for sites in California shows that the presence of few data points corresponding to deviatory large and small values of β H influences the correlation coefficient; the data for which the value of β H is between 0 and 0.5 show the same tendency, indicating a weak correlation between the two parameters as those in Japanese sites.us, the correlation between V SH and β H is considered to be negligible in this study.

Effect of β H on V S30
e gradient extrapolation method was used to characterize the relationship between V SH (H < 30 m) and V S30 using a single variable V SH .According to the above analysis, the correlation between V SH and β H is very weak, and both parameters reflect the site characteristics in different aspects.To explore whether β H can improve the estimation accuracy of V S30 , the effect of β H on V S30 was examined by performing a residual analysis.Residuals were obtained by estimating the V S30 in sites in California and Japan, using the gradient extrapolation method by Boore [25] and Boore et al. [26], respectively.e empirical models proposed by Boore [25] and Boore et al. [26] do not consider the variable β H .According to the principle of residual analysis, if the obtained residual exhibits significant variations with respect to β H , it can be inferred that β H significantly influences V S30 .e estimation accuracy of V S30 can be improved by introducing β H into the gradient extrapolation method.
To examine whether a strong dependence of V S30 on β H exists, Figure 4 shows the variations of residual with β H , where Figures 4(a It is noted that the data in the two areas exhibit similar tendencies.e residual for the estimation of V S30 tends to increase with β H progressively.A smaller H implies more significant progressive increase; moreover, when β H is high, the residuals tend to be greater than zero systematically.is indicates that V S30 tends to increase with β H . e reason is that for most sites, provided V SH is the same, the site with the higher rate of increase in the SWV with the depth will have a greater V S30 .erefore, it is beneficial to introduce β H into the gradient extrapolation method.

V S30 Estimation Model considering the Effect of β H
According to the above analysis, the parameter β H reflecting SWV structural characteristics in the shallow layer has a significant effect on the estimated result of V S30 .As observed from the distribution of data points in Figure 4, the residual tends to increase linearly with β H .To reflect this law, the functional form including β H was introduced into the gradient extrapolation method, and the V S30 estimation models for Japan and California sites can be expressed as equations ( 2) and (3), respectively: where δ E in equation ( 2) indicates the uniqueness of class E sites.δ E � 1 for class E, and δ E � 0 otherwise.e coefficients c 0E , c 0 , c 1 , c 2 , and c 3 in equation ( 2) and coefficients a, b, and c in equation ( 3) are regression coefficients determined using site data in this study.e coefficients c 3 in equation ( 2) and c in equation ( 3) reflect the influence of β H on V S30 .Regressions of equations ( 2) and (3) were conducted using the considered dataset to obtain the model coefficients and the residual standard deviations, as given in Tables 2 and 3, respectively.Unlike in Boore [25], the model coefficients for the estimation of V S30 according to the average SWV of 25 depths in the range of 5-29 m, at an interval of 1 m, were obtained.

Comparison of Residual Standard Deviations.
e residual standard deviation is a key index used to measure the accuracy of model estimation.To validate the effect of introducing the SWV structural characteristic parameter, the residual standard deviations σ of results obtained using equation ( 2) and the model proposed by Boore et al. [26] and those obtained using equation ( 3) and the model proposed by Boore [25] for the estimation of V S30 were compared.e results of comparison are as shown in Figure 5. Figure 5(a) shows the data in Japan, while Figure 5(b) shows the data in California.
Figure 5 shows that the standard deviations of the models proposed by Boore [25] and Boore et al. [26] for the estimation of V S30 can be significantly reduced by introducing β H .For Japan and California sites, the average reductions in the standard deviation were 29.8% and 10.4%, respectively.is indicates that the standard deviation for the estimation of V S30 in Japan sites could be more significantly reduced by considering the effect of β H , which can be explained by analyzing the variations of the velocity gradient model residual with β H , as shown in Figure 4.As shown from the comparison between Figures 4(b) and 4(f ), a more obvious correlation exists between the residual and β 15 for the estimation of V S30 in Japan; in other words, the V S30 in Japan sites has a stronger dependence on β H .
To further analyze the effect of β H on V S30 for sites from the two regions, β H was divided into intervals to analyze the differences of V S30 between the intervals.For Japan sites, the intervals of β H < 0.2 and β H > 0.8 were selected for the comparison.Owing to the sparse data available in the California sites, to ensure a uniform number of samples in each interval, the intervals of β H < 0.1 and β H > 0.3 were selected for the comparison.
e variations of individual intervals are as shown in Figure 6; Figures 6(a) and 6(b) correspond to the Japanese sites, while Figures 6(c) and 6(d) correspond to the California sites.
As shown in Figures 6(a) and 6(b), for Japan sites provided with the same V SH , the V S30 of the sites with greater β H are greater.e extent of such differences can be obtained from the coefficients given in Table 2.For the two sites with β 10 � 0.8 and β 10 � 0.2, the differences in the V S30 obtained from the same V S10 are 27%.However, because the gradient extrapolation method does not consider the effect of β 10 , the estimated error is bigger than the result in this study.is indicates that the estimation accuracy of V S30 for Japan sites can be significantly improved by introducing β H , and thus, a smaller estimation standard deviation of V S30 can be obtained.
For the California sites, the two intervals with the same V SH have few samples, and therefore, the V S30 of the sample sites within the two intervals does not show a significant difference; further, the extent of reducing the V S30 standard deviation by introducing β H is relatively insignificant.However, when V S10 is in the range of 200-320 m/s, the actual values of V S30 in the two intervals with the same V S10 but different β 10 have some differences, which show the same variations as that with the data in Japan.

Comparison of Correlation Coefficients.
e correlation coefficient can be used to effectively characterize the correlation between the estimated value and the actual value of V S30 in order to investigate the reliability of the proposed method.Using the boreholes in Japan and California, V S30 were calculated using equations ( 2) and ( 3) with V SH at Advances in Civil Engineering    Advances in Civil Engineering depths ranging from 5 to 29 m and 10 to 29 m, respectively.Further, V S30 from the California and Japan sites were also calculated using the empirical relations suggested by Boore [25] and Boore et al. [26], respectively.e Pearson correlation coefficient r between the measured and estimated V S30 for the same region is calculated as shown in Figure 7. Figure 7(a) shows the data in Japan, while Figure 7(b) shows the data in California.As shown in Figure 7, the data for the two regions show the same tendency; there is a stronger correlation between the estimated value and the actual value of V S30 obtained using the proposed method, especially when the depth H is smaller.
is indicates that the estimation accuracy of V S30 can be significantly improved by considering β H (H < 30 m).

Conclusions
We examined the effect of β H on the estimated value of V S30 ; established the V S30 estimation model considering the effect of β H ; and observed the estimation effect of the proposed model, based on data for the Japan and California sites:    8 Advances in Civil Engineering (1) For soil with depth less than H, β H and V SH are weakly correlated; these can be used as the variables to estimate V S30 simultaneously (2) e parameter β H has a significant effect on V S30 ; for the same site V SH , V S30 tends to increase with β H (3) Compared with the gradient extrapolation method, the proposed model can significantly reduce the standard deviation for the estimation of V S30 while increasing the correlation between the estimated value and the measured value of V S30

Advances in Civil Engineering
Figures 3(a)-3(d) demonstrate the tendency of site parameters in Japan whereas Figures 3(e)-3(h) show the tendency of site parameters in California.
)-4(d) show the data points in Japan and Figures 4(e)-4(h) show the data points in California.

Figure 6 :
Figure6: Comparison of variations of V S30 with V S10 and V S20 .

Table 2 :
Model coefficients for Japan sites.

Table 3 :
Model coefficients for California sites.