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

Authors: Zhijun Jiang; Shengcai Li; Lei Zhang; Tuo Song; Lingkun Chen
Journal: Advances in Civil Engineering
 (2019)

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## Abstract

The time-averaged shear wave velocity (SWV) to 30 m (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 30 m, 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). The results show that the time-averaged shear wave velocity to the depth H (H < 30 m), 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. Thus, the estimation accuracy can be significantly improved by considering the effect of βH.


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## Body

## 1. Introduction

The 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]. The “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 [2–4]. 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. [5–10]. Through 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 [11–13], the most commonly used site proxy is the time-averaged SWV to 30 m, VS30.To accurately determineVS30, 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 VS30, e.g., the VS30 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 [15–22]. The 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 [16–22]. Kuo et al. examined the estimation accuracy of VS30 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]. The bottom-constant extrapolation method is used to obtain VS30 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.The bottom-constant extrapolation method is one of the first methods used to estimate the siteVS30; 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 VS30 using the measured site data in California, Japan, and other areas. Several other scholars also engaged in the research of VS30 based on the subsurface SWV and obtained some meaningful results. Xie et al. [27] established and validated a VS30 estimation model for Beijing plain areas using the gradient extrapolation method. Dai et al. [28] proposed a VS30 estimation method based on the conditional independence property. Wang and Wang [29] and Wang et al. [30] estimated the site VS30 based on a given subsurface velocity, using the interpolation method by assuming the SWV profiles. Of the many VS30 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 VS30 of some strong motion station sites was determined using this method.The gradient extrapolation method is used to characterize the correlation betweenVSH which is the time-averaged SWV to H (H < 30 m) and VS30 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 VS30 is not considered. The 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 VS30, in order to propose an alternative method for the estimation of VS30. This study involves four main phases: introducing the parameter βH, which characterizes the SWV structural characteristics; examining the correlation between βH, VSH, and VS30 using a residual analysis; establishing an estimation model for VS30, considering the effect of βH; and assessing the estimation accuracy of the proposed model. The results obtained herein can effectively indicate the effect of the SWV structural characteristics on the estimated value of VS30, which is of great significance to improving the estimation accuracy of VS30, so as to determine a reasonable design for the ground motion.


## 2. Research Method and Basic Data

To examine the effect of the SWV structural characteristics in the given shallow layer on the estimated value ofVS30, we first introduce the parameter βH, which was first proposed by Regnier et al. [31] to characterize the behavior of the SWV profile with depth. The parameter βH 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:(1)log10VSH=βH×log10H+γ,where VSH characterizes the SWV at the depth H ,and βH and γ are determined by fitting the relationship between VSH and the depth according to equation (1).The parameterβH can reflect the rate of increase in the SWV with depth. A lower βH value means low velocity increases with depth; a higher βH value indicates a rapid velocity increases with depth. To better specify the meaning of the parameter βH, three sites from Japan, OKYH03, YMGH09, and AICH05, for which the values of VS30 are 307 m/s, 303 m/s, and 302 m/s, respectively, are selected. The SWV profiles down to 30 m for the sites selected are shown in Figure 1. The 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 VS30, the SWV structures show quite different characteristics. The SWV increase of site OKYH03 is more rapid than those of other sites. The fitted curves of the SWV of the sites with depth from equation (1) are also given in Figure 1, and the values of β30 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 β30 because the site with larger β30 shows more rapid velocity increases with depth.Figure 1
SWV profiles of OKYH03, YMGH09, and AICH05.Figure 2
Stratigraphic sections of OKYH03, YMGH09, and AICH05.To investigate whether the estimation accuracy ofVS30 is improved by introducing βH into the gradient extrapolation method, the correlations between βH and VSH, VS30 were examined based on actual site SWV data. To examine the effect of βH on VS30, values of VS30 corresponding to actual sites in California and Japan were estimated from VSH using the models proposed by Boore [25] and Boore et al. [26], respectively, with residuals obtained. The effect of βH on VS30 was examined by analyzing the dependence of the residual on βH.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. The 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.


## 3. Correlation betweenβH and VSH

The correlation betweenβH and VSH determines whether they can be used to estimate VS30 simultaneously. A strong correlation implies that the accuracy of VS30 estimated using the two parameters is similar to that using one of the two parameters. For the convenience of engineering applications, it is enough to use a single parameter to estimate VS30. To examine the correlation between βH and VSH, the following depths were selected: H = 10, 15, 20, and 25 m. Subsequently, the βH and VSH at each depth were calculated using the actual drilling data to examine the variations of VSH with βH, as shown in Figure 3. 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.Figure 3
V
SH with respect to βH. (a) Japan, H = 10 m. (b) Japan, H = 15 m. (c) Japan, H = 20 m. (d) Japan, H = 25 m. (e) California, H = 10 m. (f) California, H = 15 m. (g) California, H = 20 m. (h) California, H = 25 m.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)As noted from Figure3, the value of βH corresponds to three cases. If βH is 0, the value of SWV within the depth H is constant. If βH 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 VSH with βH did not show a well-defined tendency. For sites in California, VSH tended to slightly increase with βH, progressively. In order to quantitatively examine the correlation between VSH and βH, the Pearson correlation coefficients were calculated and are listed in Table 1.Table 1
Pearson correlation coefficients.
H (m)
10
15
20
25
Japan
−0.065
−0.032
−0.013
0.0047
California
0.390
0.460
0.500
0.500Table1 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 noted for sites in California shows that the presence of few data points corresponding to deviatory large and small values of βH influences the correlation coefficient; the data for which the value of βH is between 0 and 0.5 show the same tendency, indicating a weak correlation between the two parameters as those in Japanese sites. Thus, the correlation between VSH and βH is considered to be negligible in this study.


## 4. Effect ofβH on VS30

The gradient extrapolation method was used to characterize the relationship betweenVSH (H < 30 m) and VS30 using a single variable VSH. According to the above analysis, the correlation between VSH and βH is very weak, and both parameters reflect the site characteristics in different aspects. To explore whether βH can improve the estimation accuracy of VS30, the effect of βH on VS30 was examined by performing a residual analysis. Residuals were obtained by estimating the VS30 in sites in California and Japan, using the gradient extrapolation method by Boore [25] and Boore et al. [26], respectively. The empirical models proposed by Boore [25] and Boore et al. [26] do not consider the variable βH. According to the principle of residual analysis, if the obtained residual exhibits significant variations with respect to βH, it can be inferred that βH significantly influences VS30. The estimation accuracy of VS30 can be improved by introducing βH into the gradient extrapolation method.To examine whether a strong dependence ofVS30 on βH exists, Figure 4 shows the variations of residual with βH, where Figures 4(a)–4(d) show the data points in Japan and Figures 4(e)–4(h) show the data points in California.Figure 4
Distribution of residualVS30 with βH. (a) Japan, H = 10 m. (b) Japan, H = 15 m. (c) Japan, H = 20 m. (d) Japan, H = 25 m. (e) California, H = 10 m. (f) California, H = 15 m. (g) California, H = 20 m. (h) California, H = 25 m.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)It is noted that the data in the two areas exhibit similar tendencies. The residual for the estimation ofVS30 tends to increase with βH progressively. A smaller H implies more significant progressive increase; moreover, when βH is high, the residuals tend to be greater than zero systematically. This indicates that VS30 tends to increase with βH. The reason is that for most sites, provided VSH is the same, the site with the higher rate of increase in the SWV with the depth will have a greater VS30. Therefore, it is beneficial to introduce βH into the gradient extrapolation method.


## 5.VS30 Estimation Model considering the Effect of βH

According to the above analysis, the parameterβH reflecting SWV structural characteristics in the shallow layer has a significant effect on the estimated result of VS30. As observed from the distribution of data points in Figure 4, the residual tends to increase linearly with βH. To reflect this law, the functional form including βH was introduced into the gradient extrapolation method, and the VS30 estimation models for Japan and California sites can be expressed as equations (2) and (3), respectively:(2)logVS30=c0EδE+c0+c1logVSH+c2logVSH2+c3βH,(3)logVS30=a+blogVSH+cβH,where δE in equation (2) indicates the uniqueness of class E sites. δE = 1 for class E, and δE = 0 otherwise. The coefficients c0E, c0, c1, c2, and c3 in equation (2) and coefficients a, b, and c in equation (3) are regression coefficients determined using site data in this study. The coefficients c3 in equation (2) and c in equation (3) reflect the influence of βH on VS30. 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 VS30 according to the average SWV of 25 depths in the range of 5–29 m, at an interval of 1 m, were obtained.Table 2
Model coefficients for Japan sites.
H (m)
Coefficients
Residual standard deviations
c
0E
c
0
c
1
c
2
c
3
5
−2.08E-01
1.03 E+00
5.79E-01
3.55E-02
1.60E-01
9.99E-02
6
−1.90E-01
9.45E-01
6.03E-01
3.68E-02
1.72E-01
9.12E-02
7
−1.76E-01
8.98E-01
6.09E-01
3.93E-02
1.67E-01
8.46E-02
8
−1.60E-01
9.19E-01
5.59E-01
5.28E-02
1.75E-01
7.76E-02
9
−1.44E-01
8.53E-01
5.82E-01
5.18E-02
1.72E-01
7.12E-02
10
−1.28E-01
8.52E-01
5.56E-01
5.98E-02
1.75E-01
6.51E-02
11
−1.11E-01
7.88E-01
5.82E-01
5.76E-02
1.71E-01
5.93E-02
12
−9.41E-02
7.53E-01
5.86E-01
5.94E-02
1.69E-01
5.41E-02
13
−7.53E-02
6.60E-01
6.37E-01
5.23E-02
1.63E-01
4.91E-02
14
−6.05E-02
6.24E-01
6.46E-01
5.26E-02
1.59E-01
4.44E-02
15
−4.95E-02
5.91E-01
6.55E-01
5.29E-02
1.51E-01
3.99E-02
16
−4.03E-02
5.51E-01
6.71E-01
5.14E-02
1.45E-01
3.58E-02
17
−3.11E-02
4.71E-01
7.20E-01
4.37E-02
1.36E-01
3.19E-02
18
−2.40E-02
4.13E-01
7.54E-01
3.84E-02
1.27E-01
2.86E-02
19
−1.84E-02
3.61E-01
7.84E-01
3.39E-02
1.16E-01
2.55E-02
20
−1.43E-02
3.21E-01
8.05E-01
3.08E-02
1.06E-01
2.27E-02
21
−1.10E-02
2.58E-01
8.45E-01
2.42E-02
9.61E-02
1.94E-02
22
−8.57E-03
2.09E-01
8.75E-01
1.94E-02
8.57E-02
1.67E-02
23
−6.85E-03
1.72E-01
8.98E-01
1.60E-02
7.48E-02
1.41E-02
24
−5.41E-03
1.43E-01
9.14E-01
1.35E-02
6.42E-02
1.19E-02
25
−4.21E-03
1.24E-01
9.24E-01
1.22E-02
5.36E-02
9.63E-03
26
−3.54E-03
1.03E-01
9.35E-01
1.05E-02
4.31E-02
7.57E-03
27
−2.33E-03
7.15E-02
9.55E-01
7.35E-03
3.24E-02
5.42E-03
28
−1.39E-03
4.49E-02
9.72E-01
4.61E-03
2.16E-02
3.53E-03
29
−5.44E-04
2.01E-02
9.87E-01
2.09E-03
1.09E-02
1.65E-03Table 3
Model coefficients for California sites.
H (m)
Coefficients
Residual standard deviations
a
b
c
5
4.96E-01
8.40E-01
2.11E-01
9.75E-02
6
4.01E-01
8.79E-01
1.90E-01
8.86E-02
7
3.54E-01
8.97E-01
1.73E-01
8.36E-02
8
3.49E-01
8.95E-01
1.73E-01
7.61E-02
9
3.24E-01
9.02E-01
1.78E-01
6.65E-02
10
2.86E-01
9.14E-01
1.73E-01
5.94E-02
11
2.36E-01
9.33E-01
1.57E-01
5.46E-02
12
2.04E-01
9.45E-01
1.41E-01
5.11E-02
13
1.89E-01
9.49E-01
1.30E-01
4.76E-02
14
1.66E-01
9.57E-01
1.18E-01
4.39E-02
15
1.45E-01
9.63E-01
1.06E-01
4.07E-02
16
1.23E-01
9.71E-01
9.14E-02
3.82E-02
17
1.07E-01
9.77E-01
7.62E-02
3.65E-02
18
9.93E-02
9.78E-01
6.86E-02
3.39E-02
19
9.14E-02
9.79E-01
6.52E-02
3.09E-02
20
8.69E-02
9.79E-01
6.31E-02
2.79E-02
21
8.26E-02
9.78E-01
5.97E-02
2.48E-02
22
7.92E-02
9.78E-01
5.63E-02
2.20E-02
23
6.73E-02
9.81E-01
5.08E-02
1.89E-02
24
5.43E-02
9.85E-01
4.40E-02
1.60E-02
25
4.18E-02
9.89E-01
3.69E-02
1.33E-02
26
2.97E-02
9.92E-01
2.92E-02
1.03E-02
27
1.84E-02
9.96E-01
2.08E-02
7.62E-03
28
1.09E-02
9.98E-01
1.35E-02
5.04E-03
29
5.40E-03
9.99E-01
6.91E-03
2.48E-03


## 6. Analysis and Discussion

### 6.1. Comparison of Residual Standard Deviations

The 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 deviationsσ 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 VS30 were compared. The 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
Comparison of standard deviations. (a) Japan. (b) California.
(a)
(b)Figure5 shows that the standard deviations of the models proposed by Boore [25] and Boore et al. [26] for the estimation of VS30 can be significantly reduced by introducing βH. For Japan and California sites, the average reductions in the standard deviation were 29.8% and 10.4%, respectively. This indicates that the standard deviation for the estimation of VS30 in Japan sites could be more significantly reduced by considering the effect of βH, which can be explained by analyzing the variations of the velocity gradient model residual with βH, 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 β15 for the estimation of VS30 in Japan; in other words, the VS30 in Japan sites has a stronger dependence on βH.To further analyze the effect ofβH on VS30 for sites from the two regions, βH was divided into intervals to analyze the differences of VS30 between the intervals. For Japan sites, the intervals of βH < 0.2 and βH > 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 βH < 0.1 and βH > 0.3 were selected for the comparison. The 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.Figure 6
Comparison of variations ofVS30 with VS10 and VS20.
(a)
(b)
(c)
(d)As shown in Figures6(a) and 6(b), for Japan sites provided with the same VSH, the VS30 of the sites with greater βH are greater. The extent of such differences can be obtained from the coefficients given in Table 2. For the two sites with β10 = 0.8 and β10 = 0.2, the differences in the VS30 obtained from the same VS10 are 27%. However, because the gradient extrapolation method does not consider the effect of β10, the estimated error is bigger than the result in this study. This indicates that the estimation accuracy of VS30 for Japan sites can be significantly improved by introducing βH, and thus, a smaller estimation standard deviation of VS30 can be obtained.For the California sites, the two intervals with the sameVSH have few samples, and therefore, the VS30 of the sample sites within the two intervals does not show a significant difference; further, the extent of reducing the VS30 standard deviation by introducing βH is relatively insignificant. However, when VS10 is in the range of 200–320 m/s, the actual values of VS30 in the two intervals with the same VS10 but different β10 have some differences, which show the same variations as that with the data in Japan.


### 6.2. Comparison of Correlation Coefficients

The correlation coefficient can be used to effectively characterize the correlation between the estimated value and the actual value ofVS30 in order to investigate the reliability of the proposed method. Using the boreholes in Japan and California, VS30 were calculated using equations (2) and (3) with VSH at depths ranging from 5 to 29 m and 10 to 29 m, respectively. Further, VS30 from the California and Japan sites were also calculated using the empirical relations suggested by Boore [25] and Boore et al. [26], respectively. The Pearson correlation coefficient r between the measured and estimated VS30 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.Figure 7
Comparison of correlation coefficients. (a) Japan. (b) California.
(a)
(b)As shown in Figure7, the data for the two regions show the same tendency; there is a stronger correlation between the estimated value and the actual value of VS30 obtained using the proposed method, especially when the depth H is smaller. This indicates that the estimation accuracy of VS30 can be significantly improved by considering βH (H < 30 m).


## 6.1. Comparison of Residual Standard Deviations

The 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 deviationsσ 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 VS30 were compared. The 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
Comparison of standard deviations. (a) Japan. (b) California.
(a)
(b)Figure5 shows that the standard deviations of the models proposed by Boore [25] and Boore et al. [26] for the estimation of VS30 can be significantly reduced by introducing βH. For Japan and California sites, the average reductions in the standard deviation were 29.8% and 10.4%, respectively. This indicates that the standard deviation for the estimation of VS30 in Japan sites could be more significantly reduced by considering the effect of βH, which can be explained by analyzing the variations of the velocity gradient model residual with βH, 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 β15 for the estimation of VS30 in Japan; in other words, the VS30 in Japan sites has a stronger dependence on βH.To further analyze the effect ofβH on VS30 for sites from the two regions, βH was divided into intervals to analyze the differences of VS30 between the intervals. For Japan sites, the intervals of βH < 0.2 and βH > 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 βH < 0.1 and βH > 0.3 were selected for the comparison. The 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.Figure 6
Comparison of variations ofVS30 with VS10 and VS20.
(a)
(b)
(c)
(d)As shown in Figures6(a) and 6(b), for Japan sites provided with the same VSH, the VS30 of the sites with greater βH are greater. The extent of such differences can be obtained from the coefficients given in Table 2. For the two sites with β10 = 0.8 and β10 = 0.2, the differences in the VS30 obtained from the same VS10 are 27%. However, because the gradient extrapolation method does not consider the effect of β10, the estimated error is bigger than the result in this study. This indicates that the estimation accuracy of VS30 for Japan sites can be significantly improved by introducing βH, and thus, a smaller estimation standard deviation of VS30 can be obtained.For the California sites, the two intervals with the sameVSH have few samples, and therefore, the VS30 of the sample sites within the two intervals does not show a significant difference; further, the extent of reducing the VS30 standard deviation by introducing βH is relatively insignificant. However, when VS10 is in the range of 200–320 m/s, the actual values of VS30 in the two intervals with the same VS10 but different β10 have some differences, which show the same variations as that with the data in Japan.


## 6.2. Comparison of Correlation Coefficients

The correlation coefficient can be used to effectively characterize the correlation between the estimated value and the actual value ofVS30 in order to investigate the reliability of the proposed method. Using the boreholes in Japan and California, VS30 were calculated using equations (2) and (3) with VSH at depths ranging from 5 to 29 m and 10 to 29 m, respectively. Further, VS30 from the California and Japan sites were also calculated using the empirical relations suggested by Boore [25] and Boore et al. [26], respectively. The Pearson correlation coefficient r between the measured and estimated VS30 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.Figure 7
Comparison of correlation coefficients. (a) Japan. (b) California.
(a)
(b)As shown in Figure7, the data for the two regions show the same tendency; there is a stronger correlation between the estimated value and the actual value of VS30 obtained using the proposed method, especially when the depth H is smaller. This indicates that the estimation accuracy of VS30 can be significantly improved by considering βH (H < 30 m).


## 7. Conclusions

We examined the effect ofβH on the estimated value of VS30; established the VS30 estimation model considering the effect of βH; and observed the estimation effect of the proposed model, based on data for the Japan and California sites:(1)
For soil with depth less thanH, βH and VSH are weakly correlated; these can be used as the variables to estimate VS30 simultaneously(2)
The parameterβH has a significant effect on VS30; for the same site VSH, VS30 tends to increase with βH(3)
Compared with the gradient extrapolation method, the proposed model can significantly reduce the standard deviation for the estimation ofVS30 while increasing the correlation between the estimated value and the measured value of VS30



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*Source: 1394905-2019-02-19.xml*