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

Jiang, Zhijun; Li, Shengcai; Zhang, Lei; Song, Tuo; Chen, Lingkun

doi:https://doi.org/10.1155/2019/1394905

Advances in Civil Engineering

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Abstract Introduction Analysis and Discussion Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2019 | Article ID 1394905 | https://doi.org/10.1155/2019/1394905

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

Zhijun Jiang,¹Shengcai Li,^1,2Lei Zhang,¹Tuo Song,¹and Lingkun Chen¹

Academic Editor: Salvatore Grasso

Received29 Sept 2018

Revised11 Dec 2018

Accepted08 Jan 2019

Published19 Feb 2019

Abstract

The time-averaged shear wave velocity (SWV) to 30 m (V_S30) 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, V_S30 cannot be determined based on the velocity profiles. To estimate the site parameter V_S30 accurately, we examined the effect of the velocity structural characteristic parameter of site profiles, β_H, on V_S30 by performing a residual analysis. Further, a method to estimate V_S30 was established considering the effect of β_H, 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), V_SH, is weakly correlated with the parameter β_H. However, β_H has a significant effect on V_S30; for the same site V_SH, V_S30 tended to increase with β_H. Compared with the extrapolation method, the proposed model can significantly reduce the standard deviation for the estimation of V_S30, while increasing the correlation between the estimated and measured values of V_S30. Thus, the estimation accuracy can be significantly improved by considering the effect of β_H.

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, 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 [15–22]. 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 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]. The 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.

The 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.

The gradient extrapolation method is used to characterize the correlation between V_SH which is the time-averaged 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. 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 V_S30, in order to propose an alternative method for the estimation of V_S30. This 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. The 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.

2. 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. The 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 characterizes the SWV at the depth ,and and are determined by fitting the relationship between and the depth according to equation (1).

The 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. 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 V_S30, 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.

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. The 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. 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 between β_H and V_SH

The 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 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. 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.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

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 well-defined 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 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. Thus, the correlation between V_SH and β_H is considered to be negligible in this study.

4. Effect of β_H on V_S30

The 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. The 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. The 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)–4(d) show the data points in Japan and Figures 4(e)–4(h) show the data points in California.

(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 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. This indicates that V_S30 tends to increase with β_H. The 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. Therefore, it is beneficial to introduce β_H into the gradient extrapolation method.

5. 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. The coefficients c_0E, 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 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.

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 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. 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.

(a)

(b)

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. This 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 β₁₅ 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. 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.

(a)

(b)

(c)

(d)

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. 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 V_S30 obtained from the same V_S10 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 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 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 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 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. The 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.

(a)

(b)

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. This indicates that the estimation accuracy of V_S30 can be significantly improved by considering β_H (H < 30 m).

7. 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:(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)The 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

Data Availability

The shear wave velocity profiles from 646 boreholes from the Japanese KiK-net network are from http://www.kyoshin.bosai.go.jp/kyoshin/db/index_en.html?all (last accessed February 2016). The shear wave velocity profiles of 135 boreholes from California are from a compendium of Boore [32], available from the online data section of http://www.daveboore.com (last accessed August 2016).

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Acknowledgments

This work was supported by Scientific Research Fund of Institute of Engineering Mechanics, China Earthquake Administration (Grant no. 2018D11), and the National Natural Science Foundation of China (Grant nos. 51478409 and 51338001). We are grateful to D. M. Boore from the U.S. Geological Survey for compiling borehole wave velocity profiles in California and making them publicly available. We are grateful to National Research Institute for Earth Science and Disaster Prevention for establishing the KiK-net network and for making the data from the network publicly available.

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Advances in Civil Engineering

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

Abstract

1. Introduction

2. Research Method and Basic Data

3. Correlation between βH and VSH

4. Effect of βH on VS30

5. VS30 Estimation Model considering the Effect of βH

6. Analysis and Discussion

6.1. Comparison of Residual Standard Deviations

6.2. Comparison of Correlation Coefficients

7. Conclusions

Data Availability

Conflicts of Interest

Acknowledgments

References

Copyright

3. Correlation between β_H and V_SH

4. Effect of β_H on V_S30

5. V_S30 Estimation Model considering the Effect of β_H