amplification behavior observed from downhole arrays

and Tsai: Site Effect of Vertical MotionAmplification Behavior Observed from Downhole Arrays Journal of GeoEngineering, Vol. 13, No. 1, pp. 039-047,LiuMarch 2018 http://dx.doi.org/10.6310/jog.2018.13(1).4

39

SITE EFFECT OF VERTICAL MOTION  AMPLIFICATION BEHAVIOR OBSERVED FROM DOWNHOLE ARRAYS Hsing-Wen Liu 1 and Chi-Chin Tsai 2 ABSTRACT Strong vertical ground motions recorded during earthquakes are critical to structure designs. Similar to horizontal motions, vertical motions can be amplified by the local site condition. However, the amplification behavior of vertical motion is different from that of horizontal motion because of distinct propagation mechanisms. In this study, three component records of five downhole arrays, considering different geological conditions, ground water tables, and intensity of motions, are analyzed to evaluate the differences of wave propagation in the vertical and horizontal directions. The amplification behavior of the two directions is characterized by the transfer function of the surface and downhole measurement. It is found that the location of ground water table highly influences the amplification of vertical motion (e.g., amplitude and nonlinearity) but does not affect the amplification of horizontal motion. These variances should be considered in the dynamic site response analysis. Key words: Downhole array, vertical ground motion, soil nonlinearity, transfer function.

1.

INTRODUCTION

The evaluation of local site effect subjected to earthquakes plays an important role in the seismic designs of engineering structures. However, most site effect studies or site response analyses have concentrated on horizontal ground motion and regarded site response as a result of the vertical propagation of shear waves in a horizontally layered system. Although the ground is simultaneously subjected to shaking in the horizontal and vertical directions during a real earthquake, the vertical ground motion has received less attention than its horizontal counterpart. As a result, knowledge on the characteristics of vertical ground motion, particularly on the relation between vertical and horizontal ground motions, is limited. Recent observations from earthquake records (Bozorgina et al. 1995) suggest that the commonly adopted vertical-to-horizontal (V/H) response spectral ratio of 2/3 (Newmark and Hall 1978) may be significantly exceeded at short periods in the near-source distance range. Moreover, the V/H ratio can be much higher than 2/3 owing to local site effect (Yang and Sato 2000; Yang and Lee 2007; Yang and Yan 2009). Elgamal and He (2004) analyzed vertical ground motions from downhole arrays around the world. Peak vertical acceleration (PVA) profiles from the TKS, KNK, SGK, Hualien, La Cienega, and Treasure Island downhole array sites show similar PVA amplification characteristics; the amplification mainly occurs within the top 20 m of the soil. PVA is amplified by a factor of 2-3 at the ground surface. In addition, this amplification characteristic is barely affected by the level of shaking and remains the same before, during, and after strong shaking. Yang and Sato (2000) investigated the difference in vertical and horizontal amplification from the three-dimensional downhole Manuscript received November 10, 2017; revised February 25, 2018; accepted February 27, 2018. 1 Former graduate student, Department of Civil Engineering, National Chung Hsing University, Taiwan. 2 Associate Professor (corresponding author), Department of Civil Engineering, National Chung Hsing University, Taiwan (e-mail: [email protected]).

array records found at the reclaimed Port Island in Kobe. The horizontal peak accelerations are reduced as seismic waves travel from the bottom to the surface. Meanwhile, the vertical motion is significantly amplified at the surface, thereby resulting in a ratio of peak V/H acceleration as large as 1.5 ~ 2.0. They further concluded that the large vertical amplification is due to the incomplete saturation of surficial soils, and they suggested the importance of considering the saturation condition of soils associated with the change of water table. Bradley et al. (2014) compared the strong vertical and horizontal records at two adjacent sites during the Christchurch earthquake. Horizontal records show a difference between the rock and soil site owing to local site effect and soil nonlinearity, while the vertical records remain similar between the two sites. Stewart et al. (2016) evaluated vertical nonlinear site effects empirically and found that the degree of nonlinearity is much less than that for the horizontal component and mostly negligible. Similarities and differences in the characteristics of the time histories between vertical and horizontal motions must be further examined. In this study, three component records of five downhole arrays, including different geological conditions, ground water tables, and intensity of motions are analyzed to evaluate the differences of wave propagation in the vertical and horizontal directions. The amplification behavior of the two directions is characterized by the transfer function (TF) of the surface and downhole measurement. This study aims to (1) compare the amplification of vertical motion and that of horizontal motion, (2) determine the dependency of the amplification behavior of vertical motion on the intensity of motion (i.e., soil nonlinearity), and (3) evaluate the effect of ground water table on the amplification behavior of vertical motion.

2.

DOWNHOLE ARRAY

Geotechnical strong-motion downhole arrays are composed of strong-motion accelerometers distributed vertically throughout a site. They provide engineers and seismologists with important data for identifying the dynamic response of a site as waves propagate through the subsurface (e.g., Tsai and Hashash 2009).

40

Journal of GeoEngineering, Vol. 13, No. 1, March 2018

Moreover, the data gathered from these arrays are used to assess the effectiveness of site response methods in capturing the response of a site during earthquake shaking (e.g., Kaklamanos et al. 2015; Zalachoris and Rathje 2015). In this study, downhole measurements are analyzed to enhance the understanding of vertical motion propagation. The arrays adopted herein satisfy the requirement of adequate geological data, multiple recorded events, and high recorded surface accelerations. A total of five arrays (Lotung, La Cienega, Wildlife, Corona, and Turkey Flat) are used. The Lotung site, located in northeastern Taiwan, comprises a recent 40 ~ 50 m thick alluvium layer overlying a Pleistocene formation that varies from 150 m to 500 m in thickness (Tang 1987). The La Cienega site, located near the section of the Santa Monica freeway (I-10) at La Cienega, is composed of recent fluvial deposits of approximately 30 m in thickness over marine deposits. The Wildlife Array was established in 1982 on a floodplain in the Imperial Valley of Southern California, wherein sand boils developed during the Westmorland earthquake. The Corona Array is located at the intersection of I15 and Hwy 91 in Riverside County, California. The Turkey Flat test area, near the town of Parkfield in the central California Coast Ranges, was established by the California Geological Survey Strong-Motion Instrumentation Program to assist in determining the state of practice in estimating the effects of surface geology on earthquake ground motion in 1987. Table 1 provides the brief information of these arrays, including the geology condition, ground water table, and number of analyzed events and associated intensities. Figure 1 shows the shear wave velocity (Vs) and compression wave velocity (Vp) profiles of these arrays. The soil profile of the Lotung site is composed of interlayered silty sand and sandy silt with gravel, over clayey silt, and silty clay (Tang 1987). The ground water level is approximately 1 m below ground surface. The geological profile of La Cienega site is composed of recent fluvial deposits of approximately 30 m in thickness over marine deposits (sands, silts, clays, and gravels) (Darragh et al. 1997). The ground water table is around 9 m below the ground surface. The near-surface geology of the Wildlife site is composed of a 2.5 ~ 3.0 m thick layer of silty clay to clayey silt that caps the site. This layer is underlain by a 3.5 ~ 4.0 m thick granular layer composed of silt, silty sand, and sandy silt. The granular layer is underlain by a

thick layer of silty clay to clay. The confined silty sand layer is approximately 2 ~ 7 m and is highly susceptible to the increase in pore pressure and potential liquefaction (Bierschwale and Stokoe 1984). The Turkey Flat test area was categorized as a shallow valley composited with 25 m deep sandy clays. Repeated measurements during the wet and dry seasons show that the water table generally remains below the sediment bedrock interface (Real 1988). The downhole recorders of the La Cienega, Corona, and Turkey Flat Arrays were obtained from the Center for Engineering Strong Motion Data, those of the Wildlife Array were obtained from the NEES@UCSB, and those of the Lotung Array were obtained from the Data Management Center for Broadband and Strong-Motion Seismology (see Data and Resources Section). The detail information of the data used for analysis can be found in the Appendix. The selected array can be divided into two main groups according to subsurface conditions according to Fig. 1. The first group includes Turkey Flat and Corona Arrays and is the unsaturated (dry) site. The groundwater table in this site is lower than the bottom or the analyzed measurements of the downhole array. Therefore, the influence of ground water is delimited in these arrays. The second group includes Lotung, La Cienega, and Wildlife and is the saturated (wet) site. These arrays are used in evaluating the influence of ground water. It’s worth to mention that in one of selected event (the Superstition Hills event in November 1987), significant excess pore pressures were generated in the Wildlife Array, and the site eventually liquefied.

3.

ANALYSIS APPROACH

In treating the measured acceleration time-history as any two locations of downhole arrays (i.e., x(t) and y(t)), a TF or spectrum ratio is calculated. The measured motions are first converted from time domain to frequency domain (i.e., X(f ) and Y(f )) by Fast Fourier Transform. Thereafter, the TF is calculated as the ratio of the Fourier amplitude of the motions at two locations (i.e., | Y(f ) |/| X(f ) |). The TF shows the amplification or de-amplification of the motion through the soil layer between two locations because of the dynamic excitation at different frequencies.

Table 1 Arrays and records used for analysis

Array

No. of Events

Measurement depth

PGA range (H)

PGA range (V)

Ground water depth

Geology condition

Reference

Lotung

10

0 m, 17 m

0.08 g ~ 0.3 g

0.02 g ~ 0.2 g

1.5 m

Interlayered silty sand and sandy silt over clayey silt

Tang (1987)

La Cienega

14

0 m, 18 m

0.003 g ~ 0.49 g

0.002 g ~ 0.082 g

9m

Silty clay over gravel Darragh et al. (1997)

Wildlife

11

0 m, 7.7 m

0.003 g ~ 0.096 g

0.001 g ~ 0.039 g

2m

Interlayer of silty clay and silty sand

Corona

2

0 m, 8 m

0.029 g ~ 0.16 g

0.01 g ~ 0.12 g

13 m

Medium- to fine-grained sand and Morton et al. (2002) lesser silt

Turkey flat

6

0 m, 23 m

0.005 g ~ 0.346 g

0.008 g ~ 0.089 g

> 25 m

Clayey sand and sandy clays

Bierschwale and Stokoe (1984)

Real (1988)

Liu and Tsai: Site Effect of Vertical MotionAmplification Behavior Observed from Downhole Arrays

41

Fig. 1 Vs and Vp profiles at the five downhole arrays

The TF of the surface and downhole measurement is theoretically a function of wave velocity V (e.g., Vs and Vp) and damping ratio of soil (). For a uniform soil layer with 1D wave propagation vertically, vertical motion is dominated by P-waves and horizontal motion is dominated by S-waves. The theoretical TF of vertical motion or horizontal motion between the surface and downhole station can be expressed as (Kramer 1996; Kontoe et al. 2013; Han et al. 2016)

TF 

1 coskh

(1)

where h is the distance between two stations, and the wave number k is

k

2f V

(2)

where f is frequency (Hz) and

V  V (1  i)

(3)

where i is imaginary unit. Therefore, the peak value of TF and its corresponding frequency (predominant frequency) depend on the V value and the damping of soil. The predominant frequency is low when the V is low, and the peak value is low when the damping is high. Moreover, a high peak value implies a high amplification between two measurements. The variations in TF under weak and strong motions are attributed to soil properties and its nonlinearity. Soil becomes highly nonlinear in large strain

Journal of GeoEngineering, Vol. 13, No. 1, March 2018

Modulus

Strain

Strain

Fig. 2

Soil modulus reduction and damping curves to represent soil nonlinearity

Fig. 3

Change of TFs of LLST16 and LLST25 at the Lotung Array because of soil nonlinearity

TF peak value

TF peak value

ranges as typically presented by modulus reduction and damping curve as shown in Fig. 2. Thus, when subjected to a strong motion the V (i.e. Vs or Vp) that is function of modulus is reduced and high damping is induced. As a result, the peak value of TF and the predominant frequency decrease. The degrees of underlying soil nonlinearity can be determined by comparing the TFs between weak and strong events. Figure 3 shows an example of the TFs of horizontal motion between the surface and at a depth of 17 m of the Lotung Array under two events; LLST16 is a strong event (PGA = 0.25 g) and LLST25 is a weak event (PGA = 0.1 g). The predominant frequency of LLST16 (2.0 Hz) is lower than that of LLST25 (2.5 Hz) because of soil nonlinearity under strong shaking. Moreover, the peak value of LLST16 is lower than that of LLST25 because a high damping of soil is induced. The TFs of each direction in all events and arrays can be referred to Liu (2016). Similarly, the amplitude of the peak and the predominant frequency corresponding to the peak of TFs between the selected station and the surface station in all events and arrays are identified for three directions separately. Thereafter, these values are plotted against the surface peak ground velocity (PGV) of the corresponding directions to determine soil nonlinearity, as shown in Figs. 4 to 8. The PGVs are calculated for the separate directions in each event. PGV is used to indicate the level of strain because it is theoretically proportional to the excited strain. For example, the maximum shear strain and the maximum compression strain near the surface is proportional to PGV/Vs and PGV/Vp, respectively. Considering that the PGV is high (i.e., a large strain), the amplitude of the peak and the predominant frequency are expected to decrease due to soil nonlinearity.

Damping ratio

42

PGV (cm/s)

PGV (cm/s)

(b) Vertical

Predominant frequency (Hz)

Predominant frequency (Hz)

(a) Horizontal

PGV (cm/s) (c) Horizontal

PGV (cm/s) (d) Vertical

Fig. 4 Peak value (top) and the corresponding frequency (bottom) against PGV at the Lotung Array

TF peak value

TF peak value

Liu and Tsai: Site Effect of Vertical MotionAmplification Behavior Observed from Downhole Arrays

PGV (cm/s)

PGV (cm/s)

(b) Vertical

Predominant frequency (Hz)

Predominant frequency (Hz)

(a) Horizontal

PGV (cm/s)

PGV (cm/s) (c) Horizontal

(d) Vertical

TF peak value

TF peak value

Fig. 5 Peak value (top) and the corresponding frequency (bottom) against PGV at the La Cienega Array

PGV (cm/s)

PGV (cm/s)

Fig. 6

(b) Vertical

Predominant frequency (Hz)

Predominant frequency (Hz)

(a) Horizontal

PGV (cm/s)

PGV (cm/s)

(c) Horizontal

(d) Vertical

Peak value (top) and the corresponding frequency (bottom) against PGV at the Wildlife Array. The solid symbols indicate liquefaction event

43

TF peak value

TF peak value

Journal of GeoEngineering, Vol. 13, No. 1, March 2018

PGV (cm/s)

PGV (cm/s) (b) Vertical

Predominant frequency (Hz)

Predominant frequency (Hz)

(a) Horizontal

PGV (cm/s)

PGV (cm/s)

(c) Horizontal

(d) Vertical

TF peak value

TF peak value

Fig. 7 Peak value (top) and the corresponding frequency (bottom) against PGV at the Corona Array

PGV (cm/s)

(a) Horizontal

(b) Vertical

Predominant frequency (Hz)

PGV (cm/s)

Predominant frequency (Hz)

44

PGV (cm/s)

PGV (cm/s)

(c) Horizontal

(d) Vertical

Fig. 8 Peak value (top) and the corresponding frequency (bottom) against PGV at the Turkey Flat Array

Liu and Tsai: Site Effect of Vertical MotionAmplification Behavior Observed from Downhole Arrays

(a) NS

Elmore ranch Superstition hills

Amplitude

Figures 4 to 8 show the amplitude of the peak and the predominant frequency of the TFs against the PGV for the five downhole arrays. The trend line is based on the regression analysis of the data point assuming linear correlation. Overall, the peak value of the horizontal direction is higher than that of the vertical direction at the wet sites (i.e., Lotung and La Cienega Arrays). This finding implies that the vertical direction shows less amplification compared with the horizontal direction. By contrast, the amount of amplification is similar to the vertical and horizontal directions at the dry site. The result of such observation is due to the coupling effect of fluids and solids that induce additional damping when propagating vertical motion at wet sites as pointed by previous studies of numerical simulation (Nogami and Kazama 1992; Tong and Patrick 2008; Wu and Wang 2009; Kontoe et al. 2013). However, the amplification is higher in the vertical direction than in the horizontal one in the Wildlife array (wet site). The reason is attributed to the high impedance ratio exhibited in Vp below and above ground water table and not shown in Vs as indicated by (Yang and Yan 2009). In terms of the predominant frequency, the vertical direction is three to four times larger than the horizontal direction for the wet arrays, whereas this difference is approximately two times for the dry arrays. The difference between the predominant frequencies of the horizontal and vertical directions is attributed to the difference in Vs and Vp as shown in Fig. 1. The peak value and the predominant frequency in the horizontal direction decrease as the PGV increases for most of the arrays because of soil nonlinearity. The decreasing trend is significant for the predominant frequency. By contrast, these trends are not observed in the vertical direction, especially for the wet sites (Figs. 4 to 6). Ideally, the nonlinear behavior observed in the horizontal direction should also be presented in the vertical direction in all arrays even though the PGV level in the vertical direction is lower than that in the horizontal directions. This is because the correlated relationship between Vs and Vp and is shown in the numerical simulation by Yang and Yan (2009). However, as observed from Figs. 4 to 8, the hypothesis is only applicable for the dry site. In the Turkey Flat and Corona arrays, a similar trend of variation (not a typical decreasing trend as expected) is observed in the vertical and horizontal directions. By contrast, the arrays at the wet sites show nearly no change of predominant frequency for the vertical motions against the PGV. The differences in behavior among these arrays are attributed to the presence of shallow groundwater table. Turkey Flat and Corona arrays are two dry sites. In these sites, the groundwater table is lower than the analyzed measurement, whereas the other array sites have groundwater tables near the ground surface. The water can take the compression stress but cannot take the shear stress during wave propagation. Therefore, distinct nonlinear behavior is induced when propagating shear waves (horizontal direction) and compression waves (vertical direction). In the horizontal direction, shear waves are propagated by the solid medium (i.e., skeleton of soil) and are unaffected by the water unless excessive pore water pressure is generated during the shaking. By contrast, compression waves are propagated by the soil and water in the vertical direction. The vertical wave propagation is dominated by the water because of its higher bulk modulus than that of the soil. Therefore, an abrupt transition of Vp from lower than 500 m/s to higher than 1500 m/s (Fig. 1) indicates the position of the groundwater table. As a result, even if the horizontal direction exhibits a nonlinear

behavior caused by the soil, the vertical direction still presents a linear behavior for the saturated condition. A good example is illustrated by the Wildlife Array. Figure 9 shows vertical and horizontal TFs of liquefaction and non-liquefaction event at the Wildlife array. In the Superstition Hill event, liquefaction occurs and induces a significant soil nonlinearity. Although significant nonlinearity (i.e., substantial reductions in the predominant frequency) occurs in the horizontal direction because of liquefaction, a nearly linear behavior (i.e., no change of the predominant frequency) is observed in the vertical direction. Such difference is also presented in Fig. 6, with the solid symbol indicating liquefaction case. The observed behavior of less nonlinearity for vertical motions is in consistence with the result of fully coupled, nonlinear numerical analysis at liquefiable sites (Yang and Lee 2007). By contrast, the nonlinearity shown in the horizontal direction for the Turkey Flat and Corona Arrays is also presented in the vertical direction because the sites are dry and are unaffected by the water. The empirical results of ground motion prediction equations that show nearly linear behavior in vertical motion (Stewart et al. 2016; Bozorgnia and Campbell 2015) may imply that most sites have shallow groundwater tables.

Frequency (Hz) (b) EW

Amplitude

ANALYSIS RESULTS

Frequency (Hz) (c) Vertical

Amplitude

4.

45

Frequency (Hz)

Fig. 9

Horizontal (a) and (b) and Vertical (c) TFs of liquefaction (Superstition Hill) and non-liquefaction event (Elmore Ranch) at the Wildlife Array

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Journal of GeoEngineering, Vol. 13, No. 1, March 2018

5.

CONCLUSIONS

Three component records of five downhole arrays are analyzed to evaluate the differences of wave propagation in the vertical and horizontal directions. The amplification behavior of the two directions is characterized by the TF of the surface and downhole measurement. The findings of this study are as follows: (1) the amplification of vertical motion is generally less significant than that of horizontal motion, (2) the amplification behavior of vertical motion is less dependent on the intensity of motion (i.e., exhibiting less soil nonlinearity), and (3) the abovementioned nonlinear amplification behavior of vertical motion is highly dependent on the location of groundwater table. These observations indicate that the amplification behavior in the vertical and horizontal directions differs for wet sites. The reason is that the vertical motions are due to compressional stresses transmitted by pore fluids in the presence of a shallow groundwater table. Therefore, groundwater table should be considered in the dynamic site response analysis and the ground motion prediction of vertical motion. Although the empirical ground motion prediction equations (e.g., Stewart et al. 2016; Bozorgnia and Campbell 2015) show the linear behavior of vertical motion, such observation is only valid for wet sites. By contrast, the nonlinear behavior of vertical motion at dry sites depends on that of the horizontal one.

DATA AND RESOURCES The Center for Engineering Strong Motion Data database was searched using http://www.strongmotioncenter.org/cgi-bin/ CESMD/search_options.pl (last accessed August 2016). The NEES@UCSB was searched using http://nees.ucsb.edu/dataportal (last accessed August 2016). The Data Management Center for Broadband and Strong-Motion Seismology was searched using http://www.earth.sinica.edu.tw/~smdmc/llsst/ llsstevent.htm (last accessed August 2016).

ACKNOWLEDGEMENTS This work was supported by the Ministry of Science and Technology, Taiwan under Award No. MOST 105-2628-E-005002-MY3. The authors gratefully acknowledge such support.

REFERENCES Bierschwale, J.G. and Stokoe, K.H.I. (1984). Analytical Evaluation of Liquefaction Potential of Sands Subjected to the 1981 Westmorland Earthquake. Geotechnical Engineering Report GR 84-15, University of Texas, Austin. Bozorgina, Y., Niazi, M., and Campbell, K.W. (1995). “Characteristics of free-field vertical ground motion during the Northridge earthquake.” Earthquake Spectra, 11(4), 515525. doi:10.1193/1.1585825 Bozorgnia, Y. and Campbell, K.W. (2016). “Vertical ground motion model for PGA, PGV, and Linear response spectra using the NGA-West2 database.” Earthquake Spectra, 32(2), 9791004. Bradley, B.A., Quigley, M.C., Van Dissen, R.J., and Litchfield, N.J. (2014). “Ground motion and seismic source aspects of the canterbury.” Earthquake Sequence, 30(1), 115. Darragh, R., Graizer, V., and Shakal, A. (1997). Site Characterization and Site Response Effects at CSMIP Stations: Tarzana and La Cienega Near the Santa Monica Freeway (I-10). (p. 262): Calif. Div. Mines and Geology. Elgamal, A. and He, L.C. (2004). “Vertical earthquake ground motion records: An overview.” Journal of Earthquake Engineering, 8(5), 663697.

Han, B., Zdravkovic, L., and Kontoe, S. (2016). “Numerical and analytical investigation of compressional wave propagation in saturated soils.” Computers and Geotechnics, 75, 93102. Kaklamanos, J., Baise, L.G., Thompson, E.M., and Dorfmann, L. (2015). “Comparison of 1D linear, equivalent-linear, and nonlinear site response models at six KiK-net validation sites.” Soil Dynamics and Earthquake Engineering, 69, 207219. Kontoe, S., Christopoulos, A., and May, R. “Site response analysis for verical ground motion.” In M. Papadrakakis, V. Papadopoulos, and V. Plevris (Eds.), 4th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Kos Island, Greece, 12-14 June 2013. Kramer, S.L. (1996). Geotechnical Earthquake Engineering (Prentice-Hall international series in civil engineering and engineering mechanics). Upper Saddle River, N.J.: Prentice Hall. Liu, H.W. (2016). Analysis of Vertical Ground Motion by Downhole Measurements, Master Thesis, National Chung Is this in English or in chinese? Hsing University. Morton, D.M., Gray, C.H., Bovard, K.R., and Michael, D. (2002). Geologic Map of the Corona North 7.5’ Quadrangle, Riverside and San Bernardino Counties, California. U.S. Geological Survey. Newmark, N.M. and Hall, W.J. (1978). “Seismic design criteria for pipelines and facilities.” Journal of the Technical Councils of ASCE, 104(1), 91107. Nogami, T. and Kazama, M. (1992). “Dynamic response analysis of submerged soil by thin layer element method.” Soil Dynamic Earthquake Engineering, 11, 1726. Real, C.R. (1988). Turkey Flat, USA Site Effects Test Area: Report 2, Site Characterization. Calif. Div. of Mines and Geology. Stewart, J.P., Boore, D.M., Seyhan, E., and Atkinson, G.M. (2016). “NGA-West2 equations for predicting vertical-component PGA, PGV, and 5%-damped PSA from shallow crustal earthquakes.” Earthquake Spectra, 32(2), 10051031. Tang, H.T. (1987). Large-Scale Soil Structure Interaction. Electric Power Research Institute. Tong, Q. and Patrick, J. (2008). “Numerical analysis of 1-D compression wave propagation in saturated poroelastic media.” International Journal for Numerical and Analytical Methods in Geomechanics, 32, 161187. Tsai, C.-C. and Hashash, Y.M.A. (2009). “Learning of dynamic soil behavior from downhole arrays.” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 135(6), 745757, doi:10.1061/(ASCE)GT.1943-5606.0000050 Wu, C.-H. and Wang, J.-H. (2009). “Vertical ground motion analysis for submerged pore-elastic media with random void ratios.” Computers and Geotechnics, 36, 968976. Yang, J. and Lee, C.M. (2007). “Characteristics of vertical and horizontal ground motions recorded during the Niigata-ken Chuetsu, Japan Earthquake of 23 October 2004.” Engineering Geology, 94(1-2), 5064. Yang, J. and Sato, T. (2000). “Interpretation of seismic vertical amplification observed at an array site.” Bulletin of the Seismological Society of America, 90(2), 275285. Yang, J. and Yan, X.R. (2009). “Factors affecting site response to multi-directional earthquake loading.” Engineering Geology, 107(3-4), 7787, doi:10.1016/j.enggeo.2009.04.002 Zalachoris, G. and Rathje, E. (2015). “Evaluation of onedimensional site response techniques using borehole arrays.” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 141(12), doi:10.1061/(ASCE)GT.1943-5606.0001366

Liu and Tsai: Site Effect of Vertical MotionAmplification Behavior Observed from Downhole Arrays

47

APPENDIX Table A1 Event No.

Records of the Lotung Array used for analysis

Date (M/D/Y)

Magnitude

Epicenter dist. (km)

Measurement depth (m)

LLST7

5/20/1986

6.2

66.2

0, 6, 11, 17

LLST9

7/11/1986

3.7

5.0

0, 6, 11, 17

LLST11

7/17/1986

4.3

6.0

0, 6, 11, 17

LLST12

LLST13

LLST14

LLST15

LLST25

LLST16

LLST18

7/30/1986

7/30/1986

7/30/1986

8/05/1986

11/10/1987

11/14/1986

11/15/1986

5.8

6.2

4.2

4.2

4.9

6.8

4.0

5.2

0, 6, 11, 17



0, 6, 11, 17

4.7

0, 6, 11, 17

4.9

0, 6, 11, 17

26.9

0, 6, 11, 17

77.9

0, 6, 11, 17

77.9

0, 6, 11, 17

Direction PGA (g) NS EW V NS EW V NS EW V NS EW V NS EW V NS EW V NS EW V NS EW V NS EW V NS EW V

0.27 0.3 0.16 0.11 0.17 0.06 0.16 0.13 0.15 0.19 0.16 0.20 0.09 0.14 0.1 0.08 0.08 0.11 0.11 0.17 0.06 0.1 0.08 0.02 0.25 0.18 0.13 0.03 0.05 0.03

Table A2 Records of the La Cienega Array used for analysis Event name

Date (M/D/Y)

Hector Mine99

10/16/1999

7.1

203.9

0, 18

Hollywood

9/09/2001

4.2

4.3

0, 18

Big Bear City 2/22/2003

Epicenter Measurement Magnitude dist. (km) depth (m)

5.4

144.3

0, 18

Anza

6/12/2005

5.6

176.6

0, 18

Chino Hills

7/29/2008

5.4

57.3

0, 18

San Bernardino

1/08/2009

4.5

99.5

0, 18

Marin Del Rey

1/23/2009

3.4

10.3

0, 18

Inglewood

5/17/2009

4.7

11.4

0, 18

San Simeon 12/22/2009

6.5

310.3

0, 18

Whittier Narrows

3/16/2010

4.4

28.6

0, 18

Calexico

4/04/2010

7.2

347.6

0, 18

Encino

3/17/2014

4.4

14.7

0, 18

Iahabra

3/28/2014

5.1

43.8

0, 18

Direction NS EW V NS EW V NS EW V NS EW V NS EW V EW V V NS EW V NS EW V NS EW V NS EW V NS EW V NS EW V NS EW V

PGA (g) 0.034 0.03 0.008 0.219 0.49 0.082 0.008 0.011 0.002 0.005 0.006 0.002 0.028 0.03 0.01 0.011 0.002 0.002 0.004 0.012 Please check 0.005 0.773 0.11 0.033 0.004 0.003 0.002 0.016 0.013 0.006 0.01 0.009 0.004 0.106 0.074 0.033 0.012 0.012 0.003

Table A3 Records of the Wildlife Array used for analysis Event Date Epicenter Measurement Magnitude No. (M/D/Y) dist. (km) depth (m) WLA1 (Superstition 11/23/1987 6.6 31 0, 7.5 Hills) WLA2 (Elmore 11/23/1987 6.2 23 0, 7.5 Ranch) WLA3

6/12/2005

5.2

108.2

0, 7.7

WLA4

6/12/2005

5.6

109.1

0, 7.7

WLA5

2/09/2008

5.4

78.8

0, 7.7

WLA6

2/11/2008

5.1

89.5

0, 7.7

WLA7

2/19/2008

5.01

76.8

0, 7.7

WLA8

4/05/2010

5.1

54.9

0, 7.7

WLA9

4/05/2010

5.1

56.9

0, 7.7

WLA10

4/05/2010

5.0

58.3

0, 7.7

WLA11

6/15/2010

5.72

57.4

0, 7.7

Direction NS EW V NS EW V NS EW V NS EW V NS EW V NS EW V NS EW V NS EW V NS EW V NS EW V NS EW V

PGA (g) 0.205 0.183 0.420 0.128 0.128 0.180 0.009 0.007 0.002 0.009 0.007 0.002 0.005 0.006 0.002 0.003 0.004 0.002 0.003 0.003 0.001 0.014 0.012 0.005 0.009 0.005 0.004 0.004 0.005 0.003 0.032 0.030 0.012

Table A4 Records of the Corona Array used for analysis Event name

Date (M/D/Y)

Magnitude

Epicenter dist. (km)

Measurement depth (m)

Anza

6/12/2005

5.2

98.8

0, 8

Chino Hills

7/29/2008

5.4

21.6

0, 8

Direction NS EW V NS EW V

PGA (g) 0.035 0.029 0.01 0.11 0.16 0.12

Table A5 Records of the Turkey Flat Array used for analysis Event No.

Date (M/D/Y)

Magnitude

Epicenter dist. (km)

Measurement depth (m)

Main

9/28/2004

6.0

8.2

0, 11, 23

AS1

9/28/2004

4.2

5.9

0, 11, 23

AS2

9/28/2004

4.0

5.9

0, 11, 23

AS3

9/28/2004

3.7

7

0, 11, 23

AS4

9/28/2004

3.6

14.7

0, 11, 23

AS5

9/28/2004

3.1

6.4

0, 11, 23

Direction NS EW V NS EW V NS EW V NS EW V NS EW V NS EW V

PGA (g) 0.292 0.292 0.088 0.188 0.346 0.046 0.148 0.143 0.089 0.011 0.048 0.021 0.005 0.014 0.008 0.007 0.038 0.016

48

Journal of GeoEngineering, Vol. 13, No. 1, March 2018