Effects of soil cross-sectional modeling on the site fundamental period.

One of the most important tools in earthquake engineering is the site fundamental period. A site fundamental period can be determined by one of three methods; the approximate method, the microtremors' spectra, and the dynamic site response analysis. The dynamic site response analysis and the approximate method require the determination of the site's soil cross-sectional model in the form of the shear wave velocity profile(s). The shear wave velocity model for a certain location can be determined by invasive methods such as cross-hole tests, or by non-invasive methods such as Controlled Source Spectral Analysis of Surface Waves tests, which is also referred to as the CXW test. This paper examines the effects of the different soil cross-sectional modeling methods on the site fundamental period. In addition, the results are also compared with the site fundamental period from microtremors' records. To achieve this objective, a site was selected and different tests as well as microtremors recordings were performed at different locations within the site. The tests included cross-hole as well as CXW tests. The results showed that using different methods to determine a site fundamental period can lead to significantly different results.

INTRODUCTION

A site soil cross-sectional model of its shear wave velocity (SWV) can be determined by invasive tests such the cross-hole (CH) tests, or by the more economical non-invasive tests, such as Controlled Source Spectral Analysis of Surface Waves tests, which is also referred to as the CXW test. The National Earthquake Hazard Reduction Program (NEHRP) Provisions General Procedure (FEMA, 2003), requires the SWV model to be determined for the site's top 30 m, or to the bedrock, whichever is less. For a site with (n) soil layers, the Provisions define the site average SWV ([bar.v.sub.s]) as:

[bar.v.sub.s] = [n.summation over (i = 1)] [d.sub.i]/[n.summation over (i=1)] ([d.sub.i]/[v.sub.si]) (1)

where ([d.sub.i]) and ([v.sub.si]) are layer's (i) thickness and SWV, respectively. The site fundamental period (FP), (T) (also called the site characteristic period) can be determined or estimated by one of the following methods:

1. The approximate method (Kramer, 1996):

[T.sub.s] = 4H/[bar.v.sub.s] (2)

where H is the thickness of the soil cross-sectional model

2. The microtremors' spectral ratios method (Nakamura et al, 1986): This method utilizes records of microtremors at the site in question. The procedure is to select a section of the records to be analyzed. Concurrent sections of all three components of the record are then segmented into 20 to 30 seconds long segments. The segments are tapered, and a fast Fourier transform is performed on each segment. The segments are then smoothed before calculating the

[(H/V).sub.m] as follows:

[(H/V].sub.m] = [square root of ([S.sup.2.sub.EW] + [S.sup.2.sub.NS]/ [S.sub.v] (3)

where:

[S.sub.EW] = the smoothed east-west component of the record.

[S.sub.NS] = the smoothed north-south component of the record.

[S.sub.V] = the smoothed vertical component of the record.

The site FP is the period at which the peaks of the plots occur.

3. The dynamic site response analysis (DSRA) method: This method utilizes the site soil SWV cross-sectional model and its soil properties. These soil properties include the soil unit weight, the modulus reduction curve, the damping curve, and the layers' thickness (Kramer, 1996). The water table depth for the soil cross-sectional model is also required for this type of analysis. There are a number of available computer programs for performing DSRA, including SHAKE and ProShake (EduPro Civil Systems, 1998).

THE TESTING SITE

A seismically active site was selected to conduct the required field tests. The site is located on the northeastern coast of the Gulf of Aqaba, which is the most seismically active area in Saudi Arabia. The general site coordinates are approximately 340 57.3" east, and 29[degrees] 21.5" north. The site has an area of one square kilometer and its elevation above sea level varies from 0 m at the shore line to 30 m the site's east side. Figure (1) shows the site location and an approximate east-west cross-section.

[FIGURE 1 OMITTED]

METHODOLOGY

DSRA can be performed using one, two, or three-dimensional SWV models. However, a one-dimensional soil SWV model is adequate to capture first-order site response characteristics (FEMA, 2003). In addition to the soil cross-sectional SWV model and the soil properties, the DSRA requires the determination of the water table and bedrock depths (when the bedrock depth is < 30 m). Therefore, additional conventional exploration in the form of Standard Penetration Test (SPT), and vertical electric sounding (VES) were conducted at the site. The SPT was used to estimate the soil properties and determine the depth of the water table at each test's location. Since the SPT boreholes did not reach the bedrock, the VES tests were used to estimate the depth and inclination of the bedrock at the site. The type and number of tests that were conducted at the site were:

i. Twelve SPT

ii. Four CH tests

iii. Four CXW tests

iv. Three Microtremors recording stations

v. East-west and north-south VES to estimate bedrock depth and inclination

The tests were arranged so that at each CH tests location, one SPT and one CXW test were undertaken.

TESTS RESULTS

The soil cross-sectional SWV model was established at four locations within the site. One set of the four models was based on the SWV results of the CH tests, while another set was based on the SWV results of the CXW tests. The results of the CH tests were corrected for the presence of casing. Figure (2) shows an example of the CH and CXW tests results. The two sets were subsequently used to calculate the site approximate FP, and to perform DSRA using the program ProShake. Two randomly generated earthquakes were used in the DSRA. A previous study showed that the expected peak ground acceleration (PGA) for 10% probability of being exceeded in 50 and 100 years for the research area were about 0.2g and 0.3g, respectively (Al-Haddad et al, 1998). The two random earthquakes were based on records of regional earthquakes and were scaled to produce PGA at the site that is compatible with these values. The DSRA was repeated four times for each soil cross-sectional model using the two earthquakes and two damping ratios of 5% and 10%.

[FIGURE 2 OMITTED]

Microtremors recording stations were established at three locations at the site, namely DRA1, DRB1, and DRB3. Figure (3) shows the microtremors spectral ratios plots at station DRB1

[FIGURE 3 OMITTED]

Table (1) presents a comparison of the results of the site's approximate FP based on the results of the CH and CXW tests. The results show that the difference between the values of the FPs of the two tests at each location can be as high as 66% (expressed as a percentage of the lower FP value).

Table (2) presents the site's FP from the DSRA based on the soil cross-sectional models of the CH and CXW tests, and using the two earthquakes and two damping ratios. Table (3) presents the percentage of the differences in the value of the FP from the two tests for each location. The percentage of the difference in the values of the FP for each location varies from 0% to 328%. Table (4) presents the results of the microtremors FP of the three stations at the site.

Figure (4) shows the variations of the site FP based on the cross-sectional modeling method, the damping ratio, and the input earthquake.

[FIGURE 4 OMITTED]

CONCLUSIONS

The results show that different soil cross-sectional modeling methods can lead to significantly different FP for the same location. For this site the difference in the FP values for the same location were up to 66% for the approximate method, and 328% for the DSRA method, depending on the input earthquake and the damping ratio. The microtremors FP were not consistent, although the FP of DRB1 and DRB3 showed good agreement with the FP values of the DSRA.

REFERENCES

Al-haddad, etal, "A Study Leading to Preliminary Seismic Design Criteria for the Kingdom", King Abdul Aziz City for Science ant Technology, Riyadh, Saudi Arabia, 1998, p.65.

EduPro Civil Systems, Inc., "ProShake Ground Response Analysis Program, Version 1.1", User Manual, Redmond, Washington 

FEMA, "NEHRP Recommended Provisions for Seismic Regulations for New Buildings", 2000 Edition, Part 1-Provisions, Washington, DC, 2001, pp. 39-48

Kramer, Steven L., "Geotechnical Earthquake Engineering", Prentice Hall, Upper Saddle River, NJ, 1996.

Nakamura, Y., and Ueno, M., "A Simple Estimation of dynamic Characteristics of Subsoil", Proceedings of the 7th Japan Earthquake Engineering Symposium, pp. 265-279.

MUSAID ASSAF

KACST-Science and Technology Unit 2600 Virginia Ave. NW, Suite 800 Washington, DC 20037, U.S.A.

Table 1: The site approximate FP from the CH tests and the
corresponding CXW tests

               CH Test        CXW Test
Test         Approximate     Approximate     FP Difference
Location      FP (sec)        FP (sec)           as %

D5             0.381           0.2294            66.1
D6             0.274           0.3604            31.5
D11            0.315           0.3235             2.7
D12            0.4396          0.3399            29.3
Average        0.3524          0.3133            32.4

Table 2: The site FPs by the dynamic site response analysis

                       Site FPs (sec)

                       Earthquake One          Earthquake Two
Test      Test
Type      Location     5% Damping              5% Damping

CXW       D5           0.064       0.064       0.25        0.064
Tests     D6           0.064       0.054       0.32        0.098
          D11          0.077       0.077       0.098       0.098
          D12          0.064       0.054       0.077       0.054
Average                0.06725     0.06225     0.18625     0.0785

Cross     D5CH         0.064       0.054       0.088       0.088
Hole      D6CH         0.064       0.054       0.098       0.098
Tests     D11CH        0.064       0.064       0.098       0.077
          D12CH        0.077       0.064       0.33        0.064
Average                0.06725     0.059       0.1535      0.08175

Table 3: Percentage of the difference between the
values of the DSRA FPs of the CH and CXW tests

               Earthquake          Earthquake
                 RAN230              RAN330
Test
Location       5% Damping          5% Damping

D5            0        18.5      184.0     37.5
D6            0         0        226.5      0
D11          20.3      20.3        0       27.2
D12          20.3      18.5      328.5     18.5

Table 4: The site FP s of the microtremors spectral ratios

Recording Location     DRA1      DRB1      DRB3
FP (sec)               0.294     0.159     0.070872