Nonlinear Site Response Analysis Using SASW Data in the New Madrid Seismic Zone (USA): Case Study

New Madrid seismic zone (NMSZ) in the United States, is one the most active dangereous seismic zones, where NS and EW highways are crossing. According to the satellite data in this zone, during the strongest earthquakes of 1811-1812, a lot of liquefaction phenomena were observed in the Missisipi embankment. Based on historical and intensity data, the moment magnitude of the strongest shock of 12/16/1811 at 02h15m a.m. earthquake, is propsed to be Mw = 7.0-7.5. As there is a lack of strong motion data, for the study of nonlinear site response analysis of two sites under bridge construction, synthetic accelerograms were used. For determination of soil profiles, SASW technique was used and compared with other in-situ techniques. This paper focuses on the engineering significance of the geophysical methods used for the purpose ground response analysis.


Introduction
The New Madrid Seismic Zone (NMSZ) represents the most hazardous seismic zone in the central and eastern US.
The great earthquakes of 1811-1812 caused extensive ground failures (especially liquefaction), and evidence of this phenomena can be seen even today on satellite images.
The great thickness of the soil sediments has been the focus to study the amplification or de-amplification given input strong ground motions with PGA > 0.4g due to degradation of shear moduli and increase of strains in depth.  [4]. As can be seen from this figure the red area show the present day most active seismic zone .
As there are no strong motion records in this area, therefore synthetic ground motions were used. This paper focuses on the engineering significance of the geophysical method used for the purpose ground response analysis assuming that the resolution and quality of SASW data would be sufficient for the purpose of ground response analysis in shallow and deep soil deposits such as the ones present in the NMSZ.
Author of this paper participated in FHWA project for bridges in NMSZ with a research team of Missouri S&T, in Rolla Seismic Activity of New Madrid Zone (NMSZ)

Maximum expected magnitude according to statistical data
Generally it's known that the size of small earthquakes(M < 6.5) is better measured by body wave magnitudes (mb), (saturated at the value about 6.5).
Based on the earthquake catalogue for the period 1795-1995 for New Madrid Zone [3], all the magnitudes are given as body wave magnitudes (mb).

Conversion of mb magnitudes to Ms magnitudes
For NMSZ all mb magnitudes were transformed to Ms magnitudes according to the relationship [5]: mb = 0.56Ms + 2.9.
It can be seen that cumulative relationships: logN(mb) and log N(Ms) are more reliable (greater coefficients of correlation (0.963 & 0.969) and b-values are very small (b = 0.30-0.35) which confirms very high tectonic activity of NMSZ.
According to non cumulative graph log n (Ms) relationship it can be observed that: The minimum magnitude to be considered should be mb

Maximum expected magnitude according to seismic intensity data for the New Madrid earthquakes of 1811-1812
As can be seen from the log n(Ms) graph there is a lack of data for magnitudes mb = 5.5 -7.5 or Ms = 4.7 -8.2.
As at the time when New Madrid earthquake occurred were no instruments, the most reliable data are those on seismic intensities felt during this earthquake, which was felt widely in CEUS.
There are a lot of publications concern this problem, but we took into consideration two of them [7,8].

The generalized isoseismal map of NMSZ earthquakes
The isoseismal map of the shock of December 16,1811, is characterized by an unusually large felt area, with intensities of V as far away as the southeast Atlantic coastal area.

Assessment of the magnitude of New Madrid earthquakes from seismic intensities
The size of large ones (M > 6.5) is better measured by Ms especially for those in the range 6.5 -8.0, but saturates above that value.
The assessed expected maximum earthquake following the linear extrapolation of cumulative plotts should be about: Ms = 7.0 -7.5   which coincides with the seismic intensity MM = VIII according to the isoseismal map, but there are differences from 8-11 degrees.

Geotectonic model
The Bridges sites under investigation are situated on the top of thick sediments overlying the Reelfoot Rift in New Madrid Zone.
The bridges are part of the located alongI-55 highway in the southeast corner of the state of Missouri near the cities of Hayti and Steele.

Depth to bedrock
For the determination of the depth to Paleozoic bedrocks the data from MoDNR [1] were used (

Modification of strong ground motions generated by the Reelfoot Rift by geological conditions
The thickness of soil layer on the top of hard Paleozoic rocks was derived from the data supplied by MoDNR (Table 2): (1)

Shear wave velocity (V s ) models
For the generation of synthetic ground motions the velocity models for Mid-America & NMSZ according to the inversion of teleseismic data were used [10], so named Soil USGS96 source model (M5).
The preliminary sediment thickness for the model was 1000m thick for New Madrid Seismic Zone.

Strong Motion Parameters according to Seismic Hazard Maps
According to the USGS seismic hazard maps for PE = 2% in T = 50yrs, by entering a latitude and longitude for A, and L bridge sites at the USGS-National Seismic Hazard Mapping Project the strong motion parameters listed in Table 4 can be deduced.
The distances and magnitudes used to calculate these hazard values were found according to the USGS special tables for PGA, 0.

Computer Codes
For generating synthetic motions, Boore's SMSIM package [11] is used in which: using input data were M W , D(km), h(m), number of simulations, and seed number, were computed acceleration time history, peak motions (PGA, PGV, PGD), and response spectra for a given damping (5%).

Acceleration time histories (Synthetics) [12]
Synthetics used as input motions were generated for different thickness of sediments (H) on the top of consolidated sediments overlying the Paleozoic bedrock.

Synthetics for H = 0m
Correspond to generation of synthetics on free surface of rocks.

Dependence of synthetic PGA values from H (m)
From the figure 7 it can be seen the decrease 2 times of PGA values on bedrocks (at H = 650m) to free surface (H = 0m).

PGA values for H=0m (on the top of Paleozoic rocks)
It's the common case of the generation of synthetics on hard rocks, taking the thickness of overlying layer H=0m.
As an example are presented 3 synthetics for the same Seed=123 for different magnitudes and distances (Table 5).

Comparison of Sa spectra for synthetics with H=0m &H=650m
Sa spectra for H = 0m (blue lines) are characterized by the highest response values versus smaller periods (0.04-0.16sec).

Comparison of Sa spectra for synthetics with H = 650m for point source model with those for composite model
From figure 12 it can be seen that the average Sa spectra (D = 0.05) for both Point Source (H = 650m) (red line) and Composite Model (blue lines) are very close to each other concerning the shape, but they differ concerning the amplitudes.

Strong Motion Parameters According to NEHRP Maps
The USGS 1996 seismic hazard maps for PE = 2% in T = 50yrs by entering a latitude and longitude for two bridge sites at the website of National Seismic Hazard Mapping Project [10] were used to find the corresponding seismic hazard parameters ( Table 6).
The distances and magnitudes used to calculate these hazard values were found according to the USGS special tables for PGA, 02.sec   The upper part with a thickness of 80m is characterized by the nonlinear response of sediments. At depths below the response is elastic one.
3. The increase of the thickness of sediments on the top of Paleozoic rocks by 50 meters (L site) has a very small influence on the mean PGA average value (only 0.01g less).

Soil profiles based on shear wave velocity data
The soil profiles of the bridge sites were compiled using geologiclitho logical data and shear wave velocity data from two sources: CH and SASW data.
For L site (Figure 16 a) the SASW testing was performed nearby the location where a seismic cone penetrometer (SCPT) was previously advanced.
For A site (Figure 16b) both SASW and cross-hole data were acquired in addition to the SCPT data at that site.

Results of Nonlinear Response Analysis for RW and CH Models Soil Response Profiles
Sa spectra for the shallow soil profile(h~60m) show small differences in the ground response analysis (at periods T = 0.5 -1.5).
Most of the differences are seen in periods T < 0.5 sec., which tend to be of little significance for bridges and possibly an artificial product of the synthetic motions.

S a spectra for deep profile
For a deep soil profile the differences in Sa spectra are even less pronounced and comparisons between the SASW and CH data are difficult to identify.

Conclusions
For soil profiles modeled using geophysical techniques in NMSZ: 1. Equivalent non-linear response analysis for shallow soil model (h~60m) is most pronounced for CH model compared with SASW model. and show small differences in the range T = 0.5 -1.5sec.
The most differences are seen in the range T < 0.5 sec., which tend to be of little significance for bridges.
2. For deep soil profiles (compiled by SASW and CH data ), using the point source model, to generate the synthetics, those differences are even less pronounced and comparisons between the SASW and CH data are difficult to identify.
3. Therefore advantages of using high quality CH data for use in ground response are not justified.
4. SASW surface geophysics results tend to satisfy the engineering requirements for ground response analysis.
5. For shallower deposits and more intrinsic soil-structure interaction analysis the CH geophysical characterization may be justified.
Based on this analysis the main problem in NMSZ is not the high level of amplitudes of strong ground motions, but possible ground failure phenomena to be developed during future strong earthquakes, to be taken into account for the bridges in this area by increasing bearing capacity of the soils and foundations.