ML12258A326

Limited Appearance Statement of Klaus H. Jacob Opposing Indian Point, Units 2 and 3 License Renewal Application

ML12258A326
Person / Time
Site:	Indian Point
Issue date:	09/09/2012
From:	Jacob K - No Known Affiliation
To:	NRC/SECY/RAS
SECY RAS
References
50-247-LR, 50-286-LR, ASLBP 07-858-03-LR-BD01, RAS E-782
Download: ML12258A326 (114)

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Attachments: jacob@ldeo.columbia.edu Sunday, September 09, 2012 1:29 AM Docket, Hearing Siarnacki, Anne; jacob@ldeo.columbia.edu Formal Comment re Indian Point Hearings IP for NRC.pdf; Tappan Zee Bridge Seismic Study.pdf I herewith place the attached comment (PDF named "IP for NRC") formally into the record of the hearings on Indian Point and ask for full consideration of its content and reasoning. Also attached is a second document (Seismic Hazard Assessment of the TZB, a bridge in close vicinity to the Indian Point location). It is referred to in my formal comment. Respectfully Klaus H. Jacob, Ph.D. Seismologist PO Box 217 Piermont NY 10968 This message was sent using IMP, the Internet Messaging Program. DOCKETED USNRC September 10, 2012 (8:15 a.m.) OFFICE OF SECRETARY RULEMAKINGS AND ADJUDICATIONS STAFF <4-4ýZ-AI-6sk

RE: Indian Point License Extension Hearings TO: hearing.docket@nrc.gov, anne.siamacki@nrc.gov FROM: Klaus H. Jacob, Ph.D. Seismologist PO Box 217 Piermont NY jacob(&ldeo.columbia.edu DATE: 09/09/2012 It is my professional opinion as a seismologist, that unless various components, systems and facilities at the Indian Point, NY, Nuclear Power Site pass any one or all of a number of tests and criteria (see below), that the Indian Point (IP) nuclear power reactors #2 and

1. 3 shall NOT be permitted to operate beyond their respective initial 40-year license termination dates.

The tests to be performed by NRC shall include the following:

1) Virginia Earthquake as Test Case. If you were to apply SIMULTANEOUSLY all 3-components (1 vertical, 2 horizontals) ground motions in the TIMEDOMAIN (without any filtering to limit high-frequency content, especially in the range from 10 to 100Hz) as obtained for the Mw 5.8 Virginia earthquake of August 23, 2011, at the North Anna Power Station, and using the response of all systems and components at the IP site to these ground motions in the time domain, and if then the conditional risk of releasing any significant amount of radioactivity from the IP site exceeds the (annual) probability value of 10^-4/year 1, then the IP site shall be considered having failed that test.

2) TZB Study Test Earthquakes. Use in an equivalent test to (1) the hard-rock ground motions from the attached 1995 report for the seismic hazard assessment of the existing Tappan Zee Bridge (TZB). The TZB, crossing the Hudson only less then 20 miles south of the IP site, resides in the same seismic regime as the IP site, except the IP site is located CLOSER (!) to the Ramapo Fault system than the TZB is located. Ground motions for hard rock conditions (Vs=3.5km/s) have been produced for distinct recurrence periods (i.e. 500, 1000, 2,500 years) as represented by discrete magnitude-I This annualprobability of IJ04/year is generally andpublicly announced by NRC as an upper limit of an "acceptable annual risk". How to visualize the 1 O^-4/year Risk? Since Risk = Hazard x Fragility x Assets; and assuming (see item 2) that the Virginia earthquake of Mw=5.8, when placed in the vicinity of the IP site is roughly a 2, 000-year event (annual probability = 0.5x10^-

3/year); and having 2 NPPs as assets at the IP site, then the implied net fragility F of any of the 2 reactors would be. F =IP Site Annual Risk / [Hazard at IP site x number of nuclear reactors at IP site], or F = [I 0^4/year] / [0. 5xl 0^-3 /year x 2 reactors at IP site] = 0. 1 = 10%. In other words the conditional fragility of the IP reactors for a 2011-Virginia-type earthquake must not exceed a 10% -chance for such a scenario event to lead to a significant release. This is not counting any additional risk contributed by the stored spent fuel in pools or dry casks.

distance (M-d) pairs given in Table 2, page 12 of the attached TZB report. Its Figure 7 shows, as an example, the transverse horizontal component ground motions for the 3 M-d pairs for the 1000-year recurrence period (10A-3 annual probability); the related M-d pairs for this recurrence period are: M 5, 6, 7 at the respective distances of 15.5, 38, and 92 km. For longer recurrence periods, the respective distances are shorter (see Table 2), and hence the ground motions stronger, but not necessarily longer in duration (depending on definition of duration). Again: when such ground motions are used, and then the conditional risk of releasing any significant amount of radioactivity from the IP site exceeds the probability value of 1 0A-4/yr, then the IP site shall be considered having failed that test.

3) Geotechnical Seismic Site Resonance for Dry Casks on Pads. Another test needs to be performed specifically for the spent fuel stored in dry casks on concrete pads at the IP site, using events of recurrence periods of 1000 years and longer as, for example, listed in Table 2 (page 12) of the TZB report. Here is the reason: The concrete pads on which the dry casks rest freestanding WITHOUT any lateral seismic constraints are subject to rocking and related rotational motions that can potentially lead to lateral displacement of casks, and even tip-over of dry casks (Note: again, ground motions for all 3-components must be considered acting SIMULTANEOUSLY when computing their effects on the stability of the dry casks! !). For the test computations the following geotechnical pad foundation details need to be considered: Are the concrete pads directly bonded to truly in-situ hard rock? If not, and if there is any aggregate fill between the solid rock and the concrete pad, then the possibility of site-amplification due to the softer fill between concrete pad and solid rock needs to be modeled correctly to see whether it leads to any strong site amplification of motions at the base of the dry casks that may very well be concentrated to very distinct high-frequency bands. Should these resonance bands by chance coincide closely with the natural rocking frequencies of the free-standing dry casks, then these could lead to cask instabilities that would not be anticipated if only the free-field rock motions were assumed to act on the base of the dry casks. (Note: This possibility was noted by the commenter at a NRC/Entergy public hearing held at least 5 years ago at a restaurant near the IP site; I had asked for respective geotechnical design details for the pads and the rocking frequencies of the dry casks; I was promised a response, but never received one! !). Should casks move (as they did in 2011 at the North Anna site), and do so that their prescribed safety distance from each other is violated, or worse, should tumble and pile on each other, this could lead to thermal overheating, or in the worst case, induce criticality with thermal run-off potentially exceeding the safety specs for the casks to maintain containment.

4) Inundation from Surges in the Hudson at 10^-4/year (or lower) Annual Probability Risk Levels. The safety for safe shut-down, stand-by power and maintained control of cooling for flooding events due to surges in the Hudson needs to be tested at the appropriate low probability levels (i.e. storm surge or tsunami recurrence periods of several thousand of years). The inundation safety assessments made in the past of the IP site (e.g. IP3 FSAR UPDATE - IP3 UFSAR) are only deterministic and not commensurate with today's available information and state of the art methodology on storm surge and tsunami risk assessment. Severe storm surges in the Hudson can be

produced by hurricanes making landfall near the NY/NJ boundary, or could be produced by earthquakes or submarine landslides along the coast near the NY bight, or even by collapse of volcanoes in the Atlantic Canary Islands. Storm surge probability to exceed a given surge height is surprisingly affected (i.e. strongly increased) by climate-change-induced sea level rise, which is forecast to accelerate more during this 21 St century than it already has accelerated during the last half century. Recent computations and observations have shown, at least for hurricane-induced storm surges, that the storm surges in the Hudson in the waters below the Bear Mountain Bridge, i.e. in the vicinity of the IP site, are very little reduced or virtually undiminished from their predicted forecast surge elevations at Sand Hook, NJ, or the Battery Park in NYC. Figure 1: The Indian Point Site along the East Shore of the Hudson River, NY. If the scant information available is correct that some relays and control systems for stand-by power operations and other critical control/operator functions are really located at elevations as low as 15ft (- 5m) above the Hudson (see attached Figure 1; the documents do not specify what is the vertical reference datum for this elevation measure; it could be 15ft above MSL, or NGVD 1929 as used by FEMA flood zone maps; or NAVD 1988; or some other reference tidal measure such as MLLW etc.); in any case, if it is true that critical control elements are at elevations of about 15ft, then its is at least conceivable that, and hence needs to be thoroughly tested whether, at probability levels of 10^-4/year or lower (recurrence periods of 10,000 years or longer) these critical control elements are potentially prone to flooding from storm surges or tsunamis in the Hudson (or not). FEMA's 1%/year storm flood zone indicates a base flood elevation of 8ft (NGVD 1929); the 0.2%/year flood elevations are on this stretch of the Hudson typically about 2 ft above the 1%/year BFE, which would approach 1Oft (NGVD 1929). This does not account for surge contributions from tsunami sources as listed above and in ten Brink et al. 2008 (USGS Report to the USNRC, revised August 22, 2008). In light of the tsunami effects on the Daiichi site in Japan, where the damage was done by an event with recurrence period of about 1,000 years, it seems appropriate to make the inundation hazards assessment of the IP site compatible with USNRC probabilistic seismic risk assessment methods, and hence events with annual probabilities of 1J0A-4/year or less need to be considered, but have not been considered probabilistically as of to-date.

TAPPAN ZEE BRIDGE SEISMIC STUDY Final Report, Part 1: Seismic Hazard Assessment, Design Ground Motions and Comments on Liquefaction Potential for the Site of the Tappan Zee Bridge, New York. Prepared by K. Jacob, S. Horton, N. Barstow, and J. Armbruster Lamont-Doherty Earth Observatory of Columbia University Route 9W, Palisades, N.Y. 10964 Phone: (914) 365 8440 Fax: (914) 365 8150 for F.R. Harris, Inc. 300 East 42nd Street New York, NY 10017 March 3, 1995

Executive Summary. A comprehensive deterministic, yet probability-related assessment of seismic hazard at the site of the Tappan Zee Bridge (TZB) in New York State is made. Site-specific ground motions on rock and soils are computed that are consistent with regional seismicity and selected earthquake recurrence periods of 500, 1000 and 2500 years. The ground motions associated with the different recurrence periods and soil conditions allow the TZB's engineer and owner to check bridge performance under different seismic loads in the current state. Comparing these response computations prior to linking criteria of seismic bridge performance to specific earthquake recurrence periods will permit the optimization of cost-effective design strategies. In more detail, the objectives of this study and report are: (1) to define the seismic, geologic and tectonic environment at the site of the TZB in a local and regional context; (2) to quantify the regional seismicity in terms of rates of earthquakes as a function of magnitude, and to choose the upper limit of magnitudes that needs to be taken into account for design considerations; (3) to define distinct seismic hazard exposure levels expressed in terms of constant (average) recurrence periods of seismic events; three constant recurrence periods CRP = 500, 1000 and 2500 years are chosen; (4) to link the constant recurrence periods to distinct magnitude-distance (M-d) "event" combinations based on rates of regional seismicity. Three discrete event magnitudes per CRP are chosen, M=5, 6 and 7; (5) to compute the three-component ground motion acceleration time series associated with the M-d event combinations for each of the three recurrence periods; the ground motions are first computed for hard-rock conditions. They are then modified for nonlinear soil response for 10 soil profiles along the TZB. For this purpose geotechnical information from prior soil borings is fully utilized; (6) to compute damped acceleration response spectra for the M-d combinations for each of the three recurrence periods; (7) to compute CRP envelope spectra for the suite of M-d combinations belonging to a single CRP; each CRP envelope spectrum represents a nearly uniform level of deterministically evaluated seismic hazard; CRP envelope spectra can be used as design spectra for linear modal analysis of the bridge and foundation structures; CRP envelope spectra fulfill a similar function as uniform hazard spectra do in a probabilistic seismic hazard assessment; (8) to smooth the CRP envelope spectra for use as design spectra and compare them to relevant code spectra (AASHTO and NYSDOT guide specifications); (9) to quantify the spatial variation of ground motions and differential displacements on rock and soils for use in multiple-support input for linear or nonlinear time-domain computer modeling of the dynamic bridge response; (10) to briefly comment on (but not quantitatively assess) the potential for soil liquefaction by simple screening procedures, and to compare predicted transient seismic strains to the limit strains under which soil samples from three TZB borings failed in prior triaxial shear lab tests. i

Table of Contents: Page EXECUTIVE

SUMMARY

TABLE OF CONTENTS ii LIST OF FIGURES iii LIST OF TABLES iv

1. Site Geology 1

2. Seismicity, Recurrence Periods, Seismic Exposure Levels and Scenario Events 4

3. Hard-Rock Ground Motions 16

4. Geotechnical Soil Profiles 22

5. Modification of Soil Parameters for Strain-Dependent Nonlinear Response 27

6. Grouping of Site-Response Computations 29

7. Equivalent Linear Approximation for Iterative Computation of Nonlinear Site Response 31

8. Essential Features of Soil Motions: Examples and Results 36

9. Design Spectra for Constant Recurrence Periods CRP=500, 1000 and 2500 Years 41

10. Spatial Variation of Ground Motions and Relative Displacements 49

11. Comments on Soil Strains and Liquefaction Potential 66 CONCLUSIONS AND RECOMMENDATIONS 73 ACKNOWLEDGMENTS 74 REFERENCES 75 APPENDICES:

Appendix A: Reprint of Paper by Horton (1994) on Modeling Ground Motions Al - Al1 Appendix B: Starting Models for Soil Profiles for all Foundation Groups B 1 - B4 Appendix C: Ground Motions, Response and Design Spectra for CRP=2500 Years C1 - C10 Appendix D: List of Pertinent Technical Communications by LDEO to FRH/H&H DI - D3 ii

List of Figures Page Figure 1: Tappan Zee Bridge CMZB) and "Manhattan Prong" seismotectonic province 2 Figure 2: Geologic section for MZB pier bents, borings and foundation groups 3 Figure 3: Instrumental and historic seismicity of the Manhattan Prong 5 Figure 4: Cumulative annual number of earthquakes vs. magnitude 7 Figure 5: Variation of seismicity parameter as a function of the lower cut-off magnitude Mic 8 Figure 6: Three-component rock accelerations for 1000-yr earthquake 17 Figure 7: Rock accelerations and response spectra for 1000-yr earthquakes 18 Figure 8: Envelope response spectra on rock for CRP= 500, 1000 and 2500 yr 21 Figure 9: Borings along the Tappan Zee Bridge available for this Report 23 Figure 10: Geologic section along TZB with location of available borings 24 Figure 11: Water content, derived shear-wave velocity, and layered velocity model 26 Figure 12: Shear modulus degradation and damping ratio vs. strain and PI 28 Figure 13: Response spectra for bent 178, at mudline and 8 feet below 32 Figure 14: Spectral transfer functions of soils at five sample sites 34 Figure 15: Comparison of rock with soil motion for linear and nonlinear soil response 35 Figure 16: 1000-yr accelerations at foundation group 3a at rock and 5 ft below mudline 38 Figure 17: 1000-yr response spectra at foundation group 3a at rock and 5 ft below mudline 39 Figure 18: 1000-yr M7 response spectra at five sites near borings bl, b7, b4, B-2, and b5 40 Figure 19: Soil motions at foundation group 3a for CRP=500 to 2500yr M7 earthquakes 42 Figure 20: Envelope response spectra (rock & soil at 3a) for CRP=500, 1000, 2500 yr 43 Figure 21: Design spectra for foundation Categories I -III, vs. AASHTO spectra 46 Figure 22: Factors contributing to spatial variation of seismic ground motion 51 Figure 23: Transverse rock displacements for CRP=2,500 years 53 Figure 24: Relative displacements vs. separation distance (Abrahamson, 1993) 55 Figure 25: Displacement records on rock for M=6 at d= 24 to 25 km 56 Figure 26: Relative displacements on rock for pier spacings 0 to 1000m at d=24-25 km 57 iii

Figure 27: Geometry for calculating the wave-passage time lag 58 Figure 28: Maximum relative displacement vs. time lag at different TZB span types 63-65 Figure 29: Seismic soil strains compared to soil failure strains vs. depth 68 Figure 30: SPT count N compared to liquefaction sreening tests 70 Figure 31: Depth intervals nominally prone to soil liquefaction 71 List of Tables Page Table 1: Seismicity parameters for the Manhattan Prong seismic source zone 9 Table 2: CRP magnitude-distance combinations for Manhattan Prong seismic zone 12 Table 3: Crustal structure used for TZB ground motion simulations 19 Table 4: Source and other parameters used for TZB ground motion simulations 19 Table 5: Plasticity index (PI) assigned to the soils at TZB site 27 Table 6: Foundation grouping proposed by H&H for Truss Deck and Main Span sections 29 Table 7: Foundation grouping for Deck-Truss and Main-Span sections based on site response 29 Table 8: Soil and rock profiles for the Trestle Section with timber friction piling 30 Table 9. Incidence angles and apparent velocities for calculating lag times for 2,500-y events 59 Table 10. Differential gneiss lagtimes for ray geometries for a CRP=-1,000 years 61 Table 11. Computed bridge-parallel lagtimes for a M=5 with CRP= 1,000 years 62 Table 12. Computed bridge-parallel lagtimes for M=6 and 7 with CRP=I,000 years 62 iv

1. Site Geology.

The Tappan Zee Bridge (TZB) is located in a geologic-tectonic unit (Figure 1), known as the Manhattan Prong which is seismically active. The basement is an allochtonous crustal sliver, probably tens of km thick, consisting mostly of Precambrian meta-sedimentary rocks that once was the eastern leading edge of the North American continental craton. During a continent - island arc collision in Paleozoic time that formed the Appalachian mountain belt, these rocks were thrust eastward (e.g. along the fault called Cameron's Line) against the approaching island arc complex. During this tectonic phase the basement rocks of the Manhattan Prong and their Paleozoic cover rocks were tightly folded with fold axis generally striking NNE-SSW. The deformed crystalline basement and metasedimentary rocks are unconformably overlain by bedded Triassic Red Sandstones, which are interbedded (to the west of the Tappan Zee Bridge location) by the intrusive igneous Palisades Diabase sill, about 300 to 400 feet thick (Figure 2). The Triassic sandstones and the Palisades Diabase sill gently dip to the WNW and are part of a NNE striking Triassic half-graben system (Newark Basin) whose western main boundary fault, the Ramapo fault, was then a normal fault steeply dipping to the ESE. This former normal fault bounds the Triassic Newark Basin against the Precambrian Hudson Highlands. The Ramapo fault system is presently reactivated as an oblique thrust responding to a E-W to NE-SW directed compressive stress regime. The basement and Triassic rocks were cut by a set of ESE-WNW striking faults, with little net offsets. They probably originated in Late Creatacious times when the Atlantic Ocean started to open and North America and Africa rifted apart. These WNW-trending faults are spaced about 5 to 10 km apart and occur throughout the entire N-S exposure of the Manhattan Prong (Figure 1). They include, for instance, the Dobbs Ferry fault zone in Westchester County, and the Dyckman Street and 125th-Street Faults, both in Manhattan. The Dobbs Ferry fault zone was the origin of a seismic event sequence in 1985 with magnitudes up to Ml-4.0. It consisted of primarily left-lateral strike-slip events at hypocentral depths of about 5km, on a cluster of mostly WNW striking fault planes aligned with the surface trace of the Dobbs Ferry fault zone. The WNW projection of this fault trend probably intersects the TZB not far from where it reaches the western shoreline of the Hudson, in South Nyack, Rockland County, NY. We consider all members of this set of WNW trending faults as candidates capable of generating earthquakes. During the Quaternary, glaciers moved over the region as far south as Long Island, Brooklyn, and Staten Island. As they advanced and retreated several times they deeply eroded the region. This process was enhanced by the fact that sea level off-shore New York was lower by at least 300 feet. 1

740 15 C-TZB 4, ItI N 1989 V~ 7 198 MAG 41 S.BTklr. Figure 1: Location of Tappan Zee Bridge (TZB) and structural features of the "Manhattan Prong" seismotectonic province. The solid circles represent earthquakes located by the LDEO seismic network for the period between about 1970 and 1990. Focal mechanisms and maximum horizontal stress directions (solid double artows) determined for three earthquake sequences (1977, 1985, and 1989) are also indicated. 2

I VIA 173 7-8 1-165 1 WEST APPR.TRESTLE SPANS - 2 34 - 35? (ON FRICTION PILES) 4*+/-48+/-3 68 122 146.,1( k,# rmJ 1 166-172 I WEST DECK RUSS SPANS 173-178 MAIN SPANS 178 175 176 Note: Bents 174 & 177 do not exist 0~ F@undaiftn Qrmpu-1 28 3a Sb 2b ý6 0 HUDSON RIVER PALISADES DIABASE / ~ % % ~ 0 -200ft -400 -600 -800 -1000 Figure 2: Bottom: Generalized geologic section showing bedrock and deep sediment configuration taken mostly from marine seismic refraction surveys made by Lamont teams in the early 1950's (Worzel and Drake, 1959) and shallow sediments in the Hudson river canyon based mostly on the geotechnical boring data described in the text. Top: Map view of the main structural elements of the Tappan Zee bridge with approximate location of pier bents (1-190), of borings (1-34, and B-1 to B-3), and of assigned foundation groups 1 - 9 (see text and Tables 7 and 8).

The glaciers carved a 700 feet deep canyon, now the location of the Hudson River where the TZB crosses it (Figure 2). The base of this canyon is covered with boldery glacial till. The glaciers layed down during their most southerly advance a sequence of endmoraines that now form the highest parts on Long Island, including Queens and Brooklyn. When the glaciers finally retreated, about 10,000 years ago, these endmoraines provided a natural dam, against the open Atlantic Ocean. The dam ponded the glacial melt waters and their sediments, forming one or several large pro-glacial lakes that covered parts of the Long Island Sound, the New Jersey Meadow Lands / Hackensack River Basin and extended northward into the Hudson River Valley. Seasonal melt cycles filled the extensive lake(s) with several hundred feet of so-called "Varved Clays". They consist of clays and silts deposited during low-flow seasons, alternating with silts and (sometimes gravelly) sands during high-flux melt seasons. At some time the coastal moraine barrier was breached (at the current mouth of the New York Harbor at the present location of the Verrazano-Narrows Bridge). The pro-glacial lake drained, and a fluvial regime began depositing sandy to gravelly deposits overlying the varved clays (Figure 2). As the sea level rose in Holocene times by about 100m (-300 feet), because of global warming and related glacial volume reduction, the open sea entered the former lacustrine, then fluvial regimes. At that time the intertidal coastal regime was established in the lowlands that essentially still exists today. This intertidal stage is characterized by the deposition in the lowlands of organic clays and silts (organic 'muds'), locally including the formation of peats. The recent configuration of these intertidal lowlands is the result of a delicate balance between sea level rise and competing isostatic vertical crustal movements related to the visco-elastic response to glacial unloading of the Earth's crust and mantle that still continues today. Locally, the mean sea level near NY City is still rising, after accounting for the coastal vertical motions, on the order of I mm per year, or a third of a foot per century. During the last few hundred years, the intertidal organic deposits have been locally modified by man, often by filling in large tracts especially along the waterfront and in former swamp areas. The highly varied geotechnical conditions at the location of the TZB are strongly controlled by all of the above geologic conditions. The site conditions (Figure 2) vary from most competent Precambrian crystalline rocks to the very recent, softests soils imaginable. These conditions pose extraordinary challenges to engineering ingenuity when attempting to find stable foundations for the TZB under both static and dynamic (seismic) loads.

2. Seismicity, Recurrence Periods, Seismic Exposure Levels and Scenario Events.

Seismicity Rates. The seismicity of the Manhattan Prong (including portions of the adjacent Newark Basin and Hudson Highlands) is fairly well documented (Figures 1, and 3a and b). 4

b") -S SUTURE 1970-90 EPICENTERS T H R U S T S BNRM TL FAU LTS 3 4 B MAGNITUDE NORMAL FAULTS + ANTICLINES BASIC DIKES GLACIAL LIMIT 0.' V.... ~41* N toCD 76 0 W 74' Figure ~ ~ ~ ~ ~ ~ STUE 1:a8a0o0ntuenal-eore esict 17-1990 EfPheMahatanPrngan THRUSTS NORMAL FAULTS .3 4 5 MAGNITUDE // 1985 iJ adjacen portionsp of inewtJerently anrew ork.deapodisoia seismicity from99)o teMnhta NCErongan catalog. Box in each map shows the area S=6,500 kmn2 evaluated to determine the a and b parameters of the Gutenberg-Richter relation. 5

LDEO has operated in this region a telemetered seismic network for more than 20 years, and the historic seismicity has been compiled into earthquake catalogs called NCEER-91 (Seeber and Armbruster, 1991). We used the combined network and historical seismicity data to establish the seismicity rates for the Manhattan Prong. The specific source area considered is outlined by the box shown in Figures 3a and 3b. It has a dimension of 50 x 130 km (source area S= 6,500 km2). The cumulative, annualized number of earthquakes, normalized to a period of 1 year and an area S= 6,500 km2, that occurred as function of magnitudes equal to or larger than M, are displayed in Figure 4. The surrounding area has only a slightly reduced level of seismicity. Figure 4 displays certain characteristics that are based on the fact that the data are compiled from a variety of sources and periods of time. For instance a jump towards decreasing rates occurs when one progresses from magnitudes M=3.0 to M=3.25. This apparent decrease is largely due to the fact that magnitude M<3 earthquakes come from the instrumental record for the period 1970-1990, while magnitudes M>3 are dominated by the historic record. An apparent upward jump, unexpected for plots of cumulative earthquake rates, occurs when progressing from M=4.75 to M=5.0. This jump is due to the fact that the catalog for historic earthquakes of M>5 is considered complete for about 300 years, while that for earthquakes with M54.75 is considered complete for a shorter period of time, about 100 to 150 years. The rates of seismicity in these different periods of catalog completeness and magnitude ranges was sufficiently non-uniform, or rates were low enough so that the occurrence or absence of a few events, or of even a single event during a reporting period, causes large apparent fluctuations in the annualized cumulative seismicity rates plotted. If the earthquake catalogs were complete and reflected uniform rates of seismicity at all magnitudes plotted, downward jumps would be likely to be less prominent. In addition - and by the very fact that cumulative rates are plotted - positive (upward) jumps would be eliminated altogether, and would be replaced by flat portions of the curve at those magnitude increments that did not contribute to the cumulative rates plotted. Such flattened curves are often observed for regions with a dominant 'characteristic earthquake' size or magnitude, for which a deficiency of events is typically observed at magnitudes just below the 'characteristic' size. These 'characteristic' earthquake models do not conform to the simple power-law seismicity model described and applied below. It is unclear whether the observed upward jump at M=5 in the Manhattan Prong plot of seismicity (Figure 4) is solely due to variable catalog completeness, or whether in fact the region tends to display a seismicity that is akin to a 'characteristic earthquake' model with enhanced occurrence of earthquakes of M>5, and diminished activity at M_<4.75. Given the cumulative rate of seimicity (Figure 4), various curve fits can be made to the observed seismicity rates using the so-called Gutenberg-Richter frequency-magnitude relation log n = a - bM ( a) 6

MANHATTAN PRONG MAGNITUDE 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 0 1.000 0.100 a LU 0.010 0 0.001 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 MAGNITUDE Figure 4. Cumulative number N of earthquakes (per year) having magnitude M or larger in the boxed source area S=6,500 km2 displayed in Fig. 3. Dashed line shows b value of 0.90 calculated using a lower cut-off magnitude of M1 =2.25. Solid line shows b=0.59 for M1c=3.75. The dotted line corresponds to the finally adopted average relationship log n = a -bM with a =- 2.305 (normalized to km-2 y-1) and b=0.775, nearly identical to a fit to the data above a cut-off M1c=3.25 (see Table 1).

MANHATTAN PRONG SEISMICITY 2r 3. 4. 5i a 1.2 1.1 1.0 1 .9 C-0 .7 .6 10000 0 1000 0.4 0 0 100

• M=6 2

3 4 5 Lower Cut-off Magnitude, MLC Figure 5. Graphical display of numbers shown also in Table 1 indicating the variation of the seismicity parameter b as a function of the lower cut-off magnitude M, above which the seismicity of the boxed area in the Manhattan Prong (see Figure 3) is used to fit a b-slope to the data (top); and (bottom) the expected average recurrence period (in years) of a magnitude 6 earthquake in the boxed area as a function of Mk 1. The error bars indicate +/- one standard deviation. 8

where n and 10a are now normalized to number of events per year per km2. One can determine for a given source region the a and b values in the Gutenberg-Richter relation as a function of the lower-cut-off magnitudes Mlc. Generally one finds that both the intercept a and and slope b vary somewhat with the lower cut-off magnitude, above which the equation (la) is fitted to the data by the so-called 'maximum-likelihood' procedure. The results of an incremental fitting procedure to the cumulative seismicity data of the Manhattan Prong seismic source zone are summarized in Table 1 and shown graphically in Figure 5. Table 1: a and b values for the Manhattan Prong seismic source zone, their standard deviations +/-da and +/-db, inferred average recurrence periods TrM=6, TrM=7 (years), and standard deviation +/-dTr M=& as a function of lower cut-off magnitude M&k. Case Ml, a +/-+a b +/-.b Tr M=6 +/-aTr M=6 Tr M=7 1 2.00 -1.9559 .252 .866.079 2,195 911 16,138 2 2.25 -1.8569 .341 .897.099 2,659 1,232 20,974 3 2.50 -1.9399 .452 .872.123 2,291 1,157 17,071 4 2.75 -2.3189 .534 .765.136 1,240 626 7,218 5 3.00 -2.2589.588 .781.147 1,355 713 8,187 6 3.25 -2.2789.614 .776.152 1,320 700 7,880 7 3.50 -2.3959 .797 .747.184 1,155 636 6,450 8 3.75 -3.0829.977 .586.207 613 312 2,365 9 4.00 -2.6539 1.220 .682.252 855 474 4,113 Mean ------- 2.305.642 .775.153 1,052 5,985 Note how the b-slope tends to decrease as only larger earthquakes are used to fit a Gutenberg-Richter relation. Also note how moderate variations in the b-values translate into large variations of the recurrence periods for the large-magnitude events (M=7). For later computations in this paper we choose the mean values a=-2.305 and b=0.775, which fall very close to the values that one would have obtained when fitting the Gutenberg-Richter relation to the data only above the cut-off magnitude Mic=3.25 (bold numbers in Table 1). The relation (la), when combined with the results from Table 1, takes the numerical form: log n = (-2.305_+0.642) - (0.775_+0.153) M (lb) Sometimes it is desirable to relate the normalized rate of events n of relation (la) with the total number of earthquakes N occurring during T (years) in the area S (km2). Let us assume that the seismicity is uniformly distributed in time and space within a source region S. Then one obtains 9

log N = log n +log S +log T (2a) or logN = a -bM +log S +log T (2b) Lets us now assume, for convenience, that the source area S is of circular shape, i.e. has the radius r, and hence the source area S---nr 2. Assume one wants to compute the area S (km2) required from which one needs to collect seismicity in a period of T (years) to produce, on average, N=I event of magnitude M or larger, then one obtains : log I =0= a-bM+log S +logT (3) With the new condition N=I, the time interval T takes on the role of average recurrence period of events with magnitudes >M in an area S located in a larger unbounded seismic source region with uniformly random seismicity in time and space. We assume that both, S and the larger source region are characterized by the same seismicity parameters a and b. Under these conditions of uniform open-ended seismicity, we now can ask at which distance d, on average, an earthquake with magnitude M would occur from any point floating in the open-ended region characterized by seismicity parameters a and b. We place the single event at that distance d which divides the circular area S=icr2 into two equal halves: an inner circle with radius d, and an outer annulus (with bounding radii d and r), that -as specified above-have equal areas. This condition implies that there is an equal chance (50-percentile) that the event lies in either region with area S/2---d 2, i.e either inside or outside the distance d. Expressing the total area S in terms of this equal-probability (50-percentile) distance d, one obtains S=27rd 2 (or d--r//2). Inserted into equation (3) this yields: log S = log (2ntd 2) = bM -a -log T (4a) log d = (bM -a -log T -log 2rn)/2 (4b) Equations (4) provide a relationship for an unbound areal seismic source with uniform seismicity parameters a and b. They yield for any given recurrence period T unique pairs of magnitude-distance combinations (M-d). When the area S is bounded, as in our example, then of course one cannot increase d indefinitely with increasing M or decreasing T because the circular area S=27rd 2 would exceed the source area S' assigned to the actual source zone (in our case S'=6,500km 2 ). On the other hand, the level of seismicity beyond the outlined boundary of the Manhattan Prong seismic source does not decrease suddenly. Rather it continues with only mildly reduced levels beyond the boundaries of the Manhattan Prong proper (see Figure 3a). Therefore, to distances of the order r5150 km from the center of the Manhattan Prong, the same seismicity parameters a and b may be used with only moderate distortion. Their usage tends to yield slightly higher estimates of hazard, than if the actually decreasing seismicity with increasing source area would have been accounted for. For instance, using earlier seismicty data based on the EPRI catalog instead of the revised 10

catalog by Seeber and Armbruster (1991), Jacob (1990) found for the seismicity extending to radial distances of 140 km from NYC the following Gutenberg-Richter relation (rate n is normalized to events per year per km2): log n = (-2.257+/- 0.1) - (0.914+/-0.05) M (5) Comparison of (lb) and (5) show that the two relations barely overlap within their standard deviations. Especially the b-values seem significantly different. The Manhattan Prong appears to be characterized by a somewhat lower b-value for the higher magnitude range, i.e. this seismic source appears to produce a higher ratio of large to small earthquakes than the seismicity of the surrounding area. Also, the actual seismicity may not neatly conform to the Gutenberg - Richter assumption of a single b-value slope over the entire permissable magnitude range. This inference follows from inspecting Table 1 (and Figure 5) which indicates a tendency, albeit associated with large uncertainties, for the b-values to decrease with increased magnitudes. The b-values for fits to the entire available magnitude range (2.0<.M<_5) are higher than those to only the mid-range magnitudes (3.25<_M<_5), which however may be more suited for extrapolating to the larger, yet in this region unobserved magnitudes 5>M>7). For all scenario events considered in this study we will use the mean values given in the bottom row of Table 1 [and Equation (lb)] for the Gutenberg-Richter relation. If the assumption of an unbound areal source of uniform random seismicity holds and equations (2) through (4) apply, then it is also true that outside the area S with radius r = d4d2 additional seismicity takes place that produces events during the time T, over and above the one event N=l stated in equation (3). However, since for any given magnitude M and time period T these additional events occur at distances r' > r, their occurrence will on average produce motions that do not exceed those modeled to occur at the median distance d=r/h2. Therefore, within the approximation of this simple model, we can ignore the lesser motions contributed by more distant events. The goodness of this approximation depends in detail, but not in essence, on the regional ground motion attenuation law, i.e. on how rapidly ground motion amplitudes decrease with distance. The attenuation law essentially acts as a weighting function for the area-weighted seismicity to contribute ground motions to a point of interest. Within the approximation of this semi-probabilistic model we have de facto chosen our weighting function to be zero for distances beyond r, and have assigned it to be a delta function positioned at a distance d=r/42, to represent the actual event distribution for a given magnitude at distances between 0 and r. In fully probabilistic methods, the exact forms of ground motion attenuation and areal seismicity weighting functions are used when integrating the hazards contributions. We chose not to apply fully probabilistic methods for this study for reasons discussed later in this report. 11I

Scenario Events with Constant Recurrence Period (CRP): Hazard-Consistent Magnitude Distance (M-d) Pairs. Seismicity is often treated as a Poissonian random process, in which all events occur independently of one another. When aftershock sequences are omitted, Poissonian behavior has been shown to be a generally good approximation for most seismicity patterns. The probability P that an event, that is part of a random process with average recurrence period T, will occur during an exposure time t is: P(%)= 100 (1-e-VT) (6) The average recurrence periods T = -t/ ln[l-(P/100)] that are associated with a 10% probability of occurrence of events during exposure times of t = 50, 100, 250, and 500 years are according to (6): T = 475, 949, 2373, and 4746 years, respectively. Instead of the actual recurrence periods, and allowing for a 5% inaccuracy, we refer to these simply as "500, 1000, 2500 and 5000-year events" or, alternatively, as events with 10% probability of occurrence in 50, 100, 250 and 500 years of exposure, respectively. Using equation (4) with the numerical values for a and b applicable to the Manhattan Prong seismic source as indicated in (lb), we obtain: log d = ( 0.775 M +2.305 -log T -log 2n)/2 (7) Inserting the constant recurrence periods (CRP) of T = 500, 1000, 2500, and 5000 years, respectively, into (6), and choosing the fixed magnitude values M = 5, 6, 7 we obtain from equation (7) the following hazard-consistent distances (km) from a central location within the (Manhattan Prong) seismic source: Table 2: Median distances d (kin) expected for earthquakes with magnitudes M and recurrence periods T (years)for an unconfined seismic source with uniform cumulative rate log n (y-1 kmi2) = -2.305 -.775 M. Magnitude M

---

Average Recurrence Period T (years)------

500 1000 2500 5000 5 22 16 10 7 6 54 38 24 17 7 131 92 58 42 12

Table 2 illustrates how the expected average epicentral distance d increases with the magnitude under consideration, and decreases with increasing recurrence period (or exposure time). Only for the largest magnitude (M=7) does the distance d substantially exceed the linear dimensions of the Manhattan Prong seismic zone, and it does so only for the two shortest exposure times (50 and 100 years). Whether or not magnitude 7 earthquakes can be generated on any of the fault systems in the region (i.e. on the WNW-striking Late-or Post-Cretaceous faults paralleling the Dobbs Ferry shear zone; the NNE striking Ramapo fault, Cameron's Line, or any other fault system) is not known. To be conservative we have included the expected distances for M=7 earthquakes since such events have occasionally occurred elsewhere along the Atlantic margin of North America, e.g. Charleston, S.C. in 1886; and near Grand Banks in maritime Canada, in 1929. Seismic Criteria. On December 6, 1993, a meeting took place in New York between the engineering firms of F.R. Harris (FRH), Hardesty & Hanover (H&H), and the New York State Thruway Authority (NYSTA). At that meeting the criteria for seismic analysis of the Tappan Zee Bridge were reviewed in the light of desired bridge performance. The engineering team proposed, and NYSTA approved a two-level approach: for the evaluation study (5%-damped) response spectra consistent with a 10% occurrence probability in 100 years were to be used for the lower hazard level, and 10% in 250 years for the higher hazard level. By approximation via equation (6) discussed earlier, we equate these design events for 10% probability of occurence in 100 years with earthquakes of a constant recurrence period (CRP) of 1,000 years; and those with 10 % probability of occurence in 250 years with a CRP of 2,500 years. The question of linking certain bridge performance criteria to CRP's of, say, 1,000 and 2,500 years, may need to be revisited by the bridge Owner in consultation with the Engineer partly in light of the results from this report and possible related findings by the Engineer. The AASHTO guidelines which are intended for ordinary bridges use a single-level instead of a two-level design approach and a CRP of about 500 years. In the final stages of this study the Engineer requested for comparison, and LDEO provided, site-specific ground motions and spectra for a CRP of 500 years at a few locations along the TZB. Also on request by the Engineer, simple generic code-shaped rather than site-specific spectral estimates were given at an early stage of this project for a CRP of 5,000 years. This large CRP value may be loosely used as a proxy for 'Maximum Credible Earthquake', although we do not recommend the usage of simple generic, code-spectral-shaped ground motion estimates for evaluating site and bridge response of a structure as critical as the TZB. 13

Communications between F.R. Harris, Hardesty & Hanover, and members of the LDEO team further clarified the details regarding the needed design ground motions. In brief they include: three-component acceleration time-series and 5% damped response spectra were to be provided for three magnitude distance pairs (M-d) per CRP. They include M=5, 6 and 7 earthquakes at the distances consistent with the recurrence periods of 1,000 and 2,500 years. We use for this purpose the magnitude-distance (M-d) combinations of Table 2. The three M-d combinations ('events') provide a measure of the variability in peak ground motions, spectral content and duration that can occur for each CRP. The task is therefore to first synthesize hard-rock ground motion time series for three (M-d) events per CRP. The time series will then be used to obtain ground motions and 5% damped response spectra for rock and soil conditions to be detailed later in this report. CRP vs. Fully Probabilistic Methodology. An alternative to proceeding with the constant recurrence period (CRP) method of constructing ground motion time series as applied in this report would have been to attempt a standard, fully probabilistic seismic hazard analysis. It may be instructive to summarize the reasons that persuaded us not to take this fully probabilistic approach. First, the CRP method as described and applied below is a hybrid between traditional probabilistic and deterministic approaches. It requires the selection of an annual probability (the inverse of the recurrence period) of the earthquakes to compute ground motions. Thus the CRP method employs at least one simple, essential probabilistic principle. The CRP method is at the same time deterministic in that it does not fully take into account the uncertainty or variability, but typically uses instead only mean or median values for all input parameters. Second, the ground motion attenuation laws for the eastern US and adjacent Canada currently published (or submitted for publication) scatter widely between authors, and even change for the same authors rapidly as new data are being considered. In this dynamic environment it is difficult to settle for a single attenuation relation or even a set of attentuation laws. The CRP approach applied here avoids the use of any explicit attenuation laws since it synthesizes the ground motions from geophysical principles and rigorous application of these principles to robust regional geophyical data, while testing the results against the few crucial ground motion observations available. Third, a probabilistic hazard analysis yields a uniform hazard spectrum, or a of set of hazard curves for discrete response spectral frequencies, but it does not yield by itself the associated time series ground motions needed for nonlinear response analysis of either the soils or the bridge structure under consideration. The methods for deriving ground motions in the time domain that correspond to a probabilistically derived uniform hazard spectrum (or to any otherwise defined target spectrum) are not fully standardized at this time. In the case of probabilistically determined uniform hazard spectra one first must "de-aggregate" the ground motion hazards into their 14

constituent, significant magnitude-distance combinations (similarly to what we perform as the first step in our CRP method). Then one must synthesize ground motions from these M-d constituent events whose response spectra must be matched against the probabilistically determined target spectrum. This matching process poses a problem for which a standardized consensus methodolgy has not yet emerged and where at least some of the individually taken approaches to tackle this problem have been sometimes considered controversial. In contrast, our CRP method yields highly realistic three-component ground motion time series for a hazard-consistent set of earthquakes with constant recurrence period or annual probability of occurrence. It is then easy to compute the response spectra for these CRP events and construct a CRP envelope spectrum from them that can be used for modal analysis, just as a uniform hazard spectrum or design spectrum would be used. Fourth and lastly, we have carried out test computations for a New York City site between fully probabilistically derived uniform hazard spectra and CRP envelop spectra using identical seismicity input. These comparisons, while dependent in detail on the specific ground motion attenuation relations used in the probabilistic approach, yield very consistently similar results. Therefore we are confident that the CRP method yields for all practical purposes equivalent results in the response-spectral domain, while having the additional advantage over probabilistic methods of yielding a set of geophysically well defined, realistic three-component ground motion records in the time domain. These are needed for nonlinear response analysis. How to obtain time series ground motions using the probabilistic procedures is, in contrast to the CRP method, not fully self-evident Not any single argument, but the combined weight of all the arguments presented above made us opt for developing and using the CRP method of ground motion simulation over standard probabilistic methods. The CRP method can be extended to account for variability and uncertainty of the input parameters by embedding it into a descision-tree or Monte Carlo procedure. Cost and time considerations usually discourage such an elaborate approach, however, and did so for this project. It is not clear to us, however, whether such additional efforts are justifiable for bridge projects in general, even for important bridges, since this would lead to a very larger number of time series ground motions that would require multiple computer runs for exploring their effects on the variability of nonlinear soil and bridge response. For any given M-d combination one can in fact use multiple random seeds in the stochastic portion (scattering function) of the subsequently described hard-rock ground motion simulation procedure, thus providing some measure of aleatoric (i.e. chance) variability in the ground motion input for allowing to explore this variability's effect on the nonlinear soil response. This option was not used for this study, but might be considered for an actual retrofit design phase. 15

3. Hard Rock Ground Motions.

Three-component synthetic accelerograms (Figure 6) at a generic hard-rock site are computed. The computations are repeated (Figure 7) for three magnitude-distance combinations per CRP of interest (see Table 2). To compute the hard-rock motions we use a method developed by Horton (1994). A copy of Horton's paper outlining the method is enclosed as Appendix A. Once the hard-rock ground motions are computed, they are then propagated computationally through different soil columns providing site-specific ground motions at specified locations along the TZB crossing. Results of this procedure for the 1,000 year ground motions have been reported to the Engineer in an Interim Report (Jacob et al.; January 7, 1994). Portions of the following text, and some tables and figures are taken from that report, while its detailed data appendices are omitted for brevity. For a given M-d combination per CRP, the computation using the Horton (1994) procedure yields three components of hard-rock ground motions (Figure 6). They are: vertical (Z, positive up), horizontal radial (R, positive forward) in the direction away from the epicenter, and horizontal tangential (T, positive to the right). The three computed ground motion components have been rotated at some angle to their theoretical direction of incidence in a non-scattering flat-layered Earth. This rotation simulates effects from scattering and lateral heterogeneities in the Earth's velocity structure and avoids unrealistic polarization into strictly SH-polarized shear-waves on the T component, and pure P (compressional) and SV (vertically polarized shear) motions on the Z and R components. Consequently, the computed hard-rock ground motions have intentionally "cross talk" between the new Z, R, and T components to mimic actual seismic motions quasi-realistically. However, for purposes of migrating the motions through the soil layers, we will -out of necessity-assume that the impure T component represents pure SH particle motion, and R and Z combinations are strictly combinations of SV and P motions. As can be seen from Figure 6 the dominant component is the transverse horizontal (T) component of ground acceleration, followed in amplitude by the radial horizontal (R) component; the vertical (Z) component has little energy associated with the S-wave and related Lg and surface waves which, at the distance of 38 km, occur about 5 seconds after the first P-wave arrival and produce the largest ground motions on the two horizontal components. The crustal structure, and source parameters that were used to simulate the hard-rock ground motions are summarized in Table 3 and 4. 16

Earthquake, M=6, dist=38km, 3 components: Radial, Transverse, Vertical "*100-- M6 38krn T-50 JR -10 100] M6 38km Z 50-0 -50 0 5 10 1-5 20 25 30 35 Time [sec) Figure 6. Three components of computed hard-rock accelerations for an earthquake with a recurrence period of 1,000 years, and related magnitude-distance (M-d) combination of M=6 at d=38km. The three components are from top to bottom: R, radial; T, transverse; and Z, vertical component.

S-2 lI M6 92km T-CN SC= 10 20 30 40 50 60 Time [sec] 1.esponse Spectra, 5percent domped, lO00yr Eorthquoke, Tronsverse component, M=5 15km, M=6 38km, M=7 92km I I I I I I resp/M5 15.5 T ........ resp/M6 38km T resp/M7 92km T 1.0 C 0.8.0 r" 00.5 1.0 1,5 2.0 2.5 3.0 3.5 4.0 Period [sec] Figure 7. T(QT..: Transverse components of computed hard-rock accelerations for three equally probable earthquakes with a constant recurrence period (CRP) of 1,O00 years, but different magnitude-distance (M-d) combinations M=5 at d=1 5.5 kin; M=6 at d=38km; and M=7 at d=-92 km. (Bottom): 5% damped response spectra for the same 1000-year accelerations shown above. Note the small earthquake at short distance dominates the short periods, the large earthquake at large distance the long periods. The envelope to the three spectra is called a CRP envelope response spectrum. 18

Table 3: "New England" Crustal Structure Used in the TZB Ground Motion Simulations. Layer Thickness Depth to Top P-velocity S-velocity Density Qp Qs (km) (kim) (kmWs) (kins) (glcm3) (intrinsic*) 1 2.0 0.0 6.00 3.50 2.50 3000 1500 2 13.0 2.0 6.10 3.60 2.60 6000 3000 3 25.0 15.0 7.00 4.10 2.90 6000 3000 4 00 40.0 8.10 4.70 3.20 6000 3000

• These Q factors represent only the intrinsic anelastic absorption (attenuation) of crustal materials.

The additional attenuation from scattering is separately accounted for by the procedure of Horton (1994). Table 4: Source Parameters Used for the 7ZB Ground Motion Simulations Magn. Moment Stress Comer Focal Strike Dip Rake M Mo Drop Frequ. Depth (degr) -------- (NmxlO16) (bar) (Hz) (kcm) 5 3.98 100 1.10 7 0 80 20 6 126.00 100 0.35 7 observed at 22.5 degrees 7 3980.00 100 0.11 7 from strike Since the transverse (T) component provides the dominant ground motions we concentrate our following discussions and illustrations on this component, although the R and Z components were also computed for all instances discussed here. The top portion of Figure 7 shows the hard-rock acceleration time series for three equally probable magnitude-distance (M-d) combinations, given a constant recurrence period CRP=1,000 years: M=5 at 15.5km; M=6 at 38km; and M=7 at 92km. The lower portion of that figure shows the 5% damped response spectra for the same three 1,000-year events. While the three time series have very similar peak accelerations of about 0.15 to 0.20g, their durations and frequency content are radically different. The different frequency contents of events belonging to the same CRP are clearly visible in the response spectra (Figure 7, bottom): at short periods (T<0.2s), the amplitudes of the smallest earthquake at shortest distance (M=5, d=15.5km) clearly dominate; at long periods T>ls, the largest earthquake at the largest distance (M=7, d=92km) clearly dominates; while at the intermediate periods (0.2s_<T51.0s), all three considered earthquakes have amplitudes of nearly comparable levels. One can construct a CRP envelope response spectrum taking the maximum response from all considered M-d events for a given CRP at any given response period T. This CRP envelope response spectrum can be used as a first-order approximation to a uniform or constant hazard spectrum, and hence as a design spectrum (for hard rock site conditions) for the CRP under consideration, here 1,000 years. It is interesting to compare the CRP envelope spectra for different CRPs of 500, 1000 and 2500 19

years (Figure 8). As one would expect, the amplitudes of the spectra are generally larger for longer recurrence periods. In this case, however, anomalies occur at response-spectral periods between about T=1.2 and 1.9 and beyond 3 seconds. At these periods the envelope response spectral amplitudes for the 1,000-year events exceed those for the 2,500 year events. This is due to the fact that one of the 1,000-year events (M=7 at d=92km) is located at a distance at which post-critical Moho reflections for this particular crustal structure arrive. Equivalent observations are frequently made from recorded data in the distance range where post-critically reflected Moho arrivals emerge. Note that these post-critically reflected arrivals are preferentially occuring at intermediate to long spectral periods, and in this case dominate in the narrow band of about 1 to 2 seconds. The strength of this feature, and the critical distance at which it appears, will somewhat depend on the regional crustal structure. It shows up quite prominently at d-100 km for the crustal structur used in this case (see for example Figure 1 of Appendix A). The discussed anomalous amplitude reversal between the 1000 and 2500-year CRP envelope spectra (Figure 8) points to the fact that the CRP-method used here with only three M-d combinations is not a perfect substitute for a full-blown probabilistic hazards assessment. However, if we had carried out the CRP method in such a way that at least one M-d combination always had a distance close to or just beyond where post-critical Moho-arrivals emerge, then a normal sequencing of CRP envelop response spectra would have been obtained. This demonstrates that one must pay attention to discretizing the CRP method either finely enough (chosing many M-d combinations); or one must otherwise assure that at least one distance among all the M-d combinations is chosen to 'coincide with the post-critical Moho reflection distances. The prominence of 1 to 2-second periods in the post-critical reflection arrivals are of particular interest for the TZB project because -as we will see later-both the soil response and the main-span structure of the bridge have important resonances, and hence dynamic amplifications, at these periods. Therefore, increased input at these resonance periods can lead to important engineering consequences, including nonlinear response of soils and structures. It is primarily for these practical reasons that we must pay careful attention to otherwise rather subtle seismological phenomena. Once the hard-rock motions have been computed for various constant recurrence periods, both in the time and response-spectral domain, then they can be used as input to determine the response of soils overlying the bedrock. In order to compute the soil response one must first establish the geotechnical properties of the soils present. Intially we determine the low-strain elastic soil properties from geotechnical boring data, which then need to be modified for high-strain degradation of the shear modulus under realistic seismic strain levels. 20

Spectra, 5percent damped, Transverse, 3 Recurrence II I/I 0.. 5 10 5 - ""......""°* I 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4. Period [sec] Figure 8. Constant recurrence period (CRP) envelope response spectra for three different constant recurrence periods of CRP = 500, 1,000 and 2,500 years. Note that the 1,000-year spectrum exceeds the 2,500-year spectrum at periods between about 1 and 2 seconds because of contributions from super-critical Moho reflections for the constituent 1,000-year event of M=7 being located at d=92 km.

4. Geotechnical Soil Profiles: Shear-Wave Velocity at Low Strains as Starting Model in an Iterative Process.

A variety of pre-existing data were consulted to derive the soil profiles and their geotechnical properties for seismic site response analysis. A compilation of borings along the TZB was made (Figure 9). The available information includes data from the Draft Geotechnical Report by Greiner Inc. (1992), a soil profile developed by Hardesty & Hanover (1993), and a fortuitously found report on soil tests (Anonymous, undated). This valuable, undated and unattributed document was found in Columbia University archives. It may have been generated in the soil laboratory of Prof. Donald Burmister, Columbia University, who appears to have acted as a soils expert and consultant to the original TZB project in the early-to-mid-1950s. This report provides a variety of laboratory test results on boring samples, including complete profiles of the moisture content for the 1952-Borings #1 through 11; a tightly sampled depth profile of the Plasticity Index (PI) for Boring

1. 1, and Triaxial Shear Strength test results for most of the 1952-borings #1 through 11.

Other documents reporting results from marine geophysical surveys were consulted in order to construct the deeper portions of the section not penetrated by borings, including the bedrock configurations (Figures 2 and 10). Two publications reporting on early seismic refraction surveys performed by former LDEO researchers were particularly helpful in this respect, i.e. those by Worzel and Drake (1959), and Herron et al. (1968). An important publication on sediment acoustics for interpreting the geotechnical properties of the fluvio-marine sediments in the Hudson River estuary in terms of their wave-propagation properties is that by Stoll (1988). We rely heavily on this treatise for determining the density and shear-velocity depth profiles. In particular Stoll's equations (6.2), (6.3) and (6.4) are used to compute the shear modulus and shear wave velocity from the void ratio or water content as a function of depth. For this task the following formulas and empirical constants are applied in our numerical calculations: Vs = (p./ds)" 2 (8) with vs= shear wave velocity (m/s)

g. = shear modulus (kPa),

ds = in-situ density of porous, water-saturated soil (g/cm 3 or t/m3) Note: lt/m3 = 9.81 kPa/m; (t = metric ton = 106 grams) 1Pa (Pascal) = IN/m2 ; (N = Newton) g'= 9.81 m/s 2 (Earth's gravity acceleration) 22

3 9 a a a 13 8 B-.. B-3,'.. 19520,Q a ° a ,N. ,,a' a a a ,a' a a a aX a ,O ' 952 0 GEOTECHNICAL BORE HOLES 199202 0 5000 ft a !aI I I I Figure 9. Map view of borings along the Tappan Zee Bridge (TaB) across the Hudson River that were available for this Report. Locations of borings indicated by open circles are poorly known. The 1992-borings by Greiner Inc. are labeled with a prefix B-.

B-1 S-2 S-3 1? 11 13 2? 7 3 4 20 8 9 5 BORING 6 100 - 5 8.5 ....... ~..............

o.

o %300% %,°% % .°............... ...... °. .°.......... .° -500. % -550 ~ % Figure 10. Inferred simplified geologic cross section (bottom) and schematic map/side-view (top) of the Tappan Zee Bridge (TZB) with borings whose information was used in this Report.

and ds= dw (l+w)/(w+i/Gs) (9) with w = water content = mass ratio of water to dry soil particles = e/Gs; e = void ratio = volume ratio of voids to soil particles Gs-2.65 ; specific mass of ft soil particles (relative to water) Gw--1.0 ; specific mass of pore water (relative to water) dw =1.0 g/cm 3 or t/m3 (density of water); and g = p. a [exp -(be)] (So'/p)n) FF (10) with Pa= Ibar = 100 kN/m2 = 100 kPa; atmospheric pressure 1 atm = Ibar = 100 kPa; a = 2526 (empirical constant for marine clays, silts and sands, see Stoll, 1988) b=l.5 (empirical constant for marine clays, silts and sands, see Stoll, 1988) e = void ratio = Gsw (11) so'= effective stress = [(1+2ko)/3] p0 (12)

k. - 0.5; this is the coefficient of earth pressure at rest = sh' / s,';

it represents the ratio of horizontal to vertical effective stress; the value adopted here implies normally consolidated soils; p0= f[(1-13) (Gs-Gw) dw ] dz; (13) P. is the effective (buoyant) overburden pressure at depth z; B = e/(l+e) = soil porosity, with void ratio e= Gsw (14) n--0.45 (empirical constant for marine clays, silts and sands, see Stoll, 1988) FF=2.0 (empirical constant for marine clays, silts and sands, see Stoll, 1988) The procedure by Stoll (1988) starts with a depth profile of water content w(z) as the sole input (Figure 11), from which one then calculates in successive steps the depth profiles of: void ratio, soil porosity, in-situ soil density, effective (buoyant) overburden pressure, effective stress, shear modulus, and -finally-shear wave velocity. Both shear wave velocity and in-situ soil density are needed to compute the seismic site response which modifies the hard-rock input motions. The shear-wave velocity depth functions are then lumped together into models of layers with a constant velocity in each layer. These layered models can then be used with existing programs for wave propagation through layered media, to migrate the various waves (P, SV, SH waves) through the stack of layers to obtain site response. One detail is important when computing the averaged velocity for each layer. The average velocity V must be computed such that the vertical traveltime across the layer with constant velocity V and total layer thickness H=X hi matches the vertical travel time with variable velocities vi representative of discrete depth intervals with thicknesses hi within the layer H. This condition is met when: V = H/ (hi/ vi). (15a) with H=X hi. (15b) 25

WATER CONTENT (decimal) SHEAR WAVE VELOCITY Vs (mWs) VELOCITY model Vs (mls) 0 100 200 300 400 500 60C 100 200 300 I I I 400 500 60 I I )0 U~t.. 4 boreholes b I b 7.............. b4 --- B2 --------- b5-0- 10-boreholes b I b 7............. b4 - B 2 --------- b5-20-30-201 30A 0 50 -100 a) -152 .200 a-0* 40-5 0-60-70-0on 40-0.. 50-70- -250 Figure 11. Depth profiles for 5 sample borings (from west to east: bl, b7, b4, B-2, and b5) showing the quantities: measured water content (left), the derived shear-wave velocity (center), and the layered velocity model (right) for which the lumped discrete constant shear-wave layer-velocities are computed to yield equivalent vertical shear-wave travel times in each layer. Note depth scale in meters (left) and feet (right). The depths are measured below the mean sea level. The shallowest measurement is at or just below the mudline and hence indicates the mean water depth at the location of that boring. Note that shear-wave velocities as low as 30m/s (=100ftts) are present. The anomalous high water content in boring bl at depth =18m (54ft) is associated with a layer of peat.

5. Modification of Soil Parameters for Strain-Dependent Nonlinear Response Simulated by Equivalent Linear Approximation.

So far we have been concerned with soil properties in their linear elastic range (that apply for infinitesimally small cyclic strains). Vucetic and Dobry (1991) describe the shear modulus degradation, G/Gmax, and the increase of the coefficient 'beta' of soil damping, 13=1/(2Q) (83=damping; Q=seismic quality factor), as a function of finite-amplitude cyclic shear strains. They show that non-linear soil behavior for different soils can be characterized by a single property, the Plasticity Index PI = PL - LL. The PL is the water content at the Plastic Limit, and LL the water content at the Liquid Limit (obtained from the Atterberg Limit tests). In particular we use the author's Fig. 5 and 6 summarized in our Figure 12. It shows that the shear modulus degrades less as a function of increasing strain the higher the plasticity index (PI) of the soil, and the soil damping is lower at any given strain level, the higher the PI. Based largely on the data quoted in the geotechnical reports, we assign the following PI values to the various types of soils and rocks, overlying the crystalline metasediments (i.e. gneisses etc.): Table 5: Plasticity Index (PI) Assigned to the Soils at TZB Site. Rock or Soil PI Organic Silts 30 Silty Clays 15 Silty Clays with some Sand 10 Sand 3 Varved Clays (interbedded clays and sands) 3 Gravel 0 Triassic Red Sandstone 0* Serpentinite 0o *

• The concept of plasticity is not applicable to rocks.

We reiterate: the higher the PI value, the less degradation of the shear modulus, and the less increase in damping for finite strains. The strata to which we assign a nominal PI=oo are assumed to not show any strain-dependence of their shear moduli or coefficients of damping; i.e. the intrinsic damping values and shear velocities for these materials (with PI=oo) are assumed to remain unaffected by the level of ground motions they experience. The same of course is assumed for the basement rocks not listed here. We assigned a relatively low PI to the varved clays for the following reasons. Their sand layers will readily show degradation, while the clays will do so to a much lesser degree (since by themselves they have a higher PI). However, since the overall behavior of a stack of layers is dominated by the behavior of the most degradable layers, we feel that a relatively low PI is warranted for the bulk behavior of the varved clays. We have not numerically tested this hypothesis. 27

E P=4200 0 0.2 - 0.0 1 3 0.0001 0.001 0.01 0.1 1 10 CYCLIC SHEAR STRAIN, (%) 25-PI =0 15 20-30 os1~ 50 100 z 10-200 5 0 0.0001 0.001 0.01 0.1 1 10 CYCLIC SHEAR STRAIN, (%) Figure 12. (Top): Shear modulus degradation G/Gmx (labeled here WpPmax) as a function of cyclic shear strain (in %) for soils with different plasticity index, P1. (Bottom): Damping ratio 6 as a function of cyclic shear strain for soils with different PI. Both curves are taken from Vucetic and Dobry (1991) and apply to normally consolidated or only slightly overconsolidated soils. 28

The curves of G/Gmax vs. strain and 13 vs. strain given in Vucetic and Dobry (1991) were tabulated for computer use, with PI as a parameter that guides which table to enter during the computations of strain-dependent site response.

6. Grouping of Site-Repsonse Computations In a letter dated Dec. 1, 1993, Hardesty & Hanover (H&H) had specified seven foundation groups for which the site-specific ground motions needed to be determined at two depth levels - at the Pier Underside and at Rock Elevation (see Table 6). We had to further subdivide these groups since some of them showed distinctly different soil and site response characteristics within a single group. Table 6 provides an overview for the original groupings proposed by H&H, while the revised grouping as necessitated by site response considerations is shown in Table 7 for the Deck Truss and Main Spans, and in Table 8 for the Trestle Spans on timber piling.

Table 6: Foundation Grouping Proposed by H&H (12/1/93) for Deck Truss and Main Span Sections ---Group #---- Pier Bents Pier Rock

---

Nearest Available Borings -------

Represented Underside (ft) Elev.(ft) ID 1 2 3 4 5 6 7 166-168 169-173 &178 175-176 179-180 181-184 185-189 190 -24 -42 -42 -24 -24 -24 -30 -200 -240 -300 -200 -150 -70 -30 4 B-1 &20at 169-173; B-3 &9at#178 8 &B-2 at#175; 9&B-3 at#176 5, (9 ?) 5 6 On Rock Table 7: Foundation Grouping for Deck-Truss and Main-Span Sections Taking into Account the Site Response Characteristics Group Pier Pier Nearest --Layering Used for Site Response Computations*-- Bents Under-Borings, -...... Depth (ft) below MSL to Top of Layer-------- Represented side (ft) ID) Org.Silts I Sands I Varved CI. I Gravel I Sandst. I Gneiss Depth (ft) @ which Rock Motions Requested by LDEO H&H LDEO-Rock 1 166-168 -24 4 -14 -115 -176 -223 -789 -227 -200 -3 2a 169-173 -42 B-i -21 -118 -183 -244 -654 -251 -240 -7 3a 175 -42 B-2, (8) -37 -109 -208 -234 -260 -545 -260 -300 0 3b 176 -42 B-3, (9) -37 -122 -145 -280 -299 -300 -19 2b 178 -42 (B-3, 9) -34 -127 -134 -209 -219 -222 -240 -3 4 179-180 -24 (9, 5) -24 -92 -122 -145 168 -195 -200 -27 5 181-184 -24 5 -11 -79 -109 -132 155 -161 -150 -6 6 185-189 -24 6 -7 -33 -61 -66 -79 -70 -13 7 190 -30 rock --- ? -30 -30 -30 0

• The actual boring information (water-content) is used for determining shear wave velocity and soil density, where available. The stratigraphy and materials assigned are only approximate and serve primarily for allowing reference to Table 5 in which the PI values are listed that were used in the nonlinear site response computations.

29

Table 8: Examples of Soil and Rock Profiles for the Trestle Section with Foundations on Timber-(Friction) Piling Reaching to Average Depths of about -75 ft (below MSL). Group Nearest --1952-Borings

---

......... Layering Used for Site Response Computations*.......-------

Pier ID Max. Penetr. - Depth (ft) below MSL to Top of Layer --.-.---------.... Bent # Depth (ft) Org.Silts Sands Varved Cl. Gravel Sandst. Gneiss 8 34 - 35 1 -224 -9 (+clay and peat) -120 -210 -223 -2750 9 100 (+/-10) 7 -161 -11 -130(+ silts, clays) -430 -450 -1200

• The actual boring information (water-content) is used for determining shear wave velocity and soil density, where available.

The stratigraphy and materials assigned are only approximate and serve primarily for allowing reference to Table 5 in which the PI values are listed that were used in the nonlinear site response computations. The boring locations are shown in map view in Figure 9, and in combined map and side-views in Figures 2 and 10. The boring information and inferred geology are compiled from sources as identified in the preceding sections. Where possible, we relate the boring ID# to the nearest Pier Bent # for ease of locating the borings. The deeper strata and bedrock configurations, shown in Figure 2 to depths of more than 1,000 feet below mean sea level (MSL) that were not penetrated by the borings, are -as stated earlier-taken from Worzel et al. (1959) based on marine seismic refraction surveys carried out by LDEO teams in the early 50's during the initial stages of the TZ bridge design and planning. Figure 2 also shows the location of those 1952-borings for which we have no records, i.e.boring # 12 through 34. If these additional boring results had been available to us, they would have greatly helped to better resolve the velocity structure at the TZB crossing. In contrast, Figures 9 and 10 show only those borings whose results were fully available to us for determining the shear wave velocity and density profiles. The borings with information pertinent to end-pile (driven to bedrock) foundations of the Deck Truss and Main Span Sections of the TZB, i.e. between Pier Bent # 166 and 190 (proceeding from W to E, with nearest Pier Bent # in parentheses) include: the 1952-borings # 4 (-164), 20 (170), 8 (175), 9 (176), 5 (-181 to 182), and 6 (=188); and the 1992-Greiner borings labeled B-1 (170), B-2 (175), and B-3 (176). For their locations see Figures 2, 9, and 10. The Trestle-Span segments of the TZB that cross the western half of the River (Pier Bent # 1-165) are founded on friction (timber) piling penetrating, on average, to depths of about -75ft below MSL. H&H requested (by letter dated Sep.15, 1993) that ground motion acceleration time series and response spectra be provided at two depth levels: at elevation -30ft which corresponds to the modeled lateral point of fixity for the piles under static load; and -75ft which is near the pile tip 30

for most of the timber piles. We computed ground motions for two locations (Table 8), near Pier Bent # 34-35 and #100. They are located close to 1952-borings # 1 and 7, respectively. More densely spaced profiles can only be constructed by interpolation between borings. Lateral variations of soil/rock configurations with correspondingly different site response characteristics may be significant as one approaches the western shore of the Hudson near Nyack, N.Y. Some details of Table 7 need further explanation. In some instances the actual soil/bedrock interface determined from nearby borings is at a larger depth than the theoretical values specified in the H&H letter request. Since the frequency-dependent soil response is quite sensitive to the thickness of layers, ignoring the actual bedrock depth would in some instances change the shape of the spectra. To avoid such spectral distortion we need to use the actual bedrock depth, and the input motions in rock should be defined either at the depth of the bedrock/soil interface or a few feet below, well inside the reference rock. The last three columns of Table 7 indicate the depths (below MSL) at which the rock motions were defined (column labeled "LDEO"), at what depths they were originally requested (column "H&H"), and the depth interval below the rock/soil interface for the points at which the rock input motions were determined ("LDEO - Rock"). Another problem occurs at the top of the soil column. We calculated ground motions at the requested depths (varying in elevation below MSL from -24 to -42 feet; see column 3 of Table 7), but these depths do not necessarily coincide with the top of the soil column (as determined from nearby borings). Mud thickness ranges from 0 to 21 feet above the H&H-specified depths. The 'effect of this additional mud is illustrated in Figure 13. The response spectra shown are those for Group 2b (Pier Bent 178), with one set of spectra given at the mudline (at an estimated elevation of about -34 ft), the other set of spectra about 8 feet below the mudline at the H&H-specified elevation -42 feet. The spectra show that the effects of depth of burial below the mudline on the response are -as expected-most pronounced at the shortest reponse periods, i.e. for T<_0.5 seconds.

7. Equivalent Linear Approximation for Iterative Computation of Nonlinear Site Response.

The following procedure was used to compute the location-specific, soil-response-modified ground motions and their response spectra. For each constant recurrence period under consideration, three-component hard-rock motions for three magnitude/distance combinations had been computed by the method of Horton (1994) as described earlier. These motions were computed assuming free-surface conditions at gneiss bedrock sites (for example, the gneiss outcrop at the site of Pier Bent #190 in Westchester, see Figure 2). 31

RLqon,, 3ocrto4 S ¢nt dotoed. 3 C.nels Respone Uo: Wee coffyomds 3,- 30 OA3 -~0.1 53 0.1 es03p/.5S 15 2b.= I '-.- tsp/-n5 15 2b.00 4aP/.46535NOW0

• 1 0

V - 4SP/aS 35 2b.1 0 resp/aS 15 2b5 T S- -. r 1p/n5 35 2b.s I 0.15 OA 042 t 4a 05 30 U, 2.0 2.5 5.0 3.5 Q, SRespopnse Spociro. 5psercon domnped. 3 Corrpert, -0 3 0 ,0 13.5 2.0 2.5 Peod IoCJ 3.0 15 4 Ix ....respl. 39 A.,OOR resp/m* 30 0b0 Rap M: Wecio ne Cosnpeoudsi -rp/rn3382&S R --rMA6 r,382b.,5I - -sp/MO 38 25s I .0,4

• "0,4 0.2 A!

-rs M 35 Period [Sec) Rapeon.~

Spoctra, 5Wep orolmped.

3 Cornponnls rap/mI 92 2b..005 0 i esp/m7 9273AM 0.4 13.2 9 rap/m.82 2"."\\

1.

-4.0 ......~ 1ý 1... o/, 233 I . 0.4 0.4 'I "Z, 0. -4Al -~ -i V.44 ~ ~ ~ PV [3 .3 -20 3.0 ]3, 4.0 3.0 U.* 3.0 3.5 2.0 Penod [sec] i[";;;-:................ 3.0 35 4.0 Figure 13. 5%-damped Response Spectra [g] at the same Foundation Group (2b) near Pier Bent 178, but computed-for different depth levels. On the left are spectra at the mudline (elevation -34 ft), at the right are the spectra for 8 feet below the mudline (elevation -42 ft). The three spectra are, from top to bottom, for the three 1,000-year recurrence-period earthquakes M=5 at 15km, M=6 at 38km, and M=7 at 92km, respectively. Note high accelerations at short periods at the mudline, compared to 8 feet deep into the mud (organic silts). Three lines on each graph show the transverse (T, dotted), radial (R, solid), and vertical (Z, broken) component of motion. 32

For use as input motions at the bottom of the actual rock or soil columns that overlie the gneiss at the reference depth, one must remove from the computed motions the effects of free-surface boundary conditions which invoke certain components of the stress tensor to be zero. To achieve this, the free-surface motions must be divided by a factor of 2. In doing so we equate the gneiss with the uppermost layer, Layer 1, in our crustal model listed in Table 3 (i.e. with a shear velocity v, =3.5 km/s). The angles of emergence of seismic body waves in the gneiss were. computed for the different M-d combinations (and are found, for instance for the 1,000-year events, to be of the order of 60 degrees or more from vertical); they are used as angles of incidence at the bottom of the stack in order to migrate the waves through the layers of overlying rocks and/or soils. Migrating the input motions through the layered soils is normally done with programs like SHAKE, which iterate the non-linear behavior of soils using step-wise linear visco-elastic behavior with shear modulus and damping changed from one iterative step to the next, according to layer strains computed in the previous step. The disadvantage of SHAKE is that it is written only'for SH waves (horizontally polarized shear waves), and for vertically approaching waves only. To circumvent these limitations we use an existing full-wave code for arbitrary off-vertical incidence which allows migration of P and SV, and of SH waves. The code is based on Kennett and Kerry (1979) which provides a complex spectral transfer function in the frequency domain. Examples for the moduli (amplitudes) of the linear transfer functions during the first iteration are shown for five boring sites in Figure 14. The hard-rock ground motions are propagated through the soils by multiplying the complex hard-rock Fourier spectra by the complex soil transfer function in the frequency domain. To compute layer strains (at different depth levels) we transfer the spectral soil accelerations in each layer back into the time domain, integrate only the transverse particle accelerations AT(t) to particle velocity VT(t) and then compute an approximate average (RMS) strain Erms for the SH motions from the relation EmsSH = [2/( 7 vs) [(lIt') 1 [VT(t)]2 dt ]112 (16) t'l where t'1 and t'2 and hence t = t'2 - t'1 are chosen such that the Erms obtained contains the value between the 5-percentile and 95-percentile of the Erms total over the entire RMS velocity (or strain) record; vs is the local shear wave velocity of the soil layer at the depth of interest. The approximate RMS strain so calculated for each layer is then used to determine the new shear modulus (or shear wave velocity) and damping in the corresponding layer from the curves G/Gmax 33

HUDSON PALISADES DIABASE / RIVER METAMORPHIC BASEMENT: 0 -ZOftt -400 -600 -W0 -bo I.- SEDIMENT TRANSFER FUNCTIONS 20 Q) E 10 0 0 1 2 3 4 Frequency (Hz) Figure 14. (Bottom): Amplitude of computed Fourier-spectral transfer functions of the soil vs. rock motions at five sample sites at borings (from west to east) bl, b7, b4, B-2, and b5 whose locations are shown above. The site response shown here represents the linear soil behavior only. (Top): Location of the five sample borings (heavy vertical lines) for which linear site response factors are given. 34

a) M7 rock 0. a I I ~~~............. +........ ilt*I..... =.---....................... M7Nnlna -0.1 0.4 - A M7 sediment linear 0.2- .2 -0.2-10 20 30 40 50 60 70 Time (s) b)Linear ond Non-lineor, Transverse, M=7, dist=92km, Borehole B2, depth 1.5m 1......... M7 Non-linear 4 / °" 1-1 2 2 ,-.108.................. fl =6 6 V)\\ 10-1 L A \\ ,10-1 2 4t 5L 6' 7L 8 9'100 2 3' 4L 5L 6 7L 8 9 101 Frequency [Hz] Figure 15. Comparison of rock input motion with soil motions for both linear and nonlinear soil response computation (a) in the time domain and (b) in the Fourier-spectral domain. The example shows ground motions from a 1,000-year earthquake with M=7 at d=92 km observed on rock and at boring B-2, 1.5m below the mudline. Fourier-spectral ratios are normalized to the rock motions. 35

vs. strain and 0 vs. strain (Figure 12) given by Vucetic and Dobry (1991). The new vs and B values are then used to calculate a new transfer function. The process is repeated several times until the changes in shear moduli and damping coefficients between iterations become insignificantly small. Usually this happens after 4 to 5 iterations. The final three-component acceleration records are computed at the specified depths using moduli and damping coefficients from the last iteration. These final accelerograms are processed to obtain 5% damped acceleration response spectra Sa(To) for each component T, R, and Z. (Note: To means the natural period of the damped oscillator). Figure 15 shows an example where the transverse horizontal motion from a M=7 earthquake at a distance of 92km observed at a rock surface outcrop (e.g. like near Pier Bent 190) is compared to the transverse motion at a depth of 1.5 meter below the mudline at boring B-2 (i.e. near the main-span caisson of Pier Bent 175) assuming linear and non-linear soil response. The comparisons both in the time and frequency domains clearly show how high frequencies are suppressed (above 4 Hz), and how longer periods (at about 1 Hz) are strongly amplified by factors of up to about 10; and how the nonlinear soil response shifts the soil resonance peaks to lower frequencies (or longer periods), in this case from about 1 Hz to about 0.6 Hz, thus exciting many of the long-period (i.e. fundamental) modes of the main-span structure much more than if they would be founded on hard rock. The linear soil response constitutes the result from the first step in the iteration procedure to obtain nonlinear response by stepwise equivalent linear methods. We have included as an Appendix B a full listing of the starting models for the soil and rock profiles for use in the soil response computations for all 11 foundation groups listed in Tables 7 and 8, except for foundation group # 7, which constitutes the hard-rock outcrop on gneiss, i.e. the reference rock. Note that the wave velocities and Q factors listed in the Appendix represent low-strain starting models to be modified as explained earlier according to strain information computed for each event from equation (16) and soil degradation shown in Figure 12.

8. Essential Features of Soil-Motions:

Examples and Results. We show here only representative examples of results and discuss their main features. Complete results for the 1,000-year earthquake time records and 5%-damped response spectra were delivered to the Engineer earlier in digital form on diskettes and as two Data Appendices of an Interim Report dated January 7, 1994 (Jacob et al., 1994). The first Data Appendix contained the 5%-damped Response Spectral Accelerations (in units of g) as a function of oscillator period T (sec); the second Data Appendix contained the Acceleration Time Series (also in g) as a function of time. The combined data sets included 3 components of motions, i.e. T, Z and R for three 1,000-year 36

earthquakes with magnitudes M=5, 6, 7 at distances d=15, 38, and 92 km, respectively. Results were given for the 11 foundation groups listed in Tables 7 and 8 and for two depth levels near the top and bottom of piles near rock (except for foundation group 7, which is for rock only). These combinations amount to a total of (3x3x1 lx2)-(3x3)=189 spectra and 189 time series. Soil vs. Rock Motions. From these earlier reported extensive data sets for the 1,000-year events we show here only a set of representative examples, one each for the time domain and the 5%-damped response-spectral domain. We focus on the three-component rock and soil motions at the site of Foundation Group 3a near the main-span caisson at Pier Bent # 175 whose underlying rock and soil column is best represented by Boring B-2. The time-domain results are compiled in Figure 16, while the response-spectral domain results are shown in Figure 17. As can be seen from the time series and spectra alike, the transverse component T, mostly composed of SH waves, dominates the level of shaking, especially on soils where they experience considerable amplification at long periods and some absorbtion at short periods (high frequencies), a result already presented in Figure 15. Soil amplication is most prominent for the largest of the three 'equally likely' magnitude-distance combinations, i.e. the M=7 at 92 km. The latter provides large input motions at long periods. At shorter periods, and in rock, (or at sites with thin soil cover not shown here) the motions associated with the smaller earthquake at short distance (M=5 at 15km) can be quite forceful and dominate the spectral response. In some of these instances the R and Z components also can take on a moderately important role. Response Profile Across the Hudson River, To show the influence of the nonlinear response of different soil profiles we compare the 5%-damped response spectra for the same earthquake, i.e. M=7 at 92 km and CRP=1,000 years, at different locations across the Hudson River (Figure 18). The same boring locations as those chosen for Figure 14, which showed the effects of linear soil response, are used. Comparing the spectra in general, but particularly those for borings bI and b5, shows that the combined thickness of the two shallowest layers, composed of organic silts and and silty sands, causes the long-period site amplification and fundamental period to increase, while it causes the high frequencies (short periods, < lsec) to be attenuated. Also remember that boring bl contains a very weak peat layer (Figure 11) contributing to the unusual response. The large site response at boring B-2 is partly explained by higher water content, i.e. lower shear-strength and shear velocities than in most other profiles (Figure 11); and partly by the depth of fixity at which the response is computed since it implies at this boring a depth of only 5 feet of soil below the mudline. The low shear velocities contribute to high layer strains (equ. 16), which in turn contribute to nonlinear soil degradation (Figure 12). Note from comparison with Figure 17 that the increasing long-period excitation as one progresses from M=5, 6 to 7 apparently induces a 37

m0 92 3o.r R 0.2-0.` 0 .2-O` .0. t 0.1 Wfl 92 3a., m7 92 3o.$ R 0.2 -0.2 -0.4 m7 92 ks I 0.2 O. O`*- ra0 92.ks 1 0d.2 _o`.,,, f, -02 -0.4 m7 92 3o, Z 0.2 O`: 20 30i T". (~Cj Tr.4 [sM) Figure 16. Six panels of ground accelerations [g] at the site of Foundation Group 3a near the main-span caisson at Pier Bent # 175 with rock/soil profile represented by Boring B-2. Each panel has three-component time series: radial=R, transverse=T, and vertical= Z. The motions in the left column are in rock at the bottom of end-piling; those on the right are at elevation -42 ft below MSL which is 5 ft below the mudline. All motions are for earthquakes with a constant recurrence period CRP=l,000 years, however the 3 panel rows represent different M-d combinations, from top to bottom: M=7 and d--92km, M=6 and d=38km, and M=5 and d=15km. Note variation of time scale for M=7, 6, and 5. 38

Retspo S0*pm, 0r4 do*,cpad. 3 CsPonKIs Rei*, Smtro, 5mmalt d.., 3 Ctim-1s - mp/n.5 38 koj R resp/m6 38 3o,r T 4~.~/ffk38 3M 1 I I I esp/mS 383.A L -remsp/mfi383 04 0

• o.s R 30.3 T 3O.S 1

~01 I t \\.- I I IS "s/m 1 3 oi * ' R\\./6153. -- sp/mS 15 3wa T "- ~P/n6 15 30., -) 0.5 1.0.,5 2.0 2.5 3.0 3.5 4.0 0.a as a .5 2.0 2.9 3.0 3.5...40 Frie1p/ Six pe of rrspns Ia sets i Gru 3 eaheminsanciso at PirBesnt5 # 1o. 5 0it roksi prfle resented by Boring 0.a. o i 0.4 0 0

0.

1

a.0 2

-i ' i *'.0 2....... ... 5 3 .......0 33,

• . I.0 0*, O.5 1.0 0.

.0 8.9"i ii * " i~ 3.

• 0 3.......... 4. 0 Figure 17. Six panels of 5%-damped response acceleration spectra [g] at the site of Foundation Group 3a near the main-span caisson at Pier Bent # 1 75 with rock/soil profile represented by Boring B-2. Each panel has three component spectra: R (solid), T (dotted), and Z (broken). The motions in the left column are in rock at the bottom of end-piling; those on the right are at elevation -42 ft below MSL which is 5 ft below the mudline. All motions are for earthquakes with a constant recurrence period CRP=1,000 years, however the 3 panel rows represent different M-d combinations, from top to bottom: M=7 and d=92km, M=6 and d=38km, and M=5 and d=15km.

39

HUDSON RIVER PALISADES DIABASE ORGANIC SILT / SILTY SAND VARVED CLAYS, GRAVELS hI /k7 SILTS & SAND / .i Z. Io Period [sec] Figure 18. (Bottom): 5%-damped response spectra at five sample sites near borings (from west to east) bl, b7, b4, B-2, and b5. Response spectra are for 1000-year event M=7 at 92km distance. The response spectra include nonlinear soil behavior. (Top): Location of the five sample borings (marked by heavy vertical lines) for which soil response spectra are shown below. 40

nonlinear 'runaway' degradation as one approaches the motion for the M=7 earthquake. Much of the long-period excitation for this event originates from the 'fortuitous' post-critical Moho reflections referred to earlier. The spectral behavior and non-linear response at this site and for this event show how complicated the interactions of the many different factors influencing the ground motions sometimes can be. This example represents the most extreme nonlinear response among all cases computed in this study. It may serve as a worst-case scenario and a warning that nonlinear dynamic soil behavior may be effective for some earthquakes under consideration at some locations where Tappan Zee Bridge foundations are embedded into these dynamically rather soft soils. Response Variation with Different Recurrence Periods: 500. 1000. 2500 Years. To further expand on the response at this site, but also to highlight the effects of different earthquake recurrence periods on the ground motions in the time and response-spectral domains, we compare the soil motion results for three different constant recurrence periods, CRP= 500, 1000, and 2500 years. We focus on the transverse (T) component of the soil motions, again at the site of Foundation Group 3a near the main-span caisson at Pier Bent # 175 whose underlying rock and soil column is represented by Boring B-2. Both time and response-spectral domain results are compiled in Figure 19. In the time domain we show only the results for the M=7 event, which for these three recurrence periods is located at a distance of d=131, 92 and 58 km, respectively (see Table 2). For the response-spectral domain we use instead of individual response spectra the CRP envelope response spectra as defined earlier. They envelope the spectra for all magnitude-distance combinations for a given CRP. Figure 19 reiterates the point made earlier that at the distance of d=92 km this 1000-year event contains much energy at the 1 to 2-sec period range excited by post-critical Moho reflections and amplified by nonlinear soil response. Another feature of the ground motions is that the smaller the event distance (i.e. the larger the recurrence period, CRP), the larger the short-period spectral content, especially for the CRP envelope spectra, whose short-period portions are dominated by the close-in smallest earthquake considered (M=5). On the other hand, the soft sediments attenuate considerably the short-period content compared to the relative spectral shapes on hard rock. This is vividly demonstrated by the comparison of hard-rock and soil-response-modified CRP envelope response spectra shown in Figure 20.

9. Design Spectra for Constant Recurrence Periods CRP= 500, 1000 and 2500 Years.

Design spectra typically are used for linear modal analysis of structures. If the structural analysis 4,, computer programs that are used accomodate multi-support inputs then the use of different response-spectral shapes at the different support points may reflect the local soil conditions at each support point in spectral amplitude content. However, this does not preserve the phase relationships 41

A 0 m7. 58 3a.s 1.2500 4n 60 80 1.2 EnveJope Response Spectro, Group ja Main Span 1.5m below mudline, 3 0ifferent CRP;: 500yr, l000yr, 2500yr 3a.500.env 3,.100l.en, 3a.2500.env F l l i I. .0

0.

.52 02

63.

-~-I 53 I \\/ Ii \\ perod (romto t botom CRi =50,/ 100 an 250yasadascatddsacs(=3,9 O / " " / andO 58 Ian) fo eathuae wit the sam Maniud M=7 Not doinn moin wit I to periods for the distance d=92 km (CRP=1000 years). (Bottomn): Comparison of 3 different CRP envelope response spectra for CRP = 500, 1000 and 2500 years. The envelope spectra represent earthquakes with three magnitudes, M=5, 6 and 7 at their CRP-consistent distances. 42

Hard Rack Envelope Response Spectra, 5percent damped, Transverse, 3 Recurrence periods [yrs]: 500,. 1000. 2500 I I I rock.500.env 1I 0. .roclc.1000.eny rock.2500.env-n n ,, i i I f i i i 11 'b 0.5 1.0 1.5 2.0 Period [sec]

• C Tn
• h A

2.5 4.U Period [sec] Figure 20. Comparison of envelope response spectra for different recurrence periods (CRP=500, 1000, 2500 years) at a rock-outcrop (top) and in soils at foundation group 3a, 5 feet below the mudline (bottom), showing how strongly the soils attenuate short-period and amplify long-period motions. 43

of input motions between different support points. These phase relations can only be accomodated if the linear or nonlinear response analysis is performed in the time domain. For the purpose to perform modal analyses, F.R. Harris and Hardesty & Hanover requested smoothed versions of the actual response spectra; responding to these requests, LDEO delivered design spectra on February 22, 1994 for 1000-year events; and for 500-year events on June 15, 1994. We repeat here the salient points of these communications and add a section regarding results for the 2500-year events that have not been reported before. The bulk of new ground motion data for a CRP of 2500 years is compiled in Appendix C. All earlier data communications regarding CRPs of 1000 and 500 years are contained in Appendix D. The design spectra are based on smoothing, simplifying or combining into similar spectral shape groups the more detailed location-specific 5%-damped response spectra for the transverse horizontal ground motion component, T. We use initially the same "foundation groups" earlier described in Section 6 (see Tables 7 and 8), but in some instances we lump them further together into "foundation categories" as described in these earlier communication and reiterated below, based on type of foundations and proximity to certain types of superstructures. For the submission of the results from the 1000-year recurrence period, the Foundation Categories I through m had been defined as follows, based on the earlier defined Foundation Groups (see Tables 7 and 8, and Figure 2): Category I. Composed of Foundation Groups 2a (Piers 169-173); 2b (176); 3a (175); and 3b (178). This category concerns primarily the main spans with caisson-plus-pile foundations. Piles reach rock. Category_ Il. Composed of Foundation Groups 1 (Piers 166-168), and 4 - 7 (179-190): These are primarily the west and east deck truss sections with cofferdam-plus-pile foundations. Piles reach rock. Category_ II., Composed of Foundation Groups 8 and 9 (near Piers 35+/-5 and 100+/-10, respectively): These are the west trestle sections with wooden friction pile foundations. Piles ending in the soils, rather on rock. When combining response spectra from different borings into a foundation group or category it is important to remember that the spectra not only represent response of different soil columns, but also they represent motions at different depths below the mud-line. Given a constant depth below mean water level, the depth below mudline will vary when the depth of the mudline below mean water level varies, as it does in many instances. 44

The depths below mean sea level (MSL) for which the smoothed design spectra are given, apply to those earlier listed in Table 7 and 8, but are now applied to categories instead of foundation groups: Category I: -42 feet Category II: -24 feet (except for Group #7, Pier 190, where it reflects rock at -30ft) Category III: -30 feet (i.e. at the depth of the modeled point of pile fixity). For the 1000-year-event submission all data from all foundation groups as listed were used in the following manner: the smoothed design spectra for Categories I and 11 are based on estimates of the mean plus one standard deviation of the spectra from the different locations in each Category. The smoothed design spectra for Category III represent the envelop of the two constitutent locations, since one cannot determine a meaningful standard deviation when only two spectra are given. After submission of the 1000-year design spectra on 2/22/94, a meeting between representatives of F.R. Harris, Hardesty & Hanover and LDEO was held at Lamont on 3/8/94, during which it was decided that LDEO would supply in addition to the 1,000-year design spectra smoothed design spectra for seismic events with 500-year recurrence periods. These 500-year spectra were intended primarily for information and comparison. We pointed out at the meeting, and repeat here, that by merely supplying the 500-year spectra, we do not imply that they necessarily should be used for design and evaluation purposes. But their availability allows a more informed decision process considering different cost/benefit options. Similar arguments can be made for the 2,500-year spectra provided below. At the 3/8/94 meeting it was agreed that instead of repeating the very extensive non-linear computations of soil response for all foundation groups within the three foundation Categories 1, 11, and III, we would use only a single foundation group within each category. We apply the same rationale to deriving the 2500-year design spectra. Hence, instead of the original configurations for the 1000-year events based on multiple groups within each Category we use the following foundation groups as proxies to compute the 500 and 2,500-year design spectra: Foundation Category I.: Group 3a (mostly for main-spans on caissons with end pilings to rock) Foundation CategMory II.: Group 4 (mostly for deck trusseskofferdams with end pilings to rock) Foundation Category III.: Group 9 (primarily for trestle sections on timber friction pilings) We present here only the analytic formulations of design spectra (for graphical display see Figure 21), without also providing the period-by-period, numerically smoothed spectral values that were referred to as Option B in the earlier two submissions of the design spectra. In some cases 45

0) CO, Category If Response Q t5 a) C-) 0C 0)a-1.0-0.8-0.6-0.4-0.2-i 2500yr S... ........ p q x....... O. Category III Resp 500r 0.0-0 I 2 Period (sec) 3 4 Figure 21. Smooth design spectra for CRP of 500, 1000 and 2500 years for three Foundation Categories, top to bottom, I through HI, compared with AASHTO/NYSDOT guide spectra of the form C9m=.2AS/Tm2/3<2.5A for a soil-factor S3= 1.5 and seismic zone coefficient A--0.19. 46

the closed analytic form of the spectra could be readily obtained by fitting only two separate curve segments to the data points, while for others three separate segments were needed to fit the data sufficiently well. The segments for each curve are labeled by numbers in () before each formula in such a way that the numbers increase with increasing periods. The analytic forms allow calculation of the smoothed, 5%-damped response spectral ordinates Sa9g] for any period T up to 4 seconds as follows:

1. For a CRP of 1000 Years:

CategoryI: [mean plus one standard deviation for Foundation Groups 2a (Piers 169-173); 2b (176); 3a (175); and 3b (178)]: (1): Sa[g] = 0.8 for periods T<1.77 sec (17a) (2): log Sa1g9 ='-3.2 log T + log 5.0 for T>1.77sec (17b) Category II: [mean plus one standard deviation for Foundation Groups 1 (Piers 166-168), and 4 - 7 (179-190)]: (1): Sj[g] = 0.9 for periods T<0.25 sec (18a) (2): log Sa9g] = -0.4167 log T + log 0.505 for 0.25sec<Tcl1.75sec (18b) (3): log Sjg] = -2.745 log T + log 1.858 for periods T>1.75sec (18c) Category III: [mean between Foundation Groups 8 and 9 (near Piers 35+/-5 and 100+/-10, respectively) ]: (1): Sjg] = 0.6 for periods T<1.95 sec (19a) (2): log Sa[g] = -3.459 log T + log 6.043 for periods T>1.95sec (19b)

2. For a CRP of 500 Years:

Category 1: [with Foundation Group 3a, near main span Pier Bent 175, as proxy]; (1): Sa[g] = 0.70 for periods T<1.00 sec (20a) (2): log Sj[g] = -3.807 log T - 0.155 for 1.00<T<2.00 sec (20b) (3) S,[g] = 0.05 for T>2.00 sec (20c) Category HI: [with Foundation Group 4, near Pier Bent 179, as proxy] (1): Sa[g] = 0.70 for periods T51.00 sec (21a) (2): log Sa[g] = -3.807 log T - 0.155 for 1.00<T<2.00 sec (21b) (3) Sj[g] = 0.05 for T>2.00 sec (21c) Category. III: [with Foundation Group 9, near Pier Bent 100, as proxy] (1): Sjg] = 0.40 for periods T51.00 sec (22a) (2): log Sa[g] = -3.00 log T - 0.398 for 1.00<T<2.00 sec (22b) (3) S,[g] = 0.05 for T>2.00 sec (22c) 47

3. For a CRP of 2500 Years (for details of this new submission see Appendix C):

Category: [with Foundation Group 3a, near main span Pier Bent 175, as proxy]; (1): SaIg] = 0.90 for periods T51.00 sec (23a) (2): log Sajg] = -0.8480 log T + log 0.9000 for 1.00<T<2.00 sec (23b) (3) log Sa[g] = -3.0589 log T + log 4.1677 for T>2.00 sec (23c) Category II: [with Foundation Group 4, near Pier Bent 179, as proxy] (1): Sa[g] = 1.40 for periods T<0.75 sec (24a) (2): log Sa[g] = -1.654 log T + log 0.8706 for 0.75<T<2.00 see (24b) (3) log Sa[g] = -2.745 log T + log 1.8580 for T>2.00 sec (24c) Caltg._*y...: [with Foundation Group 9, near Pier Bent 100, as proxy] (1): Sa[g] = 0.80 for periods T50.80 sec (25a) (2): log Sa[g] = -0.9338 log T + log 0.6495 for 0.80<T<2.00 sec (25b) (3) log Sa[g] = -2.7655 log T + log 2.3119 for T>2.00 sec (25c) It is apparent from Figure 21 by comparing the 500-, 1000- and 2500-yr design spectra that the spectral amplitudes can differ between different CRPs by a factor as high as 10 at some period ranges. Much of this variation can be attributed to the fact that the long-period excitation, even on hard-rock, increases with recurrence period mostly due to the greater proximity of the larger earthquakes (especially M=7). This causes rather strong nonlinear soil stiffness degradation for some of the 1000- and 2500-yr motions, but generally does not for the 500-yr motions. In fact, the lack of nonlinearity for the 500-year motions causes at periods near 1 second for Category II to exceed the 1000-year motions whose more nonlinear spectral shape had to be fitted by a triple-segmented curve compared to the 500 and 2500-year spectra, which are better fit by a double-segmented curve. The fact that this feature occurs only for the Category II and not Category I and III spectra has to do with the particular soils that happen to be present in the soil profiles. Comparison to AASHTO Code Spectra. In Figure 21 we also show AASHTO/NYSDOT code design spectra for comparison with our site-specific smooth design spectra for CRPs of 500, 1000 and 2500 years. The AASHTO/NYSDOT code design spectrum is based on the following formula: Csm = 1.2 A S / T. 213 < 2.5 A (26) In accordance with AASHTO (1992) prescribed definitions we assign a soil-factor S3=1.5 for the deep soft soils, and we use the seismic zone coefficient A=0. 19 as prescribed by NYSDOT Engineering Instructions (1990, 1992) for most NY State sites. Tm (in seconds) represents the natural period of the structure used in the modal analysis. Figure 21 shows that, with the exception of Category III and CRP=500 years, the proposed design spectra exceed the AASHTO/NYSDOT guide spectrum by a factor of up to about 2 at short 48

periods (Tm<l s), but often fall below the AASHTO/NYSDOT guide spectrum for long periods (Tm>3s). Details depend on the recurrence period and Foundation Category considered. As discussed elsewhere, two factors are responsible for the differences between the site-specific design spectra and AASHTO spectra (Note: AASHTO spectra represent a CRP of 475 years): (i) the AASHTO code prescribes a too gradual fall-off proportional to l/Tm2 /3 of spectral design accelerations for periods TmŽ.l sec, compared to a more rapid fall-off of actual ground motions, often in excess of 1/Tm2 for periods longer than the fundamental soil resonance period. The reason is that the AASHTO spectral shapes are based largely on western US seismic conditions and data. (ii) the AASHTO soil factor of S3=1.5 is too low to correctly describe the soil amplification on soft soils present at the site of the TZB. It is noteworthy that the recently adopted (2/21/95) New York City Building Code seismic provisions allow for soft-soil to hard-rock site amplification of S4/So=2.5/0.67=3.75 (Jacob, 1993) to modifiy the western-US-derived spectral shapes for eastern-US hard-rock conditions. Regrettably, current (1992) AASHTO specifications do not allow for such an option. These comments may suffice to indicate how poorly the AASHTO spectrum conforms to eastern US ground motion spectra on hard rock. This statement applies whether the recurrence period chosen is 500, 1000 or 2500 years (see Figure 21 of this report).

10. Spatial Variation of Ground Motions and Relative Displacements.

When a seismic wavefield passes the foundation of a bridge it can produce relative displacements in the multiple-point-supported, jointed structure of the bridge. For instance, large relative motions in a bridge across unrestrained bearing joints with mechanically limited displacement capacities or seat widths, may lead to collapse because the large displacements may unseat some spans (example: the Bay-Bridge between San Francisco and Oakland during the Loma Prieta earthquake on October 17, 1989). When the seismic wave field passes, the different support points of the structure generally experience different motions at different times during the event. The relative displacements between foundation points are the kinematic free-field relative displacements. They need to be distinguished from the dynamic relative displacements within the structure due to its response to input motions. 49

How to combine the kinematic free-field and dynamic structural, relative displacements depends on the structural analysis method, i.e. whether modal analysis is used, or whether time series analysis is used either with or without consideration of the spatial variation of ground motions. Since this report only addresses input motions and not structural response, we discuss here only the kinematic spatial variations of the free-field ground motions. A number of factors contribute to spatial variation of ground motion, including: wave-passage effect; ray-path incoherency; extended source effects; and attenuation. These factors are illustrated in Figure 22 taken from Abrahamson (1993).

• wave passage effects are induced by the lagging of similar ground motions as the coherent portions of the wave field propagate across the footprint of the structure. This effect can be deterministically estimated. The time-dependent difference of two (lagged) displacement records (i.e. twice integrated accelerograms) yields a relative displacement record. Its maximum relative displacement amplitude depends on the frequency content of the wave field and the time lags; these in turn depend on spacing between the two points along the structure under consideration and the apparent wave velocity and angle of approach of the wave field with respect to the structure. We will show below deterministic estimates of this wave passage effect on soft soils between the foundations of individual spans along the TZB.
• incoherency effects represent the relative displacements due to wave passage of the incoherent, randomly scattered portions of the wave field. This effect can.only be statistically quantified.

Relative displacements due to incoherency tend to increase with frequency and spacing. At small spacing distances (550m) incoherency may dominate over the coherent wave passage effect. But for larger distances the coherent wave passage effect tends to dominate. A conservative (safe) engineering rule for support spacings typical for the Tappan Zee Bridge, is to assume that the combined wave passage and incoherency effects yield combined displacements that measure about twice the displacements due to the coherent wave passage effect alone.

• extended seismic source and geometrical spreading attenuation effects can usually be ignored for eastern US conditions since on average the epicentral distances tend to be large compared to most seismic source dimensions or lateral extent of most structures.

These combined kinematic free-field displacements typically measure amplitudes in the eastern US seismic environment that rarely reach or exceed a foot. They generally tend to be smaller than the relative displacements dynamically induced in the structure, if we define here the latter as the structure's dynamic response to the input accelerations without considering their spatial variations. However, for long-span bridges with joints that have limited capacity to accomodate displacements, 50

Figure 22. Factors contributing to spatial variation of seismic ground motion for similar site conditions: attenuation due to different closest-distance to the fault; wave passage effect due to oblique upward seismic wave propagation; extended source effect due to mixing of waves from different points on the fault (waves arriving at site I from fault segment A interfere with waves arriving from fault segment B); ray path incoherency due to scattering or complex wave propagation (from Abrahamson, 1993) 51

it is evident that careful attention has to be paid to the relative displacements induced by the spatial variation of ground motions. Before we estimate the wave-propagation effects on soft soils near the TZB, let us first discuss the simpler case of an assumed flat bedrock surface. For this case we use the 2,500-year recurrence period M=7 earthquake at a distance-of 58 km. Hard Rock Relative Displacements. Peak ground displacements at a bedrock site near the TZB as large as 10 cm (--4 inches) are computed from twice integrated hard-rock acceleration records for the magnitude M=7 event at d=58km consistent with a 2,500-year recurrence period (Figure 23). In considering spatial variation of ground motion without local soil effects, the largest relative displacement in principle obtainable from the wave-passage effect alone for this event is if the displacement-dominated portions of the records at two stations were 180 degrees out of phase. Therefore, for the event considered here, the relative ground displacements between piers could not exceed about twice the zero-to-peak amplitude, i.e. 20 cm (-8 inches). However, as we will see later, the actual factors contributing to spatial variation are unlikely to produce displacement records 180 degrees out of phase. Therefore, relative displacements on rock for distances compatible with actual span lengths are likely to be smaller than 20 cm (-8 inches). On soil they tend to be larger. Attenuation from geometrical spreading of body waves (P or S) occurs with l/r as the waves travel through the Earth. Thus, the relative amplitude change is -dr/r which implies for every dr=lkm of travel an amplitude reduction by 10-1 at r=10km and 10-2 at r=100km, which is the approximate distance range for events considered here. The largest span length of the TZB is less than 1 km. Therefore geometric attenuation produces an amplitude reduction of at most a few percent between support points of the main spans, too small to be considered for spatial variation of the ground motions. The phase coherence is a measure of the difference between two seismograms s(xi,t) and s(x 2,t) recorded at position x, and x2. It can be defined as C(f,Af,Ax) = I (s*(x 1 'f) s(x 2,f)) 12 (S*(X 1,f)S(X l,f)X S*(X2,f)S(X 2,f)) (27) where s(xl,f) is the Fourier transform of s(xl,t) over frequency f; <> denotes boxcar averaging over a frequency interval df or averaging at frequency f over multiple windows; and

• denotes complex conjugation.

The lack of phase coherence between two seismograms due to the same earthquake recorded at 52

2,500-YEAR EARTHQUAKE C E (-) C Time [seconds) Figure 23: Displacement time histories, on -hard rock, transverse component, for events with a common recurrence period CRP=2,500 years. Displacements are derived from acceleration time histories by double integration and high-pass filtering at 0.05 Hz. 53

different locations can be attributed to a wave passage effect, a path incoherence, and an extended source effect. The wave passage effect can be partly eliminated by systematically shifting the two time series to find the lag time which produces the maximum phase coherence. A "best" lag can be found for each frequency, but generally the "best" lag for the whole seismogram is found. When the seismograms are lagged to appropriately account for wave propagation, the phase coherence measures the combined path coherence and source effect called the incoherency below. Figure 24 from a recent study by Abrahamson (1993) shows the effect of incoherency (solid circles) on predicted relative ground motion compared to the wave passage effect (solid line) and the combined effect (triangle). The relative displacement is observed to increase with separation distance, and although both factors contribute, the combined effect is dominated by the wave passage effect particularly for distances greater than 100 m. Further, the peak ground displacements in that study were around 30 cm, and the relative displacements at 1000 m were around 20 cm. From this we conclude that the wave passage effect will be the dominant factor contributing to relative displacements for the TZB. In Figure 24, the relative displacement due to incoherency at 1000 m is around 3 cm or 10% of the peak ground displacement. The wave passage effect can be eliminated or introduced between two time series by applying an appropriate time lag. Given a displacement time history for hard-rock near the TZB, the approximate relative ground displacement between two rock sites is obtained by simply lagging this time series and subtracting. Record sections showing variation of displacement time histories (due to wave propagation effect) over distance separations comparable to scale lengths of the TZB, i.e. 50 - 1000 meters are shown in Figure 25. The two record sections are produced by two different methods. The top record section is produced by calculating the complete synthetic seismogram at each epicentral distance. The bottom record section is produced with a simpler method: by time lagging the initial synthetic seismogram (at 24km) using travel times appropriate for the S-wave propagation. The two methods yield virtually identical results; thus using the simpler time-lag method to account for wave propagation is reasonable for flat rock sites. The peak displacement is about 5 cm for the magnitude 6 earthquake (transverse component) illustrated in Figure 25. Figure 26 shows relative displacement on hard rock for the same earthquake over distance separations 0 to 1000 m due to the wave propagation effect alone. In this example the earthquake azimuth is along the bridge axis. This azimuth gives the largest time lag. The relative displacement increases with separation distance producing a maximum relative displacement of 3.2 cm for a separation of 1000m. The reference (epicentral) distance is 24 km for this example. The wave propagation effect can be accounted for using the simple time lag method. Figure 27 illustrates the derivation of the formula to calculate the time lag, 2", given separation distance x 54

100 10 10 A" C: 10 000 o, ,.~00 ,°,,

• AA 0

E 0 0 00 0,, Wae-asag .0 10 101 Sepaatio Dit ncoee(n) y

0. 1'ou Figure 24: Maximum relative displacements as a function of separation distance (from Abrahamson, 1993). The effects from wave passage and incoherency are shown separately and combined. The dashed lines correspond to constant strains of 103 and 1O-4.

55

a) 20-24.0 24.2 24.4 24.6. 24.B 25.0 5.2 cm Distance (kin) Ti--- b) 20-I!- 24.0 24.2 24.4 24.6 24.8 25.0 Distance (kin) Figure 25: (a). Synthetic displacement records for a M=6 earthquake computed at six epicentral distances from 24 to 25 km. (b). Displacement records obtained at the same six distances by lagging the reference record (at 24 kIn) by lags "C = x / Vapp, where x is the separation distance from the reference location and Vap is the apparent velocity (see Figure 27). 56

3-10 t3,.2 cm I I I I I,, 24.0... 24.2 - 24.4 24.6 24.8 25.0 Distonce (km) Figure 26: Differential displacement records at various distances (from 0 to 1,000m) relative to the reference record (at 24 kin) obtained by the time-lag method. 57

ELEVATION VIEW Ray Path PLAN VIEW Figure 27. Diagram showing geometry for calculating the wave-passage time lag . Elevation view shows the emerging wave front with inclination i defined as the angle between the ray path (direction normal to the wavefront) and vertical so that Vapp= Vs / sin i. The plan view shows the azimuth 0 defined as the angle between the bridge axis and thle earthquake epicenter so that -" = x cos 9 / Vapp,. 58

from some reference point. The orientation (with respect to the bridge) of an incoming wave front is characterized by the vertical angle of incidence, i (elevation view) and the azimuth of approach, 0, (plan view). If we consider an S-wave, the apparent velocity, Vapp, is equal to or larger than the S-wave velocity, VS, in the upper layer, which is 3.5 km/s in our velocity model. The angle of incidence as well as the apparent velocity for each of the three 2,500-year earthquake magnitude-distance pairs is given in Table 9 (i is distance dependent). Table 9. Incidence angles and apparent velocities for calculating lag times for 2,500-yr events. Magnitude Epicentral Distance (Iam) incidence angle i(degrees) Vapp (km/s) 5 10 55 4.3 6 24 67 3.8 7 58 70 3.72 Given any separation distance x (e.g. the distance between the piers of the main spans) and azimuth of approach, the time lag can be calculated from the relationship: =x cos &fVapp (28) where Vap = VS / sin i (29) These time lags should be applied to both the acceleration and displacement time histories when used as input at the different support points of the bridge. As pointed out earlier, two types of relative displacements must be considered in earthquake engineering analysis of extended bridge structures: (1) the dynamically induced relative displacements within the structure due to the differential dynamic response of the various portions of the bridge, given the input accelerations; and (2) kinematic displacements which originate as free-field relative displacements at the different support points from the spatial variations of the entire displacement wave field that passes beneath the bridge. These spatial variations include the (coherent) wave-passage effect and non-coherent contributions from ray path incoherency (scattering) and extended source effects. The kinematic relative displacements from the wave-passage effect at any pair of-bridge support points can be obtained by lagging [according to Equations (28) and (29)] the transient ground displacement time series (i.e. the twice-integrated ground accelerations), and computing the running difference values of the lagged time series at the two respective foundation points. Each so-obtained differential displacement time series d(t) has a maximum value, dmax. This dmax reflects, however, only the coherent wave passage effect and neglects the incoherent contributions from ray path incoherency (scattering) and extended-source 59

effects. As was shown in the example of Figure 24, the incoherent contributions tend to amplify the maximum relative displacements Dm. for the combined motions over those of the wave passage effects, dmax, alone. The absolute values of the maximum relative displacements caused by incoherence also increase with separation distance between support points, but they generally do not increase as rapidly as those caused by the wave passage effect (at least for distances up to a few kIn). One can define a multiplier, k, when applied to the wave passage effect dma, that yields the combined (coherent plus incoherent) maximum relative dispacement Dmax=kdma. For the examples shown in Figure 24, this factor k (the ratio of amplitudes marked by solid triangles to solid line) is smaller than a factor of 2 for all except the shortest separation distances, x_<50m. Longitudinal separation distances for support points along the TZB main-and deck-truss spans are all larger than 50 m. We recommend for estimating engineering values of total (combined coherent and incoherent) maximum relative displacement Dmax between support points to use a factor of not less than k= '/2 but not more than k=2 for multiplying the relative displacements dmax that are obtained considering the wave passage effect alone. [Note: a review panel of a similar study for the Queensboro Bridge in New York City insisted on a factor of k=2]. The so-obtained kinematic maximum relative displacements Dm.x should be applied in a positive and negative direction when checking their effects on the bridge and its structure elements (for instance seat width of bearings, joints, abutments etc.). Kinematic Free-Field Relative Displacements on Soils for Main and Deck-Truss Spans Along the Tappan Zee Bridge. The soil-response corrected acceleration records provided by LDEO to F.R. Harris have full fidelity of timing and phase, save two factors: (i) the wave propagation lagtimes in the gneiss, "Tg, from traveltime differentials due to seismic waves having to travel different distances obliquely upward through the gneiss of the metamorphic basement rock. These lags originate because the gneiss interface with the overlying Triassic sandstone or soils varies in depth along the axis of the TZB. These depth variations of the top of the gneiss are illustrated in Figures 2 and 10, and are listed in Table 7 under the column labeled "Gneiss". If the differential depth of the top of the gneiss between two adjacent foundation groups is defined as Ah, then the differential gneiss travel time between these two foundation points is 'g= + (Ah / cos i) / v, gneiss (30) where i is the angle of emergence of the seismic wave front in the gneiss with respect to the vertical, and vs gneiss is the shear wave velocity in the gneiss (assumed to be 3.5 km/s). A positive delay in equation (30) applies to the record of the more easterly located foundation point relative to 60

the record of a more westerly location, because the depth to the top of gneiss decreases from west to east, and hence easterly locations require an extra vertical distance for the waves to travel through the gneiss. Since i is dependent on the epicentral distance d to the source at an assumed constant hypocentral depth of 7.0 km, and since d varies for a given constant recurrence period CRP with magnitude M, the gneiss delays, 'r.5, vary with magnitude and recurrence period. Table 10 provides a listing of the pertinent parameters and results for computing the delays, "rg, for all M-d combinations for a 1,000-year event. We use a CRP of 1,000 years as an illustrative example to compute the delays, "T-g, because this CRP had produced the largest nonlinear soil response for its M=7 earthquake at d=92 km, thus resulting in the largest displacement records obtained during this TZB study. Table 10. Computation of dhfferential gneiss lagtimes, "rg, according to equation (30), due to shearwaves traveling differential depths Ah through the gneiss for ray geometries appropriate for a CRP=1,000 years. The angle i of emergence for the M=5 is 630, and that for the M=6 and 7 is 690. Foundation Span Ah Ah 7- =(Ah/cos i)/ vs neiss Group Delimited [ft] [km] for MI=5 M=6 atnd 7 Pair by Pier # [sec] [sec] 1 -->2a 168 --> 169 135 0.041 0.026 0.033 2a --> 3a 173 --> 175 109 0.033 0.021 0.026 3a --> 3b 175 --> 176 265 0.081 0.051 0.064 3b -->2b 176--> 178 61 0.019 0.012 0.015 2b--> 4 178--> 179 51 0.015 0.010 0.012 6 -->7 189--> 190 36 0.011 0.007 0.009 (ii) the horizontal wave propagation effect produces lagtimes, T, due to the approach direction in azimuth. We have quantified these lagtimes by equations (28) and (29) for hard-rock conditions. According to Snell's law, the apparent velocity along a raypath does not change during propagation through a layered stack of soils. Therefore equations (28) and (29) apply unchanged to both soils and rocks. The gneiss lags quantified in equation (30) and Table 10 apply uniformly regardless from which direction the seismic waves approach. The horizontal wave propagation lags as quantified in equations (28) and (29) are azimuthally dependent. The largest combined lag between accelerograms at a more easterly station vs. an adjacent westerly station occurs when the waves propagate along the axis of the bridge from west to east; and the smallest when they propagate from east to west along the bridge axis. We call these bracketing delays the bridge-parallel lag, T j, Tgii = + =[(Ah / cos i) / vs gneiss ] +/- [x sin i / vs gneiss] (31) 61

where the + in eqn. (31) applies for wave propagation along the bridge axis from west to east, and the - for east to west; x is the separation between foundation points. With these quantities we can compute the delays for the 1,000-year earthquakes for M=5 (i=630), and for M=6 and 7 (i=690) as indicated in Tables 11 and 12, respectively: Table 11. Computation of bridge-parallel lagtimes, " t, according to equation (31), due to shearwaves traveling W-->E and E--> W, respectively for ray geometries appropriate for a M=5 earthquake with CRP=1,000 years. The angle i of emergence for the M=5 is 630. Foundation Span Group Delimited x x g +/-x sin i / 3.5km/s "I11 W->E i11E->W Pair by Pier # [ft] [km] [sec] [sec] [sec] [sec] 1 -- > 2a 168 --> 169 250 0.076 0.026 0.019 +0.045 +0.007 2a -- > 3a 173 -- > 175 602 0.183 0.021 0.047 +0.068 -0.026 3a-->3b 175--> 176 1,212 0.369 0.051 0.094 +0.145 -0.043 3b--> 2b 176--> 178 602 0.183 0.012 0.047 +0.059 -0.035 2b--> 4 178--> 179 245 0.075 0.010 0.019 +0.029 -0.009 6 -- > 7 189--> 190 235 0.072 0.007 0.018 +0.025 -0.011 Table 12. Computation of bridge-parallel lagtimes, C I, according to equation (31), due to shearwaves traveling W-->E and E--> W, respectively for ray geometries appropriate for M-6 and 7 earthquakes with CRP=1,000 years. The angle i of emergence for the M=6 and 7 is 690. Foundation Span Group Delimited x x +/-g +/-x sin i /3.5km/s i 1l W->E C11 E->W Pair by Pier # [ft] [km] [sec] [see] [see] [sec] 1 -- >2a 168--> 169 250 0.076 0.033 0.020 +0.053 +0.013 2a -- > 3a 173 -- > 175 602 0.183 0.026 0.049 +0.075 -0.023 3a--> 3b 175 --> 176 1,212 0.369 0.064 0.098 +0.162 -0.034 3b --> 2b 176 -- > 178 602 0.183 0.015 0.049 +0.064 -0.034 2b--> 4 178--> 179 245 0.075 0.012 0.020 +0.032 -0.008 6 --> 7 189--> 190 235 0.072 0.009 0.019 +0.028 -0.010 In Figure 28 a through f, we show plots of the span-specific maximum differential displacements of the tangential component of ground motion. These relative displacements originate between records of the site-specific ground displacements from adjacent foundation groups, as a function of generalized lag times between the records that include pier-specific nonlinear site-response for the M=5 and M=6 and 7 events and distances appropriate for the a 1,000-year recurrence period. We superimpose onto these plots two sets of vertical lines, one for the M=5, and another for the M=6 and 7 earthquakes. These lines represent the appropriate delays for N-S wave propagation, i.e. normal to the bridge axis producing only the gneiss delay, Z"' ; and for the W->E and E->W propagation directions, respectively, producing the delays 1i1 w->E and V 11 E->w taken from Tables 11 and 12 for the appropriate magnitudes M=5, and M=6 and 7, respectively. These graphs indicate the ranges of permissable delays and differential displacements associated 62

Max Rel Disp vs Time Log btw TZB piers 168 and 169, Trans, M=5, 6, 7 W E2 .15 E -o tu. I m7 6-m6 (a) I I I iI .9, -Ii i R I I I I I I I 11........... -0.20 -0.15. -0.10 Max Rel 1') V m7 6m6 2 .5 -0.05 0.00 Time Log [sec] 0.05 0.1 0.15 0.20 Time Log [sec] Figure 28. Absolute value of maximum relative displacement (cm) of transverse component vs. time lag (sec) between displacement records at adjacent piers: (a) piers 168 - 169 (west deck truss span); (b) piers 173 - 175 (west side span). 63

~m7 i 6-I- m6 E I .E 21-' m5 (C)I" -. 20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 Time Log [sec] Mox.Rel Disp vs Time Log btw TZB piers 176 ond 178, Tronsverse, M= 5, 6, 7 10- "*8 m7 '7 S4-E4 ~m6 I I m5 S-I I -)" II I (d) , I , ~ I I I I .20 -0,15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 Time Log [sec] Figure 28 continued: (c) piers 175 - 176 (central main span); (d) piers 176 - 178 (east side span); 64

7F m7 m6 I E EI (e) -* 20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 Time Log [sec] Max Rel Disp vs Time Log btw TZB piers 189 ond 190, Tronsverse, M= 5, 6, 7 5 I I I I 4t "CI 0 gI Iil S2-0I .E m6 m5- - -.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 Time Log [sec] Figure 28 continued: (e) piers 178 - 179 (east deck truss); (f) piers 189 - 190 (east deck truss). 65

with the kinematic wave-passage effect only at and between the respective piers indicated. The permissable values are highlighted by solid circles which mark the intersections of the proper magnitude-dependent delays (vertical lines) with the proper magnitude-dependent, differential displacement curve. As can be seen from Figure 28, for much larger delays (corresponding to larger hypothetical span lengths that effectively do not exist for the TZB), the differential free-field displacements can exceed 10 cm or more. The largest relative displacements occur for the main span between piers 175 and 176, where they reach for W->E wave propagation =8.5 cm for the M=7 earthquake, -7 cm for the M=6, and -2.5 cm for M=5 earthquake. It is also noteworthy that the curves for differential displacement are generally not symmetric, i.e. positive and negative delays of equal amplitude do not necessarily produce equal differential displacements. This implies that the relative displacements can be strongly dependent on the direction of wave approach, which is unpredictable in this seismic environment. Figure 28 shows the absolute value of the maximum differential displacement only for the tangential ground motion component (T). Since the displacements for the tangential component of motion tend to be larger in amplitude than for the longitudinal (L) or vertical (Z) components, it follows that the maximum differential displacements for these other components should not exceed those plotted for the T component. The free-field displacements depicted in Figure 28 represent only the kinematic displacements from the soil-response-corrected coherent wave passage, effect. To account for any potential incoherency effects discussed earlier, we may take the same approach taken for the rock motions of multiplying the wave passage displacements with a factor V2*_<k<2. Doubling would yield quite conservative estimates of the maximum relative displacements to represent the combined contributions from coherent wave passage and wave incoherency due to scattering and other contributions. This would bring the largest relative free-field displacements to be considered for the TZB main span to about 18 cm (" 1/2 ft). Shorter span lengths are expected to experience lesser differential displacements of the free-field motions between adjacent foundation points. Note that the given diplacements represent absolute values. As pointed out earlier for the hard-rock motions, we suggest that the so obtained kinematic maximum relative displacements Dmax should be applied in a positive and negative direction (shortening or lengthening along or across spans) when checking their effects on the bridge and its structure elements (for instance seat width of bearings, joints, windlocks, dampers, restrainers, abutments etc.).

11. Comments on Soil Strains and Liquefaction Potential.

A limited project task was specified for this study to comment on liquefaction potential. Such a task is distinct from carrying out a full assessment of liquefaction hazards at the TZB site that 66

typically would be performed by a geotechnical expert that the LDEO team, consisting of seismological experts, is not qualified to provide. However, since in the course of computing the soil ground motions LDEO developed data and information that have bearing on liquefaction potential, we briefly discuss here these findings. There are several issues involved in the soil and foundation response to earthquakes that typically would be considered by a geotechnical/foundation expert: (1) reduction or loss of bearing strength from cyclic (seismic) loading in the soft cohesive soils (organic/silty to sandy clays); (2) pore pressure build-up in unconsolidated, noncohesive granular soils (sands, silts) potentially leading to liquefaction, lateral spreads and/or settlement; (3) slope instability; (4) potential response to the above listed processes by (a) the friction pile groups of the western approach trestle spans, (b) the coffer dams and end piles to rock of the deck truss sections, and (c) the caissons and end piles to rock of the main spans and vicinity. The assessment of the response of these different foundation systems involves consideration of soil-structure-interaction that we are not qualified to comment on. We only describe here information related to the free-field soil features, as if the foundations were not present. Transient Seismic Soil Strains. When computationally migrating the ground motions through the nonlinearly responding soils by an equivalent elastic iterative procedure accounting for stepwise degradation of the soil properties (shear modulus and damping), we had to determine the RMS strains in the individual soil layers. One can compare these RMS soil strains with the strains from triaxial shear tests at which failure of the tested soil samples had occurred in the laboratory (Greiner Inc., 1992). Figure 29 compares our computed RMS shear strains for the soil motions during the M=5, 6, and 7 earthquakes with a constant recurrence period CRP=1,000 years at those locations (Borings B-1, B-2, and B-3) from which samples were tested in triaxial cyclic shear tests (Greiner Inc., 1992). The free-field soil strains vary about a factor of 10 or less between the motions induced by the smallest (M=5) and largest (M=7) magnitude considered, almost independent of depth below mudline. Except for the first few feet below the mudline where strains reach about 1%, the large majority of the seismically induced RMS strains in the soils range from a few tenths to about a hundredth of a % strain, which is far below the strains of about a few % at which soils had failed in the lab tests. Thus, for most of the pile penetration depth, with the possible exception of the first few feet below the mudline, the transient seismic RMS strains are 1 to 2 orders of magnitude (factors 10 to 100) below the failure strains measured in the laboratory tests. While the computed seismic RMS free-field strains and lab-test peak strains are somewhat different measures of strain, the large safety factors on the order of 10 or more appear to indicate that loss of shear strength in the free field should not be a major problem. The question how the free-field strains might be modified in the vicinity of a pile group, or near the surface of an individual pile, is not the subject of this report but may need some consideration by a foundation expert before one can conclude from the 67

I 1.0-0 U U U U -u U U UN a a a. U U U a C 0I) 0-J 0.0 -4 A A -1.0-0 0 0 8 O 0 M=7 M=6 M=5 A 00 -2.0- -3.0 0 00 0 A 0 i 50 I 100 150 2 200 250 Depth (ft) below soil/water interface Figure 29: RMS transient seismic strains in soils as a function of depth below mud line for CRP=1000y, M=5, 6, and 7 earthquakes, compared with strains at which soil samples, according to Greiner Inc. (1992), failed in laboratory triaxial shear tests (solid squares). For details see text.

above arguments that the lab-tested soils will not fail near the foundations during events of the magnitudes and distances considered here. Simple Screening Tests for Liquefaction Potential. Although cyclic stress ratios can be computed by a geotechnical expert from the information provided in this seismic report that would allow to quantify the liquefaction potential, as seismologists we must limit ourselves here to simple qualitative screening tests. We apply screening tests for liquefaction potential like those given in the New York City seismic building code or found in the literature. We use the simple uncorrected standard penetration test (SPT) blow counts, N, in sandy to silty materials as a function of depth for those borings for which the blow count is given [by Greiner Inc. (1992) for the 1992 borings; and by Anonymous (undated) for the 1952 borings]. Figure 30 shows the N-values taken from these reports for the different borings along the TZB, plotted vs. depth, in comparison with a number of discriminants (lines labeled by encircled numbers 1 through 4). Discriminant 1 and 2 are taken from the New York City building code, or the equivalent formulation in the draft of the NY State seismic code, for seismic zone C (Jacob, 1993). The NY City building-code screening-procedure states that when the blow count in specified non-cohesive materials is lower than N = 5 + 0.2D(ft) [curve 1], where D is depth (ft) of the soil with standard penetration test (SPT) blow count N, then liquefaction is deemed likely. If the SPT blow count is lower than N = 15 + 0.2D(ft) [curve 2] then liquefaction is deemed possible; if it is above that latter threshold, then liquefaction is deemed unlikely. It should be kept in mind, however, that this procedure is generally intended for ordinary buildings and not necessarily for critical structures. Therefore even if the soils at the TZB site pass this screening test, and especially if they pass it marginally, one must not take this as sure indication that liquefaction would not occur under the site-specific ground motions used for TZB retrofit design. Discriminants marked by lines 3 and 4 are taken from Faccioli and Resendiz (1976, p.131) based on Japanese data applicable to a seismically more active environment. Discriminant 3 invokes a critical SPT blow count Nr = 2 D(m) - (2/3) D(ft), below which liquefaction is considered possible. Discriminant 4 shows the empirical Nr for observations of a particular earthquake, the Niigata earthquake in Japan. Both discriminants, 3 and 4, are based on magnitude M-7 or larger earthquakes at very short nearfield distances, and hence are not directly applicable for the lower seismic hazard levels considered here for the TZB site. But they show that many N vs. depth values obtained for the TZB borings at depth below 70 feet would be considered potentially liquefiable in .these more severe seismic hazard conditions. If we follow the guidance given by the NY City guidelines (discriminant 1 and 2), then one can infer from Figure 30 that indeed some liquefaction 69

0 0 50 20

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2. 1 x
3. 2A
4. 7 V
5. 4 +

1952 - r'l-\\#80 o10o

1. 9 x /

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.0 12 90 25O 50 B-30 10 150 + J 0 360 + I 200 i Ix. 25010 0 50 100 150 N, SPT Blow Count Per Feet Figure 30: Standard penetration test (SPT) blow count, N, vs. depth for borings indicated, compared to screening test discriminants (lines labeled 1-4). Where the borings measure lower N-values than the discriminants indicate at any given depth then a nominal potential for liquefaction exists. See text. 70

B -1 B -2 B -3 5 B R N 12 -1..? 11 13 2? 7 3 4 20 8 9 0 BORINGR "39 ORGANIC 16': xg SILTY SAN* ..o.. V VE ~~~y... - 150 ............ ? '585 xCLY V7:::::ii::* IT

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~ .16************::::::::::::::**************::::::... 270 SANDS*' 30

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GRAVEL G E S 27 -300% -4 5 0 SAND* o...... °.................... -35 STONE%% " " 50 o*°o%% OOo °o. II -450 Figure 31: Geologic section along the TZB-. 'Me depth intervals which according to screening tests of boring data are nominally prone to soil liquefaction, are indicated by solid black shading.

potential may exist, especially for soils encountered in the 1952-boring #4 at depths between 100 and 200 feet; for the 1952-boring #5 mostly at depth between 80 and 100 feet; and for portions of the 1992-boring B-1 at depths between 100 and 150 feet. These and all other depth intervals considered potentially prone to liquefaction according to this simple screening test are highlighted (by solid black patterns) in Figure 31. While pore pressure buildup may be possible in these soils characterized by low SPT blow counts, this does not necessarily imply large displacements which depend on whether the fluids can be mobilized at such relatively large depths. The grain size distributions reported for some depth intervals and soils sampled by the 1992-borings (Greiner Inc., 1992) characterizes in some, but not all, instances the soils as liquefiable over limited depth ranges. Given these findings one may ask how large may the displacements be that could be associated with any liquefaction, if liquefaction should occur. A rough estimate of the expected average displacements associated with liquefaction can be found in the recent literature. The estimates are derived from empirical data compiled by Youd et al. (1989) for case studies of liquefaction caused by past earthquakes in the central and eastern US and adjacent Canada. The quantity used is called liquefaction severity index (LSI). The LSI predicts a lateral average displacement (in inches) as a function of moment magnitude M and epicentral distance d (1am), provided liquefiable materials are present: log LSI (inches) = -1.90 + 0.73M - 1.41d (kim) < log 100 (32) Given the M-d combinations for magnitude 5-, 6-, and 7 earthquakes for recurrence periods of 500 to 5,000 years for the New York area (Table 2), one obtains from the above relation nominal average LSI displacements between about 1 and 8 inches. The above screening relations are used only to judge qualitatively whether a liquefaction potential may exist at the TZB site. Some of the soils nominally fail these qualitative screening tests at certain depth ranges, and therefore should be considered marginally liquefiable until proved otherwise. The above qualitative screening procedure is not a substitute for a quantitative liquefaction assessment, which this study does not represent. Potential Slope Instabilities. From the contour map of the mudline and the geologic section (Figures 9, 10 and 31) and the compiled soil section provided by Hardesty and Hanover (1993), it is apparent that the maximum slope of the mud/water interface measures on the order of only *1% west of the main shipping channel towards the shore with Rockland County, but measures between 3 and 8% on the slopes bordering either side of the main shipping channel near the main spans. Only a formal stability analysis of these slopes, especially near the main channel, can show whether mass movement of slopes under seismic conditions may affect the caissons and 72

other foundation systems of the main span that border the shipping channel. Since any mass movement tends to slide downslope towards the deepest portions of the channel, the main span is likely to experience pier tilting and compression (shortening), while the spans crossing the updip locus of onset of any slope failure would experience pier tilting and extension (lengthening). Conclusions and Recommendations. For the site of the Tappan Zee Bridge (TZB) we have determined the magnitude-distance pairs that are consistent with a given recurrence period and the regional seismicty. Given these seismicity parameters, we then compute three-component ground motions on hard rock, and on soils for 10 additional sites along the TZB accounting for nonlinear soil response largely based on prior boring data. This is done in greater spatial detail for events with 1000-year recurrence periods than for recurrence periods of 500 and 2500 years; for the latter two a smaller set of sites is considered that act as proxies for three generalized foundation categories. All motions represent free-field motions. Soil-structure interaction (SSI) has not been considered. From these free-field accelerations in the time domain, 5%-damped response spectra and constant-recurrence-period (CRP) envelope spectra are computed. These CRP envelope spectra (for the transverse component only, which is generally the largest of the three components of motions) are smoothed for use as design spectra in those cases where linear modal analysis is utilized by the engineer for computing the foundation and/or structural bridge response. We have compared our design spectra to AASHTO-and NYSDOT-compatible design spectra and find differences that are strongly frequency-dependent and also depend on the recurrence period (CRP) of events considered. We also note that ground motions and design spectra show anomalous high amplitudes for events located at a post-critical arrival distance of about 90 km. This feature of the ground motions causes the 1000-year M=7 event at d=92 km to have higher motions than the 2500-year M=7 earthquake at d=58km. A consequence of this geophysically explicable feature is that at response periods of about 2 seconds the 1000-year envelope spectrum exceeds the 2500-year envelope spectrum. We have provided ground motions for recurrence periods of 500, 1000, and 2500 years. Should for any reasons a design level ever be chosen for any portion of the bridge that uses a CRP=2500 years, then for any given structural response period T.21 sec, the higher of the envelope-spectral values among the 1000 and 2500-yr envelope spectrum should be used rather than the 2500-yr value itself to account for the anomalous post-critical arrivals foam distances near 90 km. 73

In the case of nonlinear structural analyses, the ground motion time series instead of the spectra are used. Because in time-domain computations one can account for how spatial variations contribute to bridge response, we have provided formulas to compute lag times for ground motions that need to be considered between adjacent piers of the bridge. We also have computed the maximum amplitude of relative displacements between adjacent piers for typical foundation combinations, by lagging the twice integrated acceleration records and accounting for the azimuth of wave approach between the earthquake and the bridge. These free-field differential displacements account, however, only for the coherent wave-passage effects. Therefore we recommend mutiplying these coherent wave-passage relative displacements with a factor V2*k*2 to account for effects from various incoherencies in the wave motions. We have compared the computed RMS seismic transient strains with the failure strains obtained from prior triaxial shear test data provided to us. We find that the transient strains are on average substantially lower than the lab-measured failure strains of the sampled soils. This statement is limited to strains in the free-field and does not include effects from soil-structure interaction (SSI). We have applied a simple sreening test to the earlier measured SPT blow counts to qualitatively (but not quantitatively) evaluate the potential for liquefaction. In some limited depth ranges, generally at depths > 80 feet below the mudline, some liquefaction in sands, silts or gravels appears possible. Total displacements appear on average to be small for the considered magnitude distance combinations. This conclusion is based on using recently published estimates for the liquefaction severity index (LSI) calibrated by eastern North American case studies. Geotechnical methods exist to determine quantitatively the liquefaction potential and assess possible consequences, if any, for the various types of foundations and superstructure systems of the bridge. They are not the subject of this seismological study. We point out the existence of slopes near the main shipping channels, since slopes are known to be potentially prone to failure under seismic loads. Acknowledgments: We thank the staff of F.R. Harris and Hardesty & Hanover for full cooperation and support in this project, and the New York State Thruway Authority for allowing us to contribute to the evaluation for seismic retrofit of the Tappan Zee Bridge; and for gratiously extending the delivery date of this report beyond its original target. We gratefully acknowledge discussions with Prof. Robert Stoll of Columbia University on soil properties and for his making us aware of earlier studies of Hudson Riverand New York Harbor soils. This study greatly benefitted from basic research at LDEO supported by the National Center for Earthquake Engineering Research, NCEER. 74

References AASHTO (1992), Standard Specifications for Highway Bridges, American Assoc. of State Highway & Transportation Officials. 15th Edition, Washington D.C. Abrahamson, N. A. (1993). Spatial Variation of Multiple Support Inputs. Proceedings, First US Seminar, Seismic Evaluation and Retrofit of Steel Bridges. UC Berkeley, Dept. of Civil Engineering, and Calif. Dept. of Transportation, Division of Structures, San Francisco, CA, Oct. 18, 1993. Anonymous (undated, post-1952 ?). Soil Laboratory Test Data for the NY State Thruway Crossing of the Hudson River Between Tarrytown and Nyack, New York. Faccioli, E. and D. Resendiz (1976). Soil dynamics: behavior including liquefaction. Chapter 4 in: C. Lomnitz and E. Rosenblueth (editors), Development in Geotechnical Engineering. Seismic Risk Engineering Decisions. Elsevier, Amsterdam-Oxford-New York. 1976. pp. 71-139. Greiner Inc. (1992). Draft Geotechnical Report - Design of Ship Collision Protection System for Tappan Zee Bridge, Nyack to Tarrytown, NY; prepared for NYSTA; November 1992. Hardesty and Hanover (1993). Print (drawing) of draft soil profile developed by Hardesty & Hanover (forwarded to LDEO by letter dated 6/9/93). Herron, E., J. Dorman, and C. Drake (1968). Seismic Study of the Sediments in the Hudson River. J. Geophys. Res., 73, 10; pp.4701-4709. Horton, S.P. (1994). Simulation of Strong Ground Motion in Eastern North America. Submitted to Proceedings, 5th U.S. National Conference on Earthquake Engineeing; Chicago, July 10-14, 1994. EERI. Jacob, K. (1993). Seismic design ground motions and site reponse. pp. 133-147, in: Designing structures to withstand disasters, ASCE Metropoitan Section, The Structures Group, Spring Seminar 1993, New York. Jacob, K.H. (1990) Quantitative estimates of seismic hazards, and proposed design ground motions for New York City, in: Bridges and Buildings of the 90's, Spring Seminar 1990, pp. B36-B54. The Structures Group, Metropolitan Section, Am. Soc. Civil Engin., - ASCE, New York, NY. Jacob, K. N. Barstow, S. Horton, J. Armbruster and L. Seeber (1994). Tappan Zea Seismic Study: Design Ground Motions and Response Spectra at the Foundation Levels of the Tappan Zee Bridge for Operating-Base Events (OBE) (10% probability in 100 years), LDEO Report (with two Data Appendices) to F.R. Harris Inc. in NYC; Palisades NY, January 7, 1994. Kennett, B.L.N. and N.J. Kerry (1979). Seismic waves in a stratified half space. Geophys. J. R. Astr. Soc. 57, 557-583. New York State Department of Transportation (1990/92). Engineering Instruction: (1): Standard Specifications for Highway Bridge Design - Seismic Criteria; dated 3/28/90; and (2): Interim Seismic Policy Concerning Bridges Programmed for Rehabilitation; dated 10/14/92. Albany, New York. Seeber, L. and J.G. Armbruster (1991). The NCEER-91 Catalog: Improved Intensity-Based Magnitudes and Recurrence Relations for U.S. Earthquakes East of New Madrid. Technical Report NCEER-91-002I, April 28, 1991; NCEER, Buffalo, N.Y. Stoll, R.S. (1988). Sediment Acoustics. Columbia University. Vucetic, M. and R. Dobry (1991). Effect of Soil Plasticity on Cyclic Response. ASCE J. Geotech. Eng., Vol. 117, No. 1, pp. 89-107, January 1991, Paper # 25418. Worzel, J.L. and C.L. Drake (1959). Structure Section Across the Hudson River at Nyack, N.Y., from Seismic Observations. Annals of the New York Academy of Sciences, Vol. 80, Article 4, pp. 1092-1105, Sept 21, 1959. Youd T.L., D.M.Perkins and W.G.Turner (1989), Liquefaction severity index attenuation for the eastern United States. In: O'Rourke T.D. and M.Hamada [editors] (1989), Proceedings from the second US-Japan workshop on liquefaction, large ground deformation and their effects on lifelines. Tech. Report NCEER-89-0032, Buffalo NY. pp.438-452. 75

APPENDICES Pages Appendix A: Reprint of Paper by Horton (1994) on Modeling Ground Motions Al-All Appendix B: Starting Models for Soil Profiles for all Foundation Groups BI - B4 Appendix C: Ground Motions, Response and Design Spectra for CRP=-2500 Years Cl-C10 Appendix D: List of Pertinent Technical Coomunications by LDEO to FRH / H&H DI - D3 A-i

APPENDIX A Reprint of Paper by Horton (1994) on Modeling Ground Motions Pages A1-A12 A-ii

APPENDIX A t I Ot-I +': EARTHQUAKE AWARENESS AND MITIGATION ACROSS THE NATION P R 0 C E E D I N G S VOLUME III -Al--

SIMULATION OF STRONG GROUND MOTION IN EASTERN NORTH AMERICA Stephen P. Horton 1 ABSTRACT We present a method of simulating earthquake strong ground motion (SGM) that emphasizes geophysical parameterization of the source and earth model while stochastically simulating the complex character of observed earthquake seismograms. The method is intended to provide regionally distinct hard-rock acceleration time histories for use in engineering response studies (e.g. shake table or numerical studies of the nonlinear response of structures), and is motivated by the lack of appropriate observational data particularly in areas of low to moderate seismicity such as the eastern United States. It extends stochastic simulations that model SGM as bandlimited white noise by 1) applying a more realistic earth model and 2) applying a region-specific scattering function. Introduction Methods of simulating strong ground motion (SGM) from earthquakes range from purely statistical to purely deterministic. The need to produce synthetic acceleration time histories applicable to regions where SGM observations are not plentiful such as eastern North America (ENA) motivates us to avoid purely statistical parameterizations of the ground motion, and to seek a method that can be geophysically parameterized. Purely deterministic synthetic ground motions can be routinely produced for simple geophysical models of the source and earth, but these time histories do not show the complexity of observed seismograms due to the unmodeled complexity of the real earth. Modeling this complexity deterministically is generally inappropriate because our knowledge of the 3-D. structure of the earth is limited and also because some aspects of the earthquake process are truly stochastic. A compromise solution is to model some parts of SGM determinstically and others stochastically. Boore (1983) introduced a methodology where the shape of SGM recordings is modeled stochastically while the amplitude and frequency content is determined from a simple source and earth model. We extend that methodology by applying a more realistic crustal model to better account for seismic wave propagation and substituting a region specific scattering function for the shaping function used by Boore (1983). The method is partly deterministic and partly stochastic. The deterministic part is the calculation of synthetic seismograms representing the primary arrivals from an earthquake propagating in laterally-homogeneous flat-layered medium. This utilizes current knowledge of regional crustal structure, and since the Green's functions are calculated using a discrete wave-1 Associate Research Scientist, Lamont-Doherty Earth Observatory of Columbia University, Palisades, NY 10964. -A2-

number integration method produces synthetics with contributions from all possible phases including super-critically reflected S-waves and surface waves which have been shown to be important contributors to SGM at larger epicentral distances in the eastern US (Burger et al. 1987). The Boore (1983) method only considered propagation of the direct S-wave in an elastic half space. The stochastic part of the method involves redistributing a portion of the energy from the primary arrivals into the latter portion of the seismic wave-train by convolving a scattering function with the synthetics. This mimics scattering due to random inhomogeneity in the real earth. We develop a scattering function appropriate for ENA from forward scattering theory (Sato, 1984) that is constrained by observations of SGM duration for records of ENA earthquakes in the third section of the paper. The form of the scattering function is chosen so that scattered energy from the primary phases (synthetics) is conserved, and that the amount of energy scattered results in the duration of the simulated SGM being consistent with the observed duration of the SGM records. Finally, we compare simulated seismograms to observed SGM records from the M5.8 Saguenay earthquake to test the validity of our approach. Synthetics: The Deterministic Part. The synthetics offer a mechanism to deterministically apply regional geophysical knowledge to the simulation of SGM. In this section, we outline the procedure for calculating the synthetics and briefly address the simplifying assumptions regarding the source and earth model. The synthetics are obtained by convolving the impulse response of a homogeneous flat-layered crustal model with a simple source model. In the frequency domain, this procedure is given by A(f) = S(f) G(f) (1) where S(f) represents the source and G(f) is the crustal Green's function. We follow Boore (1983) in adopting the simple source model suggested by Brune (1970). This model, S(f)=M M 1+()]f (2) specifies the average amplitude and spectral content of the far-field displacement spectra resulting from a shear dislocation on a circular fault having instantaneous stress release. M0 is the seismic moment (dyne-cm), and fc is the corner frequency. Since Sa(f) = (2gt)2 S(f) (3) the acceleration spectra increases as-f2 below the corner frequency and is flat above the corner, and so is shaped to high-pass filter the Green's function. The seismic moment, Mo, is the independent variable related to source size. Hanks and Kanamori (1979) relate MQ (dyne-cm) to magnitude by log M0 = 1.5 Mw + 16.1 (4) Source scaling relates the source spectra to the size of an earthquake. In western North America constant-stress scaling (e.g. Brune, 1970) is generally accepted for moderate size earthquakes. However, Nuttli (1983) has suggested an increasing-stress scaling for ENA -A3-

a) 0 20-E I.) 466) C4) 50 100 150 200 250 Epicentral Distance (kin) 10, b)

8.

PEAK 6i xc DIRECT 4 - 22 1._2_ 102 - 8-21 5 67.3 12-Epicentral Distance (km) Figure I a). A record section of synthetic acceleration seismograms calculated for a Maritime Canadian Crustal Model. Shown are the transverse components due to a vertical strike-slip fault with MO = 1e20 dyne-cm and fc = 4.0 Hz observed at 0 degrees from strike. b). The peak acceleration (inverted triangle) measured for each time history and the amplitude of the direct S-wave (asterisk). While the amplitude of the direct S-wave decreases monotonically with distance, the peak amplitude increases significantly at 90 km due to the onset of the post-critical Moho reflection. -A4-

earthquakes. Boore and Atkinson (1987) discuss this issue at some length concluding that evidence favoring an increasing-stressscaling is inconclusive. We follow their example in adopting the constant-stress scaling for our simulations. For constant-stress scaling, fc is related to M0 and Aa (bars), the stress parameter, by I c= 4.9x 106 3(Aa/Mo)* (5) f3 is the shear wave velocity near the source (km/s). Act = 100 bars is commonly used for ENA (Boore and Atkinson, 1987). However, Boore and Atkinson (1992) suggest that a stress parameter of 500 bars is required to match the high frequency spectra of the Saguenay earthquake, and so this parameter is not well determined in ENA. The impulse response of the crustal model (G(f)) is calculated using a discrete wavenumber integration program, PROSE (Apsel and Luco, 1983; Luco and Apsel, 1983) assuming a flat-layered crustal model. In using a one-dimensional velocity model, we assume that to first order wave propagation is dominated by vertical velocity variations. This has been a fundamental tenet of seismological research for many years, and we simply exploit that assumption. A summary of published structure models for ENA is given in Appendix A of Barker et al..(1988). These models are often obtained from seismic refraction surveys and are generally sufficiently accurate to predict arrival times of direct-waves. Q-models are somewhat less well determined given the trade-offs in geometric attenuation, source spectral fall-off and Q. The discrete wavenumber integration technique used to produce the Green's functions accounts for the propagation of all possible phases in a layered half-space including direct waves, supercritically reflected waves and surface waves. The synthetics are also non-stationary in frequency content and amplitude.- Figure la is a record section of synthetic acceleration seismograms calculated for a Maritime Canadian Crustal Model, see Table 1. The peak acceleration in each trace is associated with an individual phase: the direct S-wave at close distances ( < 60 km ) and post-critical reflections at larger distances ( > 90 km). Figure lb compares the peak acceleration to the amplitude of the direct S-wave -with increasing distance. While the amplitude of the direct S-wave decreases monotonically with distance, the peak amplitude increases significantly at 90 km due to the onset of the post-critical Moho reflection. The distance at which post-critical reflections start to dominate the direct S-wave depends on the crustal model and the source depth. Table 1. Maritime Canadian Crustal Model (Burger et al., 1987; Frankel, 1991) 13 (km/s) a(km/s) p (g/cm 3) QP Qa* Thickness (km) 3.10 5.40 2.40 300 600 0.5 3.30 5.80 2.50 3000 6000 3.0 3.70 6.35 2.80 3000 6000 26.5 4.00 7.35 2.92 3000 6000 10.0 4.75 8.33 3.39 3000 6000 le28 Scattering Function: The Stochastic Part. The scattering function is a tool by which geophysical knowledge of the earth can be applied to the SGM simulations in a stochastic manner. In this section, we obtain an approximate formula for the increase in SGM duration due to scattering with distance for ENA, and briefly outline the assumptions behind the scattering function used in the simulations. -A5-

1W I I I I I II-I V 00 60-0 V V 20 -0 du o x' dur m* 0 dur oho 7 dur $og Herrmanni M-l odel 0 100 200 300 400 500 600 Epicentral Distance (km) Figure 2. Increase in duration of SGM with increasing epicentral distance for ENA earthquakes. The source duration (1/fc) assuming a stress drop of 100 bars has been subtracted from the measured duration. ENA earthquakes include Franklin Falls, NH; a Mirimichi aftershock; Nahanni; Perry, OH and Sakenay. Although a variety of scattering phenomena operate in the earth, we are concerned with scattered energy that has significant amplitude relative to the primary arrivals and so contributes to the duration of SGM. Typically this energy arrives around the time of the primary arrival and so the geometry of the ray paths of the scattered wave should. favor forward scattering, especially at larger distances. Diffraction, focusing and interference are the dominant processes. Sato (1984) has shown that an originally impulse-like wave envelope is broadened by forward scattering and that the temporal change in the power spectral density at frequency f0 is represented by *m=o) n~ (_1)n (2n+l)ex4

• nl~

(6) where t' is time relative to the arrival time of the primary phase, and tm is controlled by the relative amount of scattering. This formulation assumes a Gaussian autocorrelation function for the random inhomogeneities in the medium, see Sato (1984) and Scherbaum and Sato (1991) for more details. Scherbaum (1993) has applied an envelope of this form in a stochastic simulation of the SGM due to the Roermond Earthquake, and we adopt this form for the envelope of our scattering function. In our application, tm is linearly related to the duration of the envelope, and the envelope is constrained to have a duration consistent with the duration of observed SGM records for earthquakes in ENA. -A6-

b) Scatterer 0.2 -0.2 40 c) Simulation 20 -400 20" d) Observed 0~ I -20' 0 5 10 15 20 25 30 35 40 Seconds Figure 3a). Synthetic ground motion at station S 17. b). Scattering function. c). Simulated ground motion. d). Observed ground motion at station 17. Figure 2 shows the duration of selected SGM records of ENA earthquakes plotted as a function of epicentral distance. The duration is defined as the time interval between the 95% and 5% levels of the cumulative integral of acceleration squared (Boore, 1983). We subtracted the source duration (1/fc) from the observed duration before plotting. Earthquakes from the central US are not included in this figure. Although a large scatter is observed, SGM duration increases with epicentral distance. A linear increase of duration of Td = 2.0 + 0.125R where R is epicentral distance in km (dashed line in figure 2) would approximate the mean duration value at R. A number of factors contribute to the increase in SGM duration with distance. Herrmann (1985) has suggested that the onset of post-critical Moho reflections causes a discontinuous increase in the duration of ground motion with distance (for synthetic transverse component seismograms) that can be approximated by a linear increase of Td = (1/fc) + 0.05R (solid line in Figure 2). This is a lower bound to the observed duration. Assuming the difference between the observed duration and that predicted by Herrmann (1985) is due to scattering, gives an increase in duration just due to scattering of Td = 2.0 + 0.075R. We use this formula to constrain the duration of the scattering function used in the simulation. Since the increase of Td = (1/fc) + 0.05R is approximately accounted for by the synthetics, the convolution with the scattering function (Td = 2.0 + 0.075R) results in simulated SGM records with durations consistent with the mean durations observed in Figure 2. G' is the envelope of the scattering function. The scattering function is formed by multiplying a random number by the value of the envelope at each time (t'). Energy is conserved in convolving the scattering function with the synthetics, since the cumulative integral of G' is equal to one. This results in the reduced amplitude of the primary arrivals since their energy is redistributed into the wavetrain. It is important that intrinsic Q is used to calculate the Green's functions since the effect of the scattering function is the same as scattering Q. That is, it reduces the amplitude of the primary arrivals. -A7-

4 -I 2 r ) 0 I 0 8 Q*4 6! IlI ~I q i 2till II J 't S10-6 I 4 2 2 3 4 5 6789 2 3 4 5 6789 2 10-10 10 Frequency (hz) Figure 4. Fourier Spectra of the observed and simulated SGM at station 17. The spectral levels are similar above 5 Hz, but the simulation overestimates the spectra at low frequencies. Comparison with Saguenay Observations The method of simulating SGM utilizes the fact that some aspects of earthquake seismograms are deterministic while others are stochastic by combining a deterministic calculation of the amplitude and arrival time of the primary phases with a stochastic dispersal of part of that energy into the scattered wave-train. In this section, we illustrate the method by simulating an observed recording from the Saguenay earthquake. This is the largest earthquake in ENA having SGM recordings, but it is unusual in many respects including source depth and source spectral shape. The procedure is illustrated in Figure 3 by simulating a recording (the vertical component at station 17) at 64 km epicentral distance from the Saguenay Earthquake. The synthetic, Figure 3a, is computed by convolving a simple source model with the Green's function for a 5-layer Maritime Canadian crustal model, see Table 1. For New York State, Frankel (1991) has determined a value of 3000 for a frequency-independent intrinsic Q. We have used an intrinsic shear wave Q of 3000 as suggested for New York in all layers except the first. Here we arbitrarily assigned a S-wave Q value of 300. The P-wave Q was assumed to be twice the shear wave Q in each layer. The simple source spectrum convolved with the Green's function has a moment of 6.63x1024 dyne-cm (Mw = 5.8) and a stress drop of 150 bars. A source depth = 29km, strike = 325', dip = 640 and rake = -540 are used in all synthetic calculations. The arrival of the P-wave and the S-wave are marked in Figure 3a. Note the arrival of other phases having significant amplitude even at this epicentral distance (64km) before the onset of supercritical Moho reflections. The scattering function shown in Figure 3b is generated by multiplying the scattering envelope G' by a random number at each time interval. Convolution of the synthetic -A8-

50 "Vertical 5 Simulated Radial U- ~Vertical 10 15 20 25 30 A Seconds Figure 5. Observed and simulated SGM at station 17. The observations and simulations have similar amplitudes and duration for all three components. with the scattering function results in the simulation, Figure 3c. The simulation and the observed record shown in Figure 3d are similar in both amplitude and duration. Figure 4 shows the Fourier amplitude spectra for the observed and simulated SGM in Figure 3. While the two spectra have comparable amplitude spectra above 4 or 5 Hz, the simulation overestimates the frequency content at lower frequencies. This may be attributed to the unusual character of the SGM records of the Saguenay earthquake which Boore and Atkinson (1992) have shown appear to have less intermediate frequency (0.2 - 2Hz) energy than is consistent with a simple omega-square source model and a seismic moment (constrained from teleseismic records) of 6.63x1024 dyne-cm. Figure 5 shows three orthogonal components of the observed (top) and simulated (bottom) SGM at station 17. The observed horizontal SGM have been rotated into radial and transverse components relative to the source to receiver azimuth. The high degree of similarity between the horizontal components as well as comparable amplitudes prior to the arrival of the S-wave (around 20 seconds) is indicative of a significant amount cross-component scattering. We mimic this cross-component scattering by rotating the synthetic horizontal components by 30' around a vertical axis and the vertical and radial components by 200 around the new transverse axis. The resulting simulated SGM after convolution with the scattering function is. similar in amplitude and duriation to the observed SGM for all components. -A9-

Conclusion We have presented an extension to Boore's stochastic method (Boore, 1983) for simulating SGM time histories. The method applies a more realistic crustal model to better account for wave propagation and substitutes a regional scattering function for the generic shaping function employed by Boore. The character of the simulated SGM is constrained by using available knowledge of gross regional crustal structure and source parameters. A limitation of earlier stochastic models when applied to the eastern US stems from modelling the propagation of only the direct S-wave. Although peak ground acceleration close to the epicenter is associated with the direct S-wave, peak acceleration increases discontinously approximately 90 km from the source due to the onset of supercritical Moho reflections while the amplitude of the direct S-wave continues to decrease monotonically. Thus, the direct S-wave does not adequately represent the seismic wave-field at larger distances which are important in the eastern US. We model the propagation of all phases through a vertically layered earth model appropriate to the region of interest. This approach better accounts for the amplitude attenuation of supercritical reflections, as well as, other important phases (e.g. Lg waves) in the seismic wave-field. Modelling more of the seismic wave-field also accounts for part of the increase in SGM duration with increasing epicentral distance observed in SGM records of ENA earthquakes. We introduce a scattering function to mimic scattering by random inhomogeneity in the real earth to account for the coda waves. The form of the scattering function is chosen so that scattered energy from the synthetics is conserved, and that the amount of energy scattered results in the duration-of the simulated SGM being consistent with the observed duration of the SGM records As an example, SGM recordings from the Mw 5.8 Saguenay earthquake of November 25, 1988 are simulated making simple assumptions concerning regional crustal structure and source parameters. These assumptions are that wave propagation can be modeled by a simple five layered Canadian Maritime crustal model and that the earthquake has a simple point source with a Brune spectrum and a stress drop of 150 bars. In spite of the simplifying assumptions, the resulting simulated ground motions are comparable in both amplitude and duration to the observed seismograms although the assumption of a simple omega-square source model causes over prediction of intermediate frequencies (0.2 to 2 Hz). The current procedure provides simulations that are non-stationary in both amplitude and frequency. Future work may explore the utilization of alternative source models with two corner frequencies bracketing the Brune corner frequency. Such models attempt to mimic asperities on the rupture surface. Acknowledgements This work was funded by grants NCEER 92-1001 and 1002. REFERENCES Apsel, R. J. and J. E. Luco. "On the Green's Functions for a Layered Half-Space, Part II." Bull. Seism. Soc. Am. 73 (1983): 931-951. Barker, J. S., P. G. Somerville and J. P. McLaren. "Modeling of Ground-Motion Attenuation in Eastern North America." EPRI NP-5577 (1988). -A10-

Boore, D. M. "Stochastic Simulation of High-Frequency Ground Motions Based on Seismological Models of the Radiated Spectra." Bull. Seism. Soc. Am. 73 (December, 1983): 1865-1894. Boore, D. M. and G. M. Atkinson. "Stochastic Prediction of Ground Motion and Spectral Response Parameters at Hard-Rock Sites in Eastern North America." Bull. Seism. Soc. Am. 77 (April, 1987): 440-467. Boore, D. M. and G. M. Atkinson. "Source Spectra for the 1988 Saguenay, Quebec, Earthquakes." Bull. Seism. Soc. Am. 82 (April, 1992): 683-719. Brune, J. N. "Tectonic Stress and the Spectra of Seismic Shear Waves from Earthquakes." J. Geophys. Res. 75 (1970): 4997-5009. Burger, R. w., P. G. Sommerville, J. S. Barker, R. B. Herrmann and D. V. Helmberger. "The Effect of Crustal Structure on Strong Ground Motion Attenuation Relations in Eastern North America." Bull. Seism. Soc. Am. 77 (1987): 420-439. Frankel, A. "Mechanisms of Seismic Attenuation in the Crust: Scattering and Anelasticity in New York State, South Africa and Southern California." I. Geophys. Res. 96 (April, 1991): 6269-6289. Hanks, T. C. and H. Kanamori. "A Moment Magnitude Scale." J. Geophys. Res, 84 (1979): 2348-2350. Herrmann, R. B. "An Extension of Random Vibration Theory Estimates of Strong Ground Motion to Large Distances." Bull. Seism. Soc. Am. 75 (1985): 1447-1453. Luco, J. E. and R. J. Apsel. "On the Green's Functions for a Layered Half-Space, Part I." Bull. Seism. Soc. Arm 73 (1983): 909-929. Nuttli, 0. W. "Average Seismic Source-Parameter Relations for Mid-Plate Earthquakes." Bull. Seism. Soc. Am. 73 (1983): 519-535. Scherbaurp, F. "Modelling the Roermond Earthquake of April 13, 1992 by Stochastic Simulation of Its High Frequency Strong Ground Motion." submitted to Geophys. J. Int. Scherbaum, F. and H. Sato. "Inversionof Full Seismogram Envelopes Based on the Parabolic Approximation: Estimation of Randomness and Attenuation in Southeast Honshu, Japan." J. Geophys. Res. 96 (February, 1991): 2223-2232. Sato, H. "Broadening of Seismogram Envelopes in Randomly Inhomogeneous Lithosphere Based on the Parabolic Approximation: Southeastern Honshu, Japan." J. Geophys. Res. 94 (December, 1984): 17735-17747. -All-

APPENDIX B Starting Models for Soil Profiles for all Foundation Groups Pages B 1 - B4 B-i

SOIL PROFILES SIMPLIFIED FROM BOREHOLE DATA Vp and Vs, P-and S-wave velocity (m/s) Qp and Qs, P-and S-wave quality factors PI, Plasticity Index GROUP 1 (borehole b4) Thick-Dens-ness Vp Vs ity Qp Qs PI (m) (m/s) (m/s) (g/cc) 10.5 800 105 1.6 50 15 30 20.5 800 164 1.7 50 15 30 18.5 1500 330 1.9 200 40 3 14.5 1500 406 2.1 200 40 3 172.0 3500 2000 2.7 1000 500 Rk

• 4000.0 6000 3500 2.8 2000 1000 Rk
• GROUP 2a (Borehole BI)

Thick-Dens-ness Vp Vs ity Qp Qs PI (m) (m/s) (m/s) (g/cc) 2.0 600 52 1.5 20 5 30 5.0 600 95 1.6 20 10 30 1.5 600 175 1.8 20 15 15 10.5 800 128 1.6 50 15 15 10.5 800 171 1.6 50 15 15 13.5 800 276 1.8 50 40 10 6.0 1500 366 2.0 200 40 3 18.5 1500 332 1.9 200 40 3 5.0 2500 1500 2.6 500 100 Rk

• 122.0 3500 2000 2.7 1000 500 Rk
• 4000.0 6000 3500 2.8 2000 1000 Rk
• GROUP 2b Thick-Dens-ness Vp Vs ity Qp Qs PI (m)

(m/s) (m/s) (g/cc) 6.0 600 80 1.4 20 5 30 20.0 800 180 2.4 50 15 30 2.0 1500 330 2.5 200 40 3 23.0 1500 300 2.5 200 40 3 3.0 1500 400 2.6 200 40 0 4000.0 6000 3500 2.8 2000 1000 Rk * -B2-

GROUP 3a (Borehole B2) Thick-Dens-ness Vp Vs ity Qp Qs PI (M) (m/s) (m/s) (g/cc) 3.0 600 31 1.5 20 5 30 12.0 600 122 1.6 20 15 30 7.0 600 199 1.7 20 15 15 30.0 1500 270 1.8 200 40 3 8.0 1500 323 1.8 200 40 3 8.0 1500 434 2.1 200 40 0 87.0 3500 2000 2.7 1000 500 Rk

• 4000.0 6000 3500 2.8 2000 1000 Rk
• GROUP 3b (Borehole B3)

Thick-Dens-ness Vp Vs ity Qp Qs PI (M) (m/s) (m/s) (g/cc) 5.0 600 90 1.6 20 5 30 6.0 800 117 1.6 50 15 30 15.0 800 181 1.7 50 15 20 7.0 1500 331 2.0 200 40 3 29.0 1500 289 1.8 200 40 3 12.0 1500 325 1.8 200 40 3 17.0 2500 1500 2.6, 500 100 Rk

• 4000.0 6000 3500 2.8 2000 1000 Rk
• GROUP 4 and GROUP 5 (borehole b5)

Thick-Dens-ness Vp Vs ity Qp Qs PI (M) (m/s) (m/s) (g/cc) 7.0 500 64 1.5 20 5 30 14.0 800 177 1.7 50 15 30 9.0 1500 346 2.1 200 40 3 7.0 1500 279 1.8 200 40 3 7.0 1500 460 2.3 200 40 0 4000.0 6000 3500 2.8 2000 1000 Rk * -B3-

GROUP 6 (borehole b6) Thick-Dens-ness Vp Vs ity Qp Qs PI (M) (m/s) (m/s) (g/cc) 2.5 500 82 1.6 20 5 30 2.5 800 175 1.8 50 15 30 3.0 1500 244 2.0 200 40 3 8.5 1500 326 2.2 200 40 3 1.5 1500 402 2.3 200 40 0 4000.0 6000 3500 2.8 2000 1000 Rk

• GROUP 7 is Hard Rock, no soil profile GROUP 8 (borehole bl)

Thick-Dens-ness Vp Vs ity Qp Qs PI (M) (m/s) (m/s) (g/cc) 14.0 800 119 1.6 50 15 30 2.0 500 46 1.3 50 5 30 17.0 800 179 1.7 50 15 30 31.0 1500 300 1.8 200 40 3 4.0 1500 573 2.6 200 40 0 770.0 3500 2000 2.7 1000 500 Rk

• 4000.0 6000 3500 2.8 2000 1000 Rk
• GROUP 9 (borehole b7)

Thick-Dens-ness Vp Vs ity Qp Qs PI (M) (m/s) (m/s) (g/cc) 4.0 800 105 1.7 50 15 30 20.0 800 162 1.7 50 15 30 12.0 800 250 1.8 50 40 30 30.0 1500 425 2.2 200 40 3 34.0 1500 550 2.5 200 40 3 28.0 1500 650 2.5 200 40 3 6.0 1500 750 2.6 200 40 0 232.0 3500 2000 2.7 1000 500 Rk

• 4000.0 6000 3500 2.8 2000 1000 Rk *
• Rk, Rock layers, Plasticity Index does not apply

-B4-

APPENDIX C Ground Motions, Response and Design Spectra for CRP=2500 Years Pages Ci-ClO -Cl -

TZB Croup 3a, 2500yr EQ: Transverse nonlinear response 1.5m below mudline: m5 at 10km, m6 at 24km, m7 at 58km 2 I I I I I I I I I ' I 2* m5/m5 10 3a.s t.2500 0 I I I I m6/m6 24 3a.s t.2500 C'4

• m7/m7 5

a.s t.20 -- E 1-_ I m7 m7 58 3o~s t.2500 _ 0 0 1 2 I 40I 5 0 10 20 30 40 5 Time [sec]

TZB Group 4 2500yr EQ: Transverse nonlinear response 0.3m below mudline: m5 at 10km m6 at 24km, m7 at 58km I I I I I I I I I I I 4 m5/250m5 4.s t-2 0

• -2 rn6/250m6 4.s t-U2 E

C 00

• -4-_

3C:) 4-m7/250m7 4.s t 2-x< -4, I ,I Time [sec]

.0. 2-- C:) C) 2-0 CN f I I 0 10 20 Time [sec] 30 40 50

TZB Group3a, Transverse non-linear response spectra, 2500yr EQs: m5 at 10km, m6 at 24km, m7 at 58km SI' I I I I I' m5/resp/m5 10 3o.s t.2500 1.0-m6/resp/m6 24 3a.s t.2500-1 ,..' "-m7/resp/m7 58 3a.s t.2500 i! 0.8- _ I~i 0.6 Cn U) I l 0.. I'.." I I '/ \\ I -I -\\. lo j

0.

0 0 5 1 0 \\ Pro / \\ck I / 0.2 N. 0.8o 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Period [sec]

C 0 a, a, C-) C-) -~ C-) a, C,) a, U) 0 C') a, 2.0 Period

TZB Group 9, 2500yr CRP: Transverse nonlinear response 6m below mudline: m5 at 10km, m6 at 24km, m7 at-{ 8km m5/resp/250m5 9.s t 1.0 ......... m6/resp/250m6 9.s t _, - m7/resp/250m7 9.s t 0.8-11 it." W 0.4 4* I/\\' 0.2-N Q- -\\- .0. 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Period [sec]

1. 3a.2500.env I I E C-, a, U~) a, U) 0 0~ U) a, a, 0~ 0 a, w 0.5 1.0 1.5 Period [sec]

TZB Group 4: 2500YR Envelope response spectrm, 5percent damped I E-- CDM F= =3 CL co CL 0 bLJ 4.0 Period [sec]

TZB Group 9: 2500YR Envelope response spectrm, 5percent damped F-, E C-) ci) w~ cn C: W) C0 0.L 2.0 Period [sec] 4.0

APPENDIX D List of Pertinent Technical Coomunications by LDEO to FRH / H&H Pages D 1-D3 -Dl-

List of Pertinent Technical Coomunications by LDEO to FRH / H&H 7/3/93: Tappan Zee Bridge Seismic Study. Preliminary Report # 1: Report of Reconnaissance Data Gathered June 22, 1993 at the Tappan Zee Bridge. Prepared by N. Barstow, J. Armbruster, S. Horton and K. Jacob; Lamont-Doherty Earth Observatory of Columbia University, Palisades NY 10964. For F.R. Harris Inc., New York, NY. July 9, 1993. 9 pp. 6 Figures. 7/12/93: Fax by K.H. Jacob of LDEO to P. Muccino of FRH (for forwarding to K.K. Chen);

Subject:

Response to Inquiry regarding Caltrans Spectra for interim usage at TZB site. pp. 7. 9/2/93: Tappan Zee Bridge Seismic Study. Interim Report # 2: Results from Ambient Vibration Measurements Taken Near and on the Tappan Zee Bridge, July 20-22, and August 4-6, 1993. Prepared by K. Jacob, J. Armbruster, S. Horton and N. Barstow; Lamont-Doherty Earth Observatory of Columbia University, Palisades NY 10964. For F.R. Harris Inc., New York, NY. September 2, 1993. 17 pp. 17 Figures. 10/7/93: Fax by K.H. Jacob of LDEO to P. Muccino / S. Pourhamidi of FRH containing six pages concerning examples of 5000-year event (M=5,6,7) hard-rock motions and response spectra, in comparison with idealized design spectra for SO and S4 soil conditions according to NYC-type soil classification as examples of "Maximum Earthquakes". 1/7/94: Tappan Zee Bridge Seismic Study. Design Ground Motions and Response Spectra at the Foundation Levels of the Tappan Zee Bridge for Operating-Base Events (OBE) (10% Probability in 100 Years). Prepared by K. Jacob, N. Barstow, S. Horton and J. Armbruster; Lamont-Doherty Earth Observatory of Columbia University, Palisades NY 10964. For F.R. Harris Inc., New York, NY. January 7, 1994. 11 pp. of Text with 5 Figures, 8 Tables, and 2 Data Appendices (5% Response Spectra and Time Series). Also submitted: Data diskette with data as listed in this Report. 1/11/94: Fax by N. Barstow of LDEO: to P. Muccino of FRH.

Subject:

Expect Resubmission of Results for Foundation Group 3a to replace those in Report submitted on 1/7/1993. 2/7/94: Surface mail from LDEO to FRH: Resubmission of data (disk) and 12 Figures for Foundation Group 3a for Report submitted on 1/7/1993 as indicated in Fax of 1/11/94. 2/22/94: Fax by K.H. Jacob of LDEO to P. Muccino of FRH. with cc. to H&H, Attn. C. Rolwood.

Subject:

Smoothed Design Spectra for 1000-yr Recurrence Period Ground Motions at the Foundation Level of the Tappan Zee Bridge. (For Foundation Categories I,1I, and III). Text with Option A: Formulas; Option B: Table; and 3 Figures. 5 pp. 4/1/94: Surface mail by J. Armbruster of LDEO to S. Pourhamidi of FRH: Tables of longitudinal, vertical, transverse and torsional modes, listing: observation panel, time window, power-spectral amplitudes and phase angle. 13 Tables for 13 Modes plus cover letter.

5/9/94: Surface mail by N. Barstow of LDEO to C. Rolwood of H&H.

Subject:

Shear Modulus Degradation. Text, Table and Figure describing (for Foundation Groups 3a and 3b and for 2 layers each) the depth ranges below mudline, shear modulus ratio (final/initial) and computed strains for the 1000-yr M=7 at d=92km event. Layer strains varied between 0.171 and 1.156% strain. Figure shows strain values for all computed 1000-yr events as a function of depth in comparison to strains measured at failure in triaxial shear tests performed by Greiner Inc., 1992. 1 Text Page, 1 Figure. 6/15/94: Fax by K.H. Jacob of LDEO to V.P. Wagh of FRH. with cc. to H&H, Attn. C. Rolwood.

Subject:

Smoothed Design Spectra for 500-yr Recurrence Period Ground Motions at Selected Locations and Foundation Levels of the Tappan Zee Bridge. (For Foundation Categories 1,11, and 1I). By Formulas and Table; 3 Figures. 5 pp. 2/20/95: Tappan Zee Bridge Seismic Study. Unreviewed Draft for Final Report, Part 1: Seismic Hazard Assessment, Design Ground Motions and Comments on Liquefaction Potential for the Site of the Tappan Zee Bridge, New York. Prepared by K. Jacob, S. Horton, N. Barstow and J. Armbruster; Lamont-Doherty Earth Observatory of Columbia University, Palisades NY 10964. For F.R. Harris Inc., New York, NY. February 20, 1995. 74 pp. 31 Figures, 12 Tables and 3 Appendices. 3/6/95: Tappan Zee Bridge Seismic Study. Final Report, Part 1: Seismic Hazard Assessment, Design Ground Motions and Comments on Liquefaction Potential for the Site of the Tappan Zee Bridge, New York. Prepared by K. Jacob, S. Horton, N. Barstow and J. Armbruster; Lamont-Doherty Earth Observatory of Columbia University, Palisades NY 10964. For F.R. Harris Inc., New York, NY. February 20, 1995. 74 pp. 31 Figures, 12 Tables and 4 Appendices. 3/6/95: Tappan Zee Bridge Seismic Study. Final Report, Part 2: Ambient Vibration Measurements on the Tappan Zee Bridge and Identification of Structural Modes. Prepared by K. Jacob, J. Armbruster, N. Barstow and S. Horton; Lamont-Doherty Earth Observatory of Columbia University, Palisades NY 10964. For F.R. Harris Inc., New York, NY. March 6, 1995. Figures, Tables, Appendices. -D 3-}}