Project Summary

 

 

PREDICTIVE EQUATIONS FOR SOIL SHEAR-WAVE VELOCITIES

LOWER HUDSON VALLEY, NEW YORK

 

By

 

Gary N. Nottis

 

MCEER Intern

Lamont-Doherty Earth Observatory of Columbia University, Palisades, New York

 

 

 

            The Lamont-Doherty Earth Observatory (LDEO) is a member of the New York City-area Consortium for Earthquake Loss Mitigation (NYCEM).  NYCEM members are currently carrying-out various tasks under a multi-year study funded by the Federal Emergency Management Agency (FEMA) and coordinated by the Multidisciplinary Center for Earthquake Engineering Research (MCEER).  A Year 3 task underway at the LDEO is an improved earthquake loss estimation study for a 31-county area including and surrounding the New York City metropolitan area.  This area was previously studied by researchers at Princeton University, using the HAZUS computer program and the assumption of a single soil type.  The new study would incorporate varied soil types.

A critical input to the HAZUS program is a map of soils presented in terms of earthquake site classes.  Such maps are generated using surficial geology maps, bedrock geology maps, depth to bedrock information, borehole logs and accompanying geotechnical information, and shear-wave velocity profiles for the surficial materials.  Time-constraints and finite resources prevent the collection of the necessary boring logs for the 31-county study area.  The various geological maps and depth to bedrock information are readily available either digitally or as paper copy.  In order to generate the required soils map for HAZUS, equations that could predict shear-wave velocity as a function of depth would be needed for the various kinds of surficial materials.

A readily available collection of over 2,100 borehole logs for (1) abandoned electricity generation sites, and (2) highway projects in the mid-Hudson Valley was used to conduct a study, similar to one done in Shelby County, Tennessee in 1989.  Look-up tables of soil unit weights correlated to either relative density for cohesionless soils, or consistency for cohesive soils, were created from available geotechnical data for the boreholes.  A predictive equation was also created to estimate the undrained shear strength (Su) of cohesive soils using Standard Penetration Test (SPT) blow-counts.  These data were then used to estimate the shear modulus (Go) of soil layers as noted on borehole logs.  The shear-wave velocity of a soil layer can then be determined from the following equation.

 

 

Vs = (Go/p)0.5

 

where p is the soil density determined from the soil unit weight, and Vs is the shear-wave velocity.

Borehole logs were available for seven kinds of surficial materials.  These include alluvium or uncertain age, and Wisconsin-age glacial deposits.  The glacial deposits consist of lake deltas, lake sands, lake silts and clays, outwash, and tills.  These kinds of surficial materials cover about 77% of the 31-county study area.

The generation of the necessary equations to predict shear-wave velocity began with the selection of at least 4 representative borehole logs for each kind of material.  Then for each layer noted on a borehole log, an average shear-wave velocity was determined using either data recorded on the logs, or data from the look-up tables.  The depth of the mid-point of each layer was also recorded.  The predictive equations for each kind of surficial material were then created by  plotting the mid-point depth values and corresponding shear-wave velocity values from the appropriate borehole logs on a graph, and then best-fitting an equation of the form  y = a*xb.  Equations of this form are usually used to relate shear-wave velocity and depth.  Correlation coefficients for the determined equations ranged from r = 0.39 to 0.97.  The predictive equations are presented in the table below.

 

 

Predictive Equations For Shear-Wave Velocity As A Function Of Depth

For Surficial Materials Of  The Lower Hudson Valley

 

 

Surficial

Material

 

No. of

Borings

 

No. of

Data Points

 

 

Predictive Equation*

 

 

r**

Recommended

Depth Range for

Equation (feet)

Alluvium and

Alluvial Fans

 

5

 

15

 

Vs = 564.41*D0.1377

 

0.39

 

0 – 50

 

Glacial Kames

 

5

 

12

 

Vs = 106.87*D0.664

 

0.97

 

0 – 60

Glacial Lake

Delta

 

4

 

9

 

Vs = 520.02*D0.1623

 

----

 

0 – 30

Glacial Lake

Sands

 

5

 

11

 

Vs = 244.69*D0.3468

 

0.88

 

0 – 50

Glacial Lake

Silts and Clays

 

8

 

28

 

Vs = 619.81*D0.1561

 

----

 

0 – 100

Glacial Outwash

Sand and Gravel

 

5

 

27

 

Vs = 301.52*D0.3225

 

0.45

 

0 – 100

 

Glacial Tills

 

5

 

21

 

Vs = 626.38*D0.2239

 

0.41

 

0 – 100

 

 *     D = Depth in feet, and Vs = Shear-wave velocity in feet/second

 **   r = correlation coefficient.  No value is listed if equation was determined with only a

       subset of  available data points.

    

A comparison was made between the average shear-wave velocities computed from the predictive equations, and reported field measurements of shear-wave velocities in surficial materials for counties within the 31-county study area.  The field shear-wave measurements presented are usually for the upper 30 to 40 feet of a surficial material.  Thus for the comparison, the predictive equations were used to determine average shear-wave velocities for the same depth interval.  A table with the comparisons is given below.

 

 

Comparison Between Predicted And Measured Shear-Wave Velocities

In The Upper 35 Feet Of Surficial Materials Within The Project Area

 

 

 

 

Surficial

Materials

Predicted Shear-Wave Velocity (feet/second)

From Predictive

Equations

Measured Shear-Wave Velocities (feet/second)

 

Bergen County, NJ

 

Hudson County, NJ

 

Dutchess County, NY

 

Westchester County,

NY

Alluvium and Alluvial Fans

 

825

 

809-1214

 

629-995

 

358-1433

 

600

Glacial Kames

719

 

 

 

269-1460

889

Glacial Lake Sand

647

846

916-925

269-833

538

Glacial Lake Silts and Clays

 

953

 

826-925

 

 

 

269-1532

 

764-1191

Glacial Outwash

743

 

 

246-1063

489-2296

Glacial

Tills

1166

1013-2109

 

358-2614

636-2109

 

            The predicted shear-wave velocities are comparable to those measured.  It can be concluded that the predictive equations may be used in the process to generate a reasonable soil map for input into the HAZUS program.  These relations should be used with caution.  Shear-wave velocity estimates for the surficial materials covering the other 23% of the 31-county study area will need to be determined by the project’s principal investigator.