Project Summary
PREDICTIVE EQUATIONS FOR SOIL SHEARWAVE VELOCITIES
LOWER HUDSON VALLEY, NEW YORK
By
Gary N. Nottis
MCEER Intern
LamontDoherty Earth Observatory of Columbia University, Palisades, New
York
The LamontDoherty Earth Observatory (LDEO) is a member of the New York Cityarea Consortium for Earthquake Loss Mitigation (NYCEM). NYCEM members are currently carryingout various tasks under a multiyear 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 31county 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 shearwave velocity profiles for the surficial materials. Timeconstraints and finite resources prevent the collection of the necessary boring logs for the 31county 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 shearwave 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 midHudson Valley was used to conduct a study, similar to one done in Shelby County, Tennessee in 1989. Lookup 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) blowcounts. These data were then used to estimate the shear modulus (G_{o}) of soil layers as noted on borehole logs. The shearwave velocity of a soil layer can then be determined from the following equation.
V_{s} = (G_{o}/p)^{0.5}
where p is the soil density determined from the soil unit weight, and V_{s} is the shearwave velocity.
Borehole logs were available for seven kinds of surficial materials. These include alluvium or uncertain age, and Wisconsinage 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 31county study area.
The generation of the necessary equations to predict shearwave 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 shearwave velocity was determined using either data recorded on the logs, or data from the lookup tables. The depth of the midpoint of each layer was also recorded. The predictive equations for each kind of surficial material were then created by plotting the midpoint depth values and corresponding shearwave velocity values from the appropriate borehole logs on a graph, and then bestfitting an equation of the form y = a*x^{b}. Equations of this form are usually used to relate shearwave 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 ShearWave
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 
V_{s} = 564.41*D^{0.1377} 
0.39 
0 – 50 
Glacial Kames 
5 
12 
V_{s} = 106.87*D^{0.664} 
0.97 
0 – 60 
Glacial Lake Delta 
4 
9 
V_{s} = 520.02*D^{0.1623} 
 
0 – 30 
Glacial Lake Sands 
5 
11 
V_{s} = 244.69*D^{0.3468} 
0.88 
0 – 50 
Glacial Lake Silts and Clays 
8 
28 
V_{s} = 619.81*D^{0.1561} 
 
0 – 100 
Glacial Outwash Sand and Gravel 
5 
27 
V_{s} = 301.52*D^{0.3225} 
0.45 
0 – 100 
Glacial Tills 
5 
21 
V_{s }= 626.38*D^{0.2239} 
0.41 
0 – 100 
* D = Depth in feet, and Vs = Shearwave 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 shearwave velocities computed from the predictive equations, and reported field measurements of shearwave velocities in surficial materials for counties within the 31county study area. The field shearwave 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 shearwave velocities for the same depth interval. A table with the comparisons is given below.
Comparison Between Predicted And Measured
ShearWave Velocities In The Upper 35 Feet Of Surficial
Materials Within The Project Area 

Surficial Materials 
Predicted ShearWave Velocity (feet/second) From Predictive Equations 
Measured ShearWave Velocities (feet/second) 

Bergen County, NJ 
Hudson County, NJ 
Dutchess County, NY 
Westchester County, NY 

Alluvium and Alluvial Fans 
825 
8091214 
629995 
3581433 
600 
Glacial Kames 
719 


2691460 
889 
Glacial Lake Sand 
647 
846 
916925 
269833 
538 
Glacial Lake Silts and Clays 
953 
826925 

2691532 
7641191 
Glacial Outwash 
743 


2461063 
4892296 
Glacial Tills 
1166 
10132109 

3582614 
6362109 
The predicted shearwave 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. Shearwave velocity estimates for the surficial materials covering the other 23% of the 31county study area will need to be determined by the project’s principal investigator.