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Robertson's Remarks #5: Estimating shear wave velocity, Vs from CPT

The shear wave velocity (Vs) is a very useful parameter since it links directly to the small strain shear stiffness of the soil (G0). Although direct measurement of Vs is preferred over estimates, relationships with cone resistance, qt can be useful for smaller low risk projects, where Vs measurements are not always taken.  There are many existing relationships between qt and Vs (or G0), but most were developed for either sands or clays and generally relatively young deposits.  Although strong relationships between Vs and qt exist, some variability should be expected due to factors such as age and cementation.  The accumulated 20 years of experience with seismic CPT results has produced an updated relationship between cone resistance and Vs for a wide range of soils, using the CPT Normalized Soil Behavior Charts (SBT), based on Qtn and F. 

Based on over 100 SCPT profiles from 22 sites in California combined with published data, a set of contours of normalized shear wave velocity, Vs1 was developed on the normalized SBT Qtn – Fr chart, as shown in the Figure below, where:

Vs1 =  Vs (pa / sigma'vo)^0.25                                                                        [1]

Since the CPT measurements are normalized in terms of Qtn and Fr, the resulting shear wave velocity values are also normalized.  The data used to develop the relationship were from deposits that ranged from Holocene to Pleistocene age and were predominately uncemented.  Most Holocene age deposits have Vs1 values less than 250 m/s (820 ft/s).  In general, the Holocene age data tends to plot in the center-lower left portion of the SBTn chart, whereas the Pleistocene age data tends to plot in the center-upper right portion of the chart. 

Based on the contours shown in the Figure, Vs can be estimated using:

Vs = [alphavs  (qt – sigmav)/pa]^0.5                                                                  [2]                                                                                               
Where: pa is atmospheric pressure in the same units as qt and sigmav to make (qt – sigmav)/pa dimensionless.  Since the shape of the contours for alphavs is similar to those of the SBT index Ic, avs can be estimated using:

alphavs  = 10(0.55 Ic + 1.68) in units of (m/s)^2 [3]
or
alphavs  = [10.76] 10(0.55 Ic + 1.68) in units of (ft/s)^2 [4]
           
Knowledge of soil age would improve the correlations but often the age of the deposit is not always known in advance for most small low risk projects.  Hence, the general relationship shown in the Figure and equation 2 is recommended for most Holocene to Pleistocene age deposits.  The predicted shear wave velocity using equation 2 in Pleistocene age deposits may be somewhat under estimated.