Chap. 12] MISCELLANEOUS GEOPHYSICAL METHODS 921 



Measurements of the response characteristics of the ground may be 

 made (1) at the vibrator itself (for which purpose a vibration detector may 

 be set up on the vibrator), and (2) at one or more outside points. The 

 observations under (1) are intended to give several quantities, all as func- 

 tions of frequency: (a) amplitude, (6) phase shift, (c) power, and (d) 

 compaction. Lastly, the variation of natural frequency and damping of 

 the ground with a change in mass (ballast) may be measured. Observa- 

 tions at points removed from the vibrator determine the following quanti- 

 ties: (a) amplitude as a function of frequency, (h) amplitude as a function 

 of distance (and, therefore, the existence of reflections and refractions), (c) 

 phase or travel time as a function of distance, and, finally, (d) phase speed 

 as a function of frequency (dispersion). 



The variation of amplitude with frequency is measured with a detector 

 mounted on the vibrator, or with one or several detectors some distance 

 away. The frequency response may be taken from a continuous record 

 by getting the shaker up to top speed and allowing it to run down, or by 

 adjusting its frequency in steps of two cycles and taking individual records 

 for each frequency interval. The record amplitude is converted to true 

 ground amplitude by means of the calibration curve of the recording in- 

 strument or recording channel and is further reduced to constant impressed 

 force by correcting for the variation of the centrifugal force with frequency. 

 By plotting the reduced amplitude against frequency, a peaked curve 

 (see Fig. 12-20) is obtained. The location of the peak indicates the 

 resonance frequency; the steepness of the slope away from the resonance 

 peak varies inversely with the damping. The damping factor e or the 

 relative damping t/, which is equal to the ratio e/wo , may be calculated 

 from the frequencies ahead of and past the resonance point at which the 

 amplitude has dropped to one-half of the resonance amplitude. The 

 natural undamped frequency is then computed from the resonance fre- 

 quency and the damping (see Chapter 9, section iv). 



Natural frequency and damping are important characteristics of the 

 surface soil and are closely related to its bearing capacity and compaction. 

 Soils having a natural frequency of from 25 to 32 cycles may be loaded 

 with 2.5 to 5 kilograms per square centimeter.^^ From the natural ground 

 frequency and the mass of the vibrator (plus a certain amount of ground, 

 see below) the equivalent sprmg constant of the ground can be calculated. 

 Upon repetition of vibrator experiments, it will be found that both reso- 

 nance frequency and damping are sUghtly greater the second time, owing to 

 compaction resulting from the ground vibration. The resonance fre- 

 quency'' also increases somewhat with the surface of the vibrator, corre- 

 sponding to a larger spring area, that is, to a stiifer spring. The damping 



M Ibid. 



