tions of the error vectors computed at check points 
for four different experiments. These check points 
were located near the outside edges of the tunnel mo- 
del where no displacement was expected. The overall 
mean (dr) and standard deviation (oy) of the error 
vectors amounted 0.04 mm and * 0.10 mm respectively, 
which are in excellent agreement with the results ob- 
tained from the displacement-free test discussed in 
the above paragraph. Thus, it can be concluded that 
the present instrumentation and procedure can yield 
an accuracy of * 0.15 mm in measuring the movement 
vectors of the sand particles. It can also be con- 
DISPLACEMENT VvECTOn 
cluded from Table 1 that the x and y components of 
particle movement can be measured with an accuracy of 
about + 0.1 mm and + 0.07 mm respectively. 
CONCLUSION 
Through the use of analytical photogrammetric tech- 
niques and a non-metric camera, a solution has been 
developed for an otherwise very difficult measurement 
problem. The method is still being refined and im- 
proved, and the advantages of a metric camera in such 
an application is also being investigated. 
  
  
  
  
  
  
  
  
^ & > => 3 
ue A iis m + + 
4 CE 7*4 07€«*« 7| 
  
  
  
  
co 180 MLLIMNETEnS 
Figure 5. 
16 
Movement Vectors of Sand Particles