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mmm an as 
— 
Figure 1. Schematic Drawing of the Tunnel Model 
During a test, the larger diameter construction shield 
is winched away from the glass plate at incremental 
distances. As the shield is winched away, the sand par- 
ticles surrounding the model move in to fill the void. 
The objective of the study is to measure the directions 
amd magnitudes of the particle movements at various 
distances from the tunnel. 
To serve as photogrammetric control points, eleven 
targets were attached to the outside face of the glass 
plate. The distances between these targets were measu- 
red with a calibrated meter bar to + 0.1 mm. The X and 
Y coordinates of these targets were then computed by 
the method of least-squares. The solution had 21 de- 
grees of freedom, and the maximum standard error in 
the computed X and Y coordinates amounted to + 0.09 mm. 
Figure 2 is a sample copy (reduced for this publica- 
tion) of an actual photograph used for measuring 
particle movement. 
Figure 2 Sample Photograph for Measuring Particle 
Movement (Reduced for Publication) 
  
13 
It was determined from analytical ray tracing that 
photographic image distortions caused by refraction of 
the glass plate could result in errors amounting to as 
much as + 0.04 mm (or 2.52) in the magnitude of the 
computed displacement vectors. Since the distortions 
caused by refraction is systematic, the index of re- 
fraction of the glass plate was determined in place so 
that refraction correction can be applied. The index 
of refraction, N, was determined to be 1.428 + 0.015. 
DATA ACQUISITION 
When the steel-framed box is loaded with sand, the 
glass plate itself is distorted from a truly planar 
surface by the weight of sand. Prior to photography 
during each test, the curvature of the glass plate is 
measured by a rectangular array of 25 strain gauges. 
Figure 3 illustrates the typical distortion pattern. 
The distortion vectors are pendicular to the planar 
position of the glass plate and towards the camera. 
A permanent camera stand is bolted to the floor at a 
distance of approximately 1.8 m in front of the glass 
plate. There is no gross change in the camera position 
from test to test. A Kodak, bellows-type press camera 
with a 20 cm x 25 cm format and a 152-mm focal length 
Ektar lens is used for photography. It belongs to the 
Photographic Services of the University of Illinois 
at Urbana-Champaign. The camera together with a photo- 
grapher are hired for each test. It is the only camera 
which has the required resolution and which can be 
conveniently made available for this study. The bel- 
lows are braced during the test in order to minimize 
the changes in the interior orientation of the camera. 
Kodak Plus X Pan film with an ASA of 200 is used. At 
the stated object distance of 1.8 m, the cross- 
sectional view of the model virtually fills the entire 
photograph as shown in Figure 2. 
An initial, "no-movement" photograph is taken with the 
end of the construction shield being in contact with 
the inside face of the glass plate. The shield is then 
winched away from the plate in increments of six inches. 
After each incremental move, a photograph is taken. 
For the sake of clarity, throughout the remainder of 
this paper, the initial photograph will be referred to 
as "photo 1" and any subsequent photograph taken after 
the tunnel shield has been moved will be referred to 
as "photo 2". 
During each test, spring loaded strain gauges are 
mounted on the top surface of the sandy soil as is 
visible in Figure 2, and electromagnetic strain gauges 
are buried along a vertical line just above the center 
line of the tunnel model. These gauges are read after 
each incremental move of the shield. These gauge 
readings measure the displacements in the vertical 
direction only. 
Stereoscopic coordinate measurements are made on a 
WILD STK-1 stereocomparator. Photo 1 is placed on the 
right stage plate of the comparator, and photo 2 is 
placed on the left stage plate. The y-axes of the 
photographs are made approximately parallel with the 
x-axis of the comparator. This arrangement of the 
photographs serve two purposes. Firstly, since the 
largest component of particle movement is along the 
vertical (or y) direction, this arrangement dramatizes 
the apparent relief in the sand surface caused by 
motion parallax. Secondly, this arrangement permits 
the y-component of movement to be measured more 
accurately than the x-component. The coordinates of 
all eleven control points as well as about 350 other 
points well distributed over the cross-sectional area 
are usually measured.