MEASUREMENT OF DISPLACEMENTS AROUND 
TUNNEL MODELS BY MOTION PARALLAX 
Kam W Wong 
and 
Alan P Vonderohe 
Department of Civil Engineering 
University of Illinois at Urbana-Champaign 
ABSTRACT 
Analytical and close-range photogrammetric techniques 
are being used to measure displacements of sandy soils 
around tunnel models. The method is based on the 
motion-parallax phenomenon. From the same camera posi- 
tion, "before" and "after" displacement photography 
are taken of a vertical cross-section of the tunnel 
model through a 9.5-mm thick glass plate. A Kodak, 
bellows-type, press camera with a 20 cm x 25 cm format 
and a 305-mm focal length Ektar lens is used for 
photography. Stereoscopic coordinate measurements are 
made on a WILD STK-1 stereocomparator. The analytical 
solution provides correction for instability of the 
camera's interior and exterior orientation between 
photography, and for refraction and non-planarity of 
the glass plate. Displacement vectors can be deter- 
mined with an accuracy of * 0.15 mm at one sigma (c) 
level. 
INTRODUCTION 
One of the major concerns in constructing underground 
tunnels in urban areas is to minimize the damages 
caused by ground settlement. In the Department of 
Civil Engineering at the University of Illinois at 
Urbana-Champaign, a model has been set up in the 
laboratory to study the effects of soil conditions and 
tunnel geometry on the displacement of sandy soils 
surrounding a tunnel. 
Conventionally, particle displacements in models of 
this type have been measured by spring-loaded strain 
gauges mounted on the surface of the model, and by 
electromagnetic strain gauges buried in the sand. 
Although the gauges can yield displacement information 
at points located both on and within the model, the 
number of displacement points is limited by the number 
of gauges that can be practically installed. Moreover, 
the gauges themselves may influence the displacement 
behavior of the sandy soils. 
Applications of photogrammetric methods for measuring 
particle movement in this type of models have been 
. reported by Andrawes, Butterfield, et al (1970, 1971 
12 
and 1973). From the same camera position, "before" and 
"after" displacement photography are taken of a verti- 
cal cross-section of the tunnel model through a plate 
of glass. Because of the motion parallax effect, the 
positional displacement of the sand particles will be 
represented by the relief in the stereo model. This 
method has the major advantage that displacements at 
any number of points over a large cross-sectional area 
can be accurately mapped. In all the application cases 
discussed in the above references, relatively small 
models were involved, and photogrammetric stereo- 
plotters were used to plot the contours of the dis- 
placement vectors. 
In the present study, the cross-sectional area of the 
model to be photographed measured 1.4 m x 0.9 m. In 
order to obtain adequate resolution of the sand par- 
ticles, a large format camera is therefore needed. In 
order to provide greater convenience and higher accu- 
racy in both data reduction and analysis, a fully ana- 
lytical solution is employed. Stereoscopic coordinate 
measurements are made on a WILD STK-1 stereocomparator. 
The analytical solution provides correction for insta- 
bility of the camera's interior and exterior orienta- 
tion between photography, and for refraction and non- 
planarity of the glass plate. Graphical illustrations 
such as displacement contours, diagrams of displace- 
ment vectors, and displacement profiles can be gene- 
rated directly from the computer. 
THE TUNNEL MODEL 
As shown in Figure 1, the tunnel model is housed in a 
steel-framed box which has a 9.5-mm thick glass plate 
at one of the longitudinal sides. A 152-mm diameter 
steel pipe represents the tunnel lining and a close- 
fitting, larger diameter brass pipe represents the 
construction shield. The soil surrounding the tunnel 
is consisted of well-graded sand with grain sizes 
ranging from 0.2 mm to 0.8 mm. The density of the sand 
is controlled by varying the height of fall during its 
placement and by the degree of compaction. 
13-mm Steel Plate 
9.5-mm Glass td 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
25-mm Steel Base Plate 
  
—— 
ze 
Tunnel 
Shield 
  
(Fig la)