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Using equation (1) and (3):
At point a, u a = u o r o /r a , where r a is the distance of point a to the centre of the second tunnel.
At point b, u b = u o r o /r b , where r a is the distance of point a to the centre of the second tunnel.
The maximum diametrical distortion, δ d is defined as δ d = u a - u b
The radial distortion is given by:
δ r = δ d /2 (4)
Morgan (1961) showed that the bending moment due to distortion over radius is given by:
M = (3EIδ r )/ r o
2
(5)
Based on equations (4) and (5), the additional distortional moment in the first tunnel lining due to the
second tunnel construction can be calculated. The total bending moments for structural design of the
segments are superimposed by adding the additional distortional moment to the moment due to ground
loading, assuming the hoop thrust remains unchanged.
3. ALLOWABLE ADDITIONAL DISTORTION FOR CONSTRUCTION
The method outlined in Section 2.3 above can be used to make allowance in the design of the tunnel
lining to cater for the effect of the second tunnel construction on the first tunnel. However, it is
difficult to monitor such effect during construction as the method relies on the prompt assessment of
the volume loss generated by the second tunnel construction. This back analysis of the volume loss is
typically not readily available at the time of tunnel construction. It is thus not practicable to use
volume loss as a controlling parameter during construction. In order to overcome this shortcoming, it
is proposed to use the conventional convergence monitoring as a means to ensure that the additional
distortion of the first tunnel due to the second tunnel construction is within the capacity of the lining of
the first tunnel.
Additional analyses have been carried out in the design of CCL3 tunnel lining to determine the
allowable additional diametrical distortion for construction. This allowable diametrical distortion is
not only for the effect of second tunnel construction, but also for the effects of all other construction
activities, for example cross passage construction. In the analyses, it has been assumed that the ring
has a reduced moment of inertia as recommended by Muir Wood (1975). The following steps are
taken to determine the allowable diametrical distortion for construction:
• The hoop thrust and moment under the ground loading and surcharge are calculated based on the
method described by Muir Wood (1975) and modified by Curtis (1976);
• The spare moment capacity is taken as the difference between the ultimate capacity based on the
reinforcement provided and the calculated moment due to the ground loading and surcharge. Both
ULS and SLS are checked and the lesser of the two is taken as the spare moment capacity that the
ring has for construction.
• This spare moment capacity is converted into radial distortion with the use of Equation (10). This
distortion multiplied by two is thus the allowable diametrical distortion for construction.
Assuming the allowable diametrical distortion will be fully developed during construction, the ring is
checked for the capacity of 15mm distortion allowed for long term due to adjacent future unknown
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