TUNNEL ENGINEERING

Fig. 20.20 Stresses in liner ring may be
computed by assuming it cut at crown C.
The vertical shear at the crown is zero, and the
moment is
ðp 1
Mc ¼ RTc Mdf (20:3)
p 0
where R ¼ radius of ring
M ¼ bending moment at any point U due to
loads on CU
f ¼ angle between U and crown C
With the thrust and moment at the crown known,
the stresses at any point on the ring can be
computed, as for an arch (Art. 6.71).
(A set of equations is presented in Chapter 15B
‘‘Tunnel Structures, Structural Engineering Handbook,’’
2000 Update for ENGnetBASE, Edited by
Wai-Fah Chen and Lian Duan, CRC Press, 2000
(www.crcpress.com).)
Loads on a lining include its own weight and
internal loads, weight of soil above the tunnel
(submerged soil for tunnels below water level),
reaction due to vertical loads, uniform horizontal
pressure due to soil and water above the crown,
and triangular horizontal pressure due to soil and
water below the crown.
Magnitude of loads on tunnel liners depends on
types of soil, depth below surface, loads from
adjacent foundations, and surface loads. These will
require careful analysis, in which observations
made on previous tunnels in similar materials will
be most helpful.
In rock, the quality of the rock will affect the
loads that are carried by the tunnel, and loads
carried by any initial rock support may effect the
TUNNEL ENGINEERING
Tunnel Engineering n 20.41
loads carried by the secondary lining. Compression
of competent rock due to outward displacement of
the tunnel lining in a pressure tunnel may also
need to be considered. Often those linings must be
designed to take the full internal pressure. Beyond
100 psi internal pressure, reinforced concrete liners
may no longer be sufficient and steel liners may be
needed. If a tunnel is watertight, the interior lining
is usually designed to carry at least the full external
water pressure, since leaks in any outer linings will
eventually lead to full transfer of the hydraulic
head. If the tunnel is drained, at least some of the
hydrostatic head should be considered. Blasting
may also disturb the rock locally, leading to loads
different to those of a bored tunnel.
Following the derivation of moments, axial
thrust and shears, the concrete cross section can be
designed accordingly, and steel or fiber reinforcement
placed accordingly as needed. Tension cracks
in themselves do not necessarily result in failure,
whereas through-cracks (often caused by shrinkage)
can cause leakage and corrode exposed steel. It
is usually undesirable for cracks to extend more
than halfway through the section. Typical steel
reinforcement for crack control may reach 0.28% or
more of the section area. Restraints at the exterior
face due to keying into an irregular rock surface
may change the calculated behavior. Linings with
irregular width are more likely to crack at the
thinnest sections or at initial ground support
embedments. Waterstops are used at construction
joints to reduce leakage.
Because of flexibility, tunnel liner rings can offer
only limited resistance to bending produced by
unbalanced vertical and horizontal forces. The
lining and soil will distort together until a state of
equilibrium is obtained. If the deflection, in,
exceeds more than 1.5D/10, where D is the tunnel
diameter, ft, the lining may have to be temporarily
braced with tie rods when it leaves the shield until
the final loading conditions and passive pressures
have been developed. In certain soft materials,
when shields were shoved blind (without material
being excavated), initial horizontal pressures
exceeded the vertical loads, so that the vertical
diameter lengthened temporarily. Ultimately, the
section reverted to approximately its initial circular
configuration.
When a lining is in rock, determination of the
loads imposed on the lining need to be done with
care. Stable rock may distribute the stresses around
the tunnel, and if impervious, may leave any
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