Civil Engineering Reference
In-Depth Information
Horizontal and vertical ground displacement
caused by S waves
S waves are sinusoidal and travel at half the velocity of P waves; they have
both a vertical and horizontal component. They dictate the peak ground
acceleration (PGA) and peak ground velocities (PGV) that are used in
design. PGV is a more relevant parameter for underground structures and
PGA for above-ground structures. The tunnel structure will distort accord-
ing to the direction of travel of the waves and their angle of incidence on
the tunnel. This behavior is sometimes referred to as snaking. It will cause
vertical and horizontal bending moments in the structure, and where there
are joints, will cause joints to open and close due to the curvature of the
structure.
Racking
This is the result of ground shaking and the inertia in the ground stratigra-
phy, causing a horizontal distortion of the ground mass—in effect, a shear
wave passing vertically up through the ground. In a circular section tunnel,
this will cause ovaling, and in a rectangular tunnel, this will cause racking
whereby the rectangular section is distorted to a trapezoidal shape, as seen
in Figure 9.24. This will cause large bending moments and shear forces in
the structural walls, particularly at the stiff wall-slab connections.
Deformed shape during
wave motion
Tunnel structure before
wave
Shear wave front
Figure 9.24
Racking behavior due to vertically propagating shear wave. (Adapted from
Hashash 2001.)
