A History of Research and a Review of Recent Developments

Loads on underground structures 81
If the soil surrounds the structure and rests at its natural angle of repose, its
presence will considerably reduce the value of the coefficient of drag on the
front face and at the same time buttress the structure against lateral movement.
Underground structural loading is also influenced by the flexibility of the
structure in relation to the properties of the surrounding soil and the soilstructure
interaction effects that occur as the structure begins to deflect under
shock pressures. The structure and its surrounding soil form a composite body,
the loading on which can be influenced by soil-arching and the disturbance to
the natural properties of the soil.
Much of the early work in this field was driven by the need to assess nuclear
weapon effects, and there are good summaries of the problem in the reports
by Newmark and others, and by Glasstone and Dolan, discussed earlier in
references [4.2] and [4.5]. Using their work as a basis, we will discuss first the
structural loading that comes from blast-induced ground shock. We saw earlier
that there are two types of air-blast-induced ground motion. In that where the
velocity v of the shock front exceeds the dilational seismic velocity (u) of the
soil, there is a sloping shock front below ground. If v=u, the ground shock
front becomes almost vertical near the surface, and if v=u, the shock front in
the ground outruns that in the air. The relationship of pressure with duration
will attenuate as greater depths of soil are considered, and Figure 4.5, from
the work of Newmark [4.8] illustrates this. As the depth increases the rise
time is longer, there is a lower peak pressure and a longer decay. The total
impulse (i.e. area under the pressure-time curve) remains about the same, and
it was established experimentally that the rise time at any depth was about
half the time of transit of the shock front to the point considered. The changes
in shape of the pressure pulse were a direct result of the stress-strain
characteristics of the soil in unidirectional compression. A simplified empirical
equation was proposed by Newmark and Haltiwanger [4.9], which gave
Figure 4.5 Attenuation of pressure wave with depth (from Newmark, ref. 4.8).