where i is the trough width parameter, k is an empirical constant related
to the soil type, and z is tunnel depth, i.e. the vertical distance from
ground surface to the tunnel centerline.
Considering the twin tunnels, Suwansawat and Einstein [14]
found that the trough width parameter i, which is obtained from
the additional settlement trough over the following tunnel, was in
agreement with O'Reilly and New's work [8]. It found that the empirical
constant k falls within the bound of 0.4 and 0.5, which was similar
to most cases of tunneling projects in clay layers.
Chi, S.Y et al. [17] also summarized the relationship between
trough width i and tunnel depth z by using the angle of the influence
zone of ground settlement (i.e. β) as follows: