Page 228 - Numerical Analysis and Modelling in Geomechanics

PARAMETER ESTIMATION USING EXTENDED BAYESIAN METHOD 209

Figure 7.2 Measurement of displacement by extensometer from ground surface.

Treatment of measured displacements
As displacements measured from borehole extensometers and convergence are
more reliable than stresses (Sakurai 1983:1163), observed displacements are
mainly used in this study. If the overburden height of the underground opening is
less than 60 m, extensometers can be installed from the ground surface using
groutable anchors and mechanical transducers as shown in Figure 7.2 (Dunnicliff
1988). The displacements measured by these schemes appear to be reliable.
However, convergence is generally measured inside the tunnel because of its
simplicity; the measured convergence inside the tunnel is only a part of the total
deformation. To estimate the absolute displacement, mathematical analyses
should be performed using an appropriate characteristic line of deformation.
It is known that ground movement begins to take place about one to three
tunnel diameters ahead of a tunnel face, and is completed when the tunnel face
advances to a distance of about three diameters of the tunnel (Lo, Lukajic and
Ogawa 1984:128). The characteristic line of deformation due to face advance is
presented in Figure 7.3.
As shown in Figure 7.3, the absolute displacement is the sum of three
components: deformation ahead of the face (u ), missed deformation behind the
0
face (u ), and measured deformation (u ). Therefore, to obtain an unbiased
m
i
(absolute) deformation, u i and u 0 must be estimated. To estimate u , a
i
characteristic line is assumed based on the measured convergence shape, and by
the extrapolation technique (Gerald and Wheatley 1994). The deformation
occurring ahead of the tunnel face (u ) can be obtained empirically or
0
numerically. It is known that u 0 constitutes about 30 percent of the absolute
displacement (Hanafy and Emery 1980:119; Panet and Guenot 1982:197).
However, this value might be mostly applicable to hard rock conditions. Three-
dimensional finite difference analysis was performed and compared with the two-
dimensional analysis to obtain the ratios in three typical ground conditions (Lee,
Kim, Choi and Choi 1996:87): weathered rock, soft rock, and hard rock. The