2. TBM tunneling using a disc cutter

The assessment of the feasibility of TBM tunneling is often complicated by
the large number of parameters that should be taken into account. The most
frequently used parameters, and those considered to be most important, are given
below.

c [MPa]: Uniaxial compression strength

H_{T} [g^{-1/2}]: Total hardness

Is [MPa]: Point load index

F_{N} [kN]: Thrust force (force normal to the rock surface)

F_{R} [kN]: Rolling force (force parallel to the rock surface)

p [mm]: Penetration

d [mm]: Cutter diameter

[]: Edge angle of disc cutter (included angle)

s [mm]: Cutter spacing

D [m]: Diameter of cutter-head (excavation diameter)

w [rpm]: Rotation speed

U [m/s]: Circumferential velocity (= pDw/60)

r [%]: Net working rate defined by Eq. (3)

H [m/h]: Penetration rate (= 0.06pw)

Hmean [m/h]: Mean penetration rate through hours of excavation (= 0.5H)

V [m/h]: Advance rate (= 0.01rH)

Among these parameters, the relationship between forces and rock strength has
been studied extensively. It is known that besides penetration, they are related
to cutter diameter, edge angle, cutter spacing and other parameters. However, to
date only a few formulae considering such parameters have been proposed. Some
examples of published formulae for F_{N} and F_{R} are given in
Table 1. Of these, only the formulae of Roxborough and Phillips (1975) and Sanio
(1985) are based on theoretical consideration or equations of equilibrium. Gong
et al. (1995) recently proposed a slight modification to Sanio's formula. The
formulae of Takaoka et al. (1968), Nishimatsu et al. (1975) and Snowdon et al.
(1982) are based on laboratory tests, whereas the others were formulated in
reference to in situ data or field practice.

Figure 1 shows the relationship between F_{N} and p under the
conditions d = 300 mm, s = 10p, f = 90o, and sc = 100 MPa. Line No.1 is given by
the formula proposed by Snowdon et al. (1982), and is consistent with those
suggested by Sanio (1985), Nelson et al. (1985) and Nishimatsu et al. (1975). It
should be noted however that these formulae produce similar results only under
these conditions. For example, changing the uniaxial compression strength
introduces differences in these formulae. Snowdon et al. (1982) purported that F_{N}
is proportional to the uniaxial compression strength, whereas Sanio (1985)
suggested that F_{N} is proportion to Is^{1/2}. The point load
index Is is approximately proportional to c, and hence there is a considerable
difference between the strength dependences of these models. Sanio (1985)
proposed a formula that considered the cutter spacing. However, if a suitable
spacing is selected for each case and changed according to c and other
conditions, the evaluation of the formulae becomes rather complicated and
difficult. Nelson and O'Rourke (1983) suggested a formula in which total
hardness
H_{T} is selected as a variable expressing rock strength. If the total
hardness is calculated as
H_{T} = 0.3c , a similar result for F_{N} as that of Snowdon
et al. (1982) and Sanio (1985) can be obtained when sc is close to 100 MPa.
However, if
H_{T} is related to c in this way, the influence of sc on F_{N}
becomes smaller than in the other formulations, that is, F_{N} becomes
larger when sc is small and smaller when c is large. In the case of the
Roxborough and Phillips (1975) model, a mean peak value is selected and the
value of F_{N} becomes a little larger. The value calculated from Graham
(1976) is also somewhat larger.

Figure 2 shows the relationship between F_{R}/F_{N} and p.
From the figure, F_{R}/F_{N} increases gradually with p, in most
cases approximately in proportion to p^{1/2}. However, there exists significant
differences between models at longer penetration lengths.

As mentioned above, F_{R} and F_{N} have been studied
extensively. Here, we focus on the hypotheses that F_{R} and F_{N}
are influenced by the cutter spacing s and are dependent on the extent of disc
cutter wear or cutter edge width (Rostami and Ozdemir, 1993). Unfortunately,
there is much uncertainty concerning the influence of these two parameters.

If we know that sc expresses rock strength and disc parameters such as d and
, and that the penetration p can be calculated from F_{N}, then the
penetration rate H can be calculated according to the equation

H = 0.06pw (1)

In this equation, w usually decreases with increasing excavation diameter D because it is necessary to keep the circumferential cutter velocity below a certain speed. There are several opinions regarding this problem; the following equation is an example (Saito et al., 1971):

w = 40/D (2)

Equation (2) and Snowdon's formula can be substituted into Eq. (1), eliminating w and p, respectively. Equation (1) can then be rewritten as shown in Table 2, where it is listed along with other proposed equations for estimating H. Figure 3 shows H calculated using the equations in Table 2 as it varies according to sc. The equations proposed by McFeat-Smith and Tarkoy (1979) and Snowdon (1982) are similar to a certain extent. The values predicted by Ikeda and Nishimatsu (1981) appear quite low; even with an index of discontinuity of k = 0.2, or assuming very high discontinuity, H is still small. This equation is also notable in that H changes only a little with increasing c. The equation proposed by the authors based on the data obtained by Saito et al. (1971) is consistent with that of Ikeda and Nishimatsu when the uniaxial compression strength is larger than 100 MPa, however there is a significant difference below that value.

Through careful examination and evaluation of field data, we found that the cutting speed can be estimated using the equation of McFeat-Smith and Tarkoy (1979) or Snowdon (1982) with reasonable accuracy. Ikeda and Nishimatsu's equation is based on relatively old domestic data and reflects the complicated geological conditions and contract systems in Japan.

Equations for the thrust force applied to the cutter head and torque are also listed in Table 2.