1026
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
the experimental test is much smaller than that from the DEM
modelling. Again this could be caused by differences in
dilatancy between the Toyoura sand and the spherical DEM
elements. The particle shape of the Toyoura sand is well known
to be sub-angular, so that in Toyoura sand it may be possible to
establish the ground arch even in a loose density state. On the
other hand, the spherical particles, even at the close packing
achieved in the numerical simulations, may not establish an
effective ground arch, so that the effect of the settlement of the
trapdoor could propagate up through the sand layer to the
surface above.
Here, we have verified that the earth pressure on the trapdoor
and the surroundings could be modelled using DEM methods.
On the other hand, the surface settlement could not be evaluated
using a simple calculation in the DEM analysis. In near future,
we would like to extend the DEM modelling to include the
stabilisation of the tunnel face using shotcrete, rock-bolts, and
steel arch supports and also improve the modelling of ground
surface settlement.
3.2
Gravity flow tests
The above confirms that the DEM analysis expresses well the
vertical stress as the trapdoor lowered; although the settlement
of the surface of the sand above the trapdoor is least
satisfactorily modeled. Here, we wish to investigate the
distribution of the vertical stress on the floor adjacent to the
position of the trapdoor during the gravity flow following the
deletion of the trapdoor. This might give some insight into the
processes following a small collapse of a part of the roof of a
tunnel. After small collapse, the stresses at the foot of the
ground arch may increase to such an extent that total collapse
occurs.
Figure 5 shows the vertical stress against elapsed time after
the trapdoor was removed. The elapsed time of 0.4sec
corresponds with the displacement of the trapdoor of 2.0mm in
the Figure 2. The vertical stress at element A undergoes a rapid
cyclic variation suggesting that in the DEM simulations the
establishment of the ground arch is a complex dynamic process
rather than a static one. The vertical stresses on elements B and
C were not much changed from the initial vertical stress
calculated when the bed of spherical particles had come to
equilibrium.
Figure 6 shows the vertical stress against the horizontal
distance from the centre of the trapdoor at an elapsed time of
0.3sec after the trapdoor was removed. The elapsed time of
0.3sec corresponds with the displacement of the trapdoor of
1.5mm in the Figure 2. Note that the vertical stress at element A,
just next to the trapdoor during gravity flow was 2.26 times that
calculated at the displacement of the trapdoor of 1.5mm when
the trapdoor was lowered at a steady rate. This is evidence of
the increased stresses at the foot of the ground arch mentioned
in the Introduction.
3.3
Implications for tunnel construction
With regard to tunnel construction it is possible to draw two
conclusions from the experiments of Kikumoto et al (2003) and
the DEM modeling discussed in this paper. First, the steady
lowering of the trapdoor indicates that yielding of parts of a
tunnel lining system is unlikely to generate large increases in
loading on adjacent parts of the lining. Second, sudden
collapses of part of the tunnel face may induce dynamic effects
which lead to large increases in loads on other parts of the
system. This in turn provides some indication for the
effectiveness of the New Austrian Tunnelling Method, that is
the immediate placement of support provided by the NATM
even before it is fully stiffened, is effective because it prevents
even partial collapses.
4 CONCLUSIONS
We performed DEM analysis of a bed of sand modeled using
spherical particles in order to investigate how the distribution of
the vertical stress on the supporting lower boundary of the sand
container changed during steady lowering of the trapdoor and
during gravity flow following the sudden removal of the
trapdoor. The summary of the results obtained from this work is
as follows:
1) The DEM analysis modeled well the changes in vertical
stress during lowering of the trapdoor, Figures 2 and 3.
2) The DEM calculated settlement of the surface of the sand
above the trapdoor severely over-predicted the
experimentally observed values, Figure 4. Our suggested
explanation for this difference is that the relatively large
spherical particles used in the DEM modeling do not
represent adequately the dilatancy properties of Toyoura
sand.
3) During gravity flow, after the sudden removal of the
trapdoor, the vertical stress on the floor immediately
adjacent showed a complex dynamic variation. With
increasing lateral distance from the opening this variation
was much less significant, Figure 5.
4) The maximum vertical stresses on the floor next to the
opening, after the sudden removal of the trapdoor, were
several times larger than the maxima when the trapdoor
was lowered at a steady rate, Figure 6.
5) In both the steady lowering of the trapdoor and the gravity
flow after the sudden removal, the lateral distribution of
the vertical stress on the floor calculated with the DEM
software exhibited a saw-tooth variation (Figures 3 and 6).
The implications of this DEM modelling for tunnel construction
is that even a yielding support system, such as shotcreting
applied to a tunnel heading immediately after excavation, is
very significant because it protects against large dynamic
pressure that could be induced during a partial collapse.
5 REFERENCES
Costa, Y. D., Zornberg, J. G., Bueno B. S. and Costa C. L. 2009. Failure
mechanisms in sand over a deep active trapdoor,
Journal of
Geotechnical and Geoenvironmental Engineering
, ASCE, 1741-
1753.
Hori, T., Kikkawa, N., Okita, T. and Mitachi, T. 2010. Measurement of
S-wave and P-wave velocities by Bender Element tests,
Proc. of the
6
th
conference of the Kanto Branch of the Japanese Geotechnical
Society (GeoKanto2010)
, 4p (in Japanese).
Itasca Consulting Group Inc. 2012. Particle Flow Code in 3 Dimensions
Theory and Background.
Kikumoto, M. & Kishida, K. 2003. Mechanical behavior on the sandy
ground through the 3-D trapdoor experiment,
Proc. of the 12
th
Asian Regional Conference on Soil Mechanics & Geotechnical
Engineering
, 4p.
Kikumoto, M., Kimura, M., Kishida, K. and Adachi, T. 2003. Three
dimensional trapdoor experiments and its numerical analyses on the
mechanical behavior during tunnel excavation,
Journal of
Geotechnical Engineering
(III), Journal of Japan Society of Civil
Engineers, Vol. 65, No. 750, 145-158 (in Japanese).
Kiyama H. and Fujimura H. 1983
. Application of Cundall’s discrete
block method to gravity flow analysis of rock-like granular
materials,
Journal of Japan Society of Civil Engineers
, No. 187, pp.
95-108 (in Japanese).
Murayama S. and Matsuoka H. 1971. Earth pressure on tunnels in sandy
ground,
Journal of Japan Society of Civil Engineers
, No. 333, pp.
137-146 (in Japanese).
Rabcewicz, L. V. 1964a, b, 1965. The New Austrian Tunneling Method,
part one, two and three,
Water Power
, November, December and
January, 453-457, 511-515 and 19-24.
Terzaghi, K. 1936. Stress distribution in dry and saturated sand above a
yielding trap-door,
Proc. 1
st
International Conference on Soil
Mechanics and Foundation Engineering
, Cambridge, Mass., 35-39.
