1734
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
Relations of a most critical supporting pressure q* and a
trap door width D are shown in Figures 7 and 8 for various
consolidation stresses and internal friction angles. If q* is
positive, a trap door is stable without upward supporting
pressures. It is well observed that a trap door is more stable if a
consolidation stress
p
and/or an internal friction angle
φ
are
larger. In other words, a critical trap door width without upward
supporting pressures is larger, if a consolidation stress and/or an
internal friction angle are larger.
Same results can be arranged as relations of a size of a
loosened soil
α
and a trap door width D shown in Figures 9 and
10. As a width of a trap door increases, a size parameter a also
increases but much drastically. This indicates that a ground arch
action is less effective for larger width cases.
It should be noted that a merit and a limit of rigid-plastic
analysis in practical engineering. In this article, calculated
critical pressures q* are at the instant of failure. After the
occurrence of a failure, soil strength may change due to a
subsequent behavior, such as plastic hardening or softening with
volumetric change. However, such post failure behavior is out
of scope in rigid-plastic calculations. If such evolutionary
behavior is crucial, it is not recommended to use rigid-plastic
calculations. However, a short term stability accompanied by
unloading is dominant for a stability problem of a trap door,
because subsequent behavior of soils is not an engineering
interest. For this kind of problems, rigid-plastic calculations are
advantageous for engineering practice, because it is easy to
conduct parametric studies with less numbers of parameters of
models.
4 CONCLUSIONS
In this article, stability of a trap door buried in a modified Cam-
clay soil supported by a uniform upward pressure is investigated.
Conclusions of this study are summarized as follows,
Rigid-plastic calculation is proposed to evaluate necessary
upward pressures to support a trap door. A failure mode of a
soil above a trap door is modeled as a parabolic shape with
linearly distributed velocities. Modified Cam-clay model with
the associated flow rule is adopted. Because it is focused on the
initiation of failures, no evolutionary behavior such as strain
hardening / softening is considered in the analysis.
Numerical results show that critical upward pressures q* for
the stability of a trap door are a function of material properties
of a soil (p
y
’ and M or
φ
) and a width of a trap door D. If q* is
negative for a certain case, it means that a trap door is stable
without an upward supporting pressure. In general, if a trap door
buried in same soils, it is less stable for larger width cases.
Relation of a trap door width D and a size parameter
α
which is
linked to a size of a loosened soil zone above a trap door is also
quantitatively evaluated for various soil conditions. A parameter
α
drastically increases with the increase of a trap door width D,
which reflects a ground arch action around a trap door.
A proposed method is simple, but also based on the rigorous
theoretical background. As this method requires less
computational time and cost, it might be promising for
parametric studies necessary for practical engineering, such as
preliminary design.
5 ACKNOWLEDGEMENTS
The authors indebted to Mr..Nobuo Sakata (a former graduate
student of Kanazawa University) for his help in conducting
numerical works in this article.
