ETL 1110-2-344
31 Dec 93
directions, the resulting nodal forces cancel. In
of the rock is fairly well known. This is especially
order to keep the nodal forces due to uplift pres-
true if the permeability is thought to be anisotropic.
sures from canceling, a thin pervious elastic region
c. Finite element model.
is placed between the two impervious regions (mon-
olith and foundation). The pervious elastic region
simulates the pipe in the pipe flow analogy shown
(1) The monolith, the backfill above the stair-
in Figure A-3. This region corresponds to the ele-
step pattern on the back side of the monolith, and a
ments where pore pressures are prescribed as
portion of the foundation near the monolith are
described in paragraph 3c. The result of this
idealized by the finite element mesh shown in Fig-
approach is that the nodal forces due to the uplift
ure A-4. This mesh consists of 1020 elements and
pressures are transferred to the monolith and the
1236 nodes. A rectangular region of the rock foun-
foundation one row of elements away from the
dation, 192 ft wide and 92 ft in depth, is modeled.
interface. There is also a small horizontal force due
The vertical plane on the left side of this region is
to the pore pressure gradient in the horizontal direc-
aligned with the center line of the main lock cham-
tion transmitted to the monolith and the foundation
ber. The left-most vertical face of the monolith is
which results in some shear stresses. This has only
52 ft to the right of the main lock chamber center
a minor influence on the computation of final crack
line. The entire mesh of the model consists of
length.
4-node quadrilateral elements which include a
(4) The uplift model described by Case 3 is
performance for bending modes (Reich 1992). The
only practical for the traditional method of analysis.
plane strain idealization is used to define the stress-
An infinitely rigid foundation would be modeled in
strain relations for the entire model. Strain and
a finite element analysis using either pinned sup-
stress values are computed at the nodes using a
ports or a combination of pinned and roller supports
variational recovery technique (Zienkiewicz et al.
located along the base of the monolith. Since the
1985).
nodes on the uncracked portion of the base of the
monolith are fixed in the vertical direction, it is
(2) The material properties for the concrete,
impossible to prescribe pressures on the base of the
rock, soil, and interface are given in Table A-1,
monolith. The addition of a thin pervious region at
Poisson's ratio, γ the dry unit weight, γs the satu-
the base, described above for Cases 1 and 2, could
rated unit weight, γw the unit weight of water, KH
also be applied for Case 3.
the horizontal earth pressure coefficient, and KV the
vertical earth pressure coefficient. Elastic properties
(5) Regardless of how the analysis is per-
for the concrete and rock are assumed to be identi-
formed, be it either the traditional method or finite
cal. The loads applied to the mesh correspond to
element analysis, the most fundamental issue to be
those shown in Figure A-2. A lock water elevation
addressed in the modeling of uplift pressures is the
of 340.0 ft and a backfill saturation elevation of
flow regime. Once the flow regime has been estab-
396 ft are assumed. For the prediction of cracking,
lished, the determination of the uplift pressures is
the crack induced by this force system is confined
rather straightforward. In the absence of field data
to the interface between the foundation and the
from piezometers, the assumption of a linear
monolith.
variation in pressure, which corresponds to a true
steady-state condition, is the most reasonable.
(a) Bi-material interface. The modeled region
When piezometric data are available, the assump-
includes bi-material interfaces at the base of the
tion of a linear variation in pressure between adja-
monolith (concrete/rock interface) and at the back
cent piezometers may be reasonable, provided the
of the monolith (concrete/soil interface). Special
resulting uplift pressure profile is relatively smooth.
considerations are required to enable the computa-
If drains are present and functioning properly, a
tion of unique nodal strain and stress values for
seepage flow analysis may be required as the
each of the two materials on a bi-material interface.
assumption of a linear variation in pressure would
To enforce continuity, yet maintain the ability to
be unconservative for this situation. In general,
compute unique strain and stress values, master and
determining uplift pressures from a seepage flow
slave nodes have been utilized. Master and slave
analysis should be avoided unless the permeability
A-4