EP 1110-2-12
30 Sep 95
and ground shaking, they should be used with
The three-dimensional analysis is even more time
caution.
consuming and complex, but the principles and
general procedure are similar to the two-dimensional
analysis described.
e. Simplified DFD analysis procedure. The
simplified procedure described below was used to
f. Acceptable response to DFD. When the seis-
investigate concrete stresses due to fault displacement
in the Auburn Dam in California (U.S. Department of
mic activity associated with the design earthquake
the Interior, Bureau of Reclamation 1980). The dam
consists of both fault displacement and ground shak-
and foundation are modeled with finite elements with
ing, stresses for the combined response described in
the mesh geometry adjusted to allow the fault to be
paragraph 2-3d must satisfy the allowable tensile
properly oriented. Refer to Figure 2-2. The
stress criteria of paragraph 2-2e. Beyond these
foundation model consists of a fixed block with
tensile stress requirements, additional consideration is
conventional boundary supports, and a movable block
required regarding general performance requirements
with special boundary conditions that allow forces to
of Chapter 4 related to dam safety and operations in
be applied at the boundary parallel to the fault to
the event of foundation fault displacement. The
produce the DFD. The fixed and movable block are
potential fault displacement and the effect it has on
separated by elastic orthotropic elements which allow
the dam must be evaluated on a case-by-case basis.
the sharp displacement discontinuity to take place as
The analysis procedures described above for
the movable block displaces upward.
evaluating the effect of fault displacement are rough
approximations, but they do provide an indication of
(1) The finite element model is first loaded with
the extent of the fracture zones that could occur in
the gravity loads followed by the hydrostatic loads,
the foundation or lower portions of the RCC dam.
and finally the movable block is forced to undergo
The analysis results must be coupled with
the DFD. Each loading is applied incrementally.
considerable judgment to determine if this damage
After each loading increment, tensile stresses are
could lead to the erosion of the foundation or RCC
evaluated and elements are softened in areas where
materials to the extent that finally causes an
the tensile strength is exceeded. Elements are soft-
uncontrolled release of the reservoir.
ened by reducing their elastic modulus until the
tensile stress is eliminated. Most elements requiring
g. Dam failures caused by fault displacements.
softening are located in the foundation because joint-
To help identify some of the judgment factors
ing and discontinuities in the rock prevent it from
involved in evaluating sites with fault displacement
sustaining high tensile stress. When the DFD is
potential, the following is a brief review of historical
reached, the extent of the tensile failure areas is
information on dams that failed directly or indirectly
evaluated. The dam tends to bridge over the fracture
as a result of fault displacement. Differential dis-
zone in the foundation. Resulting stresses induced in
placements across a fault have been recorded due to:
the RCC are obtained from the finite element analysis
triggering of the fault by a seismic event; a difference
for the final increment of loading which produced the
in consolidation of materials on either side of the
DFD.
fault; a reduction in resistance to fault movement
created by the lubricating effects of water, or the
(2) The method of incremental loading and soft-
erosion of fault materials by flowing water; and
ening of element properties allows the use of a
increase in hydrostatic pressures along the fault.
simplified static, linear-elastic finite element analysis
approach. Disadvantages of the procedure are that it
(1) Earth-fill dams, concrete gravity dams, and
gives only an approximation of the complex nonlinear
concrete arch dams have failed due to fault move-
behavior associated with fault displacement, it is time
ments. Failures of the Baldwin Hills earth-fill dam,
consuming, and it requires considerable judgment.
the Malpasset concrete arch dam, and the St. Francis
concrete gravity dam (James et al. 1988) can all be
(3) The example shown in Figure 2-2 is typical
attributed in part to forces and movements occurring
for a normal or reverse fault where the fault strike is
along fault surfaces. Although these forces and
approximately parallel to the dam axis so a two-
movements were not triggered by seismic activity, it
dimensional analysis is adequate. If the fault strike is
can be surmised that if a seismic event had occurred,
not close to parallel to the dam axis, or for a strike-
it would have likely triggered similar failures. These
slip fault, a three-dimensional analysis is required.
examples show that fault movement can cause a
2-4
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