EP 1110-2-12
30 Sep 95
Chapter 8
stress analyses including the dynamic stress analysis
phase can be based on 2-D representation of the dam
Dynamic Analysis Methods and
cross-section. The design example provided in
Procedures
Appendix D presents a typical 2-D analysis. It dem-
onstrates the most common procedure where a 2-D
cross section of the structure is analyzed. However,
8-1. Attributes of Dynamic Analysis Methods
most principles and procedures applying to the 2-D
analysis also apply, or may be adapted to a 3-D anal-
A dynamic analysis method is identified by four
ysis discussed below.
attributes: (1) material behavior, (2) design earth-
quake definition, (3) dimensional representation of
(2) Three-dimensional (3-D) analysis. Occasion-
project conditions, and (4) model configuration. The
ally there are exceptions to the assumption justifying
first two attributes have been discussed in preceding
2-D analysis. Dams in narrow canyons with a large
chapters. They are briefly summarized below, fol-
enough ratio of height of the dam to distance between
lowed by a more detailed discussion of the latter two
abutments may cause significant two-way distribution
attributes.
of stresses. Dams which are aligned on a curved axis
may also allow significant transfer of stress into the
a. Material behavior. This attribute defines
abutments by arch action. Unusual shaped monoliths
material behavior as either (1) linear-elastic or
where there is substantial variation in the transverse
(2) nonlinear. Associated with each of these two
cross section across the width of the monolith also
types of material behavior is a unique criterion for
may not be analyzed satisfactorily by 2-D methods.
establishing acceptable response. Refer to para-
Another exception occurs when the trace of a poten-
graphs 2-2d, 2-2e, and 3-10.
tial fault slip is not parallel or nearly parallel to the
dam axis. In this situation, a 2-D foundation fault
b. Design earthquake definition. This attribute
displacement analysis will not adequately represent
establishes which of two options will be used to
project conditions. All of these situations indicate the
specify the free field ground motion for the design
need for 3-D analysis if the response is to be deter-
earthquakes. The options are (1) design response
mined to a reasonable degree of accuracy.
spectra and (2) ground motion time-history records.
Refer to Chapter 5 for details.
(a) Ground motion direction. The 3-D analysis
introduces additional variables into the dynamic anal-
c. Dimensional representation of project condi-
ysis. One important variable is determining the criti-
tions. This attribute defines whether project condi-
cal direction of the horizontal ground motion. This
tions will be represented in (1) two dimensions or
introduces a second horizontal component of ground
(2) three dimensions. Project conditions refer to the
motion into the dynamic analysis. The critical direc-
geometry of the dam, the foundation, and the reser-
tion is defined by transforming the design earthquake
voir that have an affect on the seismic response.
ground motion into a pair of orthogonal components.
Examples of features governing which of these two
Since no method exists to determine the critical direc-
options is appropriate include such things as layout of
tion directly, it usually becomes necessary to make
the dam axis, shape of the dam monoliths, foundation
some rough approximations.
conditions, and orientation of potential fault slips if
applicable.
(b) Simplified approach. This approach to deter-
mining the critical horizontal direction of ground
(1) Two-dimensional (2-D) analysis. In the
motion is to select two orthogonal direction vectors
analysis of most gravity dams, it is assumed that the
(in the horizontal plane), and assume that the critical
dam is composed of individual transverse vertical
tensile stress at various locations on the dam will
elements or cantilevers each of which carry loads to
occur when the direction of ground motion is near
the foundation without transfer of load between adja-
one or the other vector. Since the accompanying
cent elements. This assumption also applies to most
orthogonal ground motion component is small, the
RCC dams including dams with transverse joints that
stresses are assumed negligible and are neglected.
separate the dam into several monoliths, and dams
Often the direction vectors are assumed to be the
with monolithic construction that contain no trans-
upstream-downstream direction, and the cross-stream
verse joints. This assumption is usually valid, and
8-1
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