Dingee Reservoir Final Seismic Report - East Bay Municipal Utility ...

Table 8
Seismic Slope Stability Analysis Results
Yield Coefficients (FS ~1.0)
Section Downstream, K y Upstream, K y
A-A’ 0.15 g 0.45 g
7.4.2 Earthquake-Induced Newmark Displacements
The seismic slope deformations were evaluated using a simplified Newmark sliding block
analysis (1965). The method is based on the assumption of rigid-perfectly plastic stress-strain
behavior and potential failure surface using a sliding-block type approach. In the sliding-block
approach, a slope is idealized as a rigid mass above a plane of sliding with specified yield
acceleration. If design acceleration levels of the block are lower than the yield acceleration, no
movement will occur along the sliding plane. If the design accelerations are higher than the
yield acceleration, there will be net movement between the block and the base, i.e.
displacements. The horizontal displacements of the sliding block are calculated by double
integrating the difference between the earthquake-induced average acceleration of the slide mass
and its yield acceleration with respect to time.
These time histories were then double integrated using the computer program SHAKE2000 to
develop the displacement time history for a yield coefficient of 0.15g. Plate 25 shows a plot of
the estimated deformation on the downstream slope of the dam for the three time histories
considered for both normal and reverse polarity cases that can be either the maximum or
minimum.
Table 9: Newmark Slope Displacement Estimates
Average of 3 Earthquakes
Yield Accel. Max Average Min
0.10 4.01 3.45 2.90
0.15 2.23 1.82 1.40
0.20 1.28 1.05 0.82
0.25 0.73 0.63 0.52
0.30 0.40 0.37 0.34
The figure below and Table 9 summarize the results of the Newmark slope deformation
estimates for the downstream slope verses different values of yield acceleration. The minimum,
maximum, and arithmetic average values of displacements are shown in Table 9. The maximum
refers to the higher of the normal or reverse polarity values from the site specific time history. A
conservative best estimate for the yield acceleration for the downstream slope from our stability
evaluations was 0.15g. We calculated the range for the average horizontal deformations to be
1.4 to 2.2 feet. We computed the average horizontal displacement to be about 3½ feet and the
corresponding crest settlement to be less than 2 feet for the historic high reservoir storage levels
of 772-feet.
Seismic Stability Evaluation Report
Dingee Reservoir Dam
19
August 2008