Geotechnical Engineering Circular No. 9 Design, Analysis, and Testing of Laterally Loaded Deep Foundations that Support Transportation Facilities



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Soldier Rev B
SEISMIC
8.3.1
Equivalent Static Seismic Force
Structures must be designed for seismic loads and liquefaction potential. AASHTO (2014) presents a site- specific procedure for approximating seismic loading by using a dimensionless elastic seismic response coefficient. This coefficient depends on the acceleration coefficient, site effects, and the predominant period of vibration of the structure. From this coefficient, the equivalent static horizontal seismic force,
P
e
(x) can be determined depending on the equivalent weight of the superstructure (Hannigan et al. 2016). Alternatively, more complex methods can be used for critical structures located in areas of high seismic risk. The following paragraphs present a description of the procedure for estimating seismic loads and guidance on the analysis procedures used in the seismic design of deep foundations. The first step is to define the site ground coefficient and spectral coefficients based onsite conditions. The site peak ground acceleration coefficient, PGA, short period spectral coefficient, S
s
, and long period spectral coefficient, S, are determined from USGS contour seismic maps, presented in AASHTO (2014) Section 3.10.2.1. The
USGS website has a tool for determining these coefficients based on location and site classification (Hannigan et al. 2016). Results of the subsurface investigation can be used to determine the site classification using methods outlined in AASHTO (2014) Section 3.10.3.1. Site factors corresponding to the zero-period, short-period and long-period ranges of acceleration are specified by site class for various PGA, S
s
, and S
1
coefficient values in AASHTO (2014) Section 3.10.3.2. Using values determined in the previous steps, the design five-percent-damped-design response spectrum can be created using procedures in AASHTO (2014) Section 3.10.3.3. The elastic seismic response coefficient can then be determined as follows


118 For periods less than or equal to, the elastic seismic coefficient for the mth mode of vibration, C
sm
, shall betaken as
𝐢𝐢
π‘ π‘ π‘šπ‘š
= 𝐴𝐴
𝑠𝑠
+ (𝑆𝑆
𝐷𝐷𝑆𝑆
βˆ’ 𝐴𝐴
𝑆𝑆
)(
𝑇𝑇
π‘šπ‘š
𝑇𝑇
0
) Equation 8-1) Where As
= F
pga
PGA.
S
DS
= F
a
S
s.
PGA = Peak ground acceleration coefficient on rock (Site Class BS s Horizontal response spectral acceleration coefficient at sec period on rock (Site Class B. Tm Period of vibration of mth modes. T Reference period used to define spectral shape = 0.2T
s
(s). Ts
= Corner period at which spectrum changes from being independent of period to being inversely proportional to period = S
D1
/S
DS
(s). For periods greater than or equal to T
0
and less than or equal to Ts, the elastic seismic coefficient, C
sm
, shall betaken as
𝐢𝐢
π‘ π‘ π‘šπ‘š
= Equation 8-2) For periods greater than Ts the elastic seismic coefficient, C
sm
, shall betaken as
𝐢𝐢
π‘ π‘ π‘šπ‘š
= Equation 8-3) Where SD F
v
S
1.
S
1
= Horizontal response spectral acceleration coefficient at 1.0 sec period on rock (Site Class B). The elastic seismic response coefficient can then be used to determine the equivalent static force using Equation 8-4 (Hannigan et al. 2016).
𝑃𝑃
𝑒𝑒
(π‘₯π‘₯) = 𝐢𝐢
π‘ π‘ π‘šπ‘š
π‘Šπ‘Š Equation 8-4) Where
P
e
(x) = Equivalent static horizontal seismic force acting on superstructure.
C
sm
= Elastic seismic response coefficient (dimensionless. W = Equivalent weight of the superstructure. Once the equivalent static force is determined, the structural engineer applies the force to the superstructure following the procedure described in AASHTO (2014) Section 4.7.4.3. Table 8-1 presents the seismic zone of abridge depending on the coefficient S
D1
(Hannigan et al. 2016). For multispan bridges with a seismic zone of 2 through 4, a liquefaction assessment is required.


119 The factored loads resulting from the seismic analysis should be applied to the foundation and analyzed as outlined in Chapter 5. Methods described in Chapters 6 and 7 can be used as appropriate for individual and group analyses.

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