Maximum Seismic Coefficients for Design

C.X.4.3

The maximum seismic coefficient (kmax)

for computation of seismic lateral wall loads shall be determined on the basis of the PGA at

the ground surface (i.e., kmax = Fpga PGA),

The definition of kmax is identical to As

used in the current AASHTO LRFD

Bridge Design Specifications. Different

except for walls founded on Category A soil

(hard rock) where kmax shall be based on 1.2

times the site-adjusted peak ground acceleration coefficient (i.e., kmax = 1.2 Fpga

PGA). If permitted by the Owner, wall-height adjustment factors are allowed for walls greater than 20 feet in height. For wall heights greater than 70 feet, special seismic design studies shall be performed.

proposed Specifications to be consistent with historic use of “k” in the evaluation of seismic earth pressures.

The designer can conservatively kmax

for design; however, various studies have shown that the ground motions in the mass of soil behind the wall will often be lower than the kmax at the ground surface,

particularly for taller walls. The following discussions outline the adjustment that can be used by the designer to account for this effect and the rationale for the adjustment.

Height-Dependent Adjustments for Wall Heights from 20 to 70 feet

For values of H greater than 20 feet but less than 70 feet, the seismic coefficient used to compute lateral loads acting on a freestanding retaining wall may be modified to account for the effects of spatially varying ground motions behind the wall, using the following equation:

kav = α kmax (C.X.4.3-1)

where

kmax = Fpga PGA

α = fill height reduction factor For Site Category C, D, and E

α = 1 + 0.01H [(0.5β) - 1] C.X.4.3-2) where

H = fill height (feet)

β= FvS1/ kmax

For Site Category A and B (hard and soft

rock foundation soils), the values of α

given by Equation C.X.4.3-1 is increased by a factor of 1.2.

Height-Dependent Adjustments for Wall Heights > 70 feet

For wall heights greater than 70 feet, special seismic design studies involving the use of numerical models should be conducted. These special studies are required in view of the potential consequences of failure of these very tall walls, as well as limitations in the simplified wave scattering methodology.

Basis for Height Adjustment Factor

The basis for the height-dependent reduction factor described above is related to the response of the soil mass behind the retaining wall. Common practice in selecting the seismic coefficient for retaining wall design has been to assume rigid body soil response in the backfill behind a retaining wall. In this approach the maximum seismic coefficient (kmax) is assumed equal to the

Fpga PGA when evaluating lateral forces

acting on an active pressure failure zone. Whereas this assumption may be reasonable for wall heights less than about 20 feet, for higher walls, the magnitude of accelerations in soils behind the wall will vary spatially as shown schematically in Figure C.X.4-2.

The nature and variation of the incoherent ground motions is complex and will be influenced by the dynamic response of the wall-soil system to the input earthquake ground motions. In addition to wall height the acceleration distribution will depend on factors such as the frequency characteristics of the input ground motions, the stiffness contrast between backfill and foundation soils, and wall slope. From a design standpoint, the net effect of the spatially varying ground motions can be represented by an averaging process over a potential active pressure zone, leading to a time history of average acceleration

and hence a maximum average acceleration or seismic coefficient as shown in Figure C.X.4-2.

To evaluate this averaging process, the results of a series of analytical studies are documented in the NCHRP 12-70 Report (NCHRP, 2008). An evaluation of these results forms the basis for the simplified equations C.X.4.3-1 and C.X.4.3-2. The analytical studies included wave scattering analyses assuming elastic soil media using different wall heights and slopes and a range of earthquake time histories. The acceleration time histories simulated spectral shapes representative of Western United States (WUS) and Central and Eastern United States (CEUS) sites and reflected different earthquake magnitudes and site conditions.

Additional height-dependent, one- dimensional SHAKE (Schnaebel et al., 1972) analyses were also conducted to evaluate the influence of nonlinear soil behavior and stiffness contrasts between backfill and foundation soils. These studies were also calibrated against finite element studies for MSE walls documented by Segrestin and Bastick (1988), which form the basis for the average maximum acceleration equation

(a function of As) given in the current

AASHTO LRFD Bridge Design

Specifications for MSE walls.

The results of these studies demonstrate that the ratio of the maximum average seismic coefficient (kav) to kmax (the α factor) is primarily

dependent on the wall height and the

shape of the acceleration spectra (the β

factor). The acceleration level has a lesser effect. It was also found that equations C.X.4.3-1 and C.X.4.3-2 could be applied to slopes.

Figure C.X.4-2 Average Seismic Coefficient Concept

X.4.4 Displacement-Related Seismic