Enfoques de aprendizaje y rendimiento académico

Y.5.1 General C.Y.5.1

Seismic loads in the slope shall be determined using a seismic coefficient estimated in accordance with simplified method summarized in Article X.4 or using numerical modeling methods, subject to the approval of the Owner. A load factor γp = 1.0

shall be used in conjunction with the methodology give in this Section of the Specifications to determine the seismic loads.

The load factor for live load in Extreme

Event I (per AASHTO LRFD Bridge Design

Specifications Section 3) shall be determined

on a project-specific basis, except where the slope supports a heavily traveled roadway. For this case live loads shall be included in seismic design, and the load factor (γp) for live load

shall be at least equal to 0.5.

As in the case of retaining walls (Article X.4.4), where limited (e.g., 1 to 2 inches) permanent displacement of the slope is allowed

The simplified method described in Article X.4 allows determination of the seismic coefficient (kmax = Fpga PGA) within the slope.

Adjustment factors are included within the methodology described in Article X.4 for incorporating permanent soil movement. Effects of wave scattering may also be considered if the slope is greater than 20 feet in height (i.e., kav = α kmax).

The seismic coefficient after adjustment for scattering and permanent soil movement is multiplied by the mass of the soil within the potential failure zone to define the inertial load during seismic loading. Most commercially available slope stability computer programs allow this load and the resulting pseudo-static seismic stability to be determined by specifying the seismic coefficient and allowing the program to search for critical failure surfaces.

by the Owner, a 50% reduction in the maximum seismic coefficient shall be permitted.

For sites that are not susceptible to liquefaction or are not comprised of sensitive soil conditions, a seismic analysis of a cut or fill slope is not required if the site-adjusted peak ground acceleration coefficient (i.e., Fpga

PGA) at the ground surface for the site is less than the values listed in the following table, unless allowed or required otherwise by the Owner.

Slope Angle Fpga PGA

3H:1V 0.3 2H:1V 0.2 If liquefiable or sensitive soils exist within

or support the slope, the minimum acceptable acceleration without requiring a stability analysis shall be 0.15g, as long as the SPT blowcount measured in the field at an energy

of 60% (N60) is greater than 5 blows per foot

(bpf).

shaking are generally neglected from the seismic stability assessment. The rationale for neglecting the vertical acceleration is that for soils with strengths dominated by friction the cyclic increases and decreases in normal stresses on potential failure planes (and associated increases and decreases in strength) due to vertical acceleration time histories, tend to cancel out the net effects on incremental slope displacements in, for example, a Newmark displacement analysis. In the case of cohesive soils, changes in normal stresses will not affect soil strengths, and hence the vertical accelerations have minimal effect on displacements.

The location of the critical failure surface during seismic loading will usually be flatter than the failure surface determined for gravity loading. Therefore, the computer analyses should be allowed to “search” for the critical surface rather than fixing the failure surface for gravity loading and then applying the seismic coefficient.

When using scattering concepts in Article X.4.3, it is necessary to estimate the height of the slope involved in the wave scattering phenomenon. The height of the slope is defined as the maximum distance between the ground surface and the potential failure surface. As with the design of retaining walls, a scattering factor of 1.0 should be used if the height of the slope is less than 20 feet.

The slope angle used in screening refers to the average angle of the slope above the retaining wall. If the slope is characterized by a non-uniform slope condition, the average angle of the slope should be used. Linear interpolation can be used when determining the need for a seismic analysis for slopes between those given in the table.

For critical slopes the simplified method given in Article X.4 may not adequately model the geometry or soil conditions within the slope. In this case numerical methods involving the use of 2-dimensional finite element or finite difference methods offers an alternative approach for determining the

seismic loads in the slope. Because of the stoctastic nature of earthquake ground motions, the earthquake demand for dynamic analyses needs to utilize multiple sets of input records. Current practice is to use either three or seven earthquake records during numerical modeling. If three records are used, the results are enveloped to define the expected response. This approach is generally considered conservative, and the trend has been to conduct analyses for more sets of input motions so that the results are statistically more stable (i.e., achieving a reliable mean and standard deviation). Experience has been that it is necessary to analyze a minimum of seven sets of spectrum-compatible input motions to obtain a statistically stable estimate of response. The response spectra for these records, whether three or seven are used, should be consistent with the design response spectra at rock level.

A cutoff on the lower level of earthquake loading requiring a seismic analysis was set on the basis of the slope angle. For most slopes meeting the static C/D ratio of 1.0 using the static resistance factors of 0.75 or 0.65 as given

in Section 11 of the AASHTO LRFD Bridge

Design Specifications (i.e., FS = 1.3 and 1.5,

respectively), the inertial force resulting from kmax will still result in a C/D ratio of 1.0 or

higher (i.e., FS ≥ 1.0). For this condition the slope is predicted to be stable under seismic loading.

If liquefaction is possible at a site because of low SPT blowcount or CPT end resistance values, the no-analysis ground acceleration limit must be reduced to a lower value. As long as the soils are not extremely loose (e.g., SPT blowcount < 5 bpf), liquefaction is very unlikely for peak ground surface acceleration levels of 0.15g or less. For convenience the SPT blowcount for this cutoff is the field value adjusted for 60% energy (i.e., N60).

Y.6 LIMIT STATES AND RESISTANCE FACTORS

Y.6.1 General C.Y.6.1

Seismic performance of slopes and embankments shall be evaluated in accordance with the requirements of Extreme Event I given in Table 3.4.1 of the Specifications. Except as required otherwise by the Owner, the

resistance factor (φr) during the seismic

stability assessment shall be 1.0, except where M > 7.5 as discussed in Article Y4.1.1.

A slope not requiring seismic stability analyses shall demonstrate a capacity-to- demand ratio of greater than 1.0 using resistance factors of 0.75 for natural slopes and 0.65 for engineered slopes (i.e., FS > 1.3 for natural slopes and 1.5 for engineered slopes).

A resistance factor of 1.0 is used in the global stability analysis. While use of a resistance factor of less than 1.0 in limit equilibrium seismic stability analysis will be conservative, for the reasons given in Article X.6 and in view of the unlikely occurrence of the design earthquake, use of a resistance factor of 1.0 is recommended. Lower resistance factors can lead to costly mitigation procedures that have a low likelihood of being needed.

As discussed in Article Y.4.1.1, a reduction in strength using a factor of 0.9 is recommended in the stability analyses if M > 7.5. This reduction is included to account for potential cyclic degradation in strength and is not simply introduced to be conservative.

The use of a resistance factor of 1.0 is particularly critical for displacement-based design methods. If a resistance factor is introduced for displacement-based analyses, estimates of displacements will normally be too high, and therefore, potentially lead to unrealistic decisions regarding the need for modifications to the structure or ground to resist these movements.