Análisis de la secuencia de consenso - Análisis de los Datos

3. Presentación y Análisis de Datos 29

3.2. Análisis de los Datos

3.2.1. Análisis de la secuencia de consenso

Bridges shall be designed to have a low probability of collapse but may suffer significant damage and disruption to service when subject to earthquake ground motions that have a seven percent probability of exceedance in 75 yr. Partial or complete replacement may be required. Higher levels of performance may be used with the authorization of the Bridge Owner.

Earthquake loads shall be taken to be horizontal force effects determined in accordance with the provisions of Article 4.7.4 on the basis of the elastic response coefficient, C_sm, specified in Article 3.10.4, and the equivalent weight of the superstructure, and adjusted by the response modification factor, R, specified in Article 3.10.7.1.

C3.10.1

The design earthquake motions and forces specified in these provisions are based on a low probability of their being exceeded during the normal life expectancy of a bridge. Bridges that are designed and detailed in accordance with these provisions may suffer damage, but should have low probability of collapse due to seismically induced ground shaking.

The principles used for the development of these Specifications are:

• Small to moderate earthquakes should be resisted within the elastic range of the structural components without significant damage;

3-52 AASHTOLRFDBRIDGE DESIGN SPECIFICATIONS

The provisions herein shall apply to bridges of conventional construction. The Owner shall specify and/or approve appropriate provisions for nonconventional construction. Unless otherwise specified by the Owner, these provisions need not be applied to completely buried structures.

Seismic effects for box culverts and buried structures need not be considered, except where they cross active faults.

The potential for soil liquefaction and slope movements shall be considered.

• Realistic seismic ground motion intensities and forces should be used in the design procedures; and

• Exposure to shaking from large earthquakes should not cause collapse of all or part of the bridge. Where possible, damage that does occur should be readily detectable and accessible for inspection and repair.

Bridge Owners may choose to mandate higher levels of performance for special bridges.

Earthquake loads are given by the product of the elastic seismic response coefficient C_sm and the equivalent weight of the superstructure. The equivalent weight is a function of the actual weight and bridge configuration and is automatically included in both the single-mode and multimode methods of analysis specified in Article 4.7.4. Design and detailing provisions for bridges to minimize their susceptibility to damage from earthquakes are contained in Sections 3, 4, 5, 6, 7, 10, and 11. A flow chart summarizing these provisions is presented in Appendix A3.

Conventional bridges include those with slab, beam, box girder, or truss superstructures, and single- or multiple-column piers, wall-type piers, or pile-bent substructures. In addition, conventional bridges are founded on shallow or piled footings, or shafts.

Substructures for conventional bridges are also listed in Table 3.10.7.1-1. Nonconventional bridges include bridges with cable-stayed/cable-suspended superstructures, bridges with truss towers or hollow piers for substructures, and arch bridges.

These Specifications are considered to be “force-based” wherein a bridge is designed to have adequate strength (capacity) to resist earthquake forces (demands).

In recent years, there has been a trend away from “force-based” procedures to those that are “displacement-based,”

wherein a bridge is designed to have adequate displacement capacity to accommodate earthquake demands. Displacement-based procedures are believed to more reliably identify the limit states that cause damage leading to collapse, and in some cases produce more efficient designs against collapse. It is recommended that the displacement capacity of bridges designed in accordance with these Specifications, be checked using a displacement-based procedure, particularly those bridges in high seismic zones. The AASHTO Guide Specifications for LRFD Seismic Design (AASHTO, 2009), are

“displacement-based.”

SECTION 3:LOADS AND LOAD FACTORS 3-53

3.10.2—Seismic Hazard

The seismic hazard at a bridge site shall be characterized by the acceleration response spectrum for the site and the site factors for the relevant site class.

The acceleration spectrum shall be determined using either the General Procedure specified in Article 3.10.2.1 or the Site Specific Procedure specified in Article 3.10.2.2.

A Site-Specific Procedure shall be used if any one of the following conditions exist:

• The site is located within 6 mi. of an active fault,

• The site is classified as Site Class F (Article 3.10.3.1),

• Long-duration earthquakes are expected in the region,

• The importance of the bridge is such that a lower probability of exceedance (and therefore a longer return period) should be considered.

If time histories of ground acceleration are used to characterize the seismic hazard for the site, they shall be determined in accordance with Article 4.7.4.3.4b.

3.10.2.1—General Procedure

The General Procedure shall use the peak ground acceleration coefficient (PGA) and the short- and long-period spectral acceleration coefficients (S_S and S₁ respectively) to calculate the spectrum as specified in Article 3.10.4. Values of PGA, S_S and S₁ shall be determined from either Figures 3.10.2.1-1 to 3.10.2.1-21 as appropriate, or from state ground motion maps approved by the Owner.

Linear interpolation shall be used for sites located between contour lines or between a contour line and a local maximum or minimum.

The effect of site class on the seismic hazard shall be as specified in Article 3.10.3.

C3.10.2.1

Values for the coefficients PGA, S_S and S₁ are expressed in percent in Figures 3.10.2.1-1 to 3.10.2.1-21. Numerical values are obtained by dividing contour values by 100. Local maxima and minima are given inside the highest and lowest contour for a particular region.

The above coefficients are based on a uniform risk model of seismic hazard. The probability that a coefficient will not be exceeded at a given location during a 75-yr period is estimated to be about 93 percent, i.e., a seven percent probability of exceedance. The use of a 75-yr interval to characterize this probability is an arbitrary convenience and does not imply that all bridges are thought to have a useful life of 75 yr.

It can be shown that an event with the above probability of exceedance has a return period of about 1,000 yr and is called the design earthquake. Larger earthquakes than that implied by the above set of coefficients have a finite probability of occurrence throughout the United States.

Values for the ground coefficient (PGA) and the spectral coefficients (S_S and S₁) are also available on the USGS 2007 Seismic Parameters CD, which is included with this book. Coefficients are given by the longitude and latitude of the bridge site, or by the zip code for the site.

In lieu of using the national ground motion maps in Figures 3.10.2.1-1 to 3.10.2.1-21, values for the coefficients PGA, SS and S1 may be derived from approved state ground motion maps. To be acceptable, the development of state maps should conform to the following:

• The definition of design ground motions should be the same as described in Articles 3.10.1 and 3.10.2.

• Ground motion maps should be based on a detailed analysis demonstrated to lead to a quantification of ground motion, at a regional scale, that is as accurate or more so, as is achieved in the national maps. The analysis should include: characterization of seismic sources and ground motion that incorporates current scientific knowledge; incorporation of uncertainty in seismic source models, ground motion models, and parameter values used in the analysis; and detailed documentation of map development.

Detailed peer review should be undertaken as deemed appropriate by the Owner. The peer review process should include one or more individuals from the U.S. Geological Survey who participated in the development of the national maps.

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Figure 3.10.2.1-1—Horizontal Peak Ground Acceleration Coefficient for the Conterminous United States (PGA) with Seven Percent Probability of Exceedance in 75 yr (Approx. 1000-yr Return Period)

Figure 3.10.2.1-1 (continued)—Horizontal Peak Ground Acceleration Coefficient for the Conterminous United States (PGA) with Seven Percent Probability of Exceedance in 75 yr (Approx. 1000-yr Return Period)

Figure 3.10.2.1-2—Horizontal Response Spectral Acceleration Coefficient for the Conterminous United States at Period of 0.2 s (SS) with Seven Percent Probability of Exceedance in 75 yr (Approx. 1000-yr Return Period) and Five Percent Critical Damping

Figure 3.10.2.1-2 (continued)—Horizontal Response Spectral Acceleration Coefficient for the Conterminous United States at Period of 0.2 s (SS) with Seven Percent Probability of Exceedance in 75 yr (Approx. 1000-yr Return Period) and Five Percent Critical Damping

Figure 3.10.2.1-3—Horizontal Response Spectral Acceleration Coefficient for the Conterminous United States at Period of 1.0 s (S1) with Seven Percent Probability of Exceedance in 75 yr (Approx. 1000-yr Return Period) and Five Percent Critical Damping

Figure 3.10.2.1-3 (continued)—Horizontal Response Spectral Acceleration Coefficient for the Conterminous United States at Period of 1.0 s (S₁) with Seven Percent Probability of Exceedance in 75 yr (Approx. 1000-yr Return Period) and Five Percent Critical Damping

LRFDBRIDGEDESIGNSPECIFICATIONS

ontal Peak Ground Acceleration Coefficient for Region 1 (PGA) with Seven Percent Probability r (Approx. 1000-yr Return Period)

TION3:LOADS AND LOAD FACTORS3-63

ontal Peak Ground Acceleration Coefficient for Region 1 (PGA) with Seven Percent of Exceedance in 75 yr (Approx. 1000-yr Return Period)

LRFDBRIDGEDESIGNSPECIFICATIONS

re 3.10.2.1-5—Horizontal Response Spectral Acceleration Coefficient for Region 1 at Period of 0.2 s (SS) with of Exceedance in 75 yr (Approx. 1000-yr Return Period) and Five Percent Critical Damping

TION3:LOADS AND LOAD FACTORS3-65 re 3.10.2.1-5 (continued)—Horizontal Response Spectral Acceleration Coefficient for Region 1 at Period of 0.2 s (SS) ith Seven Percent Probability of Exceedance in 75 yr (Approx. 1000-yr Return Period) and Five Percent Critical

LRFDBRIDGEDESIGNSPECIFICATIONS

re 3.10.2.1-6—Horizontal Response Spectral Acceleration Coefficient for Region 1 at Period of 1.0 s (S1) with of Exceedance in 75 yr (Approx. 1000-yr Return Period) and Five Percent Critical Damping

TION3:LOADS AND LOAD FACTORS3-67 re 3.10.2.1-6 (continued)—Horizontal Response Spectral Acceleration Coefficient for Region 1 at Period of 1.0 s (S1) ith Seven Percent Probability of Exceedance in 75 yr (Approx. 1000-yr Return Period) and Five Percent Critical

LRFDBRIDGEDESIGNSPECIFICATIONS

ontal Peak Ground Acceleration Coefficient for Region 2 (PGA) with Seven Percent Probability r (Approx. 1000-yr Return Period)

TION3:LOADS AND LOAD FACTORS3-69 re 3.10.2.1-8—Horizontal Response Spectral Acceleration Coefficient for Region 2 at Period of 0.2 s (SS) with of Exceedance in 75 yr (Approx. 1000-yr Return Period) and Five Percent Critical Damping

LRFDBRIDGEDESIGNSPECIFICATIONS

re 3.10.2.1-9—Horizontal Response Spectral Acceleration Coefficient for Region 2 at Period of 1.0 s (S1) with of Exceedance in 75 yr (Approx. 1000-yr Return Period) and Five Percent Critical Damping

TION3:LOADS AND LOAD FACTORS3-71

ontal Peak Ground Acceleration Coefficient for Region 3 (PGA) with Seven Percent of Exceedance in 75 yr (Approx. 1000-yr Return Period)

LRFDBRIDGEDESIGNSPECIFICATIONS

ontal Response Spectral Acceleration Coefficient for Region 3 at Period of 0.2 s (SS) with of Exceedance in 75 yr (Approx. 1000-yr Return Period) and Five Percent Critical Damping

TION3:LOADS AND LOAD FACTORS3-73

ontal Response Spectral Acceleration Coefficient for Region 3 at Period of 1.0 s (S1) with of Exceedance in 75 yr (Approx. 1000-yr Return Period) and Five Percent Critical Damping

Figure 3.10.2.1-13—Horizontal Peak Ground Acceleration Coefficient for Region 4 (PGA) with Seven Percent Probability of Exceedance in 75 yr (Approx. 1000-yr Return Period)

Figure 3.10.2.1-14—Horizontal Response Spectral Acceleration Coefficients for Region 4 at Periods of 0.2 s (S_S) and 1.0 s (S₁) with Seven Percent Probability of Exceedance in 75 yr (Approx. 1000-yr Return Period) and Five Percent Critical Damping

Figure 3.10.2.1-15—Horizontal Peak Ground Acceleration Coefficient for Hawaii (PGA) with Seven Percent Probability of Exceedance in 75 yr (Approx. 1000-yr Return Period)

Figure 3.10.2.1-16—Horizontal Response Spectral Acceleration Coefficients for Hawaii at Periods of 0.2 s (S_S) and 1.0 s (S₁) with Seven Percent Probability of Exceedance in 75 yr (Approx. 1000-yr Return Period) and Five Percent Critical Damping

LRFDBRIDGEDESIGNSPECIFICATIONS

ontal Peak Ground Acceleration Coefficient for Alaska (PGA) with Seven Percent Probability r (Approx. 1000-yr Return Period)

TION3:LOADS AND LOAD FACTORS3-79

ontal Response Spectral Acceleration Coefficient for Alaska at Period of 0.2 s (SS) with of Exceedance in 75 yr (Approx. 1000-yr Return Period) and Five Percent Critical Damping

LRFDBRIDGEDESIGNSPECIFICATIONS

ontal Response Spectral Acceleration Coefficient for Alaska at Period of 1.0 s (S1) with of Exceedance in 75 yr (Approx. 1000-yr Return Period) and Five Percent Critical Damping

Figure 3.10.2.1-20—Horizontal Peak Ground Acceleration Coefficient for Puerto Rico, Culebra, Vieques, St. Thomas, St. John, and St. Croix (PGA) with Seven Percent Probability of Exceedance in 75 yr (Approx. 1000-yr Return Period)

3-82 AASHTOLRFDBRIDGE DESIGN SPECIFICATIONS

Figure 3.10.2.1-21—Horizontal Response Spectral Acceleration Coefficients for Puerto Rico, Culebra, Vieques, St. Thomas, St. John, and St. Croix at Periods of 0.2 s (SS) and 1.0 s (S1) with Seven Percent Probability of Exceedance in 75 yr (Approx. 1000-yr Return Period) and Five Percent Critical Damping

SECTION 3:LOADS AND LOAD FACTORS 3-83

3.10.2.2—Site Specific Procedure

A site-specific procedure to develop design response spectra of earthquake ground motions shall be performed when required by Article 3.10.2 and may be performed for any site. The objective of the site-specific probabilistic ground-motion analysis should be to generate a uniform-hazard acceleration response spectrum considering a seven percent probability of exceedance in 75 yr for spectral values over the entire period range of interest. This analysis should involve establishing:

• The contributing seismic sources;

• An upper-bound earthquake magnitude for each source zone;

• Median attenuation relations for acceleration response spectral values and their associated standard deviations;

• A magnitude-recurrence relation for each source zone; and

• A fault-rupture-length relation for each contributing fault.

Uncertainties in source modeling and parameter values shall be taken into consideration. Detailed documentation of ground-motion analysis is required and shall be peer reviewed.

Where analyses to determine site soil response effects are required by Articles 3.10.3.1 for Site Class F soils, the influence of the local soil conditions shall be determined based on site-specific geotechnical investigations and dynamic site response analyses.

For sites located within 6 miles of an active surface or a shallow fault, as depicted in the USGS Active Fault Map, studies shall be considered to quantify near-fault effects on ground motions to determine if these could significantly influence the bridge response.

A deterministic spectrum may be utilized in regions having known active faults if the deterministic spectrum is no less than two-thirds of the probabilistic spectrum in the region of 0.5TF to 2TF of the spectrum where TF is the bridge fundamental period. Where use of a deterministic spectrum is appropriate, the spectrum shall be either:

• the envelope of a median spectra calculated for characteristic maximum magnitude earthquakes on known active faults; or

• a deterministic spectra may be defined for each fault, and, in the absence of a clearly controlling spectra, each spectrum should be used.

C3.10.2.2

The intent in conducting a site-specific probabilistic ground motion study is to develop ground motions that are more accurate for the local seismic and site conditions than can be determined from national ground motion maps and the procedure of Article 3.10.2.1.

Accordingly, such studies should be comprehensive and incorporate current scientific interpretations at a regional scale. Because there are typically scientifically credible alternatives for models and parameter values used to characterize seismic sources and ground-motion attenuation, it is important to incorporate these uncertainties formally in a site-specific probabilistic analysis. Examples of these uncertainties include seismic source location, extent and geometry; maximum earthquake magnitude; earthquake recurrence rate; and ground-motion attenuation relationship.

Near-fault effects on horizontal response spectra include:

• Higher ground motions due to the proximity of the active fault;

• Directivity effects that increase ground motions for periods greater than 0.5 s if the fault rupture propagates toward the site; and

• Directionality effects that increase ground motions for periods greater than 0.5 s in the direction normal (perpendicular) to the strike of the fault.

If the active fault is included and appropriately modeled in the development of national ground motion maps, then the first effect above is already included in the national ground motion maps. The second and third effects are not included in the national maps. These effects are significant only for periods longer than 0.5 s and normally would be evaluated only for essential or critical bridges having natural periods of vibration longer than 0.5 s. Further discussions of the second and third effects are contained in Somerville (1997) and Somerville et al. (1997).

The fault-normal component of near-field (D < 6 mi.) motion may contain relatively long-duration velocity pulses which can cause severe nonlinear structural response, predictable only through nonlinear time-history analyses. For this case the recorded near-field horizontal components of motion need to be transformed into principal components before modifying them to be response-spectrum-compatible.

The ratio of vertical-to-horizontal ground motions increases for short-period motions in the near-fault environment.

Where response spectra are determined from a site- specific study, the spectra shall not be lower than two-thirds of the response spectra determined using the general procedure of Article 3.10.2.1 in the region of 0.5TF to 2TF of the spectrum where TF is the bridge fundamental period.

3.10.3—Site Effects

Site classes and site factors specified herein shall be used in the General Procedure for characterizing the seismic hazard specified in Article 3.10.4.

C3.10.3

The behavior of a bridge during an earthquake is strongly related to the soil conditions at the site. Soils can amplify ground motions in the underlying rock, sometimes by factors of two or more. The extent of this amplification is dependent on the profile of soil types at the site and the intensity of shaking in the rock below.

Sites are classified by type and profile for the purpose of defining the overall seismic hazard, which is quantified as the product of the soil amplification and the intensity of shaking in the underlying rock.

3.10.3.1—Site Class Definitions

A site shall be classified as A though F in accordance with the site class definitions in Table 3.10.3.1-1. Sites shall be classified by their stiffness as determined by the shear wave velocity in the upper 100 ft. Standard Penetration Test (SPT), blow counts and undrained shear strengths of soil samples from soil borings may also be used to classify sites as indicated in Table 3.10.3.1-1.

C3.10.3.1

Steps that may be followed to classify a site are given in Table C3.10.3.1-1.

Table 3.10.3.1-1—Site Class Definitions

Site

Class Soil Type and Profile

A Hard rock with measured shear wave velocity, v_s> 5,000 ft/s B Rock with 2,500 ft/sec < v < 5,000 ft/s _s

C Very dense soil and soil rock with 1,200 ft/sec < v < 2,500 ft/s, _s or with either N > 50 blows/ft, or s > 2.0 ksf _u

D Stiff soil with 600 ft/s < v < 1,200 ft/s, or with either 15 < N < 50 blows/ft, _s or 1.0 < s < 2.0 ksf _u

E Soil profile with v < 600 ft/s or with either N < 15 blows/ft or _s s < 1.0 ksf, or any profile with more _u than 10 ft of soft clay defined as soil with PI > 20, w > 40 percent and s < 0.5 ksf _u

F Soils requiring site-specific evaluations, such as:

• Peats or highly organic clays (H > 10 ft of peat or highly organic clay where H = thickness of soil)

• Very high plasticity clays (H > 25 ft with PI > 75)

• Very thick soft/medium stiff clays (H >120 ft)

Exceptions: Where the soil properties are not known in sufficient detail to determine the site class, a site investigation shall be undertaken sufficient to determine the site class. Site classes E or F should not be assumed unless the authority having jurisdiction determines that site classes E or F could be present at the site or in the event that

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