# 3103F.4.2 Design Earthquake Motion Parameters

The earthquake ground motion parameters of peak ground acceleration, spectral acceleration and earthquake magnitude are modified for site amplification and near fault directivity effects. The resulting values are the Design Peak Ground Acceleration (DPGA), Design Spectral Acceleration (DSA) and Design Earthquake Magnitude (DEM).

For Site Classes A through E (Section 3103F.4.2.1), peak ground and design spectral accelerations may be obtained from:

- U.S. Geological Survey (USGS) published data as discussed in Section 3103F.4.2.2, or
- A site-specific probabilistic seismic hazard analysis (PSHA) as discussed in Section 3103F.4.2.3.

Site-specific PSHA is required for Site Class F.

Unless stated otherwise, the DSA values are for 5 percent damping; values at other levels may be obtained as per Section 3103F.4.2.9.

The appropriate probability levels associated with DPGA and DSA for different seismic performance levels are provided in Table 31F-4-1. Deterministic earthquake motions, which are used only for comparison to the probabilistic results, are addressed in Section 3103F.4.2.7.

The evaluation of Design Earthquake Magnitude (DEM), is discussed in Section 3103F.4.2.8. This parameter is required when acceleration time histories (Section 3103F.4.2.10) are addressed or if liquefaction potential (Section 3106F.4) is being evaluated.

The following Site Classes, defined in Section 3106F.2, shall be used in developing values of DSA and DPGA:

A, B, C, D, E and F

For Site Class F, a site-specific response analysis is required per Section 3103F.4.2.5.

Earthquake ground motion parameters can be obtained directly from the US Seismic Design Maps tool available at the USGS website (http://earthquake.usgs.gov/designmaps/us/application.php) for the site condition(s) appropriate for the MOT site and the selected probability of exceedance. For this purpose, select the "2013 ASCE 41" as the design code reference document (based on 2008 USGS hazard data available), "Custom" under the Earthquake Hazard Level option, required Probability of Exceedance (in 50 years), and appropriate Site Soil Classification(s) for the MOT site. The USGS tool directly provides the peak ground and spectral accelerations for the selected hazard level and site condition(s).

The alternative method of obtaining earthquake ground motion parameters, from the most current USGS data for selected hazard level and site condition(s), is permitted. If needed, the data for appropriate probability of exceedance may be obtained using the procedure described in Chapter 1 of FEMA 356 [3.1], and corrected for the MOT site as discussed in Section 3103F.4.2.4 or Section 3103F.4.2.5.

Site-specific Probabilistic Seismic Hazard Analysis (PSHA) shall use appropriate seismic sources and their characterization, attenuation relationships, probability of exceedance, and site soil conditions. Site-specific PSHA shall be conducted by a qualified California registered civil engineer with a California authorization as a geotechnical engineer per Section 3102F.3.4.8.

If site-specific PSHA is used for Site Classes A, B, C, D or E, results from the site-specific PSHA shall be compared with those from the USGS published data as described in Section 3103F.4.2.2. If the two sets of values differ significantly, a justification for using the characterization chosen shall be provided. If DPGA and DSA from site-specific PSHA are less than 80 percent of the values from USGS data, a peer review may be required.

When the MOT site class is different from the Site Classes B to C boundary, site amplification effects shall be incorporated in peak ground accelerations and spectral accelerations. This may be accomplished using a simplified method or a site-specific evaluation (Section 3103F.4.2.5).

For a given site class, the following procedure from Chapter 1 of FEMA 356 [3.1] presents a simplified method that may be used to incorporate the site amplification effects for peak ground acceleration and spectral acceleration computed for the Site Classes B and C boundary.

Calculate the spectral acceleration values at 0.20 and 1.0 second period:

(3-1)

(3-2)

**where:**F _{a}= site coefficient obtained from Table 31F-3-3 F _{v}= site coefficient obtained from Table 31F-3-4 S _{S}= short period (usually at 0.20 seconds) spectral acceleration value (for the boundary of Site Classes B and C) obtained using Section 3103F.4.2.2, or at the period corresponding to the peak in spectral acceleration values when obtained from Section 3103F.4.2.3 S _{1}= spectral acceleration value (for the boundary of Site Classes B and C) at 1.0 second period S _{XS}= spectral acceleration value obtained using the short period S _{s}and factored by Table 31F-3-3 for the site class under consideration.S _{X1}= spectral acceleration value obtained using the 1.0 second period S _{1}and factored by Table 31F-3-4 for the site class under consideration.(3-3)

where:

PGA _{X}= peak ground acceleration corresponding to the site class under consideration. When the value of PGA

_{X}is less than the peak ground acceleration obtained following Section 3103F.4.2.2 or Section 3103F.4.2.3, an explanation of the results shall be provided.- PGA
_{X}, S_{XS}, and S_{X1}constitute three spectral acceleration values for the site class under consideration corresponding to periods of 0, S_{S}(usually 0.2 seconds), and 1.0 second, respectively. The final response spectra, without consideration for near-fault directivity effects, values of S

_{a}for the site class under consideration may be obtained using the following equations (for 5 percent critical damping):(3-4)

**where:**T = Period corresponding to calculated S _{a}T _{0}= Period at which the constant acceleration and constant velocity regions of the design spectrum intersect for 0.2T

_{0}< T < T_{0}(3-5)

for T

_{0}> T_{0}(3-6)

**where:**(3-7)

The resulting PGA

_{X}is the DPGA. However, the S_{a}shall be modified for near-fault directivity effects, per Section 3103F.4.2.6 to obtain the final DSAs.

SITE CLASS | S_{s} | ||||

< 0.25 | 0.5 | 0.75 | 1.0 | > 1.25 | |

A | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 |

B | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 |

C | 1.2 | 1.2 | 1.1 | 1.0 | 1.0 |

D | 1.6 | 1.4 | 1.2 | 1.1 | 1.0 |

E | 2.5 | 1.7 | 1.2 | 0.9 | 0.9 |

F | * | * | * | * | * |

**Note:** Linear interpolation can he used to estimate values of F_{a} for intermediate values of S_{s}.

* Site-specific dynamic site response analysis shall be performed.

SITE CLASS | S_{1} | ||||

< 0.1 | 0.2 | 0.3 | 0.4 | > 0.5 | |

A | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 |

B | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 |

C | 1.7 | 1.6 | 1.5 | 1.4 | 1.3 |

D | 2.4 | 2.0 | 1.8 | 1.6 | 1.5 |

E | 3.5 | 3.2 | 2.8 | 2.4 | 2.4 |

F | * | * | * | * | * |

As an alternative to the procedure presented in Section 3103F.4.2.4, a site-specific response analysis may be performed. For Site Class F a site-specific response analysis is required. The analysis shall be either an equivalent linear or nonlinear analysis. Appropriate acceleration time histories as discussed in Section 3103F.4.2.10 shall be used.

In general, an equivalent linear analysis using, for example, SHAKE91 [3.2] is acceptable when the strength and stiffness of soils are unlikely to change significantly during the seismic shaking, and the level of shaking is not large. A nonlinear analysis should be used when the strength and/or stiffness of soils could significantly change during the seismic shaking or significant nonlinearity of soils is expected because of high seismic shaking levels.

The choice of the method used in site response analysis shall be justified considering the expected stress-strain behavior of soils under the shaking level considered in the analysis.

Site-specific site response analysis may be performed using one-dimensional analysis. However, to the extent that MOTs often involve slopes or earth retaining structures, the one-dimensional analysis should be used judiciously. When one-dimensional analysis cannot be justified or is not adequate, two-dimensional equivalent linear or nonlinear response analysis shall be performed. Site-specific response analysis results shall be compared to those based on the simplified method of Section 3103F.4.2.4 for reasonableness.

The peak ground accelerations obtained from this site-specific evaluation are DPGAs and the spectral accelerations are DSAs as long as the near-fault directivity effects addressed in Section 3103F.4.2.6 are appropriately incorporated into the time histories (Section 3103F.4.2.10).

When the site is 15 km (9.3 miles) or closer to a seismic source that can significantly affect the site, near-fault directivity effects shall be reflected in the spectral acceleration values and in the deterministic spectral acceleration values of Section 3103F.4.2.7.

Two methods are available for incorporating directivity effects:

- Directivity effects may be reflected in the spectral acceleration values in a deterministic manner by using well established procedures such as that described in Somerville, et al. [3.3]. The critical seismic sources and their characterization developed as part of the deterministic ground motion parameters (Section 3103F.4.2.7) should be used to evaluate the directivity effects. The resulting adjustments in spectral acceleration values may be applied in the probabilistic spectral acceleration values developed per Section 3103F.4.2.4 or 3103F.4.2.5. Such adjustment can be independent of the probability levels of spectral accelerations.
- Directivity effects may be incorporated in the results of site specific PSHA per Section 3103F.4.2.3. In this case, the directivity effects will also depend on the probability level of spectral accelerations.

If spectral accelerations are obtained in this manner, the effects of site amplification using either Section 3103F.4.2.4, 3103F.4.2.5 or an equivalent method (if justified) shall be incorporated.

Deterministic ground motions from "scenario" earthquakes may be used for comparison purposes. Deterministic peak ground accelerations and spectral accelerations may be obtained using the "Critical Seismic Source" with maximum earthquake magnitude and its closest appropriate distance to the MOT. "Critical Seismic Source" is that which results in the largest computed median peak ground acceleration and spectral acceleration values when appropriate attenuation relationships are used. The values obtained from multiple attenuation relationships should be used to calculate the median peak ground acceleration and spectral acceleration values.

For comparison, the values of peak ground accelerations and spectral accelerations may be obtained from the USGS maps [3.1], corresponding to the Maximum Considered Earthquake (MCE). In this case, the median values of peak ground acceleration and spectral acceleration values shall be 2/3 (see Section 1.6 of FEMA 356 [3.1]) of the values shown on the USGS maps.

The Design Earthquake Magnitude used in developing site-specific acceleration time histories (Section 3103F.4.2.10) or liquefaction assessment (Section 3106F.4) is obtained using either of the following two methods:

- The design earthquake may be selected as the largest earthquake magnitude associated with the critical seismic source. The distance shall be taken as the closest distance from the source to the site. The resulting design earthquake shall be associated with all DPGA values for the site, irrespective of probability levels.
- The design earthquake (DEQ) may be obtained for each DPGA or DSA value and associated probability level by determining the corresponding dominant distance and magnitude. These are the values of the distance and magnitude that contribute the most to the mean seismic hazards estimates for the probability of interest. They are usually determined by locating the summits of the 3-D surface of contribution of each small interval of magnitude and distance to the total mean hazards estimate. If this 3-D surface shows several modes with approximate weight of more than 20 percent of the total, several DEQs may be considered, and the DEQ leading to the most conservative design parameters shall be used.

Design Spectral Acceleration (DSA) values at damping other than 5 percent shall be obtained by using a procedure given in Chapter 1 of FEMA 356 [3.1], and is denoted as DSA_{d}. The following procedure does not include near-fault directivity effects.

(3-8)

(3-9)

(3-10)

**where:**

T | = | period |

T_{0} | = | S_{X1} /S_{XS} |

B_{S} | = | Coefficient used to adjust the short period spectral response, for the effect of viscous damping. |

B_{1} | = | Coefficient used to adjust one-second period spectral response, for the effect of viscous damping |

Values of B_{S} and B_{1} are obtained from Table 31F-3-5.

Such a procedure shall incorporate the near-fault directivity effects when the MOT is 15 km (9.3 miles) or closer to a significant seismic source.

DAMPING (%) | B_{s} | B_{1} |

< 2 | 0.8 | 0.8 |

5 | 1.0 | 1.0 |

10 | 1.3 | 1.2 |

20 | 1.8 | 1.5 |

30 | 2.3 | 1.7 |

40 | 2.7 | 1.9 |

> 50 | 3.0 | 2.0 |

**Note:** Linear interpolation should be used for damping values not specifically listed.

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