March 2016

Structural engineers know the mechanics of the seismic provisions of the *International Building Code* (IBC) and ASCE 7-10. They know how to get S_{s} and S_{1} for a site and apply the equations to calculate a seismic response coefficient (C_{s}) that is used to calculate the seismic base shear, which is used to size the seismic resisting elements of the building. However, many do not understand the background behind the equations and the coefficients.

The purpose of this article is to establish a foundation for a common understanding as an aid in discussing seismic concepts with owners, clients, and other engineers.

## Earthquakes vs. Ground Motion

### Talking Point #1

Engineers design for a specific ground motion shaking intensity, not a specific earthquake.

### Talking Point #2

The IBC mandates the Maximum Considered Earthquake (MCE_{R}) ground motion that must be considered in the design process.

Earthquakes cause the earth to shake. It is the ground shaking caused by the earthquake that causes building movement and damage. The code writers didn’t do us any favors by using the terms *Maximum Considered Earthquake* and *Design Earthquake* (sometimes referred to as the Design Basis Earthquake). Using these terms alone implies that we are designing for a specific earthquake. The MCE_{R} is a ground shaking intensity, given as a response acceleration, which is generally caused by a range of earthquakes of different magnitudes from several earthquake sources, or in some areas, a single earthquake from a dominant earthquake source. Engineers should be clear and use the phrase *Maximum Considered Earthquake Ground Motion* to emphasize that it is the ground motion shaking intensity we are designing for and not the earthquake.

### Talking Point #3

Beginning in 2012, the IBC established a risk-modified MCE_{R}, which is based on a uniform risk of building collapse (1% in 50 years, or 1/5000 per year), and results in the same risk of a building collapse in New York, Atlanta, Seattle, and the rest of the country.

The Uniform Hazard MCE ground shaking intensity is no longer used in building design (see Talking Point #16). To get the MCE_{R}, the Uniform Hazard ground shaking intensity is increased or decreased until there is a 1% probability of building collapse in 50 years. In most areas of the country, the code shaking intensity is reduced from the Uniform Hazard, meaning that a shaking intensity matching the MCE_{R} is likely to occur more often than a shaking intensity matching the older MCE.

### Talking Point #4

The MCE_{R} is the ground shaking intensity that the IBC requires to be considered, but larger shaking intensities are possible. In reality, the MCE_{R} should be thought of as the *minimum* ground shaking intensity that must be considered.

### Talking Point #5

A specific fault rupture or a specific magnitude earthquake may not cause an MCE_{R} level ground shaking intensity. A fault could rupture many times before it results in the MCE_{R} level ground shaking intensity being reached or exceeded. The maximum expected earthquake on a fault may not cause an MCE_{R} level ground shaking intensity, but conversely, it is also possible that it could cause the MCE_{R} level ground shaking intensity to be exceeded.

### Talking Point #6

Even though the MCE_{R} is the *considered* ground shaking intensity, building design and performance is usually based on an intensity of 2/3 of the MCE_{R} (see Talking Point #8), which this article will call the design ground shaking intensity.

## Code Performance Expectations

It is important to understand the life safety performance expectations of the code and to be able to clearly communicate these to clients and building owners.

### Talking Point #7

Although the term Life Safety has specific meaning to engineers, it can have other interpretations and be misconstrued by clients and owners.

Three key damage states not specifically mentioned but implied by the IBC are Immediate Occupancy, Life Safety, and Collapse Prevention. A building owner who would be satisfied with a Collapse Prevention damage state may say that they want a Life Safety damage state because they misunderstand the terms. Here are simple definitions of performance expectations:

*Immediate Occupancy*: A building can be used after some cleanup occurs and can be occupied during the repairs to fix building damage.*Life Safety*: A building could have significant structural damage, but it has reserve structural capacity to resist aftershocks. The building may not be able to be occupied until after repairs are made.*Collapse Prevention*: A building has been pushed to the limits of its strength and stiffness and is on the verge of collapse. Aftershocks may cause the building to collapse.

### Talking Point #8

For an accurate discussion of performance expectation, engineers must provide clients and building owners with a clear understanding of the expected building performance *and* the ground shaking intensity at which that building performance is expected to occur.

The implied safety objective of the IBC is to achieve Life Safety if the building site experiences a ground shaking intensity equal to the design ground shaking intensity (2/3 MCE_{R}) and to achieve Collapse Prevention if the building site experiences a ground shaking intensity equal to the MCE_{R}.

The IBC uses a Seismic Importance Factor of 1.5 for essential facilities to increase the strength of the building and reduce the ductility demand on the structure. The objective for an essential facility, such as a hospital, is to achieve Immediate Occupancy if the building site experiences a ground shaking intensity equal to the design ground shaking intensity (2/3 MCE_{R}) and to achieve Life Safety if the building site experiences a ground shaking intensity equal to the MCE_{R}. Note that a hospital may not be operational if it experiences the MCE_{R} ground shaking intensity.

### Talking Point #9

The risk of collapse is reduced for buildings that are designed using Seismic Importance Factors of 1.25 or 1.5. Seismic Importance Factors are intended to improve the building performance at the design ground shaking intensity (2/3 MCE_{R}) and at the MCE_{R} ground shaking intensity. This is accomplished by reducing the Response Modification Factor (R). Note that the Seismic Importance Factor is not applied to the demand coefficient (S_{DS} or S_{D1}).

### Talking Point #10

The IBC allows for a very small risk of building collapse.

1) There is a 1% in 50 years probability (1/5000 per year) that a building will collapse due to a seismic event.

2) Up to 10% of buildings designed and constructed per the IBC could experience some collapse when subjected to the MCE_{R} ground shaking intensity.

### Talking Point #11

Nonstructural components are designed for the design ground shaking intensity (2/3MCE_{R}), and there are no performance goals for a MCE_{R} level ground shaking intensity.

At the design ground shaking intensity (2/3 MCE_{R}), components with an I_{p} = 1.0 can be expected to have major damage, but significant falling hazards are avoided. Components with an I_{p} = 1.5 can have limited damage, but should remain functional. There should be no expectation that essential components will be operational for the MCE_{R} ground shaking intensity. At MCE_{R} intensity, nonstructural elements may fall, causing localized deaths.

## Code Ground Motions

The following is a very brief description covering basic concepts about how the S_{s} and S_{1} values found on the USGS website are derived. These values could be based on either a deterministic or a probabilistic ground motion shaking intensity.

## Deterministic Ground Motions

### Talking Point #12

A deterministic ground motion analysis for a specific fault will predict a range of ground shaking intensities from a specific magnitude earthquake.

### Talking Point #13

It is only possible to predict a range of ground shaking intensities from a specific earthquake at a specific site. It is impossible to predict what the exact ground shaking intensity will be at a specific site.

When a specific magnitude earthquake happens, the ground shaking intensity around the region could vary greatly. Areas close by each other can have very different levels of ground shaking intensity. Recordings from previous same-magnitude earthquakes show that there is a wide range of possible shaking intensities. Engineers and seismologists who have studied earthquake ground motions can only predict a range of shaking intensities from a specific earthquake based on fault type, distance, site conditions, and other factors because there is so much variability in these parameters. The ground motion prediction equations provide a median shaking intensity and a standard deviation, from which the range of shaking intensities can be calculated, and do not predict what the exact ground shaking intensity will be.

Predicting what the ground shaking intensity will be from a future earthquake is like predicting when a kernel of popcorn will pop. Some kernels pop early, some pop late. If you were given a kernel of popcorn, you could not predict when it will pop, but you could say that there is a 50% likelihood that it would pop before the median time. Or, you could say that there is an 84% likelihood that it would pop before the median + one standard deviation time. So the question is not, “When will it pop?” but “How likely is it to pop before a specific period of time?” Likewise, it is not appropriate to guess what the exact ground shaking intensity will be from a magnitude X earthquake. Instead, it is better to ask, “What is the ground shaking intensity level where there is an 84% likelihood that a magnitude X earthquake will cause a ground shaking intensity less than this level?” This question could also be asked for 50%, or any other percentile.

This estimation of ground motion shaking intensity is called a deterministic approach. From a code standpoint, a deterministic ground motion looks at the 84^{th} percentile response acceleration from all nearby active faults and selects the largest response acceleration (shaking intensity).

## Probabilistic Ground Motions

### Talking Point #14

Probabilistic ground motions refer to the probability that a specific ground shaking intensity level will be exceeded. They do not refer to a specific magnitude earthquake (see Talking Point #1).

Deterministic ground motion predictions assume that a characteristic earthquake occurs, but they do not consider the likelihood of it occurring. Probabilistic ground motions add another dimension by considering the probability that a specific magnitude earthquake will actually occur. They are expressed as a probability that a specific level of ground shaking intensity will be exceeded in a specific period of time. For example, a 10% in 50 year ground shaking intensity means that there is a 10% probability that the shaking intensity will be exceeded in 50 years. It could also be stated that there is a 1/475 probability that in any one year the shaking intensity would be exceeded. A 2% in 50 year ground shaking intensity is larger and rarer. There is only a 1/2475 probability that the shaking intensity will be exceeded in any year.

### Talking Point #15

The USGS acknowledges that a magnitude 7.5 earthquake could occur anywhere in the United States. If a probabilistic ground shaking intensity is low, it is not because there can never be a large magnitude earthquake; it is because the probability of a large magnitude earthquake is very low.

A probabilistic ground shaking intensity is based on the probability of various size earthquakes impacting a specific location. It considers both nearby and distant faults, and considers how many very small to large earthquakes have occurred in the area. It is a complicated process to calculate a probabilistic ground motion, and is beyond the scope of this article.

## Deterministic Caps

### Talking Point #16

The older MCE (prior to the 2012 IBC) is a Uniform Hazard ground shaking intensity with a 2% in 50 year probability of being exceeded (1/2475 per year).

When a 2% in 50 year probabilistic ground shaking intensity is calculated for every location around the United States, areas with many active faults will have very high ground shaking intensities, and areas with no active faults will have much lower ground shaking intensities. Each location has the same probability that the calculated ground shaking intensity will be exceeded: 2% in 50 years, or 1/2475 per year. This creates what is referred to as a “Uniform Hazard.”

Because some areas of California have many active faults, it results in very high probabilistic ground shaking intensities. It was decided to cap the MCE based on the deterministic ground shaking intensity of the controlling nearby fault. The MCE_{R} also uses a deterministic cap. The current cap is based on the 84^{th} percentile deterministic ground shaking intensity.

### Talking Point #17

When the MCE_{R} ground shaking intensity (see Talking Point #3) is based on the deterministic cap, then the shaking intensity will be lower than the risk adjusted Uniform Hazard ground shaking intensity. Because it is lower, the risk of building collapse is greater than the IBC objective of 1% in 50 years, and it is likely to occur more often than either the 2% in 50 year Uniform Hazard or the risk adjusted Uniform Hazard ground shaking intensities.

## Concluding Thoughts

This article only scratched the surface on many topics. Hopefully the information provided will whet our appetite to learn more and establish a common understanding for discussing seismic concepts.▪

USGS website: http://earthquake.usgs.gov/designmaps/us/application.php.

This article is based on an article and is used with permission from the SEAU News, *Seismic Communication: Let’s Get on the Same Page*, May 2015.

The following are references to learn more about the specific Talking Points:

ASCE/SEI 7-10, *Minimum Design Loads for Building and Other Structures*, 3^{rd} Printing

NEHRP* Recommended Seismic Provisions for New Buildings and Other Structures*, FEMA P-1050-1/2015 Edition

**Talking Points #1 and #2:** ASCE 7-10, Section C11.1, *Nature of Earthquake ‘Loads’*, and Section C21.2.

**Talking Point #3: **ASCE 7-10, Section C11.4. See ASCE 7-10 Figures 22-17 and 22-18 for the Mapped Risk Coefficients, C_{R}, that are applied to the 2% in 50-year Uniform Hazard ground motion shaking intensity.

**Talking Point #4:** ASCE 7-10, Section C11.4. Even though MCE is an acronym for Maximum Considered Earthquake, it must not be considered as the largest ground motion shaking intensity that can occur at a specific site. In its current use, it does *not* stand for Maximum Credible Earthquake. MCE_{R} is the lowest ground motion shaking intensity that the code allows to be used.

**Talking Point #5:** ASCE 7-10, Section C11.4. If MCE_{R} is capped by the deterministic value, a fault rupture for a specific earthquake has an 84% chance of causing a shaking intensity less than the 84^{th} percentile deterministic ground motion. If MCE_{R} is based on a probabilistic ground motion, then it does not relate to a specific earthquake magnitude, and a fault rupture could result in a larger or smaller shaking intensity than MCE_{R}.

**Talking Point #6:** ASCE 7-10, Sections C1.4 and C11.4.4, and NEHRP, Section 1.1.2, Page 2.

**Talking Point #7 and #8**: ASCE 7-10, Section C11.5 introduces the concepts of Immediate Occupancy, Life Safety, and Collapse Prevention, but does not discuss them in detail. The best discussion of these damage states or performance levels is found in ASCE/SEI 41-13, *Seismic Evaluation and Retrofit of Existing Buildings*. Refer to Table C2-3 for a brief description.

**Talking Point #8:** ASCE 7-10, Section C11.5.

**Talking Point #9:** ASCE 7-10, Section C11.5.1, NEHRP, Section 1.1.1, Pages 2 and 3, and Section 2.1.1, Pages 4 and 5.

**Talking Point #10:** The code deems these probabilities as an “acceptable level of seismic safety.” ASCE 7-10, Section C11.4, NEHRP, Section 1.1.1, Pages 1and 2, and Sections 2.1 and 2.1.1, Pages 4 and 5.

**Talking Point #11**: ASCE 7-10, Section C13.1.3, NEHRP, Sections 1.1.2, 1.1.4, and 1.1.5, Pages 2 and 3, and Section 2.1.2, Page 6

**Talking Points #12, #13, and #14:** ASCE 7-10, Sections C21.2.1 and C21.2.2. There are many sources that discuss the differences between deterministic and probabilistic ground motions. One of them is: Baker J.W. (2008) *An Introduction to Probabilistic Seismic Hazard Analysis (PSHA)*. White Paper. Version 1.3. 72 pp. http://web.stanford.edu/~bakerjw/publications.html

**Talking Point #15**: Petersen, M.D., Moschetti, M.P., Powers, P.M., Mueller, C.S., Haller, K.M., Frankel, A.D., Zeng, Yuehua, Rezaeian, Sanaz, Harmsen, S.C., Boyd, O.S., Field, Ned, Chen, Rui, Rukstales, K.S., Luco, Nico, Wheeler, R.L., Williams, R.A., and Olsen, A.H., 2014, *Documentation for the 2014 Update of the United States National Seismic Hazard Maps*: U.S. Geological Survey Open-File Report 2014-1091, 243 p., http://dx.doi.org/10.333/ofr20141091, Pages 24, 28-31.

**Talking Point #16:** ASCE 7-10, Section C11.4, NEHRP, Section 1.1.1, Page 1 and 2, and Section 2.1.1, Pages 4 and 5.

**Talking Point #17: **ASCE 7-10, Section C11.4.