Seismic Design and Performance Verification
1.4 Building Performance
1.4.1 Anticipated Response of Buildings to Earthquake Ground Shaking
Ground shaking is the main focus of most earthquake-resistant building designs. Ground failure associated with surface fault rupture, landslides, and soil liquefaction can also be concerns. These latter effects can be mitigated through building siting, ground improvement, or a foundation designed to support the structure despite the ground failure. Other secondary effects such as tsunami, fire, and lifeline disruption can also be considered in exceptional cases.
Effects of ground shaking can be represented through a linear response spectrum, which plots the acceleration of a linear-elastic oscillator as a function of its vibration period. Figure 1.7 plots the design earthquake response spectrum for a site on the University of California, Berkeley campus based on the provisions of ASCE 7, for the Design Earthquake (DE) shaking level. This response spectrum is a smoothed representation of the
ground motion, having spectral ordinates equal to two-thirds of the Maximum Considered Earthquake (MCE), and serves as a basis for building design. (For additional details on the design approach, see Chapter 11.) Using the approximation that the fundamental vibration period of a building is approximately T = 0.1N, we would estimate the period for a 5-story building to be approximately 0.5 s, while that for a 10-story building would be approximately 1 s. Corresponding spectral accelerations are approximately 1.6g and 0.9g, respectively. Thus, crude estimates for the design base shears, assuming linear-elastic response, are approximately 1.6W and 0.9W, respectively, where W is the building weight.
FIGURE 1.7 Design response spectrum for Design Earthquake (DE) for 5% damped linear response in accordance with ASCE 7.
Although it is possible to design buildings to have strengths corresponding to these design base shears, to do so would require very robust lateral-force-resisting systems. Economic and functional constraints would make such designs impractical except in unusual cases. Thus, most buildings are designed with base-shear strength lower than the strength required for linear-elastic response. A consequence is that inelastic response and corresponding damage must be anticipated for buildings subjected to DE-level ground motions. Expected building performance capability can be determined, in part, by the degree of inelastic response anticipated and by how that inelastic response is manifest in damage to the structural system.
1.4.2 Performance Concepts
Building performance can be expressed in multiple ways. In building design practice today, the most common approach is to define a series of performance objectives. A performance objective is a statement of the expected building performance conditioned on it having been subjected to a particular loading. For example, TBI (2010) recommends that a tall building be designed to satisfy the following two performance objectives:
1. The building shall have a small probability of life-threatening collapse given that it has been subjected to rare earthquake ground shaking defined as the Maximum Considered Earthquake (MCE) shaking level.
2. The building shall have a small probability of damage requiring repair given that it has been subjected to more frequent ground
shaking defined as the Service Level Earthquake (SLE) shaking level.
According to this procedure, the building must be analyzed for two different performance objectives and it must satisfy both to be considered to have code-equivalent performance.
The concept of discrete performance objectives became firmly established in the 1990s with the introduction of the Vision 2000 Committee report on performance-based seismic design of buildings (SEAOC, 1995) and the development of performance-based assessment procedures for existing buildings (ATC 40, 1996; FEMA 273, 1997). Figure 1.8 illustrates the performance objectives suggested in SEAOC (1995), but using performance level designations of ASCE 41 (which supersedes FEMA 273). For the Basic Objective, which would apply to the vast majority of buildings, the performance objectives would be Operational for Frequent shaking, Immediate Occupancy for Occasional shaking, Life Safety for Rare shaking, and Collapse Prevention for Very Rare shaking. Proposed return periods for these different shaking levels are shown in parentheses.
For more critical structures, higher performance objectives were suggested (Figure 1.8).
FIGURE 1.8 Performance objectives suggested by SEAOC (1995).
An early concept was to relate performance levels to the physical condition of the building as it was subjected to increasing lateral deformation (SEAOC, 1995). Figure 1.9 illustrates three performance levels introduced in FEMA 273 (1997) and continued in ASCE 41 (2013).
The performance level Immediate Occupancy corresponds to a state in which some damage may have occurred, but after cosmetic repairs the structure can be occupied and functional. Collapse Prevention is a point in the response just prior to onset of collapse. Life Safety is a term used to define a performance state with a “comfortable” margin below the collapse state. In ASCE 41, the margin is set at about three-quarters of the displacement corresponding to the collapse performance state, but in ASCE 7 and the building code, this margin is two-thirds. Figure 1.9 implies that performance states are a function of the deformations imposed on the structural and nonstructural systems. Performance of contents and other items that are not rigidly fixed to the structural system can instead be a function of floor acceleration or velocity.
FIGURE 1.9 Visualization of performance levels. (Personal communication with R.
Hamburger.)
Building performance should be defined by the performance of the building system as a whole. It can be difficult, however, to quantify performance metrics for building systems. Therefore, as a practical matter, a common practice is to define system performance based on the performance of individual structural (or nonstructural) components that compose the building system. In effect, the building performance is defined as being equal to the worst performance of any of the components of the building.
This approach, which is adopted in ASCE 41, tends to be a very conservative approach.
The preceding discussion emphasizes the current approach of gauging performance using structural engineering metrics, such as displacement, story drift, floor acceleration, inelastic deformation, and component forces, all compared with values that are considered acceptable. It is also feasible to translate these engineering metrics into damage states, and from there into consequences such as casualties, repair costs, and downtime. This approach is not commonly applied today, but the capabilities exist and are occasionally applied for special buildings. The interested reader is referred to Yang et al. (2009) and FEMA P-58 (2012).
1.4.3 Use, Occupancy, and Risk Classifications
Figure 1.8 introduced the idea that building performance objectives should depend on the risk that the building poses to its occupants and the surrounding community. This idea is incorporated in current U.S. building codes. In ASCE 7, four different Risk Categories are defined, as summarized in Table 1.1. The vast majority of buildings correspond to Risk Category II. ASCE 7 imposes more stringent requirements for buildings with higher Risk Category, consistent with the larger population of people put at risk if the building should fail to perform. Higher design forces are also imposed through application of an importance factor, Ie, listed in Table 1.1.
TABLE 1.1 Risk Category* of Buildings and Other Structures (adapted from ASCE 7)
1.4.4 Building Performance Expectations
The commentary to ASCE 7 quantifies the intended performance for buildings in different Risk Categories. Table 1.2 summarizes the anticipated reliability values. These values have not been validated with experience or in-depth analysis, but instead are notional values that represent the intent of
the building code committee.
FEMA P-695 (2009) also suggests that the probability of collapse due to MCE ground motions should be limited to 10% for Risk Category II buildings. FEMA P-695 presents a detailed methodology for determining collapse probability of classes of buildings. Several case studies have used the methodology to benchmark performance of modern buildings, with results reported in FEMA P-695 (2009) and NIST (2010).
The collapse probabilities in Table 1.2 indicate the probabilities for an individual building given that it has been subjected to ground shaking at the MCE level. It should be noted that the term MCE, or Maximum Considered Earthquake, actually does not refer to an earthquake, but instead refers to the shaking that occurs at a site given the occurrence of an earthquake. MCE- level shaking generally indicates both a rare earthquake and unusually high ground shaking given the occurrence of that earthquake. Thus, one should not expect that all buildings in a region will be subjected to MCE-level shaking in any given earthquake. Instead, only a subset of buildings might experience MCE-level shaking, with the rest experiencing lower shaking intensity.
Thus, over a region, the collapse probability for a population of new buildings is lower than the values indicated in Table 1.2.
TABLE 1.2 Anticipated Reliability (Maximum Probability of Failure) for Buildings Conditioned on the Occurrence of MCE Shaking
Starting with the 2010 edition of ASCE 7, the earthquake design values for most locations in the United States have been adjusted so that structures having standard collapse fragility (thought to be a lower bound on the actual fragility of code-conforming structures) will have a collapse probability of 1% in 50 years. Near known active faults with significant slip rates and with characteristic earthquakes having magnitudes in excess of about 6.0, the design values are limited by 84th percentile spectral values associated with a characteristic earthquake on the fault. At these latter locations, the
calculated probability of collapse will be somewhat higher, and in some cases much higher, than in locations not near such faults. For additional information on the derivation of the design values, see Luco et al. (2007) and NEHRP (2009).