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Cyclic Loading of Soil During Earthquakes

The information about the cyclic loading of the soil during an earthquake is essential for any evaluation of liquefaction and potential ground failure. The ground motions used to represent the cyclic loading are applied for the initial liquefaction hazard assessment and, if necessary, in the design of mitigation strategies involving ground treatment. Fundamentally, the best measure of cyclic demand would account for the intensity, duration, and to a lesser extent the frequency content of the input motions. These three aspects of loading are explicitly accounted for using energy-based concepts, wherein the cyclic energy per unit volume of soil can be calculated from time-histories of particle motion or stress-strain plots. Although energy methods have been successfully applied to laboratory data and field case studies (Sunisakul 2004) these methods have not been widely adopted in engineering practice. Instead, the most commonly employed methods of analysis relate the intensity of shaking to either the horizontal acceleration or cyclic stress in the soil layer of interest, and the duration of the motions through simple, empirical magnitude-dependent scaling factors (Youd et al 2001, Seed et al 2003, Idriss and Boulanger, 2004). The characteristics of the horizontal ground motions within the soil column (i.e. acceleration, stress, strain time histories) are often computed using dynamic soil response models such as SHAKE (Schnabel et al 1972), ProShake 2004, DESRA (Lee and Finn 1978) and SUMDES (Li et al 2000). The input, or bedrock, ground motions required for these numerical models are selected on the basis of their similarity to target motions established using empirical ground motion relationships that account for factors such as the style of faulting, earthquake magnitude, source-to-site distance, and rock stiffness. Recorded ground motions can be easily obtained from on-line catalogs (web sites for CGS, COSMOS, MCEER, PEER, and USGS ground motion catalogs are provided in the reference list under Strong Motion Databases).

The characteristics of the bedrock, or firm soil, motions at a specific site will depend on several geologic and geographic variables. These include

1) The regional tectonic environment,


2) The seismicity of the region,


3) The proximity of the site to active faults, and


4) on the exposure interval of interest in design (e.g. 500, 1,000, or 2,500 year motions).

A complete seismic hazard evaluation for ground motions at a site must address both the spatial and temporal occurrence of earthquakes. In Oregon, the primary seismic sources are associated with the Cascadia Subduction Zone (interface or “mega-thrust,” and intraplate or intra-slab earthquakes), shallow crustal events, and to a lesser degree seismicity related to volcanic activity. The locations of each of these earthquake sources have been determined, or in some cases estimated, using an array of geologic and geophysical methods of field investigation, in situ imaging, and numerical modeling. The faults have been mapped (Geomatrix 1995, USGS 2004b, c) using the latest input and consensus from the geoscience community. The geoscience community acknowledges that the current understanding of seismicity rates in Oregon is incomplete due to factors such as the short historic record of earthquakes, the relatively long recurrence interval between events, and environmental controls that obliterate the geomorphic expression of most faults. To account for this source of uncertainty most seismic hazard analyses incorporate spatially random, “areal sources” to the collective hazard in the region. Once the locations of all of the regional sources have been established the occurrence of earthquakes as a function of time and magnitude (i.e. the rate of seismicity) is required.


The full characterization of source locations and the rate of occurrence of earthquakes is the basis of the seismic hazard evaluation. These primary factors, along with the location of the site relative to the faults, are used to estimate the characteristics of the ground motions utilized in analysis. The temporal occurrence of earthquakes along a specific fault defines the rate of seismicity associated with that source. Of primary interest in seismic analysis and design is the aggregate seismicity for all sources that may impact the structure of interest. This requires that the rate of seismicity for all sources is estimated. The recurrence interval of the maximum credible earthquake along a specific fault is often based on its slip rate and the rupture area required for an event of that magnitude (McGuire 2004). The likelihood of ground motions of a certain level is then a function of the rate of seismicity and the length of the time over which the observation is made. The time interval is referred to alternatively as the exposure time, mean return time, or recurrence interval, and it is specified for each project based on the importance of the structure. The exposure times associated with these designations are 500 and 1,000 years, respectively. The intensity and duration of the ground motions at a given site will be different for these two return periods, and the liquefaction hazard will clearly reflect these differences.

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