ArticlesSeismic Design Considerations for Atlantic CanadaAuthor: Valerie Latour, EIT and Perry Mitchelmore, P. Eng. of Meco (Mitchelmore Engineering Company Ltd.) 1. INTRODUCTIONDesign professionals are well acquainted with dead, live and environmental loading on structures. Design professionals are also increasingly getting well acquainted with earthquake loading on structures. Despite the fact this familiarity period has lasted for many decades, there is still a gap between analytical knowledge and practice. The most recent edition of the Canadian Dam Association Dam Safety Guidelines (CDA 2007) concurrently provides a significant contribution to the knowledge base available to engineers for practical design applications while making practical design more challenging. The Guidelines (CDA 2007) present separate descriptions of seismic hazard assessment and seismic analysis. Seismic hazard assessment provides the engineering community with an understanding of the characteristics of seismic hazard, methods of evaluating the hazard and appropriate parameters for seismic evaluation. The seismic analysis is presented separately for geotechnical and structural considerations but are reasonably similar. The challenge for the user is to interpret the intention between the assessment and the analysis. The Guideline's seismic hazard assessment technical bulletin introduces a new term, "Earthquake Design Ground Motion (EDGM)" to define the parameters for seismic design. The EDGM may include earthquake magnitude and distance, peak ground motion parameters, acceleration response spectra and any potential foundation fault displacements. For dams, the selected parameters in seismic design are the best estimate, or mean, value. The mean value is different from, and generally larger than, the median value available through the National building Code of Canada (NBCC 2005). Canada is fortunate in that dams don't tend to be located on active faults which means the EDGM is nearly always established by a site specific Probabilistic Seismic Hazard Assessment (PSHA), available from the Geological Survey of Canada. The site specific seismic assessment will provide parameters necessary for design, including peak ground acceleration (PGA) and response spectra for different return periods. More detailed information on sources, distance and time histories will require more investigation. The estimate the EDGM should consider (i) local and regional geotectonic information and (ii) a statistical analysis of historical earthquakes. Using the EDGM, the challenge for designers is to incorporate the parameters from the seismic hazard assessment into available methods of analysis. Methods of analysis tend to be available at two levels; (i) preliminary analysis, which is largely empirical and based on experience in western North American and (ii) detailed analysis, which are highly analytical and based on mathematical models. The Guidelines recommend a progressive approach, starting from a screening level and progressing to full detailed analysis until the design professional is satisfied that the structure is safe. It sounds fairly simple, but there are peculiarities that the design professional must be aware of when merging the available seismic parameters with the available methods. This paper will attempt to clarify differences between seismic response for concrete gravity dam structures in Eastern North American (ENA) and Western North American (WNA), important considerations in applying empirical methods from difference regions and suggest appropriate methods for simplified analysis. 2. METHODS OF ANALYSISIn general, the method of seismic analysis is related to the importance of the structure, the consequences of failure, the type of structure and the seismicity of the region. The Guidelines recommend a phased approach for most dams, starting with simple analysis and progressing to more complex methods until satisfied the structure is safe. 2.1 Pseudo-Static AnalysisThe pseudo-static seismic analysis is a rigid body, limit equilibrium method of analysis that was traditionally used for design in low seismic risk areas where there was no risk of foundation liquefaction. The method represents dynamic forces by an "equivalent" seismic coefficient multiplied by the structural mass directed horizontally, i.e., orthogonal to the weight vector. Although this method is still used by some design professionals in the preliminary stages of design or safety review, many over simplifications of this analysis method have been realized. These over simplifications can lead to both overly conservative and non-conservative results. Traditionally, one of the many challenges of the pseudo-static analysis was selection of the seismic coefficient. The tendency was to use the Peak Ground Acceleration (PGA) value, expressed as a percentage of gravity, g, as substitute for the seismic coefficient. This practice was not recommended but there was little guidance on appropriate choices with regards to the link between the seismic parameters used in the pseudo static analysis and equivalent earthquake magnitude. In his Rankine lecture on the subject, Harry Seed (Seed, 1979) used a Newmark analysis procedure to demonstrate that for soils that do not lose more than fifteen (15) percent of their strength during shaking or develop excessive pore pressures, it is only necessary to perform a pseudo-static analysis for seismic coefficient 0.1g for a magnitude 6.5 earthquake and 0.15g for a magnitude 8.6 earthquakes and obtain a factor of safety of 1.15. These benchmarks, intended for embankment dams, were largely adopted in practice for all dams when the pseudo-static method was used. Specified factor of safety values are required against overturning, sliding and over stressing of the structure - no tension is permitted. In the pseudo-static seismic analyses, the no tension criteria as well as the large factors of safety against overturning and sliding could be achieved due to the unrealistically small earthquake forces being applied to the structure (Chopra and Zhang, 1991). 2.2 Dynamic AnalysisA dynamic analysis is used to consider the dynamic amplification of the earthquake acceleration over the height of a flexible dam responding in its elastic range of motion (Leger and Ftima, 2004). These analyses address many of the over simplifications inherent to the pseudo-static method. In dynamic analyses, the compressibility of the reservoir water as well as the flexible nature of structure and the dynamic dam-reservoir-foundation relationship can be taken into account. Traditionally, conditions requiring a dynamic analysis to be completed included; dams with active faults directly beneath the dam or reservoir, unusual geometry, large masses near the top of the dam and dams that are higher than fifty feet (15.24m) (USDI, 1987). The International Council on Large Dams (Bulletin 72) suggests that, when assessing a dam in good condition, a dynamic analysis should be applied when the peak ground acceleration (PGA) is greater than 0.25tg and the CEA suggests that a dynamic approach be applied when the pseudo-spectral acceleration at the fundamental period of the dam structure is greater than 0.35g. Many different linear dynamic analysis methods are available for seismic analysis of dams. These analyses ranger from simplified methods that can be computed by hand to more in-depth analyses that use computer models. 2.2.1 Pseudo-Dynamic AnalysesThe pseudo-dynamic seismic analysis is also a rigid body, limit equilibrium method of analysis. However, it uses a response spectral analysis procedure to develop the equivalent static load for rigid body analysis. In the pseudo-dynamic analysis, the dam is treated as a flexible structure and the reservoir is treated as a compressible fluid. The seismic loading depends on the fundamental mode of seismic response of the dam due to the applied horizontal ground motion. The pseudo-dynamic method of analysis is discussed in more detail in section 3.1 of this report. 2.2.2 Linear Dynamic AnalysesFor concrete gravity dams, it is reasonable, in most cases, to assume that they dynamic response of the structure will be linear for low to moderate intensity earthquakes (NRC, 1990). A linear analysis is only appropriate for concrete bending in the structure's elastic range of motion. If significant cracking is expected a non-linear analysis is required (Ghrib et al, 1995). Brittle materials such as concrete tend to have significant variations in elasticity depending on the rate of loading -during rapid loading the modulus of elasticity for concrete increases by approximately 25% (NRC, 1990) allowing for a larger range of motion in the elastic range. For more complex analysis, linear time history analysis method. transient effects of the inertial forces are considered using an accelerogram and the dynamic equations of motion are solved over time (Ghrib et al, 1995). A single impulse of earthquake stress will be generally result in a failure of the structure even if cracking of the concrete is induced because there is not enough time for large displacements (Ghrib et al, 1995). Small cracks that may develop as a result of a single impulse can close before water is able to enter and cause a large displacement. 2.2.3 Non-Linear AnalysisA non-linear analysis is used to quantify motion of a concrete dam structure in its plastic range of motion including cracking; sliding and rocking under seismic ground motions (Leger and Ftima, 2004). A non-linear analysis is required in cases where severe damage is predicted or where the failure condition is approached in the linear analysis and the dynamic behaviour of the dam is drastically changed from the linear response mechanism (NRC, 1990). These non-linear methods generally employ a finite element model and are labour intensive and thus expensive. 3 ANALYSIS FOR ATLANTIC CANADAWhen choosing a seismic analysis method for design or evaluation of dams in Atlantic Canada, the design professional must consider that, generally, popular analysis methods were developed for large dams on the west coast of North America. It should not be assumed that a method developed in California can be directly applied to a small concrete gravity dam in Atlantic Canada. The differences in earthquakes characteristics in Eastern North American (ENA) and Western North America (WNA) are due to differences in the physical properties of the Earth's crust attenuates peak motions very slowly with high peak ground acceleration (PGA) values resulting from relatively small earthquakes over a short duration. In WNA, the crust attenuates the peak ground motions rapidly and high PGA values result from large earthquakes over long durations (Lin and Adams, 2007). What this suggests is that, for example, a seismic event with a PGA of 0.20g. In addition, the high frequency, short period character of ENA earthquakes may, theoretically, be more damaging to small concrete dams with short natural frequencies than WNA earthquakes (James et al, 2004). So while "Big" earthquakes are less common in ENA, designers in Atlantic Canada need to be cautious when choosing an analysis method for seismic design of concrete gravity dams. The seismic coefficients used in a pseudo-static analysis are a function of earthquake magnitude, which is not a spectral parameter, making traditional pseudo-static analyses susceptible to underestimating the affect that an ENA earthquake will have on a low period structure. These differences indicate that analyses developed for WNA earthquakes, based on prescribed PGA values, will result in non-conservative results if used directly for ENA. By contrast, a pseudo-dynamic Newmark-type sliding block analysis that compares a calculated critical acceleration required to initiate sliding to the expected PGA may result in an overly conservative result in ENA since relatively small, short duration earthquakes can have large PGAs. Without developing an appropriate method for adjusting peak ground motion parameters to be used in ENA analyses, methods that rely on site specific spectral parameters are more appropriate, as prescribed in the Guidelines. As a result of these observations, the ideal preliminary design method for designers in Atlantic Canada is a simplified pseudo-dynamic analysis that relies on spectral acceleration input parameters. 3.1 Analysis Method - Pseudo DynamicFor small (less than 15.24 m high), concrete gravity ams in Atlantic Canada, an appropriate preliminary analysis method is the pseudo-dynamic analysis. Using a simplified procedure and considering only the fundamental vibration mode, which is an appropriate assumption for small rigid dams, this method is relatively simple and time effective and thus, cost effective. In addition to the issues raised concerning the applicability of WNA methods in ENA, the benefits of using a pseudo-dynamic analysis over a pseudo-static analysis include the consideration of the affects of the dam-water-foundation interactions and water compressibility - which are not accounted for in the pseudo-static analysis and are considered to play integral roles in the dam's response to earthquake-induced ground motion. The beam model is often used when analysing concrete gravity dams. The accuracy of this model decreases for higher periods. Small gravity dams are short period structures and their response is mainly in the fundamental mode, making the beam model of analysis appropriate (Ghobarah et al, 1994). 3.2 Design ExampleTo illustrate the preliminary seismic evaluation of a concrete gravity dam, a design example will be used and the earthquake forces expected will be calculated. The Great Barren Dam, located in Tusket Nova Scotia, will be analysed. The Great Barren Dam was reconstructed in the summer of 2008. The dam consistes of a concrete gravity spillway section founded on bedrock matted with earth embankment sections on each end. 3.2.1 Required ParametersThe site specific mean value ground motion parameters for this site were calculated by the Geological Survey of Canada. The dam safety classification for this structure was determined to be high and therefore the ground motion parameters used are for a probability of 0.000404 p.a. or one in 2500 year return period. The parameters are given then Table 1. Soil Class C, from the NBCC (2005), is used in this case even though the dam is founded on bedrock. This is because the scope of the geotechnical investigation did not include sampling and testing of the bedrock for economic reasons. As a result, the rock could not be confidently classified as Class A, hard rock or Class B, rock so Class C was used to be conservative.
Table 1: Ground motion parameters for NBCC soil class C (very dense soil and soft rock).
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The damping ratio of the dam 
is calculated from equation (4). 
the added damping ratio due to hydrodynamic effects and 
the added damping due to dam-foundation rock interaction, a factor dependent on the modulus of elasticity of the concrete the depth of water in the reservoir and the absorptiveness of the reservoir bottom is a function of the modulus of elasticity of the concrete and the foundation rock. These factor values are selected from tables given in Fenves and Chopra, 1986.
is computed from equation (5) where 
is computed from equation (6).
is the function of the fundamental vibration mode shape. A summary of calculated values as well as design parameters selected for use in the analysis is given in Table 3.
used to calculate f1(y) was evaluated at a period of 0.2; the lowest period reported in the seismic hazard calculation for a 5% damping ratio. The fundamental vibration period of the dam was found in equation (1) is 0.012 seconds. The damping ratio that is to be applied to this spectral acceleration, as calculated in equation (4) is 7.5%.
and solving for Hs, a conventional concrete gravity dam has to be sixty-six (66) meters high to have a fundamental vibration period of 0.2 s. This suggests that for the majority of concrete gravity dams in Atlantic Canada, using the parameters available, the spectral acceleration is underestimated..JPG)
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