Seismic Analysis Methods

Understanding Seismic Analysis in the Canadian Context

Seismic analysis represents one of the most critical aspects of structural engineering, ensuring that buildings, bridges, and infrastructure can withstand the dynamic forces generated by earthquakes. While Atlantic Canada may not experience the dramatic seismic events that characterise regions along the Pacific Ring of Fire, the region is far from immune to earthquake activity. Nova Scotia and the broader Maritime provinces sit within a seismically active zone, with historical records documenting significant events that underscore the importance of rigorous seismic design.

The 1929 Grand Banks earthquake, measuring 7.2 on the Richter scale, triggered a devastating tsunami that claimed 28 lives in Newfoundland and remains one of Canada's most significant seismic disasters. More recently, numerous smaller earthquakes occur throughout Atlantic Canada annually, serving as constant reminders that seismic analysis must be an integral component of any structural engineering project in the region.

For engineers and project managers working in Nova Scotia and the Maritimes, understanding the various methods of seismic analysis is essential for ensuring compliance with the National Building Code of Canada (NBCC) while delivering structures that protect occupants and maintain functionality during and after seismic events.

Equivalent Static Force Procedure: The Foundation of Seismic Design

The Equivalent Static Force Procedure (ESFP) represents the most fundamental approach to seismic analysis and serves as the starting point for many engineering projects. This method simplifies the complex dynamic behaviour of structures during earthquakes by converting seismic forces into equivalent static loads that can be applied to the structure for analysis.

How the Method Works

Under the ESFP, the total seismic base shear (V) is calculated using the following key parameters:

• Spectral acceleration values derived from the site-specific seismic hazard data provided in the NBCC

• Building importance factor (IE) ranging from 1.0 for normal buildings to 1.5 for post-disaster facilities

• Ductility-related force modification factor (Rd) reflecting the structure's ability to dissipate energy through inelastic deformation

• Overstrength-related force modification factor (Ro) accounting for the reserve strength in structural systems

• Building weight (W) including dead loads and applicable portions of live loads

For structures in Amherst and surrounding areas of Nova Scotia, the spectral acceleration values at 0.2 seconds (Sa(0.2)) typically range from 0.23g to 0.28g, while values at 1.0 second (Sa(1.0)) range from 0.059g to 0.072g. These values, while moderate compared to western Canada, still necessitate careful consideration in structural design.

Applicability and Limitations

The ESFP is most appropriate for regular structures with predictable dynamic behaviour. According to the NBCC 2020, this method may be used for structures meeting specific criteria, including buildings with a fundamental period less than 2.0 seconds and heights not exceeding 60 metres for most structural systems. However, structures with significant irregularities—whether vertical, horizontal, or torsional—may require more sophisticated analysis methods.

Modal Response Spectrum Analysis: Capturing Dynamic Behaviour

Modal Response Spectrum Analysis (MRSA) provides a more refined approach to seismic design by explicitly considering the dynamic characteristics of structures. This method acknowledges that buildings do not respond uniformly to ground motion but instead vibrate in distinct patterns called mode shapes.

The Modal Analysis Process

MRSA involves several interconnected steps that progressively build a comprehensive picture of structural response:

• Eigenvalue analysis to determine the natural frequencies and mode shapes of the structure

• Calculation of modal participation factors quantifying how much each mode contributes to the overall response

• Application of the design response spectrum to determine the maximum response in each mode

• Modal combination using methods such as Square Root of Sum of Squares (SRSS) or Complete Quadratic Combination (CQC) to obtain total response quantities

For most practical applications, the analysis must include sufficient modes to capture at least 90% of the total building mass in each principal direction. In typical low-rise to mid-rise structures common throughout Nova Scotia's commercial and institutional sectors, this often requires consideration of the first three to six modes.

Advantages for Maritime Projects

MRSA offers particular advantages for the types of structures frequently encountered in Atlantic Canada's built environment. Heritage buildings undergoing seismic retrofitting, industrial facilities with irregular mass distributions, and institutional buildings with complex floor plans all benefit from the enhanced accuracy this method provides. The moderate computational requirements of MRSA make it accessible for routine engineering practice while delivering results that better capture actual structural behaviour than equivalent static methods.

Linear and Nonlinear Time History Analysis

Time history analysis represents the most sophisticated category of seismic analysis methods, involving the step-by-step simulation of structural response to actual or synthetic earthquake ground motion records. This approach provides the most realistic representation of how structures behave during seismic events.

Linear Time History Analysis

Linear time history analysis (LTHA) maintains the assumption of elastic structural behaviour while capturing the time-varying nature of seismic response. This method requires:

• Selection of appropriate ground motion records that match the site's seismic hazard characteristics

• Scaling of records to ensure compatibility with the design spectrum over the relevant period range

• Numerical integration to solve the equations of motion at discrete time steps, typically ranging from 0.001 to 0.02 seconds

• Statistical treatment of results from multiple ground motion records to establish design values

The NBCC requires a minimum of eleven ground motion records when using time history analysis, with the average response values used for design. This requirement ensures that the inherent variability in earthquake ground motion is adequately addressed.

Nonlinear Time History Analysis

Nonlinear time history analysis (NLTHA) extends the methodology to include the inelastic behaviour of structural components. This advanced technique explicitly models yielding, strength degradation, and energy dissipation mechanisms that occur as structures are pushed beyond their elastic limits.

NLTHA is particularly valuable for:

• Performance-based design projects requiring explicit verification of performance objectives

• Seismic isolation and energy dissipation systems where device behaviour is inherently nonlinear

• Assessment of existing structures to determine actual collapse margins and retrofit requirements

• Critical infrastructure such as hospitals, emergency response centres, and essential lifeline facilities

While NLTHA demands significant computational resources and engineering expertise, modern software tools have made this method increasingly accessible for projects warranting its application.

Pushover Analysis and Performance-Based Design

Nonlinear static procedures, commonly known as pushover analysis, offer a practical middle ground between linear methods and full nonlinear time history analysis. This approach has gained significant traction in Canadian engineering practice, particularly for seismic assessment and retrofit projects.

Methodology and Implementation

Pushover analysis involves applying incrementally increasing lateral loads to a structural model while tracking the progression of damage and the development of plastic hinges. The resulting pushover curve—plotting base shear against roof displacement—provides essential insights into structural behaviour:

• Initial stiffness characterising elastic behaviour

• Yield point marking the onset of significant inelastic action

• Post-yield behaviour revealing the structure's ductility and reserve capacity

• Ultimate capacity identifying potential failure mechanisms

The capacity spectrum method, which overlays the pushover curve with seismic demand, enables engineers to estimate the expected performance point for a given seismic intensity. This graphical approach facilitates understanding of whether a structure will meet specific performance objectives, such as immediate occupancy, life safety, or collapse prevention.

Applications in Existing Building Assessment

Many communities throughout Nova Scotia contain heritage buildings and older structures designed before modern seismic provisions were established. Pushover analysis provides an invaluable tool for assessing these buildings, identifying deficiencies, and developing targeted retrofit strategies that address the most critical vulnerabilities while respecting architectural and historical significance.

Site-Specific Seismic Hazard Analysis

While the NBCC provides generalised seismic hazard values for locations across Canada, certain projects benefit from site-specific seismic hazard analysis (SSHA). This approach develops customised ground motion parameters that better reflect local geological conditions and seismic source characteristics.

Deterministic and Probabilistic Approaches

Site-specific analysis may employ either deterministic or probabilistic methodologies:

Deterministic seismic hazard analysis (DSHA) identifies the maximum credible earthquake from known seismic sources and calculates the resulting ground motion at the site. This approach is often used for critical facilities where the consequences of failure are unacceptable.

Probabilistic seismic hazard analysis (PSHA) integrates contributions from all potential seismic sources, accounting for the frequency of occurrence and ground motion variability. The NBCC seismic hazard values are derived from PSHA conducted by Natural Resources Canada, targeting a 2% probability of exceedance in 50 years.

Site Response Analysis

Local soil conditions can dramatically amplify or modify earthquake ground motion. Site response analysis, using software tools such as SHAKE or DEEPSOIL, models the propagation of seismic waves through soil deposits to determine site-specific spectral accelerations. This is particularly relevant for projects on soft soil sites, such as those found in certain areas of the Minas Basin region and along river valleys throughout Nova Scotia.

Site classification under the NBCC ranges from Site Class A (hard rock) through Site Class E (soft soil), with corresponding amplification factors that can increase spectral accelerations by factors of 2.0 or more for soft soil sites compared to reference rock conditions.

Selecting the Appropriate Analysis Method

Choosing the most suitable seismic analysis method requires careful consideration of multiple factors that balance accuracy, efficiency, and regulatory requirements.

Key Decision Factors

Engineers should evaluate the following considerations when selecting an analysis approach:

• Structural regularity: Buildings with significant irregularities typically require dynamic analysis methods

• Building height and period: Taller structures with longer fundamental periods may require MRSA or time history analysis

• Importance category: Post-disaster and high-importance structures warrant more rigorous analysis

• Performance objectives: Enhanced performance targets may necessitate nonlinear analysis methods

• Site conditions: Unusual soil profiles may require site-specific ground motion development

• Project budget and schedule: More sophisticated methods require additional time and resources

Integrated Analysis Strategies

Experienced engineers often employ multiple analysis methods within a single project. Preliminary design may utilise equivalent static procedures for rapid iteration, followed by modal response spectrum analysis for final design verification. For structures with seismic isolation or energy dissipation systems, nonlinear time history analysis may be required to validate system performance while simpler methods guide the initial design.

Partner with Sangster Engineering Ltd. for Your Seismic Analysis Needs

Navigating the complexities of seismic analysis requires both technical expertise and practical experience. At Sangster Engineering Ltd., our team of professional engineers brings deep knowledge of seismic design principles combined with extensive experience serving clients throughout Nova Scotia and Atlantic Canada.

Whether your project involves new construction requiring code-compliant seismic design, assessment and retrofit of existing structures, or specialised analysis for critical facilities, we provide the engineering excellence your project demands. Our familiarity with local geological conditions, regional construction practices, and the specific requirements of Maritime projects ensures that your structure will be designed to perform safely and reliably.

Contact Sangster Engineering Ltd. today to discuss your seismic analysis requirements. Our Amherst-based team is ready to deliver professional engineering solutions that protect your investment and the people who depend on your structures. Let us put our expertise to work for your next project.

Partner with Sangster Engineering

At Sangster Engineering Ltd. in Amherst, Nova Scotia, we bring decades of engineering experience to every project. Serving clients across Atlantic Canada and beyond.

Contact us today to discuss your engineering needs.