Comprehensive Overview - Design Spectrum in Seismic Engineering

1. Introduction

The term "seismic design" implies the intention to safely design structures in response to the natural phenomenon of earthquakes. To achieve this objective, it is crucial to have a precise understanding of the size and characteristics of earthquakes that may occur in the specific area where the structure is to be built. This is a fundamental premise, recognized by engineers and technicians alike.

We are entering an era of remarkable technological revolution, exemplified by deep learning artificial intelligence such as ChatGPT, which interacts with humans, and autonomous vehicles. However, as demonstrated by the devastating earthquake in Turkey in February 2023, the occurrence of major earthquakes remains an unpredictable and unknown aspect of our world that humans cannot foresee.

Furthermore, it is also impossible to accurately predict the maximum acceleration and frequency characteristics of seismic waves that will act as seismic loads. Consequently, claiming to design safely for earthquakes in a situation where the size and nature of the impending earthquake are not precisely known is not logically sound.

Engineers often satisfy themselves with the notion that as long as they follow the procedures outlined in the national guidelines, even if they may not fully comprehend the underlying significance.

In reference to the "Common Application Items for Seismic Design Standards" issued by the South Korea Ministry of Public Safety and Security in April 2017, I will attempt to explain the background and physical meaning of determining the shape of the response spectrum based solely on the concepts in my mind, without consulting a separate reference book.

An explanation devoid of any equations may not resonate with engineers. Therefore, I plan to provide a separate explanation using mathematical concepts such as differential equations to elucidate the phenomena of "free vibration of a single-degree-of-freedom system" and the process of solving "forced vibration of a single-degree-of-freedom system," both of which involve the physics of vibration.

In fact, understanding the principle of superposition known from Maxwell-Betti's reciprocity theorem and eigenvalue problems in structural dynamics, studying how in a linear system, the response of a multi-degree-of-freedom system can be expressed as the summation of responses from single-degree-of-freedom systems, indicates a deep comprehension of dynamics in the field of structural engineering.

• Maxwell–Betti Law

• Linear system

• Single-degree-of-freedom system, SDOF system

• Multi-degree-of-freedom system, MDOF system

Reflecting on my past experiences of self-study without specifically having a teacher, I believe that gaining insight, regardless of the field of study, is the most challenging aspect.

Eigenvalue problems are a crucial concept not only in structural engineering but also in physics. Solving problems related to eigenvalue in physics, such as those encountered in systems of linear equations learned in middle school, where the right-hand side terms are all zero, reveals solutions expressed not as specific values for variables but as proportional relationships. Recognizing this fact broadens the scope of understanding.

2. Response Spectrum Generation Method

Figure-1 is considered the most representative diagram illustrating the concept of the response spectrum. If you can explain this figure well to yourself, it means you have accurately understood the concept of the response spectrum.

However, understanding the response spectrum based solely on this might have some limitations.

What might be missing?

To fully comprehend the response spectrum, it is necessary to understand the terms relative velocity, relative displacement, and absolute acceleration. However, students often tend to overlook the meanings of the words "relative" and "absolute" when reading dynamics textbooks.

So, what exactly do "relative" and "absolute" mean?

When we write the differential equations for a moving object, the reference coordinate system is set to the ground, the lower part of the oscillating object. In the case of a train moving at a constant speed, the fact that we don't feel any force is a frequently mentioned aspect of Einstein's theory of relativity. Velocity and displacement have meaning only when relative displacement and relative velocity occur in the object's reference coordinate system.

In other words, velocity response and displacement response have physical significance only when there is relative velocity and relative displacement in the object's reference coordinate system.

On the other hand, acceleration becomes the actual acceleration when the relative acceleration of an object and the ground acceleration are added, resulting in absolute acceleration. In other words, acceleration response has physical significance when it is represented by absolute acceleration.

Furthermore, during the initial introduction of seismic design in Korea, engineers, not understanding why mass units should be input in analysis program parameters, made errors by entering the weight multiplied by gravity, leading to miscalculation of the natural period. There were cases where such errors were discovered during construction without anyone being aware.

The main reason for the design earthquake force shortage due to incorrect natural period calculation was also a significant factor in the "Busan Gwangan Bridge Truss Connection Bridge" being changed to a seismic isolation during construction.

The reason for inputting mass units rather than weight units, which include gravity, in dynamics is as follows:

In a spacecraft not influenced by gravity, all objects float regardless of their mass. However, understanding that "when pushing two objects horizontally with different masses, it is not the same force required, but the resistance varies proportionally to the mass" clarifies the rationale.

The significance of the response spectrum in seismic design lies in its role as the most fundamental representation for estimating the magnitude and shape of the seismic forces to be encountered in the future.

Just as human faces vary, the shapes of observed seismic wave response spectra are diverse. However, akin to the distinct differences in shapes between humans and animals allowing for rough classification, understanding seismic wave characteristics involves a rough classification based on the response spectrum.

While it may not be possible to precisely identify the shape of a response spectrum for a specific seismic wave, examining special cases for a single-degree-of-freedom system can help understand the general meaning of the response spectrum and its application in specific scenarios.

First, let's consider the case where the natural period is 0.

A state with a natural period of 0 can be envisioned as the object completely adhering to the ground, as depicted in (Figure-2) (1). If the object is completely stuck to the ground as if glued, the relative displacement, relative velocity, and relative acceleration of the object with respect to the ground would all be zero.

In the response spectrum, the acceleration response is defined as the absolute acceleration, which has physical significance, and the relative acceleration corresponding to the 0 period is zero. Therefore, the acceleration response spectrum represents the maximum acceleration value of the input seismic wave.

Second, let's consider the case where the period is infinite(∞).

An infinite period implies supporting an extremely massive mass with an extremely light spring, as illustrated in (Figure-2) (2). If seismic forces act on such a structure, the ground will never vibrate the structure, and the ground will move alone.

In other words, the displacement response of a structure with an infinite period does not diverge to infinity but converges to the maximum value of seismic displacement.

Intuitive values related to the input seismic wave and response spectrum are represented by these two scenarios.

The other aspects related to frequency characteristics depend on factors such as the size and destructive mechanism of the seismic layer, the propagation path of the seismic wave, and the surface soil conditions of the observation area.

3. Standard Design Responce Spectrum

To understand the concept of seismic design as defined in each country, one must delve into the explanation of design response spectra.

However, being earthquake-prone countries, the design response spectra shapes of advanced nations like the United States and Japan differ, and even within Korea, the shapes and forms of design response spectra applied in civil and architectural fields vary significantly. This diversity in shapes and concepts poses limitations in explanations.

The author feels a bit frustrated about the increasing level of detail in understanding an unknown area where we might not even know how seismic waves of a certain magnitude will propagate.

There is little we can know about the shape of a spectrum for a given seismic waveform, except for the following two facts.

• In the case of a period being 0, the maximum response acceleration is equal to the maximum ground acceleration.

• In the case of a period being infinite, the maximum displacement converges to the ground displacement.

Since the development of seismographs in the 1940s in the United States, a comprehensive analysis of the average characteristics of seismic waves observed worldwide reveals a tendency for "acceleration response to increase up to approximately 1 second, which is the short-period range," but beyond that, "acceleration response decreases as the period lengthens."

The U.S. AASHTO (American Association of State Highway and Transportation Officials) regulations, adopted by the standard specifications for road bridges in South Korea, represent the most straightforward expression of the frequency characteristics of seismic waves (Figure-3.1).

In the very short period range, the seismic wave's maximum acceleration is somewhat overestimated, but handling it horizontally in the short-period range is straightforward. Since there are not many structures falling into this range, and from a design perspective, it is on the side of safety, it can be accepted.

If the decrease in response in the long-period range is estimated too significantly, it may result in underestimating seismic forces for increasingly larger structures. However, the value "period (T) to the power of (2/3)," representing the tendency to decrease, is not an exact value, but it is considered to represent the characteristics of seismic waves observed worldwide.

Furthermore, setting proportionally larger values for weaker soils based on the type of ground is very logical. Ground types are not straightforward, and while there could be more types if detailed, they are simply classified into four types.

Along with the shape of the spectrum, another challenging value to predict is the maximum acceleration of seismic waves. In the United States, it is calculated based on the seismic activity in the western region, which experiences many earthquakes.

Recent seismic observations show a gradual increase in maximum acceleration, interpreted not as a significant increase in seismic activity but rather as an improvement in the precision of measurement instruments, leading to larger recordings of short-period components.

In April 2017, when looking at the standard spectrum presented by the South Korean Ministry of Public Safety and Security, it has become much more complex.

Based on my experience drawing many seismic spectra during my study abroad at the Japan Earthquake Research Institute, specifying the characteristics of future seismic waves in detail does not necessarily lead to an improvement in seismic performance.

Furthermore, the values of maximum design acceleration are increasingly deviating from observational records. In the 90s, it was believed that earthquakes exceeding 1.0g would not occur. However, in the 1995 Kobe earthquake, the acceleration exceeded 0.7g, and the Fukushima earthquake, which caused damage to nuclear power plants due to a tsunami, recorded a maximum acceleration exceeding 3.0g.

With questions arising about why structures did not collapse even with records exceeding 10 times the design seismic force, doubts are raised about potential errors in our seismic design practices.

The most convincing explanation interprets the interaction between the ground and the structure. In the case of weak ground, the observed records are significant due to ground amplification effects, but the effect of energy dissipation through ground-induced damping, resulting from the interaction between the ground and the structure, is also substantial.

4. What factors influence the frequency characteristics?

How are the frequency characteristics determining the shape of the spectrum determined?

Figure 4 depicts various characteristics inherent in seismic waves, such as the causative fault movement, wave propagation path, and amplification characteristics of the surface ground, which are the causes of earthquakes.

First, the characteristics of seismic waves are significantly influenced by the size of the active fault, which determines the seismic scale, and the fault model that determines the destruction pattern of the fault.
In essence, if the size of the fault that is being destroyed is larger, the duration of the earthquake tends to be longer, and there is a tendency for long-period components to develop. While this logic is easily understandable, there are too many unknowns, such as the size and location of the active fault.

Second, seismic waves are influenced by the path from the fault where the earthquake starts to the observation point.
When the wave path passes through a solid bedrock layer, the short-period components become stronger with each pass compared to seismic waves passing through weak bedrock layers. Additionally, seismic waves passing through a large-scale earthquake and covering long distances contain many long-period components.
Furthermore, even for small-scale earthquakes, when the distance is short, they tend to have many short-period components. This is because higher-frequency components reflect a tendency for greater attenuation compared to lower-frequency components.
This phenomenon can be compared to the principle where low-frequency AM broadcasts travel farther than high-frequency FM broadcasts.
While these explanations make sense, it's valid to acknowledge that not knowing the location of the earthquake occurrence also means not knowing the path.

Third, downtown areas are mostly formed in the distant past by sediments carried by rivers. The surface soil is composed of weaker ground compared to the path of bedrock through which seismic waves are transmitted, and the amplification effect due to the surface soil is very significant.

Unlike the first two factors mentioned earlier, there is much that we can relatively comprehend in this regard.

Currently, on a national scale, there is a large research project underway to identify active faults, predict the locations, and sizes of earthquakes that could occur on the Korean Peninsula.

However, the author believes that predicting major earthquakes occurring in deep-seated areas through surface observations such as aerial photographs and trench investigations still has limitations. Such geological research concludes that further investigations should continue even after the research project is completed.

5. Closing Remarks

The response spectrum is nothing more than a precalculated graph for all periods assuming the structure is elastic. However, as one understands its significance, it explains everything about seismic waves and remains the most crucial data for earthquake-resistant design, enabling the prediction of seismic damage to structures.

If someone were to show the response spectrum for a certain seismic damage area and ask for an analysis of the causes, even if it were a posthumous prescription, a logical explanation would be possible. However, without the response spectrum, it would be impossible.

Before humanity developed seismometers and observed seismic waves to understand the characteristics of the response spectrum, high-rise buildings couldn't be constructed, considering seismic forces as inertial forces proportional to mass.

The analysis of the response spectrum revealed that seismic waves have a characteristic of strong energy in short-period components but gradually decreasing energy in long-period components. This discovery led to the emergence of new construction methods such as base-isolated structures along with the construction of high-rise buildings.

Looking at the National Disaster Management Agency's design spectrum (Figure 3.2), the reason for setting a transition period from 3.0 seconds to 1/T, changing the slope from 1/T to 1/T^2, is to reduce the phenomenon of divergence as the period lengthens, enabling the design of structures with large displacements, such as base-isolated structures.

Structures dominated by gravity have a high safety margin for vertical loads such as permanent loads. Still, structurally, they are vulnerable to horizontal loads like earthquakes. However, maintaining a structure elastically for seismic forces with a low probability of occurrence throughout its lifespan is not economically viable.

Rather than paying for absolute safety against earthquakes, people would prefer to pay for a more prosperous life. Therefore, the purpose of seismic design is to pursue elastic design for small earthquakes and ductile design to prevent loss of life due to the complete collapse of structures in the event of a large earthquake.

Ductile design for structures using the unreliable material of reinforced concrete is a very challenging issue. In the AASHTO regulations for designing bridges in the United States, the concept of elastic design is transformed into the concept of ductile design by using the response modification coefficient, a constant divided by the elastic seismic force. Understanding the meaning of the response modification coefficient is the true understanding of seismic design.

In the next part, we will delve into the meaning of the response modification coefficient.

About the Editor

Gyusik Jeon

Doctor of Architectural Engineering Over 20 years of experience

Dr. Gyusik Jeon, with over 20 years of experience in Architectural Engineering, has a diverse career including roles at KEPCO's Power Research Institute (1980-1997), Technical Director at Unison Construction (1997-2000), and currently works with a seismic base isolators production company. He graduated from Busan National University in Civil Engineering and holds a Master's and Ph.D. from the University of Tokyo's Seismic Research Institute.

 

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