1. Introduction
When people generally refer to a structure being designed for seismic resistance, there is a widespread misconception not only among the general public but also among civil and architectural professionals. Many believe that a structure designed for seismic resistance is inherently safe against earthquakes.
This misconception often stems from the perception that seismic design involves performing elastic analysis for the design seismic forces provided by response spectra. There is a common understanding, often learned in academic settings, that the elastic analysis procedures have a very high margin of safety.
However, in reality, seismic design, as stated in the design codes of all countries, is not about designing the structure to be safe against the given design earthquake. The objective of seismic design, as outlined in various design codes, is to propose technical methods to secure sufficient safety against earthquakes with a low probability of occurrence during the structural lifespan.
Providing adequate safety for low-probability seismic events is challenging both technically and economically. It is not straightforward to ensure seismic stability for rare earthquakes that may occur over the structure's lifespan. Additionally, it is economically impractical unless advanced materials such as carbon fibers, which are lighter and stronger than conventional concrete made from gravel and sand, become widely available.
Therefore, the fundamental concepts of seismic design given in design codes for structures like bridges, including road and bridge design codes, are:
(1) Minimizing loss of human life,
(2) Allowing partial damage to bridge components during an earthquake while preventing overall collapse,
(3) Ensuring the basic functionality of the bridge even during seismic events.
In other words, for seismic events smaller than the design seismic force, structural components should resist within the elastic range without significant damage. However, for seismic events larger than the design seismic force, the definition is limited to preventing either partial or total collapse of the structure.
If one does not grasp the philosophical concept introduced in seismic design definitions, it can lead to the misconception that structures built after the establishment of seismic design standards are sufficiently safe, while only structures built before face issues.
The road and bridge design code(in South Korea) does not precisely describe the specific procedures required for designers to accept these design concepts. The crucial factor determining the size of seismic forces, which is vital in deciding the cross-section of components, involves dividing a constant named the response modification factor during the design process.
In essence, designers, without questioning, follow the procedures outlined in the code. They calculate the resistance moment of the structure using the modified seismic force obtained by dividing it by the response modification factor. They also perform detailed reinforcement according to the section. As a result, even civil and architectural professionals may not be aware of where the concept of partial damage was introduced in the code.
Therefore, without a clear understanding of the response modification factor, including the experiential and conceptual judgments of the experts involved in formulating the code, professionals, including the author, cannot truly comprehend the fundamental concepts of seismic design.
The application of the response modification factor in seismic design aims to simplify the complex seismic design procedures for non-dynamic specialists and was introduced in the U.S. AASHTO. However, in Japan, a country highly prone to earthquakes, where seismic design is a paramount consideration, this concept has not been adopted. It doesn't mean that Japan designs for elasticity against earthquakes; instead, designers are allowed discretion to ensure ductility up to the considered yielding range.
In Japan, the range of yielding is left to the discretion of the designer. In contrast, the U.S. and South Korea define the range of yielding in the code based on the form and location of components.
Against this backdrop, there is a material limitation in that reinforced concrete, the material used in structural construction, is heavier in weight compared to its strength. This makes it impractical to design structures to resist the given seismic forces without incurring damage. Furthermore, unlike natural disasters such as floods and droughts, earthquakes do not occur frequently during the lifespan of a structure. Therefore, there is a societal agreement to accept partial damage to promote economic feasibility.
2. Response Modification Factor, R
The following items explaining the meaning inherent in the response modification factor (also known as the reduction factor) include not only the South Korean road and bridge design code but also lack clear evidence even in the U.S. AASHTO. Therefore, the author's subjective judgment is included.
Hence, it is suggested to consider this opinion not as an absolute value but rather as a reference material necessary for understanding the meaning of the response modification factor.
2.1 Material Overstrength
In the concept of seismic design, as defined, it allows for partial damage to occur in the structure due to the design seismic forces. Furthermore, from the perspective of occurrence frequency, it can be considered more logical to fully utilize the safety margin included in the design method for vertical loads, as all designers understand.
As commonly understood in allowable stress design and strength design, the design strength of components is set lower than the actual failure strength, and the actual cross-sectional area of the component is determined to be larger than the calculated cross-sectional area. This difference is referred to as Material Overstrength.
It is widely acknowledged among civil and architectural engineers how challenging it is to quantitatively determine the material overstrength of actual components. Here, let's make a rough estimate that the material overstrength is approximately in the range of 1.5 to 2.0.
2.2 Structural Redundancy
Structural ductility is relatively easy to quantify compared to the material overstrength but may be a somewhat challenging concept for those who haven't studied the failure mechanisms.
To understand the concept of structural ductility, let's briefly mention the concepts of allowable stress design and strength design.
Allowable Stress Design (ASD) begins with the notion that if the compressive concrete stress assumed in a triangular stress distribution reaches the allowable stress considering the safety factor for a given design load, the entire structure is considered to be in a state of failure.
Strength Design Method (SDM) involves the concept that if, for the actual load multiplied by the load factor, the stress distribution of the compressive concrete becomes the actual failure distribution in the form of a rectangular shape, even for a single member, the entire structure is considered to have failed.
However, in actual structures, as shown in Figure-1, even if a single member reaches a yielding state for the design load calculated using the strength design method (P), the structure does not collapse. The member in a state of failure stress is referred to as a Plastic Hinge, but the structure as a whole remains intact.
Then, under what loading conditions will actual structures experience collapse?
In a simple rahmen structure, as shown in Figure-1,
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if a load exceeding the design load (P) defined in the strength design method is applied,
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the member that has already reached the plastic hinge state can no longer bear additional load,
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and other members that have not reached the state of failure stress will then bear the excess load.
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Ultimately, when the plastic hinge, which becomes the collapse mechanism, is formed, the structural system collapses.
In Figure-2, depicting a ramen-type beam with the same cross-section as in Figure-1, the collapse load is 1.5 times higher than the initial collapse load observed in Figure-1.
The theoretical background for applying a response modification factor of '5' in multi-span structures, as opposed to '3' for simple beams, is based on road and bridge design codes(in Sounth Korea).
In the structural system of the target structure, after the initial formation of the yielding hinge, predicting where the yielding hinge that eventually leads to the collapse mechanism will occur, and designing to induce the yielding hinge in a way that achieves the most fundamental goal of minimizing human injury, in other words, ensuring the structurally safest collapse mechanism occurs, is the design approach considering the collapse mechanism.
However, in seismic design, unlike fixed loads, the design load is interconnected with the structural system and changes. Therefore, structural ductility is applied during the verification stage where the designer checks for the occurrence of an undesirable collapse mechanism for the designed structural system. However, except for special structures, it is not commonly used in most designs.
2.3 Ductility Factor
While the first two variables may be somewhat understandable in comprehending the concept of the response modification factor, the ductility factor is the most challenging and, at the same time, the most uncertain variable.
Earthquakes are not phenomena that occur frequently during the lifespan of a structure. Therefore, the concept of seismic design originates from a societal agreement that suggests economically designing structures to prevent complete collapse and minimize human casualties by ensuring sufficient ductility in components, rather than fully preparing for the worst-case scenario at a significant economic burden.
The ductility factor aligns with this concept of seismic design.
i. The Law of Conservation of Energy
In the 1940s, the invention of seismometers capable of recording short-period seismic waves enabled the identification of powerful earthquakes. This, combined with the field of seismology, led to a comprehensive understanding of powerful earthquakes. Subsequently, in the 1960s to 1970s, seismic analysis of structures began in earnest, with a focus on the United States and Japan.
In this process, as per Newmark (1973), in the short-period range, as illustrated in Figure-3,
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The results obtained from the analysis under the assumption of structural elasticity and
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the results obtained by reducing the yield strength and conducting the analysis into the plastic region show that
It has been proposed that the law of conservation of energy, suggesting that the input energy to the structure is similar, is applicable (Triangle O-A-A' = Trapezoid O-B-C-D).
However, the law of conservation of energy mentioned here does not refer to an absolute law in physics. It is merely a compilation of common-sense results, noting that as the yield strength is lowered while conducting nonlinear analysis for numerous seismic waves on short structures with natural periods around 0.5 seconds, the displacement increases. The intuitive result that lower yield strength leads to larger displacements in nonlinear analysis is akin to the unpredictability of the trajectory of a rugby ball – it varies depending on the characteristics of seismic waves or nonlinear models, making predictions impossible.
Nevertheless, the observation that there is a tendency for the input energy to remain constant provides insights into predicting the results of nonlinear analysis from elastic analysis.
It is worth noting that for structures with a natural period longer than 1.0 second, a law of displacement constancy, which shows a tendency for response displacement to remain constant with changes in yield strength, has been proposed when performing seismic analysis. However, this law of displacement constancy is more of an interpretation result based on the fact that for structures with longer periods, there is less plastic deformation compared to short-period structures due to the lower number of vibration cycles.
ii. The Relationship Between the Law of Conservation of Energy and Destructive Experiments
Next, let's examine the correlation between the law of conservation of energy, which is a result of numerical analysis used to implement the practical nonlinearity of the member, and destructive experiments conducted on actual members.
Figure-4 illustrates the results of a horizontal loading test conducted on a real reinforced concrete member in Japan. As observed in the figure, once yielding occurs, there is a phenomenon where displacement increases without a significant reduction in yield strength, and this phenomenon is referred to as ductility.
Ductility does not increase simply with the increase in cross-sectional area and main reinforcement amount; rather, it depends on the details of confinement reinforcement such as hoop and spiral reinforcement.
In other words, ductility is a variable that determines how well the fragments of confined concrete, surrounded by confinement reinforcements such as hoops and spirals, can withstand until collapse, even though the concrete has failed due to bending moments.
Therefore, in seismic design, it is not an exaggeration to say that the entire design procedure revolves around how to detail the confinement reinforcements such as hoops and spirals to ensure ductility after yielding and how to handle the end zones.
When evaluating the ductility of well-designed and well-constructed members through experiments, the ductility factor (μ=δo/δy), representing the ratio of failure displacement to yield displacement, is typically around 4 to 5, as seen in Figure-4.
Therefore, applying the relationship between ductility factor and yield strength derived from the law of conservation of energy, assuming a ductility factor of around 4 for members, allows for a yield strength reduction of approximately 2.5 times. Even assuming a ductility factor of around 3 and designing with a yield strength reduced to about 2.2 times, the collapse prevention design concept can still be upheld.
3. Determining the Response Modification Coefficient
As shown in Table-1, according to the design code for bridges in South Korea, the response modification coefficient (also known as the seismic response coefficient) is defined as 3 for the piers with single-span column configuration receiving moments, and 5 for the piers with multi-span column configuration resembling frames.
|
Substructure R |
Connection Part R |
|---|---|
|
Wall Pier 2 |
Spuerstructure & Abutment 0.8 |
|
Reinforced concrete pile (Bent)
|
Expansion joints within the space of the superstructure 1.0 |
|
Single Column 3 |
Column, Pier or Pile & Cap-bema or Superstructure 1.0 |
|
Steel or Composite steel and Concrete pile
|
|
|
Multi-column 5 |
Column or Pier & Foundation 1.0 |
Tab-1 Responce Modification Coefficient, R
Firstly, let's consider the value of 3 defined for single-span piers. Single-span piers do not have structural ductility, so considerations are required only for strength reduction due to ductility and material yield strength.
While the exact rationale behind the determination of the number 3 by the committees in the United States for these two factors is not precisely known to the author,
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Regarding the material capacity, it is generally considered at a safety factor of 1.5.
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Regarding the plastic strain, it is considered that even accounting for construction errors where shear reinforcement may not be perfectly installed, a ductility factor of at least 2.5 can be sufficiently ensured in practical structures.
From the equation of The Law of Conservation of Energy, it is judged that the yield strength can be reduced to about 2, and the author understands it to be determined as approximately 1.5×2=3. Some experts in South Korea seem to interpret this as determined solely by the ductility without considering material ductility, but such an interpretation is not valid.
In the case of multi-span structures, the factor of 3, initially determined for short-span piers, is understood to be adjusted to 5 by considering structural ductility of 1.5.
Additionally, the exclusion of shear force and the application of response modification factors only to moments are defined with a priority on ensuring the safety of human lives in structural design. Unlike moment failure, shear failure involves a sudden, catastrophic collapse that does not provide warning opportunities, thus response modification factors are not applied to shear for safety reasons.
While bridge structures are relatively simple in form compared to architectural structures, architectural structures, with their complex shapes and diverse types of components, involve intricate calculations for the values defined in seismic design standards. The concept of seismic force resistance systems in architectural standards introduces a broader array of terms such as response modification factors, system over-strength factors, and displacement amplification factors, making the overall process more complex.
If permitted, I would appreciate an opportunity to elaborate further.
4. Closing Remark
The determination of the response modification factor, a value with the most significant impact on the design loads, was defined while discussing the affairs of the world and sipping coffee. Knowing this fact, designers may sometimes feel a sense of futility about the efforts made to avoid any violation of the specifications in the design process, especially when compared to the meticulousness required in structural calculations, where even a small error of around 1% in the calculations can lead to structural collapse.
However, the reason for introducing the response modification factor as a procedure to simplify complex nonlinear analyses is rooted in the acknowledgment that seismic force calculation in design is a natural phenomenon with much lower accuracy compared to structural calculation formulas.
The code specifies terms such as "probabilistic earthquake during the structure's lifespan" or "earthquake with a frequency of occurrence once in a 1,000 years." Despite the narrow geography of the Korean Peninsula, Seoul and Gyeonggi Province are classified with high seismic zones, while Gangwon Province and Jeolla Province are designated with lower seismic zones. Nevertheless, given the unpredictability of accurately forecasting the size of an earthquake occurring once in a thousand years, and the challenge of determining whether earthquakes in Gangwon and Jeolla provinces are inherently smaller than those in Gyeonggi and Gyeongsang provinces, accurately calculating response modification factors holds limited significance when considering the inherent uncertainty in seismic force calculations.
However, this doesn't imply that one can be careless in structural calculations since seismic force calculations themselves are inherently inaccurate due to uncertainties in predicting seismic forces in nature. Competent designers must assess the structure comprehensively, akin to seeing the forest without fixating on individual trees.
Currently, our society is witnessing the advent of a new transformer in the Fourth Industrial Revolution with the unveiling of artificial intelligence in natural language processing, known as GPT-4. While studying numerical analysis programs related to seismic design in the 1980s, the author experienced that reducing the time interval △T of seismic waves through the advancement of electronic computers led to more accurate interpretations that were less dependent on algorithms than theoretical analysis methods.
Even in the field of artificial intelligence, which mimics the neural networks of the human brain and learns on its own, there is an evaluation that as computational capabilities increase with a growing amount of input data, machines are approaching the singularity where they surpass humans.
In the realm of numerical analysis for seismic design, the question arises: Will the day come when machine-based methods, rather than relying on human insight such as response modification factors, are introduced to judge the seismic safety?
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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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