Earthquakes are not in the Weather Forecast program, simply because they cannot be predicted. Although Vietnam is not in a strong earthquake zone, the data of more than 200 years of observations does not guarantee that a disaster will not occur. The knowledge of engineers helps construction works to be the place to preserve human life in earthquakes. This series of articles tries to explain this issue in the most popular way possible🆗
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In the previous article, we learned that earthquakes, according to the latest TC, are represented by the Ground Acceleration Peak, showing whether each area of land is strong or weak. Why is it 50 years for the probability value of being exceeded? Because 50 years is the normal lifespan used for houses. We already know that according to Newton’s second law, having acceleration means knowing how much earthquake force acts on the structure. According to that principle, we consider how the structure accelerates when there is an earthquake.
📖Earthquake on construction works
What happens to the house when there is an earthquake?
Imagine you are sitting in a car, suddenly braking hard. You will be pushed forward. It is because your body suddenly reduces its speed from 100km/h to zero in 3 seconds. The body is affected by a force similar to weight in the horizontal direction. It is called the inertial force. According to Newton’s second law, it is equal to your mass multiplied by the acceleration.
When the ground shakes, it forces the foundations of the building to vibrate. If you are on the ground floor of a building, you may be violently thrown, as shown above. The acceleration of the ground acts as a “pump” of energy into the structure. This energy increases as the ground continues to shake. A strong earthquake has tremendous energy. If the structure is not designed to withstand this energy, it will collapse.
🖼 photo_The structure shakes with the ground But we should not design the structure to contain such a large amount of energy, it is too wasteful 💰, compared to the very low probability of an earthquake. The wise design is to make the structure capable of dissipating the earthquake energy that impacts it. How does it work?
When a force acts on an object, the force creates work that moves it from its original state. If the object does not deform, that energy (work) is equal to the force times the distance. Part of it is lost due to the resistance that prevents the object from moving the entire distance. The other part is that the object is always deformed. The magnitude of the force multiplied by the deformation is called the deformation potential energy, which is also the part of the energy that is dissipated. Similarly, in an earthquake, its energy is transmitted to the structure and dissipated due to:
💎Deformation:
– Elastic deformation: increases or decreases proportionally to the force. The area under the graph, as shown below, is the dissipated structural energy.
🖼 image_Energy dissipated by elastic and plastic deformation Energy in the elastic region: the area of the blue triangle is very small compared to the area in the plastic deformation region. Therefore, seismic design does not mean that the structure is too large.
– Inelastic (plastic) deformation: the force does not increase but the deformation keeps increasing. This leads to an increase in energy dissipated. If the structure is not flexible, it cannot withstand fatigue due to repeated earthquake loads hundreds of times as shown below
🖼 image_ Earthquake Repetitive Load
The structure in this figure has great strength and ductility when subjected to both compression and tension, due to the sign of the repetitive load. The diagram above shows that the area under the curve in the elastic region, when the deformation is less than 1mm, is very small compared to the remaining area when the structural deformation is up to 15mm. This is the beauty of ductility. It contributes greatly to the ability to dissipate earthquake energy, after the damping resistance below.
Therefore, ensuring the ductility of the structure is an important factor when designing a seismic-resistant structure.
💎Damping resistance: proportional to the velocity of movement. It is the factor that causes the vibration to gradually dampen. The faster the building vibrates, the faster it dissipates energy. The difficulty is that we do not know how much damping ratio each building has, which can range from 1.5% for high-rise buildings to 5% for low-rise concrete buildings.
The lower the building, the faster it dissipates energy, it stops oscillating more quickly after the earthquake ends than a high-rise building. The reason is that in addition to its lower viscous damping coefficient, it also has a longer natural period of oscillation than a low-rise building. Because the damping energy is released with each oscillation cycle.
🖼 image_ Damping makes the oscillation gradually dampen
For example, the oscillation of a building in 20 seconds as shown in the chart above, a low-rise building has an oscillation period of 1s and a high-rise building has an oscillation period of 5s. Thus, in 20s, the low-rise building oscillates 20 times and the high-rise building 4 times. Assuming that the 2 buildings have the same viscous damping ratio, the energy released is 5% per cycle of the total energy of each building. Thus, a low-rise building with more oscillations in the same period of time will release energy faster. That is why low-rise buildings dampen oscillations faster after an earthquake.
So is damping good or not for the house? Of course, we do not want the house to shake forever. So we expect the damping coefficient of our house to be as large as possible.
Why is it called viscous damping?
Take the popular type of damping, for example, the piston in the oil of a shock absorber. This type has a resistance force proportional to the speed of movement, the structure of the house also works like that.
The standard uses a viscous resistance coefficient of 5%. Why is it 5% and not another number? Oh boy, I can’t explain it. If you know, please share it in the comments below 🥰
📖Earthquake standards
Currently, the effective Vietnamese standard is TCVN 9386:2012 “Design of structures for earthquake resistance”. Compiled based on Eurocode 8 “Design of structures for earthquake resistance”. The ground acceleration data in the standard is according to the administrative place name, similar to QCVN 02:2009 “Natural data in construction”.
Accordingly, the project ensures earthquake resistance (can withstand earthquakes) when it meets 2 criteria:
– Does not collapse when subjected to a reference earthquake
– Limits damage when subjected to earthquakes with a frequency higher than the reference earthquake
so that people can escape in time, ensuring safety of life.
📘Vocabulary
📖No-collapse requirement (NCR)
The structure can withstand a reference earthquake, with a return period of TR=TNCR=475 years, equivalent to a probability of exceeding PR=PNCR=10% in TL=50 years. There is an importance factor γI representing different levels of reliability.
To achieve this criterion, the load-bearing structure needs to:
– ensure durability
– have Ductility and energy dissipation. The tool is the design method according to the Bearing Capacity (Capacity design)
…
Details of the requirements for houses are in section 4.4.2 of the standard.
📖Damage limitation requirement (DLR)
Withstand earthquakes with a higher probability of occurrence: the return period is TR=TDLR=95 years, equivalent to the probability of exceeding PR=PDLR=10% in TL=10 years
To achieve this criterion, for buildings, the standard only requires a limit on relative displacement between floors, according to 4.4.3.
The relative displacement is equal to the difference in horizontal displacement between any two floors on the height of that floor.
📖Response Spectrum
is the main tool to determine the earthquake force acting on the structure
As mentioned, when there is an earthquake, the ground acceleration is the stimulating factor that makes the structure vibrate and shake. Like all physical objects, the house also has its own oscillation cycle, it oscillates at its own frequency. This cycle depends on the number of floors, stiffness… of the house. The natural oscillation period says a lot about the mechanical properties of each house. If measured, the maximum oscillation acceleration corresponding to the natural oscillation periods of different structures can be obtained, in the form of a graph as below:
🖼 image_ Response spectrum
that is the form of Response spectrum often used in seismic resistance of construction. The horizontal axis is the period, the vertical axis is the largest oscillation acceleration.
Why is it called Spectrum? Remember popular physics, the 7 colors of the rainbow 🌈 why does light scatter into countless colors like that. That color range is a type of spectrum, called Spectrum. Similarly, called response spectrum, is a response range of different constructions (each house has its own oscillation period) in an earthquake. What reaction? It can be anything: displacement spectrum, velocity spectrum, acceleration spectrum. In the most commonly used standard is the acceleration spectrum. From acceleration, we deduce force according to Newton’s second law: multiply acceleration by mass.
As in clause 4.3.3.2.2 of TC, the earthquake force at the foundation (bottom shear force Fb) is equal to:
$$F_b=S_d(T_1)m\lambda$$
$S_d(T_1)$) is the spectral ordinate (acceleration) corresponding to the natural oscillation period (basic oscillation) T1 of the house
m is the total mass of the house participating in the oscillation
From the bottom shear force, each floor of the house is subjected to a horizontal force distributed according to the ratio of formula (4.10) of the code:
$$F_i=F_b\frac{s_im_i}{\sum{s_jm_j}}$$
where
$F_i$: horizontal earthquake force distributed to the i-th floor
$s_i,s_j$: displacement of the floor masses mi,mj in the basic vibration mode
$m_i,m_j$: mass of the i-th, j floors
In fact, the calculation software is more complicated, but the above illustrates the basic principle of earthquake force transmission in construction.
There are 2 basic types of response spectrum:
– 📖Elastic response spectrum: when the structure’s response is linear elastic, the response is the largest acceleration called the elastic response spectrum.
– 📖Design spectrum: due to the structure’s plasticity (nonlinear behavior) and energy dissipation, the actual earthquake force acting on the structure is not as large as when the above linear elastic response.
But nonlinear analysis of structures is very complicated, inconvenient in the practice of engineers compared to linear elastic analysis. The TC’s approach is to use the response spectrum reduced from the elastic response spectrum, through the response coefficient q, on the structure’s elasticity diagram. This new spectrum is called the design spectrum.
The shape of the response spectrum depends on the region of different strong and weak earthquakes, in TCVN there is only one form of the response spectrum (Eurocode has 2).
The design spectrum chart formula given in 3.2.2.5 of TC, depends on:
– $a_g$: ground acceleration, indicating the strength of the earthquake that is likely to occur at the construction site
– Type of ground at the construction site: due to different type A ground (see below)
– q: response coefficient, reduces the spectrum by putting q in the denominator
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📖Just babble the background A, Why must classify ABC?
Because the ground according to depth into many layers from soft to hard each other. The earthquake transmitted in the soil depends on its hardness. Suppose 1 match The earthquake emitted from a deep deep fault zone. Earthquake There is a different frequency than on the ground (trauma). For 2 reasons: 1 is the right wave transmitted through a certain distance, losing energy, that is, acceleration is reduced. 2 is that the wave is also shaped according to the soil properties it passes through. Classes The soil is like a filter, because each type of soil reacts with a certain frequency of earthquake oscillates with its own frequency.
Hence the reaction spectrum will vary from all kinds Different soil. That is essential to classify the ground, which works are not standing On the ground.
🖼 image_Response spectrum with different types of ground
Hard ground, even Rock, behaves like a hard shaking table vibrating violently, very high frequency. The structures that react to high frequency are low-rise buildings. High-rise buildings do not easily react to high-frequency shaking because it has a large natural oscillation cycle.
Soft soil, the weaker the soil, the more it behaves like water to low-rise buildings. Imagine like a boat in a storm, low-rise buildings are not affected by shaking on weak ground. On the contrary, high-rise buildings on weak ground are subject to much greater earthquake force than on good ground. Because weak soil vibrates at a longer cycle, it is easy to add nrgh to the long cycle of high-rise buildings.
Article 3.1.2 of TC classifies the soil as follows:
– A: rock foundation
– B: gravelly soil, very dense sand or very hard clay
– C: gravelly soil, dense sand, medium dense or hard clay
– S1: soil with soft clay/silt layer of high plasticity (plasticity index IP>40) and high humidity, with a thickness of at least 10 m
…
How hard and dense is quantified by the average shear wave velocity number $v_{s,30}$, of the soil layers within 30m from the ground surface
$h_i, v_i$ is the thickness, shear wave velocity of the i-th layer among the N soil layers in that 30m.
In case there are no conditions to conduct shear wave velocity experiments during geological surveys, it is possible to use more common $N_{SPT}$ data to classify the ground, in a similar way as follows:
