When an earthquake occurs, the intensity of ground shaking can vary significantly from one location to another. This variation is primarily due to the geological properties of the site where the earthquake is taking place. Understanding these local site effects is essential for predicting the potential impact of an earthquake on a specific location and taking appropriate measures to mitigate its effects.
What are Local Site Effects?
Local site effects refer to the amplification or attenuation of ground motion during an earthquake that occurs due to the geological properties of the site. The intensity of ground shaking during an earthquake is affected by a combination of factors such as the earthquake’s magnitude, distance from the epicenter, and the type of soil and rock present at the site. Different types of soil and rock have different levels of stiffness and density, which affect the way they respond to seismic waves.
For instance, soft soil and loose sediment layers can amplify the ground shaking during an earthquake, while hard rock can attenuate it. This amplification effect can be particularly severe in urban areas, where man-made structures can interact with the soil to create resonance, leading to a significant increase in ground motion. In contrast, hilly or mountainous areas with hard rock are less likely to experience strong ground motion during an earthquake.
Why is it important to consider Local Site Effects?
Understanding local site effects is crucial for assessing the potential impact of an earthquake on a specific location. It helps in predicting the intensity of ground shaking and the resulting damage to buildings, infrastructure, and human life. Site-specific assessments can also help in developing effective earthquake-resistant designs and building codes that consider the geological properties of the site.
For example, tall buildings located on soft soil or reclaimed land can be particularly vulnerable to earthquake-induced ground motion. These buildings may need additional reinforcement and foundation design to withstand the amplified shaking. Similarly, bridges, tunnels, and other critical infrastructure located in high-risk areas may require special attention to ensure their safety during an earthquake.
Local Site Effect during 2015 Gorkha Earthquake
The 2015 Gorkha earthquake, also known as the Nepal earthquake, was a devastating earthquake that occurred on April 25, 2015, with a magnitude of 7.8 on the Richter scale. The earthquake caused widespread damage and loss of life in Nepal and neighboring countries, with a death toll of over 8,000 people.
In the case of the 2015 Gorkha earthquake, the local site effect played a significant role in the damage that occurred in Kathmandu, the capital of Nepal. Kathmandu is situated on a sedimentary basin, which is known to amplify the seismic waves generated by earthquakes. The city’s geology, coupled with the haphazard urban development, created an environment that was highly susceptible to seismic waves.
The valley is composed of layers of sediments that have been deposited by the rivers that flow through it over millions of years. The city is built on a mix of soft and hard sediments, which means that the ground shaking was amplified in some parts of the city and attenuated in others. This led to significant variations in the damage that was caused to buildings and infrastructure. In some areas of the city, the ground shaking was amplified by a factor of two or more. In other areas of the city, the ground shaking was attenuated by the presence of hard rock, which meant that buildings were less likely to collapse.
To demonstrate the local site effect, I have conducted a simulation using python to analyze the response of a multi-degree-of-freedom (MDOF) system to the acceleration time histories obtained from three different locations in the Kathmandu Valley: Kritipur, Patan, and Thimi. The locations of the stations are clearly marked on the map below:
The simulation involved modeling the MDOF system using appropriate structural and mechanical properties and inputting the acceleration time histories obtained from the three different locations in the valley. The properties of the MDOF system are as follows:
Lumped mass at each floor = 1000 KN
Stiffness at each floor = 2467 KN/m
Number of floors = 4
The result from the simulation is shown in the video below:
The simulation presented above provides interesting insights into the local site effects that occurred during the 2015 Gorkha earthquake in the Kathmandu Valley. We observed that, although the peak ground acceleration (PGA) values were similar in all three sites (Kritipur, Patan, and Thimi), the response of the MDOF system to the acceleration time histories varied significantly depending on the geological conditions of the site.
In Kritipur, where the soil is underlain by rocky strata, the energy dissipation during the earthquake was high, leading to attenuation of lower frequency wave forms and higher frequency content in the wave. Consequently, the MDOF system responded with low oscillation to the acceleration time history from Kritipur, as the attenuated waveform did not significantly affect the system modeled with the structural properties used in the simulation.
On the other hand, in Thimi, where there is sediment deposit, the wave was amplified and the frequency content decreased. This led to higher oscillation of the MDOF system to the acceleration time history obtained from Thimi. The amplification of the wave was due to the interaction of the seismic waves with the soft sedimentary layers, which tend to amplify the ground motion. The decrease in frequency content was due to the dispersion of the wave, as the different frequencies traveled at different speeds through the heterogeneous soil layers.
Overall, the simulation highlights the importance of understanding the local site effects in earthquake risk assessments and designing more resilient structures. By accounting for the local site effects, it is possible to identify areas of high seismic hazard and design structures that are better able to withstand the effects of earthquakes. This can help to reduce the risk of damage and loss of life during earthquakes, particularly in regions of high seismic hazard such as the Kathmandu Valley.
Natural frequency is a fundamental concept in physics and engineering that describes the frequency at which a system oscillates when disturbed from its equilibrium position. Although it’s an essential concept, many of us fail when we try to communicate this terminology. In this blog, I will explain natural frequency in simple terms and provide demonstrations to help illustrate its significance. Additionally, we will discuss its importance in earthquake-resistant building design.
The natural frequency of a system is the frequency at which it oscillates when it is disturbed from its equilibrium position with no external forces acting on it. This frequency is determined by the system’s properties, such as its mass, stiffness, and damping. The natural frequency is often denoted by the symbol (omega) and is measured in Hertz (Hz).
For example, consider a mass hanging from a spring. When the mass is pulled down and released, it oscillates up and down at a certain frequency. This frequency is the natural frequency of the system and is given by:
where is the spring constant and is the mass.
Equation 1 provides the natural frequency in an ideal scenario where there is no damping. However, in reality, there is energy dissipation in each oscillation cycle, which is known as damping. To account for this, we need to incorporate a damping coefficient () into the system. The resulting damped natural frequency is given by:
where is the damping ratio and its expression in terms of damping coefficient is given as:
where is the damping coefficient of the system.
Simulation of a SDOF System
Now that we have examined the fundamental equation for natural frequency, let’s explore this concept through a simulation of a single-degree-of-freedom system. To simulate the motion of a single-degree-of-freedom system with no external force, we need to solve the equation of motion. This equation can be expressed as follows:
where, is the displacement from the mean postion, is the velocity and is the acceleration.
Consider a system with mass attached to a spring with stiffness and a damping ratio of . Suppose we initially pull the system to a distance from its equilibrium position and then release it. The system will then oscillate back and forth at a certain frequency, which is the natural frequency of the system.
If we apply a larger displacement to the system initially, we might expect it to vibrate at a different frequency than when we apply a smaller displacement. However, this is not the case. The natural frequency remains constant, regardless of the initial displacement. The only difference between the two scenarios is the amplitude of the vibration. When we apply a larger initial displacement, the system oscillates with a greater amplitude, resulting in more rapid vibration. Conversely, when we apply a smaller initial displacement, the system oscillates with a smaller amplitude, resulting in a slower vibration. Thus, the natural frequency of the system remains constant, while the amplitude of the vibration changes with the initial displacement.
Now let’s look at the simulation for two different cases: a) undamped condition, and b) damped condition.
a.) Undamped Case:
If we put in equation 4 and solve for then we get the expression:
where is the initial displacement and is the velocity.
Based on the above equation, the result of the simulation in python is as follows:
b.) Damped Case:
Considering the damping coefficient in equation 4 the solution to the equation is:
The result of the simulation of this equation in python is as follows:
From the simulations presented above, it is evident that when an initial displacement is applied to a single degree of freedom system and released, it oscillates in a harmonic manner. This oscillation frequency is known as the natural frequency of the system, which is determined by the system’s properties such as its mass, stiffness, and damping. The natural frequency is a fundamental characteristic of the system and plays a crucial role in determining its behavior.
Since we have understood the natural frequency, we can talk about resonance. Resonance is a phenomenon that occurs when a system is forced to oscillate at its natural frequency or a multiple of its natural frequency. When a system is excited by an external force at or near its natural frequency, the amplitude of the system’s oscillation can increase dramatically, even if the external force is relatively weak. This is because the energy supplied by the external force is being added to the system at just the right time to reinforce its oscillations.
Resonance can be beneficial or detrimental, depending on the context. For example, in musical instruments, resonance is used to amplify sound by matching the frequency of the sound wave to the natural frequency of the instrument. In contrast, resonance can be a cause of structural failure in buildings and bridges, as the oscillations caused by external forces can become so large that they cause the structure to vibrate uncontrollably, leading to damage or collapse.
During an earthquake, resonance can occur in a building when the frequency of ground motion matches with the natural frequency of the building. The natural frequency of a building varies depending on its mass and stiffness as shown in the equation 1. For example, a tall building will have a lower natural frequency compared to a shorter building. Similarly, if we increase the stiffness of a building with the addition of lateral load-resisting members like shear walls, then the natural frequency increases.
In addition, there are several factors that affect the frequency content of an earthquake, such as the type of soil. If the soil is rocky, the frequency of vibration is high but the amplitude is low. Conversely, if the soil is relatively loose, the frequency of vibration is low but the amplitude is high. If the frequency of ground motion matches with the natural frequency of the building, it can cause devastating effects.
The resonance condition is clearly seen in the simulation below where three buildings with different heights are placed in a Shake Table. The Shake Table is built by me and my friends at the research lab of Khwopa College of Engineering. . In the simulation, the input is a discontinuous sine wave signal with varying frequency, starting at 5 Hz and ending at 0.8 Hz with a decrement of 0.2 Hz every 5 seconds. Similarly, the amplitude increases from 5 mm to 20 mm. The graph of input motion is shown below:
Figure: Input motion of the Simulation
In the simulation, it can be observed that during the initial high frequency of the ground motion, the shortest building vibrates more compared to the other two buildings. However, as the frequency gradually decreases, the middle building starts to vibrate more. Finally, when the frequency becomes very low, the tall building vibrates significantly more than the other two buildings. This indicates that the buildings with different heights will have different natural frequencies, and they will vibrate differently in response to ground motion with varying frequencies.
Earthquake Resistant design
From the above simulation, we can say that resonance can cause serious damage to structures during an earthquake. Therefore, it’s essential to design buildings in such a way that they do not resonate with the ground motion during an earthquake. To achieve this, we must first understand the ground motion parameters of the site where the building is to be constructed. These parameters are directly dependent on soil conditions, nearest faults, past seismic activities, etc., and are obtained through various seismic analyses. Based on the information we plot a response spectrum of the ground motion that is most likely to occur.
Based on the response spectrum, engineers design the building to have a natural frequency that is different from the ground motion. If the building’s natural frequency matches the frequency of the ground motion during an earthquake, resonance can occur, and the structure can suffer serious damage. To prevent this, engineers adjust the mass and stiffness of the building so that it does not resonate with the ground motion. This is typically achieved by adding lateral load-resisting elements like shear walls to increase the building’s stiffness, thus increasing its natural frequency. Also, other methods like tuned mass damper and base isolation can also be considered. By designing buildings in this way, we can reduce the risk of damage and ensure the safety of people and property during an earthquake.
The python code and simulation results are attached below:
On February 6, 2023, a powerful magnitude 7.7 earthquake struck south-central Turkey near the border with Syria at 4:15 a.m. local time, causing widespread damage and affecting many lives. The quake was quickly followed by a magnitude 6.7 aftershock just 11 minutes later, adding to the already chaotic situation. This earthquake is one of the strongest to hit the region in recent years, and its effects were felt far beyond the immediate area.
As a structural engineer, I was curious about the ground motion generated by the earthquake and decided to simulate it in the Shake Table at the Khwopa College of Engineering's research lab. To do this, I first needed the time series data of the earthquake, which I was able to download from the Disaster and Emergency Management Authority (AFAD) of Turkey. The data included East-West Acceleration, North-South Acceleration, and Up-Down Acceleration. The files are as follows:
Since the shake table can only simulate earthquakes in a single direction, the N-S direction was taken because it had a higher Peak Ground Acceleration (PGA) which is 0.51 g. The Acceleration time history is as shown below:
On integrating the acceleration data, we found that the peak displacement was 63 cm. However, our shake table could only give a maximum stroke of 9 cm so the data needed to be scaled down. While scaling down the data, there was a problem.
Scaling down the displacement of the earthquake would also decrease the acceleration in proportion, resulting in a weaker motion on the shake table platform. To accurately represent the actual inertial force during the actual earthquake, it was necessary to keep the acceleration constant. But in order to do so, the sample time had to be reduced proportionally, ultimately decreasing the total time duration of the earthquake. This compression of time can be seen in the graph below.
In the above graph, the top row displays the actual acceleration, velocity, and displacement time series, while the bottom row shows the scaled data. It can be observed that while the acceleration remains unchanged, the total time duration has been shortened. Conversely, both the velocity and displacement have been reduced.
An alternative approach would be to maintain the velocity constant while scaling down the displacement, which would result in a PGA of around 3g (which is very high). On the other hand, decreasing the displacement without compressing the total time would lower the PGA to 0.3g. However, for this particular simulation, we opted to keep the acceleration constant. A video of this simulation is presented below:
In this video, we can observe the devastating impact of a strong shock wave over a brief period, causing widespread damage to structures in Turkey and Syria.
The displacement of the shake table recorded by encoder is as shown below: