Earthquake forces are the most destructive loads engineers have to deal with. Why are
these loads so deadly and is there something we can do to mitigate their effects?
The destructive power of earthquakes has been demonstrated many times over the last
centuries. Even though earthquakes appear random,
their frequency of occurrence and location is somewhat predictable. Our understanding
of tectonic plates, geological features and empirical data enabled engineers and geoscientists
to create seismic hazard assessment maps that predict these events. Predicting earthquakes
does not mean pinpointing the exact date but rather estimating the probability of occurrence
and their magnitude which can then be matched with an appropriate design that balances cost
and risk. The process of seismic or earthquake hazard assessment for the most
part is a statistical operation that works best in modeling events which we do not fully understand
but have lots of empirical data for. To actually understand why the seismic forces
are so destructive we would have to understand the main forces that a structure is exposed
to during its life. For their entire life, structures are subjected to gravity loads.
Gravity loads consist of any mass that is accelerated by gravity and pushes vertically down
on the structure. These masses can be the mass of the building material itself, accumulated snow,
or human actions. Engineers have become very good at dealing with gravity loads,
most of the time these loads are transferred to the ground with an outstanding success.
Besides gravity loads, there are also lateral loads which act in a horizontal direction
such as wind or earthquake forces. The earthquake loads occur as a result of ground
acceleration (or shaking) that is transferred to the building. This is pretty intuitive and
can be replicated with a stack of blocks. If the system is accelerated fast enough,
like the stack on the left, the inertial forces of each block will overcome the frictional forces
and separate from the stack. This analogy can be extended to structures, although,
structures are flexible and do not displace rigidly but rather deform internally. This
internal deformation is shown in terms of sustained damage and is key in dissipating
a portion of the kinetic energy transferred from the moving ground into the building.
But the reason why damage occurs in the first place can be traced back to Newton’s Second Law.
Any accelerated mass requires that same amount of force to be restraint.
The restraining force in the blocks system on the left is the friction force that keeps the
blocks from sliding past one another. In regular building, the slabs compose
the majority of the structural mass and are therefore associated with large inertial force.
The force keeping this mass restraint comes from the structural members such as columns, walls,
or bracings that try to oppose this motion. Since the structural members at the base have
to resist the inertial force of the entire mass above. Usually, the structural damage is concentrated
around this area of the building. This damage can be seen on the picture on the left
which shows the damage caused to the Hanshin viaduct during the Kobe earthquake. In this case,
the viaduct was too massive, producing huge base forces that the columns could not support. Similar
scenario occurred with the Cypress Street Viaduct during the Loma Prieta earthquake.
However, it is worth noting that fully restraining a structure against earthquake
loads without sustaining damage is a very costly and impractical approach due to the
enormous magnitude of the seismic loads. The estimated peak ground
acceleration for some places in California is as high as 1g. If the structure was
perfectly rigid during an earthquake with a peak ground acceleration of 1g,
the structure would undergo base forces as if it was built horizontally outwards from
a cliff. Obviously, such structure is not feasible. No (practical) material can withstand
such forces. Because earthquakes shift direction rapidly,
they do not sustain high accelerations for long periods; therefore, structures that have longer
periods tend to be exposed to smaller loads. In other words, moving out of sync with the
earthquake would help the structure by canceling out some of the motion. This can be seen on the
so-called spectral acceleration plots. I won’t go into detail how these plots are developed, but it
is clear that for longer periods of vibration the acceleration is significantly reduced.
A period of vibration is the time that it takes the structure to complete one full oscillation.
The period is dependent on the properties of the structure itself. Mainly, the mass and stiffness.
The stiffness of a structure is heavily influenced by its height. This is because the stiffness is
inversely proportional to the cubic power of the height. Even though taller buildings are more
massive, due to the extra material, their stiffness is exponentially reduced due to their height.
Therefore, taller structures end up in the long period range on the response spectrum.
Since taller structures vibrate (more) out of sync with earthquakes, contrary to popular believe, they
perform better during an earthquake. But keep in mind the response of a structure is also dependent
on many other parameters that are not mentioned in this video such as the underlain soils. Soft soils
could amplify the response of the structure making a moderate earthquake much more dangerous.
The magnitude of the earthquake, as popular as it is, does not tell us the whole picture about
a seismic event. The engineering practice and underlain soils are just as important as the
magnitude itself. For example, the Loma Prieta earthquake of 1989 with magnitude
of 6.9 resulted in 63 casualties, the 1995 earthquake in Kobe with a magnitude of 6.9 killed
around 6000 people. In comparison the 2010 Haiti earthquake measuring 7.0 resulted in more
than 160 000 deaths. Clearly well-engineered structures could and do make all the difference.
The currently accepted design practice relies on allowing structural damage
but no complete collapse. The sustained damage plays a crucial role in dissipating the energy
transferred from the seismic waves. Structures would often be severely damaged and unusable
after an earthquake event but would maintain their gravity loads. Maintaining the gravity loads is
paramount because even though the seismic forces destroy/damage the structure, ultimately,
the gravity loads are responsible for the majority of the casualties in these events.
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