THE END OF EARTHQUAKE HAZARD
Unlike some other natural disasters such as droughts, floods, or hurricanes, earthquakes are selectively destructive to humans. Other life forms are relatively immune to earthquake damage. As we learn to diagnose and prevent earthquake disasters we may begin to reflect on the impending demise of earthquake hazard. What will happen when human societies will be as little affected by this hazard as social insects are today--a modest goal, considering our relative technological superiority over ants or bees?
In the next few decades, fundamental advances in structural design and building technology are likely to reverse the current trend toward increased vulnerability of structures to earthquakes, which has been attributed to changes in land use since the 1950's related to urbanization. Recent seismic disasters in Mexico City, the San Francisco Bay area, and Kobe were clearly related to soft ground conditions. Thus one key advance in the control for seismic disasters will probably occur in the field of site-conditioned design of construction systems.
The vision of a society without earthquake risk may seem utopian to some. But Utopia is here already. Some structures in common use are both economical and earthquake-proof, owing to the fact--first pointed out by James N. Brune--that the effects of earthquakes are bounded. The free-surface ground acceleration remains below 2 g, a theoretical inference which has been confirmed by available strong-motion observations of earthquakes. But an acceleration of twice gravity can be handled easily by any automobile. It might be objected that cars are unsafe as compared with homes, but this is not the fault of earthquakes. It is due to the fact that our driving habits are even more pernicious than our structural designs. The point is that our homes, our offices, our bridges, and our freeways should be made at least as earthquake-resistant as our cars.
This was but a distant dream a few decades ago, but it has become a reality on hard-ground sites throughout the world. After the 1922 Chile earthquake the Carnegie Institution of Washington issued a booklet purporting to instruct peasants in the art of reinforcing adobe construction with twigs and branches. Today in Chile as in Mexico adobe is but a distant memory. There is hardly anyone left who is old enough to remember how to make adobes. On the other hand, hazardous construction on soft ground has spread all over the industrialized world.
Norman Haskell and Frank Press discovered coupling between Rayleigh waves and P waves around 1950. The effect was first observed at the interface between water and ice, and later between soil and air. These seismologists realized that coupling represented an efficient mode of propagation of seismic energy at any interface, but as the work was done for the Air Force it was immediately classified because of its relevance to the detection of atmospheric explosions at large distances. I suspect that they realized that coupling can be just as relevant to earthquake hazard, since the coupled modes propagate efficiently along the base of soft soil layers. But the term "coupling" was dropped from the seismological literature, and eventually it was forgotten.
Coupling accounts for the monochromatic waves of finite time duration known as coda waves. A theoretical explanation was provided by Frank Press and Maurice Ewing in 1951. As the phase velocity of Rayleigh waves approaches the speed of sound in the soft layer the dispersion curve undergoes a subtle change. It develops a kink or step which has an inflection point at the coupling frequency. The coupling point matches a maximum of the group velocity. A singularity arises when the two phase velocities are equal. Coupling spawns a new, nearly vertical group-velocity curve, where each point on the curve is an Airy phase.
In a bounded basin, Octavio Novaro and coworkers in Mexico City found that the coupled mode is locked to the interface between the soft surface layer and the underlying harder sediments, and it echoes back and forth between the lateral boundaries of the basin, thus generating a quasistationary wave field with prominent nodes and antinodes. As the thickness of the soft layer is usually much smaller than the wavelength, the mode radiates to the free surface, where exotic nonlinear interactions between elastic and gravity waves are generated. The response of the basin strongly depends on the geometrical shape of the soft layer.
In the case of soft ground the phase velocity equals the speed of sound in the soft layer--usually 1.5 km/s for saturated soils. A coupled mode translates as a velocity step across an array: The apparent velocity stays constant for the duration of the wave train. Diagnostic features include coherence, monochromaticity, and constant phase velocity. These insights have been obtained by means of new experimental array techniques.
The Texcoco Array is a seismic array sited on extremely soft soil near Mexico City. The water content of the soil is above 90%, great enough so that conventional instruments tend to sink into the mud by their own weight. Roger Bilham designed a new strain seismograph that can be screwed into the mud by hand. This potent device has produced amazing strain records of coupled modes, including an intriguing DC component which had never been noticed before. Soft-ground seismology is a rapidly developing new branch having important connections with acoustics, nonlinear science, and the physics of colloids.
If damage on soft ground can often be attributed to coupling--a relatively unfamiliar and little-understood phenomenon--the consequences of this insight to earthquake engineering are immediate and remedial action is straightforward. Design on soft ground must be based on the mitigation or suppression of resonance. This was only dimly realized before, since earthquake engineers assumed that the seismic signal would be brief, incoherent, and random, whereas what we actually get on soft ground is a highly coherent, monochromatic signal of long duration.
The situation may be compared to what happens when a car travels over a cobbled road surface. The dominant frequency is given by the size of the cobblestones and by the speed of the vehicle. If we happen to hit a resonant frequency, the automobile is done for--unless fluid viscous damping has been installed. Likewise, in the basin of Mexico the dominant frequency of the ground is about 0.4 Hz, and this frequency happens to be in the range of the resonant frequency of buildings six to eighteen stories high. Altogether 371 buildings of this size collapsed in the 1985 earthquake.
Resonance is a well known problem in vibration engineering. The recommended method of remediation has been aptly summarized by a naval engineer, Dana Johansen: "Know the Input/Bound the Output/Mitigate the Difference." In Mexico City the input is a coherent seismic signal with a peak response spectral acceleration of 1 g at 0.4 Hz and a duration of up to five minutes. The output has been bounded--in the 1987 version of the Mexico City building code--at a peak response spectral design acceleration of 40% g. The gap between 1 g and 40% g is the difference which needs to be mitigated.
How can this be done? Chiefly by increasing the damping and by careful testing. In the automobile industry, new models are subjected to extensive and grueling road tests--with actual machines, not computer models. On the other hand, a full-sized building is rarely subjected to destructive testing. Reinforced concrete-frame structures have less than 5% critical damping, while cars are damped at around 23% of critical damping. When the damping is any less, a driver hits his head against the roof, while if the car is overdamped the ride is too hard. In other words, the amount of damping is determined by the customer.
Fluid viscous dampers have been used exclusively for decades because they are sturdy and require no maintenance and because their restoring force is linear with the velocity--just what we need to control resonance. Viscous dampers distributed throughout a structure can achieve the same result as base isolation at a significantly lower cost. The first high-rise building using fluid viscous dampers is now going up in Mexico City. It will be the tallest structure in Latin America, but this is beside the point. It will be safe against earthquakes. Other structures will follow suit, because the solution is economical and rational. Dampers are ideal for retrofitting, because they are much easier to install than shear walls.
When a structure is properly damped, it is prevented from oscillating wildly. It will not swing out of control, even during the strongest possible earthquake. It will not capsize as some high-rise buildings did during the 1985 Mexico earthquake. It will not go into longitudinal buckling modes as did the Hanshin Expressway in Kobe and the Cypress Freeway in Oakland. We know this from the tested performance of dampers in vibrating machinery and from the performance of damped ships in a rough sea. Engineers are not new at this game. We have been successfully dealing with the effects of coherent harmonic motion for a very long time.
In conclusion, let us be reminded that engineered structures can be routinely designed and tested against vibrations. Dampers do not seem to add substantially to the total cost because their presence encourages the structure to lose weight. Some recent research on the effects of earthquakes on soft ground seems to suggest that an analogy between buildings and cars may not be all that farfetched.
It is not officials we should attempt to convince. The complaint that earthquake strategy is a low-priority item on the agenda of governments has been heard too often. Instead, the housing industry must offer innovative, environmentally safe dwellings to the public at a price people can afford to pay. Too many of today's structures are sitting ducks for earthquakes. As a civil engineer I realize that we are trained to look at gravity as our primary challenge in structural design. The result is frequently a rigid, fragile, top-heavy, expensive, and hazardous building. But the public will not accept earthquake risk much longer.
To send a letter to the editor regarding this opinion or to write your own opinion, contact Editor John Ebel by email or telephone him at (617) 552-8300.
Posted: 22 July 1999