Earthquake Damage: Newsletter Challenge (12/04/07)

Like many questions posted on CR4 (especially by Guest) - there's not enough information to give a properly reasoned reply.

Valley: How high? How steep?

Rock & ground: How hard? How soft?

Earthquake: What magnitude? What duration?

Good assessment. Ground shaking is the primary cause of earthquake damage to man-made structures. The influence of the underlying soil on the local amplification of earthquake shaking is called the site effect. One contributor to the site amplification is the velocity at which the rock or soil transmits shear waves (S-waves). Shaking is stronger where the shear wave velocity is lower. Soft soils amplify ground shaking. The National Earthquake Hazards Reduction Program (NEHRP -- in the USA) has defined 5 soil types based on their shear-wave velocity (Vs).

Based on this one would expect the house in the valley--on the softest soil--to be damaged most with the house on the rock damaged least. However, surface geometry does not correlate well with underground features/content & therefore the resulting site effect...so one must make assumptions as Aristodle did, which seem reasonable, and for the purposes of this question substantive enough to address the issues raised by the question.

The following link from the US Geological Survey summarizes soil type & effects for the San Francisco Bay area: http://earthquake.usgs.gov/regional/nca/soiltype/

Thank you for your critique. The main problem with the question of probably the lack of what is meant by "soft". The danger of liquifaction has been repeatedly mentioned by contributors and it is a definate concern, however, soft soil does not necessarily mean saturated soil. In almost all cases liquifaction occurs when the soil is saturated and the shaking results in the point to point contact between particles being rearranged to a more compact arrangement. Without the point to point contact to support the weitht of the overlying soil (and the structures on the soil) the soil acts as a liquid until enough water drains out of the soil that point to point support between particles is re-established. In Japan earthquakes have resulted in as much as 18 inches of water comming to the surface as particles compact and poorly supported buildings sink. This is why beach sand often provides excellent support (because wave action compacted the particles as they were deposited) while nearby lake bottom sand/sediments, being uncompacted, will often quick in an earthquake.

That said, soft soil that is well drained, as if often the case in sloping valleys (depending on the type of soil - which depends generally on the type of underlying rock - some rocks granulate while others turn to clay like pparticles that do not drain well) even though soft, is not likely to liquify. By the same token it is not so much whether the ground is soft or not that makes it so dangerous, it is whether it is saturated. Saturated soil, even if it does not liquify propegates the energy from earthquakes wery well and are therefore dangerous. Soft well drained soil does not propegate energy as well, instead it tends to damp the energy and so is less dangerous. That is why the same earthquate will do much more damage after heavy rains, often causing mud slides, than during a drought. (Pack moist soil into a plastic bucket and tap with a hammer - nothing much happens. Add an inch of water and let it soak in then tap with a hammer - you can see waves propegate through the soil.)

If the soft ground does not liquify then the houses can be thought of as rafts. When there is an earthquake/tsunami the raft in deep water bounces around but is not greatly effected but the one near the shore gets hit by giant waves and the one on the shore/rock shakes a bit and gets hit with the spray from the giant waves. In earthquakes the most dangerous movement is generally lateral movement (horizontal shaking) that has been amplified by local terrain. With some exceptions vertical thrust fault movement is less dangerous than horizontal or slip fault movement, as unless such movement is very deep it seldom propagates the distances horizontally that lateral movement does. The exception is of course for those very close to the fault, to either type of fault.

Underwater this rule of thumb is reversed. Underwater movements of (large) vertical thrust faults (sea quakes) can produce large and very dangerous tsunamis. Underwater movements by horizontal slip faults seldom result in significant waves being produced.

Saturation is not always a defining factor in soil liquefaction. The most pronounced and obvious results are observed where there is fertile soil, but then again that is the habitat of choice of the human race. Soil liquefaction can take place in the desert as the various sizes of sand grains try to stratify and "arrange and infiltrate". Something like mixing powdered sugar/fine sugar/regular sugar/demarra sugar/rock sugar in a container and shaking. Some of the sugars will stratify against others, and some will infiltrate into interstitial spaces between bigger grains. If you've ever done screen sizing dried ore/slurry you'll see this happening on a small scale. The effects of this type of liquefaction can be just as devestating. The last earthquake in Kobe Japan was a good example: Long sections of "earthquake-proof" highway tressels built on well drained, compacted gravel failed while others didn't. The difference investigators noticed was that most of the tressels that failed - the huge foundation under them even though tied to driven piles was not anchored to bed rock. Many of the tressels that survived were standing on bedrock.

This is exactly what happened in Mexico City in 1985. My wife's house in Coyocan (on the south side of the city) is built on crystaline bedrock. She bearly felt the quake and there was no damage in her neighborhood. Yet the centeral part of the city, built on a filled in lake bed was completely demolished.

I agree the ppl that write these endless mystical question expect answers to the impossible. I bet any money this person also invented those "stirers" at Macdonalds you know the usless length of plastic that you try to use to stir you coffee with!!!

Incase you all missed the punch line these questions are just stirs to get you having coffee over at your morning break!!!

I agree. Water saturation of the valley soil, type of earthquake waves, soil type? tomany varibles.

Hey Guru,

Like many technocrats you look for all the facts before you make a decision.

The question is a relative one in that it asks which one basically is going to be worse off, thus even if it is just an ornament falling off the answer given is more than sufficient and clear.

If we were asking for the level of damage or whether a cliff would collapse and crush one of the houses etc etc then you would be right.

No offence intended.

One could postulate a valid answer for any of the houses depending on the detailed geology, type of quake, type of soil, water content, foundations etc.

E.G The house at the bottom will survive as it is on nice soft soil with looong deep pile foundations.

Conversely it could be wiped out by the mud slide, which may or may not contain the debris of house#2!

Similar arguments could be made for house #1.

Thus if pressed for a conclusion I would say house#2 is most vulnerable as it is on or near a disscontinuity which could easilly become the area of diferential movement.

Actually, if you look at history, the one at the bottom will fall first. As it is on soft ground, it will experience soil liquifaction which will amplify the quakes movements. This is evident in the quake that hit central Mexico a few years back. The greatest damage was in Mexico City which sets on old silt deposits of a soft lake bed.

According to geologists, as ricklee states above, soft soil or silty soil, surrounded by hills, will amplify the effects of an earthquake. This is one of the concerns for the area surrounding San Francisco. This deeply concerns me because it is one of the main Wine Producing Regions. Much like waves in an ocean.

I agree with RickLee... The town of Avezzano, (Abruzzo, central Italy), on January 13, 1915, was completely destroyed by an earthquake causing 10,710 deaths. Avezzano was and has been rebuilt on whatwas once was the bottom of the carsic lake Fucino. The lake had been completely drained between 1855 to 1869 to provide 16,000 Hectars of very fertile land. The towns nearby, on the rocky Appennines, were not affected as much.

Vince

It depends entirely on the architect and how good his design is.

Frank Lloyd Wright designed the Imperial Hotel in Japan to 'float' on the soft soil that existed at its chosen site. It survived a major earthquake.

(Unfortunatley, it didn't survive U.S. bombing during WWII.)

I agree

As the above Members have stated, insufficient information has been given.

Here in New Zealand, called in early days "The Shaky Isles", we get many earthquakes each day.

Upon the proper information being given a correct answer may well ensue.

Meanwhile enjoy the background music ....

Well, I am going to guess the right answer is the house on the softer ground inside the valley.

My only thinking is that the softer ground will act as a damper to the vibrations. I would think that the house foundation would settle, but probably be more forgiving.

On the rock itself would be worst because all the shock is transfered to the house there.

Midway between the two, on the rim, I would be concerned that the house would slide over the edge and down the valley.

No experience here, just an educated guess.

except.....

The highest house will crumble like you said because of the efficient transfer of energy between the rock and your foundation, and the rubble will come flying down the hill picking up momentum and speed as it ploughs into the halfway house, carrying it and its weakening structure down like a runaway locomotive until it buries you and your perfect structure under tons of dirt, rocks, vegetation, and assorted construction material. At least they'll be able to bury your remains in that beautiful soft soil.

except.....

The question doesn't mention that the house in the valley is directly below the other two at the bottom of the valley. With the information given, no conclusion can be made as to where the houses are in relation to each other, other than that they're "a few miles apart"

Then we would have to wonder if any of the houses are equipped with some sort of levitation devices. Maybe none of them will experience any damage in that case.

Not me! I was a Boy Scout and you never pitch your tent at the bottom of a valley! :-)

I was a Boy Scout

I knew you were a good guy. I made it to Star, wished I had gone on to Eagle. Have two boys in Scouts now. Having a great time second time around!

That's the same thing I was thinking. Especially since they went out of their way to mention that the one was near the edge and still on "softer ground" than the other.

The softer ground wouldn't transfer the vibrations to the house nearly as well as the rock would.

I don't have much knowledge on the subject either, but would have to agree with your answer...

http://seagrant.uaf.edu/features/earthquake/reduce9.html

Landslides are likely to be triggered by significant earthquakes, especially on steep slopes and in areas underlain by soft ground. During the 1964 Alaskan earthquake, much of the Turnagain Heights area of Anchorage slid toward Knik Arm because the area is underlain by a kind of soft clay that is particularly hazardous, because it is full of water and will slide easily if shaken violently. The clay in the Anchorage area and other types of soft ground can also intensify the shaking of an earthquake.

I copied that parargraph from the link.

Not enough info for any reasonable answer.

I think a case can be made for any of the houses by carefully choosing the type of construction, the composition of the soil, nearness to an ocean (tsunamis),etc.

seriously though,

Soil liquifaction would most likely happen in the moist damp earth of the valley. The seismic waves will be amplified and the energy transfer will be much more destructive. Just like exerting the same shaking force on jelly compared to a brick. Not only that, if the epicenter is shallow, the few miles of separation might just make a difference in the ammount of power transferred. The house in the valley is the loser here.

I am putting my money on the house built on rock to suffer the most damage. Surely, the hard rock will transmit eartquake vibrations to the surface which will damage the house on rock much more than the other two. The house built on soft soil in the valley will not experience these vibrations as much and therefore will be less affected.

I know it goes against biblical advice "Build your house on a rock" and all that, but I don't think the biblical writers lived in earthquake stricken areas :)

Actually the house on the rock will be the best survivor. The rock acts as a massive totally rigid structure which dampens the waves. In the Nuclear Power field we always have to look at siemic influences. The higher you go up a semi-rigid structure such as a building or soft dirt the more the waves are amplified. Think of it as a whip antenna mounted to a board, move the board around and the bottom of the antenna moves with the board, but the top will be moving 5 to 20 times greater amplitude.

If two people are in a high rise building during a mild earth quake, one on the first floor and one on the 20th floor the guy on the first floor might not even feel it, where-as the guy on the 20th floor will likely be clinging to his desk in fright.

I'll analogy you one better: Think of a board with a bowl of jello and a brick on it. Doesnt matter how much back and forth motion you put on it, the surface of the brick is only producing the same x and y plane motion as the board. The jello on the other hand is now producing an amplitude z that more destructive. Do it long enough and the surface of the jello will break down, and further compromise any foundation built on it. Like RL said, it is the whipping motion that will do more damage than just moving back and forth.

When an earthquake hits, the tremors cause the separation of larger and smaller particles, and the soil to becomes like jello. It can be ground water separating from soil (especially in poorly drained areas or clay) or even sand dunes or gravel. Try running on the spot on barren clay. In a few minutes, the clay will become wet, and if you go long enough, it will have the consistancy of jello.

One assumes that the soft earth in the valley is at an stable incline or angle, so an earth quake is not likely to cause a land slide? so as previously stated I think that the houses on soft foundations will absorb the tremor, while the house on solid foundations will move with the tremor and suffer damage, the amount depending on the quakes severity.

Regards JD.

If each of the houses are built equally strongly, and each house has properly designed foundations, and the rock is not a type to split or shear easily, then the house on the rock will withstand the quake better.

The house in the valley bottom will be damaged the most, unless it has a unitary "floating foundation" i.e. a reinforced concrete "raft" in which case it will "surf" to and fro, but survive OK.

Practical experience of this was back in 1968, working at New Zealand's Manapouri Powerhouse Project, and a 6.8 Richter Earthquake struck, causing major rockfalls, and temporary dams in river valleys, along the Southern Alps.

Down "the Hole" over 1,000 feet underground, inside a solid rock mountain, we never even noticed the quake.

When we came to the surface, at the end of our shift, there were some 3000 single men's huts all awry, having been shunted to and fro by the event.

The huts were usable and OK, because each was wooden skid mounted, but the camp and warehouse/Stores area took several weeks to get "straightened up" again.

In this situation, the buildings were restrained, by the heavy electrical cabling, which joined huts along the rows in the camp, although lines of huts waltzed around for over a minute.

Here where I live, I am around a kilometre from the twin volcano (extinct) of Banks Peninsula, which has a volcanic root extending down some 200kM.

I am also on the NZ Geonet advisory system:

http://www.geonet.org.nz/

Sometimes when there is a close (15kM away North of Christchurch, on the shallow Sefton fault), our well-made house shakes suddenly, as though a large truck has crashed into it - the house suffers no damage, even though being built on soil, over clay, bottomed onto ancient river gravels.

When the McQueen's Valley (on Banks Peninsula and 10kM away as the proverbial crow flies), seismograph records are looked at, that earthquake does not register, although seismographs some 200 kM away do register the event.

So....the Earthquake is reflected by the volcanic massif, which is mostly hidden, and we get both the transmitted shock wave, plus moments later, the reflected shock wave.

I do note that in the US, there have been some large Earthquakes, the New Madrid (Mississippi) area being again overdue for "adjustment".

http://en.wikipedia.org/wiki/New_Madrid_Earthquake

As the Question stands, there has not really been enough detail given, for an educated Engineer or Researcher to be able to achieve a totally correct answer.....

The one on the soft earth will suffer the most damage. The one on the rock will be the safest. The rock is pretty much like an extension of the footing. It changes the motion times arm equation (or something like that).

After the Northridge earthquake in California, I was working on some houses where they scrapped some hills. The tops of the hills were scraped and filled the valleys making this particular area relatively flat. The houses that were built on what was the tops of the hill were in not bad shape, while the ones build in the hollows were really wrecked. The ones that stayed up were built on rock. The others on soft dirt, or fill (compacted).

Liquifaction is the key word here. Most likely the house in the valley on the soft ground.

I totally agree that the house in the valley is the one most at risk. I rode out the "big one" in Anchorage (8.5+ on the richter) and the most damage to buildings occured wherever the ground was softest. Some of this soil was along 4th Avenue where it sank 20 feet. One new development literally slid out to Cook Inlet.

Most buildings, made of cinder block or brick, on harder ground generally had structural damage that was severe but this was poor construction for earthquake country.

Buildings of good construction on harder ground generally faired ok. At the time I lived in a mobile home and the only damage I had was some items in my refrigerator that spilled out when the door flew open and one swag lamp glass shade that hit the wall. I lost electricity but still had natural gas so we faired really well. I guess that's one time a mobile home construction was not that bad.

I live in a area that closely resembles the conditions, I'd like more details. The house on the "soft" ground would be shaken like a bowl of Jello, like Mexico City, and the ones on hard rock take seismic hits and disburse them like Kevlar. The shock waves will reverberate off the hard rock and wobble the the one on soft ground causing harmonic stresses greater than the direct energy hit going into solid rock. There are a lot of variables here like the foundation design etc..

I have to agree with those who say the house in the valley on soft soil will suffer the most damage. Here in STL we are very concerned about potential damage from the New Madrid fault, which last went off almost 200 years ago, with "the big one" that made the Mississippi River flow backwards, then re-channel itself (creating Reelfoot Lake in Illinois), and which rang church bells in Boston, about 1000 miles away.

Fortunately, the area was sparsely populated back then, St. Louis being not much more than a small town, and New Madrid itself, but a village, so the overall damage was not great. New Madrid was actually completely destroyed, and houses in St. Louis suffered substantial damage, but I found no record of loss of life due to the quake. This would be a very different story today, with major bridges spanning the Mississippi, skyscraper buildings dominating the St. Louis skyline, and a metro area population approaching 3 million.

Three prior Richter Scale 7.0+ (estimated) earthquakes caused cumulative damage when "the big one", estimated to be about 7.9 magnitude, hit within three months of the first quake. Wikipedia describes it this way:

February 7, 1812 (the New Madrid Earthquake), 0945 UTC (4:45 a.m.); 7.9 magnitude; epicenter near New Madrid, Missouri. New Madrid was destroyed. At St. Louis, Missouri, many houses were damaged severely, and their chimneys were thrown down. The meizoseismal area was characterized by general ground warping, ejections, fissuring, severe landslides, and caving of stream banks."

Maps of projected damage for another major quake in our area tend to show the worst damage following the river valleys, so that probably bears out the "soft soil" advocates, as soil liquefaction would cause sever damage as it has in many areas of San Francisco during their last "big one" which were built on "fill", and not on bedrock. The question remains though, which would suffer more, the house built "high on the rim, on rock" or the one "near the rim but still on softer ground.

Granted, mechanical energy in the form of oscillations would travel more easily through harder media, like rock, while softer media would tend to absorb the energy, thus creating the liquefaction, and tossing houses about like ships at sea in a storm. But would that energy actually result in more damage to a house built on the rock, or the one built nearby on somewhat softer soil?

My answer is that the house built on solid rock would absorb the greater vibration, but if well built, should survive the earthquake fairly well. The same could not be said for its contents, as the extreme shaking would be likely to make unsecured cabinets, bookcases, wall hangings, etc. be thrown violently about, with possible substantial property damage, especially to fragile objects like china, glass, mirrors, chandeliers and other light fixtures, as well as some furniture and appliances, etc. On the other hand, the house built on softer soil, while not nearly as susceptible to damage as the one built in the valley on extremely soft soil, could still suffer structural damage, particularly if there is any gradient in the soil compactness, i.e. one end being supported more by rocky clay, and the other by "fill", the foundation of the house could easily shift and crack, with potential structural damage resulting, as well as possible groundwater damage to any basement living or storage areas. However, the actual kinetic energy transmitted to, and absorbed by, the articles inside the house could be less than the nearby house on the rim, built on rock, due to the energy absorption of the softer ground.

This is a fear that I have, as our subdivision house is built on somewhat unequal soil from one end to the other. Although fairly high on a hill, and therefore not as susceptible to damage from liquefaction of the soil as those down in the creek valley, I did note at the time of construction that while one end of the foundation was dug with a simple back-hoe, tearing through soft clay soil, excavating the other end required the builder to bring in a machine that was essentially another back-hoe, but with the scoop replaced by what resembled a large pneumatic "jack-hammer", which was required to break up the rock in order to dig the basement. Many of the broken rocks then removed were still the size of washing machines or small refrigerators!

Similarly, when the St. Louis Gateway Arch was constructed its twin foundations were constructed deep underground. One end was blasted into solid bedrock, but the other end was found to be an area riddled with many caves, that easily collapsed with pressure placed on top by equipment and blasting. When the rubble was removed from this end, the decision was made to stabilize the area by continuous filling with concrete, but the cavities absorbed substantially more concrete than the builders ever imagined, and there was never a complete fill. Eventually, they decided just to stop and let the concrete harden, creating a fairly solid foundation which still rested on a somewhat porous sub-layer. Who know what may happen to this porous and substantially weaker layer when "the big one" eventually hits?

Later earthquakes in the New Madrid Fault zone have been harbingers of what could happen. The 1895 Charleston, MO event was equivalent to the Northridge quake in magnitude, but far exceeded it in the size of the area affected (see map below).

Wikipedia (again!) says:

"The probability of magnitude 6.0 or greater in the near future is considered significant; a 90% chance of such an earthquake by 2040 has been given. In the June 23, 2005, issue of the journal "Nature", the odds of another 8.0 event within 50 years were estimated to be between 7 and 10 percent.^[5]

Because of the unconsolidated sediments which are a major part of the underlying geology of the Mississippi embayment, as well as the river sediments along the Mississippi and Ohio River valleys to the north and east (note the red fingers extending up these valleys in the image above), large quakes have the potential for more widespread damage than major quakes on the west coast."

Comparison: the 1895 Charleston, Missouri, earthquake in the New Madrid seismic zone with the 1994 Northridge, California, earthquake. Red indicates area of structural damage, yellow indicates area where shaking was felt.

Do you think anybody actually cares enough to read all of this?

Brevity is the soul of wit.

I think the people in the red zone(s) do. I doubt StL was being witty this time.

"Reading maketh a full man, conference a ready man, and writing an exact man."

-Sir Francis Bacon

I think the people in the red zone(s) do. I doubt StL was being witty this time.

You got it Copperzincprimate! Me and another nearly 3 million in the metro STL area, plus another 1.5 million or so in Memphis, and a few more millions in Louisville, Ky, Evansville, IN, and Cincinnati, OH! Add in all the small towns and cities in between in the Mississippi and Ohio river valleys and you probably have around 10 million in the red zone! That population is larger than many Third World countries! I wonder if when the "big one" hits our little nation of "Miss-hio" would get any help (foreign aid?) from New York and California? Probably only the big-hearted Texans would come to our aid!

The last time we had a disaster of such epic proportions was during the big flood of 1993 when the Missouri and Mississippi Rivers (which join at St. Louis) flooded at the same time, creating what some wags referred to as the Sixth Great Lake or the Midwestern Sea. According to one article on the Great Flood of 1993, there was about $15 Million in damages resulting from the flood. Army National Guard units were mobilized for sandbagging and rescue duty using their many trucks and small watercraft* to help people about to be inundated or already cut-off from higher ground, stranded on roof-tops or newly created "islands". I am thinking that the devastation from the "big one" may be much greater.

* An old saying goes: the US Army has more boats than the US Navy, but the US Air Force has more trucks than the Army! Of course they also say the Navy has more aircraft than Air Force, too!" Not sure I believe that one! However, I can probably say, with no disrespect to any of the services, that the relatively small US Marine Corps has more GUTS than all the others combined (and this coming from a former USAF enlisted man). Oops, I guess you might call this just a little Off Topic! <grin>

Nice theory, but in practice, I have to wonder what Sir B. would say about the current tabloid newspapers?

I enjoyed reading it -- I appreciate all the factual information you, and others, have provided in response to this challenge -- not only thought provoking, but could be of personal relevance some day.

Earthquakes in central USA, interesting phenomenon. The nearest tectonic (not sure of the spelling) joint is the west coast, so why? Geologists speculate that the Earth's crust is thiner here than anywhere else on Earth. This makes the area unstable and is supposed to explain why New Orleans keeps sinking, as the crust is too thin to support the weight.

RickLee,

Yes, in the central USA the types of faults are poorly understood because they lie so deep under the sedimentary layers. However, I believe the reason for the sinking of the Mississippi River delta (which includes New Orleans) is more closely tied to the pumping of oil from the subsurface deposits and the slow compaction of the deposited alluvial layers. Similar sinking is found in many heavily exploited oil-producing regions (consider Long Beach CA for an example). Related activities involving pumping water for irrigation have had equal results.

--JMM

I guess I should ask my brother the geologist, but joints between tectonic plates are not the only places where earthquakes can (and do) occur with statistical regularity. Even my 8th grade "Earth Science" class taught that earthquakes can occur wherever there is a "fault", or discontinuity (like a crack), between adjoining strata of rock and that pressure can build up slowly, like pulling back a rubber band until it breaks, and then SNAP, the strata move relative to each other releasing the pressure suddenly, et voilá, earthquake.

Our largest Midwestern fault is known as the New Madrid (pronounced New Ma' drid locally) Fault, since it passes through or very near the town of New Madrid, MO which was the epicenter of "the big one" almost two hundred years ago. The reason given for the severity of our "big one" is exactly the effect of having so very few small earthquakes, i.e. the energy builds up of longer periods without being released. Whereas, in California, small to moderate quakes happen much more frequently, perhaps due to the fault being at the tectonic joint, and so energy is released periodically, and does not have a chance to build up to such a high level.

So which would you rather do, sit on a chair that has firecrackers going off every few hours underneath it, or on one that has several sticks of TNT under it which might explode in a few days, or even a week, but is guaranteed to do so eventually? Personally, I think I could learn to live with the firecrackers (wear earplugs for one thing). The thought of the TNT going off makes me extremely nervous. I could only hope that none of my loved ones or I was sitting on the chair, or even nearby, when it blew up!

Wherever the energy of the quake is dissipated, will see damage. The house on hard rock should shake the most. The house near the rim on softer ground should shake somewhat less than the high house-being less tightly coupled to bedrock. It could possibly slide into the valley, impacting the low house en route. The low house, if not damaged by falling, sliding debris, might sustain the least damage.

I need to make unjustified assumptions to give any sort of answer. The ones I choose are:

i) The area is prone to earthquakes, but only infrequently are they at a level to cause substantial damage
ii) The budget for quakeproofing each of the three houses was the same, and the methods used were appropriate to the site
iii) The magnitude of the earthquake was sufficient to destroy exactly one of the houses
iv) The epicentre was vertically below the site, and deep enough to be uniform in the subsurface region
v) The valley shape is not such as to focus the effects at the centre

Under these conditions, as indicated by others, the house on the rock will likely shake the most - but the previous survival of the rock suggests that only an exceptional quake would destroy the foundations - therefore the house would likely survive.
As regards the house near the rim, the rock edge would couple energy to its subsoil, and the sloping interface between the edges of the valley and the subsoil would further destabilise the foundations. So I would expect this to collapse with a lesser quake than the house in the centre of the valley.

If that is the case, you may ask why the major disasters have affected towns that are in or near the centres of their valleys. My hypothesis is that the greater frequency of damage near the rim means that building in these regions is better controlled - either there are fewer buildings (possibly because some have previously been destroyed and not rebuilt), or they are appropriately constructed. So the town grows in the centre of the valley - and is fine until a large event, at which point the damage is nearly universal (and catastrophic).

There will also be situations where the shape of the valley focuses energy onto the centre - but even here it takes a substantial (and relatively rare) quake to result in soil liquefaction.

What we are talking about here is the transfer of energy from the earthquake to the structure. The house on the rock will most likely feel the earthquake first even if it is further away from the fault, but the energy will be high frequency, low amplitude. (Think high voltage, low current for you electrical types) The softer soils convert the high frequency energy into lower frequency, higher amplitude waves. This energy is more dangerous to structures because of greater mechanical movement.

However, if there is a lot of soft soil it acts as a dampener so the energy attenuates. The soil liquifies at the transition points (Hard rock to soft soil) but less so further away. Therefore the house close to the rim on the soft soil is gonna get clobbered!! The house in the center of the valley will have some structural damage and the the house on the rim will lose some dishes.

This is essentially what happened in Mexico City ~ in the 1980s. The old lake, where Mixico City is largely built, was all earth fill, and the hotels and large buildings built thereon had catastrophic damage and collapse during a moderate earthquake. The soft land essentially turned into quicksand or jello. I remember many buildings down and a number of deaths.

Not even close boys

It's an east coast, west coast thing.

A 5 on the west coast is like a 3 on the east coast.

It is dependant on how fractured the plate is.

The plate under the east coast is solid like a drum

The plate on the west coast is fractured, it wont transfer the energy wave as well.

The actual answer is

Any one of them depending on how you right the assumptions.

"Not even close boys".

Is this a civil engineer, or a civil serpent?

"Any one of those?" How high a fence can you sit on - I'd say you must be a civil serpent, except that "right" is wronged.

Of course, I'd be willing to accept your condescension if you clarified what assumptions would lead where.

all of these answers scare me!

I think I'll build my next house out of Jello............

I'm changing a variable and denoting it as the State of Florida. No, we don't have life-shattering quakes here but the postulate increases probability on the destruction of all three houses. Mexican's built them and they weren't properly inspected to code. All three currently have foundation cracks and are riddled with termites. Yet, the taxes increase in an exponential manner.

For sale: 1 bd/1 bth, zero lot. Slight imperfections; perfect for that handyman. Reduced to $3.22M.

Truly amazing. Here are some general conditions about earthquakes.

1. The softer the ground the easier to have liquefaction. House falls down.

2. Structures on rock suffer the least damage of all no matter how they are built.

3. If this is a Richter 8 or higher quake they all fall down.

4. This questions is problematic due to inadequate parameters being set.

5. If you want to see any of this in action go to California and look at the damage done when the 880 freeway collapsed. All of these conditions were met and it is very interesting to see what happened and why. Damage done here was like some one had used a knife to divide things.

Here is an interesting link:

http://pubs.usgs.gov/of/2001/of01-164/of01-164.pdf

that shows the USGS predicted ground motion amplification in southern California. I think some posters on this forum have not distinguished between liquefaction (like was beautifully demonstrated in Niigata) and ground motion amplification (like was seen in the Loma Prieta quake in 1990 and Mexico City back in the '80s)

In Liquefaction the shaking turn the water bearing soil into a fluidized bed or a quicksand type of a substance. In ground motion amplification the ground has to move more to carry the same energy as a stiffer solid rock.

Imagine a rope bridge and a beam bridge spanning a distance, size them so they can both carry the same weight. now imaging that you hit each of them with a sledge hammer while someone is trying to cross. The energy input is the same, but the deflection of the rope bridge is huge (lower stiffness) and the guy trying to cross it plunges to his death. The beam bridge guy just has tickly feet when he gets to the other side and throttles you for scaring the crap out of him. I think this was confirmed by extensive research, for which it was really hard to get volunteers because who the heck wants to plunge to your death from a rope bridge.

Another thing I was told anecdotally about Mexico City was that relatively short (2~5 floor) building were built immediately adjacent to tall (25+) floor buildings and the two would oscillate at very different frequencies. this had the short building bashing into the tall ones and knocking their legs out from under them so to speak.

So, to answer the question, I think the one in the valley will experience the highest amplitude motion, but the one on the margins also have large motion and possible sliding. Even if the ground is flat but the sediment depth varies under the house then the two ends of the house will each have different motions and so will be out of phase and rip the house apart similar to the freeway overpasses at the 14/5 junction during the Northridge quake. I vote (with the usual caveats about limited information) for the middle house.

I would just like to add that whis looks like an interesting place, this is my first post here, and I am an ME not a CE or geotechnical, so even if I had more information I wouldn't know what to do with it.

Imagine a rope bridge and a beam bridge spanning a distance, size them so they can both carry the same weight. now imaging that you hit each of them with a sledge hammer while someone is trying to cross.

Yes I imagined this..

...the rope deformed in the area of impact which thus absorbed it, having virtually no effect on the bridge, sledge hammer or wielder of said hammer.

The beam bridge vibrated slightly, the hammer stopped abruptly and a fair sized shock went back up the handle to the wielder of the hammer.

I feel this is a poor analogy...it would take a prolonged application of large amplitude deflections to set a rope bridge into oscillation...a single blow just isn't going to do it!!!

I think the whole fluidisation thing has been overstated.. I think it is a specific case rather than the general one.

Please note I say 'think' I do not profess to be an expert in this field.

Yes I imagined this..

...the rope deformed in the area of impact which thus absorbed it, having virtually no effect on the bridge, sledge hammer or wielder of said hammer.

The beam bridge vibrated slightly, the hammer stopped abruptly and a fair sized shock went back up the handle to the wielder of the hammer.

So... there isn't a wave that travels through each of the spans? and the cable does not snap around like a guitar string? and the equivalent energy wave in the beam doesn't travel faster? and it is not therefore smaller? and this is not analogous to the behavior of seismic wave in soft soils vs it behavior in rock?

I have a zipline in my yard. I can hit it with my hand and watch the wave travel to the other end and reflect back. I can hit a beam and see nothing, but I know that a smaller, faster, equivalent energy wave is traveling the beam. But the amplitude is so small, and the time is so short that it doesn't couple well into anything

after poking around a little more

http://pubs.usgs.gov/fs/2001/fs001-01/fs001-01.pdf

reiterates the idea of slower, larger amplitude aves in soft soils. I am sorry you think the analogy was bad.... maybe if you put a pulley slide/ zip line in your back yard. My kids love it - thinks its very cool.

For those of you who have had any Bible study, Matt. 7:25-27 offers some good advice, although not earthquake related. The house built on solid rock will survive.

The House that does not have insurance will suffer the most damage.

The House that is insured will have the leasy damage.

The soils and rocks in the area will not make any difference because I don't care. The only difference is the one in the valley can have a nice garden, soft soil, while the one on the rocks, can only have a rock garden.

...but one cannot make a claim on insurance because the plates tipped 4 degrees upward and to the right. You policy only covers shifts of < 2 degrees and only to the left. Sorry. Should've gotten that additional policy for additional degree shift as well as the policy that includes shifts on the X,Y and Z axis (r not covered).

Your in good hands. We're there for you. Always. Rain, sleet, snow and shine. Trust us. Making a difference. The Protector.

Any more garbage SM's that I failed to mention when it comes to insurance companies?

"So simple, a Caveman could do it!" - Geico

_{Another case of "didn't read the small print".}

The house oon the rock due to the attenuation of th tremors. This one was too easy.

Friends,

I grew up in San Francisco, and my parents' house has gone through 3 big ones already. It was built on shale rock and has only had minor damage each time. Houses built in similar fashion on filled land or alluvial land all suffered much worse damage.

Assume the three houses are built in similar fashions out of similar materials. (After all, that is what is usually done!) Assume that the valley has filled slowly with sediment and similar debris over geologic history, so it has a greater depth of sediment near its center. Experience from many earthquakes shows that the house on the rocky rim of the valley will have the least damage and the house in the center the most (its soil is more moist and more recently deposited than the house near the edge of the valley). The rim of the valley may collapse, but it probably would have already in some prior earthquake in geological history.

Yes, you can design any of these houses to withstand the ground motions of an earthquake, and you should. Unfortunately, maps of almost any earthquake prone area will also show that the majority of the public services (hospitals, transportation routes, water supplies, schools, administrative buildings, jails, etc.) are built on the most damage-susceptible locations. We build where it is flat because it is easier. That is why we build in flood plains, near wetlands, on filled land, etc.

--JMM

The glass house suffered the most damage. Doesn't matter where it was, the other two were made of cardboard and recycled pop bottles.

Damage being valved by cost , glass is more expensive.

Problem solved. Get back to work.

I believe the house down in the valley on the soft earth will suffer the most damage. It is my understanding that the soft earth has a tendency to liquify and becomes very unstable during an earthquake.

All were destroyed. Everyone was so busy trying to figure out the earthquake they didn't notice the half mile wide meteor streaking down towards the valley.

Next question?

I think we all (myself included) have noted that soil liquefaction will be the primary cause of major damage to the three houses, hence the house with the highest probability of showing that phenomenom will recieve the most damage (littlest house in the valley). That is assuming that all 3 houses will be equally effected by the same tremors. I've happened upon some interesting reading that may mean that we're all wrong.

In a study of the Nevada town of Pahrump, investigators studied earthquake and nuclear test seismic waves and came up with some interesting results. The P and S seismic waves travel at different speeds, and although the amplification of resonating frequencies have the potential to do the most damage, they are only amplified by 3-6X @ 2-2.5Hz thanks to the concave geometry of the valley basin coupled with the depth of the sub-basin soil (NEHRP class C and D soil). The monitors at the rim of the basin (not in the mountains) registered an amplification of 6-7X @2.5-4.75Hz. The 3-D model of the valley indicated that this could be the result of a sharp velocity discontinuity - much like waves breaking on the beach. A similar conclusion was reached in a study of earthquakes in the Dead Sea Rift, where the P and S waves were actually funelled and focused by surrounding rock deposits. Here the researchers speculated that decreasing soil depth and width, that the deep and surface waveforms travelled created various destructive resonant frequencies greater in amplitude than that in the Dead Sea Basin. Another study in Teipei showed that the concave topography of the buisiness part of the city reacted much differently than the heavy populated slopes around the city. Looking at the area on a map, the earthquake epicenter was SE of the city, and yet the majority of the damage was in the hills/slope NW and N of the city.

So, considering these studies and assuming relative positions of the houses in the valley, I guess I have to recant and say that the house on the rim of the valley would be sticks and stones first. I guess one of my 3 answers must be right.

Ok read through this whole thing and observed all opinions some though provoking and others just provoking.

I must say the facts and figures presented by STL Engineer seem to be the most clarifying. Which is to say I agree with his analysis.

The serious part now having been said.........

What if one of the houses was built in a tree??

Clearly the house on the rock will suffer most. The border would be next and the soft ground (unless it liquified) would ride it out as the ground works a s a shock absorber. We live on a gravel bed here in Northern Idaho and a recent 4.1 quake that was 2 miles deep and about 20 horizontal miles West was not felt at all here.

the house to suffer the most damage will be the one on at the top of the rim the one at the middle will be shaken the one on soft ground may not see any thing more than a slight vibration

as an example strike a tree of few inches diameter observe the top it will shake a bit
the middle very little and the bottom null

triy it and see the proof

Earthquakes have performed this experiment - frequently. The results are at variance with what you suggest. The reason is that houses are light compared with all soil types, and the maximum velocity of the vibration depends partly on the density of the soil and partly on resonances; a transition from high density rock to lower density soil will usually immediately cause the amplitudes to increase, and the discontinuities between rock and soil are also likely to increase resonance effects. Then there is the question as to whether the foundations of the house remain intact - solid rock that is near the edge of the valley is unlikely to be fractured unless the frequency of the vibration is relatively high, whereas softer materials will stretch by far greater amounts - and soils will not normally recover their former positions

First I will make the assumption that all 3 houses are equally constructed.

I would expect the house on the hard rock to sustain the greatest amount of damage since the maximum amount of vibration from the earthquake will be transmitted through the rock to the house.

Likewise, the house on the soft ground will sustain the least amount of damage as the vibrations from the earthquake will br damped by the soft ground.

A thought on this:

Houses are very low density, soils are intermediate between house and rock, and so act as transformers to improve coupling of the energy into the houses. (Rather like tapering the impedance of a transmission line to improve coupling between lines of different impedances).

Fyz

I really have no qualifications to be attempting to provide a response to this challange question. However, I believed that soft ground would provide similar vibration damping to a house that rubber feet provide to a piece of equipment that we want to protect from damage caused by external vibrations.

Refrigeration compressors are always mounted on rubber feet or springs to prevent their vibrations from being transmitted to the surroundings and causing high cycle fatique damage.

Motor vehicles have rubber tires, springs and shock absorbers to prevent vibrations caused by road defects from being transmited to the body of the vehicle and causing damage.

Rubber feet work because they have lower effective acoustic impedance than either the source of the vibration or the article being protected. If they were intermediate between the source of the vibration and the protected item they would make matters worse rather than better. (Another way of looking at this is that the springs/rubber-feet are both light and soft compared with both of the systems between which they provide isolation.

And... even the intermediate rubber mountings or springs would be of no use if they themselves were not strong enough or well-enough fixed to withstand the vibration.

So the issue really is the type of construction used for the house in question.

If is is a stick frame house with no foundation, then it will be softer than the ground it is built on, regardless of whether it is soft ground or hard rock.

Conversely, if it is a house built to withstand seismic events, such as a rebar reinforced, poured concrete house, then it will probably be stiffer than the ground it is constructed on, regardless of the ground composition.

In the second case, the elements will indeed be stiff - but houses are box structures, and much less stiff than their elements. Acoustic impedance is of the form sqrt(E*density), where E is the relevant elastic modulus, so the reduced average density is also significant. The upshot is that nearly all (even heavily-built) concrete housing has lower effective acoustic impedance than the compressed soil, which in turn has lower acoustic impedance than solid rock.

The advantages of suitable timber-framed housing (built from oak or Douglas fir, for example) include:
that the acoustic impedance mismatch with the substrate is greater than for a concrete structure, so less energy is transferred to the building; and
that the energy absorption capability under tension is as great or greater than you can obtain with reinforced concrete (although steel is somewhat better than wood in this regard, it cannot occupy the entire volume), and the mass it has to move is rather less.

Of course, that does not mean that reinforced concrete structures cannot be made earthquake-resistant - as evidenced by an hotel I stayed in that was at the epicentre of a Richter 7.4 quake - only that the design constraints are tighter.