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### Houses in the Valley: CR4 Challenge (08/18/09)

Posted August 17, 2009 5:01 PM

This week's Challenge Question:

Three houses are located a few miles from each other near the rim of a valley. The earth in the valley is soft, while the land around the valley is hard rock. One house is high on the rim, on rock; one house is just near the rim but still on the softer ground; and one house is down in the valley on the soft earth. If an earthquake hits the area which house will suffer the most damage?

The house just near the rim will suffer the most damage. This is similar to a wave in the ocean, to the earthquake the soft ground acts more like a liquid, and the rock is like the shore. As the shock from the earthquake travels through the soft ground the wave won't do much to the surface when the ground is deep. When the wave gets close to shore where the house near the rim is, it will be large and cause the most damage.

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Check out these comments that don't yet have enough votes to be "official" good answers and, if you agree with them, rate them!
2
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#1

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/18/2009 3:05 PM

All other things being equal, the one with the least insurance.

2
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#2

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/18/2009 3:43 PM

Well, you didn't mention that all three are beneath the dam at Lake Omigod or that the dam was built by local contractors who just finished Civil Injineering school by matchbook cover.

But, all that aside, the guy near the rim, but on the soft sand. When you stand in the surf at the beach, it's right near the edge where you get knocked on your keister.

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#9

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/19/2009 12:41 AM

GA also for the Romanian engineer byline. However, if the Eastern Bloc had had McMaster-Carr, they would have been a commercial capitalist society, and the Cold War would have been unnecessary.

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#14

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/19/2009 7:25 AM

That's a true story. I worked on some contracts that the guy did also back in the 90s and he was just astonished at the "big yellow book".

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Off Topic (Score 5)
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#3

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/18/2009 3:52 PM

It all depends. On the location of the epicentre, the profile of the rock and the general strata*. Nevertheless, for most situations it's a toss-up between jim35848's solution and aristodle's (or indeed TVP45's above - GA by the way). I guess that in many cases the two will coincide, as a house on thin soil and near the rim** (and in an earthquake zone) will probably not be insurable against quake damage.

Hopefully the 'powers that be' will present a better thought-out solution than last time around.

*Is the rock tapered to massively concentrate the energy? - probably not if there's soil near the edge of the valley. Is the house down in the valley built on deeper soft ground than the one near the rim? Are the houses on soft soil designed to float (rather than rely on foundations into the soil) when the soil liquefies? Is the house on the rock strong enough to follow the movement?

**Generally, unless built for the specific situation, the most vulnerable house will be the one on the thinnest soft soil - because the soil shear is maximised, resulting in first liquefaction, and the foundations will essentially move independently of each-other.

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#6

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/18/2009 4:23 PM

And, I have to say that I gave that answer because it was obvious the questioner wanted a simple analysis. In real life, the answer depends on the frequency. For some waves, the deeper soft soil will amplify more. The rock is always better.

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#7

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/18/2009 4:24 PM

I forgot to say that aristodle and TPV45 would be correct if both the house on soft soil near the rim and the house near the centre were similar distances above water-saturated soils, or if the entire valley was dry (in which case damage would be caused by cyclic mobility rather than liquefaction).

If the house on soft soil at the edge is much further from the water-table than the one at the centre, the centre one will be the most vulnerable. As I said, "It all depends" (but I omitted some significant dependencies).

Giving due respect to cuznmonkey, perhaps I should cover all bases again, and repeat that there will even be situations where the house on the rock is most vulnerable (mainly if the taper means that the rock behaviour resembles a whip)

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#16

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/19/2009 8:13 AM

Think of the quake in Mexico City some years ago. Most of the City is built on filled land, and the quake turned the fill into "mud". Hotels etc went down in Zona Rosa.

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#4

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/18/2009 3:57 PM
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#18

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/19/2009 9:15 AM

Was thinking the very same thing - just about to search it, when I spotted your post.

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#19

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/19/2009 9:37 AM

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#25

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/19/2009 6:48 PM

Good answer.... I was thinking that the dates were a bit out and had heard this one before....

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#28

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/20/2009 5:46 AM

Technically, I think it's off topic. As no fully satisfactory answer was given the first time around, perhaps it's worth a re-run?

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#5

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/18/2009 4:22 PM

This is a trick question, to see if we've been paying attention?

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#8

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/18/2009 4:56 PM

On second thought, maybe there has been a new discovery in seismology and the answer has changed. More likely, this is a hint that participants should be submitting new challenge questions. Perhaps we need a new way of keeping score that has an option for good question. I know a few of our very best challenge questions came from the participant. Most of those have been too hard for me but they were indeed good questions. If I don't learn something every week from the challenge questions and the responses, I haven't log on.

Thanks,

Jim

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#10

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/19/2009 1:46 AM

The one down in the valley on the soft earth is likely to suffer most because viscous flow of the soft earth can undermine the foundation.

bioramani

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#11

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/19/2009 2:00 AM

Depend upon the house wether it is belong to me or you, If I, then I will suffer the most damage.

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#12

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/19/2009 2:02 AM

It will be the house on the rim. Bacause the hard rock transmits the shock wave more than the soft soil, which acts as a damper on the shock wave.

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#13

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/19/2009 2:34 AM

the house high on top of the rim on rock

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#15

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/19/2009 7:57 AM

At this point we have two contributions voted G.A.
jim's is purely whimsical (unfortunately probably incorrect, as the insurance companies will probably wriggle out of all three in any case), and TVP's is only correct under quite a narrow range of (unspecified and not-typical) circumstances. I'll therefore try and summarise as much of the actual situation as I can manage (without going on-and-on-and-on-and-on).

The short answer is that "it depends", but also that it is possible to assess the relative risk for a specific case.

Except in very specific circumstances, the house on the rock is likely to suffer least damage. The reason is that, shake as it may, its foundations are least likely to be disrupted. The specific circumstances include the location of the epicentre, the shape of the rock, and the construction of the houses. Various combinations of the following could make the house on the rock most susceptible:
the houses in the valley are built with reinforced floating foundations (i.e. to be earthquake-resistant),
the rock is sharply tapered, and the house is on a tip where the movement is amplified,
the location of the epicentre concentrates the energy at the house on the rock,
the strata under the houses in the valley are completely dry,
the house on the rock is built with narrow walls of heavy materials with minimal tensile reinforcement.

Returning to the much more common situations where the house on the rock is not the worst affected, we can now compare the other two. Again, we are looking at combinations of factors, and it is impossible to reach a conclusion without detail.
Suitable construction is significant (too obvious?)
Ditto position of epicentre and topographical focussing effects
The presence of water in the soil is often a determining factor; if one of the houses is over water, but the other is well-spaced, the foundations of the house over water are far more likely to be disrupted. (Note that this is likely but not certain to be the one near the centre of the valley).
Other things being equal, a house over ground that is less than λ/6 deep is less likely to have aggregate under it disrupted than one that is over deeper ground; however
Once the depth exceeds λ the disruption at depth can result in chaotic variations at the surface - a proportion of homes in the region will be undamaged, while others will have severe damage.

Enough! It's an unaswerable question as posed. But if we take the "average" position across earthquake-prone regions, houses near the centres of valleys are most likely to be over saturated substrates, and therefore typically suffer more severe damage than those near the edges or on rock at the rim. (And that's ignoring landslides [also worst over saturated substrates] and flooding risks due to "tidal waves", broken dams, etc.)

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#17

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/19/2009 8:38 AM

This is a toss up between the one down in the valley on soft soil and the one near the rim on softer ground. As the soft soil will transmit the most vibration to the structure down in the valley. Where as the softer soil on the one higher up would flow down hill taking the structure with it.

So if the all the homes are constructed equally I would say the one near the rim on softer soil. As not only is the structure going to be impacted by the ground vibrations of the quake but the soil is going to tend to flow down hill under mining the foundation.

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#20

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/19/2009 9:41 AM

The construction of the house is also a factor: whether it is flexible or rigid will determine how well it will withstand a shock.

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#21

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/19/2009 11:11 AM

on rock is better and build it accordingly.

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#22

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/19/2009 12:06 PM

There are many factors that will determine which house will suffer the most damage. First off, I would separate the damage into two categories - structural damage and property damage.

The magnitude of structural damage will depend on how and when the foundation was designed. A well-designed, modern foundation in a high risk zone could suffer less damage that an old, poorly designed one in a low risk zone. The orientation of the house relative to the quake propagation direction will also affect how much structural damage occurs, since the house will flex differently depending on how its foundation is moving, which will change how stresses are distributed. However, soil liquefaction will probably be the largest factor to determine damage. During the Loma Prieta quake (San Francisco 1989, 7.1 magnitude), the buildings that were located on fill near the bay experienced the most damage, mainly due to liquefaction of the fill. The soft soil in the valley will be more susceptible to liquefaction than bedrock, so if the houses are all of the same design then I would say the one in the valley will suffer the most structural damage.

The magnitude of property damage is highly dependent on how furnishings are oriented relative to the propagation direction of the quake. Similar to a boat that steers into the waves to avoid capsizing, furnishings that are oriented with their greater dimension parallel to the quake propagation direction are less likely to topple than those that are perpendicular. This is one reason why all furnishings should be anchored to a wall in quake sensitive areas, although the items contained on or in them probably won't be secure. As an example, during Loma Prieta my apartment building suffered no structural damage and my apartment itself had very little property damage. My neighbor directly above me only had minor damage as well. However, the apartment diagonally up from me suffered tremendous property damage, mainly due to the orientation of their furnishings. So again, if all three houses are of equal design and are oriented such that a common reference line points to the epicenter, then I would say the house in the valley will suffer the most property damage because it should experience the most movement due to soil liquefaction.

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#23

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/19/2009 1:55 PM

Based on what I saw at earthquake park in Alaska the rim is not where you want to be. Also the house at the bottom will receive the most damage when the house on the rim slides or falls on it.

Mac

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#24

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/19/2009 4:31 PM

THE ONE LOCATED ON THE ROCKS AT THE RIM OF THE VALLEY. THE SOFTER CLAYEY SOIL THAT THE OTHER TWO HOUSES ARE LOCATED ON WOULD ABSORB THE VIBRATIONS, THAT IS, DAMPEN THE VIBRATIONS, WHILE THE ROCK WOULD AMPLIFY THESE SAID VIBRATIONS. THUS CAUSING EXTENSIVE DAMAGE.

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#26

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/20/2009 2:40 AM

The house that stands on rocks will suffer more. It has something to do with velocity of shock waves being highrer in denser materials and sometimes more than one shockwaves converge and meet at one point which is disastreous. If you are willing to travel to Pakistan's northern areas and Kashmir, you would see some awe-inspiring scenes - complete mountain side sliding off and blocking the river forming permanent lakes created by the disastereous earthquake of October 5, 2008. No significant damage was reported from Pakistan's most populated province - Punjab which is mostly plains.

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#27

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/20/2009 5:44 AM

I think you meant Oct 8th 2005?
As I said before, it depends - but...
In this case the debris was sufficient to block rivers, so it entirely bridged some valleys. As it is unlikely a housewould be built on a rock spur, the principal risk for that house would be if it was in the path of a landslide, the same issue as for the house in the valley near the rim. Given the extent of the landslides, and that the house near the rim is lower than the one on the rock, the house in the valley near the rim is more likely to be buried than the one on the rock. That is in addition to any direct risk to the foundations, which remains higher for the houses in the valley. Finally, I suspect that the reason houses in the Punjab survived is that they were much further from the epicentre, contrary to the "few miles apart" required by the challenge.

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#29

### Re: Houses in the Valley: CR4 Challenge (08/18/09)

08/23/2009 9:37 AM

If an earthquake hits the area the house which is high on the rim ,on rock will suffer the most damage

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