Most Conservative Equation

godtabh

Looking for some help.

I have a list of equations below.

I'm looking for which is the most conservative and which is the least.

Set 1
K0= 1-sinɸ'
K0= 1-.404 tanɸ'/1+ sinɸ'
K0= tan(45-ɸ'/2)
K0= √2-sinɸ'/√2+sinɸ'

Set 2
K0= .24+.31log Ip
K0= .42+.004log Ip

I havent a clue why one would be conservative and why it wouldnt be.

Best I can figure you would want Ko with the lowest number as the lower the number the more conservative it is.

Any one have any ideas? Or suggestions

breadmonkey

What's the context? Is it something to do with soils?

Pherekydes

I'm presuming it's to do with hypothesis testing? To lower the alpha value you pick the most conservative test.

OP?

godtabh

Yeah its to do with soils. Ko is the cofficeint of earth pressure and ɸ' is the angel of shear resitance.

Ip is the Plasticity index.

What I've done is graphed Ko against for differenct values of ɸ' and Ip. The ɸ' graphs are similar to each other as are the Ip graphs. The values arent the same but the apperance is.

breadmonkey

ehhhhhh.....

differentiate wrt ɸ', equate to 0, check for max/min and compare the results???

godtabh

breadmonkey wrote: »

ehhhhhh.....

differentiate wrt ɸ', equate to 0, check for max/min and compare the results???

Why would you differentiate?

As far as I can tell thats not the object of the excercise. I think its just a matter of plotting each against each and compairing the results and as I said I think the concervative answer is the smallest one.

breadmonkey

kearnsr wrote: »

Best I can figure you would want Ko with the lowest number as the lower the number the more conservative it is.

I was going on what you said here. If you want the lowest value of K0 then you can find the value of ɸ' that minimises each function by what I said previously.

EDIT: Although you'll prbably be given a value of ɸ' to work with so what I said is probably useless inretrospect.

godtabh

breadmonkey wrote: »

I was going on what you said here. If you want the lowest value of K0 then you can find the value of ɸ' that minimises each function by what I said previously.

EDIT: Although you'll prbably be given a value of ɸ' to work with so what I said is probably useless inretrospect.

Yeah I've been given a range of values for ɸ' to determine Ko

chris85

Ok well this is bit different.

Ok well my view on being the most conservative would be to go with the equation that yields the highest value of K0. Bear in mind this is from an engineering design point of view. My thinking for suggesting the highest value is below.

it sounds like ideally you want to keep K0 low compared the angle of shear. The most radical solution will keep this K0 value really low as it does not allow any room for error.
The conservative solution would then be the highest as this allows for a wide variety of situations.

Put in other words if you need to budget money for a week and you estimate you will need €80 for grocery shopping. The conservative approach would be to say €90-100 is required in case there are any deviations in prices etc.

Does that make sense?

godtabh

chris85 wrote: »

Ok well this is bit different.

Ok well my view on being the most conservative would be to go with the equation that yields the highest value of K0. Bear in mind this is from an engineering design point of view. My thinking for suggesting the highest value is below.

it sounds like ideally you want to keep K0 low compared the angle of shear. The most radical solution will keep this K0 value really low as it does not allow any room for error.
The conservative solution would then be the highest as this allows for a wide variety of situations.

Put in other words if you need to budget money for a week and you estimate you will need €80 for grocery shopping. The conservative approach would be to say €90-100 is required in case there are any deviations in prices etc.

Does that make sense?

Thats what I've been thinking. I just need to figure out if Ko should be high or low for desgin.

chris85

kearnsr wrote: »

Thats what I've been thinking. I just need to figure out if Ko should be high or low for desgin.

Yeah know what you mean kearnsr.

is it possible to explain the problem more just to get a broader look at the problem.

I think it all depends on what way the problem needs to approached

godtabh

KThink the most conservative approach would be that which gives you the highest value of horizontal effective stress, say if you were designing a retaining wall for example, (However usually for design we used the active earth co-efficient, ka = (1-sinΦ/1+sinΦ). Of the 3 equations I looked at onmy spreadsheet Tan(45 -Φ/2) gave highest values, therefore most conservative of those.

So I'm going with the higher the value of Ko the more conservative it is at it gives a higher effective stress

chris85

kearnsr wrote: »

KThink the most conservative approach would be that which gives you the highest value of horizontal effective stress, say if you were designing a retaining wall for example, (However usually for design we used the active earth co-efficient, ka = (1-sinΦ/1+sinΦ). Of the 3 equations I looked at onmy spreadsheet Tan(45 -Φ/2) gave highest values, therefore most conservative of those.

So I'm going with the higher the value of Ko the more conservative it is at it gives a higher effective stress

Easiest way to do it would be to put each of the equations on a spreadsheet and input a range of values for angle of shear. Graph the results and will give you a good idea what you are looking at.