 Now suppose we have a situation like this where we have 10 meters of clay and let's say we know the coefficient of volume compressibility the 0.3 meter squared per mega Newton It's often written in terms of meter squared per mega Newton rather than meter squared per kilonewton just to make This number a little bit more manageable So we have a clay we know it's a coefficient of volume compressibility and it's 10 meters thick And let's say we have a water table that's at the surface here And so the clay is fully saturated just to make things simple now What would happen if we put a An embankment let's say two meters of embankment over the top of this clay layer with a known unit weight Or the question is how much settlement would we get so what is delta range? That's what we're trying to figure out Well, the first thing we need to do is calculate what the change in stress is on the top of this clay layer So what is the stress caused by the embankment? at this point of the change in stress so to do that we We calculate this the stress by Almost like we were treating this this embankment as a layer of soil As we did in our previous videos, so we take the unit weight And killing newtons per meter cubed and we multiply that by its thickness of two meters so the stress or the change in stress is equal to the unit weight of the embankment multiplied by its thickness Which equals 40 kilonewtons per meter squared so that's the change in stress That's exerted on the top of the clay here the next thing we need to do is Convert this mv value into units that are the same as the our stress value So they're currently in meter squared per magniton and we need to convert them into meter squared per kilonewton So to do that we take our mv value and we divide it by a thousand so our mv value equals zero point three divided by a thousand Meter squared per kilonewton, okay in an initial height h0 Is equal to 10 meters So it's the initial thickness of the clay there So we put that into our formula of Delta H and Delta H Is equal to the change in stress which is 40 multiplied by the mv value 0.3 over a thousand Multiplied by 10 meters our initial sample thickness so our Delta H in this example equals 0.12 meters or 12 centimeters So that's an example about how we apply This a simple Total settlement formula to this sort of example A little bit of a reality check so if you get numbers out of your calculation like this 0.12 meters or 12 centimeters then that it somehow seems reasonable for a 10 meter layer of clay if you had a Consolidation or total settlement value of 12 meters then you might think that something was wrong with your calculation So it's worth checking that these numbers make sense when they come out So there's some cavities this this model of Consolidation it this formula assumes that the The soil is a confined confined and fully elastic So we just need to remember that when we're applying this formula it assumes that soils are Fully elastic which they're not and it assumes that they're confined which they're not So I'm going to show show you in the next video a method for deriving your coefficient of volume compressibility from laboratory experiments or a fully confined laboratory experiment There is no substitution though for doing In-situ consolidation Experiments because we often find that the MV value derived from lab experiments is not exactly the same as What we might derive from field work or In-situ field experiments, so it's worth doing those field experiments if you have budget within the project that you're working on The ultimate consequence of that is is it if you have difference and difference it So the ultimate consequence of that is if you have difference in MV values you have a difference in total settlement and You might have more settlement than what you originally planned for and so your structures might fail Standards if you are just relying solely on laboratory experiments So it's worth doing those in-situ field experiments. So I mean we're waiting to represent that mathematically is that your MV value You can see that it's got inverse stress units and what actually it is in terms of For fully confined cases is that it's well not equal to almost equal to The Young's modulus or the Young's modulus elasticity in Unconfined Cases your MV value is well equal to One plus your Poisson's ratio So it's there's an inverse relationship between Young's modulus here But there's a factor and you don't have to worry about the details here But there's a factor of Poisson's ratio now put a link to an explanation of what Poisson's ratio is Essentially, it's how the material Deflects out as you're loading it so In an unconfined case this this situation happens So you get that your MV value actually changes depending on whether you're looking at a confined or an unconfined case What that means in terms of total settlement is something like this So if I draw a graph that looks something like this where I have Poisson's ratio on my x-axis and The y-axis is the difference between the predicted settlements for confined and unconfined cases We can draw a line like this, which is the the ratio of Delta H Two over Delta H three now Delta H two is our Partially confined and Delta H three is our unconfined and you can see that if If the settlements were equal so if the partially confined settlement was equal to the unconfined settlement Then this line wouldn't deviate from one. It would just stay as one But we can see that as we increase our Poisson's ratio The partially confined the unconfined settles more than the partially confined now this is a this line here is the difference between Delta H one which is the confined case or confined set predicted settlement and Delta H three which is the The unconfined and we can see that in this situation with our increase in Poisson's ratio We have quite a marked deviation from or the mark difference in the total settlements so please be aware of these kivites and when using the MV value It's still really quite useful to you to use it When we're doing simple calculations, but there are complexities to this that we need to be aware of