 So, the angle of friction and cohesion, collectively known as shear strength parameters, are material specific parameters. So, in this video I'm going to talk about a method for deriving them experimentally called the Shea Box Test. Now, a Shea Box looks like this. You can see that there's two confining rings in a space figure sample to sit in the middle. When a lid goes onto the top where you can suspend a known normal stress onto your sample. Now the shear force is created when the two halves of the Shea Box move away from each other. So, this is what a Shea Box looks like in profile as a cartoon. You can see that we have two halves of the Shea Box here. Our sample sits in the middle of the Shea Box and on the top we have a lid. Now we put that Shea Box into a rig that fixes the bottom half of the Shea Box through a force transducer. So, that bottom half of the Shea Box stays fixed but we can measure the force going through it. What we do is we suspend a normal load onto the lid of the Shea Box. So, we put a normal load or a normal force onto the lid of the Shea Box and we create our shear force using a drive motor which pushes the top half of the box away from the bottom half. So, we have a drive motor which pushes the top half of the box away from the bottom and that creates the shear force within the sample. Now, if we take that normal force and we divide it by the cross-sectional area of the box which in a standard Shea Box test is 60mm by 60mm although you can get different sized Shea Boxes. But if we take that normal force and we divide it by the cross-sectional area of the Shea Box, what that equals is the normal stress. Now, if we take the force that we are measuring in this force transducer and we divide that by the cross-sectional area of the box, what we get is the shear stress. That's going through the sample. So, in the Shea Box test we create shear force or we steadily ramp up the shear force that's going through our sample until the point that the material fails and we do that for a fixed normal force. So, the key assumption that we make within the Shea Box test is that the normal stress created by the normal force is the normal effective stress. So, we assume that the effects of pore water pressure within our sample or the change in pore water pressure during our test is zero. That's an important assumption and we'll come back to that in a second. But what we want to do in the Shea Box test is represent this information on a more cool on failure envelope. So, if we plot the shear stress against normal effective stress, what we want to do is generate the straight line or the more cool on failure line. So, to do that from the Shea Box test, essentially we keep the normal force constant or the normal stress constant throughout the test and we increase the shear stress until the material fails. Now, if we know the normal stress and we know the point at which the shear stress at the point of failure, we can draw one point on this graph. So, the normal stress and if we know the shear stress of failure, we get a point. Let's say it's that. What we want to do in a Shea Box test is replicate that a number of times at different normal forces. So, at different points along this x-axis, we want to recreate this test and record the shear stress at failure. So, we'll stick a different normal load onto the top of the Shea Box with a new sample, stick a new normal stress on and then share the sample until it fails. So, if we increase the normal stress and we record the shear stress at failure, we'll get another point here and we do this three or four times until we can get our straight line. If we draw a line through the data, we have our more cool on failure envelope. We can take the gradient of that line, which is tan phi. So, if we take the inverse tan of the gradient, we get our phi and we also take the intercept here, which is the cohesion and that has units of whatever stress unit you had your shear stress in. So, Killing Newton's per meter squared in most cases. So, we found phi and we found the cohesion. So, that's our shear strength parameter. So, how do we know which shear stress to record or how do we know when the sample is failed? Well, to do that we need to measure two of the properties and that's the shear strain and the volumetric strain of the sample. But to measure that in the Shea Box test, what we do is we have transducer, a displacement transducer, not a force transducer this time, but a displacement transducer that measures the displacement of the lid. So, we measure how, whether the lid moves up or down during the test. So, we can measure the change in height of the sample, delta H. And if we take that delta H and we divide it by the initial sample height, so H0, initial sample height, delta H over H0, that's equal to our volumetric strain. So, how do we measure shear strain within our sample? Well, the shear strain is defined like this. So, if we had a block of material and we subjected that block of material to a shear stress tau, that block of material will tend to deform in this way. So, you would get the material deforming like this. So, shear strain is defined by this angle, the angle at which the material displaces through. And essentially that's equivalent to the horizontal displacement, or X, divided by the initial height, say it's 0. So, shear strain, when we come to the shear box test, is defined by the, this displacement X, and we measure that through another, using another transducer. So, the displacement X divided by the initial height. So, shear strain gamma is equal to delta X over H0. So, if we record these through the course of the shear box test, we can assess how the material is straining and record the shear stress at the point of failure. So, if we plot a stress versus strain diagram of the shear box test, it looks something like this. So, if we plot a stress strain curve for a, during a shear box test with strain on the X axis and stress on the Y axis, it will look something like this, where we get an increase in strain and stress, or stress with strain, till we reached a peak, it would come down and then fail. So, this is a classic stress strain diagram for initially dense soil. Loose soils behave slightly differently and we don't get this apparent peak, where the material just strains like that. We'll come back to why these behave differently in a second, but there's some artifacts of this curve that we need to point out now. Well, the question is, at which point do we take the material to have failed? Is it failure after the peak? Is it failure in the residual, or is it failure in the critical or the residual? So, let's just level those up. We have a peak, we have a critical, and we have a residual strength. So, which shear stress do we take for a more cool on failure envelope? Well, the answer is a little bit complicated. In a shear box test, we'll record all three if it's available and depending on which situation or which design situation that we're looking at, we might use a peak, a critical, or a residual. So, for now, we'll just record all three in the shear box test and we'll deal with which situations to use those different values when we talk about design. So, if we come back to the well cool on failure envelope with the normal effective stress on the x-axis and the shear stress on the y-axis, and we draw all three of those lines, the peak, the critical, and the residual, it should look something like this. We'll not always have a peak, that only exists for initially dense soils, but if it's there we should record it. And from these three lines, we can generate shear strength parameters. And we'll come back to you later when we're talking about geotechnical design, when we distinguish between these three lines. But for now, let's just record all three.