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Video 1
Hello everyone. Let us understand the suction stress characteristic curve. Lu and Likos in 2006 have proposed the Concept of Suction Stress to consider the physicochemical forces and capillary forces due to surface tension in the air-water interface. And any other forces that are not considered in the previous study are included as suction stress into the effective stress principle. So, the advantage of suction stress is that it is valid for any given soil and all differentforces are considered into the suction stress. Now let us understand how the suction stress characteristic curve varies for different soils and how this is related to the soilwater characteristic curve. So, the suction stress characteristic curve, a how it varies etcetera we will define based on how the soil-water characteristic curve regimes change. So, if this is the soil-water characteristic curve for a given soil, here y-axis is u a - u w that is a matrix suction and a or x-axis, volumetric water content is given. Now the curve varies inthis particular manner. So, this is θs, saturated volumetric water content, and the air entry suction value of this particular soil is somewhere here so, this is u a - u w AEV. So, this is u a - u w, Aev air entry value and beyond that, the water content decreases drastically with an increase in the matric suction and the change in the water contentstarts decreasing with increasing in suction after certain pressure. And beyond a certain suction value, it is very difficult to draw the water by increasing the suction in the soil. So, if this is a residual water content θ r, so if different zones are considered in thisparticular manner in the first zone. So, this is a saturated state of the soil even though, the pore water pressure is negative. And this is a second stage where drastically the water content decreases with an increase in the suction and this is the third stage where the rateof the decrease in water content will start decreasing and fourth stage which is a residual stage where water is held around the particles in hydration. So, this is a hydration stage where water is available as a thin film around the clay platelets. So, this is an SWCC Soil Water Characteristic Curve So, now, the suction stress characteristic curve can be drawn, here the x-axis has θ volumetric water content so, on the y-axis σs dash. So, the σs` is suction stress so, how this suction stress should vary know. So, as we have the equation and for the suction stress that is σs` = a change in the stresses due to physicochemical forces PC + σ capillary + χ(u a - u w )this is one of the expressions which was given by Lu and Likos. So, this is not found in the textbooks So here in the first stage of soil-water characteristic curve or the initial first regime, so the change in the physicochemical aspects of clays are insignificant because, the change in the volumetric water content is very small watercontent decreases very insignificantly. The change in the physicochemical aspects become 0. So, this aspect for the I regime the PC is negligible, changing the physicochemical aspects of the soil are negligible and the capillary phenomena is also negligible in the I zone or I regime where the water content is nearly = the saturatedvolumetric water content or the soil is saturated state. So, then you have χ into u a - u w. So, here χ is also approximately k = 1. And whatever the variation in u a - u w, you will see it in suction stress. So, therefore, whatever the change you see here, similar change you will see in suction stress. So, in the beginning,so in the first regime, so beyond that, as in this case this is u a - u w is less than or equalsto u a - u w AEV Air Entry Value. In the second regime, so in this expression where, u a - u w is more than u a - u w is AEV, so soiled desaturates quickly and capillary forces would start increasing. And the electrostatic repulsion will start decreasing in the soil and attractive force are nearly constant, provided the soil grains would not come close to each other or the change in the pore size distribution does not change significantly, but if the soil desaturates quickly then the van der Waals forces remain nearly constant, but then the repulsive pressures within the soil mass will start decreasing. So, this is insignificant which is close to 0 but the capillary forces are significantly higher, they start increasing. So, their effect is nearly negligible. So, as this desaturates, the capillary forces would shoot up and the contribution is essentially from the capillaryforces. So, beyond this in the third regime where the repulsive pressures diminish and the attractive force if inter particles distance decreases, due to desaturation. So, the overall increase will reduce because of this and capillary effects also start diminishing, this starts approaching a constant value. And for sands, this value startsdecreasing because the effect of the capillary force is also getting reduced. After all, the amount of moisture that is available in the soils is getting reduced and the physicochemical force anyways is not significant in sands. So, therefore for sands this will starts decreasing in the third regime, so, this is the third regime. And in the fourth regime, water is held as thin-film surround clay platelets, theamount of water that is available in the soils is only available for hydration of exchangeable cations and hydration of layers of different inner layers of clay platelets. If it is you will have multi-layer hydration, that is the water equivalent to multi-layer hydration is available in clays and a single layer of hydration may be available around sand platelets. So, the suction stress essentially the capillary force is 0 and a σ PC is anyways 0. And χ reduces to a very small value until approaches close to 0. In the case of sands, this goesto 0, but in the case of clays because, it attractive forces are the van der Waal forces still exits, which gets a constant value somewhere like this. So, this is the suction stresscharacteristic curve of a given soil, this is for sands and this is for clays. So, it approaches a constant value somewhere here. Similarly, this same graph can be drawn for u a - u w that is matric suction on the x-axis, u a - uw on the x-axis, and suction stress on the y-axis. So, initially, the suction stress increases at the same rate as the matric suction value, it follows 1 is to 1 linear relationship. And beyond that, the increase in the suction stress decreases with an increase in the suction and which becomes nearly constant for a particular time. But in the case of sands, this suction stress decreases and becomes 0 at one particular matricsuction. So, this is for sands and this is for clays. So, initially, there will be 1 is to 1, linearly it increases and beyond this, this is a non-linear behavior and it starts decreasing in suction stress becomes constant because of the contribution of only van der Waal forces andsuch short-range forces are dominated at that particular suction value. So, how to understand this suction stress characteristic curve? When we plot the strength the more column envelopes τf versus τf versus σ n, normal stress, we get a failure envelope for saturated soil somewhat like this. And for unsaturated soils the cohesion intercepts the intercept value increases, it increases in this manner. This is theobservation from the experiments, suction controlled direct shear stress or suction controlled triaxial test these are the observations I have a discussed earlier, this is a failure and overlap saturated soil that is, τf = C` + σf` tanϕ`. So, this is the angle of internal friction this is ϕ` and this is C`. And similarly, this is the envelope for τf equals to some C1` + σf` tan ϕ1` we can write, and this is another failureoverlap C2` + σf` tan ϕ2`. So, however, we have observed that the ϕ`= ϕ1` = ϕ2` from the experimental data that, all these lines are parallel to each other. So, this is external observation. So, the angle of internal friction is a metal constant it does not vary or it does not depend on the suction and which is constant. So, when we extend these lines back on to σ n axis, so back on to this negative axis, this is this negative axis is your tension. So, when you extend this τf is 0 at this particular point, therefore, the σs` is C2` by tanϕ` and here the point is C1` by tanϕ` and here, this point is c` by tanϕ`. So, if this becomes your matric suction, u a - u w that is a representation of negative pore water pressure within the soil. So, this particular value when you are drawing for a given matric suction, this is done for one particular given matric suction u a - u w of set 2 and this is u a - u w of say 1 and this is u a - u w = 0. So, this is for 0 and u a - u w some particular value and this is u a - u w some particular value here. So, then the profile that you get is somewhat like this. So, this is uncorrected suction stress characteristic curve, suction stress characteristic curve, and this is corrected and made it to go from the origin, then this becomes somewhat like this. So, this is corrected SSCC, Suction Stress Characteristic Curve. So, this σs` is this is for σ s and this is σs` which = σ s - σ c naught. So, this is how the corrected suction stress characteristic curve can be obtained for any given for suction stress characteristic curve or the effective stress can be determined for a given suction value using the measured data from suction controlled tests. When the data of deviatoric stress q, that is a σ 1 - σ 3 deviatoric stress or it could be τf, if it is a direct shear test. q is deviatoric stress into triaxial tests, which = σ 1 - σ 3 in triaxial tests and τf phase, the shear stress applied on the soil in direct shear. And on the x-axis, you can either show σ the net normal stress or it can be represented with p whichis mean stress. So, the mean stress represented here is σ 1 + σ 3 by 2 and here this is σ 1 - σ 3 so, there is deviatoric stress. So, when this is this is plotted then, you get a series of straight lines with a nearly the angle of internal friction = ϕ`, but different intercept, for different matric suction values. So, this is u - u w increasing up so, the strength is increasing for any given mean stress. So, this test data can be interpreted by computing the obtaining the cohesion intercept; say, for example, C 1 and for this 1 is a C1`, once this is obtained and a ϕ` is anyways is available. So, this particular point is C` by tanϕ` and this is C1` by tanϕ`. So, these values are available. So, therefore, these are the suction stress values, σ s values. The matric suction at which, these tests are conducted is also known, so, therefore, u a - u w axis is known, and this y-axis values are obtained from cohesion intercepts, and therefore, the σ s is known and u a - u w is known. So, therefore, they can plot σ s versus u a - u w. This is essentially the variation is somewhat like this and also we can plot q, the deviatoric stress versus p dash, that is effective mean stress. So, as we know the effective stress values, therefore, we can compute the mean effective stress values, then you get a unique straight line, this itself is a failure envelope. As we could determine the true effective stress from the SSCC, we can obtain the unique failure envelope for different matric suction ranges. Let us understand by example the problem.
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