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    Soil MechanicsProf. B.V.S. Viswanathan

    Department of Civil EngineeringIndian Institute of Technolog! Bom"a

    #ecture $ %&

    Shear Strength of Soils#ecture 'o.(

    Students we have gradually come to the very last lecture on the shear strength of soils. We haveseen 6 different aspects connected to the shear strength of soils over the last 6 lectures and todayis the concluding lecture on whatever items are still remaining with respect to shear strength ofsoils which a typical student should know. As usual lets take a quick look at whatever we hadpassed through in the last lecture.

    (Refer Slide ime! "!#$ min%

    &n the last lecture we saw quiet in detail what are the drained test' what are undrained test othdirect shear and tria)ial shear and where they are used and we even saw some numericale)amples. We also saw that it is possile to look at the topic of shear strength in a totallydifferent way in terms of the soil. hat is how does cohesionless soil ehave under shear andhow cohesive soil ehaves under shear. We saw in particular the application of the differenttypes of drained and undrained test with a typical e)ample of the earth dam. *uring the course of

    life of an earth dam there are several stages it passes through starting from construction toreservoir filling and drawdown to long term staility. And under each conditions the shearparameters which must e used in order to test the safety of the earth dam will vary and the typeof that will give the appropriate parameters will also vary.+or e)ample the ,* test which we saw was good for a slow construction and also for long termstaility where in consolidation would have already taken place that mean drainage would haveoccurred' shear stress also does not produce any pore pressure.

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    (Refer Slide ime! -!-# min%

    n the other hand suppose a dam has already een filled' the reservoir is full and the reservoir isemptied somewhat suddenly rapidly relatively for certain purpose. hen the test that is applicaleand the corresponding parameter would e the consolidated undrained test ecause the earth damhas already undergone the consolidation during its life time filling up the reservoir. /ut nowsudden depreciation of reservoir produces shear stresses under undrained condition. And ifsuppose we are uilding a dam very rapidly then pore pressures get developed even duringconstruction they do not have time to dissipate and therefore the staility of the dam even duringconstruction has to e kept in mind and that short term staility is est determined underundrained conditions using parameters that derived from a 00 test.

    (Refer Slide ime! 1$!"6 min%

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    So if you take construction' if it is slow and pore pressures are allowed to dissipate there isconsolidation in drainage' s is equal to c dash plus sigma dash tan phi dash where all theparameters involved are drained parameters and effective parameters. &f the construction is onthe other hand rapid' pore pressures are not allowed to dissipate' the shear strength equationecomes s is equal to cuplus sigma tan phi u where c u and phiu corresponds to undrained

    conditions. &f drawdown is eing considered the parameters which will e applicale will e c cuand phicuand the shear strength equation would e s is equal to ccu plus sigma tan phicu. 0nderlong term conditions once again drained parameters will apply and s is equal to c dash plussigma dash tan phi dash. here are a numer of factors which affect shear strength' we mustknow them and their influence and so we spent quiet sometime in the last lecture to understandthe impact of many factors which affect the shear strength.2ere is simply a list which & am reproducing to remind what are the factors which influenceshear strength. he first three factors shape and gradation of particles' relative density thecompaction the denseness with which the soil is packed and the confining pressure that is appliedto the soil or the confining pressure under which the soil is at any given depth. hese are all

    parameters which are particularly important from point of view of shear strength of cohesion lesssoils. n the other hand for cohesive soils what are more important oviously ecause of theirlow permeaility are drainage conditions' degree of saturation' rate of loading.

    (Refer Slide ime! 16!13 min%

    &n addition to this there is another important parameter which during the course of todays lecturewe will pay some attention to that is the stress history. he history which shows what kind ofstress the soil has undergone in the past' this is particularly important for clayey soils. 4et uslook at the shear strength from point of view of the type of soil. &f you have a cohesionless soiland su5ected to direct shear test' this is a kind of relationship you will get etween shear stressand the shear displacement. &f it is a dense soil it will undergo a little it of compression and thene)pansion.

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    (Refer Slide ime! 16!#" min%

    &f it is a loose sand it will under compression continuously. here will e a peak shear stress andan ultimate shear stress as the displacement increases. he same thing can e oserved in atria)ial test also' for dense sand there is a peak' for loose sand there is no marked peak. 4oosesand undergoes compaction or compression' dense sand undergoes a little it of compressioninitially ut then undergoes e)pansion susequently' it ecomes loosened.

    (Refer Slide ime! 1!17 min%

    So with respect to ehavior of a soil whether it is cohesionless or cohesive under shear we cansee a few special points which are summari8ed here.

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    (Refer Slide ime! 1!#1 min%

    ne there is a peak and an ultimate which we saw in the previous diagram. *ense sands undergoan e)pansion mostly although they undergo a little it of compression initially' loose sandsundergo compression. here is a significant volume change the amount of compression or theamount of e)pansion is quiet significant under shear.

    Suppose we prevent this volume change then what will happen is the shear stress that isresponsile for causing this volume change will not orne y the soil and the soil will tend toehave like a liquid and thats known as liquefaction. We also saw last time' having talked aout

    liquefaction what is critical void ratio and how that can e used to decide whether soil willliquefy under a given condition or not. he concept of critical void ratio can e very easilyunderstood from the statement which & made a few minutes ack that dense sand undergoe)pansion' loose sand undergo compression.

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    (Refer Slide ime! 13!$3 min%

    (Refer Slide ime! 17!#3 min%

    Suppose you have a sand which is neither loose nor dense relatively speaking then if the void

    ratio remains unchanged throughout shear then thats the soil which will undergo liquefactionecause it doesnt undergo volume change during shear and since it is unale to undergo volumechange during shear it will liquefy. So whats that void ratio at which the soil will ehave likethis that can e otained y plotting void ratio change with a)ial strain as shown here and findingout which is the void ratio where the volume change will e nullified and that is known as ,9R.*epending upon the type of tria)ial test we do' there are different values of ,9R. he mostpopularly used one is the ,asagrande ,9R which is nothing ut the void ratio efore application

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    of sigma# and constant sigma#,9R is also possile' constant volume ,9R is also possile todetermine.

    (Refer Slide ime! "1!"1 min%

    &n the second instant where the constant volume ,9R test is conducted e 1after the application ofsigma#is used as the critical void ratio. :ow in todays lecture we will see an assortment oftopics which & am calling as special topics' all of which are very important. Some of them areslightly advanced and & will try to give an e)posure to these topics rather than go into greatdetails. +or e)ample let me start with a list of these so called special topics.

    (Refer Slide ime! "1!#7 min%

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    ;eak and residual shear strengths is something which we need to understand very well which isvery important from the point of view of particularly slope staility or staility of any structurealso. hen we need to understand something known as pore pressure coefficients then what arestress paths< & had mentioned that shear strength of a clayey soil particularly depends upon thestress history. So one needs to know what is the path through which this stresses have changed.

    hen we need to know something aout failure' we have only een seeing so far the =ohrcoulom theory ut there are other theories as well ecause sometime the soils do not ehavestrictly according to the =ohr coulom theory although it is universally valid and universallyused also. /ut there are theories which are particularly applicale to clays especially in theplastic deformation stage and those are known etter as yield theories. We will have to see thosealso. And then finally we will see a very important test called cyclic tria)ial test. hese are dayswere awareness aout earthquakes and their damage has increased like anything ecause of pastrecent e)periences.

    here is one test known as the cyclic tria)ial test which is useful in determining the liquefactionstrength of a soil. &t helps us to predict under what conditions a soil will liquefy and whether the

    present condition is indicative of a potential to liquefy or not. So site characteri8ation' siteassessment from point o