Shear Strength of Soil

11 ShearStrength of Soil The shearstrength of a soil massis the internal resistanceper unit area that the soil masscan otTerto resistfailure and sliding along any plane insideit. One must under- standthe nature of shearingresistance in order to analyzesoil stabilityproblems such as bearing capacity,slope stability,and lateral pressureon earthretainingstructures. 11.1 Mohr -Coulomb Failure Criterion Mohr ( 1900)presented a theory for rupture in materialsthat contendedthat a ma- terial fails becauseof a critical combination of normal stressand shcaringstress, and not from either maximum normal or shear stressalone. Thus. the functional rela- tionship between normal stressand shearstress on a failure plane can be expressed in the followins form: r1: f@) (11. 1) Thc failureenvelope defined by Eq.(11.1) is a curvedline. For most soil me- chanicsproblems, it is sufficientto approximatethe shearstress on the failure plane as a linear function of the normal stress(Coulomb. 1776).This linear function can be written as rf=c*crtan$ (11.2) where c : cohesion d : angle of internal friction o : normal stresson the failure plane r/ : shearstrength The preceding equation is called the Mohr-Coulomb failure criterion. In saturated soil, the total normal stress at a point is the sum of the effective stress(n') and pore water pressure(tt), or o:o'ltt 311 312 Chapter 11 Shear Strength of Soil Table 11. ? Typical Values of Drained Angle of Friction for Sands and Silts Soil type d'(des1 Sand: Rr,tundedgrains Loose 27-30 Medium 30-35 Dense 35-38 Sand: Angulur grains Loose 30-35 Medium 3.5- 4t) Dense 40-45 Gravel with some sand 34,48 Sl/ts 26-35 The effectivestress a' is carried by the soil solids.The Mohr-Coulomb failure criterion, expressedin terms of efTectivestress, will bc clf the form - T| ,'' * tr' tan <[' (11.3) where c' : cohesionand @' : friction angle,based on effeotivestrcss. Thus, E,qs.(11.2) and (11.3)are expressionsof shearstrength based on total stressand effectivestress. The value of c' for sand and inorganic silt is 0. For nor- mally consolidatedclays, c' can be approximated at 0. Overconsolidatedclays have valuesof c' that are greaterthan 0. The angleol friction, ry'',is sometimesrcfcrred to ' as the drained angLeo.f .frictbn. Typical values of <f for some granular soils arc given in Table1 1.1. The signilicanccof Eq. ( I 1.3)can be explainedby referring to Fig. I L l, which showsan clemental soil mass.Let the effectivenormal stressand the shearstress on a (a) Figure 11.I Mohr-Coulomb failurecriterion 11'2 rncrinationof the prane of Fairurecaused by shear 313 the plane ab be o' and r, respectively.Figure 11.1bshows the plot of the failure envelope definedby Eq. (11.3).If the magnitudesof o' and r on planeab are suchthat they plot as point,4 in Figure 11.1b,shear failure will not occur along the plane. If the effective normal stress and the shear stress on plane ab plot as point B (which falls on the failure envelope),shear failure will occur along that plane. A state of stresson a plane representedby point C cannot exist,because it plots abovethe failure envelope,and shearfailure in a soil would have occurrcd alreadv. 11.2 lnclination of the Plane of Failure caused by shear As statedby the Mohr-Coulomb failure crittlrion, failure from shearwill occurwhen the shearstress on a plane reachesa value given by Eq. (1 1.3).To determine the inclination of the failure plane with the major principal plane, refer to Figure 11.2, where c\ and oi are, respectively,the major and minor effectiveprincipal stresses. The failure plane EFmakes an angled with the major principal plane.To determine the angle0 and the relationshipbetween rrj and ai, refer to Figure 11.3,which is a plot of the Mohr'.scircle for the state of stressshown in Figure I 1.2 (see chapter 9j. In Figure 11.3,fghis thc failure envelopedefined by the relationshipr[: c, * o, tan$, . The radialline ab definesthe major principalplane (CD in Figure'11.2),and the ra- dial lineaddefines the failureplane (E-Fin Figure 1l.z).ltcan be shownthat Lbad: 2e:90*d'.or 0:45+9 ( 2 r1.4) Again.from Figure11.3. ad (r1.-s) fa:stna Tu - .fO+ Ou : c' ct>rg'-ojt'i (11.6a) 2 U 01, a O'I Ef1'ectivenormal stress Figure | 1.2 Inclination of failure plane in soil with major principal plane Figure 71.3 Mohr'scircle and failureenvelope 314 Chapter 11 Shear Strength of Soil Also, ot-ol aa:r ( l 1.6b) 2 SubstitutingEqs. (11.6a) and (11.6b) into Eq. (11.5),we obtain o\-ot 2 sin@' : o,, _f o,. c'cot$'+ t- /l+sind'\ / cos6'\ 'i -.'1[r (1 1.7) sind/*"\r ,ino,/ However, I + sin@':tan'145*^/ d'\ 1 - sin q5' Z) and cos d' / (b' \ I "t*,t-tan\45+ 2) Thus, : (11.8) o\ o\,un'(+s. +) * ,r',^n(ot . +) An expressionsimilar to Eq. (11.tt)could alsobe derived usingEq. (11.2)(thal is, total stressparameters c and @),or rr) - . rr,,""(0, -- ( l l.e) ut ttun'(+.s, f) 1t.3 Laboratory Test for Determination of Shear Strength Parameters There are several laboratory methods now available to determine the shear strength parameters (i.e., q 6, c' , 6') of various soil specimensin the laboratory. They are as follows: a. Direct shear test b. Triaxial test c. Direct simple shear test d. Plane strain triaxial test e. Torsional rins shear test 11.4 DirectShear Test 315 The direct shear test and the triaxial test are the two commonly used techniques for determining the shear strength parameters. These two tests will be described in de- tail in the sections that follow. 11.4 Direct Shear Test The direct sheartest is the oldest and simplestform of sheartest arrangement.A diagram of the direct sheartest apparatusis shown in Figure 11.4. The teit equipment consistsof a metal shearbox in which the soil specimenis placed.The soil rp..i."n, may be squareor circular in plan. The sizeof the specimensgenerally ur",l is about 51mm x 5Lmm or102mm x 102mm(2in.x2in.or4in. x 4in.) acrossand about 2-5mm (1 in.) high. The box is split horizontally into halves.Normal force on the specimenis applied from the top of the shear box. The normal stresson the speci- mens can be as great as 10-50kN/m2 (150 lb/in.r). Shear force is applied by moving one-half of the box relative to the other to causefailure in the soil specimen. Depending on the equipment, the sheartest can be either stresscontrolled or strain controlled. In stress-controlledtests, the shearforce is applied in equal incre- ments until the specimenfails. The failure occursalong the plane of split of the shear box. After the application of each incremental load, the shear displacementof the top half of the box is measuredby a horizontal dial gauge.Thc changein the height of the specimen(and thus the volume changeof the specimen)during the test .un b" obtained from the readingsof a dial gaugethat measuresthe vertical movement of the upper loading plate. In strain-controlledtests, a constant rate of shear displacementis applied to one-half of the box by a motor that acts through gears.The constantrate of shear displacementis measuredby a horizontal dial gauge.The resistingshear force of the soil correspondingto any sheardisplacement can be measureclby a horizontal prov- ing ring or load cell. The volume changeof the specimenduring the test is obtained Normal force Porousstone € Shear force Porousstone Figure 11.4 Diagram of direct shear test arrangement 316 Chapter 11 Shear Strength of Soil Figure 1?.5 Strain-controllcddirect shear test equipmcnt (courtesy of Soiltest,Inc., Lake Bluff,Illinois) in a manner similar to that in the stress-controlledtests. Figure 11.5 shows a photo- graph of strain-controlleddirect sheartest equipment. The advantageof the strain-controlledtests is that in the caseof densesand, peak shearresistance (that is, at failurc) as well as lessershear resistance (that is,at a point after failure called ultimate streng,th)can be observed and plotted. In stresscontrolled tests,only the peak shear resistancecan be observedand plotted. Note that the peak shearresistance in stress-controlledtests can be only approximatedbe- causefailure occurs at a stresslevel somewherebetween the prefailure load increment and the failure load increment.Nevertheless, compared with strain-controlled tests,stress-controlled tests probably model real field situationsbetter. For a given test,the normal stresscan be calculatedas Normal force o : Normal stress: (11.10) Cross-sectionalarea of the specimen The resistinsshear stress for anv sheardisplacement can be calculatedas Resistinsshear force r : Shearstress : (11.11) Cross-sectionalarea of the specimen Figure 11.6 shows a typical plot of shear stressand change in the height of the specimen against shear displacement for dry loose and dense sands.These observa- tions were obtained from a strain-controlled test. The following generalizationscan 11.4 DirectShear Test 317 E a Sheardisplacentent .='c x u)T F dF = r) o a o U Figure 11.6 PloIof shearstress ancl changc in heightof specimenagainst shear displace- mentfor looseand dcnse dry sand(dircct shcar test) be developedfrom Figure I 1.6regarding the variation of resistingshear stress with sheardisplacement: 1. ln loose sand,the resistingshear stress increases with sheardisplacement until a failure shearstress of 11is reached.After that, the shearresistance remains approximatelyconstant for any further increasein the sheardisplacement. 2. In densesand, the resistingshear stress increases with sheardisplacement until it reaches a failure stressof rr. This rlis called the peak shear strength. After failure stressis attained,the resistingshear stress gradually decreasesas shear displacementincreases until it finalty reachesa constantvalue called the ultimate .shear.strength.

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