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NPTEL- Advanced Geotechnical Engineering Module 4 Lecture 21 Pore water pressure and shear strength - 5 Topics 1.3 SHEAR STRENGTH OF COHESIVE SOILS 1.3.1 Triaxial Testing in Clays Consolidated drained test Consolidated undrained test Unconsolidated undrained test 1.3 SHEAR STRENGTH OF COHESIVE SOILS The shear strength of cohesive soils can, generally, be determined in the laboratory by either direct shear test equipment or triaxial shear test equipment; however, the triaxial test is more commonly used. Only the shear strength of saturated cohesive soils will be treated here. The shear strength based on the effective stress can be given by [equation 3] . For normally consolidated clays, and, for overconsolidated clays, . 1.3.1 Triaxial Testing in Clays The basic features of the triaxial test equipment were shown in Figure 4. 5. Three conventional types of tests are conducted with clay soils in the laboratory: 1. Consolidated drained test or drained test (CD test or d test). 2. Consolidated undrained test (CU test). 3. Unconsolidated undrained test (UU test). Each of these tests will be separately considered in the following sections. Consolidated drained test For the consolidated drained test the saturated soil specimen is first subjected to a confining pressure through the chamber fluid; as a result, the pore water pressure of the sample will increase by . The connection to the drainage is kept open for complete drainage so that becomes equal to zero. Then the deviator stress (piston stress) is increased at a very slow rate, keeping the drainage valve open to allow complete dissipation of the resulting pore water pressure . Figure 4.17 shows the nature of the variation of the deviator stress with axial strain. From Figure 4.17, it must also be pointed out that, during the Dept. of Civil Engg. Indian Institute of Technology, Kanpur 1 NPTEL- Advanced Geotechnical Engineering application of the deviator stress, the volume of the specimen gradually reduces for normally consolidated clays. However, overconsolidated clays go through some reduction of volume initially but then expand. In a consolidated drained test, the total stress is equal to the effective stress since the excess pore water pressure is zero. At failure, the maximum effective principal stress is where is the deviator stress at failure. The minimum effective principal stress is . Figure 4.17 Consolidation drained triaxial tests in clay (a) application of confining pressure (b) application of deviator stress From the results of a number of tests conducted using several specimens, the Mohr’s circles at failure can be plotted as shown in Figure 4.18. The values of c and are obtained by drawing a common tangent to these Mohr’s circles, which is the Mohr-Coulomb envelope. For normally consolidated clays (Figure 4.18a), we can see that . Thus the equation of the Mohr-Coulomb envelope can be given by . The slope of the failure envelope will give us the angle of friction of the soil. As shown by equation (5) for these soils Dept. of Civil Engg. Indian Institute of Technology, Kanpur 2 NPTEL- Advanced Geotechnical Engineering Figure 4.18 Failure envelopes for (a) normally consolidated and (b) overconsolidated clays from consolidated drained triaxial tests The plane of failure makes an angle of with the major principal plane. For overconsolidated clays (Figure 4.18b), . So, the shear strength follows the equation the values of can be determined by measuring the intercept of the failure envelope on the shear stress axis and the slope of the failure envelope, respectively. To obtain a general relation between , refer to Figure 4.19, from which Dept. of Civil Engg. Indian Institute of Technology, Kanpur 3 NPTEL- Advanced Geotechnical Engineering Figure 4.19 Derivation of equation (21) (20) or (21) Note that the plane of failure makes an angle of with the major principal plane. If a clay s initially consolidated by an encompassing chamber pressure of and allowed to swell under a reduced chamber pressure of , the specimen will be overconsolidated. The failure envelope obtained from consolidated drained triaxial tests of these types of specimens has two distinct branches, as shown in Figure 4.20. Portion of the failure envelope has a flatter slope with a cohesion intercept, and the portion represents a normally consolidated stage following the equation Dept. of Civil Engg. Indian Institute of Technology, Kanpur 4 NPTEL- Advanced Geotechnical Engineering Figure 4.20 Failure envelope of a clay with perconsoldation pressure The shear strength of clays at very large strains is referred to as residual shear strength (i.e., the ultimate shear strength). It has been proved that the residual strength of a given soil is independent of past stress history (22) (i.e., the c components is 0). For triaxial tests, (23) Where The residual friction angle in clays is of importance in subjects such as the long-term stability of slopes. Consolidated undrained test In the consolidated undrained test, the soil specimen is first consolidated by a chamber confining pressure ; full drainage from the specimen is allowed. After complete dissipation of excess pore water pressure, , generated by the confining pressure, the deviator stress is increased to cause failure of the specimen. During this phase of loading, the drainage line from the specimen is closed. Since drainage is not permitted, the pore water pressure (pore water pressure due to deviator stress, ) in the specimen increases. Simultaneous measurements of and are made during the test. Figure 4.21 shows the nature of the Dept. of Civil Engg. Indian Institute of Technology, Kanpur 5 NPTEL- Advanced Geotechnical Engineering variation of and with axial strain; also shown is the nature of the variation of the pore water pressure parameter see equation (5 from chapter 4)] with axial strain. The value of A at failure, is positive for normally consolidated clays and becomes negative for overconsolidated clays. Thus, is dependent on the overconsolidated ratio. The overconsolidation ratio, OCR, for triaxial test conditions may be defined as Figure 4.21 Consolidation undrained triaxial test. (a) Application of confining pressure (b) application of deviator stress (24) Where is the maximum chamber pressure at which the specimen is consolidated and then allowed to rebound under a chamber pressure of . At failure, = = Dept. of Civil Engg. Indian Institute of Technology, Kanpur 6 NPTEL- Advanced Geotechnical Engineering consolidated undrained tests on a number of specimens can be conducted to determine the shear strength parameters of a soil, as shown for the case of a normally consolidated clay in Figure 4.22. The total-stress Mohr’s circles (circles A and B) for two tests are shown by the broken lines. The effective-stress Mohr’s circles C and D correspond to the total-stress circles Ai and B, respectively. Since C and D are effectivestress circles at failure, a common tangent drawn to these circles will give the Mohr-Coulomb failure envelope given by the equation . If we draw a common tangent to the total-stress circles, it will be a straight line passing through the origin. This is the total-stress failure envelope, and it may be given by Figure 4.22 Consolidated undrained test results-normally consolidated clay (25) Where is the consolidated undrained angle of friction. The total-stress failure envelope for an over consolidated clay will be of the nature shown in Figure 4.23 and can be given by the relation Dept. of Civil Engg. Indian Institute of Technology, Kanpur 7 NPTEL- Advanced Geotechnical Engineering Figure 4.23 Consolidated undrained test-total stress envelope for overconsolidated clay (26) Where is the intercept of the total-stress failure envelope along the shear stress axis. The shear strength parameters for overconsolidated clay based on effective stress, i. e., obtained by plotting the effective-stress Mohr’s circle and then drawing a common tangent to can be As in consolidated drained tests, shear failure in the specimen can be produced by axial compression or extension by changing the loading conditions. Unconsolidated undrained test In unconsolidated undrained triaxial tests, drainage from the specimen is not allowed at any stage. First, the chamber confining pressure is applied, after which the deviator stress is increased until failure occurs. For these tests. Total major principal stress Total minor principal stress Tests of this type can be performed quickly since drainage is not allowed. For a saturated soil, the deviator stress at failure, is practically the same irrespective of the confining pressure (Figure 4.24). So, the total-stress failure envelope can be assumed to be a horizontal line, and . The undrained shear strength can be expressed as Dept. of Civil Engg. Indian Institute of Technology, Kanpur 8 NPTEL- Advanced Geotechnical Engineering Figure 4.24 Unconsolidated undrained triaxial test Figure 4.25 Dept. of Civil Engg. Indian Institute of Technology, Kanpur 9 NPTEL- Advanced Geotechnical Engineering (27) This generally referred to as the shear strength based on concept. The fact that the strength of saturated clay sin unconsolidated undrained loading conditions is the same irrespective of the confining pressure can be explained with the help of Figure 4.25. If a saturated clay specimen A is consolidated under a chamber confining pressure of and then sheared to failure under undrained conditions, the Mohr’s circle at failure will be represented by circle no 1. The effective-stress Mohr’s circle corresponding to circle no 1 is circle no. 2, which touches the effective-stress failure envelope. If a similar soil specimen B, consolidated under a chamber confining pressure of is subjected to an additional confining pressure of without allowing drainage, the pre water pressure will increase by . We saw in chapter 4 that and, for saturated soils, . Since the effective confining pressure of specimen B is the same as specimen A, it will fall with the same deviator stress, . The total-stress Mohr’s circle for this specimen (i.e., B) at failure can be given by circle no. 3. So, at failure, for specimen B Total minor principal stress Total major principal stress The effective stresses for the specimen are as follows: Effective major principal stress Effective minor principal stress = The above principal stresses are the same as those we had for specimen A. thus, the effective-stress Mohr’s circle at failure for specimen B will be the same as that for specimen A, i.e., circle no 1. The value of could be of any magnitude in specimen B; in all cases, would be the same Example 1 Consolidated drained triaxial tests on two specimens of a soil gave the following results: Test no. Deviator stress at failure Confining pressure 1 2 Determine the values of c and 70 92 440.4 474.7 for the soil. Solution From equation (21), ) . For test ; . So, Dept. of Civil Engg. Indian Institute of Technology, Kanpur 10 NPTEL- Advanced Geotechnical Engineering (a) Similarly, for test ; . Thus, (b) Subtracting equation (a) from (b), Substituting in equation (a) Example 2 A normally consolidated clay specimen was subjected to a consolidated undrained test. At failure, , , and . Determine . Solution Referring to Figure 4.26, Hence Again, So, Hence Dept. of Civil Engg. Indian Institute of Technology, Kanpur 11 NPTEL- Advanced Geotechnical Engineering Figure 4.26 Example 3 For a saturated clay soil, the following are the results of some consolidated drained triaxial tests at failure: Test no. 1 2 3 4 Draw a 60 90 110 180 diagram, and from that determine Solution The diagram of be written in the form 25.6 36.5 44.0 68.0 for the soil. is shown in Figure 4.27; this is a straight line, and the equation of it may Dept. of Civil Engg. Indian Institute of Technology, Kanpur 12 NPTEL- Advanced Geotechnical Engineering Figure 4.27 (a) Now equation (20) can be written in the form (b) Comparing equations (a) and (b) we find 27, and . So, and . From Figure 4. And Dept. of Civil Engg. Indian Institute of Technology, Kanpur 13