Shear strength of soils

Detailed content on shear strength of soils, principles of effective stresses, tests conducted to determine the shear strength of soils and its applications, dilatancy, thixotropy and sensitivity.

1. SHEAR STRENGTH OF SOILS

2. CONTENTS Shear strength of soils Stress condition at a point in a soil mass Relationship between principal stresses and cohesion Mohr circle of stresses Mohr coulumb f ailure theory Effective stresses Factors effecting shear strength of soils Tests on soil Direct shear Triaxial test Unconfined compressive strength Vane shear test Shear strength characteristics of sands Critical Void ratio Sensitivity and thixotrophy of cohesive soils

3. SHEAR STRENGTH OF SOILS: Soils consist of individual particles that can slide and roll relative to one another. Shear strength of a soil is equal to the maximum value of shear stress that can be mobilized within a soil mass without failure taking place. The shear strength of soil is a function of stresses applied to it as well as the manner in which these stresses are applied. Acknowledge of shear strength of soils is necessary to determine the bearing capacity of foundations, the lateral pressure exerted on retaining walls and the stability of slopes.

4. STRESS CONDITION AT A POINT IN A SOIL MASS Through every point in a stressed body there are three planes at right angles to each other which are unique as compared to all the other planes passing through the point, because they are subjected only to normal stresses with no accompanying shearing stresses acting on the planes. These three planes are called principal planes, and the normal stresses acting on these planes are principal stresses. Ordinarily the three principal stresses at a point differ in magnitude. They may be designated as the major principal stress the intermediate principal stress , and the minor principal stress Principal stresses at a point in a stressed body are important because, once they are evaluated, the stresses on any other plane through the point can be determined. Many problems in foundation engineering can be approximated by considering only two-dimensional stress conditions. The influence of the intermediate principal stress on failure may be considered as not very significant.

5. A Two-Dimensional Demonstration of the Existence of Principal Planes: Consider the body (Fig. 8.6(a)) is subjected to a system of forces such as F1,F2, F3 and F4 whose magnitudes and lines of action are known .

6. RELATIONSHIP BETWEEN THE PRINCIPAL STRESSES AND COHESION c If the shearing resistance s of a soil depends on both friction and cohesion, sliding failure occurs in accordance with the Coulomb Eq. (8.3), that is, when

7. MOHR CIRCLE OF STRESS

8. MOHR-COULOMB FAILURE THEORY Various theories relating to the stress condition in engineering materials at the time of failure are available in the engineering literature. Each of these theories may explain satisfactorily the actions of certain kinds of materials at the time they fail, but no one of them is applicable to all materials . The failure of a soil mass is more nearly in accordance with the tenets of the Mohr theory of failure than with those of any other theory and the interpretation of the triaxial compression test depends to a large extent on this fact. The Mohr theory is based on the postulate that a material will fail when the shearing stress on the plane along which the failure is presumed to occur is a unique function of the normal stress acting on that plane. The material fails along the plane only when the angle between the resultant of the shearing stress and the normal stress is a maximum , that is, where the combination of normal and shearing stresses produces the maximum obliquity angle .

9. According to Coulomb's Law, the condition of failure is that the shear stress

10. In Fig 8.1 l(b) M o N and M o N 1 are the lines that satisfy Coulomb's condition of failure. If the stress at a given point within a cylindrical specimen under triaxial compression is represented by Mohr circle 1, it may be noted that every plane through this point has a shearing stress which is smaller than the shearing strength . For example, if the plane AA in Fig. 8.1 l(a) is the assumed failure plane, the normal and shear stresses on this plane at any intermediate stage of loading are represented by point b on Mohr circle1 where the line P o b is parallel to the plane AA The shearing stress on this plane is ab which is less than the shearing strength ac at the same normal stress Oa .

11. Under this stress condition there is no possibility of failure. On the other hand it would not be possible to apply the stress condition represented by Mohr stress circle 2 to this sample because it is not possible for shearing stresses to be greater than the shearing strength. At the normal stress Of, the shearing stress on plane AA is shown to be f h which is greater than the shear strength of the materials f g which is not possible. Mohr circle 3 in the figure is tangent to the shear strength line M o N and M o N 1 at points e and e respectively . On the same plane AA at normal stress Od, the shearing stress de is the same as the shearing strength de. Failure is therefore imminent on plane AA at the normal stress Od and shearing stress de.

12. The equation for the shearing stress de is where 0 is the slope of the line MQN which is the maximum angle of obliquity on the failure plane. The value of the obliquity angle can never exceed <5m = 0, the angle of shearing resistance, without the occurrence of failure. The shear strength line MQN which is tangent to Mohr circle 3 is called the Mohr envelope or line of rupture. The Mohr envelope may be assumed as a straight line although it is curved under certain conditions. The Mohr circle which is tangential to the shear strength line is called the Mohr circle of rupture.

13. Thus the Mohr envelope constitutes a shear diagram and is a graph of the Coulomb equation for shearing stress. This is called the Mohr-Coulomb Failure Theory. The principal objective of a triaxial compression test is to establish the Mohr envelope for the soil being tested. The cohesion and the angle of shearing resistance can be determined from this envelope. When the cohesion of the soil is zero, that is, when the soil is cohesionless , the Mohr envelope passes through the origin.

14. EFFECTIVE STRESSES So far, the discussion has been based on consideration of total stresses. It is to be noted that the strength and deformation characteristics of a soil can be understood better by visualizing it as a compressible skeleton of solid particles enclosing voids. The voids may completely be filled with water or partly with water and air. Shear stresses are to be carried only by the skeleton of solid particles . However, the total normal stresses on any plane are, in general, the sum of two components. Total normal stress = component of stress carried by solid particles + pressure in the fluid in the void space.

15. This visualization of the distribution of stresses between solid and fluid has two important consequences: When a specimen of soil is subjected to external pressure, the volume change of the specimen is not due to the total normal stress but due to the difference between the total normal stress and the pressure of the fluid in the void space . The pressure in the fluid is the pore pressure u. The difference which is called the effective stress d may now be expressed as The shear strength of soils, as of all granular materials, is largely determined by the frictional forces arising during slip at the contacts between the soil particles. These are clearly a function of the component of normal stress carried by the solid skeleton rather than of the total normal stress. For practical purposes the shear strength equation of Coulomb is given by the expression

16. The effective stress parameters c' and 0' of a given sample of soil may be determined provided the pore pressure u developed during the shear test is measured. The pore pressure u is developed when the testing of the soil is done under undrained conditions . However, if free drainage takes place during testing, there will not be any development of pore pressure. In such cases , the total stresses themselves are effective stresses.

17. Factors Effecting shear strength of soils soil composition (basic soil material ): mineralogy, grain size and grain size distribution, shape of particles, pore fluid type and content, ions on grain and in pore fluid. state (initial): Defined by the initial void ratio, effective normal stress and shear stress (stress history). State can be described by terms such as: loose, dense, overconsolidated , normally consolidated, stiff, soft, contractive, dilative, etc .

18. structure: Refers to the arrangement of particles within the soil mass the manner the particles are packed or distributed. Features such as layers, joints, fissures, slickensides, voids, pockets, cementation, etc., are part of the structure. Structure of soils is described by terms such as: undisturbed, disturbed, remolded, compacted, cemented; flocculent, honey-combed, single-grained; flocculated, deflocculated; stratified, layered, laminated; isotropic and anisotropic. Loading conditions: Effective stress path, i.e., drained, and undrained; and type of loading, i.e., magnitude, rate (static, dynamic), and time history (monotonic, cyclic)

19. TESTS ON SOIL

20. DIRECT SHEAR STRENGTH

21. TRI-AXIAL

22. UNCONFINED COMPRESSIVE STRENGTH

23. The unconfined compression test is a special case of a triaxial compression test in which the allround pressure = 0 The tests are carried out only on saturated samples which can stand without any lateral support The test, is, therefore, applicable to cohesive soils only. The test is an undrained test and is based on the assumption that there is no moisture loss during the test. The unconfined compression test is one of the simplest and quickest tests used for the determination of the shear strength of cohesive soils . These tests can also be performed in the field by making use of simple loading equipment. Any compression testing apparatus with arrangement for strain control may be used for testing the samples . The axial load may be applied mechanically or pneumatically.

24. Specimens of height to diameter ratio of 2 are normally used for the tests. The sample fails either by shearing on an inclined plane (if the soil is of brittle type) or by bulging. The vertical stress at any stage of loading is obtained by dividing the total vertical load by the cross-sectional area. The cross-sectional area of the sample increases with the increase in compression. The cross-sectional area A at any stage of loading of the sample may be computed on the basic assumption that the total volume of the sample remains the same. That is

25. The unconfined compression test (UC) is a special case of the unconsolidated-undrained (UU ) triaxial compression test (TX-AC). The only difference between the UC test and UU test is that a total confining pressure under which no drainage was permitted was applied in the latter test. Because of the absence of any confining pressure in the UC test, a premature failure through a weak zone may terminate an unconfined compression test . For typical soft clays, premature failure is not likely to decrease the undrained shear strength by more than 5%. Fig 8.23 shows a comparison of undrained shear strength values from unconfined compression tests and from triaxial compression tests on soft- Natsushima clay from Tokyo Bay.

26. The properties of the soil are: There is a unique relationship between remolded undrained shear strength and the liquidity index,as shown in Fig. 8.24 (after Terzaghi et al., 1996). This plot includes soft clay soil and silt deposits obtained from different parts of the world.

27. VANE SHEAR TESTS From experience it has been found that the vane test can be used as a reliable in-situ test for determining the shear strength of soft-sensitive clays. It is in deep beds of such material that the vane test is most valuable, for the simple reason that there is at present no other method known by which the shear strength of these clays can be measured. Repeated attempts, particularly in Sweden, have failed to obtain undisturbed samples from depths of more than about 10 meters in normally consolidated clays of high sensitivity even using the most modern form of thin-walled piston samplers . In these soils the vane is indispensable.

28. The vane should be regarded as a method to be used under the following conditions : The clay is normally consolidated and sensitive. Only the undrained shear strength is required. It has been determined that the vane gives results similar to those obtained from unconfined compression tests on undisturbed samples. The soil mass should be in a saturated condition if the vane test is to be applied. The vane test cannot be applied to partially saturated soils to which the angle of shearing resistance is not zero.

29. Description of the Vane The vane consists of a steel rod having at one end four small projecting blades or vanes parallel to its axis, and situated at 90° intervals around the rod. A post hole borer is first employed to bore a hole up to a point just above the required depth. The rod is pushed or driven carefully until the vanes are embedded at the required depth . At the other end of the rod above the surface of the ground a torsion head is used to apply a horizontal torque and this is applied at a uniform speed of about 0.1° per sec until the soil fails, thus generating a cylinder of soil.

30. The area consists of the peripheral surface of the cylinder and the two round ends. The first moment of these areas divided by the applied moment gives the unit shear value of the soil. Fig. 8.32(a) gives a diagrammatic sketch of a field vane. Determination of Cohesion or Shear Strength of Soil Consider the cylinder of soil generated by the blades of the vane when they are inserted into the undisturbed soil in-situ and gradually turned or rotated about the axis of the shaft or vane axis. The turning moment applied at the torsion head above the ground is equal to the force multiplied by the eccentricity .

31. Shear Strength Characteristics of Sand Shear strength characteristics of sandy soils depend on the drainage conditions in addition to several other param­eters as discussed in the following subsections. Shear Strength Characteristics of Saturated Sands during Drained Shear : It is nearly impossible to test undisturbed samples of cohesionless soils in either the direct shear or the triaxial compression test. Only the remolded samples are, therefore, used and the samples are to be compacted approx­imately to the in situ density. The direct shear test, being simpler and more rapid, is most commonly used.

32. The shear strength characteristics of dry and saturated sands are the same, provided the excess pore pressure is zero for saturated sands during the test. Hence , to conduct drained tests, dry sands are commonly used, as it is somewhat more difficult to test saturated sands. Typical curves relating principal stress difference and axial strain for dense and loose sand specimens in drained triaxial compression tests are shown in Fig. 13.25. Similar curves are obtained relating shear stress and shear displacement in direct shear tests. For dense sand, the deviator stress increases with increase in axial strain until a maximum deviator stress is reached.

33. After reaching the peak stress, the deviator stress decreases with further increase in the strain . For loose sand, there is no peak stress and the deviator stress increases continually with increase in axial strain. However , the rate of increase of stress per unit strain (modulus) for loose sand is less than that of dense sand. The ultimate deviator stress is approximately the same for both dense sand and loose sand.

34. Figure 13.26 shows the volumetric strain as a function of axial strain for dense sand and loose sand. The volume of soil specimen decreases with increase in axial strain for loose sand. In case of dense sand, the volumetric strain initially decreases with increase of axial strain until the sample attains some minimum volume. The volume then increases with further increase of axial strain.

35. In a properly carried out drained triaxial test, a common tangent can be drawn for all the Mohr’s circles of stress as shown in Fig. 13.27. The failure plane for each of the samples makes an angle a with the horizontal as shown, which is approximately given by

36. In AOCD of Fig. 13.27, alternate expression for ɸ   in terms of the principal stress ratio may be written as The shear strength of sands is derived basically from sliding friction between soil grains. In addition to the frictional component, the shear strength of dense sand has another component which is influenced by arrangement of soil particles. The soil grains are highly irregular in shape and have to be lifted over one another for sliding to occur. This effect is known as interlocking.

37. In dense sand, there is a considerable degree of interlocking between particles and this interlocking must be overcome before shear failure can take place. This is in addition to the frictional resistance due to sliding between particles. The characteristic stress-strain curve for dense sand shows a peak stress at a relatively low strain and thereafter as the interlocking is overcome, the stress necessary for additional strain decreases rapidly and becomes constant with increasing strain The degree of interlocking will be greatest in the case of very dense, well-graded sands consisting of angular particles.

38. As strain increases beyond the peak point on the stress-strain diagram, the interlocking stress is overcome. The ultimate shear strength (principal stress difference in the case of a triaxial test) and void ratio for dense and loose sand specimens are essentially equal under the same all-round pressure as indicated in Fig. 13.25. Thus, at the ultimate state, shearing takes place at constant volume, the corresponding friction angle being denoted as ɸ CV ‘. The reduction in the degree of interlocking produces an increase in volume of the specimen during shearing as shown in Fig. 13.26, by the relationship between the volumetric strain and axial strain.

39. In the case of loose sand, there is no significant particle interlocking to be overcome, because of lesser particle interference, and the principal stress difference increases gradually to an ultimate value without a prior peak. Thus, the shear strength of loose sands is essentially due to sliding friction between soil particles. It is a function of effective normal stress at the point of contact and increases linearly with the same. The failure of loose sands at large strains may be described as progressive failure compared to the relatively sudden failure of dense sands at low strains.

40. Only the drained strength of sand is normally relevant in practice and typical values of the friction angle for loose sands and dense sands are given in Table 13.3. In the case of dense sands, peak value of in-plane strain can be 4° or 5° higher than the corresponding value obtained by conventional triaxial tests. This increase is negligible in the case of loose sands. 2. Effect of Void Ratio and Confining Pressure on Volume Change : The initial void ratio of the soil specimen has a significant effect on the volume change during shear . Loose sands, having high initial void ratio, tend to decrease in volume, since they do not have any interlocking effect and permit closer particle movement during shear.

41. Dense sands with low initial void ratio have high degree of interlocking, which when overcome, produce an increase in the volume of the specimen during shear . The effect of confining pressure is to increase the density of the soil specimen and hence reduce the void ratio. Dense sand under low confining pressure behaves similar to loose sand under high confining pressure. 3. Characteristics of Saturated Sands during Undrained Shear : There is no advantage in using undrained test on cohesionless soils, since they tend to drain very fast in situ in most cases, as the permeability is high and the loads are applied relatively gradually.

42. A consolidated quick test on samples of sand may be performed in a triaxial compression apparatus, since the box shear apparatus is not suitable for this purpose. A sample of sand completely saturated is consolidated under an all-round pressure at a known initial void ratio. The sample is then sheared by keeping the drainage valve open and applying the deviator stress at a slow rate . Typical Mohr’s circles of stress of samples subjected to c-q test are shown in Fig. 13.28. The Mohr’s failure enve­lope is curved at low pressure and approaches a straight line with a slope angle of ɸ cq . Pore pressures are usually measured and the effective Mohr’s stress circles are drawn as shown by dashed lines. A straight Mohr-Coulomb failure envelope is obtained with a slope angle of ɸ’ cq .

43. Critical void ratio Casagrande (1936) performed drained, strain-controlled triaxial tests on initially loose and initially dense sand specimens. The results (figure 6.5) which form the cornerstone of modern understanding of soil strength behavior showed that all specimens tested at the same effective confining pressure approached the same density when sheared to large strains. Initially loose specimens contracted, or densified, during shearing and initially dense specimens first contracted, but then very quickly began to dilate. At large strains, all specimens approached the same density and continued to shear with constant shearing resistance. The void ratio corresponding to this constant density was termed the critical void ratio

44. By performing tests at different effective confining pressures, Casagrande found that the critical void ratio was uniquely related to the effective confining pressure, and called the locus the critical void ratio (CVR) line (figure 6.9) by defining the state of the soil in terms of void ratio and effective confining pressure the CVR line could be used to mark the boundary between loose (contractive) and dense (dilative) states . Figure 6.5 (a) Stress-strain and (b) stress-void curves for loose and dense sands at the same effective confining pressure.

45. Loose sand exhibits contractive behavior (decreasing void ratio) and dense sand exhibit dilative behavior (increasing void ratio) during shearing. by the time large strains have developed both specimens have reached the critical void ratio and mobilize the same large strain shearing. Sensitivity of cohesive soils: Cohesive soils upon remoulding , lose a part of shear strength. The loss of strength of clay soils from remoulding is caused primarily by the destruction of the clay particle structure that was developed during the original process of sedimentation and also disturbance to water molecules in adsorbed layer. Sensitivity is the measure of loss of strength with remoulding . Sensitivity, S t  is defined as the ratio of unconfined compressive strength of clay in undisturbed state to unconfined compressive strength of a same clay in remoulded state at unaltered water content.

46. Clays are classified according to their sensitivity values as shown in Table

47. Highly over consolidated clays are classified as insensitive. S t  is mostly 1 or >1, but for fissured clays S t  <1 because drawback in undisturbed soil is rectified in remoulded state . The  sensitivity of most clays ranges from about 1 to 8; however, highly flocculent marine clay deposits may have sensitivity ratios ranging from about 10 to 80. Some clay turn to viscous liquids upon remoulding , and these clays are referred to as “quick” clays . Thixotropy of cohesive soils: When clays with flocculent structure lose strength due to disturbance or remoulding . Loss of strength is partly due to permanent destruction of structure and reorientation of molecules in adsorbed layer. Strength loss with destruction of structure can’t recovered with time.

48. However, remoulded soil left undisturbed at same water content, regain part of strength due to gradual reorientation of adsorbed molecules of water. This phenomenon of strength loss-strength gain, with no change in volume or water content, is called ‘ Thixotropy ’(from the Greek  thix , meaning ‘touch’ and  tropein , meaning ‘to change’). This may also be said to be “a process of softening caused by remoulding , followed by a time-dependent return to the original harder state”. Higher the sensitivity, larger thixotropic hardening. Extent of strength gain depends on type of the clay mineral.

49. Mineral that absorb large quantity of water in lattice structure, such as Montmorillonite  has greater thixotropic gain compared to other stable clay minerals. Figure.1. shows the gain in strength of soil due to thixotropic effect. Thixotropy  has important applications in connection with pile-driving operations. The immediate frictional strength of thixotropic clay in driven piles is less compared to frictional strength after one month, because strength gain with passage of time . Thixotropy of clays

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