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    Module 1

    (Lecture 4)





    4.1.1 Direct Shear Test 4.1.2 Triaxial Tests



    4.1.3 Drained Friction Angle of Granular Soils 4.1.4 Drained Friction Angle of Cohesive Soils




    4.1.4 Metal Strips 4.1.5 Nonbiodegradable Fabrics 4.1.6 Geogrids

    4.7 PROBLEMS


    SHEAR STRENGTH The shear strength, s, of a soil, in terms of effective stress, is

    s = c + tan [1.82]


    = effective normal stress on plane of shearing

    c = cohesion, or apparent cohesion

    = angle of friction

    Equation (82) is referred to as the Mohr-Coulomb failure criteria. The value of c for sands and normally consolidated clays is equal to zero. For overconsolidated clays, c >0.

    For most day-to-day work, the shear strength parameters of a soil (that is, c and ) are determined by two standard laboratory tests. They are (a) the direct shear test and (b) the triaxial test.

    Direct Shear Test

    Dry sand can be conveniently tested by direct shear tests. The sand is placed in a shear box that is split into two halves (figure 1.32a). A normal load is first applied to the specimen. Then a shear force is applied to the top half of the shear box to cause failure in the sand. The normal and shear stresses at failure are

    Figure 1.32 Direct shear test in sand: (a) schematic diagram of test equipment; (b) plot of test results to obtain the friction angle,


    = NA

    S = RA

    Where A = Area of the failure plane in soil-that is, the area of cross section of the shear box

    Several tests of this type can be conducted by varying the normal load. The angle of friction of the sand can be determined by plotting a graph of s against (= )

    = tan1 s [1.83]

    For sands, the angle of friction usually ranges from 26 to 45, increasing with the relative density of compaction. The approximate range of the relative density of compaction and the corresponding range of the angle of friction for various coarse-grained soils is shown in figure 1.33.

    Figure 1.33 Range of relative density and corresponding range of angle of friction for coarse-grained soil (after U. S. Department of the Navy, 1971)

    Triaxial Tests

    Triaxial compression tests can be conducted on sands and clays. Figure 1.34a shows a schematic diagram of the triaxial test arrangement. Essentially, it consists of placing a soil specimen confined by a rubber membrane in a Lucite chamber. An all-round confining pressure (3) is applied to the specimen by means of the chamber fluid (generally water or glycerin). An added stress () can also be applied to the specimen in the axial direction to cause failure ( = f at failure). Drainage from the specimen can be allowed or stopped, depending on the test condition. For clays, three main types of tests can be conducted with triaxial equipment:


    Figure 1.34 Triaxial test

    1. Consolidated-drained test (CD test) 2. Consolidated-undrianed test (CU test) 3. Unconsolidated-undrained test (UU test)

    Table 15 summarizes these three tests. For consolidated-drained tests, at failure,

    Major Principal effective stress = 3 = f = 1 = 1


    Minor Principal effective stress = 3 = 3

    Changing 3 allows several tests of this type to be conducted on various clay specimens. The shear strength parameters (c and ) can now be determined by plotting Mohrs circle at failure, as shown in figure 1.34b, and drawing a common tangent to the Mohrs circles. This is the Mohr-Coulomb failure envelope. (Note: For normally consolidated clay, c 0). At failure

    1 = 3tan2 45 +2 + 2c tan 45 +

    2 [1.84]

    Table 15 Summary of Triaxial Tests on Saturated Clays

    For consolidated-undrained tests, at failure,

    Major Principal total stress = 3 = f = 1

    Minor principal total stress = 3

    Major principal effective stress = (3 + f) uf = 1

    Minor principal effective stress = 3 uf = 3

    Changing 3 permits multiple tests of this type to be conducted on several soil specimens. The total stress Mohrs circles at failure can now be plotted, as shown in


    figure 1.34c, and then a common tangent can be drawn to define the failure envelope. This total stress failure envelope is defined by the equation

    s = ccu + tancu [1.85]

    Where ccu and cu are the consolidated-undrained cohesion and angle of friction respectively (Note: ccu 0 for normally consolidated clays)

    Similarly, effective stress Mohrs circles at failure can be drawn to determine the effective stress failure envelopes (figure 1.34c). They follow the relation expressed in equation (82).

    For unconsolidated-undrained triaxial tests

    Major principal total stress= 3 = f = 1

    Minor principal total stress = 3

    The total stress Mohrs circle at failure can now be drawn, as shown in figure 1.34d. For saturated clays, the value of 1 3 = f is a constant, irrespective of the chamber confining pressure, 3 (also shown in figure 1.34d). The tangent to these Mohrs circles will be a horizontal line, called the = 0 condition. The shear stress for this condition is

    s = cu = f

    2 [1.86]


    cu = undrained cohesion (or undrained shear strength)

    The pore pressure developed in the soil specimen during the unconsolidated-undrained triaxial test is

    u = ua + ud [1.87]

    The pore pressure ua is the contribution of the hydrostatic chamber pressure, 3. Hence

    ua = B3 [1.88]


    B = Skemptonspore pressure parameter

    Similarly, the pore pressure ud is the result of added axial stress, , so


    ud = A [1.89]


    A = Skemptonspore pressure parameter


    = 1 3 [1.90]

    Combining equations (87, 88, 89, and 90) gives

    u = ua + ud = B3 + A1 3 [1.91]

    The pore water pressure parameter B in soft saturated soils is 1, so

    u = 3 + A(1 3) [1.93a]

    The value of the pore water pressure parameter A at failure will vary with the type of soil. Following is a general range of the values of A at failure for various types of clayey soil encountered in nature.

    Type of soil A at failure

    Sandy clays 0.5-0.7

    Normally consolidated clays 0.5-1

    Overconsolidated clays -0.5-0

    Figure 1.35 shows a photograph of laboratory triaxial equipment.


    Figure 1.35 Triaxial test equipment


    The unconfined compression test (figure 1.36a) is a special type of unconsolidated-undrained triaxial test in which the confining pressure 3 = 0, as shown in figure 1.36b. In this test an axial stress, , is applied to the specimen to cause failure (that is, =f). The corresponding Mohrs circle is shown in figure 1.36b. Note that, for this case,


    Figure 1.36 Unconfined compression test: (a) soil specimen; (b) Mohrs circle for the test; (c) variation of qu with the degree of saturation

    Major principal total stress = f = qu

    Minor principal total stress = 0

    The axial stress at failure, f = qu is generally referred to as the unconfined compression strength. The shear strength of saturated clays under this condition ( = 0), from equation (82), is

    s = cu =qu2


    The unconfined compression strength can be used as an indicator for the consistency of clays.

    Unconfined compression tests are sometimes conducted on unsaturated soils. With the void ratio of a soil specimen remaining constant, the unconfined compression strength rapidly decreases with the degree of saturation (figure 1.36c). Figure 1.37 shows an unconfined compression test in progress.


    Figure 1.37 Unconfined compression test in progress (courtesy of Soiltest, Inc., Lake Bluff, Illinois)


    Drained Friction Angle of Granular Soils

    In general, the direct shear test yields a higher angle of friction compared to that obtained by the triaxial test. It also needs to be pointed out that the failure envelope for a given soil is actually curved. The Mohr-Coulomb failure criteria defined by equation (82) are only an approximation. Because of the curved nature of the failure envelope, a soil tested at higher normal stress will yield a lower value of . An example of that is shown in figure 1.38, which is a plot of versus the void ratio, e, for Chattahoochee River sand near Atlanta, Georgia (Vesic, 1963). These friction angles were obtained from trixial tests. Note that, for a given value of e, the magnitude of is about 4 to 5 degrees smaller when the confining pressure 3 is greater than 10 lb/in.2 (69kN/m2) compared to that when 3 < 10/in.2


    Figure 1.38 Variation of friction angle with void ratio for Chattachoochee River sand (after Vesic, 1963)

    Figure 1.39 Variation of friction angle with plasticity index for several clays (after Bjerrum and Simons, 1960)


    Drained Friction Angle of Cohesive Soils

    Figure 1.39 shows the drained friction angle , for several normally consolidated clays obtained by conducting triaxial tests (Bjerrum and Simons, 1960). It can be seen from this figure that, in general, the friction angle decreases with the increase in plasticity index. The value of generally decreases from about 37 38 with a plasticity index of about 10, to about 25 or less with a plasticity index of about 100. Similar results were also provided by Kenney (1959). The consolidated undrianed friction angle (cu ) of normally saturated clays generally ranges from 5 20.

    The consolidated drained triaxial tests is described in section 16. Figure 1.40 shows the schematic diagram of the plot of versus axial strain of a drained triaxial tests for a clay. At failure, for this test, = f. However, at large axial strain (i.e., ultimate strength condition),

    Figure 1.40 Plot of deviator stress vs. axial strain-drained triaxial test

    Major principal stress: 1(ult ) = 3 + ult

    Minor principal stress: 3(ult ) = 3

    At failure (that is, peak strength), the relationship between 1 and 3 was given by equation (84). However, for ultimate strength, it can be shown that

    1(ult ) = 3 tan2 45 +r2 [1.94]



    r = residual drained friction angle

    Figure 1.41 shows the general nature of the failure envelopes at peak strength and ultimate strength (or residual strength). The residual shear strength of clays is important in the evaluation of long-term stability of new and existing slopes and the design of remedial measures. The drained friction angles (r) of clays may be substantially smaller than the drained peak friction angles. Figure 1.42 shows the variation of r with liquid limit for some clays (Stark, 1995). It is important to note that

    Figure 1.41 Peak and residual strength envelopes for clay

    Figure 1.42 Variation of r with liquid limit for some clays (after Stark, 1995)

    1. For a given clay, r decreases with the increase in liquid limit. 2. For a given liquid limit and clay-size fractions present in the soil, the magnitude

    of r decreases with the increases in the normal effective stress. This is due to the curvilinear nature of the failure envelope.


    Undrianed Shear Strength, The undrianed shear strength, cu is an important parameter in the design of foundations. For normally consolidated clay deposits (figure 1.43), the magnitude of cu increases almost linearly with the increase of effective overburden pressure.

    Figure 1. 43 Clay deposit

    There are several empirical relations between cu and the effective overburden pressure p in the field. Some of these relationships are summarized in table 16.

    Figure 1.44 Variation of cu/p with liquidity index [based on Bjerrum and Simons (1960)]



    For many naturally deposited clay soils, the unconfined compression strength is much less when the soils are tested after remolding without any change in the moisture content. This property of clay soil is called sensitivity. The degree of sensitivity is the ratio of the unconfined compression strength in an undisturbed state to that in a remolded state, or

    St =qu (undisturbed )

    qu (remolded ) [1.95]

    Table 16 Empirical Equations Related to and Effective Overburden Pressure

    Reference Relationship Remarks

    Skempton (1957)

    cu(VST )p

    = 0.11 + 0.0037PI

    PI = plasticity index (%)

    cu(VST )= undrianed shear strenth from vane shear test

    (see chapter 3 for details for vane shear test)

    For normally consolidated clay

    Chadler (1988) cu(VST )p

    = 0.11 + 0.0037PI

    pc = preconsolidation pressure

    Can be used for over consolidated soil

    Accuracy 25%

    Not valid or sensitive and fissured clays

    Jamiolkowski et al. (1985)


    = 0.23 0.04 For lightly over consolidated clays

    Mesri (1989) cup

    = 0.22

    Bjerrum and Simons (1960)


    = f(LI)

    LI = liquidity index

    See figure 1.44 for normally consolidated clays


    [see equation (53b) for definition]

    Ladd et al. (1977)

    cup overconsolidatedcup normally consolidated

    = (OCR)0.8

    OCR = overconsolidation ratio =pcp

    The sensitivity ratio 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 remolding, and these clays are referred to as quick clays. The loss of strength of clay soils from remolding is caused primarily by the destruction of the clay particle structure that was developed during the original process of sedimentation.


    The use of reinforced earth is a recent development in the design and construction of foundations and earth-retaining structures. Reinforced earth is a construction material comprising soil that has been strengthened by tensile elements such as metal rods and/or strips, nonbiodegradable fabrics (geotextiles), geogrids, and the like. The fundamental idea of reinforcing soil is not new; in fact, it goes back several centuries. However, the present concept of systematic analysis and design was developed by a French engineer, H, Vidal (1966). The French Road Research Laboratory has done extensive research on the applicability and the beneficial effects of the use of reinforced earth as a construction material. This research has been documented in detail by Darbin (1970), Schlosser and Long (1974), and Schlosser and Vidal (1969). The test conducted involved the use of metallic strips as reinforcing material.

    Retaining walls with reinforced earth have been constructed around the world since Vidal began his work. The first reinforced earth retaining wall with metal strips as reinforcement in the United States was constructed in 1972 in southern California.

    The beneficial effects of soil reinforcement derive from (a) the soils increased tensile strength and (b) the shear resistance developed from the friction at the soil-reinforcement interfaces. Such reinforcement is comparable to that of concrete structures. Currently, most reinforced earth design is done with free-draining granular soil only. Thus the effect of pore water development in cohesive soils, which, in turn, reduces the shear strength of the soil, is avoided.



    Metal Strips

    In most instances, galvanized steel strips are used as reinforcement in soil. However, galvanized steel is subject to corrosion. The rate of corrosion depends on several environmental factors. Binquet and Lee (1975) suggested that the average rate of corrosion of galvanized steel strips varies between 0.025 and 0.050 mm/yr. so. In the actual design of reinforcement, allowance must be made for the rate of corrosion. Thus

    tc = tdesign + r(life span of structure)


    tc = actual thickness of reinforcing strips to be used in construction

    tdesign = thickness of strips determined from design calculations

    r = rate of corrosion

    Nonbiodegradable Fabrics

    Nonbiodegradable fabrics are generally referred to as geotextiles. Since 1970, the use of geotextiles in construction has increased tremendously around the world. The fabrics are usually made from petroleum products-polyester, polyethylene, and polypropylene. They may also be made from fiberglass. Geotextiles are not prepared from natural fabrics because they decay too quickly. Geotextiles may be woven, knitted, or nonwoven.

    Woven geotextiles are made of two sets of parallel filaments or strands of yarn systematically interlaced to form a planar structure. Knotted geotextiles are formed by interlocking a series of loops of one or more filaments or strands of yarn to form a planar structure. Nonwoven geotextiles are formed from filaments or short fibers arranged in an oriented or random pattern in a planar structure. These filaments or short fibers are, in the beginning arranged into a loose web. They are then bonded by one or a combination of the following processes:

    1. Chemical bonding-by glue, rubber, latex, cellulose derivative, and the like 2. Thermal bonding-by heat for partial melting of filaments 3. Mechanical bonding-by needle punching

    Needle-punched nonwoven geotextiles are thick and have high in plane permeability.

    Geotextiles have four primary uses in foundation engineering.

    1. Drainage: The fabrics can rapidly channel water from soil to various outlets, thereby providing a higher soil shear strength and hence stability.

    2. Filtration: When placed between two sol layers, one coarse grained and the other fine grained, the fabric allows free seepage of water from one layer to the other.


    However, it protects the fine-grained soil from being washed into the coarse-grained soil.

    3. Separation: Geotextiles helps keep various soil layers separate after construction and during the projected service period of the structure. For example, in the construction of highways, a clayey subgrade can be kept separate from a granular base course.

    4. Reinforcement: The tensile strength of geofabrics increases the load-bearing capacity of the soil.


    Geogrids are high-modulus polymer materials, such as polypropylene and polyethylene, and are prepared by tensile drawing. Netlon Ltd. Of the United Kingdom was the first producer of geogrids. In 1982, the Tensar Corporation, presently Tensar Earth Technologies, Inc., introduced geogrids in the United States.

    The major function of geogrids is reinforcement. Geogrids are relatively stiff netlike materials with large openings called apertures. These apertures are large enough to allow interlocking with the surrounding soil and/or rock to perform the function(s) of reinforcement and/or segregation.

    Geogrids generally are of two types: (a) biaxial geogrids and (b) unixial geogrids. Figure 1.45a and 1.45b shows the two types of geogrids just described, which are produced byTensar Earth Technologies, Inc., Unixial TENSAR grids are manufactured by stretching a punched sheet of extruded high-density polyethylene in one direction under carefully controlled conditions. This process aligns the polymers long-chain molecules in the direction of draw and results in produce with high one-directional tensile strength and modulus. Biaxial TENSAR grids are manufactured by stretching the punched sheet of polypropylene n two orthogonal directions. This process results in a product with high tensile strength and modulus I two perpendicular directions. The resulting grid apertures are either square or rectangular.


    Figure 1.45 Geogrids: (a) uniaxial; (b) biaxial (note: 1-longitudinal rib; 2-transverse bar; 3-transverse rib; 4-junction)

    The commercial geogrids currently available for soil, reinforcement have nominal rib thicknesses of about 0.02-0.06 in. (0.5-1.5 mm) and junctions of about 0.1-0.2 in. (2.5-5 mm). The grids used for sol reinforcement usually have apertures that are rectangular or elliptical in shape. The dimensions of the apertures vary from about 1-6 in. (25-150 mm). geogrids are manufactured so that the open areas of the grids are greater than 50% of the total area. They develop reinforcing strength at low strain levels, such as 2% (Carroll, 1988). Table 17 gives some properties of the TENSAR biaxial geogrids currently available commercially.


    Table 17 Properties of TENSAR Biaxial Geogrids


    Property BX 1000 BX 1100 BX 1200

    Aperture size

    Machine direction

    Cross-machine direction

    Open area

    1 in. (nominal)

    1.3 in. (nominal)

    70% (minimum)

    1 in. (nominal)

    1.3 in. (nominal)

    74% (nominal)

    1 in. (nominal)

    1.3 in. (nominal)

    77% (nominal)



    0.09 in. (nominal)

    0.11 in. (nominal)

    0.16 in. (nominal)

    Tensile modulus

    Machine direction

    Cross-machine direction

    12,500 lb/ft (minimum)

    12,500 lb/ft (minimum)

    14,5000 lb/ft (minimum)

    20,000 lb/ft (minimum)

    18,500 lb/ft (minimum)

    30,000 lb/ft (minimum)



    Carbon black

    97% (minimum)

    2% (minimum)

    99% (nominal)

    1% (nominal)

    99% (nominal)

    1% (nominal)


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