Figure 5. Failure envelope for clay obtained from drained direct shear tests.

Figure 4 shows the results of a drained direct shear test on over-consolidated clay.  Figure 5 shows the plot of t_f against s� obtained from a number of drained direct shear tests on a normally consolidated and over-consolidated clay.  Note that the value of c� � 0 for a normally consolidated clay. 

 

B. General Comments on Direct Shear Test  

The direct shear test is the simplest to perform and most economical for a dry or saturated sandy soil, but it has some disadvantages.  The reliability of the results may be questioned because the soil is not allowed to fail along the weakest plane but is forced to fail along the plane of the split of the shear box.  Equally important, the shear stress distribution over the shear surface of the specimen is not uniform.  

Figure 6. Interface of a foundation material and soil.

 

In many foundation design problems, one must determine the angle of friction between the soil and the material in which the foundation is constructed (Figure 6). The foundation material may be concrete, steel, or wood.  The shear strength along the surface of contact of the soil and the foundation can be given as

                                                                                             (5)

where 

c_a� = adhesion

 d  = effective angle of friction between the soil and foundation material

The shear strength parameters between a soil and a foundation material can be conveniently determined by a direct shear test.  This is a great advantage of the direct shear test, and then the soil can be placed above it (that is, in the top part of the box) and the test can be conducted in the usual manner.

Triaxial Shear Test (General)

The triaxial shear test is one of the most reliable methods available for determining shear strength parameters.  It is widely used for research and conventional testing.  A diagram of the triaxial test layout is show in Figure 7.

Figure 7. Diagram of triaxial test equipment (after Bishop and Bjerrum, 1960)

In this test, a soil specimen about 36 mm (1.4 in.) in diameter and 76 mm (3 in.) long is generally used.  The specimen is encased in a thin rubber membrane placed inside a plastic cylindrical chamber that is usually filled with water or glycerine. The specimen is subjected to a confining pressure by compression of the fluid in the chamber.  To cause shear failure in the specimen, one must apply axial stress through a vertical loading ram (deviator sress). This stress can be applied in one of the two ways:

1. Application of dead weights or hydraulic pressure in equal increments until the specimen fails.

2. Application of axial deformation at a constant rate by means of a geared or hydraulic loading press.  This is strain-controlled test.

The axial load applied by the loading ram corresponding to a given axial deforamtion is measured by a proving ring or load cell attached to the ram. Connections to measure drainage into or out of the specimen, or to measure pressure in the pore water (as per the test conditions), are also provided.  The following three standard types of triaxial tests are generally conducted:

1. Consolidated-drained test or drained test (CD test)

2.  Consolidated-undrained test (CU test) 

3. Unconsolidated-undrained test or undrained test (UU test)

A. Consolidated-Drained (CD) Triaxial Test

In the CD test, the saturated specimen is the first subjected to an all-around confining pressure, s₃, by compression of the chamber.  As confining pressure is applied, the pore water pressure of the specimen increases by u_c (if drainage is prevented).  This increase in the pore water pressure can be expressed as a non-dimensional parameter in the form

                                                                                                         (6)

where B = Skempton�s pore pressure parameter (Skempton, 1954).

For saturated soft soils, B is approximately equal to 1; however, for saturated stiff soils, the magnitude of B can be less than 1.  Black and Lee (1973) gave the theoretical values of B for various soils at complete saturation.  These values are listed in Table 1.  

Table 1 Theoretical values of B at complete saturation.

If the connection to drainage is opened, dissipation of the excess pore water pressure, and thus consolidation, will occur.  With time, u_c, will become equal to 0. In saturated soil, the change in the volume of the specimen (DV_c) that takes place during consolidation can be obtained from the volume of pore water drained.  The deviator stress, Ds_d, on the specimen is increased very slowly.  The drainage connection is kept open, and the slow rate of deviator stress application allows complete dissipation of any pore water pressure that developed as a result (Du_d = 0).

Because the pore water pressure developed during the test is completely dissipated, we have

total and effective confining stress = s₃ = s�₃                                                            (7)

and

total and effective axial stress at failure = s₃ + (Ds_d)_f = s₁ = s�₁                                     (8)

In a triaxial test, s�₁ is the major principal effective stress at failure and s�₃ is the minor principal effective stress at failure.

Several tests on similar specimens can be conducted by varying the confining pressure.  With the major and minor stresses at failure for each test the Mohr�s circles can be drawn and the failure envelopes can be obtained.  Figure 8 shows the type of effective stress failure envelope obtained for tests on sand and normally consolidated clay. The coordinates of the point of tangency of the failure envelope with a Mohr�s circle (that is, point A) give the stresses (normal) and shear) on the failure plane of that test specimen. 

Figure 8. Effective stress failure envelope from drained tests on sand and normally consolidated clay.

Over-consolidation results when clay is initially consolidated under an all-around chamber pressure of s_c (= s�_c) and is allowed to swell by reducing the chamber pressure to s₃ (= s�₃).  The failure envelope obtained from drained triaxial tests of such over-consolidated clay specimens shows two distinct branches.  The first of which has a flatter slope with a cohesion intercept, and the shear strength equation for this branch can be written as

                                                                                      (9)

The second portion of the failure envelope represents a normally consolidated stage of soil and follows the equation

                                                                                                                    (10)

A consolidated-drained triaxal test on a clayey soil may take several days to complete.  This amount of time is required because deviator stress must be applied very slowly to ensure full drainage from the soil specimen.  For this reason, the CD type of triaxial test is uncommon.  

B. Comments on Drained and Residual Friction Angles of Clays  

The drained angle of friction, f�, generally decreases with the plasticity index of soil. This fact is illustrated in Figure 9 for a number of clays from data reported by Kenney (1959).  Although the data are considerably scattered, the general pattern seems to hold. 

At a very high clay content, f_r� approaches the value of the angle of sliding friction for sheet minerals.  For highly plastic sodium montmorillonites, the magnitude of f_r� may be as low as 3 to 4�.  

Figure 9. Variation of sin f' with plasticity index for a number of soils.

C. Consolidated-Undrained Triaxial Test

The consolidate-unrained test is the most common type of triaxial test.  In this test, the saturated soil specimen is first consolidated by an all-around chamber fluid pressure, s₃, that results in drainage.  After the pore water pressure generated by the application of confining pressure is dissipated, the deviator stress, Ds_d, on the specimen is increased to cause shear failure.  During this phase of the test, the drainage line from the specimen is kept closed.  Because drainage is not permitted, the pore water pressure, Du_d, will increase.  During the test, simultaneous measurements of Ds_d and Du_d are made.  The increase in the pore water pressure, Du_d��, can be expressed in a non-dimensional form as

                                                                                                      (11)

where  = Skempton�s pore pressure parameter (Skempton, 1954).  

In loose sand and normally consolidated clay, the pore water pressure increases with strain to a certain limit, beyond which it decreases and becomes negative (with respect to the atmospheric pressure).  This decrease is because of a tendency of the soil to dilate.

Figure 10. Total and effective stress failure envelopes for consolidated undrained triaxial tests. (Note: The figure assumes that no back pressure is applied.

Tests on several similar specimens with varying confining pressures may be conducted to determine the shear strength parameters. Figure 10 shows the total and effective stress Mohr�s circles at failure obtained from consolidated-undrained triaxial tests in sand and normally consolidated clay.  Note that A and B are two total stress Mohr�s circles obtained from two tests.  C and D are the effective stress Mohr�s circles corresponding to total stress circles A and B, respectively.  The diameters of circles A and C are the same; similarly, the diameters of circles B and D are the same.  

In Figure 10, the total stress failure envelope can be obtained by drawing a line that touches all the total stress Mohr�s circles.  For sand and normally consolidated clays, this will be approximately a straight line passing through the origin and may be expressed by the equation

                                                                                             (12)

where 

s = total stress

f = the angle that the total stress failure envelope makes with the normal stress axis, also known as the consolidated-undrained angle of shearing resistance

Again referring to Figure 10, we see that the failure envelope that is tangent to all the effective stress Mohr�s circles can be represented by the equation , which is the same

 as that from consolidated-drained tests.

In over consolidated clays, the total stress failure envelope obtained from consolidated-undrained tests will take the shape shown in Figure 11.  The straight line a�b� is represented by the equation

                                                                                       (13)

and the straight line b�c� follows the relationship given by Eq. 12. The effective stress failure envelope drawn from the effective stress Mohr�s circles will be similar to that shown in Figure 11.

Figure 11. Total stress failure envelope obtained from consolidated-undrained tests in over-consolidated clay.

Consolidated-drained tests on clays soils take considerable time.  For this reason, consolidated-undrained tests can be conducted on such soils with pore pressure measurements to obtain the drained shear strength parameters.  Because drainage is not allowed in these tests during the application of deviator stress, they can be performed quickly.

Skempton�s pore water pressure parameter  was defined in Eq. 11.  At failure, the parameter  can be written as

                                                                                   (14)

The general range of  values in most clay soils is as follows:

• Normally consolidated clays: 0.5 to 1
• Over-consolidated clays: -0.5 to 0.

D. Unconsolidated-Undrained Triaxial Test  

Drainage from the soil specimen is not permitted during the application of chamber pressure s₃ In unconsolidated-undrained tests.  The test specimen is sheared to failure by the application of deviator stress, Ds₃, and drainage is prevented.  Because drainage is not allowed at any stage, the test can be performed quickly.  Because of the application of chamber confining pressure s₃, the pore water pressure in the soil specimen will increase by u_c.  A further increase in the pore water pressure (Du_d) will occur because of the deviator stress application. 

This test is usually conducted on clay specimens and depends on a very important strength concept for cohesive soils if the soil is fully saturated.  The added axial stress at failure (Ds_d)_f is practically the same regardless of the chamber confining pressure. This property is shown in Figure 12.  The failure envelope for the total stress Mohr�s circles becomes a horizontal line and hence is called a f = 0 condition.  Thus, we have

                                                                                                   (15)

where c_u = undrained shear strength and is equal to the radius of Mohr�s circles.  

Note that the f = 0 concept is applicable to only saturated clays and silts.

Figure 12. Total stress Mohr's circles and failure envelope (f=0) obtained from unconsolidated-undrained triaxial tests on fully saturated cohesive soil.

Unconfined Compression Test (UCT)

The unconfined compression test is a special type of unconsolidated-undrained test that is commonly used for clay specimens.  In this test, the confining pressure s₃ is 0.  An axial load is rapidly applied to the specimen to cause failure.  At failure, the total minor principal stress is zero and the total major prinicipl stress is s₁ .  Figure 13 shows a result of an UCT.

Figure 13. Unconfined compression test.

Because the undrained shear strength is independent of the confining pressure as long as the soil is fully saturated and fully undrained, we have

                                                                                      (16)

where q_u is the unconfined compression strength.  Table 2 gives the approximate consistencies of clays on the basis of their unconfined compression strength. 

Table 2. General relationship of consistency and unconfined compression strength of clays.

Theoretically, for similar saturated clay specimens, the unconfined compression tests and the unconsolidated-undrained triaxial tests should yield the same values of c_u.  In practice, however, unconfined compression tests on saturated clays yield slightly lower values of c_u than those obtained from unconsolidated-undrained tests.

References

[1]   Bowles, Joseph E., Engineering Properties of Soils and Their Measurements, 

       3^rd edition, 1986.

[2]   Das, Braja M., Principles of Geotechnical Engineering, 5^th edition, 2002. 

[3]   Geotechnical Engineering Manual