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Strength and Deformation
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Introduction
The shear strength of soil is generally characterized by the Mohr–Coulomb failure criterion. This criterion
states that there is a linear relationship between the shear strength on the failure plane at failure (τff) and
the normal stress on the failure plane at failure (σff) as given in the following equation:
(17.1)
where φ is the friction angle and c is the intrinsic cohesion. The strength parameters (φ, c) are used
directly in many stability calculations, including bearing capacity of shallow footings, slope stability, and
stability of retaining walls. The line defined by Eq. (17.1) is called the failure envelope. A Mohr’s circle
tangent to a point on the failure envelope (σff, τff) intersects the x-axis at the major and minor principal
stresses at failure (σ1f, σ3f) as shown in Fig. 17.1. For many soils, the failure envelope is actually slightly
concave down rather than a straight line. However, for most situations Eq. (17.1) can be used with a
reasonable degree of accuracy provided the strength parameters are determined over the range of stresses
that will be encountered in the field problem. For a comprehensive review of Mohr’s circles and the
Mohr–Coulomb failure criterion, see Lambe and Whitman [1969] and Holtz and Kovacs [1981].
Laboratory Tests for Shear Strength
The choice of appropriate shear strength tests for a particular project depends on the soil type, whether
the parameters will be used in a total or effective stress analysis, and the relative importance of the
structure. Laboratory tests are discussed in this chapter and field tests were discussed in Chapter 15.
Common laboratory tests include direct shear, triaxial, direct simple shear, unconfined compression, and
laboratory vane. The applicability, advantages, disadvantages, and sources of additional information for
each test are summarized in Table 17.1.
Of the available tests, the triaxial test is often used for important projects because of the advantages
listed in Table 17.1. The types of triaxial tests are classified according to their drainage conditions during
the consolidation and shearing phases of the tests. In a consolidated-drained (CD) test the sample is fully
drained during both the consolidation and shear phases of the test. This test can be used to determine
the strength parameters based on effective stresses for both coarse- and fine-grained soils. However, the
requirement that the sample be sheared slowly enough to allow for complete drainage makes this test
impractical for fine-grained soils. In a consolidated-undrained (CU) test the sample is drained during
consolidation but is sheared with no drainage. This test can be used for fine-grained soils to determine
strength parameters based on total stresses or, if pore pressures are measured during shear, strength
parameters based on effective stresses. For the latter use, a CU test is preferred over a CD test because a
CU test can be sheared much more quickly than a CD test. In an unconsolidated-undrained (UU) test
the sample is undrained during both the consolidation and shear phases. The test can be used to determine
the undrained shear strength of fine-grained soils. Further discussion of triaxial tests is given in Holtz
and Kovacs [1981] and Head [1982, 1986].
Shear Strength of Cohesive Soils
The friction angle of cohesive soil based on effective stresses generally decreases as the plasticity increases.
This is shown for normally consolidated clays in Fig. 17.4. The c′ of normally consolidated, noncemented
clays with a preconsolidation stress (defined in Chapter 19) of less than 10,000 to 20,000 psf (500 to
1000 kPa) is generally less than 100 to 200 psf (5 to 10 kPa) [Ladd, 1971]. Overconsolidated clays generally
have a lower φ′ and a higher c′ than normally consolidated clays. Compacted clays at low stresses also
have a much higher c′ [Holtz and Kovacs, 1981].
The shear strength of cohesive soils based on effective stresses is generally determined using a CU
triaxial test with pore pressure measurements. To obtain accurate pore pressure measurements it is
necessary to fully saturate the sample using the techniques described in U.S. Army [1970], Black and Lee
[1973], and Holtz and Kovacs [1981]. This test can be run much more quickly than a CD triaxial test
and it has been shown that the φ′ from both tests are similar [Bjerrum and Simons, 1960].
Elastic Modulus of Granular Soils
The elastic modulus (Es) of granular soils based on effective stresses is a function of grain size, gradation,
mineral composition of the soil grains, grain shape, soil type, relative density, soil particle arrangement,
stress level, and prestress [Lambe and Whitman, 1969; Ladd et al., 1977; Lambrechts and Leonards, 1978].
A granular soil is prestressed if, at some point in its history, it has experienced a stress level that is greater
than is currently acting on the soil. This is analogous to overconsolidation of a fine-grained soil, which
is discussed in Chapter 19. Of the several factors controlling Es, the ones having the largest influence are
prestress, which can increase Es by more than a factor of six, and extreme differences in relative density,
which can make a fivefold difference in Es [Lambrechts and Leonards, 1978].