Much of the earth pressure theory, and the behaviour of earth-retaining structures, is dominated by considerations of shear strength. Most struc-tural engineers think in terms of strength characteristics (such as the com-pressive strength of concrete or the ultimate tensile strength of steel) that are constant and unaffected by ambient compressive stress levels. Geotechnical
engineers, on the other hand, are concerned with materials that are com-posed of at least two and sometimes three phases (soil particles, water and air). Soils generally have relatively high compressibility and low strength when compared with other construction materials. Such strength as they have is highly stress dependent and frictional in its nature but is also a func-tion of density.
Consider a block placed on a flat frictional surface and subjected to a normal force N (Figure 1.1). The maximum shear force T that can be applied horizontally to the block before it slides can be related to the coef-ficient of friction, μ, between the block and the surface, and to the normal force. In soil mechanics terms, we would write
T = N · tan ϕ (1.1)
or by dividing by the contact area to obtain stresses,
τ = σ.tan ϕ (1.2) where tan ϕ is equivalent to the coefficient of friction, μ.
Soils behave in a similar if more complex way. First, they are usually a mixture of soil particles and water (and possibly air—see succeeding text).
An element of saturated soil under external pressure (‘total stress’) will con-tain water which is also under pressure (‘pore water pressure’). Consider a sealed rubber balloon full of soil and water (Figure 1.2). The total stress applied to the outside of the balloon is carried partly by the pore water pressure, and only the difference between the pore water pressure and the total stress is applied to the soil structure, i.e. to increase the forces between individual particles. Because, at normal rates of shear, water has negligible shear strength and its properties are unaffected by pressure increases, the pressure taken by the pore water does not contribute to the overall strength of the soil.
N
T
Figure 1.1 Sliding block analogy.
For saturated soil, the numerical difference between total stress and pore water pressure is termed as the ‘effective stress’, σ′, where
′ = −
σ σ u (1.3)
In much the same way as with the block sliding on a surface, an increase in inter-particle force leads to an increase in shear resistance:
Increase in total stress and constant pore pressure or
Constant total stress and decreasing pore pressure
⇒ strength increase and conversely
Constant total stress and increasing pore pressure or
Decreasing total stress and constant pore pressure
⇒ strength decrease
Effective stress has an additional effect, particularly in soils with platy or clayey particles. It causes the soil particles to pack more closely together. A decreased porosity (and therefore water content) resulting from an increase in
External pressure, σ
Pressure in pores, between
grains = u
Figure 1.2 Total and effective stress.
effective stress produces a further increase in strength. It is observed that if a soil exists at the same effective stress level, but different water con-tents, the lower the water content and the higher the density, the higher the strength.
The strength of soil is routinely measured in the triaxial apparatus (Figure 1.3). The soil specimen is sealed in a rubber membrane, pressurised by cell water, and has additional vertical load applied to it by a ram, until failure occurs. The axial load is measured and this, divided by the cross-sectional area of the specimen, gives the ‘deviator stress’, (σ1 – σ3), which is plotted as a function of axial strain. Figure 1.4 shows typical stress/strain curves.
Drained tests on dense sands and undrained tests on carefully sampled natural clays tend to produce results with a pronounced peak, whilst loose sands and remoulded normally consolidated clays do not. The results of such tests are plotted as Mohr circles of effective stress at failure, as shown in Figure 1.5. Each Mohr circle represents the stresses on a single specimen at failure. The position of the circle is defined by the minor effective prin-cipal stress at failure out of the chamber when the cell pressure is applied
Stud and wing nuts at 120 or 180º intervals
Figure 1.3 Triaxial apparatus. (From Clayton, C.R.I. et al., Site Investigation, 2nd ed.
Blackwell Scientific, Oxford, 1995. Downloadable from www.geotechnique.
info.)
′ = −
σ3 (cell pressure pore water pressure) and the major effective principal stress at failure
′ = ′ +
σ1 σ3 (deviator stress)
which as an example are labelled on Figure 1.5 for one of the circles. The fail-ure envelope for five circles is shown as a dashed line in Figfail-ure 1.5. Typically, it is curved. As a result, triaxial tests should be carried out at approximately the normal effective stresses in the field, which are often low, of the order of 20–100 kPa. In conventional interpretation, the results from three tri-axial test specimens (for example, shown by the full circles in Figure 1.5) are interpreted using a best fit straight line envelope (shown by the full line in Figure 1.5) to determine values of effective cohesion intercept, c′, and effective angle of friction, ϕ′. Testing at unrealistically high effective stresses leads to high values of effective cohesion intercept, c′, which is unsafe.
Loose sand or normally consolidated clayspecimen
Dense specimen or overconsolidated clay specimen
Shearing at constant volume Deviator stress, P/A
Axial strain L
∆L P
Axial strain
= ∆L/L
Figure 1.4 Generalised stress–strain behaviour of granular soil in a drained triaxial test.
For soft, young (for example, alluvial) or compacted soils, the effective cohesion intercept should be assumed to be zero. The effective angle of fric-tion of clay may be expected to be of the order of 20°–30°, whilst that of a sand or gravel will exceed 30°.