User:Anthony Argyriou/Soil mechanics

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Soil mechanics is a discipline that applies the principles of engineering mechanics to soil to predict the mechanical behavior of soil. Soil mechanics is important in several branches of engineering, such as civil engineering, geotechnical engineering and engineering geology. It is used in the design of foundations, embankments, retaining walls, earthworks and underground openings.

Basic characteristics of soils

Soil is made up of three components: solid particles, air, and water. The particles are classified by size as clay, silt, sand, gravel, cobbles, or boulders. The amount of air and water within a sample of soil affects its behavior. The sizes and types of particles that constitute a particular soil affect its properties and thus its load-carrying ability and compressibility. Soil, like any other engineering material, distorts when placed under a load. This distortion is of two kinds - shearing, or sliding, distortion and compression. In general, soils cannot withstand tension. In some situations the particles can be cemented together and a small amount of tension may be withstood, but not for long periods.

Particles of sands and many gravels consist overwhelmingly of silica. They can be rounded due to abrasion while being transported by wind or water, or sharp-cornered, or anything in between, and are roughly equi-dimensional. Clay particles arise from weathering of rock crystals like feldspar, and commonly consist of alumino-silicate minerals. They generally have a flake-shape with a large surface area compared with their mass. As their mass is extremely small, their behaviour is governed by forces of electrostatic attraction and repulsion on their surfaces. These forces attract and adsorb water to their surfaces, with the thickness of the layer being affected by dissolved salts in the water.

Permeability and seepage

Seepage is the flow of a fluid through soil pores in any direction. After measuring or estimating the coefficient of permeability k (also called hydraulic conductivity) of a soil, the rate of seepage can be estimated. k has the units m/s and is the average velocity of water passing through a porous medium under a unit hydraulic gradient. It is the proportionality constant between average velocity and hydraulic gradient in Darcy's Law. In most natural and engineering situations the hydraulic gradient is less than one, so the value of k for a soil generally represents the maximum likely velocity of seepage. (Natural sands typically have a k of around 1x10^-3m/s, while k for clays is similar to that of concrete.) The quantity of seepage under dams and sheet piling can be estimated using the graphical construction known as a flownet.

When the seepage velocity is great enough, erosion can occur because of the frictional drag exerted on the soil particles. Vertically upwards seepage is a source of danger on the downstream side of sheet piling and beneath the toe of a dam or levee. Erosion of the soil, known as "piping", can lead to failure of the structure and to sinkhole formation. Seeping water removes soil, starting from the exit point of the seepage, and erosion advances upgradient. The term sand boil is used to describe the appearance of the discharging end of an active soil pipe.

Seepage in an upward direction reduces the effective stress within soil. In cases where the hydraulic gradient is equal to or greater than the critical gradient (i.e. when the water pressure in the soil is equal to the total vertical stress at a point), effective stress is reduced to zero. When this occurs in a non-cohesive soil, a "quick" condition is reached and the soil becomes a heavy fluid (i.e. liquefaction has occurred). Quicksand was so named because the soil particles move around and appear to be 'alive' (the biblical meaning of 'quick' - as opposed to 'dead'). (Note that it is not possible to be 'sucked down' into quicksand. On the contrary, you would float with about half your body out of the water.)

Effective stress

The concept of effective stress is one of Karl Terzaghi's most important contributions to soil mechanics. It is a measure of the stress on the soil skeleton (the collection of particles in contact with each other), and determines the ability of soil to resist shear stress. It cannot be measured in itself, but must be calculated from the difference between two parameters that can be measured or estimated with reasonable accuracy.

Effective stress (σ ' ) on a plane within a soil mass is the difference between total stress (σ) and pore water pressure (u):

σ' = σ - u

Total stress

The total stress σ is equal to the overburden pressure or stress, which is made up of the weight of soil vertically above the plane, together with any forces acting on the soil surface (e.g. the weight of a structure). Total stress increases with increasing depth in proportion to the density of the overlying soil.

Pore water pressure

The pore water pressure u is the pressure of the water on that plane in the soil, and is most commonly calculated as the hydrostatic pressure. For stability calculations in conditions of dynamic flow (under sheet piling, beneath a dam toe, or within a slope, for instance), u must be estimated from a flow net. In the situation of a horizontal water table pore water pressure increases linearly with increasing depth below it.

Shear strength

Shear strength is the maximum stress that can be applied tangentially on a plane within a soil mass before sliding occurs on that plane. Shear strength depends on to the frictional resistance between the particles at their points of contact, cohesion between particles (if any exists), and the interlocking of particles within the soil skeleton. The Mohr-Coulomb failure criterion in terms of effective stress is

$s=c'+\sigma '\tan \phi '\,$

where s is shear strength, c' is effective cohesion, σ' is effective stress, and φ' is the effective angle of friction. This 'angle of friction' is a way of expressing the average coefficient of friction µ on the sliding plane, where µ = tan φ'.

Consider firstly a mass of cohesionless soil (i.e. silts, sands or gravels). A horizontal plane within a soil mass with a horizontal surface can be compared with a table on which a brick is resting. The weight of the brick W acts vertically downwards. The force F being applied to the brick to induce sliding is parallel to the table surface. Firstly, assume a smooth brick and table, and the force required to initiate sliding F_max = W.µ_s where µ_s is the coefficient of friction between the smooth surfaces. As there is no such physical thing as perfectly smooth surfaces, the brick and table will only make contact intermittently. This could, therefore, be considered an approximation to what occurs in a loose soil.

Now consider the brick and table to have noticeably rough surfaces. Before sliding movement can occur, the brick must be forced upwards as well as forwards, which requires extra energy input in order to lift the brick. This is equivalent to the process of dilation in a dense soil which must occur before sliding can take place. The force F required to cause sliding in this case is F_max = W.µ_r where µ_r is the coefficient of friction between the rough surfaces and is greater than µ_s. Note that there is no change in the actual coefficient of friction between the materials of the brick and the table i.e. between the soil particles. The increased 'coefficient of friction' in a dense soil, expressed as a greater friction angle φ', is purely a function of the energy input required to force the particles apart, i.e. to dilate the soil, in the region of the slip plane.

The effect of water under pressure between the surfaces of the brick and table is to tend to lift the brick, i.e. to reduce the contact stress between the brick and table, thus reducing the value of F needed to cause sliding. In real soils, because of the great stiffness of the material of the soil particles, the total area of the contact points between particles in a unit area of a 'wavy' plane passing through the contact points is so small as to be close to zero. The pore pressure u can therefore be considered to act over the whole of the unit area plane and the effective stress acting across the plane σ' = σ - u is seen to be a rather abstract concept, expressing in some way the total of a huge number of tiny particle contact stresses, all of them different from each other.

Note that whether water 'lubricates' the particles and makes sliding easier is irrelevant. It has been found that, for some rock minerals, the presence of water increases the sliding coefficient of friction and, for others, decreases it. As the coefficient of friction (angle of friction) of soil is always measured or estimated by field or laboratory tests on the soil specific to an engineering project, this effect is automatically taken into account.

Soils containing a significant clay content exhibit a short-term behaviour called 'undrained strength', which can be a great source of confusion to those attempting to understand soil behaviour. This is entirely due to their extremely low permeability. Coarse-grained soils have permeabilities sufficiently great to allow transient pore pressures caused by imposed increases or decreases in load on the soil to rapidly dissipate back to their equilibrium state. In saturated fine-grained soils, an increase (say) in total stress gives rise to an equal increase in pore pressure in the soil. (This is because the soil skeleton is much more compressible than both its individual particles and the water filling the pores, and so takes none of the increased stress initially.) A hydraulic gradient is set up between the water in the stressed zone and the water in the unstressed zone surrounding it, causing water to start seeping out of the stressed zone. As this happens, the pore pressure in the stressed zone gradually decreases until it reaches its equilibrium state again (i.e. that which existed prior to the stress change), and the volume of the pore spaces in the stressed zone decreases as the soil beneath the load undergoes consolidation. This process may take years to complete, and the soil is often in the fully 'undrained' state throughout the construction period of the facility that caused the stress change.

When the stress change is applied, the effective stress within the soil does not change from its pre-construction value. The total stress on a plane in the soil is increased by the stress change due to construction (e.g. building a structure on the ground surface) and the pore pressure increases by the same amount. The difference between them - the effective stress - is, therefore, unchanged. The soil appears then to have a constant shear strength which expresses itself as an apparent (or undrained) cohesion c_u and zero friction angle φ_u = 0. The Mohr-Coulomb strength equation in terms of total stress is s = c_u.

The undrained strength is measured in field or laboratory tests in which the applied external stresses are measured, but the pore pressure is not. Internally, the soil is behaving in exactly the same way as the brick on the table described above, with the difference that, in some clays, there is real cohesion between the particles and this can be imagined as glue on the sliding surfaces. If the pore pressure were measured during testing, the soil would be seen to obey the effective stress form of the Mohr-Coulomb strength equation (as it must).

The computation of, for example, bearing capacity or slope stability is made much simpler when undrained shear strength can be used, and this is the main justification for its use.

Consolidation

Consolidation is a process by which soils decrease in volume. It occurs when stress is applied to a soil that causes the soil particles to pack together more tightly, therefore reducing volume. When this occurs in a soil that is saturated with water, water will be squeezed out of the soil. The magnitude of consolidation can be predicted by many different methods. In the Classical Method, developed by Karl Terzaghi, soils are tested with an oedometer test to determine their compression index. This can be used to predict the amount of consolidation.

When stress is removed from a consolidated soil, the soil will rebound, regaining some of the volume it had lost in the consolidation process. If the stress is reapplied, the soil will consolidate again along a recompression curve, defined by the recompression index. The soil which had its load removed is considered to be overconsolidated. This is the case for soils which have previously had glaciers on them. The highest stress that it has been subjected to is termed the preconsolidation stress. A soil which is currently experiencing its highest stress is said to be normally consolidated.

The process of consolidation is different from secondary compression, soil compaction, and other processes of volume reduction. The process can also be activated during Groundwater-related subsidence.

Lateral earth pressure

Lateral earth stress theory is used to estimate the amount of stress soil can exert perpendicular to gravity. This is the stress exerted on retaining walls. A lateral earth stress coefficient, K, is defined as the ratio of lateral (horizontal) stress to vertical stress for cohesionless soils (K=σ_h/σ_v). There are three coefficients: at-rest, active, and passive. At-rest stress is the lateral stress in the ground before any disturbance takes place. The active stress state is reached when a wall moves away from the soil under the influence of lateral stress, and results from shear failure due to reduction of lateral stress. The passive stress state is reached when a wall is pushed into the soil far enough to cause shear failure within the mass due to increase of lateral stress. There are many theories for estimating lateral earth stress; some are empirically based, and some are analytically derived.

Bearing capacity

The bearing capacity of soil is the average contact stress between a foundation and the soil which will cause shear failure in the soil. Allowable bearing stress is the bearing capacity divided by a factor of safety. Sometimes, on soft soil sites, large settlements may occur under loaded foundations without actual shear failure occurring; in such cases, the allowable bearing stress is determined with regard to the maximum allowable settlement.

Three modes of failure are possible in soil: general shear failure, local shear failure, and punching shear failure.

Slope stability

The field of slope stability encompasses the analysis of static and dynamic stability of slopes of earth and rock-fill dams, slopes of other types of embankments, excavated slopes, and natural slopes in soil and soft rock.

As seen to the right, earthen slopes can develop a cut-spherical weakness zone. The probability of this happening can be calculated in advance using a simple 2-D circular analysis package. A primary difficulty with analysis is locating the most-probable slip plane for any given situation. Many landslides have only been analyzed after the fact.

Liquefaction

Earthquake liquefaction, often referred to simply as liquefaction, is the process by which saturated, non-cohesive soil (sand and silt) loses shear strength during seismic shaking and behaves like a liquid, rather a solid. The effect on structures and buildings can be devastating, and is a major contributor to urban seismic risk.

Liquefaction occurs when a saturated sand formation is subject to cyclic shaking. The shaking causes increased pore water pressure which reduces the effective stress, and therefore reduces the shear strength of the sand. Soils most prone to liquefaction are loose sands between layers of lower permeability soil that prevent rapid dissipation of cyclic pore pressures.

Ground investigation

Ground investigation is the major means of obtaining information which will affect the planning, design and construction of a new project. It can be divided into two stages - primary and secondary. Primary investigation is usually carried out before construction and depends on the nature of the project. It may include a surface investigation (topographic survey, service placement, estimation of excavation volumes, surface grades needed for drainage), and a subsurface investigation (location of ground water, soil types, soil depth to required[bearing capacity, soil properties). The secondary investigation is usually an ongoing process throughout construction and is concerned with site accessibility, conditions and safety.

See also

• Hydrogeology (aquifer characteristics closely related to soil characteristics)
• Geotechnical engineering
• Engineering geology
• Geotechnical investigation

References

• Das, Braja, Advanced Soil Mechanics ISBN 1-56032-562-3
• Terzaghi, K., 1943, Theoretical Soil Mechanics, John Wiley and Sons, New York
• Craig, R.F., 1974, Soil Mechanics, ISBN 0-419-22450-5
• Powrie, W., Soil Mechanics, (1997), ISBN 0-415-31156-X

From http://en.wikipedia.org/w/index.php?title=Soil_mechanics&oldid=119740580