Soil mechanics

Soil mechanics is a discipline that applies principles of engineering mechanics, e.g. kinematics, dynamics, fluid mechanics, and mechanics of material, to predict the mechanical behavior of soils. Together with Rock mechanics, it is the basis for solving many engineering problems in civil engineering (geotechnical engineering), geophysical engineering and engineering geology. Some of the basic theories of soil mechanics are the basic description and classification of soil, effective stress, shear strength, consolidation, lateral earth pressure, bearing capacity, slope stability, and permeability. Foundations, embankments, retaining walls, earthworks and underground openings are all designed in part with theories from soil mechanics.

Basic characteristics of soils

A phase diagram of soil indicating the weights and volumes of air, soil, water, and voids.

Soil is usually composed of three phases: solid, liquid, and gas. The mechanical properties of soils depend directly on the interactions of these phases with each other and with applied potentials (e.g., stress, hydraulic head, electrical potential, and temperature difference).

The solid phase of soils contains various amounts of crystalline clay and non-clay minerals, noncrystalline clay material, organic matter, and precipitated salts . These minerals are commonly formed by atoms of elements such as oxygen, silicon, hydrogen, and aluminum, organized in various crystalline forms. These elements along with calcium, sodium, potassium, magnesium, and carbon comprise over 99% of the solid mass of soils.. Although, the amount of non-clay material is greater than that of clay and organic material, the latter have a greater influence in the behavior of soils. Solid particles are classified by size as clay, silt, sand, gravel, cobbles, or boulders.

The liquid phase in soils is commonly composed of water containing various types and amounts of dissolved electrolytes. Organic compounds, both soluble and immiscible are present in soils from chemical spills, leaking wastes, and contaminated groundwater.

The gas phase, in partially saturated soils, is usually air, although organic gases may be present in zones of high biological activity or in chemically contaminated soils.

Soil mineralogy controls the size, shape, and physical and chemical properties of soil particles and thus its load-carrying ability and compressibility.

The structure of a soil is the combined effects of fabric (particle association, geometrical arrangement of particles, particle groups, and pore spaces in a soil), composition, and interparticle forces. The structure of soils is also use to account for differences between the properties of natural (structured) and remolded soils (destructured). The structure of a soil reflects all facets of the soil composition, history, present state, and environment. Initial conditions dominate the structure of young deposits at high porosity or freshly compacted soils; whereas older soils at lower porosity reflect the post-depositional changes more.

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 behavior 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.

Effective stress

Spheres immersed in water, reducing effective stress.

Main article: 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):

$\sigma '=\sigma -u\,$

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

Main article: 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

Main article: Shear strength (soil)

Most problems in geotechnical engineering, e.g. bearing capacity of shallow and deep foundations, slope stability, retaining wall design, penetration resistance, soil liquefaction etc., are affected by the soil shear strength. Analytical and numerical analyses use values of shear strength for solving these engineering problems.

Shearing strength in soils is the result of the resistance to movement at interparticle contacts, due to particle interlocking, physical bonds formed across the contact areas (resulting from surface atoms sharing electrons at interparticle contacts), and chemical bonds (i.e. cementation -particles connected through a solid substance such as recrystallized calcium carbonate)

Different criteria can be used to define the point of "failure" in a stress-strain curve of a particular material. Failure and yield should not be confused. There is no unique way of defining failure. For some material failure can be assumed to be the yield point. For soils, "failure" is usually considered occurring at 15% to 20% strain . This deformation usually implies that the function of a particular structure, e.g. a building foundation, might be impaired but not have failed. Failure of the soil does not imply failure of the system. In this sense, the shear strength of soils can be defined as the maximum stress applied on any plane in a soil mass at some strain considered as "failure".

There are different failure criteria that define failure. The Mohr-Coulomb failure criterion is the most common empirical failure criterion used in soil mechanics. In terms of effective stress the Mohr-Coulomb criterion is defined as:

$\tau _{f}=c'+\sigma _{f}'\tan \phi '\,$

where $\tau _{f}\,$ is shear strength at failure, $c'\,$ is effective cohesion, $\sigma _{f}'\,$ is effective stress at failure, and $\phi '\,$ is the effective angle of friction, a parametrization of the average coefficient of friction $\mu \,$ on the sliding plane, where $\mu =tan\phi '\,$.

The stress-strain relationship of soils, and therefore the shearing strength, is affected by :

1. soil composition (basic soil material): mineralogy, grain size and grain size distribution, shape of particles, pore fluid type and content, ions on grain and in pore fluid.
2. state (initial): Define by the initial void ratio, effective normal stress and shear stress (stress history). State can be describe by terms such as: loose, dense, overconsolidated, normally consolidated, stiff, soft, contractive, dilative, etc.
3. structure: Refers to the arrangement of particles within the soil mass; the manner in which the particles are packed or distributed. Features such as layers, joints, fissures, slickensides, voids, pockets, cementation, etc, are part of the structure. Structure of soils is described by terms such as: undisturbed, disturbed, remolded, compacted, cemented; flocculent, honey-combed, single-grained; flocculated, deflocculated; stratified, layered, laminated; isotropic and anisotropic.
4. Loading conditions: Effective stress path -drained, undrained, and type of loading -magnitude, rate (static, dynamic), and time history (monotonic, cyclic).

In reality, a complete shear strength formulation would account for all these factors.

Laboratory tests, e.g. direct shear test, Triaxial shear test, simple shear test, using different drainage conditions (drained or undrained), rate of loading, range of confining pressures, and stress history, are used for determining values of shear strength: unconfined compressive strength, drained shear strength, undrained shear strength, peak strength, critical state shear strength, and residual strength.

Consolidation

Main article: Consolidation (soil)

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.

Lateral earth pressure

Main article: 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

Main article: 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

Simple slope slip section

Main article: 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.

Permeability and seepage

A cross section showing the water table varying with surface topography as well as a perched water table.

Main article: Permeability (fluid)

Seepage is the flow of a fluid through soil pores. After measuring or estimating the intrinsic permeability (κ_i), one can calculate the hydraulic conductivity (K) of a soil, and 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. A typical value of hydraulic conductivity for natural sands is 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.)

See also

• Hydrogeology, aquifer characteristics closely related to soil characteristics
• Seepage

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