Soil mechanics

Soil mechanics is a discipline that applies the principles of Engineering mechanics to predict the mechanical behavior of soil. Karl von Terzaghi, who worked on a rational approach to soil engineering, is known as the Father of Soil Mechanics.

Soil mechanics is an important discipline for many branches of engineering, such as Civil engineering, Geotechnical engineering and Engineering geology. It is used in the design of foundations to support structures, embankments, retaining walls, earthworks and underground openings.

The percolation of water through soils is of importance in the construction of tunnels and deep foundations, and obviously water-related structures like bridge pilings and dams.

Basic Charateristics of Soils

Soil is made up of 3 components: air, water, and solids. The solids are particles that range in size from clay particles the size of dust to giant boulders. The amount of air and water within a sample of soil affects its properties to carry a load. In addition, the types of particles that constitute the soil affect the properties as well.

Seepage

Seepage is the flow of a fluid through the soil pores, in downward or upward direction. Seepage under dams and sheet pile walls is often estimated using the simple graphical construction known as a flownet. When the seepage velocity is great enough, erosion of the soil can occur. It is an important consideration when any structure is designed which may experience a head difference from one point to another. Erosion of the supporting soil, also known as "piping", can lead to failure of the structure, and this is a common cause of dam failure. Seepage in upward direction reduces the effective stress of soil particles. In case the hydraulic gradient is equal to or greater than the critical gradient, effective stress reduces to zero. The condition is termed as quicksand or boiling condition.

Effective Stress σ '

The concept of effective stress is central to understanding behaviour of water under different conditions. Effective stress is a measurement of the load borne by the soil skeleton. This pressure determines the ability of soil to resist shear stress. If the effective stress in a soil is reduced to zero, quick condition is said to occur (see quicksand).

Effective stress (σ ' ) of a soil is calculated from two easily measured parameters, total stress (σ) and pore water pressure (μ) according to:

σ' = σ - μ

where all three terms have units of pressure.

Total Stress σ

The total stress σ is equal to the overburden pressure, it is simply the weight of everything which rests on the soil, including the soil above. Total stress doesn't always increase with increasing depth.

Pore water pressure μ

The pore water pressure μ can be calculated as the hydrostatic pressure of water according to fluid statics if it is assumed that the flow of water through soil is slow. This assumption is valid under most conditions (quick condition being a notable exception). Pore water pressure can be estimated as zero above the water table and increases linearly with increasing depth below the water table.

Shear strength

It is the maximum resistance a soil can offer before the occurrence of shear failure along a specific failure plane. The shear strength is related to the soil type, thus, the response of a granular soil to an applied load depends to a large extent on its density, whereas a cohesive overconsolidated soil exhibits a markedly different behaviour to that of a pond. The shear strength in soil develops due to:(i) the frictional resistance between the particles at their points of contact, (ii) cohesion between particles and (iii) interlocking between particles. The failure law given for soil as: T=c+O) where: T: Shear Stress. c: Cohesion ( for cohesionless=0). Pn: Normal Stress O : Angle of Internal Friction

Stresses and Displacements

Consolidation theory

When water flows into or out of a soil mass without causing the volume to change, the flow is known as seepage. If, on the other hand, the flow of water within a soil mass induces a volume change, then the flow is referred to as transient. The process of volume change triggered by a transient flow is known as consolidation. It is related to the change in effective stresses within the soil matrix due to a surface loading (or unloading) or variation in the water table. The excess porewater pressure (i.e. load-induced porewater pressure) generated in both cases causes the water to be either squeezed out of the soil mass (positive pore water pressure) or sucked into the soil matrix (negative porewater pressure). This movement of water continues at a changing rate until all excess pressure has dissipated, and the equilibrium of stresses has been restored according to the effective stress principle.

If at some stage during its geological history the soil has been subjected to unloading, e.g. disappearance of an ice cover or a severe erosion, then the present pressure due to the overburden pressure (self weight) is smaller than that which existed before the onset of the unloading process, and the soil is known as overconsolidated. If, on the other hand, the soil has not been subjected to any unloading during its entire geological history, then the present overburden pressure, constitutes the largest pressure that the soil has ever experienced, and the soil is referred as normally consolidated.

Lateral earth pressure

Retaining structures are subjected, apart from their self weight, to lateral thrusts whose intensity and direction depend on the movement (or lack of it) of the structure itself. The type of thrust is examined using the coefficient of earth pressure defined as:

$K= \frac{\sigma'_h}{\sigma'_v}$

If the wall does not move at all then $K$ is referred as the coefficient of earth pressure at rest $K_o$ . Where, $K_o= 1-sin(\phi)$ (Jaky's Solution, 1944).
If the wall is pushed into the soil then at failure, the coefficient $K$ reaches its maximum value known as the coefficient of passive earth pressure $K_p$ .
If the wall is moved away from the soil it supports, then at failure the ratio $K$ reaches its minimum value, known as the coefficient of active earth pressure $K_a$ .

Bearing Capacity

Ultimate bearing capacity of soil is the value of the average contact pressure between the foundation and the soil which will produce shear failure in the soil. Safe or maximum bearing capacity is the maximum contact pressure to which the soil can be subjected to without risk of shear failure. Ultimate stress is divided by the factor of safety used.

Stability of Slopes

An exposed ground surface that makes any angle other than horizontal is called an unrestrained slope. If gravity is large enough, failure of the slope can occur. Analysis of slopes is difficult and tedious to perform. Engineers wishing to perform this analysis must determine the factor of safety of the slope. This factor of safety is a function of the soil properties, angle of repose, climate, and vegetation, as well as many other factors.

In order to find the factor of safety of soil, one must first find the critical equillibrium, or loading to the precipice of the slope failing. Once this equillibrium is found, a factor of safety can be calculated based on typical loadings that can be expected.

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.

References

Azizi, F., Applied Analyses in Geotechnics, (2000), E & FN SPON.
Terzaghi, K., 1943, Theoretical Soil Mechanics, John Wiley and Sons, New York
Craig, R.F., 1974, Soil Mechanics, Spon Press, London

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