Soil mechanics is a branch of engineering mechanics that describes the behavior of
soilSoil is a natural body consisting of layers of mineral constituents of variable thicknesses, which differ from the parent materials in their morphological, physical, chemical, and mineralogical characteristics...
s. It differs from fluid mechanics and solid mechanics in the sense that soils consist of a heterogeneous mixture of fluids (usually air and water) and particles (usually
clayClay is a general term including many combinations of one or more clay minerals with traces of metal oxides and organic matter. Geologic clay deposits are mostly composed of phyllosilicate minerals containing variable amounts of water trapped in the mineral structure.- Formation :Clay minerals...
,
siltSilt is granular material of a size somewhere between sand and clay whose mineral origin is quartz and feldspar. Silt may occur as a soil or as suspended sediment in a surface water body...
,
sandSand is a naturally occurring granular material composed of finely divided rock and mineral particles.The composition of sand is highly variable, depending on the local rock sources and conditions, but the most common constituent of sand in inland continental settings and non-tropical coastal...
, and
gravelGravel is composed of unconsolidated rock fragments that have a general particle size range and include size classes from granule- to boulder-sized fragments. Gravel can be sub-categorized into granule and cobble...
) but soil may also contain organic solids, liquids, and gasses and other matter. Along with
rock mechanicsRock mechanics is the theoretical and applied science of the mechanical behaviour of rock and rock masses;also compared to the geology, it is that branch of mechanics concerned with the response of rock and rock masses to the force fields of their physical environment.Rock mechanics itself forms...
, soil mechanics provides the theoretical basis for analysis in
geotechnical engineeringGeotechnical engineering is the branch of civil engineering concerned with the engineering behavior of earth materials. Geotechnical engineering is important in civil engineering, but is also used by military, mining, petroleum, or any other engineering concerned with construction on or in the ground...
, a subdiscipline of
Civil engineeringCivil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including works like roads, bridges, canals, dams, and buildings...
. Soil mechanics is used to analyze the deformations of and flow of fluids within natural and man-made structures that are supported on or made of soil, or structures that are buried in soils. Examples applications are building and bridge foundations, retaining walls, dams, and buried pipeline systems. Principles of soil mechanics are also used in related disciplines such as geophysical engineering,
engineering geologyEngineering geology is the application of the geologic sciences to engineering practice for the purpose of assuring that the geologic factors affecting the location, design, construction, operation and maintenance of engineering works are recognized and adequately provided for...
, coastal engineering,
agricultural engineeringAgricultural engineering is the engineering discipline that applies engineering science and technology to agricultural production and processing...
,
hydrologyHydrology is the study of the movement, distribution, and quality of water on Earth and other planets, including the hydrologic cycle, water resources and environmental watershed sustainability...
and
soil physicsSoil physics is the study of soil physical properties and processes. It is applied to management and prediction under natural and managed ecosystems. Soil physics deals with the dynamics of physical soil components and their phases as solids, liquids, and gases. It draws on the principles of...
.
This article describes the genesis and composition of soil, the distinction between
pore water pressure and inter-granular
effective stress, capillary action of fluids in the pore spaces,
soil classification,
seepage and
permeability, time dependent change of volume due to squeezing water out of tiny pore spaces, also known as
consolidation,
shear strength and stiffness of soils. The shear strength of soils is primarily derived from friction between the particles and interlocking, which are very sensitive to the effective stress. The article concludes with some examples of
geotechnical engineeringGeotechnical engineering is the branch of civil engineering concerned with the engineering behavior of earth materials. Geotechnical engineering is important in civil engineering, but is also used by military, mining, petroleum, or any other engineering concerned with construction on or in the ground...
applications of the principles of soil mechanics such as slope stability, lateral earth pressure on retaining walls, and bearing capacity of foundations.
Genesis
The primary mechanism of soil creation is the weathering of rock. All rock types (
igneous rockIgneous rock is one of the three main rock types, the others being sedimentary and metamorphic rock. Igneous rock is formed through the cooling and solidification of magma or lava...
,
metamorphic rockMetamorphic rock is the transformation of an existing rock type, the protolith, in a process called metamorphism, which means "change in form". The protolith is subjected to heat and pressure causing profound physical and/or chemical change...
and
sedimentary rockSedimentary rock are types of rock that are formed by the deposition of material at the Earth's surface and within bodies of water. Sedimentation is the collective name for processes that cause mineral and/or organic particles to settle and accumulate or minerals to precipitate from a solution....
) may be broken down into small particles to create soil. Weathering mechanisms are physical weathering, chemical weathering, and biological weathering Human activities such as excavation, blasting, and waste disposal, may also create soil. Over geologic time, deeply buried soils may be altered by pressure and temperature to become metamorphic or sedimentary rock, and if melted and solidified again, they would complete the geologic cycle by becoming igneous rock.
Physical weathering includes temperature effects, freeze and thaw of water in cracks, rain, wind, impact and other mechanisms. Chemical weathering includes dissolution of matter composing a rock and precipitation in the form of another mineral.
ClayClay is a general term including many combinations of one or more clay minerals with traces of metal oxides and organic matter. Geologic clay deposits are mostly composed of phyllosilicate minerals containing variable amounts of water trapped in the mineral structure.- Formation :Clay minerals...
minerals, for example can be formed by weathering of
feldsparFeldspars are a group of rock-forming tectosilicate minerals which make up as much as 60% of the Earth's crust....
, which is the most common mineral present in igneous rock.
The most common mineral constituent of silt and sand is
quartzQuartz is the second-most-abundant mineral in the Earth's continental crust, after feldspar. It is made up of a continuous framework of SiO4 silicon–oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall formula SiO2. There are many different varieties of quartz,...
, also called silica, which has the chemical name silicon dioxide. The reason that feldspar is most common in rocks but silicon is more prevalent in soils is that feldspar is much more soluble than silica.
SiltSilt is granular material of a size somewhere between sand and clay whose mineral origin is quartz and feldspar. Silt may occur as a soil or as suspended sediment in a surface water body...
,
SandSand is a naturally occurring granular material composed of finely divided rock and mineral particles.The composition of sand is highly variable, depending on the local rock sources and conditions, but the most common constituent of sand in inland continental settings and non-tropical coastal...
, and
GravelGravel is composed of unconsolidated rock fragments that have a general particle size range and include size classes from granule- to boulder-sized fragments. Gravel can be sub-categorized into granule and cobble...
are basically little pieces of broken
rockIn geology, rock or stone is a naturally occurring solid aggregate of minerals and/or mineraloids.The Earth's outer solid layer, the lithosphere, is made of rock. In general rocks are of three types, namely, igneous, sedimentary, and metamorphic...
s.
According to the
Unified Soil Classification SystemThe Unified Soil Classification System is a soil classification system used in engineering and geology to describe the texture and grain size of a soil. The classification system can be applied to most unconsolidated materials, and is represented by a two-letter symbol...
, silt particle sizes are in the range of 0.002 mm to 0.075 mm and sand particles have sizes in the range of 0.075 mm to 4.75 mm.
Gravel particles are broken pieces of rock in the size range 4.75 mm to 100 mm.
Particles larger than gravel are called cobbles and boulders.
Transport
Soil deposits are affected by the mechanism of transport and deposition to their location. Soils that are not transported are called residual soils -- they exist at the same location as the rock from which they were generated.
Decomposed graniteDecomposed granite, also known as DG, is granitic rock that has weathered to the point that it readily fractures into smaller pieces or chunks of weak rock. Further weathering produces rock that easily crumbles into mixtures of gravel, sand, and silt-sized particles with some clay...
is a common example of a residual soil. The common mechanisms of transport are the actions of gravity, ice, water, and wind. Wind blown soils include dune sands and
loessLoess is an aeolian sediment formed by the accumulation of wind-blown silt, typically in the 20–50 micrometre size range, twenty percent or less clay and the balance equal parts sand and silt that are loosely cemented by calcium carbonate...
. Water carries particles of different size depending on the speed of the water, thus soils transported by water are graded according to their size. Silt and clay may settle out in a lake, and gravel and sand collect at the bottom of a river bed. Wind blown soil deposits (aeolian soils) also tend to be sorted according to their grain size. Erosion at the base of
glacierA glacier is a large persistent body of ice that forms where the accumulation of snow exceeds its ablation over many years, often centuries. At least 0.1 km² in area and 50 m thick, but often much larger, a glacier slowly deforms and flows due to stresses induced by its weight...
s is powerful enough to pick up large rocks and boulders as well as soil; soils dropped by melting ice can be a well graded mixture of widely varying particle sizes. Gravity on its own may also carry particles down from the top of a mountain to make a pile of soil and boulders at the base; soil deposits transported by gravity are called
colluviumColluvium is the name for loose bodies of sediment that have been deposited or built up at the bottom of a low-grade slope or against a barrier on that slope, transported by gravity. The deposits that collect at the foot of a steep slope or cliff are also known by the same name. Colluvium often...
.
The mechanism of transport also has a major effect on the particle shape. For example, low velocity grinding in a river bed will produce rounded particles. Freshly fractured colluvium particles often have a very angular shape.
Soil mineralogy
Silts, sands and gravels are classified by their size, and hence they may consist of a variety of minerals. Owing to the stability of quartz compared to other rock minerals, quartz is the most common constituent of sand and silt . Mica, and feldspar are other common minerals present in sands and silts. The mineral constituents of gravel may be more similar to that of the parent rock.
The common
clayClay is a general term including many combinations of one or more clay minerals with traces of metal oxides and organic matter. Geologic clay deposits are mostly composed of phyllosilicate minerals containing variable amounts of water trapped in the mineral structure.- Formation :Clay minerals...
minerals are
montmorilloniteMontmorillonite is a very soft phyllosilicate group of minerals that typically form in microscopic crystals, forming a clay. It is named after Montmorillon in France. Montmorillonite, a member of the smectite family, is a 2:1 clay, meaning that it has 2 tetrahedral sheets sandwiching a central...
or smectite,
illiteIllite is a non-expanding, clay-sized, micaceous mineral. Illite is a phyllosilicate or layered alumino-silicate. Its structure is constituted by the repetition of tetrahedron – octahedron – tetrahedron layers. The interlayer space is mainly occupied by poorly hydrated potassium cations...
, and
kaoliniteKaolinite is a clay mineral, part of the group of industrial minerals, with the chemical composition Al2Si2O54. It is a layered silicate mineral, with one tetrahedral sheet linked through oxygen atoms to one octahedral sheet of alumina octahedra...
or kaolin. These minerals tend to form in sheet or plate like structures, with length typically ranging between
and
and thickness typically ranging between
and
, and they have a relatively large specific surface area. The specific surface area (SSA) is defined as the ratio of the surface area of particles to the mass of the particles. Clay minerals typically have specific surface areas in the range of 10 to 1,000 square meters per gram of solid. Due to the large surface area available for chemical, electrostatic, and
van der WaalsIn physical chemistry, the van der Waals force , named after Dutch scientist Johannes Diderik van der Waals, is the sum of the attractive or repulsive forces between molecules other than those due to covalent bonds or to the electrostatic interaction of ions with one another or with neutral...
interaction, the mechanical behavior of clay minerals is very sensitive to the amount of pore fluid available and the type and amount of dissolved ions in the pore fluid.
The minerals of soils are predominantly formed by atoms of oxygen, silicon, hydrogen, and aluminum, organized in various crystalline forms. These elements along with calcium, sodium, potassium, magnesium, and carbon constitute over 99 per cent of the solid mass of soils.
Grain size distribution
Soils consist of a mixture of particles of different size, shape and mineralogy. Because the size of the particles obviously has a significant effect on the soil behavior, the grain size and grain size distribution are used to classify soils. The grain size distribution describes the relative proportions of particles of various sizes. The grain size is often visualized in a cumulative distribution graph which, for example, plots the percentage of particles finer than a given size as a function of size. The median grain size,
, is the size for which 50% of the particle mass consists of finer particles. Soil behavior, especially the
hydraulic conductivityHydraulic conductivity, symbolically represented as K, is a property of vascular plants, soil or rock, that describes the ease with which water can move through pore spaces or fractures. It depends on the intrinsic permeability of the material and on the degree of saturation...
, tends to be dominated by the smaller particles, hence, the term "effective size", denoted by
, is defined as the size for which 10% of the particle mass consists of finer particles.
Sands and gravels that possess a wide range of particle sizes with a smooth distribution of particle sizes are called
well graded soils. If the soil particles in a sample are predominantly in a relatively narrow range of sizes, the soil are called
uniformly graded soils. If there are distinct gaps in the gradation curve, e.g., a mixture of gravel and fine sand, with no coarse sand, the soils may be called
gap graded.
Uniformly graded and
gap graded soils are both considered to be
poorly graded. There are many methods for measuring
particle size distributionThe particle-size distribution of a powder, or granular material, or particles dispersed in fluid, is a list of values or a mathematical function that defines the relative amounts of particles present, sorted according to size...
. The two traditional methods used in geotechnical engineering are sieve analysis and hydrometer analysis.
Sieve analysis
The size distribution of gravel and sand particles are typically measured using sieve analysis. The formal procedure is described in ASTM D6913-04(2009). A stack of sieves with accurately dimensioned holes between a mesh of wires is used to separate the particles into size bins. A known volume of dried soil, with clods broken down to individual particles, is put into the top of a stack of sieves arranged from coarse to fine. The stack of sieves is shaken for a standard period of time so that the particles are sorted into size bins. This method works reasonably well for particles in the sand and gravel size range. Fine particles tend to stick to each other, and hence the sieving process is not an effective method. If there are a lot of fines (silt and clay) present in the soil it may be necessary to run water through the sieves to wash the coarse particles and clods through.
A variety of sieve sizes are available. The boundary between sand and silt is arbitrary. According to the
Unified Soil Classification SystemThe Unified Soil Classification System is a soil classification system used in engineering and geology to describe the texture and grain size of a soil. The classification system can be applied to most unconsolidated materials, and is represented by a two-letter symbol...
, a #4 sieve (4 openings per inch) having 4.75mm opening size separates sand from gravel and a #200 sieve with an 0.075 mm opening separates sand from silt and clay. According to the British standard, 0.063 mm is the boundary between sand and silt, and 2 mm is the boundary between sand and gravel.
Hydrometer analysis
The classification of fine-grained soils, i.e., soils that are finer than sand, is determined primarily by their
Atterberg limitsThe Atterberg limits are a basic measure of the nature of a fine-grained soil. Depending on the water content of the soil, it may appear in four states: solid, semi-solid, plastic and liquid. In each state the consistency and behavior of a soil is different and thus so are its engineering properties...
, not by their grain size. If it is important to determine the grain size distribution of fine-grained soils, the hydrometer test may be performed. In the hydrometer tests, the soil particles are mixed with water and shaken to produce a dilute suspension in a glass cylinder, and then the cylinder is left to sit. A
hydrometerA hydrometer is an instrument used to measure the specific gravity of liquids; that is, the ratio of the density of the liquid to the density of water....
is used to measure the density of the suspension as a function of time. Clay particles may take several hours to settle past the depth of measurement of the hydrometer. Sand particles may take less than a second. Stoke's law provides the theoretical basis to calculate the relationship between sedimentation velocity and particle size. ASTM provides the detailed procedures for performing the Hydrometer test.
Clay particles can be sufficiently small that they never settle because they are kept in suspension by
Brownian motionBrownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...
, in which case they may be classified as
colloidA colloid is a substance microscopically dispersed evenly throughout another substance.A colloidal system consists of two separate phases: a dispersed phase and a continuous phase . A colloidal system may be solid, liquid, or gaseous.Many familiar substances are colloids, as shown in the chart below...
s.
Mass-volume relations
There are a variety of parameters used to describe the relative proportions of air, water and solid in a soil. This section defines these parameters and some of their interrelationships. The basic notation is as follows:
,
, and
represent the volumes of air, water and solids in a soil mixture;
,
, and
represent the weights of air, water and solids in a soil mixture;
,
, and
represent the masses of air, water and solids in a soil mixture;
,
, and
represent the densities of the constituents (air, water and solids) in a soil mixture;
Note that the weights, W, can be obtained by multiplying the mass, M, by the acceleration due to gravity, g; e.g.,
Specific GravitySpecific gravity is the ratio of the density of a substance to the density of a reference substance. Apparent specific gravity is the ratio of the weight of a volume of the substance to the weight of an equal volume of the reference substance. The reference substance is nearly always water for...
is the ratio of the density of one material compared to the density of pure water (
).
Specific gravity of solids,
Note that unit weights, conventionally denoted by the symbol
may be obtained by multiplying the
densityThe mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
instead of
by the acceleration due to gravity,
.
DensityThe mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
,
Bulk Density, or
Wet Density,
, are different names for the density of the mixture, i.e., the total mass of air, water, solids divided by the total volume of air water and solids (the mass of air is assumed to be zero for practical purposes):
Dry Density,
, is the mass of solids divided by the total volume of air water and solids:
Buoyant Density,
, defined as the density of the mixture minus the density of water is useful if the soil is suberged under water:
where
is the density of water
Water Content,
is the ratio of mass of water to mass of solid. It is easily measured by weighing a sample of the soil, drying it out in an oven and re-weighing. Standard procedures are described by ASTM.
Void ratio,
, is the ratio of the volume of voids to the volume of solids:
PorosityPorosity or void fraction is a measure of the void spaces in a material, and is a fraction of the volume of voids over the total volume, between 0–1, or as a percentage between 0–100%...
,
, is the ratio of volume of voids to the total volume, and is related to the void ratio:
Degree of saturation,
, is the ratio of the volume of water to the volume of voids:
From the above definitions, some useful relationships can be derived by use of basic algebra.
Effective stress and capillarity: hydrostatic conditions
To understand the mechanics of soils it is necessary to understand how normal stresses and shear stresses are shared by the different phases. Neither gas nor liquid provide significant resistance to
shear stressA shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...
. The shear resistance of soil is provided by friction and interlocking of the particles. The friction depends on the intergranular contact stresses between solid particles. The normal stresses, on the other hand, are shared by the fluid and the particles. Although the pore air is relatively compressible, and hence takes little normal stress in most
geotechnical engineeringGeotechnical engineering is the branch of civil engineering concerned with the engineering behavior of earth materials. Geotechnical engineering is important in civil engineering, but is also used by military, mining, petroleum, or any other engineering concerned with construction on or in the ground...
problems, liquid water is relatively incompressible and if the voids are saturated with water, the pore water must be squeezed out in order to pack the particles closer together.
The principle of effective stress, introduced by Karl Terzaghi, states that the effective stress
σ (i.e., the average intergranular stress between solid particles) may be calculated by a simple subtraction of the pore pressure from the total stress:
where σ
is the total stress and u
is the pore pressure. It is not practical to measure σ directly, so in practice the vertical effective stress is calculated from the pore pressure and vertical total stress. The distinction between the terms pressure and stress is also important. By definition,
pressurePressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
at a point is equal in all directions but stresses at a point can be different in different directions. In soil mechanics, compressive stresses and pressures are considered to be positive and tensile stresses are considered to be negative, which is different from the solid mechanics sign convention for stress.
Total stress
For level ground conditions, the total vertical stress at a point,
, on average, is the weight of everything above that point per unit area. The vertical stress beneath a uniform surface layer with density
, and thickness
is for example:
where
is the acceleration due to gravity, and
is the unit weight of the overlying layer. If there are multiple layers of soil or water above the point of interest, the vertical stress may be calculated by summing the product of the unit weight and thickness of all of the overlying layers. Total stress increases with increasing depth in proportion to the density of the overlying soil.
It is not possible to calculate the horizontal total stress in this way.
Lateral earth pressureLateral earth pressure is the pressure that soil exerts against a structure in a sideways direction. The common applications of lateral earth pressure theory are for the design of ground engineering structures such as retaining walls, basements, tunnels, and to determine the friction on the sides...
s are addressed elsewhere.
Hydrostatic conditions
If there is no pore water flow occurring in the soil, the pore water pressures will be hydrostatic. The
water tableThe water table is the level at which the submarine pressure is far from atmospheric pressure. It may be conveniently visualized as the 'surface' of the subsurface materials that are saturated with groundwater in a given vicinity. However, saturated conditions may extend above the water table as...
is located at the depth where the water pressure is equal to the atmospheric pressure. For hydrostatic conditions, the water pressure increases linearly with depth below the water table:
where
is the density of water, and
is the depth below the water table.
Capillary action
Due to
surface tensionSurface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects to run on the water surface...
water will rise up in a small capillary tube above a free surface of water. Likewise, water will rise up above the water table into the small pore spaces around the soil particles. In fact the soil may be completely saturated for some distance above the water table. Above the height of capillary saturation, the soil may be wet but the water content will decrease with elevation. If the water in the capillary zone is not moving, the water pressure obeys the equation of hydrostatic equilibrium,
, but note that
, is negative above the water table. Hence, hydrostatic water pressures are negative above the water table. The thickness of the zone of capillary saturation depends on the pore size, but typically, the heights vary between a centimeter or so for coarse sand to tens of meters for a silt or clay.
The surface tension of water explains why the water does not drain out of a wet sand castle or a moist ball of clay. Negative water pressures make the water stick to the particles and pull the particles to each other, friction at the particle contacts make a sand castle stable. But as soon as a wet sand castle is submerged below a free water surface, the negative pressures are lost and the castle collapses. Considering the effective stress equation,
, if the water pressure is negative, the effective stress may be positive, even on a free surface (a surface where the total normal stress is zero). The negative pore pressure pulls the particles together and causes compressive particle to particle contact forces.
Negative pore pressures in clayey soil can be much more powerful than those in sand. Negative pore pressures explain why clay soils shrink when they dry and swell as they are wetted. The swelling and shrinkage can cause major distress, especially to light structures and roads.
Later sections of this article address the pore water pressures for seepage and consolidation problems.
Soil Classification
Geotechnical engineers classify the soil particle types by performing tests on disturbed (dried, passed through sieves, and remolded) samples of the soil. This provides information about the characteristics of the soil grains themselves. It should be noted that classification of the types of grains present in a soil does not account for important effects of the
structure or
fabric of the soil, terms that describe compactness of the particles and patterns in the arrangement of particles in a load carrying framework as well as the pore size and pore fluid distributions.
Classification of soil grains
In the US and other countries, the
Unified Soil Classification SystemThe Unified Soil Classification System is a soil classification system used in engineering and geology to describe the texture and grain size of a soil. The classification system can be applied to most unconsolidated materials, and is represented by a two-letter symbol...
(USCS)is often used for soil classification. Other classification systems include the British Standard BS5390 and the AASHTO soil classification system.
Classification of sands and gravels
In the USCS, gravels (given the symbol
G) and sands (given the symbol
S) are classified according to their grain size distribution. For the USCS, gravels may be given the classification symbol
GW (well-graded gravel),
GP (poorly graded gravel),
GM (gravel with a large amount of silt), or
GC (gravel with a large amount of clay). Likewise sands may be classified as being
SW,
SP,
SM or
SC. Sands and gravels with a small but non-negligible amount of fines (5 % - 12 %) may be given a dual classification such as
SW-SC.
Atterberg Limits
Clays and Silts, often called 'fine-grained soils', are classified according to their
Atterberg limitsThe Atterberg limits are a basic measure of the nature of a fine-grained soil. Depending on the water content of the soil, it may appear in four states: solid, semi-solid, plastic and liquid. In each state the consistency and behavior of a soil is different and thus so are its engineering properties...
; the most commonly used Atterberg limits are the Liquid limit (denoted by
LL or
), Plastic Limit (denoted by
PL or
), and Shrinkage limit (denoted by
SL). The shrinkage limit corresponds to a water content below which the soil will not shrink as it dries.
The liquid limit and plastic limit are arbitrary limits determined by tradition and convention. The liquid limit is determined by measuring the water content for which a groove closes after 25 blows in a standard test. Alternatively, a fall cone test apparatus may be use to measure the liquid Limit. The undrained shear strength of remolded soil at the liquid limit is approximately 2 kPa. The plastic limit is the water content below which it is not possible to roll by hand the soil into 3 mm diameter cylinders. The soil cracks or breaks up as it is rolled down to this diameter. Remolded soil at the plastic limit is quite stiff, having an undrained shear strength of the order of about 200 kPa.
The Plasticity index of a particular soil specimen is defined as the difference between the Liquid limit and the Plastic limit of the specimen; it is an indicator of how much water the soil particles in the specimen can absorb. The plasticity index is the difference in water contents between states when the soil is relatively soft and the soil is relatively brittle when molded by hand.
Classification of silts and clays
According to the
Unified Soil Classification SystemThe Unified Soil Classification System is a soil classification system used in engineering and geology to describe the texture and grain size of a soil. The classification system can be applied to most unconsolidated materials, and is represented by a two-letter symbol...
(USCS), silts and clays are classified by plotting the values of their plasticity index and liquid limit on a plasticity chart. The A-Line on the chart separates clays (given the USCS symbol
C) from silts (given the symbol
M). LL=50% separates high plasticity soils (given the modifier symbol
H) from low plasticity soils (given the modifier symbol
L). A soil that plots above the A-line and has LL>50% would, for example, be classified as
CH. Other possible classifications of silts and clays are
ML,
CL and
MH. If the Atterberg limits plot in the"hatched" region on the graph near the origin, the soils are given the dual classification 'CL-ML'.
Liquidity Index
The effects of the water content on the strength of saturated remolded soils can be quantified by the use of the
liquidity index,
LI:
When the LI is 1, remolded soil is at the liquid limit and it has an undrained shear strength of about 2 kPa. When the soil is at the plastic limit, the LI is 0 and the undrained shear strength is about 200 kPa.
Relative density
The density of sands (cohesionless soils) is often characterized by the relative density,
where:
is the "maximum void ratio" corresponding to a very loose state,
is the "minimum void ratio" corresponding to a very dense state and e is the in situ void ratio. Methods used to calculate relative density are defined in ASTM D4254-00(2006).
Thus if
the sand or gravel is very dense, and if
the soil is extremely loose and unstable.
Seepage: steady state flow of water
If fluid pressures in a soil deposit are uniformly increasing with depth according to
then hydrostatic conditions will prevail and the fluids will not be flowing through the soil.
is the depth below the water table. However, if the water table is sloping or there is a perched water table as indicated in the accompanying sketch, then seepage will occur. For steady state seepage, the seepage velocities are not varying with time. If the water tables are changing levels with time, or if the soil is in the process of consolidation, then steady state conditions do not apply.
Darcy's law
Darcy's lawDarcy's law is a phenomenologically derived constitutive equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on the results of experiments on the flow of water through beds of sand...
states that the volume of flow of the pore fluid through a porous medium per unit time is proportional to the rate of change of excess fluid pressure with distance. The constant of proportionality includes the viscosity of the fluid and the intrinsic permeability of the soil. For the simple case of a horizontal tube filled with soil
The total discharge,
(units of volume per time, e.g., ft³/s or m³/s) is proportional to the
intrinsic permeabilityPermeability in fluid mechanics and the earth sciences is a measure of the ability of a porous material to allow fluids to pass through it.- Units :...
,
, the cross sectional area,
, and rate of pore pressure change with distance,
, and inversely proportional to the dynamic viscosity of the fluid,
. The negative sign is needed because fluids flow from high pressure to low pressure. So if the change in pressure is negative (in the
-direction) then the flow will be positive (in the
-direction). The above equation works well for a horizontal tube, but if the tube was inclined so that point b was a different elevation than point a, the equation would not work. The effect of elevation is accounted for by replacing the pore pressure by
excess pore pressure,
defined as:
where
is the depth measured from an arbitrary elevation reference (datum). Replacing
by
we obtain a more general equation for flow:
Dividing both sides of the equation by
, and expressing the rate of change of excess pore pressure as a
derivativeIn calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...
, we obtain a more general equation for the apparent velocity in the x-direction:
where
has units of velocity and is called the
Darcy velocity, or
discharge velocity. The
seepage velocity 
(average velocity of fluid molecules in the pores) is related to the Darcy velocity, and the porosity,
Civil engineerA civil engineer is a person who practices civil engineering; the application of planning, designing, constructing, maintaining, and operating infrastructures while protecting the public and environmental health, as well as improving existing infrastructures that have been neglected.Originally, a...
s predominantly work on problems that involve water and predominantly work on problems on earth (in earths gravity). For this class of problems, civil engineers will often write Darcy's law in a much simpler form :
where
is called
permeability, and is defined as
, and i is called the
hydraulic gradient. The hydraulic gradient is the rate of change of total head with distance. The total head,
at a point is defined as the height (measured relative to the datum) to which water would raise in a
piezometerA piezometer is either a device used to measure static liquid pressure in a system by measuring the height to which a column of the liquid rises against gravity, or a device which measures the pressure of groundwater at a specific point...
at that point. The total head is related to the excess water pressure by:
and the
is zero if the datum for head measurement is chosen at the same elevation as the origin for the depth, z used to calculate
.
Typical values of permeability
Values of the permeability,
, can vary by many orders of magnitude depending on the soil type. Clays may have permeability as small as about
, gravels may have permeability up to about
. Layering and heterogeneity and disturbance during the sampling and testing process make the accurate measurement of soil permeability a very difficult problem.
Flow nets
Darcy's Law applies in one, two or three dimensions. In two or three dimensions, steady state seepage is described by
Laplace's equationIn mathematics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties. This is often written as:where ∆ = ∇² is the Laplace operator and \varphi is a scalar function...
. Computer programs are available to solve this equation. But traditionally two-dimensional seepage problems were solved using and a graphical procedure known called flow nets. One set of lines in the flow net are in the direction of the water flow (flow lines), and the other set of lines are in the direction of constant total head (equipotential lines). Flow nets may be used for example to estimate the quantity of seepage under
damA dam is a barrier that impounds water or underground streams. Dams generally serve the primary purpose of retaining water, while other structures such as floodgates or levees are used to manage or prevent water flow into specific land regions. Hydropower and pumped-storage hydroelectricity are...
s and sheet piling.
Seepage forces and erosion
When the seepage velocity is great enough,
erosionErosion is when materials are removed from the surface and changed into something else. It only works by hydraulic actions and transport of solids in the natural environment, and leads to the deposition of these materials elsewhere...
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
sinkholeA sinkhole, also known as a sink, shake hole, swallow hole, swallet, doline or cenote, is a natural depression or hole in the Earth's surface caused by karst processes — the chemical dissolution of carbonate rocks or suffosion processes for example in sandstone...
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 pressures
Seepage in an upward direction reduces the effective stress within the soil. When the water pressure at a point in the soil is equal to the total vertical stress at that point, the effective stress is zero and the soil has no frictional resistance to deformation. For a surface layer, the vertical effective stress becomes zero within the layer when the upward hydraulic gradient is equal to the critical gradient. At zero effective stress soil has very little strength and layers of relatively impermeable soil may heave up due to the underlying water pressures. The loss in strength due to upward seepage is a common contributor to levee failures. The condition of zero effective stress associated with upward seepage is also called
liquefactionSoil liquefaction describes a phenomenon whereby a saturated soil substantially loses strength and stiffness in response to an applied stress, usually earthquake shaking or other sudden change in stress condition, causing it to behave like a liquid....
,
quicksandQuicksand is a colloid hydrogel consisting of fine granular matter , clay, and water.Water circulation underground can focus in an area with the optimal mixture of fine sands and other materials such as clay. The water moves up and then down slowly in a convection-like manner throughout a column...
, or a boiling condition. 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.)
Consolidation: transient flow of water
Consolidation is a process by which
soilSoil is a natural body consisting of layers of mineral constituents of variable thicknesses, which differ from the parent materials in their morphological, physical, chemical, and mineralogical characteristics...
s decrease in volume. It occurs when
stressIn continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...
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 time required to squeeze the water out of a thick deposit of clayey soil layer might be years. For a layer of sand, the water may be squeezed out in a matter of seconds. A building foundation or construction of a new embankment will cause the soil below to consolidate and this will cause settlement which in turn may cause distress to the building or embankment. Karl Terzaghi developed the theory of consolidation which enables prediction of the amount of settlement and the time required for the settlement to occur. Soils are tested with an
oedometer testGeotechnical investigations are performed by geotechnical engineers or engineering geologists to obtain information on the physical properties of soil and rock around a site to design earthworks and foundations for proposed structures and for repair of distress to earthworks and structures caused...
to determine their compression index and coefficient of consolidation.
When stress is removed from a consolidated soil, the soil will rebound, drawing water back into the pores and regaining some of the volume it had lost in the consolidation process. If the stress is reapplied, the soil will re-consolidate again along a recompression curve, defined by the recompression index. Soil that has been consolidated to a large pressure and has been subsequently unloaded is considered to be
overconsolidated. The maximum past vertical effective stress is termed the
preconsolidation stress. A soil which is currently experiencing the maximum past vertical effective stress is said to be
normally consolidated. The
overconsolidation ratio, (OCR) is the ratio of the maximum past vertical effective stress to the current vertical effective stress. The OCR is significant for two reasons: firstly, because the compressibility of normally consolidated soil is significantly larger than that for overconsolidated soil, and secondly, the shear behavior and dilatancy of clayey soil are related to the OCR through
critical state soil mechanicsCritical State Soil Mechanics is the area of Soil Mechanics that encompasses the conceptual models that represent the mechanical behavior of saturated remolded soils based on the Critical State concept.-Formulation:...
; highly overconsolidated clayey soils are dilatant, while normally consolidated soils tend to be contractive.
Shear behavior: stiffness and strength
The shear strength and stiffness of soil determines whether or not soil will be stable or how much it will deform. Knowledge of the strength is necessary to determine if a slope will be stable, if a building or bridge might settle too far into the ground, and the limiting pressures on a retaining wall. It is important to distinguish between failure of a soil element and the failure of a geotechnical structure (e.g., a building foundation, slope or retaining wall); some soil elements may reach their peak strength prior to failure of the structure. Different criteria can be used to define the "shear strength" and the "
yieldThe yield strength or yield point of a material is defined in engineering and materials science as the stress at which a material begins to deform plastically. Prior to the yield point the material will deform elastically and will return to its original shape when the applied stress is removed...
point" for a soil element from a
stress-strain curveDuring tensile testing of a material sample, the stress–strain curve is a graphical representation of the relationship between stress, derived from measuring the load applied on the sample, and strain, derived from measuring the deformation of the sample, i.e. elongation, compression, or distortion...
. One may define the peak shear strength as the peak of a stress strain curve, or the shear strength at critical state as the value after large strains when the shear resistance levels off. If the stress-strain curve does not stabilize before the end of shear strength test, the "strength" is sometimes considered to be the shear resistance at 15% to 20% strain. The shear strength of soil depends on many factors including the
effective stressKarl von Terzaghi first proposed the relationship for effective stress in 1936. For him, the term ‘effective’ meant the calculated stress that was effective in moving soil, or causing displacements...
and the void ratio.
The shear stiffness is important, for example, for evaluation of the magnitude of deformations of foundations and slopes prior to failure and because it is related to the shear wave velocity. The slope of the initial, nearly linear, portion of a plot of shear stress as a function of shear strain is called the
shear modulus
Friction, interlocking and dilation
Soil is an assemblage of particles that have little to no cementation while rock (such as sandstone) may consist of an assembly of particles that are strongly cemented together by chemical bonds. The shear strength of soil is primarily due to interparticle friction and therefore, the shear resistance on a plane is approximately proportional to the effective normal stress on that plane. But soil also derives significant shear resistance from interlocking of grains. If the grains are densely packed, the grains tend to spread apart from each other as they are subject to shear strain. The expansion of the particle matrix due to shearing was called dilatancy by
Osborne ReynoldsOsborne Reynolds FRS was a prominent innovator in the understanding of fluid dynamics. Separately, his studies of heat transfer between solids and fluids brought improvements in boiler and condenser design.-Life:...
. If one considers the energy required to shear an assembly of particles there is energy input by the shear force, T, moving a distance, x and there is also energy input by the normal force, N, as the sample expands a distance, y. Due to the extra energy required for the particles to dilate against the confining pressures, dilatant soils have a greater peak strength than contractive soils. Furthermore, as dilative soil grains dilate, they become looser (their void ratio increases), and their rate of dilation decreases until they reach a critical void ratio. Contractive soils become denser as they shear, and their rate of contraction decreases until they reach a critical void ratio.
The tendency for a soil to dilate or contract depends primarily on the confining pressure and the void ratio of the soil. The rate of dilation is high if the confining pressure is small and the void ratio is small. The rate of contraction is high if the confining pressure is large and the void ratio is large. As a first approximation, the regions of contraction and dilation are separated by the critical state line.
Failure criteria
After a soil reaches the critical state, it is no longer contracting or dilating and the shear stress on the failure plane
is determined by the effective normal stress on the failure plane
and critical state friction angle
:
The peak strength of the soil may be greater, however, due to the interlocking (dilatancy) contribution.
This may be stated:
Where
. However, use of a friction angle greater than the critical state value for design requires care. The peak strength will not be mobilized everywhere at the same time in a practical problem such as a foundation, slope or retaining wall. The critical state friction angle is not nearly as variable as the peak friction angle and hence it can be relied upon with confidence.
Not recognizing the significance of dilatancy, Coulomb proposed that the shear strength of soil may be expressed as a combination of adhesion and friction components :
It is now known that the
and
parameters in the last equation are not fundamental soil properties. In particular,
and
are different depending on the magnitude of effective stress. According to Schofield (2006), the longstanding use of
in practice has led many engineers to wrongly believe that
is a fundamental parameter. This assumption that
and
are constant can lead to overestimation of peak strengths.
Structure, fabric, and chemistry
In addition to the friction and interlocking (dilatancy) components of strength, the structure and fabric also play a significant role in the soil behavior. The structure and fabric include factors such as the spacing and arrangement of the solid particles or the amount and spatial distribution of pore water; in some cases cementitious material accumulates at particle-particle contacts. Mechanical behavior of soil is affected by the density of the particles and their structure or arrangement of the particles as well as the amount and spatial distribution of fluids present (e.g., water and air voids). Other factors include the electrical charge of the particles, chemistry of pore water, chemical bonds (i.e. cementation -particles connected through a solid substance such as recrystallized calcium carbonate)
Drained and undrained shear
The presence of nearly incompressible fluids such as water in the pore spaces affects the ability for the pores to dilate or contract.
If the pores are saturated with water, water must be sucked into the dilating pore spaces to fill the expanding pores (this phenomenon is visible at the beach when apparently dry spots form around feet that press into the wet sand).
Similarly, for contractive soil, water must be squeezed out of the pore spaces to allow contraction to take place.
Dilation of the voids causes negative water pressures that draw fluid into the pores, and contraction of the voids causes positive pore pressures to push the water out of the pores. If the rate of shearing is very large compared to the rate that water can be sucked into or squeezed out of the dilating or contracting pore spaces, then the shearing is called undrained shear, if the shearing is slow enough that the water pressures are negligible, the shearing is called drained shear. During undrained shear, the water pressure u changes depending on volume change tendencies. From the effective stress equation, the change in u directly effects the effective stress by the equation:
and the strength is very sensitive to the effective stress. It follows then that the undrained shear strength of a soil may be smaller or larger than the drained shear strength depending upon whether the soil is contractive or dilative.
Shear tests
Strength parameters can be measured in the laboratory using direct shear testA direct shear test also known as shearbox test is a laboratory or field test used by geotechnical engineers to measure the shear strength properties of soil or rock material, or of discontinuties in soil or rock masses.- Soil :...
, triaxial shear test, simple shear test, fall cone test and vane shear test; there are numerous other devices and variations on these devices used in practice today. Tests conducted to characterize the strength and stiffness of the soils in the ground include the Cone penetration testThe cone penetration test is an gouda cpt testing method used to determine the geotechnical engineering properties of soils and delineating soil stratigraphy. It was initially developed in the 1950s at the Dutch Laboratory for Soil Mechanics in Delft to investigate soft soils. Based on this...
and the Standard penetration testThe standard penetration test is an in-situ dynamic penetration test designed to provide information on the geotechnical engineering properties of soil...
.
Other factors
The stress-strain relationship of soils, and therefore the shearing strength, is affected by :
- 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.
- 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.
- 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.
- Loading conditions: Effective stress path -drained, undrained, and type of loading -magnitude, rate (static, dynamic), and time history (monotonic, cyclic).
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) effective stress to vertical effective 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 stressIn continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...
between a foundationA foundation is the lowest and supporting layer of a structure. Foundations are generally divided into two categories: shallow foundations and deep foundations.-Shallow foundations:...
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.
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 been analyzed only after the fact.
See also
- Critical state soil mechanics
Critical State Soil Mechanics is the area of Soil Mechanics that encompasses the conceptual models that represent the mechanical behavior of saturated remolded soils based on the Critical State concept.-Formulation:...
- Earthquake engineering
Earthquake engineering is the scientific field concerned with protecting society, the natural and the man-made environment from earthquakes by limiting the seismic risk to socio-economically acceptable levels...
- Engineering geology
Engineering geology is the application of the geologic sciences to engineering practice for the purpose of assuring that the geologic factors affecting the location, design, construction, operation and maintenance of engineering works are recognized and adequately provided for...
- Geotechnical engineering
Geotechnical engineering is the branch of civil engineering concerned with the engineering behavior of earth materials. Geotechnical engineering is important in civil engineering, but is also used by military, mining, petroleum, or any other engineering concerned with construction on or in the ground...
- Geotechnics
Geotechnics is the application of scientific methods and engineering principles to the acquisition, interpretation, and use of knowledge of materials of the Earth's crust and earth materials for the solution of engineering problems...
- Rock mechanics
Rock mechanics is the theoretical and applied science of the mechanical behaviour of rock and rock masses;also compared to the geology, it is that branch of mechanics concerned with the response of rock and rock masses to the force fields of their physical environment.Rock mechanics itself forms...
- Slope stability analysis
The slope stability analyses are performed to assess the safe and economic design of a human-made or natural slopes and the equilibrium conditions. The term slope stability may be defined as the resistance of inclined surface to failure by sliding or collapsing...
- Hydrogeology
Hydrogeology is the area of geology that deals with the distribution and movement of groundwater in the soil and rocks of the Earth's crust, . The term geohydrology is often used interchangeably...
, aquifer characteristics closely related to soil characteristics
- Wiktionary seepage