Soil mechanics

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(Redirected from Seepage)

Soil mechanics is a branch of engineering mechanics that describes the behavior of soils. 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 clay, silt, sand, and gravel) but soil may also contain organic solids, liquids,
and gasses and other matter.[1][2][3][4] Along with rock mechanics, soil mechanics provides the theoretical basis
for analysis in geotechnical engineering,[5] a subdiscipline of Civil engineering, andengineering geology, a
subdiscipline of geology. 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.
[6]

Example 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 engineering
geology, geophysical engineering, coastal engineering, agricultural engineering, hydrology and soil physics.

The Tower of Pisa -- an example of a problem due to deformation of soil.

This article describes the genesis and composition of soil, the distinction between pore water pressure and
inter-granulareffective 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.[6] The article concludes with some examples of applications of the principles of soil mechanics such as
slope stability, lateral earth pressure on retaining walls, and bearing capacity of foundations.

Slope instability issues for a temporary flood control levee in North Dakota, 2009

Earthwork in Germany

Fox Glacier, New Zealand: Soil produced and transported by intense weathering and erosion.

Contents
[hide]

1 Genesis and composition of soils

1.1 Genesis

1.2 Transport

1.3 Soil composition

1.3.1 Soil mineralogy

1.3.2 Grain size distribution

1.3.2.1 Sieve analysis

1.3.2.2 Hydrometer analysis

1.3.3 Mass-volume relations

2 Effective stress and capillarity: hydrostatic conditions

2.1 Total stress

2.2 Pore water pressure

2.2.1 Hydrostatic conditions

2.2.2 Capillary action

3 Soil classification
3.1 Classification of soil grains

3.1.1 Classification of sands and gravels

3.1.2 Atterberg limits

3.1.3 Classification of silts and clays

3.2 Indices related to soil strength

3.2.1 Liquidity index

3.2.2 Relative density

4 Seepage: steady state flow of water

4.1 Darcy's law

4.2 Typical values of permeability

4.3 Flownets

4.4 Seepage forces and erosion

4.5 Seepage pressures

5 Consolidation: transient flow of water

6 Shear behavior: stiffness and strength

6.1 Friction, interlocking and dilation

6.2 Failure criteria

6.3 Structure, fabric, and chemistry

6.4 Drained and undrained shear

6.5 Shear tests

6.6 Other factors

7 Applications

7.1 Lateral earth pressure

7.2 Bearing capacity

7.3 Slope stability

8 See also

9 References

Genesis and composition of soils[edit source | editbeta]

Genesis[edit source | editbeta]
The primary mechanism of soil creation is the weathering of rock. All rock types (igneous rock, metamorphic
rock andsedimentary rock) may be broken down into small particles to create soil. Weathering mechanisms are
physical weathering, chemical weathering, and biological weathering

[1][2][3]

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.[3]

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. Clay minerals, for example can be formed by weathering of feldspar, which is the
most common mineral present in igneous rock.
The most common mineral constituent of silt and sand is 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.
Silt, Sand, and Gravel are basically little pieces of broken rocks.
According to the Unified Soil Classification System, 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. [1][2]

Transport[edit source | editbeta]

Example soil horizons. a) top soil and colluvium b) mature residual soil c) young residual soil d) weathered rock.

Soil deposits are affected by the mechanism of transport and deposition to their location. Soils that are not
transported are called residual soilsthey exist at the same location as the rock from which they were
generated. Decomposed granite 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 loess. 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 glaciers 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 colluvium.[1][2]

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 composition[edit source | editbeta]

Soil mineralogy[edit source | editbeta]
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. [1] The mineral constituents of
gravel may be more similar to that of the parent rock.
The common clay minerals are montmorillonite or smectite, illite, and kaolinite or kaolin. These minerals tend to
form in sheet or plate like structures, with length typically ranging between 10 7 m and 4x106 m and thickness
typically ranging between 109 m and 2x106 m, 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.
[3]

Due to the large surface area available for chemical, electrostatic, and van der Waals 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.[1]
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. [1]

Grain size distribution[edit source | editbeta]

Main article: Soil gradation
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 conductivity, 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 measuringparticle size
distribution. The two traditional methods are sieve analysis and hydrometer analysis.

Sieve analysis[edit source | editbeta]

Sieve

The size distribution of gravel and sand particles are typically measured using sieve analysis. The formal
procedure is described in ASTM D6913-04(2009). [7] 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 System, 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.[3]

Hydrometer analysis[edit source | editbeta]

The classification of fine-grained soils, i.e., soils that are finer than sand, is determined primarily by
their Atterberg limits, not by their grain size. If it is important to determine the grain size distribution of finegrained 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 hydrometer 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
motion, in which case they may be classified as colloids.

Mass-volume relations[edit source | editbeta]

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

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. [2][6] The basic notation is as follows:
,

, and
,
,

, and

represent the volumes of air, water and solids in a soil mixture;

represent the weights of air, water and solids in a soil mixture;

, and
, and

represent the masses of air, water and solids in a soil mixture;

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 Gravity 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
) of a material by the acceleration due to gravity,
Density, Bulk Density, or Wet Density,

may be obtained by multiplying the 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 submerged 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:

Porosity,

, 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[edit source | editbeta]

Spheres immersed in water, reducing effective stress.

Main article: Effective stress

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 stress. 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 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 ' (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 is the total stress and u is the pore pressure. It is

not practical to measure ' 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, pressure 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[edit source | editbeta]

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 pressures are addressed
elsewhere.

Pore water pressure[edit source | editbeta]

Main article: Pore water pressure

Hydrostatic conditions[edit source | editbeta]

Water is drawn into a small tube by surface tension. Water

pressure, u, is negative above and positive below the free
water surface

If there is no pore water flow occurring in the soil, the

pore water pressures will be hydrostatic. The water
table 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[edit source | editbeta]

Water at particle contacts

Due to surface tension 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.[3] In
fact the pore space of soil is a uniform fractal e.g. a
set of uniformly distributed D-dimensional fractals of
average linear size L. For the clay soil is has been
found that L=0.15 mm and D=2.7.[8]

intergranular contact force due to surface tension.

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.[9]

Shrinkage caused by drying

Later sections of this article address the pore water

pressures for seepage and consolidation problems.

Soil classification[edit
source | editbeta]
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. Engineering
geologists also classify soils based on their genesis
and depositional history.

Classification of soil grains[edit

source | editbeta]
In the US and other countries, the Unified Soil
Classification System (USCS) is often used for soil
classification. Other classification systems include
the British Standard BS5390 and the AASHTO soil
classification system.[3]

Classification of sands and gravels[edit

source | editbeta]
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[edit source | editbeta]

Clays and Silts, often called 'fine-grained soils', are
classified according to their Atterberg limits; the
most commonly used Atterberg limits are the Liquid
limit (denoted by LL or
by PL or

), Plastic Limit (denoted

), 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.[10] 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.[4]
[11]

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.[4][11]
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 [edit

source | editbeta]
According to the Unified Soil Classification
System (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'.

Indices related to soil strength[edit

source | editbeta]
Liquidity index[edit source | editbeta]
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.[4][12]

Relative density[edit source | editbeta]

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

is the in

situ void ratio. Methods used to calculate

relative density are defined in ASTM
D4254-00(2006).[13]
Thus if

the sand or

gravel is very dense, and if

the soil is extremely loose and unstable.

Seepage: steady state flow

of water[edit source | editbeta]
"Seepage" redirects here. For the Tech
N9ne EP, see Seepage (EP).

A cross section showing the water table

varying with surface topography as well as
a perched water table.

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[edit
source | editbeta]
Darcy's law 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

Diagram showing definitions and directions

for Darcy's law.

The total discharge,

(having units

of volume per time, e.g., ft/s or m/s),

is proportional to the intrinsic
permeability,
area,

, the cross sectional

, and rate of pore pressure

change with distance,

and inversely proportional to

thedynamic 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 derivative, we
obtain a more general equation
for the apparent velocity in the xdirection:

where

has

units of velocity and is called

the Darcy velocity (or
the specific
discharge, filtration velocity,
or superficial velocity).
The pore or interstitial
velocity

is the average

velocity of fluid molecules in

the pores; it is related to the
Darcy velocity and the
porosity

through

the Dupuit-Forchheimer
relationship

(Some authors use the

term seepage velocity to
mean the Darcy
velocity,[14] while others
use it to mean the pore
velocity.[15])
Civil
engineers predominantl
y work on problems that
involve water and

predominantly work on
problems on earth (in
earth's gravity). For this
class of problems, civil
engineers will often
write Darcy's law in a
much simpler form:[4][6][9]

where

is

the hydraulic
conductivity,
defined

as
and

,
is

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
rise in
a piezometer at
that point. The total
head is related to
the excess water
pressure by:

and
the
i
s 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
permeabil
ity[edit
source | edi
tbeta]
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.[4]

Flownets[
edit
source | edi
tbeta]
Main
article: Flowne
t
Darcy's Law
applies in one,
two or three
dimensions.[3] I
n two or three
dimensions,
steady state
seepage is
described

by Laplace's
equation.
Computer
programs are
available to
solve this
equation. But
traditionally
twodimensional
seepage
problems were
solved using
and a
graphical
procedure
known
called flownet.
[3][9][16]

One set

of lines in the
flownet 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).
Flownets may
be used to
estimate the
quantity of
seepage

under dams an
d sheet piling.

A plan flow
net to
estimate
flow of water
from a
stream to a
discharging
well

Seepage
forces
and
erosion[ed
it
source | edi
tbeta]
When the
seepage
velocity is
great
enough, erosio
n 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 "soil
piping", can
lead to failure
of the structure
and
to sinkhole for
mation.
Seeping water
removes soil,
starting from
the exit point of
the seepage,
and erosion
advances
upgradient.[17]
The term "sand
boil" is used to
describe the
appearance of
the discharging
end of an
active soil
pipe.[18]

Seepage
pressures
[edit
source | edi
tbeta]
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.[9] 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 liquefact
ion, quicksand,
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.)[19]

Consolida
tion:
transient
flow of
water[edit
source | edi
tbeta]
Main
article: Consoli
dation (soil)

Consolidation
analogy. The
piston is
supported by
water
underneath and
a spring. When a
load is applied to
the piston, water
pressure
increases to
support the load.
As the water
slowly leaks
through the
small hole, the
load is
transferred from
the water
pressure to the
spring force.

Consolidation
is a process by
which soils dec
rease 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
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 devel
oped the
theory of
consolidation
which enables
prediction of
the amount of
settlement and
the time
required for the
settlement to
occur.[20] Soils
are tested with
an oedometer
test 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 reconsolidate
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 overconsoli
dated. The
maximum past
vertical
effective stress
is termed
the preconsoli
dation stress. A
soil which is
currently

experiencing
the maximum
past vertical
effective stress
is said to
be normally
consolidated.
The overconso
lidation 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
overconsolidat
ed soil, and
secondly, the
shear behavior
and dilatancy
of clayey soil

are related to
the OCR
through critical
state soil
mechanics;
highly
overconsolidat
ed clayey soils
are dilatant,
while normally
consolidated
soils tend to be
contractive.[2][3]
[4]

Shear
behavior:
stiffness
and
strength[e
dit
source | edi
tbeta]
Main
article: shear
strength (soil)

Typical
stress strain

curve for a
drained
dilatant soil

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
"yield point" for
a soil element
from a stressstrain curve.
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.[9] The
shear strength
of soil depends
on many
factors
including
the effective
stress 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,
interlocki
ng and
dilation[ed
it
source | edi
tbeta]
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.
[3]

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
Reynolds.[12] 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.
[12]

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.

A critical
state line
separates
the dilatant
and
contractive

states for
soil

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[edi

t
source | edi
tbeta]
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
interlockin
g
(dilatancy)
contributio
n. This
may be
stated:

Wher
e

.
Howe
ver,
use of
a
frictio
n
angle
great
er
than
the
critica
l state
value
for
desig
n
requir
es
care.
The
peak
stren
gth
will
not
be
mobili
zed
every

where
at the
same
time
in a
practi
cal
probl
em
such
as a
found
ation,
slope
or
retaini
ng
wall.
The
critica
l state
frictio
n
angle
is not
nearly
as
variab
le as
the
peak
frictio
n
angle
and
hence

it can
be
relied
upon
with
confid
ence.
[3][4][12]

Not
recog
nizing
the
signifi
cance
of
dilata
ncy,
Coulo
mb
propo
sed
that
the
shear
stren
gth of
soil
may
be
expre
ssed
as a
combi
nation
of

adhes
ion
and
frictio
n
comp
onent
s:[12]

It
is
n
o
w
k
n
o
w
n
t
h
a
t
t
h
e

a
n
d

p
a
r
a

m
e
t
e
r
s
i
n
t
h
e
l
a
s
t
e
q
u
a
ti
o
n
a
r
e
n
o
t
f
u
n
d
a
m
e
n

t
a
l
s
o
il
p
r
o
p
e
rt
i
e
s
.
[3]
[6]
[1
2]
[2
1]

I
n
p
a
rt
ic
u
l
a
r,

a
n
d

a
r
e
d
if
f
e
r
e
n
t
d
e
p
e
n
d
i
n
g
o
n
t
h
e
m
a
g
n
it
u
d
e
o
f

e
ff
e
c
ti
v
e
s
tr
e
s
s
.
[6]
[2
1]

A
c
c
o
r
d
i
n
g
t
o
S
c
h
o
fi
e
l
d
(

2
0
0
6
),
[1
2]

t
h
e
l
o
n
g
s
t
a
n
d
i
n
g
u
s
e
o
f

i
n
p
r
a
c
ti
c

e
h
a
s
l
e
d
m
a
n
y
e
n
g
i
n
e
e
r
s
t
o
w
r
o
n
g
ly
b
e
li
e
v
e
t
h

a
t

is
a
f
u
n
d
a
m
e
n
t
a
l
p
a
r
a
m
e
t
e
r.
T
h
is
a
s
s
u
m
p
ti
o

n
t
h
a
t

a
n
d

a
r
e
c
o
n
s
t
a
n
t
c
a
n
l
e
a
d
t
o
o
v
e
r
e
s

ti
m
a
ti
o
n
o
f
p
e
a
k
s
tr
e
n
g
t
h
s
.
[3]
[2
1]

S
t
r
u
c
t
u
r
e
,
f

a
b
r
i
c
,
a
n
d
c
h
e
m
i
s
t
r
y
[
e
d
it
s
o
u
r
c
e
|
e
d
it
b
et

]
I
n
a
d
d
iti
o
n
t
o
t
h
e
fr
ic
ti
o
n
a
n
d
i
n
t
e
rl
o
c
ki
n
g
(
d

il
a
t
a
n
c
y
)
c
o
m
p
o
n
e
n
t
s
o
f
s
tr
e
n
g
t
h
,
t
h
e
s
tr
u
c
t

u
r
e
a
n
d
f
a
b
ri
c
a
ls
o
p
l
a
y
a
si
g
n
ifi
c
a
n
t
r
o
l
e
i
n
t
h
e

s
o
il
b
e
h
a
vi
o
r.
T
h
e
s
tr
u
c
t
u
r
e
a
n
d
f
a
b
ri
c
i
n
cl
u
d
e
f

a
c
t
o
r
s
s
u
c
h
a
s
t
h
e
s
p
a
ci
n
g
a
n
d
a
rr
a
n
g
e
m
e
n
t
o
f

t
h
e
s
o
li
d
p
a
rt
ic
l
e
s
o
r
t
h
e
a
m
o
u
n
t
a
n
d
s
p
a
ti
a
l
d
is

tr
i
b
u
ti
o
n
o
f
p
o
r
e
w
a
t
e
r;
i
n
s
o
m
e
c
a
s
e
s
c
e
m
e
n
ti
ti

o
u
s
m
a
t
e
ri
a
l
a
c
c
u
m
u
l
a
t
e
s
a
t
p
a
rt
ic
l
e
p
a
rt
ic
l
e

c
o
n
t
a
c
t
s
.
M
e
c
h
a
n
ic
a
l
b
e
h
a
vi
o
r
o
f
s
o
il
is
a
ff
e
c
t

e
d
b
y
t
h
e
d
e
n
si
t
y
o
f
t
h
e
p
a
rt
ic
l
e
s
a
n
d
t
h
e
ir
s
tr
u
c

t
u
r
e
o
r
a
rr
a
n
g
e
m
e
n
t
o
f
t
h
e
p
a
rt
ic
l
e
s
a
s
w
e
ll
a
s
t

h
e
a
m
o
u
n
t
a
n
d
s
p
a
ti
a
l
d
is
tr
i
b
u
ti
o
n
o
f
fl
u
i
d
s
p
r
e

s
e
n
t
(
e
.
g
.,
w
a
t
e
r
a
n
d
a
ir
v
o
i
d
s
).
O
t
h
e
r
f
a
c
t
o
r

s
i
n
cl
u
d
e
t
h
e
e
l
e
c
tr
ic
a
l
c
h
a
r
g
e
o
f
t
h
e
p
a
rt
ic
l
e
s

,
c
h
e
m
is
tr
y
o
f
p
o
r
e
w
a
t
e
r,
c
h
e
m
ic
a
l
b
o
n
d
s
(i
.
e
.
c

e
m
e
n
t
a
ti
o
n
p
a
rt
ic
l
e
s
c
o
n
n
e
c
t
e
d
t
h
r
o
u
g
h
a
s
o

li
d
s
u
b
s
t
a
n
c
e
s
u
c
h
a
s
r
e
c
r
y
s
t
a
lli
z
e
d
c
a
lc
i
u
m

c
a
r
b
o
n
a
t
e
)
[1]
[2
1]

D
r
a
i
n
e
d
a
n
d
u
n
d
r
a
i
n
e
d

s
h
e
a
r
[
e
d
it
s
o
u
r
c
e
|
e
d
it
b
et
a

]
T
h
e
p
r
e
s
e
n
c
e
o

f
n
e
a
rl
y
i
n
c
o
m
p
r
e
s
si
b
l
e
fl
u
i
d
s
s
u
c
h
a
s
w
a
t
e
r
i

n
t
h
e
p
o
r
e
s
p
a
c
e
s
a
ff
e
c
t
s
t
h
e
a
b
ili
t
y
f
o
r
t
h
e
p
o

r
e
s
t
o
d
il
a
t
e
o
r
c
o
n
tr
a
c
t.
If
t
h
e
p
o
r
e
s
a
r
e
s
a
t
u

r
a
t
e
d
w
it
h
w
a
t
e
r,
w
a
t
e
r
m
u
s
t
b
e
s
u
c
k
e
d
i
n
t
o
t
h

e
d
il
a
ti
n
g
p
o
r
e
s
p
a
c
e
s
t
o
fil
l
t
h
e
e
x
p
a
n
d
i
n
g
p
o
r

e
s
(t
h
is
p
h
e
n
o
m
e
n
o
n
is
vi
si
b
l
e
a
t
t
h
e
b
e
a
c
h
w
h
e
n
a

p
p
a
r
e
n
tl
y
d
r
y
s
p
o
t
s
f
o
r
m

a
r
o
u
n
d
f
e
e
t
t
h
a
t
p

r
e
s
s
i
n
t
o
t
h
e
w
e
t
s
a
n
d
).

Fo
ot
pr
es
sin
g
in
soi
l
ca

us
es
soi
l to
dil
ate
,
dr
aw
ing
wa
ter
fro
m
the
sur
fac
e
int
o
the
po
res

S
i
m
il
a
rl
y,
f
o
r
c
o
n

tr
a
c
ti
v
e
s
o
il,
w
a
t
e
r
m
u
s
t
b
e
s
q
u
e
e
z
e
d
o
u
t
o
f
t
h
e

p
o
r
e
s
p
a
c
e
s
t
o
a
ll
o
w
c
o
n
tr
a
c
ti
o
n
t
o
t
a
k
e
p
l
a
c

e
.
D
il
a
ti
o
n
o
f
t
h
e
v
o
i
d
s
c
a
u
s
e
s
n
e
g
a
ti
v
e
w
a
t
e

r
p
r
e
s
s
u
r
e
s
t
h
a
t
d
r
a
w
fl
u
i
d
i
n
t
o
t
h
e
p
o
r
e
s
,
a

n
d
c
o
n
tr
a
c
ti
o
n
o
f
t
h
e
v
o
i
d
s
c
a
u
s
e
s
p
o
si
ti
v
e
p
o
r

e
p
r
e
s
s
u
r
e
s
t
o
p
u
s
h
t
h
e
w
a
t
e
r
o
u
t
o
f
t
h
e
p
o
r
e

s
.
If
t
h
e
r
a
t
e
o
f
s
h
e
a
ri
n
g
is
v
e
r
y
l
a
r
g
e
c
o
m
p
a
r
e

d
t
o
t
h
e
r
a
t
e
t
h
a
t
w
a
t
e
r
c
a
n
b
e
s
u
c
k
e
d
i
n
t
o
o
r

s
q
u
e
e
z
e
d
o
u
t
o
f
t
h
e
d
il
a
ti
n
g
o
r
c
o
n
tr
a
c
ti
n
g
p
o
r

e
s
p
a
c
e
s
,
t
h
e
n
t
h
e
s
h
e
a
ri
n
g
is
c
a
ll
e
d
u
n
d
r
a
i
n
e

d
s
h
e
a
r,
if
t
h
e
s
h
e
a
ri
n
g
is
sl
o
w
e
n
o
u
g
h
t
h
a
t
t
h
e
w
a

t
e
r
p
r
e
s
s
u
r
e
s
a
r
e
n
e
g
li
g
i
b
l
e
,
t
h
e
s
h
e
a
ri
n
g
is

c
a
ll
e
d
d
r
a
i
n
e
d
s
h
e
a
r.
D
u
ri
n
g
u
n
d
r
a
i
n
e
d
s
h
e
a
r,

t
h
e
w
a
t
e
r
p
r
e
s
s
u
r
e
u
c
h
a
n
g
e
s
d
e
p
e
n
d
i
n
g
o
n
v

o
l
u
m
e
c
h
a
n
g
e
t
e
n
d
e
n
ci
e
s
.
F
r
o
m

t
h
e
e
ff
e
c
ti
v
e

s
tr
e
s
s
e
q
u
a
ti
o
n
,
t
h
e
c
h
a
n
g
e
i
n
u
d
ir
e
c
tl
y
e
ff
e
c
t

s
t
h
e
e
ff
e
c
ti
v
e
s
tr
e
s
s
b
y
t
h
e
e
q
u
a
ti
o
n
:

an
d
the
str
en

gth
is
ver
y
se
nsi
tiv
e
to
the
eff
ect
ive
str
es
s.
It
foll
ow
s
the
n
tha
t
the
un
dra
ine
d
sh
ear
str
en
gth
of
a

soil
ma
y
be
sm
all
er
or
lar
ger
tha
n
the
dra
ine
d
sh
ear
str
en
gth
de
pe
ndi
ng
up
on
wh
eth
er
the
soil
is
co
ntr
act

ive
or
dil
ati
ve.

S
h
e
ar
te
st
s[
ed
it
so
ur
ce
|e
dit
bet
a]

Str
en
gth
par
am
ete
rs
ca
n
be
me
as
ure
d

in
the
lab
ora
tor
y
usi
ng
dir
ect
sh
ear
tes
t, tr
iaxi
al
sh
ear
tes
t, s
im
ple
sh
ear
tes
t, f
all
co
ne
tes
ta
nd
va
ne
sh
ear

tes
t;
the
re
are
nu
me
rou
s
oth
er
de
vic
es
an
d
var
iati
on
s
on
the
se
de
vic
es
us
ed
in
pra
ctic
e
tod
ay.
Te
sts

co
nd
uct
ed
to
ch
ara
cte
riz
e
the
str
en
gth
an
d
stif
fne
ss
of
the
soil
s
in
the
gro
un
d
incl
ud
e
the
Co
ne
pe
net

rati
on
tes
ta
nd
the
Sta
nd
ard
pe
net
rati
on
tes
t.

O
th
er
fa
ct
or
s[
ed
it
so
ur
ce
|e
dit
bet
a]

Th
e
str
es

sstr
ain
rel
ati
on
shi
p
of
soil
s,
an
d
the
ref
ore
the
sh
ear
ing
str
en
gth
, is
aff
ect
ed
by:
[22]

1.

soil
co
mp
osit
ion
(ba

sic
soil
mat
eria
l):
min
eral
ogy
,
grai
n
siz
e
and
grai
n
siz
e
dist
ribu
tion
,
sha
pe
of
part
icle
s,
por
e
flui
d
typ
e
and
con

tent
,
ion
s
on
grai
n
and
in
por
e
flui
d.
2.

stat
e (i
niti
al):
Def
ine
by
the
initi
al v
oid
rati
o,
effe
ctiv
e
nor
mal
stre
ss
and
she

ar
stre
ss
(str
ess
hist
ory)
.
Sta
te
can
be
des
crib
e
by
ter
ms
suc
h
as:
loo
se,
den
se,
ove
rco
nso
lida
ted,
nor
mal
ly
con
soli
dat

ed,
stiff
,
soft
,
con
trac
tive
,
dila
tive
,
etc.
3.

str
uct
ure:
Ref
ers
to
the
arr
ang
em
ent
of
part
icle
s
wit
hin
the
soil
ma
ss;
the

ma
nne
r in
whi
ch
the
part
icle
s
are
pac
ked
or
dist
ribu
ted.
Fea
ture
s
suc
h
as
lay
ers,
join
ts,
fiss
ure
s,
slic
ken
sid
es,
voi
ds,
poc

ket
s,
ce
me
ntat
ion,
etc.
,
are
part
of
the
stru
ctur
e.
Str
uct
ure
of
soil
s is
des
crib
ed
by
ter
ms
suc
h
as:
und
istu
rbe
d,
dist
urb

ed,
rem
old
ed,
co
mp
act
ed,
ce
me
nte
d;
floc
cul
ent,
hon
eyco
mb
ed,
sin
glegrai
ned
;
floc
cul
ate
d,
defl
occ
ulat
ed;
stra
tifie
d,

lay
ere
d,
lam
inat
ed;
isot
ropi
c
and
ani
sotr
opi
c.
4.

Lo
adi
ng
con
diti
ons
:
Eff
ecti
ve
stre
ss
pat
hdrai
ned
,
und
rain
ed,
and

typ
e of
loa
din
g
-ma
gnit
ude
,
rate
(sta
tic,
dyn
ami
c),
and
tim
e
hist
ory
(mo
not
oni
c,
cycl
ic).

A
p
pl
ic
at
io
n
s[
ed

it
so
ur
ce
|e
dit
bet
a]

L
at
er
al
e
ar
th
pr
e
s
s
ur
e[
ed
it
so
ur
ce
|e
dit
bet
a]

Ma
in
arti
cle
:L

ate
ral
ea
rth
pr
es
sur
e
Lat
era
l
ear
th
str
es
s
the
ory
is
us
ed
to
est
im
ate
the
am
ou
nt
of
str
es
s
soil
ca

n
ex
ert
per
pe
ndi
cul
ar
to
gra
vity
.
Thi
s is
the
str
es
s
ex
ert
ed
on
ret
ain
ing
wal
ls.
A
lat
era
l
ear
th
str
es
s

co
effi
cie
nt,
K,
is
def
ine
d
as
the
rati
o
of
lat
era
l
(ho
riz
ont
al)
eff
ect
ive
str
es
s
to
ver
tic
al
eff
ect
ive
str
es

s
for
co
he
sio
nle
ss
soil
s
(K
='
/'

).

Th
ere
are
thr
ee
co
effi
cie
nts
:
atres
t,
act
ive
,
an
d
pa
ssi
ve.
Atres

t
str
es
s is
the
lat
era
l
str
es
s
in
the
gro
un
d
bef
ore
an
y
dis
tur
ba
nc
e
tak
es
pla
ce.
Th
e
act
ive
str
es
s

sta
te
is
rea
ch
ed
wh
en
a
wal
l
mo
ve
s
aw
ay
fro
m
the
soil
un
der
the
infl
ue
nc
e
of
lat
era
l
str
es
s,
an
d

res
ult
s
fro
m
sh
ear
fail
ure
du
e
to
red
uct
ion
of
lat
era
l
str
es
s.
Th
e
pa
ssi
ve
str
es
s
sta
te
is
rea
ch
ed

wh
en
a
wal
l is
pu
sh
ed
int
o
the
soil
far
en
ou
gh
to
ca
us
e
sh
ear
fail
ure
wit
hin
the
ma
ss
du
e
to
inc
rea
se
of

lat
era
l
str
es
s.
Th
ere
are
ma
ny
the
ori
es
for
est
im
ati
ng
lat
era
l
ear
th
str
es
s;
so
me
are
em
piri
call
yb
as
ed,

an
d
so
me
are
an
aly
tic
ally
der
ive
d.

B
e
ar
in
g
c
a
p
a
ci
ty
[e
dit
so
ur
ce
|e
dit
bet
a]

Ma
in
arti

cle
:B
ea
rin
g
ca
pa
cit
y
Th
e
be
ari
ng
ca
pa
city
of
soil
is
the
av
era
ge
co
nta
ct
str
es
sb
et
we
en
af
ou

nd
ati
on
an
d
the
soil
whi
ch
will
ca
us
e
sh
ear
fail
ure
in
the
soil
.
All
ow
abl
e
be
ari
ng
str
es
s is
the
be
ari
ng
ca

pa
city
divi
de
d
by
a
fac
tor
of
saf
ety
.
So
me
tim
es,
on
sof
t
soil
sit
es,
lar
ge
set
tle
me
nts
ma
y
oc
cur
un
der
loa

de
d
fou
nd
ati
on
s
wit
ho
ut
act
ual
sh
ear
fail
ure
oc
cur
rin
g;
in
su
ch
ca
se
s,
the
all
ow
abl
e
be
ari
ng
str
es

s is
det
er
mi
ne
d
wit
h
reg
ard
to
the
ma
xi
mu
m
all
ow
abl
e
set
tle
me
nt.

Sl
o
p
e
st
a
bi
lit
y[
ed
it

so
ur
ce
|e
dit
bet
a]

Simple
slope
slip
section

Ma
in
arti
cle
:S
lop
e
sta
bili
ty
Th
e
fiel
d
of
slo

pe
sta
bilit
y
en
co
mp
as
se
s
the
an
aly
sis
of
sta
tic
an
d
dy
na
mi
c
sta
bilit
y
of
slo
pe
s
of
ear
th
an
d
roc

kfill
da
ms
,
slo
pe
s
of
oth
er
typ
es
of
em
ba
nk
me
nts
,
ex
ca
vat
ed
slo
pe
s,
an
d
nat
ura
l
slo
pe
s
in

soil
an
d
sof
t
roc
k.
[23]

As
se
en
to
the
rig
ht,
ear
the
n
slo
pe
s
ca
n
de
vel
op
a
cut
sp
her
ical
we
ak
ne

ss
zo
ne.
Th
e
pro
ba
bilit
y
of
thi
s
ha
pp
eni
ng
ca
n
be
cal
cul
ate
d
in
ad
va
nc
e
usi
ng
a
si
mp
le
2D

cir
cul
ar
an
aly
sis
pa
ck
ag
e...
[24]

A
pri
ma
ry
diff
icul
ty
wit
h
an
aly
sis
is
loc
ati
ng
the
mo
stpro
ba
ble
slip
pla
ne

for
an
y
giv
en
sit
uat
ion
.[25]
Ma
ny
lan
dsli
de
s
ha
ve
be
en
an
aly
ze
d
onl
y
aft
er
the
fac
t.

S
e
e
al
s

o[
ed
it
so
ur
ce
|e
dit
bet
a]

Crit
ical
stat
e
soil
me
cha
nic
s

Ear
thq
uak
e
en
gin
eer
ing

En
gin
eer
ing
ge

olo
gy

Ge
ote
chn
ical
en
gin
eer
ing

Ge
ote
chn
ics

Ro
ck
me
cha
nic
s

Slo
pe
sta
bilit
y
an
aly
sis

Hy
dro
ge
olo

gy,
aq
uife
r
cha
rac
teri
stic
s
clo
sel
y
rel
ate
d
to
soil
cha
rac
teri
stic
s

Int
ern
atio
nal
So
ciet
y
for
Soi
l
Me
cha
nic

s
an
d
Ge
ote
chn
ical
En
gin
eer
ing

Wi
ktio
nar
ys
ee
pa
ge