ENV-2E1Y - Fluvial Geomorphology
2004 – 2005
Landslide which occurred on main highway west of Sao Paulo, Brazil at km 365 in late August 2002
[Colour Version of this and other photographs in this Handout may be view from the Course Web Page]
Slope Stability and Related Topics
Section 1
Introduction and Definitions
N. K. Tovey
ENV-2E1Y Fluvial Geomorphology 2004 – 2005
Section1
Slope Stability and Related Topics
1 Introduction
The massive failure of slopes within a river valley or around
a coast is one of the most significant factors affecting
development of the earth's surface. Some landslides are
massive with many millions of tonnes of material involved.
Others may be small, but nevertheless have a significant
impact on life. Indeed landslides involving less than 1 cubic
metre of material have killed people (e.g. in Kah Wah Keng
San Tsuen in the Rain Storm of 15th August 1982, Hong
Kong).
There are many factors which affect the stability of slopes:
these range from the geology of the area, the physical nature
and mechanical properties of the soil, water flow and water
pressures, slope profile, and man's influence to mention but
some of the factors. In this course, time is limited, and we
shall cover some of the basic principles of the necessary
topics needed for an understanding of these factors.
First we begin with a definition of the word Geotechnics.
Geotechnics is a broad subject which may be defined as:"the application of the laws of mechanics and
hydraulics to the mechanical problems relating to
soils and rocks"
This is typical of the definitions in many Engineering
textbooks. For our purposes in Environmental Sciences we
need to take a broader definition to include chemical
processes and perhaps more importantly with the interaction
of man with his physical environment. In this short
introductory course we cannot deal with more than a few of
the topics in the area, and we shall confine ourselves only to
those topics which have a direct bearing on the natural
environment or pose a hazard to mankind.
The course does require a little numeracy, but in almost all
cases solutions are possible via graphical means as well as
mathematical solutions, and it is these that we shall use for
the most part. The lectures will cover the theory behind the
processes, but also consider applications. Indeed, some of
the lectures will be devoted to worked examples and
applications of the techniques learnt.
We shall not be covering these aspects of foundation
engineering relating to the design of foundations for say an
oil storage tank. However, the stability of slopes and the
rate of settlement of farming land as a result of drainage
would be of importance to us.
1.1 Aims of the Course
a) that part dealing with soils and commonly referred
to as soil mechanics,
and b) that part dealing with the stability of rocks and
commonly referred to as rock mechanics.
The principle aim of the course is to introduce you to the
Basic Principles affecting the stability of slopes. For this we
shall need to cover the elementary aspects of Geotechnics, or
rather more specifically, Soil Mechanics.
The Basic Principles we shall need to cover to fulfil this
objective are:a)
an understanding of the nature of soil from a physical
(and chemical) and mechanical standpoint.
b) an understanding of how water flows in soils and in
particular the effects of water pressure on stability.
c) an understanding how the behaviour of soils and
sediments change with consolidation- this has
implications for Quaternary Studies
d) the nature of the shear strength of soils and sediments.
e) the application of the above to the stability of slopes
Subsidiary aims of the course include:a)
Instruction in field sampling and laboratory testing for
the mechanical properties of soils.
b) Considerations of managing Landslide Risk
c) The application and modification of the slope stability
ideas to the study of river bank stability.
( We hope to cover this within the formal course, but
more specifically on the Field Course).
We can divide Geotechnics into two broad groups:-
In this course, time will not permit us to make more than
occasional reference to the latter branch and we shall be
primarily concerned with the way soils deform under load
i.e. we shall study the stress- strain characteristics of soils.
In the third year Seismology option, rock mechanics is
studied further. It is necessary to have an understanding of
this behaviour of soils if we wish to predict whether or not a
landslide will occur or whether settlement to the land surface
caused by pumping creates other problems for man (e.g. the
settlement of Mexico City).
It is clearly pointless to spend money and effort in the
decoration of a building if it is structurally unsound; in a
similar manner it is pointless to design a very strong building
if little attention is paid to the foundations. Unfortunately, it
is aspects relating to the latter that have been frequently
neglected or overlooked in the past and landslide and other
disasters have arisen from attempts to economise in the
design of foundations, or in the planning or zoning of areas
of construction. In the case of landslides, these may arise
either on man-made slopes (such as in a cutting), or on
natural slopes, or on a predominantly natural slope which
has been partly affected by activities of man (e.g. a
construction site).
1.2 Background
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N. K. Tovey
ENV-2E1Y Fluvial Geomorphology 2004 – 2005
Landslides occur most frequently during or immediately
following periods of heavy rain, and it is possible to predict
whether or not a landslide is likely to occur if sufficient
measurements of critical parameters have been measured
beforehand. Such measurements include a detailed and
accurate survey of the profile of the slope, an accurate
knowledge of the height of the water table and finally the
actual mechanical properties of the soil or rock. In many
cases, it is the rise in the level of the water table which
triggers a landslide, and indeed, in Hong Kong, a few very
critical slopes are now instrumented so that when the water
table rises above a critical level, a warning is sounded.
One of the aspects which will be covered in this course,
therefore, is the prediction of slope stability. We can do this
by defining a factor of safety (Fs) as follows:-
Fs =
Forces resisting landslide movement arising
from the inherent strength of the soil
-------------------------------------------------The forces trying to cause failure
(i.e. the mobilising forces)
If the resisting forces just balance the mobilising forces then
the factor of safety (Fs) is unity and a landslide is likely to
occur. On the other hand, if the resisting forces are larger
Section1
than the mobilising forces the factor of safety is greater than
unity and the slope will be stable.
When engineers design a building or bridge using a material
such as steel, concrete or brick, the behaviour of these
components is now sufficiently well understood to enable us
to rely on their behaviour. Indeed it is very uncommon
nowadays for disasters or failures to occur in structures as a
result of an insufficient understanding of the material
properties. Failures usually occur as a result of poor design
or insufficient control during construction causing local
regions in which the material is unintentionally over
stressed. Examples are the several box-girder bridge failures
in the late 1960's early 1970's, and the collapse of the
Tacoma narrows bridge following excessive oscillations.
Engineers can specify the strength of the steel or concrete
they need in their design. Thus they may indicate that the
tensile strength of the steel to be used must not be less than
300 M Pa.
With soils and rocks, however, we cannot specify the
strength. We have to test samples taken from the site in
question and allow for the in-site strength of the material in
our calculations. It is possible to improve the properties by
soil stabilisation, but the cost is frequently prohibitive and
consideration on whether a project is undertaken depends to
a large extent on the economics of providing adequate
stability either by suitable design or soil improvement.
Fig. 1 Major Landslide which occurred in late August 2002 on main highway west of Sao Paulo at km
365. Note the people at the base of the Landslide giving n indication of scale. Also note the vertical scar
at top arising from the tension crack.
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N. K. Tovey
ENV-2E1Y Fluvial Geomorphology 2004 – 2005
Fig. 2 A second view of the landslide.
slope
Section1
Note that there were 4 man-made berms with drainage channels on this cut
1.3 Causes of Landslides and Interrelationships
Fig. 3 shows the various factors associated with a landslide.
Many are inter-related, but the key aspects immediately of
relevance are:a) surface and ground water flow
b) present slope profile
c) material properties of the soil
The surface and ground water flow are affected by the
rainfall and the hydrology of the region as well as man's
influence in the design of surface drains and in pumping.
Transient water flow may also occur during earthquakes.
The present slope profile is dependent on the geology of the
area, the possible presence of glaciation, and erosion by the
sea or rivers. In addition, man may artificially modify the
profile, and also other geomorphic slope processes such as
surface wash, aeolian processes, and creep may take place.
Weathering of the soil and the chemical characteristics of the
pre fluid affect the mechanical properties of the soil which
are also affected by loading of the ground. This latter is
affected in turn by earthquakes, ground water flow,
pumping, foundations of buildings as well as the geology,
glaciation, erosion, and slope processes.
If we know the present slope profile, the material properties,
and the surface and ground water conditions we may conduct
a slope stability analysis. Four possible outcomes may arise
from our analysis:b) the slope is in such a critical state that a landslide
occurs before the analysis is complete,
c)
sufficient time is given to issue a landslide warning,
d) the slope is dangerous, but not critical, and so
preventative measures are designed,
e)
the slope is safe and there is no danger AT THE
MOMENT.
If (c) applies then we may find that the cost of remedial
works is too great in which case we would continue to issue
landslide warnings and re assess our stability in the light of
changing water conditions. Alternatively we could build the
necessary strengthening measure to make the slope safe.
It we actually do get a landslide then effectively we have two
choices. Either we may leave the failure and remove the
consequences (e.g. evacuate people) or we can do remedial
works. The design of such works, however, has to be done
quickly, and although the resulting slope is likely to be safer
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N. K. Tovey
ENV-2E1Y Fluvial Geomorphology 2004 – 2005
than before the failure, an adequate factor of safety against
all water conditions cannot be guaranteed.
4
Section1
N. K. Tovey
ENV-2E1Y Fluvial Geomorphology 2004 – 2005
Fig. 3. Factors causing Landslides and the subsequent consequences.
4
Section1
N. K. Tovey
ENV-2E1Y Fluvial Geomorphology 2004 – 2005
Though a slope may be stable at the moment, it is still
subjected to weathering and unintentional activity by man
which may subsequently make the slope unstable.
Fig. 3 thus shows that to understand fully all the problems
relating to a landslide, many different aspects must be studied.
Geotechnics in this situation encompasses all those aspects
within the dashed lines. We need to understand the Geology
of the area, the Hydrology, the Climatic Conditions, hazards
such as earthquakes, anthropogenic activity etc, before we
can assess landslide potential. Equally, we must be mindful of
the consequence of landslides, and management decisions
should be made as much on this as the physical aspects of
landslides.
It may be more effective in some circumstances to remove the
consequences of a potential landslide rather than to attempt to
stabilise a slope. The are numerous examples of this - perhaps
the best known in the UK is the Mam Tor Landslide which
caused the closure of the main Manchester-Sheffield road in
the late 1970's.
1.4 The Nature of Soils and Sediments - some
demonstrations
It is important to realise that soil is a multi-phase material
consisting of solid particles, pore water which may contain
electrolytes, and air-voids. Organic matter can often play an
important role in the strength of soils but apart from reference
to this in the section on classification, we shall not be
considering this matter further in this introductory course.
The same is true about changes in the chemistry of the pore
fluid. This can, in some circumstances have a dramatic effect
(e.g. the development of the quick clays in Canada and
Norway).
In this course, to enable us to gain a basic understanding of the
behaviour which is not affected by the variability of nature of
the pore fluid, we shall be using distilled water as the pore
fluid.
However, we must always be mindful of the
consequence a change in pore fluid may have.
The behaviour of soils is somewhat unusual and we can
demonstrate this in the following way.
Section1
1.4.1 Demonstration 1
Firstly, if we attempt to build a sand castle using dry sand, we
will be unsuccessful, and the best we can achieve is a cone
shaped heap of sand the angle of which will be about 35o.
This angle does vary slightly with the type of sand and this
angle is known as the angle of repose. In a simplistic way the
magnitude of this angle can be used to indicate the strength of
the sand.
If we add water to the sand to make it damp it is possible to
construct sand castles with vertical sides showing that there is
an increased strength in the soil.
However, if we add an excess of water, the castle will collapse
and the sand will flow and would eventually come to rest at an
angle about half the angle of repose. Thus from this simple
demonstration we learn that the presence of water in the pores
of a soil has a critical effect on the stability of that soil. A
small amount of water can greatly increase the strength. On
the other hand excess water reduces the strength.
1.4.2 Demonstration 2
In our second demonstration we have a transparent tube
attached to a balloon (Fig. 4). The balloon is filled with water.
If we squeeze the balloon we notice that water rises in the tube
as expected. However, if we fill the balloon with sand and
water and repeat the experiment, we will see that rather
surprisingly water is drawn into the balloon as we squeeze it.
We shall consider the explanation of this apparently
anomalous behaviour in a later lecture.
1.4.3 Demonstration 3
For our third demonstration, a sample of sand is enclosed in a
rubber membrane to form a cylindrical shape approximately
75mm long and 37mm in diameter. The sample stands on a
porous stone and is connected via a tube to a burette. Initially,
the burette is placed lower than the sample so as to create a
negative water pressure (or suction) on the sample.
If the sample is gently squeezed, some resistance is felt. On
the other hand if the burette is raised to a position level with
the sample the sample exhibits little or no resistance to
deformation. Thus we see that by changing the pressure of the
water by only a small amount the strength can be drastically
reduced. If the burette is lowered, the original strength is
regained.
We may isolate the sample from the water in the burette by
closing the tap A (Fig. 5). With care we may stretch the
sample to at least double its original length, and even though it
may now be only 10mm in diameter it is now even stronger
than before, and it is only with considerable effort that we can
deform the sample. On opening the tap water is sucked into
the sample and it collapses back to its original shape. This
behaviour is thus somewhat similar to that seen in the balloon
demonstration.
Fig. 4. Balloon Demonstration
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N. K. Tovey
ENV-2E1Y Fluvial Geomorphology 2004 – 2005
Section1
we will eventually find that the rod moves very little, even
with a moderate tap. At such a point the sand is in a dense
state, and there is little development of pore pressure during
any vibration.
If we now deliberately cause water to flow in under pressure
from the base, we will notice that the rod once again descends,
the volume of the sand increases and the sand will appear to
'boil'. We have now created a quicksand which is always
associated with the upward flow of water. If the water flowing
in is now stopped, the sand will settle down in a loose state,
and the experiment may be repeated.
The process where sand (in particular) loses its strength as a
consequence of the rapid development of positive pore water
pressures in response to dynamic wading, is known as
LIQUEFACTION.
1.4.5 General comments on the demonstrations
Think about these demonstrations. What do they mean?
Some of the results are certainly surprising. The answers will
come in later lectures.
This space is left blank for notes.
Fig. 5 Demonstration of Effective Stress
1.4.4 Demonstration 4
Our final demonstration consists of a loose sand saturated with
water in a cylinder. The base of the cylinder is connected to a
tube in which we can monitor the water pressure.
A short rod stands in the sand and is quite stable. Yet if we
give the cylinder a small tap, representing an earthquake, the
rod drops downwards into the sand and disappears completely.
We can remove the rod and replace it in the sand when again
it will still be stable.
On repeating the experiment we can watch the water level in
the small tube connected to the base of the cylinder. We notice
that as the rod falls the level of water in the tube first rises
rapidly, and then slowly falls back to its original level. This
prompts the suggestion that the rise in water level is associated
with the downward movement of the rod.
However, if we remove the rod and tap the cylinder we will
still note that the water in the tube behaves in the same way.
Thus following a dynamic shock, the pore fluid exerts a
positive pore pressure and from the experience of the floppy
membrane sample we would expect the shear strength to be
reduced. This is why the rod descended, i.e. it was the pore
pressure development that caused the rod to descend and not
the other way round. If we keep on repeating the experiment
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N. K. Tovey
ENV-2E1Y Fluvial Geomorphology 2004 – 2005
1.5 Summary of topics to be covered in course.
In this introductory course on Geotechnics we shall consider
six different aspects;1) A classification of soils.
2) Permeability and the flow of water through soils.
3) Consolidation and response of soil to loading or
unloading and in particular the loading as a result of
glaciation, sediment erosion or deposition or drainage
(either artificially by man or by natural means).
4) Shear strength behaviour of soils
5) Slope Stability: Landslide Predictions:
6) River Bank Stability
Of these six we shall only have time to briefly consider
permeability, as this is covered in more depth the
Hydrogeology course. However, a knowledge of this is
important as it not only affects the way in which pore pressure
develop and dissipate and the consequent effects on the
stability of slopes, but also on the rate at which consolidation
of a soil takes place. River Bank Stability links with the
"Rivers" section taught by Richard Hey.
Section1
Generally speaking, clays exhibit a property known as
cohesion (or the "stickiness" associated with clays). A little
cohesion may be present in fine silts, but is generally absent in
the other size ranges. Thus a material lacking fine silt or clay
would be described as cohesionless.
The permeability of the soil decreases as the particle size
decreases.
For example, in gravels the permeability is of the order of mm
s-1, while in clays it is 10-7 mm/s or less. The compressibility
of the soil also increases as the particle size decreases.
1.6.2 Soil Fabric
Fig. 6. Dense and Loose packed sands.
the loose-packed sample.
Voids are larger in
1.6 Classification of Soils
1.6.1 Particle Size Distribution
We begin this discussion of the classification of soils by
considering the size distribution of particles within the soil.
There are a number of different methods for sizing the
particles of a soil, but we shall use the engineering definition
as it has the advantage of simplicity. The particles are defined
as follows:
boulders > 60mm
60mm >
gravel > 2mm
2mm >
sand
> 60 m
60m >
silt
> 2m
2 m >
clay
For each of the classes - silt sand and gravel - we may further
sub-divide into coarse, medium and fine.
Thus for sand:
2mm > coarse sand > 600 m
600 m > medium sand > 200 m
200 m > fine sand
> 60 m
In this classification the boundaries either begin with a '2' or a
'6'.
There is a problem with this, and all other classifications, in
that the term clay is used both as a classifier of size as above,
and also to define particular types of material. In the case of
sands and silts, those two terms indicate a size, whereas we
talk about quartz, feldspar etc when referring to a particular
mineral type.
The soil fabric is the geometric arrangement of the constituent
particles. For sands, the particles are quasi-spherical, although
some may be quite angular. It is, however, rare for the
maximum dimension to be greater than about three times the
minimum dimension of a particle. Some theoretical models of
sands assume that the particles are indeed spherical.
If we consider an arrangement of spherical particles we will
note that there are two extreme arrangements (Fig. 6.). There
is one arrangement in which the second layer of particles fits
exactly in the cavities left by the first layer, and one in which
the second layer lies exactly on top of the first layer. A sand
in the former situation would be a dense sand while one in the
latter situation would be loose.
Think about this. The nature of the packing of particles
will give the clue to the apparently odd behaviour of the
material in the balloon demonstration which used sand
which has particles which approximate to spheres.
Silt particles are usually much more angular than the sand
grains, while clay particles are either very platy or rod-like. It
is not difficult to imagine a very open fabric consisting of
plate-shaped particles where the thickness is less than onetenth of the diameter. Such a fabric as shown below is called
a CARD - HOUSE STRUCTURE.
Clearly if the
equilibrium of such a structure is disturbed, it will collapse
and a substantial consolidation of the soil will take place
causing a settlement of the ground surface.
In some recent Holocene deposits consisting of a high
proportion of clay, a quasi-card house structure is evident
(Fig. 7) with the volume of the voids being as high as 3 or 4
times the volume of the solid particles.
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ENV-2E1Y Fluvial Geomorphology 2004 – 2005
Section1
Cohesion is one such force, and this is manifest as the
stickiness associated with wet clays.
Fig. 7
Typical clay fabrics.
On left the fabric as the
sediment is deposited; on the right, the fabric after
vertical loading or ground water lowering.
Electron microscopic studies enable us to study the fabric and
the morphology of clays. Clays, like kaolinite, are platy and
often have a well developed crystalline form with shapes
approximating to hexagons. The plates are relatively thick
(thickness/diameter ration is approximately 0.1). Illites and
smectites are also platy, but much thinner with the particles of
smectite often having thickness/diameter ratio of around
0.001.
Other clay minerals such as halloysite are tubular and yet
others are rod shaped (Attapulgite and Sepiolite). The most
common clay minerals are kaolinite, illite, and smectite, and
most naturally occurring clays consist of mixtures of these. In
many environments, weathering can transform the minerals
from one type to another - thus along the River Yare it has
been found that the kaolinite/smectite ratio varies as one
proceeds downstream.
In some clays, particularly smectites, this surface activity is
further enhanced by the fact that isomorphous substitution of
ions in the clay mineral lattice by ions of a different valency
leave the clay particles electrically charged. Near their edges
the particles are positively charged, but over their large flat
surfaces they are negatively charged. Overall the particles are
negatively charged, and the extent of this charging is a
function of the isomorphous substitution. In kaolinites it is
normally small, but in smectites the substitution can be large.
To balance these negative charges, cations in the surrounding
pore fluid normally form a bond to the surface of the particles
often with the help of the polar water molecules. A cation water bridge can thus develop to hold the particles together.
Clearly if the chemical balance is ever upset, then this bonding
force may be substantially reduced causing a significant
reduction in the strength of the soil with consequent collapse
or failure.
Particular problems may arise if the soil is laid down in marine
conditions where the cationic strength of the pore water is
high. If this is replaced by fresh water, then much of the
intrinsic strength may be lost, although other diagentic
changes may result in cementation between particles. One
theory suggests that the quick clays of Scandanavia and
Canada have formed in marine conditions and then leached
with fresh water. The resulting material is extremely sensitive
and dramatic landslides have occurred on even shallow slopes
of no more than 1 - 2 degrees.!
The effects of the physical and chemical environment on the
soil geotechnical properties and the Atterberg Limits (see next
section) are the subject of much research, including some
carried out within the School of Environmental Sciences. In
recent years much work has been done by Canadians, and
there are many references to such work in the 1982-1984
issues of the Canadian Geotechnical Journal).
1.6.3 Atterberg Limits
Fig. 8 Cations forming a bridge between two clay particles.
The negative charges on the clay particles attract the hydrogen
ions of the water molecule. The strong negative charge on the
water molecules forms an electrostatic bond with a cation.
The same happens on the other side. The actual strength of
the bonding depends on the nature of the cation itself. Thus
divalent cations like calcium tend to form stronger bonds than
monovalent cations like sodium,
but there are some
exceptions - potassium.
All clay mineral particles are characterised by having a large
surface area to volume ratio, and in smectites this surface area
may be as large as 700 square metres per gram of soil. Clearly
any forces which are a function of surface area are likely to be
much more significant in clays than in sand where the surface
area is very small (about 0.01 square metres per gram).
The Atterberg Limits are probably the most important aspects
of soil classification in geotechnical terms. There are three
such limits, namely the liquid limit, the plastic limited and the
shrinkage limit. These limits are measured in terms of the
moisture content of the soil and span the range of situations
covered by most soils in nature.
Let us imagine an experiment where we have a wet (saturated)
soil, and suppose we are able to measure both its weight and
volume as the sample dries out. We plot the result as shown
in the following graph (Fig. 9).
Initially, the sample has a high moisture content and its
volume is large. It can flow and behaves rather like a viscous
liquid. As the sample dries out, both its volume and weight
decrease in a linear fashion until the sample no longer flows
but has the consistency of soft butter.
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ENV-2E1Y Fluvial Geomorphology 2004 – 2005
Section1
Useful Reading for reference if you are doing the Atterberg
Limits Practical:Either of the above methods may be used. For a full
description of both tests consult British Standard
BS1377 (1975).
For a discussion of the two
techniques consult Sherwood and Ryley (1970)
TRRL Report No. 223.
(Transport and Road
Research Laboratory).
1.6.4 Derived Indices
Fig. 9 Volume of saturated soil against weight.
While the above limits may be measured, the following
indices may be derived from the Atterberg Limits:
1) Liquidity Index
With further drying the sample shrinks further, still following
the straight line. As it does so, the soil becomes firmer,
although it continues to remain plastic. Eventually a point is
reached where the soil becomes brittle and begins to crumble
on deformation. After this point is reached there is little
opportunity for further shrinkage and eventually further drying
takes place without volume change. The soil is now
completely solid.
m/c - PL
(LI) = ----------LL - PL
where LL and PL refer to the moisture contents at
the Liquid Limit and Plastic Limit
respectively.
and m/c is the actual current moisture content of
the soil.
Three limits are used to define the states of soil encountered in
Geotechnics, namely the LIQUID LIMITED, the PLASTIC
LIMIT, and the SHRINKAGE LIMIT. Collectively they are
known as the ATTERBERG LIMITS.
i)
The Liquidity Index is so designed that a soil at its
Plastic Limit has a LI = 0, while at its Liquid Limited,
LI = 1.
Shrinkage Limit (SL) - The smallest water content at
which a soil can be saturated. Alternatively it is the water
content below which no further shrinkage takes place on
drying.
Thus for most soils of interest in Geotechnics (i.e.
between the Liquid and Plastic Limits), the liquidity
index will be in the range 0 to 1.
2) Plasticity Index (PI)
ii) Plastic Limit (PL) - The smallest water content at which
the soil behaves plastically. It is the boundary between the
plastic solid and semi-plastic solid in Fig. 4 above. It is
usually measured by rolling threads of soil 3mm in
diameter until they just start to crumble.
This is defined as PI = LL - PL ----------------- - (2)
Generally soils with high clay content have a high
Plasticity Index.
iii) Liquid Limit (LL) - The water content at which the soil
is practically a liquid, but still retains some shear strength.
3) Activity Index (AI)
This is defined as
Two methods are available for determining the Liquid Limit:
A) Using the Casagrande apparatus which consists of a cup
which falls through a height of 10mm. The Liquid Limit is
the moisture content when the number of blows (falls
through the height of 10mm) that are necessary to cause a
groove of standard dimensions to close over a distance of
10mm equals 25.
B) Using the fall cone apparatus. The Liquid Limit is that
moisture content of the soil at which a cone of standard
dimensions and weight will penetrate a given distance into
the soil. In the British Standard the cone angle is 60o
while the penetration distance is 20 mm. Other countries
use different standards, but these may be related to one
another if needed.
--------------------------- (1)
PI
-----% clay
=
LL - PL
------- .
% clay
The % clay is, of course, that fraction from size distribution
which is less than 2 m in equivalent spherical diameter.
Several different charts have been produced based on the
Atterberg Limits and their derived indices to produce methods
for classifying soils. Thus in the following diagram (Fig. 10) it
is noted that the Plasticity Index (i.e. the distance between the
Liquid Limited and Plastic limited line increases as the
particle size decreases.
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N. K. Tovey
ENV-2E1Y Fluvial Geomorphology 2004 – 2005
Section1
the fall cone and the Casagrande cup methods are in fact a
somewhat complex estimate of shear strength.
In the case of the Casagrande method, a series of miniature
landslides are created as the cup hits the base material. For
the fall cone, the soil undergoes shear deformation as the cone
penetrates the sample. The actual methods for measuring the
Liquid Limit are arbitrary, but the are closely controlled by a
series of Standards (e.g. BS 1377 (1975)), and the figure of
1.70 kPa represents the current best estimate.
Fig. 10 Relationship between mean particle size and moisture
content for some soils
Two points should be noted:
A) The difference between the two lines is the
Plasticity Index.
B) A greater Plasticity Index is indicative of a high
percentage of clay, an increase in toughness and
dry strength, but a decrease in permeability.
A commonly presented form of Plasticity Chart is shown
below:-
Fig. 11
Plasticity Chart.
This chart is a simplified version of the full charts which may
be found in most text books, however the main essential
features may be seen. There is a distinct boundary between
the inorganic clays on the one hand, and organic clays or
inorganic silts on the other.
Soils which are largely
cohesionless plot as points close to the origin, while soils with
high plasticity appear at the top right of the chart.
1.6.5 Uses of the Atterberg Limits
Besides being the basis of methods for the classification of
soils according to their Geotechnical properties, the Atterberg
Limits may be used to estimate the shear strength of a soil. It
has been found that the shear strength of a soil at its liquid
limit is very approximately 1.70 kPa. We would in fact expect
a nearly constant shear strength at the liquid limit since both
Fig. 12 Typical Plots of Voids Ratio Content against shear
strength. Each line represents a particular soil. Data
of voids ratio against shear strength plot on a single
line (in log space). Lines from different soils appear
to converge on a single point (known as the W point)
Several papers have been written on this including one by
Wood D.M. - Geotechnique (May 1985) where references to
other papers may be found. In the late 1950's and early 1960's
Roscoe and his co-workers developed ideas of Critical State
Soil Mechanics. They noted that the shear strength of a soil at
its Plastic Limit was VERY approximately 100 times that at
the Liquid Limit, suggesting that the shear strength of a soil is
about 170 kPa. It should be noted that this ratio is only very
approximate, and may vary over a range 100 - 240 kPa, but if
we do accept this idea we can develop other useful
relationships.
Reference: Wood D.M. Geotechnique (May, 1985)
If we plot the moisture content of a soil against its shear
strength (the latter expressed in logarithmic form), a straight
line is obtained. Fig. 12 shows a family of such curves for a
group of different soils. In addition the approximate positions
of the Liquid Limit and Plastic Limit are shown.
This family of curves may be reduced to a single line if we
replot the ordinate (y-axis) as Liquidity Index, when the
following unique curve is obtained (Fig. 13).
10
ENV-2E1Y Fluvial Geomorphology 2004 – 2005
N. K. Tovey
Section1
In many soils where the voids are saturated with water we can
calculate the voids ratio from a knowledge of only the
moisture content. We note that the voids are completely filled
with water, and that the solid particles have a Specific Gravity
(Gs) equal to 2.65. Thus the voids ratio is computed as:e = 2.65 x (moisture content)
(Remember: the Specific Gravity is defined as the ratio of the
density of a solid to that of water).
1.8 Further Applications of the Atterberg Limits
Fig. 13
Liquidity Index against shear strength.
Thus once we have determined the Atterberg Limits of a soil,
we may use Fig.13 to estimate the shear strength at ANY
moisture content. To do this we evaluate the Liquidity Index
of the soil at the current moisture content, and measure off on
the abscissa (x-axis), the corresponding shear strength. This
may be very useful for obtaining a rough indication of shear
strength but one must not expect the results to be closer than
20%. Returning to Fig. 10 it will be noticed that the lines
appear to converge, and in fact, they all converge
approximately on a single point, known as the - point. This
- point has approximate co-ordinate values of 9.5% moisture
content, and 4500 kPa.
In our work on consolidation we shall normally require the
gradient of the consolidation line to be in terms of voids ratio,
and not moisture content as indicated above. We can simply
transform the equation derived for the gradient by multiplying
it by 2.65. We normally give the gradient the symbol Cv - the
compression index.
i.e.
Cc = 1.325 (WLL - WPL)
One final application of the Atterberg Limits is the
EMPIRICAL relationship noted by Skempton relating the
non-dimensional quantity /'v to Plasticity Index (PI). ( is
the shear strength of the soil, and 'v the effective confining
stress.)
In a later part of the course we shall see that the consolidation
behaviour of soils follows a similar trend with the gradient of
the consolidation line parallel to the appropriate line shown in
Fig. 8. We can estimate the gradient as follows:(WLL - WPL)
gradient = --------------------- = 0.5(WLL - WPL) ……(3)
log(170) - log(1.7)
(Note: log(170) - log(1.7) = log(170/1.7) = log 100 = 2)
This quantity will be useful in understanding how a soil
compresses under load
Fig. 14 Relationship between /'v and PI
1.7 Two Volumetric Definitions
VOIDS RATIO - this is defined as the ratio of the volume of
the voids in a soil to the volume of
SOLID. It is given the symbol "e".
Note: this should not be confused
with the similar following definition.
POROSITY
- this is defined as the ratio of the volume
of the voids in a soil to the volume of
the WHOLE SOIL (i.e. solid +
voids). The symbol used here is "n"
Clearly e and n are related:-
n =
e
------1+e
or
e
=
n
-------1-n
The correlation is good, and the equation of the line is given
by:
--=
0.22 +
0.74 PI
'v
Note: this expression is slightly different to that used by
Skempton and referred to in many text books. Here the
quantity 'v refers to the confining vertical stress. It is thus
possible to examine how the shear strength varies with depth
since 'v is simply related to depth (see a later lecture).
IT SHOULD BE NOTED THAT THIS RELATIONSHIP
HOLDS FOR NORMALLY CONSOLIDATED CLAYS, i.e.
those which have not been unloaded in the past.
11
N. K. Tovey
ENV-2E1Y Fluvial Geomorphology 2004 – 2005
Section1
1.9 DEFINITIONS OF VOLUME AND UNIT
WEIGHT
Volume
Unit Weight
Weight
Vg
---------------------------------------------------Vw
----------------------------------------------------
s
Vs
Volume of voids =
Total Volume
Definition
Symbol
1
Voids Ratio
2
Porosity
3
Degree of Saturation
4
Water Content (% )
5
Unit Weight of Water
6
Unit Weight of Solid Particles
Unit
7
Specific Gravity
Weight
8
Bulk Unit Weight
9
Saturated Unit Weight
10
Dry Unit Weight
11
Submerged Unit Weight
Volume
Weight
Definition 8
12
=
N. K. Tovey
ENV-2E1Y Fluvial Geomorphology 2004 – 2005
1.10 Estimation of effective vertical stress at
depth
We shall need to be able to estimate the vertical stress at any
given depth in several future sections in the course.
The figure below shows three strata of different unit weights
with the water table 4m below the surface.
Section1
 (i . zi) = (1 .3 + 2 .2 + 3 .3 )
where zi is the depth of layer i
If
1 = 16 kN m-3 ,
2 = 19 kN m-3 ,
and 3 = 17 kN m-3
Total stress =
(16 x 3 + 19 x 2 + 17 x 3)
=
137 kPa (kN m -3)
We now deduct the buoyant effect of water =
40 kPa (since w = 10 kN m-3)
so effective stress =
w x. 4
137 - 40 = 97 kPa
Method 2
stress at A =
16 x 3 + 1 x 19 + 1 x (19 - 10) + 3 x (17 - 10)
|
layer 1
We shall determine the effective vertical stress at A at 8 m
below the ground surface
|
---- layer 2 -------------
|
layer 3
[19-10 is submerged unit wt of layer 2 = 2']
Method 1
= 97 kpa as before
Total Vertical Stress =
space left for notes
13
=