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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.

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.

1.1 Aims of the Course

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 Riskc) 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).

1.2 Background

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.

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.

We can divide Geotechnics into two broad groups:-

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.

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).Landslides occur most frequently during or immediately following periods of heavy rain, and it is possible to predict

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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:-

Forces resisting landslide movement arising Fs = 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 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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Fig. 2 A second view of the landslide. Note that there were 4 man-made berms with drainage channels on this cut slope

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

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likely to be safer than before the failure, an adequate factor of safety against all water conditions cannot be guaranteed.

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Fig. 3. Factors causing Landslides and the subsequent consequences.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.

Fig. 4. Balloon Demonstration

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.


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.


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. 5 Demonstration of Effective Stress


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 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.

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 soils5) 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.

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 60m > silt > 2m 2 m > clayFor 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.

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. Voids are larger in the loose-packed sample.

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 one-tenth 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.

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.

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). Cohesion is one such force, and this is manifest as the stickiness associated with wet clays.

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

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.

Fig. 9 Volume of saturated soil against weight.

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. 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) 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.

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.

iii) Liquid Limit (LL) - The water content at which the soil is practically a liquid, but still retains some shear strength.

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.

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

While the above limits may be measured, the following indices may be derived from the Atterberg Limits:

1) Liquidity Index

m/c - PL (LI) = ----------- --------------------------- (1) 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.

The Liquidity Index is so designed that a soil at its Plastic Limit has a LI = 0, while at its Liquid Limited, LI = 1.

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)

This is defined as PI = LL - PL ----------------- - (2)

Generally soils with high clay content have a high Plasticity Index.

3) Activity Index (AI)

This is defined as PI LL - PL ------ = ------- . % clay % 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.

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 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. 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).

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 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

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:-

e n n = ------- or e = -------- 1 + e 1 - n

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

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.)

Fig. 14 Relationship between /'v and PI

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.

1.9 DEFINITIONS OF VOLUME AND UNIT WEIGHT

Volume Unit Weight Weight Vg ---------------------------------------------------- Vw ---------------------------------------------------- Vs s

Volume of voids =

Total Volume =

Definitio

n

Symbol

1 Voids Ratio

Volume 2 Porosity

13

3 Degree of Saturation

Weight 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

14

Definition 8

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.

We shall determine the effective vertical stress at A at 8 m below the ground surface

Method 1

Total Vertical Stress =

(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 = w x. 4

= 40 kPa (since w = 10 kN m-3)

so effective stress = 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 ---- layer 2 ------------- layer 3 [19-10 is submerged unit wt of layer 2 = 2']

= 97 kpa as before

space left for notes

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