Shear Strength Feb2010

8/12/2019 Shear Strength Feb2010

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SHEAR STRENGTH

1.0 IntroductionStrengthis a measure of the maximum stress that can be induced in a materialwithout it failing. Strength may be expressed in terms of compressive or tensile

stress but essentially it is the materials ability to resist shear stress.

The shear strengthof a soil is the maximum value of shear stress that the soil canresist before failure occurs.

Essentially, shear strength within a soil mass is due to the frictional resistancebetween adjacent soil particles. The force transmitted between two bodies in staticcontact can be resolved into two components:

normal component N (kN), perpendicular to the interfaceand

shear (tangential)component T (kN), parallel to the interface.

T = N = N tan

where : = coefficient of friction

= angle of friction

Also the stress/strain(or displacement) curve is of interest. The curve below showsa typical stress/strain relationship for soils shearing under constant normal stress,

n.


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2Shear Strength (Dr. P McMahon)

Y yield point If soil is stressed beyond this point strain is not 100%recoverable.

P Peak shearstrength

Maximum shear stress that can be sustained, rapid loss ofstrength beyond this point.

U Ultimatestrength For loose sands and soft clays work hardening can increase theshear stress so that a maximum stress is not achieved.C Critical state

strength*After an amount of strain a soil will achieve a constant volumeand will continue to strain at this volume

R Residualstrength

After a considerable amount of strain, platy clay particles oneither side of the failure surface are re-arranged to becomemore parallel to produce a constant strength.

*Critical State soil mechanics is not covered in this module.

Principal test methods

DIRECT SHEAR TESTSShear box testVane test

INDIRECT SHEAR TESTSUniaxial compression testTriaxial compression test

2.0 Failure criterion

The Mohr-Coulomb relationship is adopted in soil mechanics. It relates the shearstress at failure (i.e. shear strength, f) on a failure plane to the normal effective

stress nacting on that plane:

f= c+ n tan Where:

f = shear strength

c = cohesion

n = normal stress

= angle of friction

Any combination of shear stress, , and normal stress, nlocated;

below the MohrCoulomb line is a safe state of stress.on the MohrCoulomb line is in a state of incipient failure.above the MohrCoulomb line has failed (impossible to plot).

Normalstress, n

Shear

Stress,

c

f= c+ n tan

Mohr-coulomb line


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All analyses of soil shear strength are dependent on three factors:

1. What are the appropriate values of cand ?- depends on soil history, type, loading, drainage.

2. What combination of nand exists within the soil mass?- found using Mohrs circle.

3. Knowing shear strength f, from 1;knowing shear stress , from 2;then the Factor of Safety against shear failure can be found:

[F of S = 3.0 for bearing capacity : 1.5 for slope stability]NOTE: BS EN ISO 1997 is changing this approach (known as EC7 !!)

3.0 Stress analysis - Mohrs circle of stress

Mohrs circle of stress provides a convenient method of analysing two dimensionalstress states.

The shear strength of a soil may be expressed in terms of the effective major

principal stress, 1, and effective minor principal stress, 3, at failureat the point

in question. At failure the straight line represented by the Mohr - Coulomb equationwill be tangential to the Mohr circle representing the state of stress, the coordinates

of the tangent point being fand f.

Also if is the angle between the major principal plane and the failure plane, then itcan be shown that:

F of S=Strength, f

Stress,

= 45 +

2


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The Mohr Coulomb failure line is often called thefailure envelopeand Mohrscircles at different values of normal stress will all be tangential to this failureenvelope.

4.0 Shear strength tests

The purpose of shear strength testing is to determine values for the shear strengthparameters cand . The drainage conditions during the test influence themeasured values considerably. Shear strength tests are carried out in two main

stages:

1. Consolidation stage. After a sample has been prepared to size and its massand water content determined, it is consolidated to a required state. This isdone either;

one dimensionallyin direct shear tests,or three dimensionally in triaxial tests.

The objective is to produce an initial stress state and to ensure full saturationin triaxial tests. The consolidation of coarse soils in direct shear tests is

virtually immediate upon load application, but may require up to 24 hours forfine soils.

2. Shearing or axial loading stage. The consolidated sample is subjected toeither

direct shearing (e.g. shear box test)or

increased in axial loading (triaxial test)

until failure occurs. Readings of vertical strain, axial load, pore waterpressure (not shear box test) and volume change are taken against time.

Shear

Stress,

Effective normalstress, n

= 45+ /2

Failure envelope, f= c+ n tan

c


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Types of laboratory shear test:

Vane testShear box testUnconfined compression test

Triaxial compression test4.1 Vane Test

This is a direct shear test used both in the laboratory and on site to determine the

undrained shear strength,cu, of firm to stiff silts and clays.

The vane consists of four rectangular blades in

a cruciform at the end of a steel rod. After thevane has been pushed into the soil (in alaboratory sample or at the bottom of aborehole), it is rotated by applying a torque tothe rod. The applied torque is measured andthe undrained shear strength of the soil iscalculated by equating the applied torque tothe shearing resistance of the shear surface(perimeter and ends of a cylinder of soil).

T = c [ ( DH xD

) + (2 D2

x2

xD

) ]2 4 3 2From which;

c =

T

D2 (H

+D

)2 6

Orc = kT

where, k = vane constant

k =

1

D2 (H

+D

)2 6

After the initial test, the vane is rotated rapidly, causing the clay to becomeremoulded and the shear strength in this condition is recorded as the remoulded

shear strength, cr.

The sensitivity of a cohesive soil is defined as the peak strength divided by the

remoulded strength i.e.

Sensitivity =cu

cr


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The higher the sensitivity value the more the soil will lose strength as a result ofdisturbance, e.g. remoulding of soil during earthworks.

Most ordinary clays have values of sensitivity up to about 4. However some quickclays have sensitivities as high as 100.

Class example 1A laboratory vane test was conducted on a sample of saturated clay soil. The vanemeasured 38.0mm high by 19.0mm diameter.

The vane was inserted into the soil to a depth of 76.0mm, rotated and a torque of2.5Nm recorded.

The vane was quickly rotated a further three revolutions and after a period ofsettling the torque was measured at 1.1 Nm

Determine: i) Peak shear strength

ii) Remoulded shear strengthiii) Sensitivity of the clay

Ans: 99.5kN/m2; 43.8 kN/m

2; 2.3

4.2 Shear Box Test

This is a direct shear test,i.e. the normal and shear stresses on the failure surfaceare measured directly. It is usually used for testing granular soils and stiff clays.

A rectangular prism of soil is cut and fitted into a square metal box that is split into

two halves horizontally. The standard box is 100mm x 100mm in plan area and alarge model, 300mm x 300mm.

Normal load is applied to the sample by dead weights via a hanger and levermechanism. Shear load is applied at a constant rate of strain by a screw jackdriven by electric motor.


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Measurements of vertical and horizontal movement are recorded from dial gauges

and readings of the shear force are read from a proving ring or load cell.

The test is repeated using different values of normal load, e.g. In the diagram

below normal stresses might be 1 = 50kN/m2, 2 = 100kN/m

2, 3 = 200kN/m

2.

Values of normal stress nand shear stress

are calculated and plotted and the value ofthe peak stress determined.

Plotting shear stress at failure f(i.e. peak stress) against normal stress nenablesthe angle of friction and the cohesion (if clay soil) to be found:

Advantages:

1. Both shear stress and normal stress can be measured directly.2. A constant normal stress can be maintained throughout the test.3. Easy test for cohesionless soils (sands and gravels) and drained tests can be

carried out in a reasonable time.

Shear stress

at failure, fkN/m

2

Cohesion, c

, angle of friction (or angle of internal shearing resistance)

50 100 200

Normal stress, n, kN/m2


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4. Volume changes can be easily measured.5. Residual strengths of clays (ie. at large values of strain) can be found by

reversing the shear direction (reversible shear box).

Disadvantages:

1. Poor, uncertain control of drainage conditions and the inability to measurepore water pressure.

2. The distribution of shear stress over the failure plane is assumed to beuniform not true, due to influence of sides and corners of box.

3. The soil is forced to fail along a predetermined failure plane may not be theweakest zone.

4. The normal stress cannot be easily changed duringtesting.


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Class example 2

A drained shear box test was carried out on a sandy clay soil with the followingresults:

Normal load (N) 108 202 295 390 484 576Shear load at failure (N) 172 227 266 323 374 425

The shear box measured 60mm x 60mm.

Determine the cohesion, c, and the angle of friction, , of the soil.

Ans: c = 32kN/m2: = 28

o

4.3 Unconfined Compression Test

This test involves axially loading a cylindrical soil sample and recording the failureload.

The samples are usually 38mm diameter and 76mm long and are placed in a testrig which is portable, self contained and hand operated useful for on sitedetermination of undrained strengths of clays. The test rig incorporates a penciltracing load against deflection (shortening) of the sample, as shown below;


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For brittle failure, the maximum compressive load defines failure.

For plastic failure (no distinct maximum), the failure load is taken as that at 20%strain (ie. 15.2mm shortening on a 76mm long sample);

Compressive strength calculations must take account of the increase in crosssectional area of the sample as the test proceeds:-

Uncorrected axial stress at failure = compressive failure Load = Foriginal cross sectional area Ao

To allow for the increase in cross sectional area,

Corrected axial stress at failure, 1 =F

(1 - )Ao

Where;

Axial strain, =change in sample height (shortening)

=h

original sample height ho

When analysed using Mohrs circle construction, since the lateral stress 3is zero,the following is drawn:


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From the above diagram, it can be seen that for saturated clay:

Undrained shear strength, cu= radius of Mohrs circle at failure

Thus

cu=1

2Advantages:

The test is fast, simple, compact and inexpensive.

Limitations:

1. The sample must be fully saturated.

2. The sample must must not contain fissures, gravel particles, air voidsetc, as these will be areas of weakness.

3. The test must be carried out quickly to ensure that undrainedconditions apply.

4. It is generally used as a comparative test (not for design purposes) to indicate if the soil is stiff, firm etc, see designations below;

Class example 3

A sample of clay, 38.0mm diameter and 76.0mm long is tested in an unconfinedcompression test. The sample fails at a load of 205N after being reduced in heightby 8.6mm.

Determine;i) The corrected compressive strength of the sample.

ii) The shear strength of the clay soil.iii) State the strength designation of this soil

Ans: 160.9kN/m2; cu= 80.5kN/m

2: firm to stiff clay

13

cu

Corrected compressive

strength, 1


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ASSESSMENT OF IN-SITU STRENGTH

Soil Type Term Field test

Sands,gravels

Loose Can be excavated with a spade;50 mm wooden peg can be easily driven

Dense Requires a pick for excavation;

50 mm wooden peg is hard to driveSlightlycemented

Visual examination;A pick removes soil in lumps which can be abraded

Silts Soft or loose Easily moulded or crushed in the fingers

Firm ordense

Can be moulded or crushed by strong pressure in thefingers

Clays Very soft Exudes between the fingers when squeezed in the hand

Soft Moulded by light finger pressureFirm Can be moulded by stronger finger pressureStiff Cannot be moulded by the fingers;

Can be indented by the thumbVery stiff Can be indented by the thumb nail

Organic, peats Firm Fibres already compressed together

Spongy Highly compressible and open structurePlastic Can be moulded in the hand and smears the fingers.

STRENGTH SCALES (NOTE: EC7 is changing the way that soil strength is assessed)

A scale (from BS 5930:1999), historically has been described in terms of undrainedshear strength, as follows:

Term Undrained shear strength, cukN/m2

Very soft < 20Soft 20 to 40Firm 40 to 75Stiff 75 to 150Very stiff 150 to 300Hard >300

Subdivisions of these strength ranges are widely (unofficially) used, as follows:

Soft to firm 40 to 50Firm 50 to 75Firm to stiff 75 to 100Stiff 100 to 150

NOTE:Level 1 BSc Lecture Material covered in BLT1013 and 2ndYear HNC Material coveredin BLT1114 provides up to date guidance for awareness of students. Refer to Lecture

Material on website for detailed exaplantion.


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4.4 Triaxial Compression Test

This is the most widely used shear strength test to provide data for designpurposes. It is suitable for most cohesive soil types except for clays sensitive to

disturbance. It is just possible to test granular soils, e.g. sand, but the sample isdifficult to setup.

The test is normally carried out in two stages;

Stage 1. Apply a constant value of all round (or cell) pressure, i.e. minorprincipal stress, 3.

Stage 2 Increase the vertical or axial stress, i.e. major principalstress, 1, until failure occurs.

Advantages;drainage conditions can be controlled, enables saturated soilsof low permeability to be consolidated, if required, as part ofthe test procedure, andpore water pressure measurements can be made.


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The sample, sealed in a rubber membrane, is positioned in the cell which, in turn, isfilled with water.

The water is pressurised to the required confining, or cell, pressure, 3.

The sample is compressed using a constant rate of drive motor until the force on thesample stops increasing, or the strain in the sample reaches 20%.The increase in cross sectional area of the sample must be taken into account when the

compressive stress is calculatedThe compressive strength is equal to the maximum applied compressive stress (or deviatorstress).

Three or more identical samples (Test 1, 2 & 3 below) are axially loaded to failure

under different values of cell pressure, 3(e.g. 3-1= 50, 3-2= 100, 3-3= 200

kN/m2). Proving ring and axial deformation dial gauges are recorded. The data is

converted to axial stress (with area correction) and graphed vs % strain. From

each plot, the stress at failure, 1, value is obtained, see 1-1, 1-2and 1-3below.

Mohrs circle constructions enable a failure envelope to be drawn, hence the shearstrength parameters c and to be determined.

Types of Triaxial Test

Engineering works will change the stresses in the soil and affect the drainage

conditions.Three common test procedures have been devised to model or represent thesechanges:

1. Unconsolidated / undrained test (quick undrained)

2. Consolidated / drained test (drained)

3. Consolidated / undrained test

3-1 3-21-1

3-31-2 1-3

n

cTest 3Test 2Test 1


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4.4.1Unconsolidated/undrained test (quick undrained)

Stage 1 Stage 2

.

3

3

.

3

3

.

F/A1

3

3

.

3

3

1

F/A

No consolidationValves A & B closed

No drainageValves A & B closed

Valve A - drainage buretteValve B - pore pressure measurement

Thisquick undrained test gives the short term undrainedshear strength value of

a saturated clay, cu. Increased pore water pressure in the short term carries the

applied load, hence the angle of friction, u, equals zero. The rate of strain isselected to ensure failure occurs within 5 to 15min, i.e. a quick test.

The main applications are in the design of shallow and pile foundations and inassessing initial stability of embankments and cuttings.

As the axial load on the sample increases, a shortening in length occurs with an

increase in the initial sample diameter (and area, Ao). A correction factor is applied

to Ao, to determine the correct axial stress at failure;

Corrected axial stress at failure, 1 =F

(1 - )Ao

Where;

Axial strain, =change in sample height (shortening)

=h

original sample height ho

3-1 3-21-1

3-31-2 1-3

n

u= 0o

cuTest 3Test 2Test 1


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NOTE: Compacted clay always has an air voids content, which means that uwould

be >0o(the value of uincreases with >Av).

Class example 4

The results of quick (unconsolidated) undrained triaxial tests on three identicalsoil samples (76.0mm long x 38.0mm diam.) at failure are:

Test No. 1 2 3Cell pressure, 3(kN/m

2) 200 400 600Axial load (N) 222 215 226

Axial deformation (mm) 9.83 10.06 10.28

Determine the shear strength parameters of the soil with respect tototal stress

Ans: : cu= 85.0kN/m2; u= 0

o


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4.4.2 Consolidated / drained test

Stage 1 Stage 2

.

3

3

.

3

3

.

F/A1

3

3

.

3

3

1

F/A

ConsolidationValves A & B open

DrainageValves A & B open


In Stage 1 drainage is allowed via the burette and the initial excess p.w.p., u,dissipates to zero as the sample consolidates and reduces in volume, V and thecross sectional area of the sample. A correction is applied for this.

In Stage 2 the loading rate is very slow (8 to 50hrs to failure depending on soiltype) in order to prevent build up of p.w.p. in the sample. A check that pore waterpressure is low or zero is made via a pressure transducer connected to valve B.

Any volume change in Stage 2 is measured as a change in burette water levelduring and up to failure. A correction is applied for the change in X.S. area.As the axial load on the sample increases, the sample becomes shorter, with aconsequent increase in sample diameter (and area). A correction is applied for this.

In order to take account of these changes, when calculating the vertical stress 1,the corrected cross sectional area of the sample, A, initially after consolidation andduring axial loading up to failure, is found from:

A = A01-(

V)

V0

1-(h

)h0Where;

A0 = initial cross sectional areaV0 = original sample volume

V = change in volumeh0 = original lengthh = change in length

The total stresses 1and 3at failure are also the effective stresses 1and 3(since p.w.p. = 0) and so the Mohrs circles for effective stress are plotted direct,see diagram below.

Test produces values of the effective stress strength parameters cdand d(also

more generally termed cand ).


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The results of the test are generally applicable to fill problems, e.g. embankmentconstruction slow build up allowing p.w.p. to dissipate as construction proceedsand the long term stability of cuttings.

Class example 5

Consolidated drained triaxial tests were carried out on three identical specimens(each 38.0mm diameter and 76.0mm long ) of the same soil sample and thefollowing data was obtained;

Sample 1 2 3

Cell pressure (kN/m2) 100 200 400

Failure load (kN) 0.297 0.458 0.794

Change in length (mm):

During consolidation, Hc 0.73 1.77 2.82

During axial loading, Ha 9.38 12.24 15.38

Change in volume (ml):

During consolidation, Vc 2.48 6.02 9.90

During axial loading, Va 5.93 6.05 6.07

Determine the shear strength parameters of the clay with respect toeffective stress.

Ans: c= 35kN/m2; = 25

o


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4.4.3 Consolidated/undrained test

Stage 1 Stage 2

.

3

3

.

3

3

.

F/A1

3

3

.

3

3

1

F/A

ConsolidationValves A & Bopen

No drainageValve A closedValve B open


In Stage 1 drainage is allowed via the burrette and the initial excess p.w.p., u,

dissipates to zero as the sample consolidates and reduces in volume, V and thecross sectional area of the sample. A correction is applied for this.

In Stage 2 the loading rate, typically 0.05mm/min (with failure typically in under3hrs), allows induced p.w.p to distribute throughout the sample, with valveB

opened to measure the build up of p.w.p. A back pressuremay be applied to thedrainage circuit, to ensure complete sample saturation.

Values of the undrained shear strength, cuand u(compacted clay always has an

air voids content, which means that uwould be >0o) may be determined.

Pore water pressure during axial loading is recorded to enable the effective stress

at failure to be determined. See effective stress strength parameters ccuand cu

(also referred to as cand ) below;


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NOTE: The value of ccuobtained by this test produces a higher value (>10kN/m2)

for the same soil than the cdvalue for the drained test (normally


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6.0 Summary

Any procedure which involves removing a sample from the ground will involvedisturbance to the soil sample, and in general this will lead to a reduced strength.Modern thin walled piston samplers can minimise disturbance to the absolute

minimum.

Most of the disturbance comes from the initial sampling. Transportation of samplesis usually not too much of a problem. Quick Clay is an exception when the effectsdisturbance may severely reduce sample strength. These effects can be minimized,however, by carefully cushioned transport arrangements.

A vane shear test causes minimum soil disturbance and weakening. But, one theother hand it cannot measure strain or deformation, nor can pore water pressurechanges be ascertained.

In the shear box test in cohesive soil pore pressures cannot be measured. Also it ismuch more difficult to cut samples from the field to the correct shape withoutcausing further disturbance and weakening. In the case of free draining granularsoils pore pressures do not develop during testing, but it is difficult to compact thesoil to its approximate in-situ value (if this is known).

The unconfined compression test suffers from the same initial sample disturbanceas the triaxial test, but has a much less accurate means of strain measurement.Furthermore it can only test samples at zero confining pressure, hence it is onlypossible to draw one Mohrs circle. The Mohr Coulomb envelope requires at leasttwo Mohrs circles at different confining pressures.

The drainage conditions in the triaxial test can be varied from the:

completely undrainedsituation immediately after construction (e.g. astructure or excavation of a cutting in clay) tofully drainedtest conditions (excess pore pressure is allowed to dissipateand volume changes as water is squeezed out/in are measured) representingof long term stability of a cutting in clay.

NOTE:In consolidated undrained tests, the pore water pressure is measured (toenable effective stress strength parameters to be assessed) but no drainageis permitted.


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Simplified assessment of bearing pressures of clay

(For preliminary design purposes only)

Consider a building with a raft foundation, bearing pressure q and foundation width B asshown below;

Assume that failure takes place along a circularsurface.

Taking moments about the point O;

Disturbing moment (per m. run);

qB xB

=qB

2

(approx)2 2

Restoring moment (per m. run) =

2BcuB = cu B

22

In site investigation, only a very small proportion of the ground is sampled. Therefore thedegree of confidence in the results is much lower than for manufactured materials. Furthermore,

soil which may not fail in shear may undergo unacceptable settlement if subject to stress close to

the ultimate bearing pressure. For these reasons a factor of safety of 3.0 against failure is

normally adopted.

For a factor of safety of 3, Restoring moment =

cu B2 = cuB

2(approx)

(since at 3.142

divided by 3 is approx1 !!)

3

qB2

= cuB2

(approx)2

q = 2cu

NOTE: For preliminary design purposes only

Thus:

Approximate safe bearing pressure = 2 x shear strength

(relevant to shallow foundations on clay)


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Implications of soil types on foundation design

Shrinkage and swelling of clay soils

Clay soils (those which usually contain over 35% of clay sized mineral particles) can absorbwater and increase in volume, or swell. Reduction of the water, or more correctly the

moisture content, will result in a corresponding decrease in volume, or shrinkage.

In clay soils, foundations constructed at a shallow level i.e with the underside less thanabout 1.0m below finished ground level are liable to subside or be lifted as the claysvolume decreases with drying in summer or increases after wetting in winter. If the site isclear of trees, strip foundations taken down to a depth of 1.0m in clay are unlikely to movesufficiently to cause structural distress. The shrinkage potential is dependant upon the soilsclay content and plasticity index.

Plasticityindex(%)

ClayFraction

%

Shrinkage(or swelling)

potential

> 3532-48

12-32< 18

> 9560-95

30.60< 30

very highhigh

mediumlow

Additional effect of trees on clay soil movement

Trees and heavy vegetational growth withdraw a considerable quantity of water from theground during their seasonal growth. This is especially true in dry summers when treesgrowing in clay of medium to high shrinkage potential cause a large reduction in the volume

of the clay in addition to that due to normal seasonal effects with consequent additionalsubsidence. With the return of heavy winter rain and the end of the growing season the

clays volume increases and, on swelling, the ground surface rises. Even without trees, thegrassed surface of an open field on clay can rise 20 - 40 mm.

Consideration must be given to the following circumstances:

i) Planting new trees on clay near to existing buildings.ii) Building on clay near existing trees.iii) Cutting trees down near to existing buildings.iv) Building on a clay site newly cleared of trees and shrubs.

BRE (Building Research Establishment) and NHBC (National House Building Council) publishguidance on practical design approaches for shrinkable clay soil formations (for example

NHBC Practice Note 3).

Foundations on sand and gravel

Sands and gravels are not subject to swelling or shrinkage. However, in a sand or gravelsoil it should be remembered that its bearing strength (simplistic terminology) will be

approximately halved for a foundation based near to, or below ground water level. Theunderside of a foundation in sand or gravel soil should be kept as high as possible to remainabove the groundwater. Formation level should though be at sufficient depth below thatinfluenced by penetration of frost.

REFERENCES

Bishop, A W and Henkel, D J (1972) The measurement of soil properties in thetriaxial test2ndEd, Pub. Edward Arnold

Shear Strength Feb2010

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