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Table of Contents

1. EFFECT OF OCR AND CONFINING PRESSURE ON SOIL PROPERTIES ......... 2

1.1 Effect of OCR on Soil Strength Parameter ( c-Φ SOIL ) ................................................. 2

Effect of OCR on the Elastic modulus of soil: ......................................................................... 4

1.2 Effect of confining Pressure on Stress-Strain Behaviour (Cohesionless Soil)................. 5

Effect of confining pressure on the Elastic modulus of soil: ................................................... 7

2. YOUNG'S MODULUS OF SOIL ..................................................................................... 8

2.1 Introduction ...................................................................................................................... 8

2.2 Factors influencing Elastic Modulus of soil ..................................................................... 8

2.3 Assessment of Elastic Modulus of soil ............................................................................ 8

2.3.1 California Bearing Ratio (CBR) ............................................................................... 9

2.3.2 Standard Penetration Test (SPT) ............................................................................. 10

2.3.3 Static Cone Penetration Test (SCPT) ...................................................................... 11

2.4 Relation Between soil Elastic Modulus (Es) and Depth ................................................ 13

3. REFERENCES ................................................................................................................. 15

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1. EFFECT OF OCR AND CONFINING PRESSURE ON SOIL

PROPERTIES

Following gives the effect of OCR on the strength parameters of the cohesive soil and confining

pressure on the non cohesive soil.

1.1 Effect of OCR on Soil Strength Parameter ( c-Φ SOIL )

OCR of soil is defined as the highest stress experienced by the soil divided by the current stress.

Following are the chart showing the effect of OCR on the ratio of the maximum deviator stress

to the confining stress, angle of internal friction and cohesion of the soil (fig. 1.1).

In the present study, all soil samples were tested after being subjected to different initial

consolidation pressure. The initial consolidation pressures (σ0‟) applied to the soil sample were

50kPa, 200kPa and 400kPa. It was found that with increase of over consolidation ratio increases,

the maximum deviator Stress/σc‟ ratio (σc‟=confining pressure), angle of internal friction and

cohesion value increases.

This effect is verified by two separate experiments. Experiments were carried on the normally

consolidated soil and Over consolidated soil.

Please note that for Normally consolidated soil OCR value is 1 and for over consolidated soil the

OCR >1.

Fig 1.1 Effect of OCR on Soil Strength

Parameters.

Sivadass, T., Lee, C.Y. & Karim M.S.A,

2003, “ Behavior of a tropical residual

soil”, ISBN 90 5809 604 1.

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Figure 1.2 represents Triaxial Test results on normally consolidated and over consolidated soil.

fig 1.2 Failure envelope for (a) Normally consolidated and (b) over-consolidated clay from

consolidated drained triaxial test. (Das B.M., “Advanced Soil Mechanics”)

The value of c is obtained by drawing a common tangent to Mohr‟s circle which is Mohr-

coulomb‟s envelope. In figure 1.2(a), it is clear that in normally consolidated clay the cohesion is

zero. But when over consolidated clay as shown in figure 1.2(b) the failure envelope makes an

intercept with the vertical giving cohesion value. Thus as the OCR value increase, the increase in

the cohesion value is observed.

Fig 1.3 Failure envelope of soil with a pre-consolidation pressure σc’.

(Das B.M., “Advanced Soil Mechanics”)

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The change in the angle of internal friction is verified in the following experimental observation.

Please refer figure1.3. If a soil is initially consolidated by an encompassing chamber pressure of

σc=σc‟, and allowed to swell under reduced chamber pressure of σ3=σ3‟, the specimen will be

over-consolidated. The failure envelope obtained from the consolidated drained triaxial tests of

this type of specimen has two distinct branches. Portion „ab‟ of the envelope has flatter slope

with a cohesion intercept and portion „bc‟ represent the normally consolidated soil with zero

cohesion. Thus as the soil turns from over-consolidated to normally consolidated or the OCR

value decreases, the angle of internal friction of the soil is increasing.

Effect of OCR on the Elastic modulus of soil:

The following correlation gives relation between the soil elastic modulus and undrained shear

strength of soil:

Es = Kc.Cu

Kc = correlation factor (Figure 1.4)

Cu = undrained shear strength, tsf

Fig. 1.4: Correlation factor based on OCR (www.geotechnicalinfo.com/youngs_modulus.html)

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1.2 Effect of confining Pressure on Stress-Strain Behaviour

(Cohesionless Soil)

Fig. 1.5. Stress Ratio ~ Axial Strain and volumetric Strain ~ Axial strain relationship from σh =

constant tests starting from isotropic Stress State (Sheared Air-dried; ε0=0.125% per minute)

(Yasin, S.J.M and Tatsuoka, F., March16&17, 2006 “Stress-Strain Behaviour of a Micacious

Sand in plane Strain condition”, Geotechnical Symposium in Roma )

Figure 1.5 shows the effect of initial density and confining stress on the stress-strain behavior of

soil where σh‟ or σh = minor principal stress or confining pressure = constant‟. The starting point

of each curve correspond to isotropic stress state of either (σh)c = 100 KPa or (σh)c = 400 KPa.

The specimens were air dried.

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The continuous lines represent the curve obtained for the test on dense sand and the dotted for

loose sand. Following are the observation:

1. Test J319C with dense initial state and low confining stress show sharp peak in „axial

stress~axial strain‟ relation and sample also starts dilating at peak stress level and still εvol

is positive (i.e. the volume is lower than the initial volume).

2. On the other hand test J318C with dense initial state and high confining pressure showed

a more ductile behavior without any sign of dilation even at peak state that resemble the

volume change behavior of loose specimens.

Thus dense sand at high confining stress may behave like a loose sand at low confining stress.

Figure 1.6 verifies the observation.

Fig 1.6 Deviator Stress and Axial Strain confining Pressure of 50 kPa, 200 kPa and 400 kPa

Sivadass, T., Lee, C.Y. & Karim M.S.A, 2003, “ Behavior of a tropical residual soil”, ISBN 90 5809 604

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Effect of confining pressure on the Elastic modulus of soil:

Fig 1.7 Relation between the initial elastic modulus and confining pressure

(Jui-Pin Wang and Hoi I. Ling, Mohri, L., 16 & 17 March 2006, “Stress Strain Behaviour Of

Compacted Sand Clay Mixture”, Geotechnical Symposium in Roma)

Figure 1.7 shows that Elastic modulus of unsaturated specimen at higher confining pressure has

high elastic modulus. Generally the initial elastic modulus increased logarithmically with

increase of confining pressure.

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2. YOUNG'S MODULUS OF SOIL

2.1 Introduction

The modulus of elasticity or Young's modulus of a soil is an elastic soil is useful for a variety of

applications within geotechnical engineering including shallow foundations, deep foundations

and slope stability or retaining structures

Young's soil modulus, Es, may be estimated from empirical correlations, laboratory test results

on undisturbed specimens and results of field tests. Laboratory tests that may be used to

estimate the soil modulus are the triaxial unconsolidated undrained compression or the triaxial

consolidated undrained compression tests. Field tests include the plate load test, cone

penetration test, standard penetration test (SPT) and the pressuremeter test.

2.2 Factors influencing Elastic Modulus of soil

Soil with closely packed particles tends to have a higher modulus. This can be determined by

looking at the soil's dry density or porosity. However, two soil samples can have the same dry

density but different structures, like loose or dense, and thus have different moduli.

Water content also impacts moduli. At low water contents the water binds the particles,

increases the stress and suction between the particles and leads to a high soil moduli. This is

especially apparent when considering the stiffness of dried clay. However, this does not hold

true for coarse grain soils. If water content rises too much, the particles are pushed apart and the

modulus is reduced.

If the soil has been subjected to stress in the past, it will impact the modulus. An over-

consolidated soil will generally have a higher modulus than the same normally-consolidated

soil.

Soils may see cementation, or a glue effect, between particles from either low water content or

chemical cementation developed at contacts. This cementation leads to an increase in modulus.

2.3 Assessment of Elastic Modulus of soil

The most useful geotechnical data with which the Elastic modulus of soil can be derived by

correlation are as follow:

1. California Bearing Ratio (CBR)

2. Standard Penetration Test (SPT)

3. Static Cone Penetration Test (SCPT)

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2.3.1 California Bearing Ratio (CBR)

Fig 2.1 Approximate correlation between CBR and long term Elastic modulus

(Design applications of raft foundation By J.A. Hemsley)

Figure 2.1 gives correlation between CBR and long term Elastic modulus. The short term

elastic modulus may be derived from the equation

Es (Long Term) = Es (Short Term) x β

Where the value of β is as found from the table below:

Soil Type Factor β

Gravel 0.9

Sand 0.8

Silt, Silty clay 0.7

Stiff clay 0.6

Soft clay 0.4

Alternatively the value of Subgrade modulus E value, in MPa, may be found using the

following convention formula:

E = 10.3 CBR

To find E based on modulus of Subgrade reaction, k, the equation is:

E = 26 k1.284

The above conversation is provided by the FAA.

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2.3.2 Standard Penetration Test (SPT)

Fig 2.2 Correlation between short term young’s modulus, SPT value and plasticity index

(Design applications of raft foundation By J.A. Hemsley)

Figure 2.2 gives correlation between young‟s modulus of soil, SPT values and plasticity index.

For sands and Gravel PI = 0.

NAVFAC DM-7.1, 1892 proposed following approximate correlation between soils young‟s

modulus and SPT value for cohesionless soil (Geotechnical Engineers Portable Handbook,

Robert W. Day):

Cohesion less soil type Es/N

(tsf ≈ 100

kPa)

Nonplastic silty sand or silt

sand mixtures

4

Clean, fine or medium sands 7

Coarse sand and sand with

little gravel

10

Sandy gravel and gravel 12

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Fig 2.3 Correlation between blow count and modulus of sand

Geotechnical and Geoenvironmental engineering handbook by R.K. Rowe

The above correlation is suggested by D‟Appolonia et al (1970), ν‟ is the Poisson‟s ratio of the

soil.

2.3.3 Static Cone Penetration Test (SCPT)

The correlation between short term young‟s modulus and SCPT/CPT value is given by

Es = α qc

Where, qc static cone penetration resistance and α is modulus correlation factor as given in the

table below:

Soil type Factor (α)

Sand -loose 5

-medium dense 8

-dense 10

Silt 12

Silty clay 15

Clay -highly plastic 20

Geotechnical and Geoenvironmental engineering handbook by R.K. Rowe suggests following

simple correlation between SCPT value and Youngs modulus:

For Long and Strip footing L/B > 10, Es = 3.5 qc.

For Axisymmetric footings or L/B = 1, Es = 2.5 qc

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Following correlation is suggested between SPT, CPT and elastic modulus (Table 5-6,

Foundation Analysis and Design, Bowels J.E. ) :

Following range of values are proposed for the Poisson‟s ratio and Elastic modulus (Das, Braja

M., “Principles of Foundation Engineering”)

Soil Poisson’s Ratio Soil Es (kPa)

Loose Sand 0.2–0.4 Soft Clay 1725–3450

Medium Sand 0.25–0.4 Hard Clay 5860–13,800

Dense Sand 0.3–0.45 Loose Sand 10,350–27,600

Silty Sand 0.2–0.4 Dense Sand 34,400–69,000

Soft Clay 0.15–0.25

Medium Clay 0.2–0.5

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A separate and simplified relation between SPT, CPT and elastic modulus is

provided in “Practical Foundation Engineering Handbook”, McGraw-Hill:

SOIL SPT (KPa) CPT (Unit of qc)

Sand

Es = 500(N + 15)

Es = 18,000 + 750N

Es = (15,000 to 22,000) lnN

Es=(2 to 4)qc

Es=2(1+Dr2)qc

Clayey sand Es = 320 (N+15) Es=(3 to 6)qc

Silty sand Es = 300 (N+6) Es=(1 to 2)qc

Gravelly sand Es = 1,200 (N+6)

Soft clay Es = (6 to 8)qc

2.4 Relation Between soil Elastic Modulus (Es) and Depth

As per Gibson Method the Elastic Soil modulus increases linearly with depth in the form:

Es = E0 + kE . Z

Where,

E0 : Value of soil modulus directly beneath the foundation base (z = 0)

KE : Rate of increase of modulus with depth (units of E per unit depth) and

Z : Depth

This relation holds good for both vertical and lateral soil elastic coefficient.

Cohesionless soil and normally consolidated clay are two cases where the stiffness is zero at the

surface and increases rather linearly with depth. The value is Es for some over-consolidated clay

and rocks are approximately constant throughout the depth (Section 3.2.3, “Single pile and pile

group under lateral loading”, Reese, L.C. and Van Impe W.F.). in Table 3.7 is suggested the

following range for Kpy (KE for lateral load) for laterally loaded piles in sand.

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Relation between horizontal soil elastic Modulus and soil Young‟s Modulus (as per Section

3.2.4.1, “Single pile and pile group under lateral loading”, Reese, L.C. and Van Impe W.F.) is

given below:

Where,

Epy : horizontal soil Elastic modulus

Es : Soil Elastic modulus

ν : Poisson‟s ratio

Ip : Influence coefficient (approximately 1.2)

The value of ξ can be approximated to 1.0 on the conservative side. Hence, Epy ≈ Es.

Hence same relation as mentioned above in table 3.7 can be assumed for soil elastic modulus as

well. Thus Kpy in the above table can be assumed to be equal to Ks on the conservative side.

The weighted average Es of the soil can be obtained using formula:

𝐸𝑠(𝑎𝑣𝑔 ) =𝐸1𝐻1 + 𝐸2𝐻2 + 𝐸3𝐻3 +⋯+ 𝐸𝑛𝐻𝑛

𝐻

Where,

E1, E2, E3, E4.. En are the Elastic modulus of different Layer of soil.

H1, H2, H3, H4.. Hn are the thickness of each Layer of soil.

H is the total thickness of the soil.

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3. REFERENCES

1. Bowels J.E. , “Foundation Analysis and Design”.

2. Das B.M., “Advanced Soil Mechanics”.

3. Das, Braja M., “Principles of Foundation Engineering”.

4. Day, R. W., “Geotechnical Engineers Portable Handbook”.

5. eHow . com (http://www.ehow.com/list_7590255_elastic-modulus-soils.html)

6. Geotechnical Info . com (http://www.geotechnicalinfo.com/youngs_modulus.html)

7. Hervé Di Benedetto, “Deformation characteristics of Geomaterials”.

8. Hoe I. Ling, Luigi Callisto, Dov Leshchinsky, Junichi Koseki, “Soil stress-strain

behavior: measurement, modeling and analysis”.

9. J.A. Hemsley, “Design applications of raft foundation”.

10. Jui-Pin Wang and Hoi I. Ling, Mohri, L., 16 & 17 March 2006, “Stress Strain Behaviour

Of Compacted Sand Clay Mixture”, Geotechnical Symposium in Roma

11. NAVFAC DM-7.1, 1892.

12. Paul W. Mayne, Harry G. Poulos (June, 1999), “Approximate displacement influence

factors for elastic shallow foundations”, Journal Of Geotechnical And Geoenvironmental

Engineering, 453-460.

13. “Practical Foundation Engineering Handbook”, McGraw-Hill.

14. Robert W. Day , “Geotechnical Engineers Portable Handbook”.

15. Reese, L.C. and Van Impe W.F., “Single pile and pile group under lateral loading”.

16. R.K. Rowe, “Geotechnical and Geoenvironmental engineering handbook”. 17. Sivadass, T., Lee, C.Y. & Karim M.S.A, 2003, “ Behavior of a tropical residual soil”, ISBN 90

5809 604.

18. Yasin, S.J.M and Tatsuoka, F., March16&17, 2006 “Stress-Strain Behaviour of a

Micacious Sand in plane Strain condition”, Geotechnical Symposium in Roma