Elastic Modulus of Soil | Soil Mechanics | Elasticity (Physics)

Table of Contents 1.

EFFE EFFECT CT OF OCR OCR AND AND CONF CONFIN INING ING PRES PRESSU SURE RE ON SO SOIL IL PROP PROPER ERTIE TIES...... S..........2 ....2

1.1 1.1

Effe Effect ct of OCR OCR on on Soi Soill Str Stren engt gth h Par Param amet eter er ( cc-Φ SOIL )......................................2

 Effect of OCR on the Elastic modulus of soil:..........................................................4 1.2

Effect Effect of of confin confining ing Press Pressure ure on on Stress Stress-St -Strai rain n Behavio Behaviour ur (Cohes (Cohesion ionles lesss Soil) Soil).............5

 Effect of confining pressure on the Elastic modulus of soil:........................................7 2.

YOUN YOUNG' G'S S MODU MODULU LUS S OF SO SOIL IL... ....... ....... ...... ....... ....... ...... ....... ....... ....... ....... ...... ....... ....... ...... ....... ....... ...... ....... ....... ....... ....... ...... ....... ........ .....8 .8

2 .1

Introduction.............................................................................................8

2.2 2.2

Facto Factors rs infl influen uenci cing ng Elas Elasti ticc Mod Modul ulus us of soil soil......................................................8

2.3 2.3

Asse Assess ssme ment nt of Elas Elasti ticc Modu Modulu luss of of soi soill............................................................8

2.3. 2.3.1 1

Cali Califforni orniaa Bea Beari ring ng Rati Ratio o (CB (CBR) R)...............................................................9

2.3. 2.3.2 2

Stan Standa dard rd Pen Penet etrrati ation Tes Testt (SPT (SPT))............................................................10

2.3. 2.3.3 3

Stat Static ic Cone Cone Pene Penetr trat atio ion n Tes Testt (SC (SCPT PT)).......................................................11

2.4 2.4 3.

Rela Relati tion on Betw Betwee een n soil soil Ela Elast stic ic Mod Modul ulus us (Es (Es)) and and Dept Depth h......................................13 REFE REFERE RENC NCES ES... ....... ....... ...... ....... ....... ...... ....... ....... ....... ....... ...... ....... ....... ...... ....... ....... ...... ....... ....... ....... ....... ...... ....... ....... ........ .......... .......... .......... .......... .........1 ....15 5

REFERENCES

1

| Page

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 O CR 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).

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.

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 ca rried 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.

1

| Page

 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 Mohrcoulomb’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 σ c’.

2

| Page

(Das B.M., “Advanced Soil Mechanics”) 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 

1

| Page

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

1

| Page

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.

1

| Page

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 ε vol 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

2

| Page

 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.

1

| Page

1.

YOUNG'S MODULUS OF SOIL

1.1 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. 1.2Factors

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 overconsolidated 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.

1.3Assessment

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)

1

| Page

1.1.1 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 k 1.284 The above conversation is provided by the FAA.

1

| Page

1.1.2 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

1

| Page

 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. 1.1.3 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:

Sand

Soil type

Factor (α)

-loose

5

-medium dense

8

-dense

10

Silt

12

Silty clay

15

Clay

1

| Page

-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

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”)

2

| Page

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

A separate and simplified relation between SPT, CPT and elastic modulus is  provided in “Practical Foundation Engineering Handbook”, McGraw-Hill: SOIL Sand

SPT (KPa) Es = 500(N + 15) Es = 18,000 + 750N Es = (15,000 to 22,000) lnN

CPT (Unit of qc) Es=(2 to 4)qc Es=2(1+Dr 2)qc

Clayey sand Silty sand Gravelly sand

Es = 320 (N+15) Es = 300 (N+6) Es = 1,200 (N+6)

Es=(3 to 6)qc Es=(1 to 2)qc

Soft clay

Es = (6 to 8)qc

1.2 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 + k  E . Z Where, E0 : K E : Z :

Value of soil modulus directly beneath the foundation base (z = 0) Rate of increase of modulus with depth (units of E per unit depth) and 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 K  py ( K  E  for lateral load) for laterally loaded piles in sand. 1

| Page

Relation between horizontal soil  per Section 3.2.4.1, “Single pile L.C. and Van Impe W.F.) is given

elastic Modulus and soil Young’s Modulus (as and pile group under lateral loading”, Reese, below:

Where, E py Es  ν Ip

: : : :

horizontal soil Elastic modulus Soil Elastic modulus Poisson’s ratio 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+…+EnHnH 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.

2

| Page

2.

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

3

| Page