soil arching in granular soil

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SOIL ARCHING IN GRANULAR SOIL By, Jithu G Francis B120055CE 1

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Page 1: Soil arching in granular soil

SOIL ARCHING IN GRANULAR SOIL

By, Jithu G Francis

B120055CE 1

Page 2: Soil arching in granular soil

OVERVIEW• Introduction • Experimental evidence of arching• Soil arching and its mechanism• State of stresses in zone of arching• Theoretical consideration of arching• Limit state analysis of arching• Conclusion

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INTRODUCTION

What is soil arching?

It is a universal phenomenon that occurs when the stress is transferred from the yielding part of the soil to the adjacent rigid zone is known arching effect of soil.

It can illustrated with the help buried pipe rather than a rigid pipe.

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EXPERIMENTAL EVIDENCE• By Hummels, F.H. and Finnan, E.J. (1920)1. Discharging sand trough a point source.2. Poured sand of 8-9 ft over wooden platform.3. 2 set of results were obtained (a). Result of conical sand pile

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(b). Result for prismatic sand piles

Conclusion“arching causes the stress to drop down at the centre of the pile sand”

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• By Vanel, L. and Howell in 1999Demonstrated the occurrence of arching due to base stress under sand piles.

(a) sand pile deposited from a line source, and (b) sand pile constructed by uniform raining, where r/R is the ratio of radius of pile to that of the height of sand pile

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SOIL ARCHING

DEFINITIONSoil arching occurs where there is a difference in the

stiffness between the installed structure and the surrounding soil.

1. MECHANISM OF SOIL ARCHINGDue to the relative displacement between the moving and

stationary soil masses their exist a shear stress.Shear stress developed maintains the yielding soil in its

original position.State of stress depends on the geometry of the yielding

region.Localized displacement causes soil arching.

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2. MANIFESTATION OF SOIL ARCHING

(a) Above trap door; (b) Between Trees; (b) Above Buried structure; (c) In Silo

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3. SOIL ARCHING IN RETAINING WALL

Arching in pile walls occurs when the soil attempt create a relative displacement

4. FACTORS AFFECTING SOIL ARCHING

From the studies of Vanel and Howell it is stated that change of soil strength as well as elasticity modules has a effect in the formation mechanism of the arch.

Some of the other factors that affect are soil compactness, pile spacing, pile diameter and the friction coefficient between sandy soil and foundation.

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5. RATIO OF SOIL ARCHING

Vertical stress ratio at the mid span of pile is one of the important parameter, i.e.

)Where ρv, is vertical stress ratio, σv is vertical stress of pile block or soil between piles and qo is the overburden pressure.

If vertical stress ratio is less then the effect of arching will be more.

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STATE OF STRESS IN THE ZONE OF ARCHING

(a) Failure caused by downward movement of a long narrow section of the base of a layer of granular soil (sand); (b) enlarged details of diagram (a); (c) shear failure in sand due to yield of lateral support by tilting about its upper

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Length of strip ‘ab’ is given by 2B.

The discontinuity in the vertical pressure gives an evidence on the existence of radial shear.

Strips will always yield in the downward direction.

Downward movement is possible only if the surface of the sliding intersect the horizontal surface of the sand at right angle

The slope of the depression will decrease from 90o to a45o+ϕ/2

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THEORIES OF ARCHINGTheories of arching mainly deals with the pressure of dry sand

on yielding horizontal strips.

THEOREM 1: The condition for equilibrium of the sand is located above the loaded strip.

THEOREM 2: The entire mass of sand located above the yielding strip is in a state of plastic equilibrium.

THEOREM 3: The pressure on the yielding strip is equal to the difference between the weight of the sand located above the strip and the total vertical frictional resistance. 14

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THEORITICAL COSIDERATION OF ARCHING

(a) Mohr Circle to show arching stresses at rough wall, (b) continuous inverted arch defined by Trajectory of Minor Principal Stresses, (c) shear line directions

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Where minor principal stress, σ3,defines a continuous compression arch that always dips downward instead of going upward and major principal stress, σ1, and if we consider stress geometry then continuous σ3 arch and the discontinuous σ1 trajectoryVertical downward movement which is met by randomized inter-particle shear movement, as at r, s and t.σh is the horizontal stress and σv is vertical stress

1. STRESSES IN THE ARCH

Soil arches when it is in plastic state, so the force equilibrium is taken as triangular element

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and Divide Eq. (6.2.1) by σ1 and now consider the soil to be in active state then we can express, thus we can rewrite the equation as

Since, now substituting this for σh we get

Now divide Eq. (6.2.3) by Eq. (6.2.4), then we get

If it is a smooth wall, then θ = 90o, then the equation formed will be known as Rankine equation, and for a rough vertical wall, θ = 45o+ϕ/2, then the equation that formed will be known as Krynine equation.

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2. RADIAL STRESS FIELD IN ARCH

Polar coordinate system

In the Mohr Coulombs circle, yield condition for purely frictional materials is represent in the form of polar coordinate system, it given by

where ø is said to be the internal frictional angle.18

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Let us consider p be the mean stress which is given by the , so we can write the above equation as

- inclination angle of the major principle stress to radius r.• The direction of the principal stress for a purely frictional

material is not clearly defined along stress-free contours.• In order to overcome this Sokoloviskii (1965) suggested that

the plane mean stress p can be expressed as the function of θ,

- unit weight of the soil

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3. SHAPE OF ARCH The arching element is bounded by surface which represents

the principal planes of zero shearing stress. If the pile is uniform in density, weight and thickness

through out then the shape will be catenary. The equation for catenary is given by

Slope is given by

a is the coefficient which depends on unit weight of sand and x is the relative distance from the centre line and has limits ±1

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LIMIT STATE ANALYSIS OF ARCHING

Limit state analysis are based on the concept of incipient collapse state.

The static theorem states that: “collapse will not occur if a safe admissible stress field can be found everywhere in the structure”.

For finding arching in the sand pile we consider a fictitious failure mechanism.

Fictitious “spreading” collapse mechanism of a prismatic sand pile. 21

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The static theorem of limit analysis directly deals with the principle of maximum plastic work, it states that the true stress field at collapse maximizes the plastic work,

Where and are the true stress and strain rate fields during collapse and is any statically accepted stress field. Incipient collapse with deflection at the base is another

mechanism for finding arching.

Deflection of base under a prismatic sand pile22

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CONCLUSIONArching is homogenous and isotropic in a granular medium.With the help of plasticity approach based on the theorems of

limit analysis helps to find some of the occurrence of arching. It is likely to provide low stressed region for supporting the

arching region. The shape of the arching is a catenary. If a statically admissible stress field is provided for supporting

then there will be less failure due to arching. If the work rate of external load acting on the soil exceeds the

rate of internal work then arching will not occur23

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REFERENCE1. Bosscher, P.J. and Gray, D.H. (1986), Soil arching in sandy slopes, Journal of Geotechnical Engg,112, 626-6452. Chang, D.C. and Kuester, E.F. (1998), Numerical Analysis of soil arching, Electromagnetic boundary problems,1280-12873. Drucker, D.C., Prager, W. and Greenberg, H.J. (1952). Extended limit design theorems for continuous media, Quarterly of Applied Math., 9, 381-389.4. Handy, L. R. (1985). The Arch in Soil Arching, Journal of Geotechnical Engg., 111, 302-318.5. Hermann,H.J.(1998), Shape of the sand piles, Physics of Dry granular Media, vol no- 23, 319-3386. Hummel, F.H. and Finnan, E.J. (1920). The distribution of pressure on surfaces supporting a mass of granular material. Minutes of proc. Inst. Civil engg., Session 1920-1921, Part II, Selected Papers 212, 369-392.7. Michalowski, R.L. and Park, N. (2005), Arching In Granular Soils, ASCE – Geotechnical Special, Publication NO-143, 255-2688. Michalowski, R.L. and Park, N. (2004). Admissible stress fields and arching in piles of sand. Submitted to Géotechnique, 2003.9. Sokolovskii, V.V. Statics of Granular Media, Oxford,Inc, Pergamon, 1965, 182-21310. Terzaghi, K., Theoretical Soil Mechanics, John Wiley and Sons, Inc., New York, N.Y, 1943, 66-7611. Vanel, L., Howell, D., Clark, D., Behringer, R.P. & Clement, E. (1999). Memories in sand: Experimental tests of construction history on stress distribution under sand piles. Physical Review E 60, No: 5, R5041-R5043.

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APPENDIX a = Mathematical coefficient in the equation for catenary B = Breadth of soil between two vertical rough wall D = Diameter of the pile qo = Overburden pressure ka = Active earth pressure coefficient, σ3/σ1 p = Mean stress which is given as = Unit weight of sandր ԑij = True strain θ = Angle of principal stress to vertical direction ø = Internal frictional angle τ = Shear stress ρv = Vertical stress ratio σv = Vertical stress of pile block σ3 = Minor principal stress σ1 = Major principal stress σh = Horizontal stress of pile block σij = True stress րi = Unit weight vector

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THANK YOU

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QUESTIONS

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