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Unit - 5

Earth Pressure

Q1) What is mean by active earth pressure?

A1) It is pressure exerted on retaining wall resulting from slight movement of wall away from filling.

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Fig.: Active earth pressure

Q2) What is mean by Passive earth pressure?

A2) When the movement of the retaining wall is such that the soil tends to horizontally.

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Fig.: Passive earth pressure

Q3) What are the assumptions mady by Rankine for Earth Pressure?

A3) Assumptions of the Rankine theory for active earth pressure are as follows:

The soil mass is semi-infinite, homogeneous dry and colesionless.

The ground surface is plane which may be horizontal or inclined.

The back of wall is vertical smooth.

The wall yields about the base thus satisfies deformation condition for plastic equilibrium.

The soil element is in state of plastic equilibrium i.e., on verge of failure.

Q4) Explain Rankine’s State of Plastic Equilibrium in soils?

A4)

Plastic equilibrium of soil: When every point of the soil body is on the verge of failure, then a body of soil is said to be in plastic equilibrium. In another word; every point of soil mass at rest condition is brought on the verge of failure by applying tension or compression, then the state so occurred is termed as a general state of plastic equilibrium.

Rankine's was the only engineer who developed the concepts of plastic equilibrium to solve the stability problems.

When plastic equilibrium conditions are realized in limited zones of soil, then it is termed as the local state of plastic equilibrium. The development of earth pressure on the retaining wall is part of backfill comes under the plastic equilibrium condition.

Rankine considered a semi-infinite mass of soil comes under a horizontal surface and a vertical boundary as shown in Fig.

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Fig.: A semi-infinite mass of soil bound by a horizontal surface and a vertical boundary

Rankine assumed the soil mass to be homogenous, cohesionless and dry

Consider a soil element at a depth 'e' subjected to horizontal stress and vertical stress. There are no shear stresses acting on the horizontal and vertical planes, hence

and

are the principal stresses.

When the soil mass as a whole is stressed in such way that the principal stresses of every point are in the same direction then it set up the network of failure plane. This network of failure plane is called as slip line field as shown in fig. Slip line field is equally inclined to the principal planes. When sufficient deformation of mass take place, only then plastic equilibrium is set up.

Q5) Explain Active States when Wall Moves Away from Backfill?

A5)

The value of horizontal stress decreases when away from backfill. If the expansion of soil element is more enough, then the value of horizontal stress (

decreases to a minimum value and state of plastic equilibrium is set up called as active Rankine state as shown in Fig.

The Mohr's stress circle shows the state of elastic equilibrium as shown in Fig.

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Fig.: Active and passive Rankine state due to wall movement

Active Rankine state:

When the Mohr's stress circle touches the strength line drawn for the soil, then soil mass is active Rankine state.

Note that plastic equilibrium state is developed due to decrease in the value of horizontal stress (

) it means it should be minor principal stress (

); vertical stress (

) and major principal stress (

), Minor principal stress due to decrease in the value of a, (horizontal stress) and Major principal stress.

Q6) Explain Earth pressure at rest?

A6)

It has been shown that active pressure exerted on the raintaing wall resulting from slight movement of the wall away from the backfill is associated with the expansion of the soil and passive pressure exists when the movement of the retaining towards the backfill which tends to compress the soil horizontally. In short, passive pressure is associated with compression.

When a soil element at a depth 'z' below the ground surface not subjected to any strain in the natural state, then the soil element in this condition is called as soil at rest condition. Earth pressure at rest exerted on the back of a rigid retaining wall can be determined by using the theory of elasticity in which soil is assumed to be elastic, homogeneous, isotropic and semiinfinite.

At rest condition, the earth pressure is expressed as follows,

P0=K0 z

Where K0=Coefficient of earth pressure

z=Effective vertical stress at depth a

Fig. shows a retaining wall of height H at rest. It is possible to determine the lateral pressure by using theory of elasticity considering the soil mass to be homogenous, elastic isotropic and a semi-infinite material provided there is no displacements at all.

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Fig.: earth pressure at rest

Q7) Explain Earth pressure on retaining wall due to submerged backfill?

A7) Fig. shows the retaining wall with backfill submerged by the natural water table saturated water. In such case, the lateral pressure is the sum of the two components.

These two components are as follows,

Lateral pressure caused by submerged weight (

) of the soil, k, y, z and

Lateral pressure caused by water (

)

$H:\unit5\IMG_20210520_143411.jpg$

Fig.: Submerged backfill

Here at any depth 2 below the horizontal surface-active pressure is given by the following expression,

Pa=Kasz+z

where, Pa=active pressure

s= submerged weight of soil (y)

unit weight of water

Fig. shows the active earth pressure distribution diagram at any depth 'z' and at the depth H.

The active pressure at the base of wall, where z H is given by the following expression,

Pa=KasH+H

Q8) Explain Backfill with Uniform Surcharge?

A8) Fig. shows the retaining wall with horizontal backfill which is loaded by a uniformly distributed surcharge of intensity "q" by assuming the vertical pressure at any, depth is increased by "q".

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Fig.: Retaining wall with backfill carrying uniform surcharge

∴Lateral active pressure at any depth 'z' is given by the following expression

Pa=Kaz+Kaq …. (At any depth z)

where z =H, then, active pressure at the base is given

Pa=KaH+Kaq ......(at height H from base of wall)

Q9) Explain Backfill with sloping surface?

A9)

Rankine's theory can also be applied for backfill with sloping surface at the constant angle

to the horizontal.

To determine the active earth pressure in such case by Rankine's theory, an additional assumption is considered that the vertical stress and lateral pressure are conjugate stresses.

The active earth pressure at a depth 'z' acting parallel to the slope is given by the following expression:

Pa= Ka γz, ...For sloping surface

Where, Ka=

$H:\unit5\IMG_20210520_143450.jpg$

Fig.: backfill with sloping surface

For horizontal ground surface; =0

Ka=

The total active pressure P, for a retaining wall having height 'II' is given by the following expression:

Pa=KaH2

Q10) What is Basic Assumptions of Coulomb's Wedge Theory?

A10) Following are the various basic assumptions of coulomb's wedge theory

The backfill is dry, non-cohesive (ie. cohesionless), homogeneous, isotropic, soil (i.e., equal elastic properties in all direction). The backfill is elastically undeformable but breakable

Backfill possessing both cohesion and internal friction or slip surface

The failure surface or slip surface is a plane surface which passes through the heel of wall

Failure is two dimensional. The backfill surface is plane and can be inclined.

The position and the line of action of the earth pressure or direction of resultant earth pressure are known. The back of the wall can be inclined to the vertical

The sliding wedge is itself considered as rigid body and the earth pressure is obtained by considering the limiting equilibrium of the sliding wedge as a whole.

Q11) Explain Rebhann’s graphical method of determination of earth pressure?

A11)

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Fig.: Graphical method by poncelet construction based on Rebhann’s principles

In 1871, Rebhann's represented a graphical method to determine the total active pressure (Pa) based on Coulomb's theory on a rough wall with a cohesionless, homogenous and inclined backfill as shown in Fig.

Fig.shows poncelet construction for non-cohesive soils or cohesionless soils (C = 0) based on the principles made by Rebhann.

Procedure of graphical method:

Following is the procedure of construction to find out the active earth pressure by graphical method refer Fig.

Draw a retaining wall to a suitable scale and measure the backfill surface angle for required position as shown in Fig.

Draw a -line EG such that it intersects the backfill surface at G.

Draw a semi-circle BQG by taking diameter as EG.

Draw the pressure line 'EO' at an angle of (a-5) with respect to o-line.

Draw FI parallel to pressure line 'EO'.

Draw a perpendicular to EG at I such that it cut the semi-circle at T.

With centre E and radius ET, draw an are such that it cut EG at J.

Draw JM parallel to FI

Now EM is a rupture line

Taking as a centre and IM as the radius draw at a such thar EG at L

After this construction from step 1 to 10, it shows the LIM. Area of LIM in its natural unirs multiplied by the unit weight of the soil () gives the active earth pressure (Pa) as follows:

Pa=Area of triangle LJM=*JM*MN

Where, =unit wt of the soil

JM length of a triangle LJM

MN=height of LJM

Pa=Active earth pressure

Q12) Explain Culmann’s graphical method of determination of earth pressure?

A12)

Culmann's graphical method is rather general method than Rebhann's method. This method is same as the trial wedge method. The force triangle or force polygon can directly be constructed on o-line EG considering EG as a load line.

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Fig.: Culmann’s graphical method for determining active earth pressure

This method can be used to evaluate the coulomb's earth pressure fr ground sa face of any configuration, different types of surcharges and layered backfills.

Fig. shows the Culmann's graphical method of determine active earth pressure (P) for non-cohesive soils or cohessionless soils (i.e., C= 0)

Graphical construction procedure;

Various steps involved in the procedure are as follows:

EF it a retaining wall as shown in Fig. 5 in 1(a) drawn to a suitable scale.

Draw -line EG at an angle with respect to horizontal.

Mark on EG, the distances EA, EC, ED, EL, EJ etc to a suitable scale representing the weight of wedges EFA, EFC, EFD, EFI, EFI etc respectively.

Draw lines parallel to pressure line ET from the points A, C, D, I J such that it intersects assumed rupture line EA, EC, ED, EI, EJ at points A, C, D,1, J respectively.

Then point A', C, D, I', J' are joined by a smooth curve representing the pressure locus.

Select point B' on the pressure locus in such way that the tangent to the curve at this point parallel to line EG

Draw B'B parallel to the pressure line ET. The magnitude of B'B" itself in its natural units gives the active earth pressure (Pa)

Points E and B' are joined and extended further so as to meet the surface of backfill at B Then EB is the rupture line.

Note that, for the plane backfill surface, the point of application of active earth pressure (Pa) is at a height 1/3 of from the base of retaining wall.

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