Earth Pressure on Retaining Structure

Relevant Course: (i)  Soil Mechanics – I or II    (ii)  Geotechnical Engineering I

Relevant Department: Civil Engineering 

Relevant Semester: 5th or 6th semester of UG (B.Tech./B.E.)

Pre- requisite : Basic Soil Mechanics (only index and engineering soil properties)

Course Description & Outline:

(i) Introduction and basic concepts of Lateral Earth Pressures

(ii) Retaining Structure and its uses

(iii) Different Theories on Earth Pressures

             (a)  Coulomb’s Earth Pressure Theory

             (b) Rankine’s Earth Pressure Theory

(iv) Culmann’s Graphical Solution Method

(v) Stability of Rigid Retaining Walls

(vi) Stability of Flexible Retaining Walls

(vii) Bracing Systems, Stability Considerations for Braced Cuts

(viii) Solved Problems

Schedule for Lecture Delivery

Session 1 :1st- Sep - 2015 (2-4 pm)

Session 2 :2nd - Sep - 2015 (2-4 pm)

Session 3 :4th- Sep - 2015  (2-4 pm)

Teacher Forum

Theories of Earth Pressures

Introduction 

  • A soil mass is stable when the slope of the surface of the soil mass is flatter than the safe slope.
  • At some locations, due to limitation of space, it is not possible to provide flat slope & the soil is to be retained at a slope steeper than the safe one. In such cases, a retaining structure is required to provide lateral support to the soil mass.
  • A retaining structure is a permanent or temporary structure which is used for providing lateral support to the soil mass or other materials.
  • The design of the retaining structure requires the determination of the magnitude & line of action of the lateral earth pressure. 
Examples of retaining Structure 
  • Retaining wall
  • Anchored bulkheads
  • Sheet piles
  • Sheeting and basement wall

Uses of retaining structures:

                              

                                       

Lateral Earth Pressure -Different Theories of Earth Pressure

  • The pressure or force exerted by soil on any boundary is called the earth pressure.
  • When the earth pressure acts on the side (back or face) of a retaining wall, it is known as the Lateral earth pressure.
  • The magnitude of the lateral earth pressure depends upon the movement of the retaining wall relative to the backfill & upon the nature of the soil
  • The lateral earth pressure is usually computed using the classical theories proposed by Coulomb (1776) & Rankine (1857). The general wedge theory proposed by Terzaghi (1943) is more general and is an improvement over the earlier theories.

 Different Theories of Earth Pressure 

  • There are two classical theories of earth pressure. They are:
    • Coulomb's earth pressure theory.
    • Rankine's earth pressure theory.
  • Coulomb published the first rigorous analysis of lateral earth pressure problem in 1776. Rankine proposed a different approach to the problem in 1857.
  • These theories propose to estimate the magnitudes of two pressures called Active earth pressure and Passive earth pressure.

Fundamental assumptions of theories:

  • The soil mass is semi infinite, homogeneous, isotropic, dry & cohesion less.
  • The ground surface is plane which may be horizontal or inclined.
  • The back of the wall is smooth & vertical (only for Rankine method).
  • The soil mass is in a state of plastic equilibrium i.e. at the verge of failure.
  • Well drained to avoid consideration of pore pressures.

Effect of wall Movement on Earth Pressure - Passive Earth Pressure

At Rest Condition

  A retaining wall with a plane vertical face,  which is backfilled with cohesion less soil , if the wall does not move even after filling the materials, the pressure exerted on the wall is known as pressure for the at rest condition of the wall.

Active Earth Pressure

  If suppose the wall gradually rotates about the point A and moves away from the backfill, the unit pressure on the wall gradually gets reduced and after a particular displacement of the wall at the top, the pressure reaches a constant value. This pressure is the minimum possible. The pressure is termed as the active earth pressure (Pa).

Passive Earth Pressure (Resistance)

    If the wall is now rotated about A towards the backfill, the pressure on the wall increases from the value of at rest condition to a maximum possible value. The maximum pressure that is developed is termed as passive earth pressure or resistance (Pp).

Source : Murthy (2009)

Development of Active and Passive Earth Pressure

Source : Murthy (2009)

The gradual increase or decrease of the pressure of the wall with the movement of the wall from the “at rest condition” may be depicted as shown in figure below.

.

  • When we are measuring the passive pressure, we are measuring the resistance of the soil against wall movement.
  •  Hence, for all practical purposes we get fully mobilised active earth pressure but partially mobilised passive earth pressure as such a large movement does not occur usually.
  • Therefore, we should design with (Pa– a small % of  Pp), as, we are making an unsafe design when we are designing with(Pa– fully mobilised Pp) and an uneconomic one when we are designing with only Pa.
  • To get fully mobilised active and passive earth pressures, the following wall movement are required approximately.

  • For dense sand, Pa  mobilised at 0.1% strain and Pp  at 5% strain.
  • For loose sand, Pa  mobilised at 0.4% strain and Pp  at 10% strain. 

Representation of Pressure by Mohr Circle - Lateral Earth Pressure

Source : Murthy (2009)

Lateral Earth Pressure for at rest condition

  • If the wall is rigid and does not move with the pressure exerted on the wall, the soil behind the wall will be in a state of elastic equilibrium.

  • The total pressure for the soil at rest condition, P0 = 0.5 K0 γH 2
  • The value of K0 depends on the relative density of sand and the process by which the deposit was formed

Different Values K0

Rankines Earth Pressure Theory - Active Earth Pressure

 

  • Assumptions: The Rankine's theory assumes that:

   

  • The ground and failure surfaces are straight planes.
  • The resultant force acts parallel to the backfill slope.
  • Soil is homogenous and isotropic.
  • In case of retaining structures, the earth retained may be filled up earth or natural soil which exerts certain lateral pressure on the wall.

Active Earth Pressure against a vertical section with horizontal surface

Source : Murthy (2009)

Passive Earth Pressure against a vertical section

Rankien's passive earth pressure in cohesionless soil 

Source : Murthy (2009)

Active Earth Pressure-Uniformlysurcharge horizontal surface

Active Earth Pressure-Backfill Partly Submerged with a Uniformly Surcharge Load and Horizontal Surface

Active Earth Pressure against a sloping cohesionless backfill surface

Rankine’s active earth pressure for sloping cohesionless backfill

Rankines Active Earth Pressure for Cohesive Soils

Rankine’s Active Earth Pressure for Cohesive Soils

Rankine’s Active Earth Pressure on Vertical Sections in Cohesive Soils

 

Effect of Water Table on Rankines Active Earth Pressure

Effect of Water Table on Rankine’s Active Earth Pressure on Vertical Sections in Cohesive Soils

  • Total Pressure due to soil = Area of (oab abdc bdf)

Limitations of the Rankine’s Earth Pressure Theory

  • The Rankine formula for passive pressure can only be used correctly when the embankment slope angle equals zero or is negative. 
  • If a large wall friction value can develop, the Rankine Theory is not correct and will give less conservative results. 
  • Rankine's theory is not intended to be used for determining earth pressures directly against a wall (friction angle does not appear in equations above).
  • The theory is intended to be used for determining earth pressures on a vertical plane within a mass of soil. 

Coulomb’s Wedge Theory

  • The Coulomb’s theory (1776) provides a method of analysis that gives the resultant horizontal force on a retaining system for any slope of wall, wall friction, and slope of backfill provided.

Assumptions :

  • The backfill is dry, cohesion less, homogeneous, isotropic and ideally plastic material, elastically undeformable but breakable.
  • The slip surface is a plane surface which passes through the heel of the wall.
  • The wall surface is rough. The resultant earth pressure on the wall is inclined at an angle δ to the normal to the wall, where δ is the angle of the friction between the wall and backfill. 
  • The sliding wedge itself acts as a rigid body & the value of the earth pressure is obtained by considering the limiting equilibrium of the sliding wedge as a whole.
  • The position and direction of the resultant earth pressure are known. The resultant pressure acts on the back of the wall at one third height of the wall from the base and is inclined at an angle  δ to the normal to the back. This angle is called the angle of wall friction.
  • The back of the wall is rough & relative movement of the wall and the soil on the back takes place which develops frictional forces that influence the direction of the resultant pressure.  

Coulomb’s Wedge Theory – Analysis Procedure

  • In Coulomb's theory, a plane failure is assumed.
  • The lateral force required to maintain the equilibrium of the wedge is found using the principles of statics.
  • The procedure is repeated for several trial surfaces.
  • The trial surface which gives the largest force for the active case, and the smallest force for the passive case, is the actual failure surface.

Coulombs Active Pressure in Cohesionless Soil

The sliding wedge ABD is in equilibrium under the three forces:

  • Weight of the wedge (W).
  • Reaction R on the slip surface BD.
  • Reaction Pa from the wall (wall reaction )/Earth pressure

Coulomb’s Wedge Theory

  • For yielding of the wall away from the backfill, the critical slip surface is that for which the wall reaction is maximum. The lateral pressure under this condition is the active pressure.
  • The main deficiency of this theory is the assumption that the slip surface is planar, therefore, the force acting on slide wedge do not generally meet when in static equilibrium condition. The actual slip surface is curved, especially in the lower part.
  • Coulomb's method does not give the point of application of the earth pressure  (Pa).
  • For convenience, the pressure distribution is sometimes assumed to be hydrostatic on the back of the wall, and the resultant pressure is assumed to act at one-third height of the wall from the base. 

Following points should be carefully noted while using Coulomb's theory:

Coulombs Wedge Theory - Active Earth Pressure

Coulomb’s Wedge Theory - Active Earth Pressure

Coulombs Earth Pressure Theory For Sand For Passive State

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Graphical Solutions for Lateral Earth Pressure

  • Culmann's graphical solution
  • The trial wedge method
  • The logarithmic spiral 

The Culmann’s Graphical Solution Method

The Culmann's solution considered wall friction , irregularity of the backfill, any surcharges (either concentrated or distributed loads), and the angle of internal friction of the soil.

This method can be adapted for stratified deposits of varying densities, but the angle of internal friction must be the same throughout the soil mass.

A rigid, plane rupture is assumed.

Essentially the solution is a graphical determination of the maximum value of the soil pressure, and a given problem may have several graphical maximum points, of which the largest value is chosen as the design value.

A solution can be made for both Active and Passive pressure

Steps in Culmann's Solution for Active Pressure 

Steps in Culmann's Solution for Active Pressure  

Fig. 1 Culmann’s solution for active earth pressure

                                              

Method to find the point of application of the resultant force (Terzaghi, 1943)

The Culmann solution provides us with only the magnitude of the active force per unit length of the retaining wall—not with the point of application of the resultant.

  •   In the figure, ABC is the failure wedge determined by Culmann’s method. Find the centre of gravity (O) of the failure wedge graphically.
  • Draw OO’ parallel to the surface of sliding, BC. The point of intersection of this line with the back face of the wall will give the point of application of Pa. Thus, Pa acts at O inclined at angle δ’ with the normal drawn to the back face of the wall.

Effect of wall friction on failure surface (Terzaghi, 1943)

Effect of wall friction on failure surface (Terzaghi, 1943)

                

Terzaghis Log-Spiral Theory For Earth Pressure

Comparison of the Coulomb and Log-Spiral failure surfaces

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Rupture Surface assumed in Terzaghi’s Wedge Theory for Passive Earth Pressure

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Design of Gravity Walls

Retaining Walls

  • Retaining walls are built in order to hold back earth which would otherwise move downwards.
  • Their purpose is to stabilize slopes and provide useful areas at different elevations, e.g. terraces for agriculture, buildings, roads and railways.

A gravity-type stone retaining wall  

(Source: https://en.wikipedia.org/wiki/Retaining_wall#/media/
File:Stone_Retaining_wall.jpg)

Why study design of Retaining Walls?

(Source: https://sites.google.com/site/metropolitanforensics/cause-and-origin-of-retaining-wall-failure)

Functions of retaining walls

  • The main function of retaining walls is to stabilize hillsides and control erosion. 
  • When roadway construction is necessary over rugged terrain with steep slopes, retaining walls can help to reduce the grades of roads and the land alongside the road.
  • Some road projects lack available land beside the travel way, requiring construction right along the toe of a slope. In these cases extensive grading may not be possible and retaining walls become necessary to allow for safe construction and acceptable slope conditions for adjacent land uses. 
  • Where soils are unstable, slopes are quite steep, or heavy runoff is present, retaining walls help to stem erosion.

  • Excessive runoff can undermine roadways and structures, and controlling sediment runoff is a major environmental and water quality consideration in road and bridge projects. In these situations, building retaining walls reduces vegetation removal and reduces erosion caused by runoff. In turn, the vegetation serves to stabilize the soil and filter out sediments and pollutants before they enter the water source, thus improving water quality.

Design Requirements for Gravity Walls

  • Gravity Retaining walls are designed to resist earth pressure by their weight.
  • The wall must be safe against sliding and overturning.
  • Also the maximum pressure exerted on the foundation soil should not exceed the safe bearing capacity of the soil.

Parameters Required for Design

  • Before actual design, the following soil parameters that influence the earth pressure and the bearing capacity of the soil must be evaluated-
           –unit weight of the soil,
           –the angle of the shearing resistance,
           –the cohesion intercept ,
           –the angle of wall friction.
  • Knowing these parameters, the lateral earth pressure and bearing capacity of the soil is determined.

Evaluation of Forces Acting on the Wall

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The above figures shows a typical trapezoidal section of a gravity retaining wall.

The forces acting on the wall per unit length are:

  • Active Earth pressure (Pa),
  • The weight of the wall (Wc),
  • The Resultant soil reaction R on the base (or Resultant of weight Wc & Pa ) striking the base at point D. There is equal and opposite reaction R' at the base between the wall and the foundation.
  •   Passive earth pressure Pp acting on the lower portion of the face of the wall, which usually small and usually neglected for design purposes. The full mobilization of passive earth pressure do not occur at the time of failure so we do not consider it. If we do not consider it, then we will be in safer side.   

Earth pressure is generally calculated using Rankine's theory or Coulomb's Earth pressure theory

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Rankine's theory:

  • A vertical line AB is drawn through the heel point.
  • It is assumed that the Rankine active condition exist along the vertical line AB. 
  • While checking the stability, the weight of the soil (Ws) above the heel in the zone ABC should also be taken in to consideration, in addition to the Earth pressure (Pa) and weight of the wall (Wc). 

Coulomb's theory

  • Coulomb's theory gives directly the lateral pressure (Pa) on the back face of the wall.
  • Pa and the Weight of the wall (Wc) need to be considered. In this case, the weight of soil (Ws) need not to be considered.
  •  Once the forces acting on the wall have been determined, the stability is checked. For convenience, the section of the retaining wall is divided in to rectangles & triangles for the computation of the weight and the determination of the line of action of the weight. 

Requirements for a Safe Design

For a safe design, the following requirement must be satisfied 

  • No Sliding  

Horizontal forces tend to slide the wall away from the fill. This tendency is resisted by friction at the base. 

Neglecting terms having Pp,

  •  No Overturning

The wall must be safe against overturning about toe. 

Neglecting terms having Pp,

A minimum factor of safety of  1.5 against overturning is recommended.

  • No Bearing Capacity Failure and No Tension  
    • The wall must be safe against overturning about toe.
    • First the line of action of the Resultant force ( e ) from centre of the base is calculated. No Tension should develop at the heel.  

                                         

  • The pressure at the toe of the wall must not exceed the allowable bearing capacity of the soil. The pressure at the base is assumed to be linear.

  • The max. Pressure at the Toe & min at the Heel is given by:

 

  • pmax should be less than the safe bearing capacity (qallow) of the soil & pmin should not be tensile in any case.

  • Tension is not desirable. The tensile strength of the soil is very small and tensile crack would develop. The effective base area is reduced.

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Sheet pile Wall

  • Sheet pile retaining walls are usually used in soft soils and tight spaces.
  • Sheet pile walls are made out of steel, vinyl or wood planks which are driven into the ground.
  • For a quick estimate the material is usually driven 1/3 above ground, 2/3 below ground, but this may be altered depending on the environment.
  • Taller sheet pile walls will need a tie-back anchor, or "deadman"placed in the soil a distance behind the face of the wall, that is tied to the wall, usually by a cable or a rod and anchors are placed behind the potential failure plane in the soil.

For design and construction of sheet pile wall, IS: 9527 (part III)- 1983 is used in India.

Types of sheet pile wall:

[Clause 5, IS: 9527(part III) – 1983]

Cantilever Sheet Pile Wall

Source : IS 9527 - Part III (1983 )

  • In the type of a cantilevered wall, sheet piling is driven to a sufficient depth into the ground to become fixed as a vertical cantilever in resisting the lateral active earth pressure.
  • This type of wall is suitable for moderate height.
  •  Walls designed as cantilevers usually undergo large lateral deflections and are readily affected by scour and erosion in front of the wall.
  •  The cantilever sheet pile derives its stability solely from the lateral resistance of the soil in which the sheet pile wall is driven.

 

Anchored Sheet Pile Wall

  • Anchored sheet pile walls are held above the driven depth by anchors provided at suitable level.
  • The anchors provide forces for the stability of the sheet pile, in addition to the lateral passive resistance of the soil into which the sheet piles are driven.
  •  It includes an anchor or tieback at or near the head of the wall.
  • More than one set of anchors or tiebacks can be used. It increases wall stability and enables taller walls to be built and sustained almost a necessity with vinyl, aluminium and fiberglass sheet piles.It is not exclusive to sheet piling; also used with other types of in situ wall systems.
  • In case of cantilever sheet pile walls if the deflection at top point of the sheet pile wall is very large, then settlement of soil takes place at top just behind the sheet pile wall.
  • So, to reduce the excessive deflections the anchors are provided. The different types of anchored sheet pile walls are shown in figure.

Anchored Sheet Pile Wall

Fig. Different types of anchored sheet pile walls

Design of anchored sheet pile walls

  • There are mainly two methods of design of anchored sheet pile walls

         1. Free earth support method

        2. Fixed earth support method

Free Earth Support Method:

  • An anchored sheet pile is said to have free earth support when the depth of embedment is small and pile rotates at its bottom tip.Thus, there is no point of inflection in the pile.
  •  It is assumed that:

           1. The base of the pile is relatively free to move, so passive resistance is                      mobilized on one face only.
           2. The lateral pressure increases linearly with depth.
           3. Wall friction is negligible.

Earth Pressure Diagram for Free earth support as per IS 9527 – Part III (1983)

Fixed Earth Support Method:

  • An anchored sheet pile is said to have fixed earth support when the depth of embedment is large and the bottom tip of the pile is fixed against rotation. Thus, there is change in curvature of pile, hence inflection point occurs. It is assumed that

           1. The base of the pile is relatively fixed, so that there is a point of contra-                    flexure above the toe of the pile.
           2. Passive resistance is mobilized on both faces.
           3. The lateral pressure increases linearly with depth.
           4. No wall friction

Earth Pressure Diagram for Fixed earth support as per IS 9527 – Part III (1983)

Comparison between fixed earth method and free earth method

The free earth support method gives a pressure distribution that would apply when the wall is on the point of failure by rotation about the anchor.

  • The fixed earth support method is unlikely to represent the true loading at any stage.
  • Both methods tend to over-estimate the bending moment in the pile.
  • The free earth support method is simpler.
  • In the fixed earth support, depth provided is more, moment through out the section reduces, so thiner section is to be provided.
  • In the free earth support, depth provided is less, moment through out the section is more than fixed earth support, so thicker section is to be provided.

Design of sheet pile wall by free earth support

The figure shows the condition for the free earth support. The deflection of the bulk head is some what similar to that of a vertical elastic beam whose lower end B is simply supported and the other end is fixed as shown in fig. The forces acting on the sheet pile are :

    1. Active pressure due to soil behind pile,
    2. Passive pressure due to soil in front of the pile,
    3. The tension in the anchor rod.


In Cohesionless soil

  • The forces acting on the wall are shown in the fig.
  • Assuming that the material above and below dredged level in cohesionless.

Fig. Forces acting on sheet pile in free earth support case (cohesionless soil)

  • From horizontal equilibrium,   

    where

       T is the tensile force in the anchor,

       P2 is the resultant earth pressure acting below the dredge level for bottom b            height of the wall,
       P1 is the resultant earth pressure acting for top (h a) height of the wall.

  • The depth a to the point of zero pressure can be determined by equating the earth pressure on both the side of the sheet pile.

  • Taking moments of all forces about anchor point M,

where,

      a is the distance of the zero earth pressure point below dredged level,
      h is height of the sheet pile above the dredged level,
      e is the distance of the anchor from the top level of sheet pile, generally taken         as 1 to 1.5m,
       Z is the distance between point of application of force P1 and O point.

  • Substituting the value of in the above equation,

  • The previous equation can be written as,

  • The above equation can be solved for b. Then, d is determined as, d = b a

  • The actual depth D is taken equal to 1.2 to 1.4 times d. The force in the anchor rod can be calculated as, T = P1 - P2

  • The values of P1 and P2 are determined from the pressure diagrams.

In Cohesive soils

  • The earth pressure distribution above the dredged line is same as that in case of cohesionless soil.
  • However the pressure below the dredge line at any point at a distance of z from dredged level is given as,

  • Therefore  , 

where, h is the height of the sheet pile above the dredged level, c is the cohesion and γ is the unit weight of the soil.

Forces acting on sheet pile in free  earth support case (cohesive soil)

  • From the horizontal equilibrium of the forces,

Where, T is the tensile force in the anchor
     P2 is the resultant earth pressure acting below the dredged level
     P1 is the resultant earth pressure acting above the dredged level.

  • Taking moments of all the forces about M

Substituting the value of   in the above equation, 

where,
      g is the distance of the tendon above dredged level,

      f is the distance between the point of application of force and tendon

      (M) = g – Z1

      The above equation can be solved for d.
      The actual depth provided is 20 to 40% more than d.

The force in the anchor rod can be calculated as, T = P1 - P2

  • The values of P1and P2 are determined from the pressure diagrams.
  • The wall becomes unstable when P2 becomes zero.

Factor of Safety as per IS code

Factor of Safety: [Clause 8.1.3, IS: 9527 (part III) – 1983]

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Bracing Systems

Introduction 

  • Deep excavations with vertical sides require lateral supports to prevent cave in of the earth and to protect the adjacent areas against ground subsidence and lateral movement of the subsoil. 
  • When excavations are shallow and ample space is available, the sides of the excavation can be sloped at a safe angle to ensure stability.
  • However, in deep excavation, especially in built up areas there may not be adequate space for providing safe slopes.
  • Moreover it becomes uneconomical to provide safe slope because of large quantities of earth involved.
  • Excavations which are laterally supported are Braced cuts. 
  • The vertical sides of the excavations are supported by a sheeting and bracing system. It consists of relatively flexible sheeting placed against excavations walls.
  • The lateral thrust on the sheeting is resisted by the horizontal members in compression (struts).

Some typical uses of Braced Excavation

  • Laying underground pipeline
  •  Construction of bridge abutment.
  •  Construction of basement.
  •  Metro railway construction
  •  Construction of subway tunnel.
  •  During a temporary underground construction.

Vertical Timber Sheet

  • In this method, vertical timber sheeting consisting of the planks of about 8 to 10 cm thick are driven around the boundary of the proposed excavation to a depth below the base of the excavation.
  • The soil between the sheeting is excavated.
  • The sheeting is held in place by a system of wales and struts.

Steel Sheet Piles

  • Piles, or sheeting, driven in close contact to form a continuous interlocking wall which resists the lateral pressure of water or earth.
  • In this method, the steel sheet pile is driven around the boundary of the proposed excavations.
  • A continuous line of pile is driven in advance of excavation. As the soil is excavated from the enclosure wales and struts are placed.

Computation of Lateral Earth Pressure on Sheetings

  • Rankine's and coulomb earth pressure theory can not be used for computation of lateral earth pressure on sheetings, as those theories are applicable to rigid retaining walls rotating about the base.
  • The sheeting and bracing system is somewhat flexible and rotation takes place at the top of the wall.
  • Sheeting are placed against the walls of the excavation when these are shallow. As the excavation proceeds downwards, the lower part of the face is free to yield inward before the next strut is placed. The inward yield of the soil increases with an increase in the depth of excavation. Thus the sheeting tilts about its top.
  • The method of earth pressure calculation has been developed by Terzaghi. Pressure distributions against the sheeting have been approximated on the assumptions that each strut support the sheeting area. These design pressure diagram are also known as apparent pressure diagram.

Apparent Pressure Diagram - Peck 1969

  • Apparent pressure diagram was first proposed by Terzaghi and Peck (1948) and later was revised by Peck (1969).         
  • The resultant active earth pressure diagram is 28% greater than the Coulomb’s active pressure for dense sand & 44% greater than for loose sand.
  • Since, the sheeting can not resist, in general, the vertical shear forces, the friction and adhesion on them are assumed to be zero.

Apparent Pressure Diagram - Peck (1969)

Design of struts

  • The struts are the structural members whose function is to transfer the earth pressure coming on the diaphragm walls due to the earth pressure from the surrounding soil.
  •  For calculation of the struts loads, apparent earth pressure diagrams proposed by Terzaghi and Peck (1948) or Peck (1969) is to be used for the designing of the bracing systems.

           H = height of the vertical cut.           (Terzaghi and Peck, 1948)

  • For Clays        

where , m = coefficient depending on the stability of the wall

Apparent Earth Pressure Diagram proposed by Terzaghi and Peck (1948)

Diaphragm Wall - Design Walls

The apparent earth pressure acting on diaphragm wall is chosen as per the type of soil existing in the field.

  • For each strut we get an effective zone over which the earth pressure acts.

  • Usually the earth pressure zones extend from centerline of one strut to that of the other, which implies that each strut takes the earth pressure on either halves upto half the vertical spacing (sv).
  • As shown zones 1,2,3 apply pressure on the struts 1,2,3. For zone 4, it is assumed that the soil in that portion does not apply pressure and it is taken up by the underlying soil.
  • Each strut load is calculated by multiplying the effective area of action of earth pressure with the apparent earth pressure (p).
  • Usually the vertical spacing of the struts are taken between 3-4 m.
  • The highest strut load is taken up for choosing the section of the
  • struts and same section is provided throughout.
  • For design of the diaphragm walls the wall is assumed to lie as a beam and the pressure distribution acting on it is shown in the figure.
  • From the pressure distribution the exact moment and forces acting on the   struts and the wall can be calculated. However, for all practical purposes, the maximum bending moment acting on the wall (Mmax ) = wl2/ 10, where l = sV.
  • Accordingly the section of the diaphragm wall is chosen based on themoment acting on it.

Design of Wales

  • The wales are structural members which transfers the load from the diaphragm walls to the struts thereby acting as beams.
  •  The design of struts is done as simply supported beams. Maximum moment on wales = (p.sV)sH2. / 8

Braced cuts in non-uniform soils

Source: NPTEL e-learning courses (www.nptel.ac.in)

Source: NPTEL e-learning courses (www.nptel.ac.in)

Stability Considerations of Braced Cuts

There are various methods by which a braced cut can be expected to attain failure. Before carrying out a braced excavation the stability criteria are first judged and adequate steps are taken up to ensure the stability. These aspects are described in the subsequent sections.

Bottom heave

  • •Consider an excavation pit as shown in the figure and the rectangular soil mass adjacent to it.
  • If this soil mass is considered as a foundation with the failure surfaces as shown, the heaving of soil will occur at the bottom of the pit due to release of overburden pressure at that point.

The pit has to be safeguarded against this heaving.

Stability against bottom heave

  • The analysis is a total stress analysis since the time of dissipation of pore water pressure is very less unless there is sandy deposit.
  • Consider a stratified soil deposit in which braced excavation was carried out as shown in the figure.

Stability against bottom heave

  • If unstability criteria occurs, the idea is to increase the depth of the diaphragm wall in order to take advantage of the layers of higher strength lying below. The failure plane as shown cannot penetrate through the hard stratum and is tangent to the same.

  • Factor of safety against bottom heave

  • F.O.S should be more than 2.0 for bottom heave.
  • The depth D is calculated as follows:

    • D= D1, since failure surface cannot penetrate the hard stratum.
    • D= 0.7B , which is obtained from bearing capacity analysis.
    •  D is taken as least of the above two values.


Clay bursting

  • This occurs when a impermeable layer (clay) lies over a permeable layer (sand).
  • At level 1-1, when there is no excavation, full overburden pressure exists. When excavation occurs, some overburden pressure is released.
  •  At the same level 1-1, upward water pressure exists due to presence of sand layer. 

  • When no excavation occurs the total overburden pressure is greater than the upthrust, but the layer of soil below the excavation pit may not have sufficient depth to resist the uplift force.
  •  Hence, if the uplift force at the excavation level becomes more, the clay layer bursts open.

Stability against piping failure or clay bursting

  • Consider the following fig. which shows the clay bursting phenomenon.
  • The cohesive force along the failure plane resists the movement of the soil mass upwards and therefore acts as  resistive force.
  • Factor of safety against clay bursting  = 

   The factor of safety for clay bursting should be more than 1.3.

Stability Considerations of Braced Cuts - Part II

  • For piping failure, the factor of safety = i / ic. where, i is the exit gradient and ic is the critical gradient.
  • Factor of safety for piping failure should be more than 1.3.

Case 1: Sand Upto Infinite Depth

Case 2: Sand Upto Finite Depth

  • Once the stability against bottom heave and clay bursting are achieved, the next step is to ensure the structural stability of the braced excavation. These include the following:

Yielding of supports

      Due to earth pressure on both sides of the excavation pit,compressive stresses are generated on the struts. When this force increases beyond safety the struts may yield.
Excessive ground movements

  • Braced excavation is carried out in places where there is scarcity of place in the surrounding to make a stable inclined slope.
  •   Now during excavation as the earth is being removed from the pit, the pressure of the foundations of the adjacent buildings tend to create pressure on the soil mass leading to the movement of the surrounding soil into the pit and there by the surrounding structures are distressed.
  • The above phenomenon is more critical for a small structure in the vicinity than a large one.

Excessive ground movements

  • The various structural members are constructed to minimize ground movements in the vicinity.
  • However, wall cannot be infinitely rigid. Irrespective of placing of struts,diaphragm wall movement cannot be prevented.
  • After some excavation is done, before a strut is placed there is a certain movement of the wall. Also, between subsequent placing of struts certain movement of wall occurs. As a result, ground movement occurs locally.
  • If the joints are subjected to such movements, excessive forces may generate leading to the distress of the structure.
  • Therefore, whatever ground movement occurs, it has to be limited to a minimum value.
  • Total ground movement is the sum total of ground movement and bottom heaving.
  • The idea of proving structural members is to minimize ground movements.
  • More rigid the structure, lesser is the ground movement

Excessive ground movements

Peck (1969) proposed a graph which indicated the ground movements and their extent for a excavation site and site conditions.

L= Distance from excavation

H = Maximum Depth of excavation

Excessive ground movements

  • Before conducting any excavation, depending on site and soil conditions, we can estimate the maximum settlement and extent of settlement that is going to occur when a excavation is carried out at that site.
  • Peck's analysis was based on experiments done over sheet pile walls.
  • Therefore, if the rigidity of the structural members can be increased the settlement values can be minimized and whatever settlement we could have got for a sheet pile wall in zone III can be found to fall in zone II due to a more rigid structure.
  • Hence, after finding out the extent of settlement, it has to be judged whether any surrounding structure falls within that range.

Reference

 Bowles,J.E.,(1996) Foundation Engineering and Design, 5th Edition.,McGraw-Hill, 1996.

 Brahma, S.P. (1993). Foundation Engineering , 5 th Ed., Tata McGraw-Hill Publishing Company, New Delhi .

Choudhury, D. (2012); Foundation Engineering, NPTEL web course,http://nptel.ac.in/courses/105101083/

 Choudhury, D., Sitharam, T. G. and Subba Rao, K. S. (2004); "Seismicdesign of earth retaining structures and foundation", Current Science , India ,87(10), 1417-1425.

 Choudhury, D. and Subbha Rao, K. S. (2002), “Seismic passiveresistance for negative wall friction”. Canadian Geotechnical Journal, 39(4), 971-981.

Clayton C. R. I. and Militisky, J. (1986), Earth Pressures and EarthRetaining Structures, Surrey Univ. Press, London

Das, B.M. (2013). Principles of Geotechnical Engineering , 8th Edition,Cengage Learning.

Das, B.M. (2013). Principles of Foundation Engineering , 8th Edition,Cengage Learning.

Gulhati, S.K. and Datta, M. (2005), Geotechnical Engineering, Tata McGraw-Hill, New Delhi.

Kerisel, J. and Absi, E. (1990), Active and Passive Earth Pressure Tables, Balkema, Rotterdam, The Netherlands.

Kramer, S. L. (1996), Geotechnical Earthquake Engineering, Prentice Hall, New Jersey.

Kurian, N. P. (1996), Design of Foundation Systems, Principles and Practices, 2nd Edition Narosa Publishing House, Chennai.

Lambe, T. W. and Whitman, R. V. (1987), Soil Mechanics, John Wileyand Sons, New York.

Leonards, G. A. (1962), Foundation Engineering, McGraw-Hill, NewYork.

Meyerhof, G. G. and Adams, S. I. (1968). “The ultimate uplift capacity of foundations”, Canadian Geotechnical Journal, 5(4), 225-244.

Murthy, V.N.S. (2002). Principles of Soil Mechanics and Foundation Engineering , 5th Edition, UBS Publishers Distributors Ltd., New Delhi .

Ranjan, G., and Rao, A.S.R. (2000). Basic and Applied Soil Mechanics ,2nd Edition, New Age International (P) Ltd. Publishers, New Delhi .

Slides for Sheet pile wall

Assignment videos For Discussion 

Forum for Bracing Systems

Forum for Bracing Systems

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Quiz - IV

Quiz - IV

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Quiz V

Quiz V

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Assignment - I

Problem 1

Determine the lateral force per unit length of the wall for Rankine’s active state of earth pressure for the retaining wall as shown in the figure. Also find the location of the resultant force.

Problem – 2

a) Maximum depth of tensile crack
b) Critical Depth, Hc
c) Rankine’s active earth force, Pbefore formation of tensile crack
d) Rankine’s active earth force, Pafter formation of tensile crack

Problem – 3

Problem – 4

Problem – 5

Using the free-earth support method, calculate the depth of embedment of the sheet pile (D) and the pull in the anchor rod (T) for the anchored bulkhead system shown in the figure below.

Problem – 6
A vertical cut 8 m wide and 10 m deep is proposed to be made. The soil layer profile is as shown in the figure. Design a suitable embedment depth of the diaphragm wall fulfilling all stability considerations. Also, compute loads on each strut, maximum bending moments on the runner beam and diaphragm wall.

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