_lateral_earth_pressure_(foundation engineering)

Department of Civil Engineering

School of Engineering & Technology

FOUNDATION ENGINEERING

No. of lectures Courses to be covered Unit to be covered

2

Role of civil engineers in selection, design and construction of foundation of civil engineering structures, Methods of soil exploration, Sampling-disturbed and undisturbed sampling

Introduction & Site Investigation

Unit 1

3

Various penetration tests, Correlation between penetration resistance and soil design parameters, Selection of foundation based on soil condition.

Introduction & Site Investigation

4Active and Passive earth pressure, Earth pressure at rest, Rankine and Coulomb’s earth pressure theories

Earth Pressure

Unit 21 Earth pressure due to surcharge Earth Pressure

2Types of shallow foundations, mechanism of load transfer, Modes of failure, Terzaghi’s bearing capacity theory

Shallow Foundations

Unit 32

Computation of bearing capacity in soils, Influence of various factors, Use of field test data in design of shallow foundations, Stresses below the foundations

Shallow Foundations

2Settlement of footings and rafts, Allowable and maximum differential settlements of buildings, Codal provisions, Proportioning of footings and rafts

Shallow Foundations

Lecture plan

1Types of pile and method of construction, Estimation of load carrying capacity of a pile

Pile Foundation

Unit 43

Static and dynamic formulae, Load carrying capacity and settlement of group of piles, Piles subjected to uplift, Negative skin friction Pile Foundation

2Pile load tests and interpretation of test data, Proportioning of piles, Codal provisions Pile Foundation

2Methods of construction, Tilt and shift, Remedial measures during sinking of well foundation Well Foundations

Unit 5

2Bearing capacity, Settlement and lateral stability of well foundation

Well Foundations

1Mode of failure mechanism, Stability analysis of infinite slopes Stability of Slopes

Unit 6

2Method of slices, Bishop’s simplified method Stability of Slopes

3Types of retaining walls-gravity, semi-gravity, cantilever and counter fort retaining walls Retaining Walls

Unit 7

1Stability analysis of retaining walls, Proportioning and design of retaining walls Retaining Walls

2

Concept of soil stabilization, Materials used, Methods of stabilization

Soil StabilizationUnit

8

Books and References:

➢ Soil Mechanics and Foundation Engineering – Arora, K.R. (Standard publishers and distributors, New Delhi, 1997)

➢ Basic and applied soil mechanics – Gopal Ranjan and Rao, A.S.R. (Wiley Eastern Ltd., New Delhi (India), 1997)

➢Principles of Foundation Engineering – Das, B.M. (PWS Publishing, California, 1999)

➢Foundation Analysis and Design – Bowles J.E. (McGraw Hill, 1994)

➢Soil Mechanics and Foundation Engineering – B.C. Punmia (S CHAND publishers)

FOUNDATION ENGG - SYLLABUS

➢Lecture Session

■ Lectures per week : 3

➢ Tutorial Session

■ Tutorial per week : 1

Lecture Contents

• Syllabus and Introduction (2 hrs)• Site Investigation(3 hrs)• Earth Pressure(5 hrs)• Shallow Foundations(6 hrs)• Pile Foundation(6 hrs)• Well Foundations(4 hrs)• Stability of Slopes(3 hrs)• Retaining Walls(4 hrs)• Soil Stabilization (2 hrs)

Introduction

• Earth Pressure– The force which is on the retaining wall when the soil is

retained at a slope steeper than it can sustain by virtue of its shearing strength.

– The magnitude of earth pressure is a function of the magnitude and nature of the absolute and relative movements of the soil and the structure.

LATERAL EARTH PRESSURES

Fig. Conditions in the case of active earth pressure

Fig. 13.3 Conditions in the case of passive earth resistance

Effect of Wall Movement on Earth Pressure

Effect of Wall Movement on Earth Pressure

• The Earth Pressure At Rest– The earth pressure that the soil mass is in a state

of rest and there are no deformations and displacements.

Earth Pressure At Rest

Rankine’s Theory of Earth Pressure

• Assumptions:– The backfill soil is isotropic, homogeneous and is cohesionless.– The soil is in a state of plastic equilibrium during active and passive

earth pressure conditions.– The rupture surface is a planar surface which is obtained by

considering the plastic equilibrium of the soil.– The backfill surface is horizontal.– The back of the wall is vertical.– The back of the wall is smooth.

Active Earth Pressure of Cohesion less Soil

Fig. Active earth pressure distribution – Rankine’s theory

Effect of Submergence(i) Lateral earth pressure due to submerged unit weight of the backfill soil; and(ii) Lateral pressure due to pore water.

Fig. Effect of submergence on lateral earth pressure

At a depth H below the surface, the lateral pressure, σh, is given by : σh = Ka. ɤ H +′ ɤw. H

Effect of partial submergence

Fig. Effect of partial submergence on lateral earth pressure

The lateral pressure above the water table is due to the most unit weight of soil, and that below the water table is the sum of that due to the submerged unit weight of the soil and the water pressure.

• where H1 = depth of submerged fill,

• Ka = active earth pressure coefficient,• H2 = depth of fill above water table (taken to be moist),• γ = moist unit weight, and• γ = submerged or effective unit weight.′

Lateral pressure at the base of wall,= KaɤH2 + Kaɤ H′ 1 + ɤwH1

Effect of Uniform Surcharge

Fig. Effect of uniform surcharge on lateral pressure

• The extra loading carried by a retaining structure is known as ‘surcharge’. It may be a uniform load (from roadway, from stacked goods, etc.), a line load (trains running parallel to the structure), or an isolated load (say, a column footing).

• In the case of a wall retaining a backfill with horizontal surface level with the top of the wall and carrying a uniform surcharge of intensity q per unit area, the vertical stress at every elevation in the backfill is considered to increase by q. As such, the lateral pressure has to increase by Ka.q.

• Thus, at any depth z, σh = Kaγ.z + Kaq

Effect of Inclined Surcharge—Sloping Backfill

The total active thrust Pa per unit length of the wall acts at (1/3)H above the base of the wall and is equal to 1/2 Kaɤ.H2; it acts parallel to the surface of the fill.

Active Earth Pressure of Cohesive Soil

Fig. Active pressure distribution for a cohesive soil

For c- φ soil For pure clay, φ = 0

Passive Earth Pressure of Cohesive Soil

Fig. Passive pressure distribution for the cohesive soil

Coulomb’s Theory of Earth Pressure

• Assumptions;– The backfill is a dry, cohesionless, homogeneous, isotropic soil.– The backfill surface is planar and can be inclined.– The back of the wall can be inclined to the vertical.– The failure surface is a plane surface which passes through the heel of

the wall.– The position and the line of action of the earth pressure are known.– The sliding wedge is considered to be a rigid body and the earth

pressure is obtained by considering the limiting equilibrium of the sliding wedge as a whole.

Coulomb’s Theory of Earth Pressure

Coulomb’s Theory of Earth Pressure

Coulomb Equations for c=0 Backfills

PROBLEMS

• What are the limiting values of the lateral earth pressure at a depth of 3 meters in a uniform sand fill with a unit weight of 20 KN/m3 and a friction angle of 35°? The ground surface is level. If a retaining wall with a vertical back face is interposed, determine the total active thrust and the total passive resistance which will act on the wall.

• A gravity retaining wall retains 12 m of a backfill, γ= 17.7 KN/m3 = 25° with a uniform horizontal φsurface. Assume the wall interface to be vertical, determine the magnitude and point of application of the total active pressure. If the water table is a height of 6 m, how far do the magnitude and the point of application of active pressure changed?

• A smooth backed vertical wall is 6.3 m high and retains a soil with a bulk unit weight of 18 KN/m3 and = 18°. The top of the soil is level with the top φof the wall and is horizontal. If the soil surface carries a uniformly distributed load of 4.5 KN/m2, determine the total active thrust on the wall per lineal meter of the wall and its point of application.

• A wall, 5.4 m high, retains sand. In the loose state the sand has void ratio of 0.63 and = 27°, while φin the dense state, the corresponding values of void ratio and are 0.36 and 45° respectively. φCompare the ratio of active and passive earth pressure in the two cases, assuming G = 2.64.

• A vertical wall with a smooth face is 7.2 m high and retains soil with a uniform surcharge angle of 9°. If the angle of internal friction of soil is 27°, compute the active earth pressure and passive earth resistance assuming = 20 kN/m3γ

• A retaining wall 9 m high retains a cohesionless soil, with an angle of internal friction 33°. The surface is level with the top of the wall. The unit weight of the top 3 m of the fill is 21 kN/m3 and that of the rest is 27 kN/m3. Find the magnitude and point of application of the resultant active thrust. It is assumed that = 33° for both the φstrata of the backfill.

• A retaining wall, 7.5 m high, retains a cohsionless backfill. The top 3 m of the fill has a unit weight of 18 kN/m3 and = 30° and the rest has unit weight φof 24 kN/m3 and = 20°. Determine the pressure φdistribution on the wall.

• A sandy loam backfill has a cohesion of 12 kN/m2 and = 20°. The unit weight is 17.0 kN/m3. What φis the depth of the tension cracks ?

• A retaining wall with a smooth vertical back retains a purely cohesive fill. Height of wall is 12 m. Unit weight of fill is 20 kN/m3. Cohesion is 1 N/cm2. What is the total active Rankine thrust on the wall? At what depth is the intensity of pressure zero and where does the resultant thrust act?

• A retaining wall with a smooth back is 12 m high and retains a two layer sand backfill with following properties:

• 0 – 6 m depth: ’ = 28φ 0, ’ = 16 KN/mɣ 3

• below 6 m: ’ = 32φ 0, ’ = 21 KN/mɣ 3

• Show the active earth pressure distribution, assuming that the water table is well below the base of the wall.

• For the retaining wall as shown below, assume that wall can yield sufficiently to develop active state. Determine the Rankine active force per unit length of wall and the location of resultant line of action.

z

γ =16 KN/m3ɸ1=30˚C1=0

γsat =19 KN/m3ɸ2=36˚C2=0

3 m

3 m

Thank you.

EARTH PRESSURE COEFFICIENTSAppendix