What is Lateral Earth Pressure? How it is important in the design of

civil engineering structures?The pressure exerted by the soil against an engineering structure or acting on a surface of surrounding soil mass is called earth pressure

Lateral pressure or horizontal stress is due to lateral stresses in soil. The ratio between the lateral and vertical effective stress is defined as coefficient of earth pressure, k

Typical Application of Retaining Structures

Magnitude and distribution of lateral pressure is important in designing structures such as retaining wall, silo, tunnel and strutted excavation.

Type of Retaining Structures

Earth Pressure Theory

Depending on the deformation characteristics of structure and hence the associated soil, lateral earth pressure may have varying magnitude; and classified as:

1. Earth pressure at rest (no deformation)2. Active earth pressure (lateral expansion) 3. Passive earth pressure (lateral contraction)

Earth Pressure At Rest

When a soil maintains the same lateral dimension regardless of the vertical pressure, the lateral pressure exerted by the soil on the structure or the lateral stress induced within the soil mass is known as earth pressure at rest. The ratio of lateral effective stress, σh, to vertical effective stress, σv, at this condition is termed as coefficient of earth pressure at rest and designated by ko.

Typical of soil Typical values of koNormally consolidated clay

Over consolidated clayCompacted clay

Heavily machine compacted clayLoose sandDense sand

Tamping sand in layers

0.40 – 0.701 – 41 – 22 – 4

0.45 – 0.500.35

May be up to 0.80

Active Earth Pressure

When a soil expands laterally due to stresses, the maximum lateral stress at which the soil fails due to shear is called active earth pressure. The ratio of lateral stress to vertical stress at this condition is termed as coefficient of active earth pressure and designated by ka.

Passive Earth Pressure

When a soil contracts laterally due to stresses, the minimum lateral stress at which it fails due to shear is called passive earth pressure. The ratio of lateral stress to vertical stress at the condition is termed as coefficient of passive earth pressure and designated by kp.

Rankine's Theory

Active Pressure for Cohesionless Soil – Horizontal Soil Surface

Active Pressure for Cohesionless Soil – Inclined Soil Surface

Coulomb Theory

Active Pressure for Cohesionless Soil

Graphical method (Cullman line construction) for cohesionless soil

Effect of Surcharge and Ground Water on Active Pressure of Cohesionless Soil

Total thrust Pa = Pa’ + Pw

= kaqz + ½ ka�’z2 + ½ �w zw2

Rankine's Theory

Active Pressure for Cohesive Soil – Horizontal Soil Surface

Tension crack- For soil with cohesion and friction (c’, �)

- For soil with cohesion only (cu, �u = 0o)

Coulomb Theory

Rankine's Theory

Passive Pressure for Cohesionless Soil - Horizontal Soil Surface

= kp �z

Rankine's Theory

Passive Pressure for Cohensionless soil – Inclined Soil Surface

Passive Pressure for Cohesionless Soil – Inclined Soil Surface

Where,

Coulomb's Theory

Earth Pressure Theory

Passive Pressure of Cohesive Soils

pp = kp �z + 2c� kp

Pp = ½ kp � z2 + 2c z � kp

Cohesive soil with �u = 0o

pp = �z + 2cu

Pp = ½ � z2 + 2cu z

Retaining Walls

Type of Retaining Walls

Design of Gravity and Reinforced Concrete Wall

Factor of safety against forward sliding of the wall, Fs, should not be less than 2.

Fs = c.B + W tan � PaH

Factor of safety against overturning, Fo, need to be checked. It is also not to be less than 2. Taking moment at wall toe

Fo = � stabilizing moment � overturning moment

Wall Drainage Systems

Design of Sheet Pile WallFree Earth Support Method

The wall is assumed to be rotating at its base (point C)

By taking moment at point O, depth of penetration d, can be calculated

In construction, the depth of wall constructed is usually increased by 20% the calculated depth, that is 1.2d

Strutted Excavation

Factor of safety against base heave

z/B Nc (for B/L = 1.0)

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