CHAPTER 4 SOIL STRESSES

Introduction We have to know the distribution of stress at a given depth to analyze the: Compressibility of soils Bearing capacity of foundations Stability of embankments Lateral pressure on retaining structure

Introduction In determining the stress distribution, we have to know the stress that will be carried by water and the stress to be carried by the solid (soil skeleton). It is involved the effective stress concept

STRESS DISTRIBUTION IN SOILS Stresses at a point in a soil layer are caused by: Added load (such as buildings, embankments, rail track Self weight of the soil layers (Geostatic stresses)

Effective stress concept 1. Water level is far away from the soil surface A h1 B h2 C

Effective stress concept 1. Water level is at the soil surface A h1 B h2 C

Effective stress concept 1. Water level is above the soil surface hw A h1 B h2 C

Effective stress concept 1. Water level is far away from the soil surface + uniform load q (kN/m2) A h1 B h2 C

Stresses in saturated soil with seepage The effective stress in soil is different from static condition when there have upward or downward seepage of water. The effective stress for downward seepage is higher than upward seepage Upward seepage

Stresses in saturated soil with seepage Downward seepage

Stresses in saturated soil with seepage Example 1 A 9 m thick of stiff saturated soil clay underlain by a layer of sand. The sand is under artesian pressure. Calculate the maximum depth of cut H that can be made in the clay.

Stresses in saturated soil with seepage Solution Heave occur when ’A is 0

Stresses in saturated soil with seepage Example 2 A cut is made in a stiff, saturated clay that is underlain by a layer of sand. What should be the height of the water, h, in the cut so that the stability of the saturated clay is not lost.

Stresses in saturated soil with seepage Solution For loss of stability, ’ = 0

VERTICAL STRESS DUE TO LOADING

Stress Due To a Point Load assumed that the soil is elastic, homogeneous and isotropic

Stress Due To a Point Load X - AXIS Horizontal stress in x direction Horizontal stress in y direction Vertical stress, z Poisson’s Ratio is when a sample of material is stretched in one direction, it tends to get thinner in the other two directions. It is defined as the ratio of the contraction strain normal to the applied load divided by the extension strain in the direction of the applied load. NOTE:  = Poisson’s Ratio

Stress Due To a Point Load X - AXIS Vertical stress Poisson’s Ratio is when a sample of material is stretched in one direction, it tends to get thinner in the other two directions. It is defined as the ratio of the contraction strain normal to the applied load divided by the extension strain in the direction of the applied load. NOTE:

Stress Due To a Line Load X - AXIS Poisson’s Ratio is when a sample of material is stretched in one direction, it tends to get thinner in the other two directions. It is defined as the ratio of the contraction strain normal to the applied load divided by the extension strain in the direction of the applied load.

Stress Due To a Line Load X - AXIS Poisson’s Ratio is when a sample of material is stretched in one direction, it tends to get thinner in the other two directions. It is defined as the ratio of the contraction strain normal to the applied load divided by the extension strain in the direction of the applied load. Note: The value of  does not include the overburden pressure of the soil above point A

Stress Due To a Uniformly Loaded Circular Area X - AXIS Example: circular foundation, water tank

Stress Due To a Uniformly Loaded Circular Area X - AXIS

Stress Due To a Rectangular Loaded Area X - AXIS Many structural foundations are rectangular. The increase in stress below the corner of a rectangular are Where; q = Load per unit area In radian Note: If the m’2+n’2+1< m’2n’2, add  to the angle.

Stress Due To a Rectangular Loaded Area X - AXIS The value of I3 also can be determine using this chart

Stress Due To a Rectangular Loaded Area The increase in stress below the center of a rectangular are Where; q = Load per unit area

Stress Due To a Rectangular Loaded Area

Lateral Earth Pressure

Lateral Earth Pressure Lateral earth pressure can be divided into: At- rest pressure Active Pressure Passive Pressure

Coefficient of earth pressure at rest At-rest Pressure Coefficient of earth pressure at rest Researchers K0 Note Jaky (1944) ’ is drained friction angle Mayne & Kulhawy (1982) For over consolidated coarse grained soil Massarsch (1979) For fine grained , normally consolidated soils

How to calculate the total force per unit length of the wall (Po)? Po = ½ Ko’H2 1/3H Ko’H

Rankine’s Theory of active and passive earth pressures Rankine’s theory assumes that: No friction on the wall The wall at the soil interface is vertical Can be used for horizontal and sloping backfill

Rankine’s active earth pressures

Rankine’s active earth pressures For cohesionless soil, c’=0 So,

Rankine’s active earth pressures For cohesion soil

Rankine’s passive earth pressures

Rankine’s passive earth pressures For cohesionless soil, c’=0 So,

Rankine’s passive earth pressures For cohesion soil

Rankine’s active pressure with sloping granular backfill

Coulomb’s Earth Pressure Coulomb’s theory assume that: Consider the wall friction Consider sloping wall Consider sloping backfill

Coulomb’s Earth Pressure

Coulomb’s Earth Pressure