Goe tech. engg. Ch# 02 strss distribution

GEOTECHNICAL ENGINEERING - II

STRESS DISTRIBUTION IN SOILS

Chapter # 02

UNIVERSITY OF SOUTH ASIA

STRESS

� When some external system of forces or loads act on a body, the internal forces equal and opposite are set up at forces equal and opposite are set up at various sections of the body, which resist the external forces. This internal force per unit area at any section of the body is known as Unit Stress or Simple Stress.

� ð = P / A

� P= Force or load acting on the body.

� A= Cross section area of the body.� A= Cross section area of the body.

� SI units is Pascal. (Pa).

� 1Pa = 1N/ m2.

SOURCES OF STRESS

� To evaluate a stress in the ground, we need to know the location, magnitude and directions of forces that causes them.them.

� So we divide these sources in to two broad categories;

1. Geo-Static Stress

2. Induced Stress

GEOSTATIC STRESS

� Geostatic stress are some time called Body stress, are those occur due to the weight of soil above the point being evaluated.

� These stresses are caused by gravity acting on the soil or rock, so the direction result in on the soil or rock, so the direction result in vertical normal stress, σZ.

� Such stresses are naturally present in the ground.

� This stress has a significant impact on the engineering behavior of soil.

� To compute the geostatic stresses at a point below the ground surface, consider a column as shown in the as shown in the figure.

� This column intercepts the soil strata with unit weight γ1, γ2 & γ3.

� So its weight is;W = dxdy Σ γH

� So the total geostatic stress at the bottom of the column is then;

σZ = w/A

σZ = dxdy Σ γH /A

σZ = Σ γH

INDUCED STRESSES

� Induced stresses are those which are caused by external loads, such as structural foundations, vehicles or fluid in a storage tank.

� These are usually caused by human � These are usually caused by human activities.

PORE PRESURE

� This is the pressure induced in the fluid (either water, or vapor and water) filling the pores.

� Pore fluid is able to transmit normal stress, but not shear, and is therefore ineffective in providing the shear resistance.

� For this reason it is sometime referred as Normal Pressure.

U = γw × h

U = Pore water pressure (KN/m³)γw = unit weight of water (9.81 KN/m³)h = height of water.

EFFECTIVE STRESS (σ’)� This is the stress transmitted through the

soil fabric via inter-granular contacts.� It is this stress component that is effective in

controlling both volume change deformation and the shear strength of soil since normal and shear stress is transmitted across grain-and shear stress is transmitted across grain-to-grain contact.

� According to Terzaghi showed that for a saturated soil, effective stress may be defined as difference b/w Total stress and Pore pressure.

σ’ = σ - U

TOTAL STRESS

� The sum of effective stress and pore water pressure is known total stress.

σ = σ’ + Uσ = σ’ + U

m.irfan B-15952