Soil Stresses (ch10)

Stress Assumptions Continuous material Homogeneous (eng. props. = at all locations) Isotropic (Modulus and are = in all directions) Linear-elastic stress-strain properties

Stress Concept

x z  normal stresses  shear stresses Ten (-), Comp (+) Clock (+), CC (-)

Strain Concept   normal strain  shear strain  = shear strain [radians]

Stress vs. Strain = Modulus

Stresses in Soils 1. Geostatic Stresses Due to soil’s self weight 2. Induced Stresses Due to added loads (structures) 3. Dynamic Stresses e.g., earthquakes

Geostatic Stresses TOTAL VERTICAL STRESS AT A POINT z = depth = 5 m A Ground surface Soil,  = 18 kN/m 3 “total vertical stress at A”

Geostatic Stresses SHEAR STRESSES If ground surface is flat, all geostatic shear stresses = zero

Geostatic Stresses PORE WATER PRESSURE AT A POINT z = 5 m A Ground surface Soil,  = 18 kN/m 3 “pore water pressure at A” h pA

Geostatic Effective Stress board

Example board

Special Case Board – submerged soils

Induced Stresses  z A  z A P   =  z   =  z +    =    = 

Bousinnesq - point loads zfzf A Point load See page 324 of your book…

Area loads q = bearing pressure = P/A  z A P Area, A B L Terminology: B < or = to L

Area loads –  z below corner zfzf B L  z below corner of a loaded area: see page 327 (book)

Area loads –  z below center Circular loaded area zfzf A q

Area loads –  z below center Square loaded area Strip loads Rectangular area See page 332 (text)

Lateral Stresses z A Ground surface Soil,  = 18 kN/m 3 = Vertical effective stress = = Horiz. eff. stress = ?

Lateral Stresses “Coefficient of lateral earth pressure”

Superposition We can only add total stresses

Stresses on other planes… So far we have  x and  z Now we want Stresses acting on other planes

The Mohr Circle Describes 2-D stresses at a point in a material Plots  and  on an = scale Each point on the MC represents the  and  on one side of an element oriented at a certain angle The angle between two points in the MC is = 2 times the angle between the planes they represent 

The Mohr Circle A1A1 A2A2 B1B1 B2B2  B2  B1  A2  A1  A2  A1  B2  B1  If we change we will get two more points on the same MC.    A B

The Mohr Circle 2121 11

The Mohr Circle – Principal Stresses Planes A and B are called principal planes when there are no shear stresses (only normal stresses) acting on them.  1 = major principal stress  3 = minor principal stress

The Mohr Circle

Direction of max principal stresses is 17 degrees c.c. from the vertical

Effective Stress Mohr Circle board

Seepage Force board

Seepage Force - Example board