The stress state at a point behind a retaining wall backfilled with dry sand is

Question

The stress state at a point behind a retaining wall backfilled with dry sand is represented by the cubical soil element (dimensions: 10 cm times 10 cm times 10 cm) shown below. The element is subjected to the forces in the figure. Draw the Molar circle for this element and determine (using both graphical and analytical methods): the location of the pole[indicating its coordinate in kPa]; the magnitude of the principal stress[kPa]; the angles between the principal stress planes and the horizontal[degrees]; the maximum shear stress[kPa]; the normal and shear stress[kPa] on a plane inclined at 20degree counterclockwise to the horizontal.

Explanation / Answer

x = -4kN

y = -8kN

xy= 2kN

now first of all find centre of circle

C = centre of circle which is equal to average of stress

C= av =(x +y)/2 =-6kN   this is the centre

R = radius of circle = (((x - y)/2)2 +xy) =8 =2.828kN

now the two points on x axis where the circle intersect x-axis

these are the principal stresses

max =av +R = -3.172kN

min =av - R = -8.828kN

now principal planes

tan2= 2(xy)/(x - y)

tan2=1

21 = 45o      22 =45+180=225o

1 =22.5o      2 = 112.5o

now the position of line on the circle perimeter

x =(x , -xy)    and Y =(y , xy)

x=(-4,-2)     and Y =(-8,2)

so this all what you need in mohr circle

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