If both the major and minor principal stresses for a soil element are known, as well as the strength parameters c'and o': A) Derive the formula that gives the orientation (the angle 0) of the theoretical failure plane. Hint: for the diagram below, assume 0₁ is acting in the vertical direction on the soil element (typical case) - i.e. the orientation of the failure plane with be measured on the Mohr's Circle from the Pole (which will be at 03). Remember a useful property of circles in terms of angles... Ko $' 03 01 0 B) Relate your answer from Part A to the failure plane assumed in Rankine's Active Earth Pressure. You can show this relationship with a simple sketch.

If both the major and minor principal stresses for a soil element are known, as well as the strength parameters c'and o': A) Derive the formula that gives the orientation (the angle 0) of the theoretical failure plane. Hint: for the diagram below, assume 0₁ is acting in the vertical direction on the soil element (typical case) - i.e. the orientation of the failure plane with be measured on the Mohr's Circle from the Pole (which will be at 03). Remember a useful property of circles in terms of angles... Ko $' 03 01 0 B) Relate your answer from Part A to the failure plane assumed in Rankine's Active Earth Pressure. You can show this relationship with a simple sketch.

Principles of Geotechnical Engineering (MindTap Course List)

9th Edition

ISBN:9781305970939

Author:Braja M. Das, Khaled Sobhan

Publisher:Braja M. Das, Khaled Sobhan

Chapter10: Stresses In A Soil Mass

Section: Chapter Questions

Problem 10.2P

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please Show complete solution and avoid rounding off intermediate values. Please write legibly. Athanks
A thin layer of clay subjected to drying develops internal shrinkage stresses. The state of effective stress at a point in this layer is shown in the figure (a) below. Plane stress condition can be assumed for this problem. Elastic modulus, E of clay is 15 MPa and Poisson's ratio, v is 0.35. Hooke's law is valid during drying, meaning that (o,- vo,) *3 where s,is the strain in x direction. 12 kPa 19 kPa Tx1y1 46 kPa 15° (a) Before curling (b) After curling
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A = 45 B = 40 C = 15
10-14. The state plane stress in a mass of dense cohesionless sand is described by the following stresses: Normal stress on horizontal plane Normal stress on vertical plane = 200 kPa Shear stress on horizontal and vertical planes 370 kPa 80 kPa %3! Determine by means of the Mohr circle the magnitude and direc- tion of the principal stresses. Is this state of stress safe against failure? (After A. Casagrande.)
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