SHEAR STRENGTH OF SOIL. Chapter 10: Sections Chapter 12: All sections except

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1 SHEAR STRENGTH OF SOIL Chapter 10: Sections Chapter 1: All sections ecept

2 TOPICS Introduction Components of Shear Strength of Soils Normal and Shear Stresses on a Plane Mohr-Coulomb Failure Criterion Laborator Shear Strength Testing Direct Shear Test Triaial Compression Test Unconfined Compression Test Field Testing (Vane test)

3 INTRODUCTION o Soil failure usuall occurs in the form of shearing along internal surface within the soil. o The shear strength of a soil mass is the internal resistance per unit area that the soil mass can offer to resist failure and sliding along an plane inside it. o The safet of an geotechnical structure is dependent on the strength of the soil. o Shear strength determination is a ver important aspect in geotechnical engineering. Understanding shear strength is the basis to analze soil stabilit problems like: Bearing capacit. Lateral pressure on earth retaining structures Slope stabilit

4 INTRODUCTION

5 Bearing Capacit Failure In most foundations and earthwork engineering, failure results from ecessive applied shear stresses. Strip footing Failure surface Mobilized shear resistance At failure, shear stress along the failure surface (mobilized shear resistance) reaches the shear strength.

6 Bearing Capacit Failure Transcona Grain Elevator, Canada (Oct. 18, 1913)

7 Bearing Capacit Failure

8 SLOPE FAILURE At failure, shear stress along the failure surface () reaches the shear strength ( f ). The soil grains slide over each other along the failure surface.

9 SLOPE FAILURE

10 Failure of Retaining Walls Retaining wall Retaining wall Failure surface Mobilized shear resistance At failure, shear stress along the failure surface (mobilized shear resistance) reaches the shear strength.

11 TOPICS Introduction Components of Shear Strength of Soils Normal and Shear Stresses on a Plane Mohr-Coulomb Failure Criterion Laborator Shear Strength Testing Direct Shear Test Triaial Compression Test Unconfined Compression Test Field Testing (Vane test)

12 SHEAR STRENGTH OF SOIL o Coulomb (1776) observed that there was a stress-dependent component of shear strength and a stress-independent component. o The stress-dependent component is similar to sliding friction in solids described above. The other component is related to the intrinsic COHESION of the material. Coulomb proposed the following equation for shear strength of soil: cohesion Friction f = shear strength of soil n = Applied normal stress C = Cohesion = Angle of internal friction (or angle of shearing resistance)

SHEAR STRENGTH OF SOIL o Cohesion (c), is a

the shear strength of soils due to friction

13 SHEAR STRENGTH OF SOIL o Cohesion (c), is a measure of the forces that cement particles of soils (stress independent). o Internal Friction angle (φ), is a measure of the shear strength of soils due to friction (stress dependent). o For granular materials, there is no cohesion between particles

14 SHEAR STRENGTH OF SOIL Saturated Soils But from the principle of effective stress Where u is the pore water pressure (p.w.p.) Then o C, or C, are called strength parameters, and we will discuss various laborator tests for their determination.

15 TOPICS Introduction Components of Shear Strength of Soils Normal and Shear Stresses on a Plane Mohr-Coulomb Failure Criterion Laborator Shear Strength Testing Direct Shear Test Triaial Compression Test Unconfined Compression Test Field Testing (Vane test)

16 Normal and Shear Stress along a Plane Chapter 10 Normal and Shear Stresses along a Plane (Sec. 10.) Pole Method for Finding Stresses along a Plane (Sec. 10.3)

17 Normal and Shear Stress along a Plane From geometr EB EF cos FB EF sin Sign Convention Normal Stresses Shear Stresses Positive Compression Counter clockwise rotation Negative Tension Clockwise rotation o Note that for convenience our sign convention has compressive forces and stresses positive because most normal stresses in geotechnical engineering are compressive. o These conventions are the opposite of those normall assumed in structural mechanics.

18 Normal and Shear Stress along a Plane *( EF ) sin *( EF sin ) cos *( EF cos ) n Similarl, *( EF ) sin *( EF cos ) cos *( EF sin ) n n F F N 0 cos *( EF sin ) T 0 sin *( EF sin ) n sin sin *( EF cos ) 0 cos cos *( EF cos ) 0 cos sin N T n cos n sin cos E n n sin F

19 cos sin sin cos n n sin cos n n Principal Planes Planes on which the shear stress is equal to zero Principal Stresses Normal stress acting on the principal planes Principal Planes & Principal Stresses

20 Principal Stresses n cos sin n sin cos () For 0 n 0 sin cos sin tan p cos (3) For an given valu es of, and Equation (3) will give two values of which are 90 degrees apart Two principal planes 90 degrees apart (1) Substituteeq (3) into eq (1) M ajor Principal Stress n M inor Principal Stress n 1 3

21 Eample 10.1

22 Construction of Mohr s Circle 1. Plot σ, as point M. Plot σ, as point R 3. Connect M and R 4. Draw a circle of diameter of the line RM about the point where the line RM crosses the horizontal ais (denote this as point O) Sign Convention Normal Stresses Shear Stresses Positive Compression Counter clockwise rotation Negative Tension Clockwise rotation o The points R and M in Figure above represent the stress conditions on plane AD and AB, respectivel. O is the point of intersection of the normal stress ais with the line RM.

23 Pole Method for Finding Stresses on a Plane There is a unique point on the Mohr s circle called the POLE (origin of planes) An straight line drawn through the pole will intersect the Mohr s circle at a point which represents the state of stress on a plane inclined at the same orientation in space as the line. Draw a line parallel to a plane on which ou know the stresses, it will intersect the circle in a point (Pole) Once the pole is known, the stresses on an plane can readil be found b simpl drawing a line from the pole parallel to that plane; the coordinates of the point of intersection with the Mohr circle determine the stresses on that plane.

24 Shear stress, Pole Method for Finding Stresses on a Plane How to determine the location of the Pole? F (, ) ( n, n ) on plane EF E P Normal stress, (, - ) Note: it is assumed that > 1. From a point of known stress coordinates and plane orientation, draw a line parallel to the plane where the stress is acting on.. The line intersecting the Mohr circle is the pole, P.

25 Shear stress, Normal and Shear Stress along a Plane Using the Pole to Determine Principal Planes F (, ) 1 E 3 Normal stress, P p (, - ) Direction of Major Principal Plane Direction of Minor Principal Plane

26 Eample 10.

Eample For the stresses of the element shown across, determine the normal stress and the shear stress on the plane inclined at a = 35 o from the horizontal reference plane.

27 Eample For the stresses of the element shown across, determine the normal stress and the shear stress on the plane inclined at a = 35 o from the horizontal reference plane. Solution Plot the Mohr circle to some convenient scale (See the figure across). Establish the POLE Draw a line through the POLE inclined at angle a = 35 o from the horizontal plane it intersects the Mohr circle at point C. a = 39 kpa a = 18.6 kpa

28 Eample The same element and stresses as in Eample ecept that the element is rotated 0 o from the horizontal as shown. Solution Since the principal stresses are the same, the Mohr circle will be the same as in Eample. Establish the POLE. Draw a line through the POLE inclined at angle a = 35 o from the plane of major principal stress. It intersects the Mohr circle at point C. The coordinates of point C ields a = 39 kpa a = 18.6 kpa

29 Eample Given the stress shown on the element across. Find the magnitude and direction of the major and minor principal stresses.

30 Eample Given the stress shown on the element across. Required: a. Evaluate a and a when a = 30 o. b.evaluate 1 and 3. c. Determine the orientation of the major and minor principal planes. d.determine the maimum shear stress and the orientation of the plane on which it acts.

31 Eample

both an analytical approach and the pole method, determine: (a) the direction of the

Quantitative Problems Problem 4-3 Figure 4-45 shows the state of stress at a point within a soil deposit. Using both an analytical approach and the pole method, determine: (a) the direction of the principal