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ENCE Subject Lecture Shear Strength Theory and Properties

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            ENCE 361
           Soil Mechanics




           Shear Strength Theory
Alternate Methods of Determing Shear Strength
                 Properties
Triaxial
  Test
Coulomb
   and
  Other
   Soil
 Models
                     Equations for
                        Shear
                       Strength


Cohesionless Soils

                     Cohesive Soils
Typical for Cohesive Soils In-
Situ:  =0




 Typical for Cohesionless
 Soils: cu = 0 (but effects
 from overconsolidation
 must be considered




Triaxial Shear
      Test
 Relationships
 Ductile and Brittle Failure




Ductile Failure      Brittle Failure
        Cohesionless Soils
Generally, c = 0
If tests show that c > 0, this is generally
 regarded as apparent cohesion and not used in
 geotechinical analysis
Strength of soil is the product of the effective
 stress and the internal friction angle



Effective stress can include additional loads
                       Internal Friction
                            Angle 

Result of frictional interaction of soil particles with
 each other
Similar to surface friction in classic statics and
 dynamics
Is a function of the angle of repose; the same in
 some types of sand, varies in others
  Angle of repose: angle between the horizontal and the
   slope of a heap produced by pouring dust or dry sand
   from a small elevation
Values of Internal Friction Angle




                     (in consolidated or
                     drained condition)
Values of Internal Friction Angle




         Also see Textbook Table 11-2
          Cohesion in Soils
True Cohesion                   Apparent Cohesion
  Cementation                     Negative pore water
     Due to the presence of        pressure
      cementing agents such as     Negative excess pore
      calcium carbonate or          water pressures due to
      iron oxide
                                    dilation (expansion)
  Electrostatic and
   electromagnetic                 Apparent mechanical
   attractions                      forces
  Primary valence
   bonding (adhesion)
     Occurs primarily during
      overconsolidation
Effect of Effective Stress on
           Cohesion
Typical Values of Cohesion

    Standard
   Penetration                      Cohesion c or
  Resistance N     Consistency        qu, kPa
       0-2          Very Soft           0-25
       2-4            Soft             25-50
       4-8         Medium Stiff        50-100
       8-15           Stiff           100-200
      15-30         Very Stiff        200-400
       >30            Hard              >400

        Also see Textbook, Table 11-3
 Failure
 Envelope
and Mohr's
  Circle
Use of Mohr's Circle to Determine
        Failure Envelope
              Ilustration 11-2
Given
  Dry Cohesionless Soil
  Tested to determine 
  Confining Pressure =
   1000 psf
  Failure Pressure = 3200
   psf
Find
  Value of 
           Illustration 11-2
Equation for failure envelope and Mohr's Circle
           1sin       1sin 
    1 3         2 c
           1sin       1sin 
Simplification for c = 0


                       1sin 
              1 3          
                       1sin 
          Illustration 11-2
Solve for (cohesionless soils only)

                  1    1 3
        sin
                        3 1
Substitute variables:
  = arcsin((3200-1000)/(3200+1000))
  = arcsin(2200/4200)
  = arcsin(0.524)
  = 31.59º
              Illustration 11-3
Given
  Granular soil
      Unit Weight = 19.6 kN/m3
      Internal Friction Angle = 35º
Proposed Structure
  Causes vertical stress to increase 60 kPa at 4m
   depth
  Causes shear stress to increase 52 kPa on horizontal
   plane at this depth
  Also consider case where water table increases to
   ground surface
          Illustration 11-3

Find
  Shearing Strength 4m below surface before
   installation of structure
  Whether soil will shear with additional load
  Whether soil will shear with additional load and
   elevation of water table
          Illustration 11-3
Solution – No Structure Load
  Overburden pressure w/o structure load @ 4 m =
   (19.6 kN/m3)(4 m) = 78.4 kPa



  Shearing resistance = (78.4) tan (35º) = 54.9 kPa
   without structure load
          Illustration 11-3
Solution – Sturctural Load, no water table
 elevation


  Soil vertical stress w/structural load = 78.4 + 60 =
   138.4 kPa
  Shearing strength w/structural load = (138.4) tan
   (35º) = 96.9 kPa > 52 kPa so shear failure does not
   occur
           Illustration 11-3
Solution – Sturctural Load, with water table
 elevation


  Soil overburden pressure = (19.6-9.81)(4) = 39.2
   kPa
  Soil vertical stress w/water table and structural load
   = 39.2 + 60 = 99.2 kPa
  Shearing strength w/water table and structural load
   = (99.2) tan (35º) = 69.46 kPa > 52 kPa so shear
   failure does not occur; however, margin of safety is
   decreased
Shear Strength of Clay
Soils with Both Cohesion and
        Internal Friction
Ideally soils are either purely cohesive or
 cohesionless
This is frequently not the case because:
  Composition of soils are mixed (combinations of
   sands, clays and silts)
  Drainage and/or remoulding of clays produces
   conditions similar to drained triaxial or direct shear
   conditions
Testing for Various Soil Conditions
Drained Triaxial Tests on Clay
           Example
Given
  Drained (S) Triaxial Test on Saturated Clay
  Sample 1
     Confining Pressure = 70 kPa
     Failure Pressure = 200 kPa
  Sample 2
     Confining Pressure = 160 kPa
     Failure Pressure = 383.5 kPa
Find
  Cohesion and Internal Friction Angle
Drained Triaxial Tests on Clay
           Example
Governing equation

        1sin       1sin 
 1 3         2 c
        1sin       1sin 
Noting that
     1sin      2 	 
             tan   
     1sin        4 2
  (angles in radians)
  Drained Triaxial Tests on Clay
             Example
  Governing equation reduces to

             	            	 
 1 3 tan   2 c tan   
             2
             4 2           4 2
  Define:

                      	 
             N tan   
                       2
                      4 2
Drained Triaxial Tests on Clay
           Example
Governing equation reduces further to

     1 3 N 2 c N 

Substituting:


     20070 N 2 c N 
    383.5160 N 2 c N 
Drained Triaxial Tests on Clay
           Example
Solving these equations
   20070 N 2 c N 
  383.5160 N 2 c N 
Results in
         c20.06 kPa
           N 2.04
      0.349 radians20º
Other Methods of Determining
       Shear Strength
Other Methods of Determining
       Shear Strength
        SPT Correlations
Internal Friction Angle

                                      0.34
           1              N 60
 
tan                           
                          v
                          
                12.220.3 
                          pa

Cohesion is in tabular form
             CPT Data
Internal Friction Angle

                  q c  vo
                        
  
17.611 log          
                  pa    pa

Cohesion in tabular form
Vane Shear Test
        Useful for a quick
         determination of shear
         stress in situ
        Generally most applicable
         to cohesive soils; good for
         determining undrained
         shear strength
Vane Shear Test Calculations
Torque of Vane
                            cu 	 D H D
 Shear                          2
  cu = undrained      T             
   shear strength                    2 6
  T = maximum
                                   T
   torque applied
                        c u
  D = diameter of                2 H   D
   vanes                     	D   
  H = height of                     2 6
   vanes
   = PI correction
Vane Shear Test Calculations




                 Correction for Plasticity Index
  Sensitivity and Vane Shear

Undrained strength determined by measuring
 maximum torque while rotating vanes at 0.1
 deg./sec.
Remoulded shear strength measured by rotating
 vane about ten (10) times, then recording a final
 torque value
Sensitivity =
 undisturbed shear strength/remoulded shear
 strength
Questions?

				
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