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          p 26
        
        
          
            Chapter 2
          
        
        
          Helical Foundation Systems
        
        
          
            CHAPTER 2
          
        
        
          HELICAL FOUNDATION SYSTEMS
        
        
          
            2.7.2 Cylindrical Shear Method
          
        
        
          The design equation for determining helical pile
        
        
          capacity by the cylindrical shear method was
        
        
          originally developed by Mitsch and Clemence
        
        
          (1985) and later modified for simplicity.
        
        
          The cylindrical shear method assumes the
        
        
          development of a soil friction column (cylinder)
        
        
          between the upper and lower helix plates along
        
        
          with individual bearing of either the upper or
        
        
          lower helix, depending upon loading direction.
        
        
          The ultimate bearing capacity is then determined
        
        
          by the summation of shear strength of the soil
        
        
          cylinder, shaft adhesion/friction and end bearing
        
        
          of either the upper or lower helix. For deep
        
        
          cylindrical shear failure to occur, spacing of the
        
        
          helix plates along the shaft is generally less than
        
        
          or equal to 3 times the diameter of the leading
        
        
          plate and the uppermost helix plate is embedded
        
        
          to a depth of at least 5 diameters. Skin friction
        
        
          along the shaft is generally ignored for shaft
        
        
          sizes less than 6 inches in outside diameter.
        
        
          Figure 2.7.2.a
        
        
          illustrates the load transfer
        
        
          mechanism for the cylindrical shear method in
        
        
          compression loading.
        
        
          The helical pile capacity by the cylindrical shear
        
        
          method can be calculated as:
        
        
          
            Q
          
        
        
          
            u
          
        
        
          
            = 2πRL(c+K
          
        
        
          
            o
          
        
        
          
            q’tanΦ)+A
          
        
        
          
            h
          
        
        
          
            (cN
          
        
        
          
            c
          
        
        
          
            +q’N
          
        
        
          
            q
          
        
        
          
            )
          
        
        
          Where,
        
        
          
            Q
          
        
        
          
            u
          
        
        
          = Ultimate Pile Capacity (lb)
        
        
          
            R
          
        
        
          = Average Helix Radius (ft)
        
        
          
            L
          
        
        
          = Total Spacing Between All Helix
        
        
          Plates (ft)
        
        
          
            c
          
        
        
          = Cohesion at the Helix Depth (lb/ft
        
        
          2
        
        
          )
        
        
          
            K
          
        
        
          
            o
          
        
        
          = Dimensionless At-Rest Earth
        
        
          Pressure Coefficient
        
        
          
            Φ
          
        
        
          = Soil Friction Angle (degrees)
        
        
          
            A
          
        
        
          h
        
        
          = Area of the Top or Bottom Helix
        
        
          Plate (ft
        
        
          2
        
        
          )
        
        
          
            q’
          
        
        
          = Effective Vertical Overburden Stress
        
        
          at A
        
        
          h
        
        
          (lb/ft
        
        
          2
        
        
          )
        
        
          
            N
          
        
        
          
            c
          
        
        
          
            , N
          
        
        
          
            q
          
        
        
          = Dimensionless Bearing Capacity
        
        
          Factors
        
        
          Refer to Section 2.7.1 for discussions
        
        
          regarding Bearing Capacity Factors and
        
        
          Critical Depth.
        
        
          Based upon previous research, the individual
        
        
          bearing method and cylindrical shear method
        
        
          should provide similar results at helix spacings
        
        
          of 2.5D to 3.5D. FSI promotes the use of the
        
        
          individual bearing method for determination of
        
        
          pile capacity due to its relative simplicity and
        
        
          since the original form from which this method
        
        
          is derived is already widely accepted by the
        
        
          geotechnical engineering community.
        
        
          Figure 2.7.2.a
        
        
          Cylindrical Shear Method