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Mathcad - Ex 13.4 CFA pile design from cone tests.xmcd

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Mathcad - Ex 13.4 CFA pile design from cone tests.xmcd Powered By Docstoc
					                             Example 13.4
        Design of continuous flight auger piles from cone tests
               Verification of strength (limit state GEO)
Design situation
Consider the design of continuous flight auger (CFA) piles for a site in
Twickenham, London. Ground conditions at the site comprise dense, becoming
loose gravelly, SAND. Cone penetration tests have been perfomed at the site
to a depth of 8m. (Data courtesy CL Associates.) The limiting average unit
shaft resistance p s and limiting unit base resistance pb at each cone location
are estimated to be:
            ⎛120kPa ⎞            ⎛2800kPa ⎞
              ⎜       ⎟          ⎜        ⎟
              ⎜120kPa ⎟          ⎜3000kPa ⎟
       ps =   ⎜       ⎟   pb =   ⎜        ⎟
              ⎜100kPa ⎟          ⎜2000kPa ⎟
              ⎜120kPa ⎟          ⎜3000kPa ⎟
              ⎝       ⎠          ⎝        ⎠
A group of N = 6 piles with diameter D = 400mm and length L = 6m are
required to carry between them a permanent action FGk = 2100kN together

with a variable action FQk = 750kN. The weight density of reinforced

                          kN
concrete is γck = 25           (as per EN 1991-1-1 Table A.1).
                           3
                          m
                                  Design Approach 1

Actions and effects
                                     ⎛ π × D2 ⎞
                                     ⎜        ⎟
The self-weight of pile is WGk =     ⎜ 4 ⎟ × L × γck = 18.8 kN
                                     ⎝        ⎠
                               ⎛A1 ⎞      ⎛1.35 ⎞          ⎛1.5 ⎞
Partial factors from Sets      ⎜ ⎟: γG = ⎜      ⎟ and γQ = ⎜ ⎟
                               ⎝A2 ⎠      ⎝ 1 ⎠            ⎝1.3 ⎠
Design total action per pile is:

       Fcd =
                    (               )
              γG × FGk + WGk + γQ × FQk ⎛664 ⎞
                                       =⎜    ⎟ kN
                             N          ⎝516 ⎠

Calculated shaft resistance
Number of cone penetration tests n = 4
                                                      ⎛905 ⎞
                                                      ⎜    ⎟
                                                      ⎜905 ⎟
Calculated shaft resistance R s =    π × D × L × ps = ⎜    ⎟   kN
                                                      ⎜754 ⎟
                                                      ⎜905 ⎟
                                                      ⎝    ⎠

                                                 ∑ Rs
Mean calculated shaft resistance R s,mean =                  = 867 kN
                                                    n

                                                        ( )
Minimum calculated shaft resistance R s,min = min R s = 754 kN


Calculated base resistance
                                                 ⎛352 ⎞
                                                 ⎜    ⎟
                                    ⎛ π × D2 ⎞
                                    ⎜        ⎟   ⎜377 ⎟
Calculated base resistance R b =    ⎜ 4 ⎟ × pb = ⎜251 ⎟        kN
                                    ⎝        ⎠   ⎜    ⎟
                                                 ⎜377 ⎟
                                                 ⎝    ⎠

                                                ∑ Rb
Mean calculated base resistance R b,mean =               = 339 kN
                                                    n

                                                        ( )
Minimum calculated base resistance R b,min = min R b = 251 kN


Calculated total resistance
Mean calculated total resistance R t,mean = R s,mean + R b,mean = 1206 kN

Minimum calculated total resistance R t,min = R s,min + R b,min = 1005 kN


Characteristic resistance
Correlation factor on mean measured resistance ξ3 = 1.31

Correlation factor on minimum measured resistance ξ4 = 1.20
For a pile group that can transfer load from weak to strong piles
(§7.6.2.2.(9)), ξ may be divided by 1.1 (but ξ 3 cannot fall beneath 1.0).
              ⎛ ξ3
              ⎜          ⎞
                         ⎟                 ξ4
Thus ξ3 = max ⎜     , 1.0⎟ = 1.19 and ξ4 =     = 1.09
              ⎝ 1.1      ⎠                 1.1
                         R t,mean                   R t,min
Calculated resistances              = 1013 kN and              = 922 kN
                             ξ3                         ξ4
Characteristic resistance should therefore be based on the minimum value.
                                          R s,min
Characteristic shaft resistance is R sk =         = 691 kN
                                             ξ4

                                           R b,min
Characteristic base resistance is R bk =             = 230 kN
                                               ξ4


Design resistance
                            ⎛R1 ⎞        ⎛1 ⎞          ⎛ 1.1 ⎞
Partial factors from Sets   ⎜ ⎟:    γs = ⎜ ⎟ and γb = ⎜      ⎟
                            ⎝R4 ⎠        ⎝1.3 ⎠        ⎝1.45 ⎠
                            R sk     R bk ⎛901 ⎞
Design resistance is R cd =      +         =⎜     ⎟ kN
                            γs        γb     ⎝691 ⎠


Verification of compression resistance
                               Fcd ⎛74 ⎞
Degree of utilization ΛGEO,1 =     =⎜ ⎟ %
                               R cd ⎝75 ⎠

Design is unacceptable if degree of utilization is > 100%




                              Design Approach 2
Actions and effects
Partial factors from set A1: γG = 1.35 and γQ = 1.5


Design total action per pile is Fcd =
                                           (            )
                                      γG × FGk + WGk + γQ × FQk
                                                                = 664 kN
                                                  N


Design resistance
Characteristic shaft and base resistances are unchanged from DA1
Partial factors from set R2: γs = 1.1 and γb = 1.1
                            R sk R bk
Design resistance is R cd =     +      = 838 kN
                             γs     γb
Verification of compression resistance
                                 Fcd
Degree of utilization ΛGEO,2 =          = 79 %
                                 R cd

Design is unacceptable if degree of utilization is > 100%


                             Design Approach 3

Actions and effects
Partial factors from set A1: γG = 1.35 and γQ = 1.5


Design total action per pile is Fcd =
                                           (           )
                                      γG × FGk + WGk + γQ × FQk
                                                                = 664 kN
                                                  N

Characteristic resistance
Partial factors from set M2 should be applied to material properties... but
since there are no material properties to factor, we will factor the
resistances instead using γφ = 1.25 . Since resistances are governed by the

minimum calculated resistance (as per DAs 1 and 2)...
                                          R s,min
Characteristic shaft resistance is R sk =         = 553 kN
                                          ξ4 × γφ

                                         R b,min
Characteristic base resistance is R bk =         = 184 kN
                                         ξ4 × γφ


Design resistance
Partial factors from set R3: γs = 1 and γb = 1

                            R sk R bk
Design resistance is R cd =     +     = 737 kN
                            γs    γb


Verification of compression resistance
                               Fcd
Degree of utilization ΛGEO,3 =      = 90 %
                               R cd

Design is unacceptable if degree of utilization is > 100%
               Design to UK National Annex to BS EN 1997-1

Characteristic resistance
Correlation factor on mean measured resistance ξ3 = 1.38

Correlation factor on minimum measured resistance ξ4 = 1.29
For a pile group that can transfer load from weak to strong piles
(§7.6.2.2.(9)), ξ may be divided by 1.1 (but ξ 3 cannot fall beneath 1.0).
              ⎛ ξ3
              ⎜          ⎞
                         ⎟                 ξ4
Thus ξ3 = max ⎜     , 1.0⎟ = 1.25 and ξ4 =     = 1.17
              ⎝ 1.1      ⎠                 1.1
                         R t,mean                           R t,min
Calculated resistances              = 961.6 kN and                    = 857 kN
                            ξ3                                ξ4

Characteristic resistance should therefore be based on the minimum value,
so...
                                          R s,min
Characteristic shaft resistance is R sk =         = 643 kN
                                             ξ4

                                                R b,min
Characteristic base resistance is R bk =                    = 214 kN
                                                   ξ4


Design resistance
                            ⎛R1 ⎞        ⎛1 ⎞          ⎛1 ⎞
Partial factors from Sets   ⎜ ⎟:    γs = ⎜ ⎟ and γb = ⎜ ⎟
                            ⎝R4 ⎠        ⎝1.6 ⎠        ⎝2 ⎠
                            R sk     R bk ⎛857 ⎞
Design resistance is R cd =      +         =⎜     ⎟ kN
                            γs        γb     ⎝509 ⎠
Verification of compression resistance
                                    Fcd        ⎛77 ⎞
Degree of utilization ΛGEO,1 =             =   ⎜ ⎟      %
                                    R cd       ⎝101 ⎠
Design is unacceptable if degree of utilization is > 100%

				
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posted:11/23/2011
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