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Masaru Hoshiya
Musashi Institute of Technology
Probability Study for a High-Capacity Micropile B
earing Mechanism
Yoshinori Otani Hirose & Co., Ltd.
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Design optimization for the HMPThe uncertainty of each composition parameter
(characteristic of ground condition , material , load)
The purpose of research
Partial Factor Design Method
Current design Code (draft) ( Allowable Stress Method)
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Today’s Topics
Effectiveness of Partial Factor Design Method
Probabilistic analysis of bearing mechanism for HMP
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Grout
BearingStratum
SteelPipe
Core(deformed re-bar)
Fig.1 Structure of HMP
Fig.2 Failure modeⅠ
Fig.3 Failure mode Ⅱ
Fig.4 Failure mode Ⅲ
Structure , failure modes of HMP
IWM2002Current design(1)
(1)
r: revision coefficient for the safety factor by the difference in how to estimate ultimate bearing capacity
n: safety factor
(2)
RC1: ultimate friction bearing capacity
RC2: steel pipe compressive strength
RC3: sum of non-steel pipe anchorage ultimate compressive strength
and steel pipe bond ultimate friction resistance
nrR
R cuca
min,, 321 CCCcu RRRR
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(3)R1: bond perimeter friction
R2: end bearing capacity
(4)
R3: ultimate compressive strength
of steel pipe grout R4: ultimate compressive strength of re-bar and steel pipe
(5)
R5: ultimate compressive strength of non-steel pipe grout R6: ultimate compressive strength of re-bar
R7: bond perimeter friction of steel pipe
4
20
0
211DqLaD
RRR
ii
C
)(85.0 1
432
CBBorCGG
C
AAFAfRRR
uuBBGG
C
LaDAfAf
RRRR
02
7653
85.0
BearingStratum
Bond Length L
Casing Plunge Length LC
Current design (failure mode Ⅰ~Ⅲ )
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IWM2002 Partial factor design method(1)
(6)
(7)
(8)
(9)
Z,Zi 0, safe≧
Z,Zi 0, failure≦
SD: dead loadSE: earthquake load
EDCCC SSRRRZ ],,min[ 321
ED SSRRZ 211
ED SSRRZ 432
ED SSRRRZ 7653
IWM2002 Partial factor design method(2)
(10)
(11)
(12)
Rj*: characteristic value of resistances (j=1 ~ 7)SD*: characteristic value of dead loadSE*: characteristic value of seismic loadφRj,γSDi, γSEi:partial factor
*1
*1
*22
*11 ESEDSDRR SSRR γγφφ
*2
*2
*44
*33 ESEDSDRR SSRR γγφφ
*3
*3
*77
*66
*55 ESEDSDRRR SSRRR γγφφφ
IWM2002 Partial factor design method(3)
(13)
(14)
(15)
αRjT,αSDi
T,αSEiT: standard sensitivity coefficient for each resistance,dead load,
seismic loadβi
T: target safety index for Zi
kRj , kSDi , kSEi: coefficient which connect mean and standard sensitivity factor of the resistances , dead load ,seismic loadVRj ,VSD ,VSE: coefficient of variation for the resistances ,dead load ,seismic lo
ad
(16)
RjRj
RjTi
TRj
R VkV
1
1 jφ
SESEi
SETi
TSEi
SEi VkV
1
1 γ
SDSDi
SDTi
TSDi
SDi VkV
1
1 γ
)(1 ifiZi
Zii P
IWM2002Mechanical Characteristics of
failure mode Ⅰ
Sensitivity Coefficients Vs. Bond Length
: αR1 bond perimeter friction : αR2 end bearing capacity
Bond length of the pile L(m)
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compression strength of the grout fG (N/mm2)
Mechanical Characteristics of failure mode Ⅱ
αR3:ultimate compressive strength of steel pipe grout
αR4:ultimate compressive strength of re-bar and steel pipe
Sensitivity Coefficients Vs. Compression Strength of Grout
IWM2002Mechanical Characteristics of
failure mode Ⅲ
:αR5 ultimate compressive strength of non-steel pipe grout :αR6 ultimate compressive strength of re-bar :αR7 bond perimeter friction of steel pipe
Sensitivity Coefficients Vs. Casing Plunge Length of Steel Pile
Casing plunge length of the steel pipe Lc(m)
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1.5 1.6 1.7 1.8 1.9 2.0 02468
10121416
1 2 3 4 5 β 1
Freq
uenc
y
02468
10121416
1 2 3 4 5 6β 2
Freq
uenc
y
10.5 11.0 11.5 12.0 12.5 13.0 13.51.5 1.6 1.7 1.8 1.9 2.0 0
5
10
15
20
25
30
1 2 3 4 5β 3
Freq
uenc
y
3.0 3.2 3.4 3.6 3.8 4.0
Histogram of Safety Index β1
Histogram of Safety Index β2
Histogram of Safety Index β3
Comparison of safety index β
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(sensitivity coefficient α)
Sensitivity Coefficients Vs.
Characteristic value Rc1*
Sensitivity Coefficients Vs.
Characteristic value Rc3*
IWM2002Comparison of Current design
code and PFD Method
Comparison of βa and βa’
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Conclusion
Partial Factor Design method can achieve optimization of HMP designs by taking into consideration the probability and dependability of the parameter which constitutes each limit state.