IWM2002

Masaru Hoshiya

Musashi Institute of Technology

Probability Study for a High-Capacity Micropile B

earing Mechanism

Yoshinori Otani Hirose & Co., Ltd.

IWM2002

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

IWM2002Dependability of resistances

(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.