IWM200 2 Masaru Hoshiya Musashi Institute of Technology Probability Study for a High-Capacity Micropile Bearing Mechanism Yoshinori Otani Hirose & Co., Ltd.

IWM200 2  Design optimization for the HMP The 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 ）

IWM200 2 Today’s Topics  Effectiveness of Partial Factor Design Method  Probabilistic analysis of bearing mechanism for HMP

IWM200 2 Grout Bearing Stratum Steel Pipe Core (deformed re-bar) Fig.1 Structure of HMP Fig.2 Failure mode Ⅰ Fig.3 Failure mode Ⅱ Fig.4 Failure mode Ⅲ Structure, failure modes of HMP

IWM200 2 Current design(1) (1) r: revision coefficient for the safety factor by the difference in how to estimate ultimate bearing capacity n: safety factor (2) R C1 : ultimate friction bearing capacity R C2 : steel pipe compressive strength R C3 : sum of non-steel pipe anchorage ultimate compressive strength and steel pipe bond ultimate friction resistance IWM200 2

(3) R 1 : bond perimeter friction R 2 : end bearing capacity (4) R 3 : ultimate compressive strength of steel pipe grout R 4 : ultimate compressive strength of re-bar and steel pipe (5) R 5 : ultimate compressive strength of non-steel pipe grout R 6 : ultimate compressive strength of re-bar R 7 : bond perimeter friction of steel pipe Bearing Stratum Bond Length L Casing Plunge Length L C Current design (failure mode Ⅰ～Ⅲ ) IWM200 2

Partial factor design method(1) (6) (7) (8) (9) Z,Z i ≧ 0, safe Z,Z i ≦ 0, failure S D : dead load S E : earthquake load

IWM200 2 Partial factor design method(2) (10) (11) (12) R j *: characteristic value of resistances (j=1 ～ 7) S D *: characteristic value of dead load S E *: characteristic value of seismic load φ Rj,γ SDi, γ SEi :partial factor

IWM200 2 Partial factor design method(3) (13) (14) (15) α Rj T,α SDi T,α SEi T : standard sensitivity coefficient for each resistance,dead load, seismic load β i T : target safety index for Z i k Rj, k SDi, k SEi : coefficient which connect mean and standard sensitivity factor of the resistances, dead load,seismic load V Rj,V SD,V SE : coefficient of variation for the resistances,dead load,seismic load (16)

IWM200 2 Mechanical Characteristics of failure mode Ⅰ Sensitivity Coefficients Vs. Bond Length : α R1 bond perimeter friction : α R2 end bearing capacity Bond length of the pile L(m)

IWM200 2 compression strength of the grout f G (N/mm 2 ) Mechanical Characteristics of failure mode Ⅱ α R3 :ultimate compressive strength of steel pipe grout α R4 :ultimate compressive strength of re-bar and steel pipe Sensitivity Coefficients Vs. Compression Strength of Grout

IWM200 2 Mechanical Characteristics of failure mode Ⅲ :α R5 ultimate compressive strength of non-steel pipe grout :α R6 ultimate compressive strength of re-bar :α R7 bond perimeter friction of steel pipe Sensitivity Coefficients Vs. Casing Plunge Length of Steel Pile Casing plunge length of the steel pipe Lc(m)

IWM200 2 Histogram of Safety Index β 1 Histogram of Safety Index β 2 Histogram of Safety Index β 3 Comparison of safety index β

IWM200 2 Dependability of resistances (sensitivity coefficient α) Sensitivity Coefficients Vs. Characteristic value R c1 * Sensitivity Coefficients Vs. Characteristic value R c3 *

IWM2002 Comparison of Current design code and PFD Method Comparison of β a and β a ’

IWM200 2 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.