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Modified Bishop method for stability analysis of weakly sloped subgrade under centrifuge model test

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Abstract

The sliding forms of weak sloped and horizontal subgrades during the sliding process differ. In addition, the sliding form of weakly sloped subgrades exhibits considerable slippage and asymmetry. The accuracy of traditional slice methods for computing the stability safety factor of weakly sloped subgrades is insufficient for a subgrade design. In this study, a novel modified Bishop method was developed to improve the accuracy of the stability safety factor for different inclination angles. The instability mechanism of the weakly sloped subgrade was considered in the proposed method using the “influential force” and “additional force” concepts. The “additional force” reflected the weight effect of the embankment fill, whereas the “influential force” reflected the effect of the potential energy difference. Numerical simulations and experimental tests were conducted to evaluate the advantages of the proposed modified Bishop method. Compared with the traditional slice method, the error between the proposed method and the exact value is less than 32.3% in calculating the safety factor.

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Abbreviations

θ 1 :

inclination of bottom of embankment

θ 2 :

inclination of bottom of soft soil layer

h :

thickness of soft soil layer at center of subgrade

h m :

thickness of soft soil layer of model

h n :

thickness of soft soil layer of prototype

a m :

acceleration of model

a n :

acceleration of prototype

g :

gravitational acceleration

N :

model ratio

τ :

horizontal tangential force

F E :

“influential force”

F θ :

“additional force”

E P :

potential energyd

r :

micro-virtual displacement

m :

mass of soil slice

h E :

horizontal height difference between M and O

e :

error

F s :

safety factor

F s1 :

average safety factor

λ :

acting position

R :

radius of sliding arc

η :

correction coefficient

X t :

x-axis of intersection point

Y i :

y-axis of intersection point

α i :

normal angle at midpoint of bottom of soil slice ‘i’

b i :

secant length of arc at bottom of soil slice ‘i’

W i :

gravity of soil slice

F Ei :

“influential force” acting on soil slice ‘i’

F θi :

“additional force” acting on soil slice ‘i’

T i :

tangential reaction force

N i :

normal reaction force

W 3k :

gravity of lateral embankment of sliding body

W 1ki :

gravity of soil slice ‘i’

c i :

cohesive force of soft soil

ϕ i :

internal friction angle of soft soil

r 1 :

bulk density of soft soil

r 2 :

bulk density of embankment filling

u i :

pore water pressure

c ′ i :

effective cohesive force of soft soil

ϕ ′ i :

effective internal friction angle of soft soil

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Acknowledgements

This study was sponsored by the National Natural Science Foundation of China (Grant No. 51609071) and the Fundamental Research Funds for the Central Universities (Nos. B200202087, B200204032).

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Authors and Affiliations

  1. Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing, 210098, China

    Ke Sheng, Bao-Ning Hong & Xin Liu

  2. Jiangsu Research Center for Geotechnical Engineering Technology, Hohai University, Nanjing, 210098, China

    Ke Sheng, Bao-Ning Hong & Xin Liu

  3. Geotechnical Research Institute, Hohai University, Nanjing, 210098, China

    Ke Sheng & Bao-Ning Hong

  4. Research Institute of Tunnel and Underground Engineering, Hohai University, Nanjing, 210098, China

    Xin Liu

  5. School of Civil Engineering, Xuzhou University of Technology, Xuzhou, 221018, China

    Hao Shan

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  1. Ke Sheng
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  2. Bao-Ning Hong
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Correspondence to Xin Liu.

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Sheng, K., Hong, BN., Liu, X. et al. Modified Bishop method for stability analysis of weakly sloped subgrade under centrifuge model test. Front. Struct. Civ. Eng. 15, 727–741 (2021). https://doi.org/10.1007/s11709-021-0730-z

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  • DOI: https://doi.org/10.1007/s11709-021-0730-z

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