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Stability Numbers for a Vertical Circular Excavation with Surcharge

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Abstract

The axisymmetric lower bound finite elements limit analysis technique has been used for computing the stability numbers (γH/c 0) for an unsupported circular vertical excavation in the presence of surcharge pressure (q). The numerical results are presented for various combinations of H/b, ϕ, m and q; the factor m incorporates the rate of linear increase of soil cohesion with depth for a fully cohesive soil medium. The computations reveal that the magnitude of γH/c 0 reduces continuously with (1) increases in the values of q, and (2) decreases in the magnitudes of m, ϕ and H/b.

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Abbreviations

b :

Radius of circular excavation

c :

Cohesion of soil at a depth h

c 0 :

Cohesion of soil along ground surface

D c :

Number of stress discontinuities in the entire discretized soil domain

E :

Number of triangular elements in the entire discretized soil domain

H :

Height of excavation

L d :

Vertical extent of soil domain defined in Fig. 1a

Fig. 1
figure 1

a Problem domain and the boundary conditions, b typical triangular element and c the chosen mesh for H/b = 7, ϕ = 0°

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L e :

Horizontal extent of soil domain defined in Fig. 1a

m :

Non-dimensional factor which incorporates the rate of linear increase of soil cohesion with depth (refer Fig. 1a)

N :

Number of nodes in the entire soil domain

q :

Surcharge pressure

ϕ :

Friction angle of soil

γ :

Unit weight of soil

σ 1 :

Major principal stress

σ 1f,i :

Major principal stress at failure associated with ith node

σ r :

Normal stress in r-direction

σ z :

Normal stress in z-direction

σ θ :

Hoop/circumferential stress

τ rz :

Shear stress

References

  1. Britto AM, Kusakabe O (1982) Stability of unsupported axisymmetric excavations in soft clay. Géotechnique 32(3):261–270

    Article  Google Scholar 

  2. Pastor J, Turgeman S (1982) Limit analysis in axisymmetrical problems: numerical determination of complete statical solutions. Int J Mech Sci 24(2):95–117

    Article  MATH  Google Scholar 

  3. Khatri VN, Kumar J (2010) Stability of an unsupported vertical circular excavation in clays under undrained condition. Comput Geotech 37(3):419–424

    Article  Google Scholar 

  4. Lyamin AV, Sloan SW (2002) Upper bound limit analysis using linear finite elements and non-linear programming. Int J Numer Anal Meth Geomech 26(2):181–216

    Article  MATH  Google Scholar 

  5. Kumar J, Chakraborty D (2012) Stability number for an unsupported vertical circular excavation in c − ϕ soil. Comput Geotech 39:79–84

    Article  Google Scholar 

  6. Kumar J, Chakraborty M, Sahoo JP (2014) Stability of unsupported vertical circular excavation. J Geotech Geoenviron Eng ASCE 140(7):04014028

    Article  Google Scholar 

  7. Kumar J, Khatri VN (2011) Bearing capacity factors of circular foundations for a general c − ϕ soil using lower bound finite element limit analysis. Int J Numer Anal Meth Geomech 35(3):393–405

    Article  MATH  Google Scholar 

  8. Bishop AW (1966) The strength of soils as engineering materials. Géotechnique 16(2):91–130

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India

    Debarghya Chakraborty

  2. Department of Civil Engineering, Indian Institute of Science, Bangalore, 560012, India

    Jyant Kumar

Authors
  1. Debarghya Chakraborty
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  2. Jyant Kumar
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Correspondence to Debarghya Chakraborty.

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Chakraborty, D., Kumar, J. Stability Numbers for a Vertical Circular Excavation with Surcharge. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 87, 115–123 (2017). https://doi.org/10.1007/s40010-016-0311-z

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  • DOI: https://doi.org/10.1007/s40010-016-0311-z

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