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Finite Element Evaluation of Vertical Bearing Capacity Factors\(N_{c}^{\prime }\), \(N_{q}^{\prime }\) and \(N_{\gamma }^{\prime }\) for Ring Footings

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Abstract

In this study, the vertical bearing capacity factors \(N_{c}^{\prime }\), \(N_{q}^{\prime }\) and \(N_{\gamma }^{\prime }\) are evaluated for smooth and rough base ring footings resting on c–ϕ soil using the finite element method. The radii ratio, (ri/ro), is the ratio of internal radius to the external radius of the ring footing, is varied from 0 to 0.75 with an increment of 0.25. The friction angle of the soil is varied from 5° to 35°, dilation angle is zero and the Mohr–Coulomb yield criterion and non-associative flow rule are used. The study is extended for the soil having a friction angle of 35° considering the non-associative flow rule with a dilation angle of 5°. The bearing capacity factors are evaluated considering cohesion, surcharge and unit weight as three separate components. Then the superposition of the three components of the bearing capacity equation is analysed. A numerical example is considered to illustrate the applicability of the finite element analysis by comparing the bearing capacities with those of the Terzaghi’s classical equation. The finite element results are presented in the form of design charts and tables for practical use.

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Abbreviations

B :

Width of strip footing

C :

Cohesion of soil

D i :

Internal diameter of ring footing

D o :

External diameter of ring footing

E :

Young’s modulus

FE:

Finite element

FEM:

Finite element method

FDM:

Finite difference method

FLAC:

Fast Lagrangian analysis of continua

N c N q N γ :

Terzaghi’s bearing capacity factors

\(N_{c}^{\prime } ,N_{q}^{\prime } ,N_{\gamma }^{\prime }\) :

Bearing capacity factors for ring footing

r i :

Internal radius of ring footing

r o :

External radius of ring footing

s c s q s γ :

Shape factors

q u :

Ultimate bearing capacity

q :

Surcharge at the base level of footing

Q u :

Ultimate failure load

Q u ′ :

Overall ultimate failure load

γ :

Unit weight of soil

ν :

Poisson’s ratio

ϕ :

Friction angle of soil

ψ :

Dilation angle

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Authors and Affiliations

  1. Computational Geomechanics Laboratory, Geotechnical Engineering Division, Department of Civil Engineering, IIT Madras, Chennai, India

    Jitesh T. Chavda & G. R. Dodagoudar

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  1. Jitesh T. Chavda
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  2. G. R. Dodagoudar
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Correspondence to Jitesh T. Chavda.

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Chavda, J.T., Dodagoudar, G.R. Finite Element Evaluation of Vertical Bearing Capacity Factors\(N_{c}^{\prime }\), \(N_{q}^{\prime }\) and \(N_{\gamma }^{\prime }\) for Ring Footings. Geotech Geol Eng 37, 741–754 (2019). https://doi.org/10.1007/s10706-018-0645-1

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  • DOI: https://doi.org/10.1007/s10706-018-0645-1

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