Abstract
This paper presents the pseudo-dynamic analysis of seismic bearing capacity of a strip footing using upper bound limit analysis. However, in the literature, the pseudo-static approach was frequently used by several researchers to compute the seismic bearing capacity factor theoretically, where the real dynamic nature of the earthquake accelerations cannot be considered. Under the seismic conditions, the values of the unit weight component of bearing capacity factor N γE are determined for different magnitudes of soil friction angle, soil amplification and seismic acceleration coefficients both in the horizontal and vertical directions. The results obtained from the present study are shown both graphically as well as in the tabular form. It is observed that the bearing capacity factor N γE decreases significantly with the increase in seismic accelerations and amplification. The results are thoroughly compared with the existing values in the literature and the significance of the present methodology for designing the shallow footing is discussed.
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Abbreviations
- F i :
-
Body forces in a body of volume V
- G :
-
Shear modulus of soil
- H :
-
Maximum depth up to which the failure zone can be extended
- H a :
-
Depth up to which the failure zone is actually extended
- N γE :
-
Unit weight component of seismic bearing capacity factor
- P u :
-
Ultimate vertical failure load
- S:
-
Boundary surface of the collapse mechanism
- T i :
-
Boundary stress vector on the surface S
- T :
-
Period of lateral shaking
- V :
-
Total volume of the collapse mechanism
- V p :
-
Primary wave velocity
- V s :
-
Shear wave velocity
- a h (z, t):
-
Horizontal earthquake acceleration at depth z and time t
- a v (z, t):
-
Vertical earthquake acceleration at depth z and time t
- b :
-
Width of strip footing
- f a :
-
Amplification factor
- g :
-
Acceleration due to gravity
- t :
-
Time of vibration
- \( \ifmmode\expandafter\dot\else\expandafter\.\fi{v}^{{p*}}_{i} \) :
-
Displacement rate
- z :
-
Any depth below the ground surface
- ϕ :
-
Soil friction angle
- α :
-
Base angle of the left triangular rigid block at left footing edge
- α h :
-
Horizontal earthquake acceleration coefficient
- α v :
-
Vertical earthquake acceleration coefficient
- β :
-
Extreme right base angle of the right triangular rigid block
- \( \ifmmode\expandafter\dot\else\expandafter\.\fi{\varepsilon }^{{p*}}_{{ij}} \) :
-
Plastic strain rate compatible with displacement rate \( \ifmmode\expandafter\dot\else\expandafter\.\fi{v}^{{p*}}_{i} \)
- γ :
-
Unit weight of the soil medium
- η :
-
Wavelength of primary wave
- λ :
-
Wavelength of shear wave
- ν :
-
Poisson’s ratio of the soil medium
- ρ :
-
Mass density of the soil medium
- ω :
-
Angular frequency
- ξ h :
-
Coefficient of horizontal contribution of P u in seismic condition
- ξ v :
-
Coefficient of vertical contribution of P u in seismic condition
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Ghosh, P. Upper bound solutions of bearing capacity of strip footing by pseudo-dynamic approach. Acta Geotech. 3, 115–123 (2008). https://doi.org/10.1007/s11440-008-0058-z
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DOI: https://doi.org/10.1007/s11440-008-0058-z