Estimation of the Seismic Bearing Capacity of Shallow Strip Footings Based on a Pseudodynamic Approach
Publication: International Journal of Geomechanics
Volume 22, Issue 9
Abstract
The bearing capacity of a shallow strip footing is investigated by a pseudodynamic method under earthquake conditions. A nonsymmetrical multiblock mechanism is herein adopted to describe the uplift failure of the foundations based on the kinematic theorem of limit analysis. This nonsymmetrical mechanism comprises a series of rigid triangular blocks that translate into the failure area. The seismic load, varying with time and space, is represented by a pseudodynamic method that considers the dynamic properties of earthquake waves. A slice method is proposed to adapt the variation in inertial force with time and depth for the convenience of calculating the earthquake-induced work rate. Then, equating the external work rate and the internal dissipation rate, the rigorous upper-bound solution of the seismic bearing capacity factors, which will be optimized by the sequential quadratic programming (SQP) in the MATLAB toolbox for searching for the optimal value, is explicitly derived. Comparisons between the present solution and previous works are made to validate the rationality and accuracy of the proposed methodology. A specific parametric analysis is conducted to reveal the influence of dynamic parameters on the bearing capacity of the strip footing. Numerical results are provided graphically as well as in the tabular form for reference in footing design.
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Data Availability Statement
Some data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.
1.
The detailed data of Figs. 5–16.
2.
The MATLAB code of the proposed procedure.
Acknowledgments
This manuscript was supported by the National Natural Science Foundation of China (Grant No. 5210081105), the Natural Science Foundation of Anhui Province (Grant No. 2108085QE250), and the Fundamental Research Funds for the Central Universities (Grant No. JZ2021HGTA0160), which are greatly appreciated.
Notation
The following symbols are used in this paper:
- ah
- horizontal seismic acceleration;
- av
- vertical seismic acceleration;
- B
- width of footing;
- c
- cohesion;
- D
- depth of footing;
- Dint
- total internal energy dissipation;
- di
- velocity discontinuity of the ith block;
- Fi
- volume force;
- f
- amplitude amplification factor;
- G
- shear modulus;
- H
- maximal failure depth;
- kh, kv
- seismic coefficients;
- li
- velocity discontinuity of the ith block;
- Nce, Nqe, Nγe
- seismic bearing capacity factors;
- Pe
- dead load transferred by superstructure;
- q
- equivalent load of covering layer;
- qce
- bearing capacity of strip footing;
- S
- boundary of the object;
- T
- period of seismic wave;
- Ti
- external force;
- t
- random time;
- t0
- initial phase lag;
- V
- volume of the object;
- V1, V2, Vi
- velocity of the Block 1, 2…i;
- Vi,i+1
- relative velocity between blocks i and i + 1;
- Vs, Vp
- velocity of seismic wave;
- velocity field;
- We
- work rate resulting from inertial force;
- Wext
- total external work rate;
- work rate resulted from Pe;
- Wq
- work rate resulted from covering layer;
- work rate done by soil weight;
- z
- random coordinate;
- φ
- internal friction angle;
- γ
- unit weight of soils;
- αi, βi
- angular variables of failure mechanisms;
- λs, λp
- wavelength of seismic wave;
- υ
- Poisson’s ratio;
- plastic strain rate field;
- effective stress; and
- ρ
- density of geomaterial.
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Published In
International Journal of Geomechanics
Volume 22 • Issue 9 • September 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Nov 23, 2021
Accepted: Mar 7, 2022
Published online: Jul 4, 2022
Published in print: Sep 1, 2022
Discussion open until: Dec 4, 2022
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