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Semi-Analytical Approach for Estimating the Viscoelastic Settlement of a Footing Resting on a Slope

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Abstract

The safety of a foundation can be viewed from two different perspectives, bearing capacity, and the settlement. There are many articles focused on the bearing capacity of a foundation built near the slope. However, investigating the settlement of the foundation rest near the slope is very limited. In order to increase the safety of the structure, besides the elastic settlement, the study of time-dependent behavior of footing is of great importance in geotechnical engineering. In this research, a semi-analytical solution has been proposed to obtain the viscoelastic settlement of a footing adjacent to a slope. Based on the developed Airy stress function, distributed stress within the slope due to foundation load was computed analytically and then displacement has been acquired by using the finite difference method. The outcome of the proposed method was compared with COMSOL finite element software and good agreement between those was observed.

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All data and material used during the study appear in the submitted article.

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Funding

The authors did not receive support from any organization for the submitted work.

Author information

Authors and Affiliations

  1. School of Mining Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Hadi Haghgouei, Ali Reza Kargar & Mohammad Hossein Khosravi

  2. Thurber Engineering Ltd., Vancouver, BC, Canada

    Mehdi Amini

Authors
  1. Hadi Haghgouei
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  2. Ali Reza Kargar
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  3. Mohammad Hossein Khosravi
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  4. Mehdi Amini
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by HH, MHK, ARK and MA. The first draft of the manuscript was written by HH and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Mohammad Hossein Khosravi.

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Conflict of interest

The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript.

Appendix

Appendix

$$g_{1} = \frac{{ - \sin \left( {\alpha - \theta } \right)\cos \,h\left( {\alpha + \theta } \right)y + \sin \left( {\alpha + \theta } \right)\cos \,h\left( {\alpha - \theta } \right)y}}{{\left( {y\sin 2\alpha - \sin \,h\left( {2\alpha y} \right)} \right)}}$$
$$g_{2} = \frac{{\sin \left( {\alpha + \theta } \right)\cos \,h\left( {\alpha - \theta } \right)y + \sin \left( {\alpha - \theta } \right)\cos \,h\left( {\alpha + \theta } \right)y}}{{\left( {y\sin 2\alpha + \sin \,h\left( {2\alpha y} \right)} \right)}}$$
$$g_{3} = \frac{{ - \cos \left( {\alpha - \theta } \right)\sin \,h\left( {\alpha + \theta } \right)y + \cos \left( {\alpha + \theta } \right)\sin \,h\left( {\alpha - \theta } \right)y}}{{\left( {y\sin 2\alpha - \sin \,h\left( {2\alpha y} \right)} \right)}}$$
$$g_{4} = \frac{{\cos \left( {\alpha + \theta } \right)\sin \,h\left( {\alpha - \theta } \right)y + \cos \left( {\alpha - \theta } \right)\sin \,h\left( {\alpha + \theta } \right)y}}{{\left( {y\sin 2\alpha + \sin \,h\left( {2\alpha y} \right)} \right)}}$$
$$g_{5} = \frac{{ - \sin \left( {\alpha - \theta } \right)\cosh \left( {\alpha + \theta } \right)y + \sin \left( {\alpha + \theta } \right)\cosh \left( {\alpha - \theta } \right)y}}{{\left( {y\sin 2\alpha - \sinh \left( {2\alpha y} \right)} \right)}}$$
$$g_{6} = \frac{{\sin \left( {\alpha + \theta } \right)\cos \,h\left( {\alpha - \theta } \right)y + \sin \left( {\alpha - \theta } \right)\cos \,h\left( {\alpha + \theta } \right)y}}{{\left( {y\sin 2\alpha + \sin \,h\left( {2\alpha y} \right)} \right)}}$$
$$g_{7} = \frac{{\sin \left( {\alpha - \theta } \right)\sin \,h\left( {\alpha + \theta } \right)y + \sin \left( {\alpha + \theta } \right)\sin \,h\left( {\alpha - \theta } \right)y}}{{y\sin \left( {2\alpha } \right) - \sin \,h\left( {2\alpha y} \right)}}$$
$$g_{8} = \frac{{\sin \left( {\alpha - \theta } \right)\sinh \left( {\alpha + \theta } \right)y - \sin \left( {\alpha + \theta } \right)\sinh \left( {\alpha - \theta } \right)y}}{{y\sin \left( {2\alpha } \right) + \sinh \left( {2\alpha y} \right)}}$$
$${\text{Residue}} = \left[ {\frac{\pi \sin \,\alpha \cos \theta }{{\sin \,2\alpha - 2\alpha }} + \frac{\pi \sin \,\alpha \cos \theta }{{\sin \,2\alpha + 2\alpha }}} \right]$$

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Haghgouei, H., Kargar, A.R., Khosravi, M.H. et al. Semi-Analytical Approach for Estimating the Viscoelastic Settlement of a Footing Resting on a Slope. Iran J Sci Technol Trans Civ Eng 46, 4557–4564 (2022). https://doi.org/10.1007/s40996-022-00860-7

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