Abstract
Hillslopes can be affected by expansion of infrastructures, roadways, and urbanization. When establishing the bearing capacity of shallow foundations placed on the top of the slopes, slope failure is one of the mechanisms that requires due attention. Unlike man-made slopes with a planar profile, the hillslopes are frequently found in a curved cross section. The current paper studies the global slope stability aspect of a footing-on-slope system using a limit equilibrium-based analytical solution to compute the factor of safety of hillslopes with a combined convex-concave cross section under a strip footing on the top. The convex and concave parts of the profile were represented as circular arcs and assumed to be connected by an inflection point. A geometric parameter namely mid-chord offset (MCO) was used to describe the curvature of circular arcs. Utilizing a log-spiral failure surface, the solution takes footing setback, footing width, and seismic coefficients into account in predicting the factor of safety and critical failure surface. A good agreement in terms of the factor of safety and critical slip surface was observed when comparing the results of the proposed analytical solution with those of finite element. Parametric studies were conducted on a given slope to examine how the stability is influenced by varying footing setback, the MCO of concave and concave segments, and the location of the inflection point. The results also indicate that the allowable load of footing on the top of combined concave-convex slopes can be decreased or increased in comparison to those placed on the planar slopes.
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Data Availability
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.
Abbreviations
- \({\rm B}\) :
-
Footing width
- MCO:
-
Mid-chord offset
- \(\lambda\) :
-
Ratio of height of inflection point to slope height
- c :
-
Cohesion
- \(\phi\) :
-
Internal friction angle
- W :
-
Weight of sliding mass
- k h :
-
Horizontal seismic coefficient
- k v :
-
Vertical seismic coefficient
- i :
-
Inflection point
- Fs :
-
Factor of safety
- S f :
-
Footing setback
- x o1, x o2 :
-
x-Coordinate of the center of convex and concave circular arc
- y o1, y o2 :
-
y-Coordinate of the center of concave and convex circular arc
- \(\beta\) :
-
Inclination of planar equivalent slope
- R 1, R 2 :
-
Radius of circular arc for concave and convex parts
- x p :
-
x-Coordinate of pole of log-spiral
- y p :
-
y-Coordinate of pole of log-spiral
- \(\gamma\) :
-
Total unit weight
- E′:
-
Effective elastic modulus
- \({\nu }{\prime}\) :
-
Effective Poisson’s ratio
- \(Q\) :
-
Footing load
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MRS wrote the relevant computer code. AR analyzed and interpreted the results and was a major contributor in writing the manuscript. All authors read and approved the final manuscript.
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Rajabian, A., Shaghaghian, M.R. Stability of Hillslopes with Compound Convex-Concave Profile Under Vertically Loaded Strip Footings. Transp. Infrastruct. Geotech. (2024). https://doi.org/10.1007/s40515-024-00382-x
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DOI: https://doi.org/10.1007/s40515-024-00382-x