Spline Search for Slip Surfaces in 3D Slopes
Publication: International Journal of Geomechanics
Volume 23, Issue 8
Abstract
A novel method involving the transformation of spline surfaces is introduced to search for the critical slip surface in a three-dimensional (3D) slope, which corresponds to the minimum limit equilibrium method factor of safety for overall slope stability. A slipping surface in a slope can be represented as the intersection of any continuous geometrical entity with the slope topography, over which the mass of sliding soil is discretized to solve for the factor of safety satisfying given equilibrium conditions. Traditionally, many researchers have searched for a critical ellipsoidal or spherical surface, or surfaces formed using other simple shapes. However, the critical slip surface in complicated cases, for example, a landslide, is seldom purely ellipsoidal or spherical, which leads to overestimations of the true factor of safety in a slope. To provide greater flexibility for transforming the shape of the slip surfaces during a global search, the geometry representing the slip surface is assumed to be in the form of a nonuniform rational basis spline (NURBS) surface in this paper. The proposed method involves varying the parameters of a parametric exponential function, which spawns control points within its domain to create NURBS surfaces. The parameters in the exponential function are varied to transform the slipping surface using a metaheuristic search algorithm, such as particle swarm optimization. A major advantage of the proposed method is that the final spline surface in the search is formulated such that it can then be locally optimized using surface altering optimization methods by adjusting the locations of its control points.
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Data Availability Statement
Some or all data, models, and codes generated or used during the study are proprietary or confidential in nature and may be provided only with restrictions:
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The numerical examples presented in this paper are available from the corresponding author upon reasonable request.
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As the study is part of the development of a commercial software, the written codes used to obtain the results of the examples cannot be provided. The algorithms provided in the code are sufficient to replicate the proposed method.
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Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 23 • Issue 8 • August 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Sep 30, 2022
Accepted: Mar 5, 2023
Published online: May 18, 2023
Published in print: Aug 1, 2023
Discussion open until: Oct 18, 2023
ASCE Technical Topics:
- Business management
- Design (by type)
- Engineering fundamentals
- Geohazards
- Geomechanics
- Geometrics
- Geotechnical engineering
- Highway and road design
- Landslides
- Mathematical functions
- Mathematics
- Models (by type)
- Optimization models
- Parameters (statistics)
- Practice and Profession
- Public administration
- Public health and safety
- Safety
- Slope stability
- Slopes
- Spline (mathematics)
- Statistics
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