@article{(Open Science Index):https://publications.waset.org/pdf/11907,
	  title     = {Using Non-Linear Programming Techniques in Determination of the Most Probable Slip Surface in 3D Slopes},
	  author    = {M. M. Toufigh and  A. R. Ahangarasr and  A. Ouria},
	  country	= {},
	  institution	= {},
	  abstract     = {Among many different methods that are used for
optimizing different engineering problems mathematical (numerical)
optimization techniques are very important because they can easily
be used and are consistent with most of engineering problems. Many
studies and researches are done on stability analysis of three
dimensional (3D) slopes and the relating probable slip surfaces and
determination of factors of safety, but in most of them force
equilibrium equations, as in simplified 2D methods, are considered
only in two directions. In other words for decreasing mathematical
calculations and also for simplifying purposes the force equilibrium
equation in 3rd direction is omitted. This point is considered in just a
few numbers of previous studies and most of them have only given a
factor of safety and they haven-t made enough effort to find the most
probable slip surface. In this study shapes of the slip surfaces are
modeled, and safety factors are calculated considering the force
equilibrium equations in all three directions, and also the moment
equilibrium equation is satisfied in the slip direction, and using
nonlinear programming techniques the shape of the most probable
slip surface is determined. The model which is used in this study is a
3D model that is composed of three upper surfaces which can cover
all defined and probable slip surfaces. In this research the meshing
process is done in a way that all elements are prismatic with
quadrilateral cross sections, and the safety factor is defined on this
quadrilateral surface in the base of the element which is a part of the
whole slip surface. The method that is used in this study to find the
most probable slip surface is the non-linear programming method in
which the objective function that must get optimized is the factor of
safety that is a function of the soil properties and the coordinates of
the nodes on the probable slip surface. The main reason for using
non-linear programming method in this research is its quick
convergence to the desired responses. The final results show a good
compatibility with the previously used classical and 2D methods and
also show a reasonable convergence speed.},
	    journal   = {International Journal of Civil and Environmental Engineering},
	  volume    = {2},
	  number    = {5},
	  year      = {2008},
	  pages     = {98 - 103},
	  ee        = {https://publications.waset.org/pdf/11907},
	  url   	= {https://publications.waset.org/vol/17},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 17, 2008},
	}