I need to have a PDF for reliability assessment of wedge failure. since, I should have an equation that identify wedge(a triangle in 2 dimension).
This is an interesting question with a number of possible answers.
In general, a wedge is a higher dimensional analog of an arc. For more about this, see Section 1.2, starting on page 3:
Cornelia O. Yuen, Jet Schemes and Truncated Wedge Schemes:
http://www.math.lsa.umich.edu/~kesmith/YuenThesis.pdf
A great introduction to wedge geometry is given in
http://www.cs.princeton.edu/~pcalamia/thesis/calamia-phd.pdf
See, for example, Section 3.2, starting on page 24 on 3D wedge geometry.
The following article might also be useful (freely downloaded from google search):
Dianqing Li , Chuangbing Zhou, Wenbo Lu, Qinghui Jiang, A system reliability approach for evaluating stability of rock wedgeswith correlated failure modes, Computers and Geotechnics 36 (2009) 1298-1307
Abstract: This paper proposes a system reliability approach for evaluating the stabilities of rock wedges considering multiple correlated failure modes....
1. Introduction: Wedge failures are the most frequently observed rock slope failures, and can occur over a wide range of geological and geometrical conditions. Accordingly, the study of wedge stability is an important component for rock slope engineering. Wedge failures are often governed by the intersection of at least two rock discontinuitysets, which require a solution of forces in three-dimensional space......
Note. There is also the more abstract notion of a Wedg, defined as a subset P of a vector space X over R satisfying: (i) P+P⊂P, (ii) ax∈P for all x∈P and a≥0. For detail, see the following books:
1. G.J.O. Jameson, Topology and normed vector spaces (Chapman and Hall, 1974) (pages 209-211, 365).
2. Charalambos D. Aliprantis, RabeeTourky, Cones and Duality, Graduate Studies in Mathematics, Volume 84, American Mathematical Society.
Chapter 1. Cones 1
§1.1. Wedges and cones
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