I am not sure whether you want us to show you an example of slope failure calculations, or you want to see failure of slope in picture. If you want to know the slope failure calculations, I would recommend you to see the standard introductory soil mechanics books to advanced books, e.g. Shear Strength and Slope Stability by Prof. James Michael Duncan, published recently by John Wiley and Sons, Inc.
If you are a student you can also get a student's evaluation version of GeoSlope software. You may not be able to use it for complex slopes, but you can use it for simple learning purposes. Give a Try.
If you want to see some other problems, e.g. reinforced slopes, then you can also check my own Doctoral Thesis (http://www.finite.info/ ). That is free and you can download print and keep a copy. It has a collection of model test (slope failures) results that we conducted in my sponsor's model testing facility. If you want to see how a reinforced slope fails in centrifuge machine, you can see my paper Pokharel, Fujii, and Miki (2000) published in IS Shikoku.
If you want to extend your knowledge on slope stability around the world, and nice beautiful pictures of world's large (regional) landslides, then you would like to see Sasa's book (Prof. Sasa of Kyoto University). Its excellent book on regional landslides.
Well, Skempton's classic paper on London's landslide is also another example.