As a former PhD student, now lecturer, it's very rare to hear of one failing a PhD viva. The most common outcome is to grant the PhD subject to minor corrections, which will be checked off by the internal examiner. Occasionally candidates will have to make major corrections for review by the external examiner, and much more rarely, candidates will be told to revise and resubmit where the process may or may not include an additional oral examination. Only the last outcome would be generally regarded as "failure".
In the first instance the student's advisor would not recommend/allow (depending on the institution) the candidate to go forward for a viva unless the work was to the standard required. In many universities, this means publishable in whole or in part, and making a non-trivial novel contribution. One way to satisfy yourself about these criteria is whether you've published anything at all to date: if you have, it answers the question that the thesis is publishable at least in part. It's very hard to "fail" (see above) if these basic criteria are met.
About related approaches, you would probably be expected to have a rationale for choosing your own approach. This would imply that you know your chosen method well, and know enough about the others to be able to make a comparative choice. E.g. if you were working in electromagnetics and chose the Finite Element Method to solve a Partial Differential Equation, you would probably want to be able to point out why you rejected Finite Differences and/or Analytical methods. But I would not expect you to be able to discuss the intricacies of Finite Differences in any great detail. The working knowledge you already have of your own approach and that of others is probably quite sufficient, as long as you can provide a strong justification for why you chose the methods you did. It's quite OK to justify based on ease of use, local availability, expediency etc.