For the most part, it isn't orthographically represented, because it isn't one of the "commonly recognized" contractions.
There are several kinds of "contractions" in English. Forms like "Don't", "won't", "aren't" are highly lexicalized and behave as single words syntactically. It's not really possible to represent a sentence like "Aren't you coming" without using a "contraction" in writing.
Forms like "I'm", "You've", "He's" are typically analyzed as containing "clitic" realizations of the auxiliary verb, which occur in specific phonological contexts. Although they could be replaced by uncontracted forms (like "I am", "You have", "He is/He has") in writing with no change in meaning, the use of these contractions is an established part of non-formal writing.
In addition to the two preceding classes of contractions, there is just the phenomenon of slurring or eliding sounds in "fast speech". Slurred pronunciations aren't very commonly represented in writing, even in non-formal contexts. "D'you've" is as good a way as any of explicitly representing a pronunciation like [djuv], but the spelling "Do you have" would also implicitly include slurred "contracted" pronunciations like this.
Similarly, even if someone pronounces "going to" as "gonna" or "want to" as "wanna", it is by no means obligatory to indicate the slurred pronunciation in writing. The "contracted" pronunciation is much more common and acceptable than the spelling. In fact, I often see non-native speakers use spellings like "gonna" and "wanna" in contexts where they are inappropriate, such as in questions on this site.