This is not a problem of dakuten in general, but is a problem specific to じ, ぢ, ず and づ. There is a bit complicated history regarding the pronunciations of these four characters, and they even have a special name, yotsugana. English Wikipedia has a dedicated article about this topic.
In short, the standard Japanese accent no longer retains the distinction between the sounds of じ vs ぢ, or ず vs づ. You can pronounce じ and ぢ either like dzi or like ji, and native Japanese speakers using the standard accent cannot even hear the difference. Please see this answer and this question for details.
Even though じ and ぢ share the same pronunciation, sometimes you want to distinguish the spelling of these two characters using Latin alphabet. Some romanization systems including 日本式 distinguish the romaji spelling of じ (
zi) and ぢ (
di). Hepburn system, which tries to approximate the sound as much as possible, does not distinguish the spelling of じ/ぢ (both
ji), or ず/づ (both
zu). If you want to write 地面 using the Hepburn system, it's "jimen".