The soldiers' food supply is about to run out.

Literal

Soldier [possessive-の] provisions [subject-が] bottom-hitting is-about-to.

底をつく is an idiom meaning 'to hit bottom' or 'to run out' — used for supplies, funds, or patience. ~かけている adds the nuance 'is on the verge of' or 'has started to,' indicating the process is underway but not yet complete.