  Although tidal dissipation in binary stars has been studied for over a
century, theoretical predictions have yet to match the observed properties of
binary populations. This work quantitatively examines the recent proposal of
tidal circularization by resonance locking, where tidal dissipation arises from
resonances between the star's natural oscillation frequencies and harmonics of
the orbital frequency, and where resonances are `locked' for an extended period
of time due to concurrent stellar evolution. We focus on tidal resonances with
axi-symmetric gravity-modes, and examine binaries with primary masses from one
to two solar masses. We find that orbital evolution via resonance locking
occurs primarily during the star's pre-main-sequence phase, with the
main-sequence phase contributing negligibly. Resonance locking, ignoring
non-linearity, can circularize binaries with peri-centre distances out to $\sim
10$ stellar radii, corresponding to circular periods of $\sim 4-6$ days.
However, we find resonantly excited gravity-modes will become nonlinear in
stellar cores, which prevents them from reaching their full, linear amplitudes.
We estimate that such a `saturated resonance lock' reduces the circularization
period by about a third, but resonance locking remains much more effective than
the cumulative actions of equilibrium tides. In a companion paper, we examine
recent binary data to compare against theory.
