  We investigate the relation between the existence of mass inflation and model
parameters of string-inspired gravity models. In order to cover various models,
we investigate a Brans-Dicke theory that is coupled to a U(1) gauge field. By
tuning a model parameter that decides the coupling between the Brans-Dicke
field and the electromagnetic field, we can make both of models such that the
Brans-Dicke field is biased toward strong or weak coupling directions after
gravitational collapses. We observe that as long as the Brans-Dicke field is
biased toward any (strong or weak) directions, there is no Cauchy horizon and
no mass inflation. Therefore, we conclude that to induce a Cauchy horizon and
mass inflation inside a charged black hole, either there is no bias of the
Brans-Dicke field as well as no Brans-Dicke hair outside the horizon or such a
biased Brans-Dicke field should be well trapped and controlled by a potential.
