Concept:
Bridge abutments are rigid retaining structures that support the bridge deck and retain the approach embankment.
Since the abutments are restrained against lateral movement, the lateral earth pressure acting on them is the earth pressure at rest.
\[
\boxed{
K_0=1-\sin\phi
}
\]
where
\[
K_0=\text{Coefficient of earth pressure at rest}.
\]
Step 1: Understand the behavior of bridge abutments.
Unlike retaining walls, bridge abutments do not move sufficiently to develop active earth pressure.
Therefore, the backfill remains in the at-rest condition.
Step 2: Identify the correct earth pressure.
Hence,
\[
\boxed{\text{Bridge abutments are designed for earth pressure at rest}.}
\]
Therefore, the correct option is
\[
\boxed{(B)\;\text{At rest earth pressure}.}
\]