  Detection of gravitational waves (GWs) produced by coalescence of compact
binaries provides a novel way to measure the luminosity distance of GW events.
Combining their redshift, they can act as standard sirens to constrain
cosmological parameters. For various GW detector networks in 2nd-generation
(2G), 2.5G and 3G, we comprehensively analyze the method to constrain the
equation-of-state (EOS) of binary neutron-stars (BNSs) and extract their
redshifts through the imprints of tidal effects in GW waveforms. We find for
these events, the observations of electromagnetic counterparts in low-redshift
range $z < 0.1$ are important for constraining the tidal effects. Considering
17 different EOSs of NSs or quark-stars, we find GW observations have strong
capability to determine the EOS. Applying the events as standard sirens, and
considering the constraints of NS's EOS derived from low-redshift observations
as prior, we can constrain the dark-energy EOS parameters $w_0$ and $w_a$. In
3G era, the potential constraints are $\Delta w_0\in (0.0006,0.004)$ and
$\Delta w_a\in(0.004,0.02)$, which are 1-3 orders smaller than those from
traditional methods, including Type Ia supernovas and baryon acoustic
oscillations. The constraints are also 1 order smaller than the method of GW
standard siren by fixing the redshifts through short-hard $\gamma$-ray bursts,
due to more available GW events in this method. Therefore, GW standard sirens,
based on the tidal effect measurement, provide a realizable and much more
powerful tool in cosmology.
