  While our current cosmological model places galaxy clusters at the nodes of a
filament network (the cosmic web), we still struggle to detect these filaments
at high redshifts. We perform a weak lensing study for a sample of 16 massive,
medium-high redshift (0.4<z<0.9) galaxy clusters from the DAFT/FADA survey,
that are imaged in at least three optical bands with Subaru/Suprime-Cam or
CFHT/MegaCam. We estimate the cluster masses using an NFW fit to the shear
profile measured in a KSB-like method, adding our contribution to the
calibration of the observable-mass relation required for cluster abundance
cosmological studies. We compute convergence maps and select structures within,
securing their detection with noise re-sampling techniques. Taking advantage of
the large field of view of our data, we study cluster environment, adding
information from galaxy density maps at the cluster redshift and from X-ray
images when available. We find that clusters show a large variety of weak
lensing maps at large scales and that they may all be embedded in filamentary
structures at megaparsec scale. We classify them in three categories according
to the smoothness of their weak lensing contours and to the amount of
substructures: relaxed (~7%), past mergers (~21.5%), recent or present mergers
(~71.5%). The fraction of clusters undergoing merging events observationally
supports the hierarchical scenario of cluster growth, and implies that massive
clusters are strongly evolving at the studied redshifts. Finally, we report the
detection of unusually elongated structures in CLJ0152, MACSJ0454, MACSJ0717,
A851, BMW1226, MACSJ1621, and MS1621.
