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.
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