A note on secants of Grassmannians

Let G(k,n) be the Grassmannian of k-subspaces in an n- dimensional complex vector space, k 3. Given a projective variety X, its s-secant variety s(X) is defined to be the closure of the union of linear spans of all the s-tuples of independent points lying on X. We classify all defective s(G(k,n)) for s  12.