We focus on structural evolution inside a deforming granular material, in threedimensions, undergoing the so-called diffuse failure, i.e. failure in the absence of strain localization.We uncover and characterize quantitatively the basic building blocks for self-organization,enabling comparisons of the material's rheology to those recently reported for dense materials undergoing localized failure. The building blocks consist of: (i) the quasi-linear, load-bearing force chains, and (ii) their supporting network of contacts, the minimal n-cycles. Our preliminary study shows that, similar to localized failure, self-organization in the system gives rise to major load-bearing, columnar force chains which are supported laterally by truss-like 3-cycles. Under continued loading, the force chains ultimately fail by buckling, precipitating a catastrophic collapse of the material. However, unlike localized failure, the buckling events uncovered here do not appear to be localized.