A tree is one of the most fundamental structures of networks and has good properties on layouts, while it is weak from a fault-tolerant point of view. Motivated by these points of view, we consider an augmentation problem for a tree to increase fault-tolerance while preserving its good properties on book-embeddings. A k-arbor-connected graph is defined to be a graph which has k spanning trees such that for any two vertices, the k paths between them in the spanning trees are pairwise edge-disjoint and internally vertex-disjoint. A minimally k-arbor-connected graph is a k-arbor-connected graph G such that deleting any edge from G does not preserve k-arbor-connectedness. A k-arbor-connected graph has the abilities to execute fault-tolerant broadcastings and protection routings as a communication network. The pagenumber of a graph is the minimum number of pages required for a book-embedding of the graph. We show that for any tree T of order n and for any k at most the radius of T, by adding new edges to T, a minimally k-arbor-connected graph \(T^*\) with pagenumber k can be obtained in O(kn) time. Since any k-arbor-connected graph cannot be embedded in \(k-1\) pages, \(T^*\) is optimal with respect to not only the number of edges added to T but also the number of pages required for a book-embedding. We also show that the restriction on the upper bound on k can be removed if T is a caterpillar. Besides, we show that for \(k \le 3\) and for any tree T of order at least 2k, a minimally k-arbor-connected graph with pagenumber k which contains T as a subgraph can be obtained in linear time. We moreover extend our result for a tree to a cactus for k greater than half of the maximum length of a cycle in the cactus, and to a unicyclic graph for any k at most the radius of the graph.