We introduce a general information access evaluation framework that can potentially handle summaries, ranked document lists and even multi-query sessions seamlessly. Our framework first builds a trailtext which represents a concatenation of all the texts read by the user during a search session, and then computes an evaluation metric called U-measure over the trailtext. Instead of discounting the value of a retrieved piece of information based on ranks, U-measure discounts it based on its position within the trailtext. U-measure takes the document length into account just like Time-Biased Gain (TBG), and has the diminishing return property. It is therefore more realistic than rank-based metrics. Furthermore, it is arguably more flexible than TBG, as it is free from the linear traversal assumption (i.e., that the user scans the ranked list from top to bottom), and can handle information access tasks other than ad hoc retrieval. This paper demonstrates the validity and versatility of the U-measure framework. Our main conclusions are: (a) For ad hoc retrieval, U-measure is at least as reliable as TBG in terms of rank correlations with traditional metrics and discriminative power; (b) For diversified search, our diversity versions of U-measure are highly correlated with state-of-the-art diversity metrics; (c) For multi-query sessions, U-measure is highly correlated with Session nDCG; and (d) Unlike rank-based metrics such as DCG, U-measure can quantify the differences between linear and nonlinear traversals in sessions. We argue that our new framework is useful for understanding the user's search behaviour and for comparison across different information access styles (e.g. examining a direct answer vs. examining a ranked list of web pages).