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Training and refreshing a web-scale Question Answering (QA) system for a multi-lingual commercial search engine often requires a huge amount of training examples. One principled idea is to mine implicit relevance feedback from user behavior recorded in search engine logs. All previous works on mining implicit relevance feedback target at relevance of web documents rather than passages. Due to several unique characteristics of QA tasks, the existing user behavior models for web documents cannot be applied to infer passage relevance. In this paper, we make the first study to explore the correlation between user behavior and passage relevance, and propose a novel approach for mining training data for Web QA. We conduct extensive experiments on four test datasets and the results show our approach significantly improves the accuracy of passage ranking without extra human labeled data. In practice, this work has proved effective to substantially reduce the human labeling cost for the QA service in a global commercial search engine, especially for languages with low resources. Our techniques have been deployed in multi-language services.