回答
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There was a succession of disasters last year in Japan like the Kumamoto earthquake and factory fires.
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There were disasters after disasters in Japan last year, like the Kumamoto earthquake and factory fires.
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One disaster succeeded another in Japan last year, like the Kumamoto earthquake and factory fires.
「相次ぐ」→「To happen in succession」、「To succeed one another」
「Disaster」→「災害」
「工場火災」→「Factory fire」
「次から次へ」→「One after another」
この3つの文はどれでも使えます。