From завали́ти (zavalýty) +‎ -ювати (-juvaty). Compare Russian зава́ливать (zaválivatʹ), Belarusian зава́льваць (zaválʹvacʹ), Czech zavalovat, Polish zawalać.

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зава́лювати • (zaváljuvaty) impf (perfective завали́ти) (transitive)

1. to cover (with thrown or fallen things)
2. to pile (to cover with heaps)
3. to fill, to fill up (with thrown or fallen things)
4. to block, to block up (with thrown or fallen things)
5. (figurative, colloquial) to bury, to inundate, to overload, to snow under, to swamp (to overburden or overwhelm with e.g. work, responsibility)
6. to collapse (to cause to collapse)
7. (figurative, colloquial) to mess up (to botch, bungle; to perform poorly on)
8. (figurative, colloquial) to fail, to flunk (not to pass: exam, test, etc.)

• Shyrokov, V. A., editor (2014), “завалювати”, in Словник української мови: у 20 т. (in Ukrainian), volumes 5 (з – зв'я́нути), Kyiv: Ukrainian Lingua-Information Fund, →ISBN, page 58
• “завалювати”, in Горох – Словозміна (in Ukrainian)

• Bilodid, I. K., editor (1972), “завалювати”, in Словник української мови: в 11 т. (in Ukrainian), volume 3 (З), Kyiv: Naukova Dumka, page 36
• A. Rysin, V. Starko, Yu. Marchenko, O. Telemko, et al. (compilers, 2007–2022), “завалювати”, in Russian-Ukrainian Dictionaries
• A. Rysin, V. Starko, et al. (compilers, 2011–2020), “завалювати”, in English–Ukrainian Dictionaries
• “завалювати”, in Kyiv Dictionary (in English)
• “завалювати”, in Словник.ua (in Ukrainian)