Hawkins (2013) notes that Kathleen Kenyon found archaeological evidence for a Late Bronze Age settlement at Jericho, and that this settlement eventually came to an end by destruction.

The narratives of Joshua’s conquest are not historical in Prof. Nigro’s opinion. See most notably p204 of The Italian-Palestinian Expedition to Tell es-Sultan, Ancient Jericho (1997–2015): Archaeology and Valorisation of Material and Immaterial Heritage here, where he concludes the section discussing the biblical narrative with:

As a basic premise, one should remember that archaeology rarely succeeds in matching written sources and excavated evidence; only the retrieval of extraordinarily well-stratified inscribed items may allow such a positive correlation (and there are many cases where this has not been enough to achieve a reliable historical reconstruction). In any case, the ruins of Tell es-Sultan include massive collapsed and burnt mudbrick structures. One may imagine that the terrible destructions suffered by the Canaanite city both in the 3rd and 2nd millennium BC had surely become part of the local shared memory, and possibly were narrated as the Jerichoans had been able to overcome them almost every time. There is no way, however, to link them directly to the Bible, except for the fact that the biblical author may have reused one of these stories to validate the historicity of his narration (Liverani 2003, 316–317). The ruins at Tell es-Sultan are far older than the alleged date of Joshua’s conquest. Moreover, if we consider the time when the biblical text was written (the 6th century BC), or that when it was orally transmitted (12–7th centuries BC), as well as the long story of its written transposition, it is clear how hazardous is any attempt to seriously identify something on the ground with biblical personages and their acts (Liverani 2003, 313–321). Nonetheless, the already famous ruins of Jericho were exploited by the biblical author giving them an everlasting fame.

He also notes (p188) that what Garstang, and later Kenyon, interpreted as ashes stemming from Joshua’s conquest in Early Bronze III city walls turned out to be powdered limestone:

In between the two walls, there were blind rooms and walkways, some of them filled with white powdered limestone; the latter was curiously misinterpreted as ashes from Joshua’s destructions by Garstang (1931, pl. I) and Kenyon (1957, 176–177, pl. 37b; 1981, 211, pl. 122).