Sometimes what is not mentioned in the Hebrew text is just as important as what is mentioned.
The home of Rahab the harlot was collocated in the wall of Jericho (Josh 2:15), and her home also opened to the top of the city wall, where she had hid the spies (Josh 2:8). The spies commanded her to stay in her home when the conquest of the city was to occur (Josh 2:19). In other words, she and her household survived notwithstanding that Rahab's residence was built inside the wall. The text does not mention that she or her family suffered from the collapse or implosion of the wall. What is mentioned is that the fatalities in the city that ensued were by the swords of the Israelites (Josh 6:21), and therefore not from collapsing walls. In other words, the wall collapsed so as to allow entrée to the Israelites, who, in turn, killed the inhabitants, plundered, and then burned the city. Thus the complete destruction of the city wall is not mentioned, but instead the complete destruction of the city itself (through subsequent plunder, killing of the people, and burning). The curse by Joshua against the city was not against anyone who rebuilt the city wall, but on anyone who refortified the city and rebuilt its gates (Josh 6:26). Please notice that the reconstruction of the city walls of the city is not mentioned in the curse of Joshua. The city was subsequently refortified some 500 years later with the reconstruction of the city gates (1 Kings 16:34); please note that the rebuilding of the city walls is not mentioned in this latter passage of 1 Kings 16:34.
In other words, what is not mentioned in the text is that the walls had been destroyed in toto. Rahab and her family escaped unscathed notwithstanding that they were hidden inside the city wall. The Hebrew text in Joshua 6:20 also mentions the adverb נֶגֶד, which means what is "straight ahead" or opposite you. After the collapse of the wall, the Israelites proceeded "straight ahead" to the part of the wall in front of them that collapsed. (The curse of Joshua suggests that this was the part of the wall where the city gates were located.) Thus the adverbial implication is that wall "in front of their face" collapsed. So what is not mentioned is that the entire wall circling the city had collapsed, but instead what collapsed was that portion of the wall "straight ahead" of them that had allowed entrée to the Israelites to kill, plunder, and then to burn the city. (People dying from collapsing walls is not mentioned.) Thus what Joshua had cursed was not the rebuilding of the city walls, but the refortifying (verb) and reestablishment (verb) of the city and its gates.
Finally, as an aside to answer the question of the original posting, an earthquake is not mentioned in the text.