Wall of Jericho left standing, no Myth

It was not until a British archaeologist named Kathleen Kenyon
reexcavated the site with modern methods in the 1950s that it was
understood what these piles of bricks were. She determined that they
were from the city wall which had collapsed when the city was destroyed!
  
Cross-section of the fallen bricks from the wall of Jericho. [Enlarge]
The story in the Bible goes on to say that when the walls collapsed, the
Israelites stormed the city and set it on fire. Archaeologists found
evidence for a massive destruction by fire just as the Bible relates.
Kenyon wrote in her excavation report, 
“The destruction was complete. Walls and floors were blackened
or reddened by fire, and every room was filled with fallen bricks,
timbers, and household utensils; in most rooms the fallen debris was
heavily burnt.”
What caused the strong walls of Jericho to collapse? The most likely
explanation is an earthquake. But the nature of the earthquake was
unusual. It struck in such a way as to allow a portion of the city wall
on the north side of the site to remain standing, while everywhere else
the wall fell.
 
The spies leave Rahab's Jericho wall house.
Rahab's house was evidently located on the north side of the city. She
was the Canaanite prostitute who hid the Israelite spies who came to
reconnoiter the city. The Bible states that her house was built against
the city wall. Before returning to the Israelite camp, the spies told
Rahab to bring her family into her house and they would be saved.
According to the Bible, Rahab's house was miraculously spared while the
rest of the city wall fell.
This is exactly what archaeologists found. The preserved city wall on
the north side of the city had houses built against it.
The timing of the earthquake and the manner in which it selectively took
down the city wall suggests something other than a natural calamity. A
Divine Force was at work. In the New Testament, we read, 
“By faith the walls of Jericho fell, after the people had
marched around them for seven days. By faith the prostitute Rahab,
because she welcomed the spies, was not killed with those who were
disobedient” (Hebrews 11:30-31).
More recent excavations
In the spring of 1997, two Italian archaeologists conducted a limited
excavation on the ancient tell of Jericho. Lorenzo Nigro and Nicolo
Marchetti, working under the auspices of the new Palestinian Department
of Archaeology, excavated for one month on the fringes of Kathleen
Kenyon's west and south trenches. Their dig was the first foreign
expedition in the Palestinian-controlled areas of the West Bank since
self-rule began in 1994.