The beru is an Akkadian unit used in Mesopotamian texts to measure distance. To find the length of the beru, we must first look in the Chicago Assyrian Dictionary (warning: large pdf file), page 208. The Dictionary records a large number of references to this unit of measurement, few of them being specific enough as to allow for the measurement of its length.
In 671 BC, Esarhaddon marched to Aphek at the border of Samaria and further marched 30 beru of land to Raphia (full account here, pg. 142). The distance from Aphek to Raphia is about 72 miles, making the beru to be about 2.4 miles. Some authorities wish Esarhaddon’s Aphek to be that at the border of Megiddo, rather than the border of Samaria, however, the relevant text expressly contradicts this assertion. Secondly, Ashurbanipal records marching for 6 beru from Damascus to Hulhuliti. If Hulhuliti is to be identified with the present Halhaleh, the 6 beru would have to be covered over a distance of 34 miles, making the beru be some 5 2/3 miles in length. Thirdly, a text of Nebuchadnezzar I records that the distance between Der and the Sha’ur was also 30 beru, the journey from Der to the Sha’ur being some 160 miles or more, making the beru be some 5 1/3 miles in length or more. Fourthly, as mentioned in the CAD, on his campaign to Bazu, Esarhaddon mentions he covered four beru in two days, making sure the beru was not a measurement directly varying with the number of days traveled. Thus, the beru was a somewhat inconsistent measurement of distance.
The beru, however, was also a unit of time; the double-hour, as also mentioned in the Chicago Assyrian Dictionary. Due to the significant variations in the length of the beru among Mesopotamian texts, even those only a few decades apart, it makes sense to consider that, as the beru of distance was likely based on the beru of time, the variations between the distances of the various measurements of the beru could be explained on the basis of marching speeds. Esarhaddon, for example, moved very slowly while moving to Raphia, frequently stopping for taking on well-water, while Ashurbanipal apparently wanted a surprise attack against the Arabs temporarily residing at Hulhuliti.
These conflicting data indicate the beru was a unit of distance without a great amount of consistency of measurement to it which was probably based on the unit of time of the same name.
Against Jebel al-Lawz 
The unquoted part of the Esarhaddon text states that the king built fortifications against Baal of Tyre, and that the king departed from “this Egypt” and headed straight for Meluhha (i.e. Thebes). Then it clarifies what “this Egypt” is. The king’s camp was at Aphek in the “land of Samerina” which must be very close to Tyre which at that time was “Egyptian” controlled, being a vassal of Taharqa. The Assyrians marched from this point to the Brook of Egypt using the coastal road. The trip was 30 beru (150 miles / 240 km) but an unspecified amount of days. The problem is the way this text is explained so that Aphek it Tel Afek and Samerina is Samaria. Aphek was the name of more than one toponym and “Samerina” was also an alternate name for Samsimuruna (Jos 11:1; 12:20; 19:15). The beru is a distance of approx. 8 km everywhere else in Assyrian texts and should not change here.
Joshua’s Shimron is in the interior of northern Israel; Samsimuruna was in coastal Lebanon. Different toponyms. It’s very true there were many Apheks on the coastal route. Your comment is very detailed; it’ll take several days to digest.
Is there any Assyrian evidence the Assyrians sometimes called Samsimuruna “Samerina”? If so, that would seriously complicate things.
Joshua’s Shimon is only in the interior of north Israel because Rainey thought so in 1976. Rainey was mistaken. Joshua’s Shimron is an alternate name for his Shimron-meron. Both names are attested in Assyrian texts as Samerina and Samsi-muruna, respectively. All texts that I have been able collect which mention Samerina associate it with Tyre, Sidon, Gubal (Byblos). Esarhaddon’s text could not be more clear that Samerina cannot possibly be the biblical city of Israelite Samaria. For scholars to suggest “beru” is an inconsistent measurement because it is only 72 miles from Tel Afek to Raphia is insane.
The location of Joshua’s Shimron certainly seems to be consistent with its traditional location in Northern Israel. Shimron is mentioned next to Achshaph in Joshua 11:1. The traditional location of Shimron is certainly much closer to Achshaph than Samsimuruna (near Jounieh?) seems to be. Making Shimron Samsimuruna would also make the border of Zebulun in Joshua 19:14-16 incoherent. The territory of Zebulun can’t border the sea, and Hannathon is over 80 miles away from Jounieh. So I cannot agree with your case for this assertion until you provide some further argument.
Shimron appears to have been called ShamÆuna during the Amarna era and one of the Amarna letters appears to be from the traditional Shimron location:
https://www.academia.edu/296813/Inscribed_in_Clay_chapters_14_Shephelah_and_south_coast_15_unidentified_cities_16_conclusion_
Not proof of a connection, but certainly increases the plausibility of the argument for the traditional Shimron location.
There was no traditional location for Joshua’s Shimron until 1976 when Rainey suggested one in Galilee. This is the point. The text of Joshua 11:1 does not suggest the toponyms named are necessarily close to another, simply that these kings were in contact with each other because of a common threat, namely Joshua. Samerina is not just mentioned in the Assyrian royal inscriptions. It is also mentioned in letters of correspondence. One of these situates the city (URU) next to a river. An official in this letter laments that: “The river running past the city of Sameri[na has dried up and] there is only one well in the whole region” (SAAS 1, 225). There has never been a river or even a seasonal watercourse running past the city of Samaria in northern Israel. This letter is from Samerina where there was an Assyrian administrative building for an Assyrian official. There are virtually no archaeological remains in Samaria between Shalmaneser V (the true destroyer of Samaria) and Sanballat of the 5th century BCE (Persian period). This gap in the archaeology is matched by the gap in the biblical record for the same city. Samerina was 30 beru north of the Brook of Egypt. The beru is approximately 9 km (Kitchen uses 10 km). It is impossible to relate these details, i.e. ca. 270 km north of Raphia, next to a seasonal watercourse, and only a single well in the whole region, to anywhere other than Lebanon. Again, the tradition of Shimron in Galilee began in 1976, not before. Shimron and Shimron-meron was one place ruled by one king conquered by Joshua, not two different places and two different kings.
I must contradict your claim as to Samaria. Peter James has cited lots of evidence that Samaria was never destroyed by the Assyrians and there really were plenty of Assyrian remains at the site. I support Na’aman’s interpretation of the conquest of Samaria (which made lots of sense to me when I read it).
Click to access hazor.pdf
Also, how do you reconcile your claim about the location of Assyrian-era Samerina with Menahem being mentioned in the Iran Stele as a Samarian? Different Menahem or different Samerina? And Sargon mentions Samaria closely in parallel with the House of Omri, claiming he plundered the latter. I believe him.
https://books.google.com/books?id=fXqLosxbxNIC&pg=PA27&dq=sargon+samaria&hl=en&sa=X&ved=0ahUKEwirxd35woDKAhUE1CYKHSzZBlEQ6AEIHTAA#v=onepage&q=sargon%20samaria&f=false
https://books.google.com/books?id=vKoUAQAAIAAJ&q=menahem+iran+stele&dq=menahem+iran+stele&hl=en&sa=X&ved=0ahUKEwj_7qDxvYDKAhWG4CYKHVhsA4QQ6AEIWTAM
And there are two wadis by Samaria, one to the North of the hill and one to the South.
I’m not sure it is really appropriate to put the names Peter James and Nadav Na’aman in the same paragraph. The Babylonian Chronicle is an independent witness supporting the biblical testimony that Samaria was destroyed by Shalmaneser V. James is trying to drastically lower the strata in the city to support his 250-year reduction of Egyptian chronology and Bronze Age interconnections. Pseudo-scholarship. The wadis you speak of have been dry since the Neolithic period. I’m talking about the Assyrian period. There has never been a river running past Samaria during the Assyrian period. Parpola knows this so he arbitrarily inserts “had dried up” in the last text I quoted. This is why I put the words in brackets. Minihime of Samerina was still ruling in 729 BCE, proven by the fact that the Iran Stele you mention gives Tiglathpileser III the Babylonian royal title “king of Sumer and Akkad.” The notion he assumed the most politically significant Babylonian title years prior to his conquest of Babylon is an example of scholarly inertia and enthusiasts trying to either prove or disprove the Hebrew Bible. The biblical Menahem was forced to pay the amazing sum of 1000 talents of silver to Pul (the Assyrian birth name of Tiglathpileser III). The Minihime of Samerina paid the normal sum of tribute like all other north Syrian kings did in 738 BCE. Northern Israel only appears in Assyrian texts under the name Bit-Humria. Sargon II imported foreigners to Bit-Humria, but Samaria was already a parking lot before he became king.