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Ibbi-Sin, son of Shu-Sin, was king of Sumer and Akkad and last king of the Ur III dynasty, and reigned c. 1963 BC-1940 BC (Short chronology). During his reign, the Sumerian empire was attacked repeatedly by Amorites. As faith in Ibbi-Sin's leadership failed, Elam declared its independence and began to raid as well.
Ibbi-Sin ordered fortifications built at the important cities of Ur and Nippur, but these efforts were not enough to stop the raids or keep the empire unified. Cities throughout Ibbi-Sin's empire fell away from a king who could not protect them, notably Isin under the Amorite ruler Ishbi-Erra. Ibbi-Sin was, by the end of his kingship, left with only the city of Ur. In 1940 BC, the Elamites, along with "tribesmen" from the region of Shimashki in the Zagros Mountains" (Stiebing 79) sacked Ur and took Ibbi-Sin captive; he was taken to the city of Elam where he was imprisoned and, at an unknown date, died.
The success of the Amorite invasion
The Amorites were considered a backward people by Mesopotamian standards; Ibbi-Sin's 17th year was officially named "Year the Amorites, the powerful south wind who, from the remote past, have not known cities, submitted to Ibbi-Sin the king of Ur." However, despite his father Shu-Sin having built a "wall of Martu" across Mesopotamia against Amorite incursions, these were penetrated early in Ibbi-Sin's reign.
Scholars have suggested that, by the reign of Ibbi-Sin, the empire was already in decline due to long-term drought—in fact, the same drought that helped to take down the Akkadian Empire c. 2193 BC may have been responsible for the fall of Ur III.
Studies of Persian Gulf sediments indicate that the stream flow of the Tigris and Euphrates was very low around 2100-2000 B.C.E. [...] Any damage to the agricultural system by enemy raids, bureaucratic mismanagement, or an inattentive ruler would result in food shortages
In years seven and eight of Ibbi-Sin's kingship, the price of grain increased to 60 times the norm. From this, we can conclude that the success of the Amorites in disrupting the Ur III empire is, at least in part, a product of attacks on the agricultural and irrigation systems; these attacks brought famine and caused an economic collapse in the empire, paving the way for the Elamites under Kindattu to strike into Ur and capture the king.