Two – Dimensional Mathematical Model to Study Erosion Problem of Tigris River Banks at Nu’maniyah
Authors: AL-Thamiry Hayder AbdulAmeer. K. , AbdulAzeez Taymaa Maziad 
Published: July 2023

The high and low water levels in Tigris River threaten the banks of the river. The study area is located on the main stream of Tigris River at Nu’maniyah City and the length of the considered reach is 5.4 km, especially the region from 400 m upstream Nu’maniyah Bridge and downstream of the bridge up to 1250 mwhich increased the risk ofthe problemthat itheading towardsthe streetand causingdanger tonearbyareas.
The aim of this research is to identify the reason of slope collapse and find proper treatments for erosion problem in the river banks with the least cost. The modeling approach consisted of several steps, the first of which is by using “mini” JET (Jet Erosion Test) device provides a simple method of measuring scour depth with the time for the riverbank and finding values of critical shear stress and erodibility factor for ten soil samples taken from right bank and bottom of Tigris River; the second of which involved setting up a static BSTEM software for two models (with and without treatment), then calculating the erosion amounts and factor of safety for the ten soil samples; the third approach involved implementing a two dimensional RMA2 to simulate four scenarios to find the velocity, water depth, and water surface elevation distributions for two models (with and without treatment). Therefore, observed erosion in other discharges in natural case near the right bank [especially at cross section that are located in Tigris River at Nu’maniyah City from 500 m upstream Nu’maniyah Bridge and cross section that are located from 1800 m downstream Nu’maniyah Bridge] is high because of high erodibility coefficient in those cross sections that causes high erosion. Also, failure occurs in natural case of Tigris River at Nu’maniyah City because of erosion near the right bank and does not occur because of slope stability failure for right bank where the range of the velocities near the right bank for the study area for most discharges is between 0.67 and 0.91 m/s. In addition to experimental work using "mini" JET device shows high erodibility coefficient in those cross sections and (2+900) which confirms that this device is very good indicator for the possibility of bank scour. The velocities upstream of the island and near the right bank in the study area are between 0.64 and 1.47 m/s, while downstream of the island is between 0.64 and 1.04 m/s. In addition to soil of Tigris River right bank at Nu’maniyah is silty soil, the scour velocity is higher than 0.5 m/s, therefore the right bank is safe against scour only when the discharges of Tigris River are less than 500 m3/s. Thus, vegetation is unsafe treatment on right bank of Tigris River at Nu’maniyah City. The velocity causes removal of plants since treatment for river bank is 0.61 m/s where velocities near bank at most discharges are higher than this limit. Thus, treatment by riprap is the proper choice on the right bank of Tigris River at Nu’maniyah City because its cost with maintenance is 2 billion IQD less than gabion treatment in addition to velocity reduction ratio along the right bank by riprap ranges from 15% to 85%, while velocity reduction ratio along the right bank by gabion ranges from 8% to 25%, respectively.