Abstract: Abstract: A safety risk has often posed a great threat to large-span greenhouse structures with the cables in extreme weather, such as snow and wind. It is very necessary to detect the broken wires in the cables of large-span greenhouse structures. However, the environmental magnetic field can dominate the magnetic memory detection for cable damage. In this study, an effective detection was presented for the broken wires using magnetic gradient tensor and magnetic charge surface integral theory, in order to remove the influence of the environmental magnetic field. The magnetic gradient tensor was then combined with the magnetic charge surface integral to derive the calculation formula for the magnetic gradient of cable wires. The characteristic information of cable wires was given before and after the wires broke. The judgment was also proposed for the wire breakage position and number of broken wires. The magnetic test was carried out to verify the evaluation. Theoretical calculation results show that there was a sudden change in the magnetic gradient curve at the wire breakage position when a broken wire occurred in a cable. As such, the baseline was established for the position of wire breakage using the bottom of the trough and the inflection point between the peak and trough of the magnetic gradient curve. Once there were two broken wires in a cable, the areas enclosed by the abrupt changes of magnetic gradient curves were 2.07, 2.89, and 2.13 times those in one broken wire, with an average value of 2.37, according to theoretical calculation. There was no effect of the cable length on the amplitude of mutation in the magnetic gradient curve. The average values of the environmental magnetic gradient's absolute values account for 0.17%, 0.92% and 0.21% of the total magnetic gradient respectively. The influence of the environmental magnetic gradient can be ignored and it can be considered that the measured total magnetic gradient is equal to the cable's own magnetic gradient. The experimental results show that the theoretical and actual wire breakage positions were 496, and 500 mm, respectively, with an error of 0.8%, in terms of the average value of abrupt changes in the magnetic gradient curves. There was a great increase in the areas and peaks/troughs depths that were surrounded by the abrupt changes of magnetic gradient curves, as the number of broken wires increased, according to the superposition effect. In order to verify the repeatability of the experiment, measurement was conducted twice for each wire-breaking condition. As for the first test results, the areas surrounded by the abrupt changes of magnetic gradient curves in the two broken wires were 1.47, 1.78, and 1.34 times those in the one broken, with an average value of 1.53. As for the second test results, the area ratios were 1.48, 1.84, and 1.31, with an average value of 1.54. The very small deviation between the results of the two measurements verified the repeatability and reliability of the monitoring. Anyway, the number of broken wires should be judged by three magnetic gradients in the practical engineering application. This finding can provide a theoretical basis for cable wire breakage monitoring, and effectively eliminate the interference of the environmental magnetic field.