## 6 Conclusions  
In previous models, researchers have conducted a lot of theoretical and experimental studies mainly on the rock-breaking process and rock-breaking force, but there has been less consideration of thermal effects. In this study, the widely used CSM model is chosen as the basic theory, and a new computational theoretical model is established. We consider the disc cutter cutting soft and hard rocks with different strengths combined with the thermal stress expression. The wear under the thermal effect is calculated, and comparative analyses are carried out. The following conclusions are obtained:  
1. The study shows that the type of cutter ring wear is dominated by abrasive wear, with even wear having the highest probability of occurrence, followed by bias wear and ring chipping. There is a negative correlation between the amount of cutter wear and the hardness of the material, and high hardness can prolong the service life. The penetration of the cutter ring in rocks of different strengths reflects different wear levels. 2. High-strength granite has the highest abrasiveness to the steel material of the cutter ring, and the cutter cutting medium-strength rock has less wear, and the full contact friction between the soft rock and the cutter increases the abrasion area and the abrasion amount, which leads to increased wear. An increase in the rock strength makes the rock CAI characteristics and cutter ring wear increase, and this index can reflect the degree of cutter ring wear. 3. In the shield tunnelling process, the wear degree of cutting hard rock is higher, and the proportion of wear types is 71% for abrasive wear and 18% for cutting ring breakage, of which uniform wear occupies 54% of the total wear. When cutting soft and hard composite strata, the proportion of abrasive wear decreases to only about 49%, and the proportion of cutter ring breakage is 41%, indicating that cutting soft rock reduces the condition of abrasive wear. 4. Comparative analyses show that the damage patterns of hard-soft rock cutting are different. In the cutting process of high-strength rock, the cutter ring wear is mainly at the bottom of the radial outer edge, with uniform wear. The area of cutter wear in cutting soft rock is mainly distributed in the area on both sides of the cutter head, which can easily produce the phenomenon of a cutter rim grinding tip. 5. With the same rock strength and considering the temperature effect, the wear depth of cutting hard rock has a power function relationship with the installation radius and is proportional to the shield distance. The predicted value is lower than the actual measured value. 6. The wear prediction model considering the thermal effect is closer to the actual value. Cutting medium-hard rock and hard rock, the maximum radius wear depth reaches 25.8 mm and 34.1 mm, respectively, and the prediction error is 3.7% and 5.1%. The errors remain within reasonable limits. 7. The predicted wear for cutting soft rock increases gradually with the radius, and the loss of wear mass shows a positive correlation with the cutting distance, with a minimum prediction error of 8.4%. It is generally lower than the actual value. X.L., conceptualisation, methodology, investigation, data curation, writing original draft, writing--review and editing and visualisation. Y.C., conceptualisation, methodology, validation, visualisation, resources and supervision. S.L., conceptualisation and methodology. T.M.F.-S., conceptualisation, methodology, validation, visualisation, resources and supervision. All authors have read and agreed to the published version of the manuscript. This research and the APC were funded by the Ministry of Science and Technology of the People's Republic of China (No. G2021013020L), the Natural Science Foundation of Shanghai Municipality (No. 22 WZ2503000), the Natural Science Foundation of Shanghai Municipality (No. 23 ZR1443600), and the China Scholarship Council (No. 202110220005). Not applicable.