## 1 Introduction  
Currently, slurry shield tunneling machines are widely utilized to excavate tunnels in complex ground, especially with high water pressures, because of their merits of high safety and efficiency [1]. In regard to slurry shield tunneling, two distinct technologies are involved: the first is hydraulic support using slurry suspension, usually with a controlled pressurized air cushion; the second involves the hydraulic conveyance of the excavated materials through a closed slurry circuit. Slurry transport plays an extremely important role in safe and highly efficient slurry shield tunneling. When slurry shield tunneling in pebble and cobble ground, rock-soil interface mixed ground, and rock ground occurs, rock particles and rock fragments are discharged due to rock chipping in the excavated soils, inevitably causing wear on the slurry discharge pipelines. Over time, the worn pipelines thin out, start leaking, and occasionally even burst. The damaged and worn slurry discharge pipelines, if not properly dealt with, will lead to tunneling machine breakdowns, tunneling delays, and cost overruns. Therefore, a thorough examination of slurry discharge pipeline damage and wear during slurry shield tunneling is of great engineering significance. As more slurry shield tunnels are built and more large rock particles are transported, this demand becomes urgent. and paper production, and other processes. As a result, particle-flow-induced damage and wear in pipelines have been noted and well studied. Theoretical derivation and laboratory testing methods have been widely used in early studies on pipeline wear. [PERSON] [2] found that the hardness parameter values of slurry and pipe materials show a strong correlation with the erosion capability of a slurry, and they suggested future abrasion studies on pipeline slurry erosion. Concerning the powder technology mechanisms of abrasive and erosive wear by hard particles in pipelines, [PERSON] [3] concluded that the dominant mechanism depends not only on the material subjected to wear and the nature of the particles but also, in many cases, on the conditions under which the particles move against the surface. [PERSON] et al. [4] established the effect of velocity, concentration, and particle size on erosion wear using a pot tester and proposed two correlations of the expected erosion wear for two pipe materials. Using a slurry pot tester, [PERSON] et al. [5] studied erosion wear due to the cutting action of solid particles in solid-liquid mixture flows and found that the parametric dependence on velocity is comparatively much stronger than that on either solid concentration or particle size. [PERSON] et al. [6] determined the critical impact velocity in the erosion of metallic materials by solid particle impact using experiments and theoretically derived the critical impact velocity by analyzing the behavior of the material surface impacted by a spherical solid particle. [PERSON] et al. [7] proposed a predictive equation for estimating erosion damage caused by solid particle impact, discussed the impact angle dependence of erosion damage to several materials, and concluded that material hardness should be a dependent variable in terms of impact velocity dependence and impact angle dependence in the equations. [PERSON] and Yoshida [8] concluded that a predictive equation containing both material hardness and the load relaxation ratio could be used to estimate experimental erosion damage data for many types of materials under a variety of impact conditions. [PERSON] et al. [9] investigated numerical models for predicting erosion due to particles in a 90\({}^{\circ}\) elbow pipe in the oil industry and tested four different correlations for the erosion rate, namely, the [PERSON], Neilson & Gilchrist, [PERSON], and [PERSON] models. [PERSON] et al. [10] proposed a semimechanistic model for the erosion of different target materials due to solid particles and found that the angle dependence in the new model changes with the particle shape and velocity. [PERSON] et al.