## 1 Introduction  
In recent years, pre-stressed concrete structures have been widely used in large bridge structures due to their significant technical and economic advantages. They are particularly favored by the engineering community for post-tensioned, pre-stressed concrete bridges due to their high strength, large span, lightweight structure, and strong crack resistance. During the production process of pre-stressed beams, pipeline grouting can not only isolate the pre-stressed steel bars from the air, making them less prone to rusting, but it can also generate a good bonding force with the pre-stressed steel bars. By transmitting the load force of the structure through the slurry, the overall integrity of the structure improves, thereby improving the crack resistance and bearing capacity of the components. Poor-quality grouting in pre-stressed pipelines can lead to the corrosion of steel strands, which has a significant impact on the safe bearing capacity and service life of pre-stressed structures and, subsequently, leads to safety accidents, such as bridge collapse. Therefore, conducting research on the detection and evaluation of grouting quality in pre-stressed pipelines has great engineering application value. Damage detection, such as through drilling and slicing, not only causes damage to the pre-stressed steel bars inside the pipelines but also has high costs and low efficiency. Non-destructive testing technology has become a key research direction for pipeline grouting quality inspection due to its advantages, such as its non-destructive nature, compatibility, and dynamism [1]. In terms of non-destructive testing technology research, [PERSON] et al. [2] used the travel time information of ultrasound to invert the internal velocity of concrete specimens and detect voids in pre-stressed pipes. [PERSON] et al. [3] used ground-penetrating radar to detect a reinforced concrete slab containing plastic corrugated pipes, and the results showed that the ground-penetrating radar method could successfully detect defects. [PERSON] and [PERSON] [4] conducted testing and research on a full-scale prefabricated U-shaped beam, a solid bridge, large-sized concrete slabs, and five concrete slabs. The results showed that the impact-echo scanning results were consistent with the actual defects, and they further showed that the most significant indication of the existence of voids was a decrease in thickness frequency or an increase in back-calculated thickness values. [PERSON] et al. [5] used the magnetic induction heating method to heat concrete specimens and identify areas without grouting. [PERSON] [6] pointed out that X-ray imaging is effective for detecting the degree of grouting voids and anchor cable corrosion in pre-stressed beams. [PERSON] et al. [7] used the SIBIE (stack imaging of spectral amplitude based on impact-echo) method to detect the grouting status of pipelines in a pre-stressed concrete slab and surface cracks in the peeling area of the concrete pier surface, and the results verified the applicability of the SIBIE method. [PERSON] et al. [8] conducted experimental studies on two types of pipeline specimens, metal and plastic, using ultrasonic velocity tomography. The results showed that ultrasonic velocity tomography can identify different degrees of grouting defects in pre-stressed pipelines. [PERSON] [9] established a three-dimensional finite element model using ANSYS/LS-DYNA and analyzed the influence of various parameters, such as the bellows type, hole thickness ratio, and wall thickness ratio, on the thickness frequency at the fully empty channel. [PERSON] [10] used ABAQUS 2020 version software to conduct numerical simulation research on the propagation of chirp signals in pre-stressed pipelines with different grouting degrees. [PERSON] et al. [11] used Gamma Ray Tomography (GRT) to validate experimental pipelines with steel strands and grouting voids, unhydrated grouting, and excess water.