## 1 Introduction  
Natural marble is one typical construction material with a long history. Due to its unique color, natural texture, sense of beauty, and grandeur effect, polished marble tile is widely used as decoration material in construction projects, such as floors, walls, columns, and stairs [1, 2]. Natural marble tile is generally cut from marble blocks using diamond saw blades or row saws, then undergoes grinding and polishing processes in sequence. Polishing is the essential step to acquire a high-gloss surface during marble tile production [3, 4, 5, 6, 7]. Due to the complex physical composition and material properties of natural marble, the polishing process of natural marble tiles results in inefficiency, poor surface quality, and a cost accounting for more than 40% of the total product cost [8, 9]. Numerous scholars have conducted extensive research on process parameters such as pressure, rotation speed, and the trajectory of abrasive grains during polishing, tailoring their approaches to the specific attributes of different marble types [3, 8, 9, 10, 11, 12, 13]. The findings have significantly contributed to the advancement of the marble polishing industry. However, most research focused on resin-bonded fixed-abrasive tools. These tools often encounter challenges in achieving uniform distribution of fine-grained or ultra-fine-grained abrasives, leading to a heightened issue of abrasive agglomeration. This agglomeration tends to generate deep scratches, which significantly impact the overall quality of the marble surface [14]. To mitigate the issues associated with traditional fixed abrasive tools, researchers have explored various approaches to develop innovative polishing tools [15; 16; 17; 18]. The sol-gel (SG) polishing pad is a semi-consolidated flexible abrasive polishing pad that features efficiency and eco-friendliness, making it a trending polishing tool at present [19]. It surpasses traditional resin polishing tools in its ability to efficiently polish marbles, yielding a high-gloss finish while streamlining processes and reducing costs [14; 18; 20; 21]. However, the heterogeneous nature of marble exhibits uneven hardness distribution on marble surfaces, which poses a challenge to achieving high-gloss marble surfaces during polishing. Using the SG polishing pad, the heterogeneous marbles undergo a trend where surface quality initially improves but then starts to deteriorate as polishing time progresses. This distinctive phenomenon is referred to as the orange peel effect, which distinguishes the marble polishing process from that of other single-crystal hard and brittle materials [5; 9; 22]. At present, the industrial production of marble mainly relies on experienced engineers to perform many tentative tests on a certain type of marble tile and then find a relatively good processing technology for actual production. This method can properly solve the problems encountered in industrial production, and the glossiness effect and economic value of polished marble are improved to a certain extent. However, this is only a qualitative method with strong subjectivity and randomness. When utilizing other types of marbles, it is necessary to repeat the tentative tests, which have low efficiency and high cost. Hence, it becomes imperative to investigate how the uneven hardness distribution of natural heterogeneous marbles affects the surface evolution mechanism during the polishing process and create a robust theoretical model to steer industrial production to enhance the surface quality of marble. Such endeavors not only improve production efficiency but also augment economic value while concurrently reducing production costs [23; 24]. In this research, a variety of marbles were polished using the SG polishing pad. The marble surface hardness and its distribution characteristics for different types of marble were analyzed. The surface glossiness throughout the polishing process was monitored, and the formation mechanism of the orange peel effect on marble surfaces was revealed.