## 1 Introduction
3D printing techniques have developed rapidly and been introduced to the field of civil engineering structures. Rapid development of the technique in the construction field depends on the development of high-performance cementitious materials compatible with 3D printers [18]. Some studies have shown that the addition of fibers in the preparation of 3D printing cementitious materials can improve structural performance [19]. [PERSON] et al. found that when fibers were aligned along the printing path, the flexural strength of the printed structure in the designated direction increases significantly [20]. [PERSON] et al. reported that when the glass fiber content was 1%, the flexural and tensile strength of the printed specimens improved significantly and in an obvious directional dependency, but there was little effect on compressive strength [21]. [PERSON] et al. demonstrated that a cementitious composite containing 0.5% basalt fibers had favorable printability and mechanical properties, and the 3D-printed samples performed obviously mechanical anisotropy [22]. The research on the anisotropic mechanics of 3D-printed fiber-reinforced materials is not adequately comprehensive. Therefore, more experiments should be carried out to promote the practical application of 3D printing techniques in the field of construction. The structure of composites includes two characteristic scales: macroscopic and microscopic. The macroscopic mechanical behavior of composites is affected by the volume fraction, shape and distribution of the components. Researchers have proposed many mathematical techniques to solve this interaction problem. The common methods include the Self-Consistent Method [23], Generalized Self-Consistent Method [24], Mori-Tanaka Method [25], Asymptotic Homogenization Method [26],and so on. The Asymptotic Homogenization Theory has developed into the main method to solve the equivalent mechanical properties of composite materials in recent years. By establishing the asymptotic displacement field that depends on the change of two-scale coordinate variables, the governing equation reflecting the microstructure is derived, and the average material properties are obtained [27]. The pore structure of concrete is an important aspect of its microstructure, which directly affects mechanical properties, frost resistance, and other macroscopic properties of concrete. Because of the increasing complexity of high-performance concrete, conventional parameters cannot effectively describe the complexity of the pore structure quantitatively, which hinders the study of the relationship between the pore structure and the macroscopic properties of concrete [28]. Fractal theory, as a new approach for describing the complexity and irregularity of matter, has been introduced and gradually applied to the study of pore structure, wherein it quantifies the complexity of the micropore structure as a fractal dimension. The relationship between the microstructure and macroscopic properties of concrete can be studied by utilizing the fractal dimension. In recent years, with advances in research, fractal models of multiple pore structures based on various pore structure characterization methods have been established, and the relationship between fractal dimension and macroscopic performance has been discussed [29; 30; 31]. [PERSON] et al. established a model of the relationship between the fractal dimension and compressive strength. Their results revealed that the fractal dimension could well-characterize the relationship between the micropore structure and the macroscopic mechanical properties [30]. [PERSON] et al. revealed that the fractal dimension obtained by a thermodynamics method could describe the pore size distribution of concrete better than that obtained using the Menger sponge model, and that there was a strong positive correlation between the mechanical properties of concrete and the fractal dimension [31]. [PERSON] et al.