## 2 Materials and Methods
### Laboratory Measurements
#### 2.2.1 Filling Material  
The epoxy resin (Figure 3a) used in this research is a transparent epoxy resin that consists of two components: resin (density: 1.12 g/cm\({}^{3}\); mass fraction: 5/8) and hardener (density: 0.98 g/cm\({}^{3}\); mass fraction: 3/8). The main properties of this epoxy resin are excellent mechanical strength, good chemical resistance, extended workability, excellent environmental moisture resistance and a short catalysis time (6 h for 1 mm sheet at 30 \({}^{\circ}\)C). The low viscosity of this epoxy resin prevents the air bubbles to remain after hardening. It also allows the epoxy resin to penetrate deep into rock cracks and fractures to be uniform after drying [50]. Considering that we used the contacts between the blocks for simulating the fractures in the lab and we aimed at studying a variety of fracture apertures, we did not inject resin in the fractures. Instead, the repair after resin drying was simulated by  
Figure 1: (**a**) Time-triggered GPR data acquisitions on two marble blocks separated with an HDPE layer. (**b**) The processed GPR data. (**c**) A single radar trace extracted from the processed GPR data.  
Figure 2: Time-triggered GPR measurements with the antenna fixed in the center of the marble blocks.  
first preparing the dried resin layers and then putting them in the fractures. This way, we ensure that the same blocks could be used in all measurements, keeping the condition of the blocks unchanged. Figure 3a demonstrates the steps we followed to prepare a couple of resin layers, each with the thickness of 1 mm. After calculating the volume of resin required for a 40 \(\times\) 40 \(\times\) 0.1 cm layer, proper volume percentages of the components A and B were mixed (1). To avoid any irregularities, a completely flat base was prepared and covered with a plastic film to prevent the resin from being attached to this base. The side walls of a 40 \(\times\) 40 cm square were prepared using adhesive silicone (2). The required volume of resin was poured on the prepared base, always keeping the base perfectly horizontal to prevent resin from flowing and being accumulated at a corner (3). Considering the objectives of our study, keeping a uniform thickness at different parts of the resin layer was very important. When the resin layer was dried, it was easily detached from the base (4) thanks to the plastic cover below it. The thickness of the resin layer was measured at different parts to control its uniform thickness. To simulate the repaired fractures with the apertures of 1 mm and 2 mm, one and two epoxy resin sheets were, respectively, placed between the marble blocks. To simulate the repair of larger fracture apertures in an economic way, PVC sheets with the relative permittivity close to the relative permittivity of epoxy resin were used as the filling material (Figure 3b). Another benefit in using PVC material is that, being industrial products, PVC sheets have uniform thickness regardless of how thin they might be. Preparing extremely thin and uniform resin sheets in the laboratory, on the other hand, is very difficult, if not impossible.  
According to the information available about the properties of various epoxy resins and PVC material, the relative permittivity of epoxy resin is usually expected to be in the range 3.5-4.7 while the permittivity of PVC is in the range 3-3.3 [51; 52; 53]. Thus, the two materials are roughly similar and we expect similar responses to GPR surveys. Additionally, since the permittivity of PVC is a bit lower than the permittivity of epoxy resin, the amplitude comparison of radar response between the air and PVC is expected to be more challenging than the comparison between the air and resin. As a matter of fact, the higher the permittivity of the filling material, the more easily it can be distinguished from the air. Similarly, to make conservative conclusions in the analytical models, we decided to assume the relative permittivity of 3.5 and 3 for epoxy resin and for PVC, respectively, i.e., the lowest values for these materials.