## 2 Study Methods and Tests Materials
### Test Materials  
In this study, cyclic triaxial testing was performed on Liugui sandy soil specimens from Kaohsiung, Taiwan. A gradation curve of Liugui coarse aggregates was developed. The applied particle size distribution curve is illustrated in Figure 3. Subsequently, Liugui sand from Kaohsiung, mudstone from Tainan, Taiwan, and kaolinite were added at 15% and 30% by weight to the soils as a replacement for the coarse aggregate. All the experimental results were compiled and analyzed using the mathematical model proposed by [PERSON] et al. [42]. First, a sieve analysis was conducted on the sandy soil specimens retrieved from Liugui District, Kaohsiung. The mudstone was collected from Tainan. According to [PERSON] and [PERSON] [52], mudstone was first discovered in Renwu District, Tainan, which is located in the southernmost region Taiwan. The specimens were all produced with a fixed dry soil unit weight of \(\gamma\)d = 16.58 kN/m\({}^{3}\). The tests conducted are listed as follows: (1) ASTM D422 for grain size distribution curve [53]; ASTM D854 for specific gravity test [53]; ASTM D423, D424, and D4318 for Arterberg limits [53]; ASTM D2487 for the Unified Soil Classification System (USCS); ASTM D2216 for soil moisture content [53]; and ASTM D4253 and ASTM 4254 for maximum and minimum density [53]. Figure 3: Particle size gradation curve of soils with different fine contents. Figure 2: Curves mapped according to different \(\beta\) values based on the model proposed by [PERSON] et al. (1976) [42]. The soil gradation parameters and general physical properties of interest are listed in Table 2. When \(\gamma_{\rm d}\) was 16.58 kN/m\({}^{3}\), the specimens with FCs of 0%, 15%, and 30% had relative densities of 14.7%, 10.2%, and 19.7%, respectively. The appearances of the three types of fines are depicted in Figure 4. The Atterberg limits of the fines and the USCS classification results are presented in Table 3. The kaolinite had the highest PI value (32), followed by the mudstone (12.4) and Liugui sand (5.7). The plasticity data, namely the Atterberg limits, PI values, and liquid limits, are presented in Figure 5. The USCS results of the three fines were all above the A line on the Casagrande plasticity chart. The USCS classifications of Liugui sand, Mudstone fines, and Kaolinite were CL-ML, CL, and CH with respect to the fine contents. A British standard geotechnical digital system (the GDS Enterprise Level Dynamic Triaxial Testing System) was used to perform cyclic triaxial tests on the soil specimens. Loading was repeatedly applied through load control, and the PWPs within the specimens were measured simultaneously during the tests. The tests performed were triaxial consolidated undrained tests. The required amounts of the test soils were determined according to the grain size gradation curves, and the soil specimens were each divided into five groups for mixing. After the base of the triaxial chamber was wiped clean and a porous stone and filter paper were placed on the top of the sample base, the rubber mold used to hold the specimens and the split mold were placed on the base. Two O-rings were used to set the rubber mold, and expansion rings were used to lock the split mold to the outside of the rubber mold. The specimens were reconstituted through wet tamping. The five samples of sandy soils were mixed with water in concentrations of 8-14% according to their distinct properties. The specimens were tamped into five layers. Subsequently, a scraper was used to scrape vertically and horizontally interlaced lines of 0.25 mm in length on the surface of each layer to avoid weak, discontinuous surfaces. After the five layers were tamped, the filter paper and porous stone were placed on the tamped surfaces of the soil specimens, and a piece of transparent acrylic was used to cover the porous stone. Eventually, each specimen was wrapped in the rubber mold and fixed using the two O-rings, and the initial preparation of the specimen was thus completed.