## 4 Test Results Analysis
### Analysis of the Results of Lignin Fiber-Improved Soil
#### 4.1.2 Direct Shear Test  
Figure 4 shows the stress-strain relationship curves of the improved soil with different lignin fiber contents under a 400 kPa vertical pressure. As shown in Figure 4, after fibers are added to the soil sample, the shear stress increases with the shear displacement and gradually decreases after reaching its peak. The shear strength of the improved soil for five different dosages is 364.15, 369.75, 386.56, 425.77, and 405.91 kPa, respectively, and the shear strength increase rates range from 20.12% to 40.57%, indicating a significant improvement in shear resistance. Figure 5 presents the fitting curve of the direct shear test for the improved soil with different lignin fiber contents. Under each vertical stress, the shear strength of the fiber-improved soil is greater than that of the untreated soil. The results indicated that the treated sample with a fiber content of 8% had the highest shear strength. This can be attributed to the optimal balance between fiber volume and dispersion within the soil matrix. At this concentration, the fibers are sufficiently abundant to significantly enhance the soil structure by bridging soil particles and providing additional resistance against shear forces. However, they are not so concentrated as to cause significant fiber agglomeration, which can weaken the soil by reducing effective stress transfer and soil particle contact, as previously discussed with reference to the findings from [PERSON] et al. [38] and [PERSON] [37]. This optimal fiber content thus maximizes the reinforcement benefits while minimizing the negative effects of over-concentration, leading to the highest shear strength observed in the samples.  
Table 4 demonstrates that the cohesion (c) and internal friction angle (\(\varphi\)) of the soil improved with lignin fiber initially increase and then decrease as the lignin fiber content increases. At 8% lignin fiber content, the cohesion rose from 166.83 kPa to a maximum value of 210.53 kPa. At 10% lignin fiber content, the cohesion slightly decreased to 204.16 kPa. Similarly, the internal friction angle (\(\varphi\)) increased from 16.12\({}^{\circ}\) to a maximum of 26.00\({}^{\circ}\) at 8% fiber content before decreasing to 24.44\({}^{\circ}\) at 10% fiber content. This phenomenon is attributed to the toughness of the fibers and their ability to absorb stress and energy during shearing. The distribution of fibers in the soil forms an effective network that prevents excessive movement and the failure of soil particles under stress, enhancing the overall shear resistance and improving the cohesive strength of the soil [6; 40]. However, when the fiber content is very high, the fibers cannot be evenly distributed in the soil, leading to the formation of fiber aggregates. This decreases the strength of the soil. The trend in the internal friction angle is similar to that of cohesion. The addition of fibers significantly changed the frictional properties of the fracture surface of the expansive soil. This is mainly due to most fibers on the shear plane not being arranged parallel to the shear direction. This enhances the interlocking between soil particles and fibers, thereby increasing the internal friction angle.