# Study on Stiffness Parameters of the Hardening Soil Model in Sandy Gravel Stratum
## 2 Large-Scale Experiments of Sandy Gravel
### Triaxial Compression Test  
The Young's moduli of triaxial loading and unloading-reloading used in the HS model are usually determined by a triaxial consolidation drainage test when the confining pressure is 100 kPa. According to the stress-strain curve, the secant stiffness at 50% of the failure load is the reference value of triaxial loading Young's modulus \(E_{50}\). When the unloading-reloading test is carried out during the triaxial test, the reference value of unloading-reloading modulus \(E_{\text{ur}}\) can be determined. The secant modulus is obtained by connecting the upper and lower points of the hysteretic circle, as shown in Figure 2.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Samples**} & \multicolumn{8}{c}{**Particle Size (mm)**} \\ \cline{2-10}  & **60** & **40** & **20** & **10** & **5** & **2** & **1** & **0.5** & **0.25** & **0.075** \\ \hline
1 & 100 & 100 & 59.74 & 32.55 & 24.56 & 20.21 & 16.95 & 13.95 & 3.49 & 0.55 \\
2 & 100 & 100 & 58.45 & 40.17 & 31.64 & 18.77 & 19.31 & 14.33 & 4.12 & 0.84 \\
3 & 100 & 100 & 60.58 & 46.35 & 29.51 & 20.84 & 16.78 & 9.73 & 2.71 & 0.89 \\ Average value & 100 & 100 & 59.59 & 39.69 & 28.57 & 19.94 & 17.68 & 12.67 & 3.44 & 0.76 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Gradation of undisturbed sandy gravel (%).  
Figure 1: Undisturbed sandy gravel gradation curve.  
This study used a large-scale testing machine to carry out the triaxial compression test, with a sample height of 600 mm and diameter of 300 mm. The maximum axial displacement of the testing machine can reach 150 mm, and the maximum axial pressure can be 250 kN, as shown in Figure 3.  
The preparation of the sandy gravel soil sample presented unique challenges, as it differs from silt or cohesive soil in its large particle size, loose composition, sharp edges, and low cohesion. As a result, conventional sample preparation methods could not be utilized. In order to effectively prepare the sample for testing, it was loaded and compacted on the instrument base, as illustrated in Figure 4. The test density was carefully controlled based on the natural density of the soil mass specified in the geological survey report. The sample was then saturated and consolidated, prior to being loaded under a confining pressure of 100 kPa. During the loading process, care was taken to avoid a high shear rate, which could result in the full discharge of pore water. A shear rate of 0.1 mm/min  
Figure 3: Large-scale triaxial compression testing machine.  
Figure 2: Stress–strain curve of \(E_{50}\) and \(E_{ur}\).  
was employed. Upon completion of a loading time of 900 min, the sample had achieved a cylindrical shape with a large middle and small ends.  
The stress-strain relationship is illustrated in Figure 5. Throughout the test, it was observed that the stress increased with increasing axial strain, exhibiting a clear parabolic relationship. A peak value of the stress-strain curve occurred at an axial strain of approximately 4%, suggesting that the specimen had undergone shear failure at this point. Following the peak value, the shear stress started to decrease as the axial strain continued to increase, demonstrating strain softening behavior. The peak strength obtained from the test was 588 kPa and the value of \(E_{50}\), calculated using the aforementioned method, was 409 kPa.  
The consolidated drained shear tests were conducted on the soil sample to determine its internal friction angle and cohesion. The tests were performed with confining pressures of 200 kPa and 300 kPa. At confining pressures of 100 kPa, 200 kPa, and 300 kPa, the  
Figure 4: Triaxial compression test process (**a**) specimen fabrication (**b**) specimen before test (**c**) specimen after test.  
Figure 5: 100 kPa undisturbed stress–strain curve.  
maximum principal stress was recorded as 688 kPa, 1212 kPa, and 1635 kPa, respectively. The calculations indicated that the soil cohesion was 48.1 kPa and the internal friction angle was 36.5\({}^{\circ}\).