# The Construction of Equivalent Particle Element Models for Conditioned Sandy Pebble
## 5 Calibration of Model Parameters
### Calibration Process
#### 5.3.3 Strength Required Parameter Set  
DE simulations of triaxial shear test are carried out successively with previously found parameter sets adopted, and the one with result closest to the experimental result is regarded as desired parameter set. Since the calculated static earth pressure at tunnel face ranges from 66.39 kPa to 92.98 kPa, and measured soil pressure at the bulkhead fluctuates between 30 kPa and 80 kPa, the soil inside shield chamber works in a low-pressure state. Therefore, the parameter sets are evaluated by the stress-strain curve measured under confining pressure of 0.4 MPa. Figure 18 presents the established discrete element models for the simulation of triaxial test. In the simulation, the confining pressure is realized by exerting body force on peripheral particles via developing custom plugin programmed in C++; the body force equals to the product of confining pressure and contact area between particle and boundary. According to [PERSON] (2017), the contact radius of particle and geometry can be approximately taken as particle radius. In the single sphere case, the 22 test specimens fall into three groups according to simulation result. The first group involves the 12 th, 14 th, 19 th, 20 th, 21 st, and 22 nd specimens. As for the six specimens, the measured stresses constantly remain zero except for the beginning of loading. This is  
Figure 17: Comparison of fitted values and numerically calculated values: (**a**) sphere model; and (**b**) cluster model. Figure 18: Discrete element models for triaxial test. because their surface energy is too low. With weak cohesive force between particles, the soil specimens have insufficient strength and self-stability. Therefore collapse occurs under the disturbance of axial load. The evolution of the 12 th specimen along with loading can be seen in Figure 19.  
Whereas, the second group consists of the 2 nd, 3 rd, 4 th, 6 th, 9 th, 11 th, 15 th, 16 th, and 18 th specimens. Compared with the first group, the nine soil specimens have developed some intensity because of the improved cohesive force between particles. Their stress-strain curves measured under the confining pressure of 0.4 MPa are shown in Figure 20. It can be seen that both the shape and value of the curves deviate greatly from the result of laboratory test (see Figure 4). Figure 21 records the evolution of the 2 nd specimen during shear process. Obviously, the soil specimen expands continuously, leading to an ongoing reduce in interlocking induced shear resistance. Once the cohesive force and friction force are not enough to resist external force, local damage begins to occur on the specimen. Along with loading, the damage area gradually gets larger and only a part of soil specimen works in the end. Figure 19: The evolution of the 12 th specimen as loading. Figure 20: The stress–strain curve of specimens in the second group. The third group, including the 1 st, 5 th, 7 th, 8 th, 10 th, 13 th, and 17 th specimens, behaves similarly with the actual soil in laboratory. The stress-strain curves of the seven specimens (see Figure 22) generally experience three stages, namely initial stage, strain hardening stage and strain softening stage (or constant strain stage). At the beginning of the second stage, the deviatoric stress rises rapidly because the closely packed particles must overcome a strong interlocking resistance for shear dislocation, but the duration is short before shear dilation occurs. When the volume of specimen increases, the soil becomes loose, resulting in weakened interlocking effect between particles and thus a reduction in growth speed of stress. Then a peak, namely peak strength, can be seen in the curve with certain expanded specimen volume. Along with the increasing shear load, the curve turns into the third stage. In this stage, the specimen keeps expanding, but the shear strength decreases. Finally, the curve fluctuates at residual strength as a result of continuous stress relaxation.