# A Novel Strutless Double-Row Structure for Deep Excavation: Working Mechanism Study and Analysis
## 2 Model Test and Numerical Model Introduction
### Numerical Simulation  
The finite element software Abaqus 2016 was used to simulate the soil-structure interaction behavior of ARPW, DRPW, and SPW systems. To accurately capture the deformation and stress characteristics of these systems, the soil was modeled using the Drucker-Prager (D-P) model, which is well-suited for simulating soil plasticity due to its smooth yield surface and robust numerical performance. To simulate the plastic behavior of soil, the Drucker-Prager (D-P) model was employed due to its smooth yield surface and robust performance in capturing soil-structure interactions. The D-P model requires two key parameters: \(\alpha\), which governs the slope of the yield surface, and k, which represents the intercept of the yield surface in the principal stress space. These parameters were derived from the Mohr-Coulomb (M-C) model parameters (\(c\): cohesion and \(\phi\): friction angle) using the conversion formulas provided in the Abaqus user manual [34]. The conversion formulas are as follows:  
\[\alpha=\frac{2\sin\phi}{\sqrt{3}(3-\sin\phi)} \tag{3}\]  
Figure 10: Test process (**a**) diagram; (**b**) excavation process. Note: RS represents the length of row spacing. \[k=\frac{6c\cos\phi}{\sqrt{3}(3-\sin\phi)} \tag{4}\]  
where \(\phi\) is the internal friction angle, and \(c\) is the cohesion of the soil, both obtained from laboratory triaxial tests. These parameters were further validated against the literature data [35], ensuring their reliability for the numerical simulations. By converting the M-C parameters to the D-P framework, we ensured that the numerical model accurately reflected the plastic behavior of the soil while leveraging the computational advantages of the D-P model, such as improved numerical stability and convergence. Additionally, a non-associated flow rule was implemented, and the angle of dilation was calibrated based on experimental data to better represent volumetric changes in the soil. The normal behavior between the pile and the soil was modeled as 'hard contact', while the tangential behavior was defined as frictional, with a friction coefficient of 0.24 derived from laboratory triaxial tests and validated against the literature data [36]. The contact interactions were implemented using the penalty method to ensure numerical stability. To ensure the reliability of the numerical model, its outputs were calibrated against experimental results obtained from physical model tests. Key parameters, including the horizontal displacement of the pile top, bending moments, and earth pressures, were compared between the simulation and experimental data. The maximum error for these parameters remained below 9%, demonstrating good agreement. In this study, the soil was discretized using C3D8 elements (3D, 8-node linear brick elements), and a sufficiently fine mesh was employed to minimize volumetric locking effects. It is important to note that the influence of groundwater, including seepage or gushing, was not considered in this study. Future work will explore the impact of groundwater on the excavation process to further enhance the model's applicability. The structural dimensions and model grouping align with the prototype of the physical model test, with detailed information provided in Tables 2-4. The elastic modulus of the polypropylene material used for the model piles was determined to be 1.5 GPa, as measured using a universal testing machine. The crossbeams were modeled using an elastic modulus of 210 GPa, corresponding to the standard value for structural steel. This assumption ensures the rigidity of the crossbeams in transferring forces between the front-row piles and back-row walls. An additional numerical simulation experiment was conducted under an 8D row spacing condition. To minimize the effects of boundary conditions, the model extends 60 m horizontally and 30 m vertically, following the insights of [PERSON] and colleagues [37], who noted that the impact zone of land subsidence from excavation typically extends to about three times the excavation depth.