# Study of Load Calculation Models for Anti-Sliding Short Piles Using Finite Difference Method
## 5 Discussion
### Numerical Simulation of Anti-Slip Short Piles  
In the realm of numerical simulation for anti-sliding short piles, it is imperative to acknowledge the constraints and obstacles linked to indoor model testing. These tests are vulnerable to uncontrollable variables that may introduce inaccuracies into the outcomes. For instance, displacement sensors, strain gauges, and soil pressure sensors may not offer real-time measurements of the internal forces and displacements of anti-sliding short piles, resulting in discrete outcomes. Therefore, in an effort to enhance the precision of the findings, this paper will utilize ABAQUS numerical simulation software to replicate the observed loading conditions in the experiments. This endeavor seeks to attain precise values for internal forces and displacements, thus providing additional validation for the stress and force models calculated for anti-sliding short piles. In this numerical model, the anti-sliding piles, derived from gypsum casting in the experiments, are treated as elastic materials, whereas the loess slide bed and sliding body are regarded as elastoplastic materials. The constitutive model utilized in this calculation is based on the elastoplastic model, specifically the Mohr-Coulomb model. The numerical simulation model replicates the dimensions of the model test at a 1:1 scale, as illustrated in Figure 19. Particular parameters for the experimental design are delineated in Table 5. Vertical self-weight is applied to the model, and stress equilibrium is upheld through the inclusion of normal constraints on the model's sides, above, below, and in front of the sliding bed. Figure 19: Numerical simulation computational model. Figure 18: Calculation diagram for the weighted average of proportional coefficients in a multilayered foundation. The computational model for numerical simulation comprises three constituents: the sliding bed, sliding body, and anti-sliding piles, as depicted in Figure 20. The model encompasses a total of 15,352 nodes and 13,384 elements, with all elements meshed utilizing the C3D8R formulation. The simulation is segregated into six loading steps, with each step progressively augmenting the load. To ensure the stability of the anti-sliding piles and avert convergence problems, a load of 10 kPa is administered in each step, culminating in a cumulative load of 60 kPa before conclusion. The specifics of the loading steps are outlined in Table 6.  
Based on the parameters outlined in Table 5, the ABAQUS software ([https://www.3 ds.com/products-services/simulia/products/abaqus/](https://www.3 ds.com/products-services/simulia/products/abaqus/), accessed on 8 November 2023) parameters have been set up to create the Mohr-Coulomb computational model. Utilizing this model, simulations have been performed to generate displacement contour plots for both the sliding body and anti-sliding piles, as illustrated in Figure 21. Additionally, an analysis of the internal forces and displacement data for both the anti-sliding piles and the sliding body has been carried out. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Loading Times** & **Earth Stress** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline
1 & found & transmit & transmit & transmit & transmit & transmit & transmit \\
2 & 10 kPa & 10 kPa & 10 kPa & 10 kPa & 10 kPa & 10 kPa \\
3 & & & 10 kPa & 10 kPa & 10 kPa & 10 kPa \\
4 & & & & 10 kPa & 10 kPa & 10 kPa \\
5 & & & & & 10 kPa & 10 kPa & 10 kPa \\
6 & & & & & & 10 kPa & 10 kPa \\
7 & & & & & & 10 kPa \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Loading steps. Figure 20: Main components: (**a**) sliding bed, (**b**) sliding body, (**c**) anti-sliding short piles.