# Study of Load Calculation Models for Anti-Sliding Short Piles Using Finite Difference Method
## 3 Model Experiment
### Experimental Design  
This paper conducts a similarity design for the model test, building on design insights from previous anti-slide pile model tests [39]. The cross-sectional dimensions of the full-scale anti-slide pile in the practical project are 1.0 \(\times\) 1.6 m\({}^{2}\), constructed of concrete. Using similarity theory and the deflection equation for anti-slide piles, the corresponding conditions for the model test are determined as follows:  
\[f=\frac{qL}{8 EI}^{4} \tag{17}\]  
In actual engineering:  
\[fp=\frac{qpLp^{4}}{8 Eplp} \tag{18}\]  
In the model experiment:  
\[fm=\frac{qmLm^{4}}{8 Eml\text{m}} \tag{19}\]  
To establish a comparison between the model pile and the pile used in the practical engineering, the following equation must be met:  
\[Cf=\frac{CqCL}{CECI} \tag{20}\]  
\[Cq=\frac{qp}{qm},CE=\frac{Ep}{Em},CI=\frac{lp}{\text{Im}},CL=\frac{Lp}{Lm},Cf= \frac{fp}{fm} \tag{21}\]  
Following similarity theory, the calculation for reinforcing the short pile used in the test is conducted. The bending moment similarity constant is determined as follows:  
\[C_{m}=\frac{M_{m}}{M_{p}}=\frac{f_{my}A_{ms}h_{m0}}{f_{py}A_{ps}h_{p0}}=\frac{ A_{ms}}{A_{ps}}C_{fy}C_{L} \tag{22}\]  
Reinforcement configuration with equivalent cross-sectional area:  
\[A_{ms}=\frac{A_{ps}f_{py}}{A_{pc}f_{pc}}.\frac{A_{mc}f_{mc}}{f_{my}}=\frac{1}{ C_{L}^{2}}.\frac{f_{mc}f_{py}}{f_{pc}f_{my}}.A_{ps} \tag{23}\]  
Shear force similarity coefficient:  
\[C_{V}=\frac{V_{m}}{V_{p}}=\frac{f_{my}A_{ms}}{f_{py}A_{ps}}=\frac{A_{ms}}{A_{ ps}}\,C_{fy} \tag{24}\]Equivalent cross-sectional area for the tie reinforcement configuration:  
\[A_{svm}=\frac{A_{psv}f_{pyc}h_{p0}}{f_{myv}h_{m0}}C_{v} \tag{25}\]  
In the equation, the variables represent the following: \(A_{ps}\): cross-sectional area of the prototype reinforcement; \(A_{pc}\): design compressive strength of concrete in the prototype structure; \(f_{pyv}\): design tensile strength of steel reinforcement in the prototype structure; \(A_{ms}\): cross-sectional area of the reinforcement in the model structure; \(A_{mc}\): cross-sectional area of gypsum in the model structure; \(f_{mc}\): design compressive strength of gypsum in the model structure; \(f_{my}\): design tensile strength of aluminum bars in the model structure. In this model test, when \(f_{y}=f_{y}{{}^{\prime}}=f_{my}=100\) N/mm\({}^{2}\), \(M=607.61\) N\(\cdot\)m, \(b=50\) mm, \(h_{0}=69\) mm, \(\alpha_{1}=1.0\), \(\zeta_{b}=0.6\),\(f_{c}=f_{mc}=7.3\) N/mm\({}^{2}\) by means of Equation (26):  
\[\alpha_{s}=\frac{M}{\alpha_{1}f_{c}bh_{0}{}^{2}} \tag{26}\]  
\(\alpha_{s}=0.348\), by means of Equation (27):  
\[fp=\frac{qpLp^{4}}{8 Eplp} \tag{18}\]0  
\(\xi=0.4488\), by means of Equation (28):  
\[fp=\frac{qpLp^{4}}{8 Eplp} \tag{18}\]1  
\(\gamma_{s}=0.776\), plug into Equation (29):  
\[fp=\frac{qpLp^{4}}{8 Eplp} \tag{18}\]2  
determined that \(A_{s}=109.43\) mm\({}^{2}\). Following the principles of similarity theory and the deflection equation for anti-slip short piles, we selected five \(\phi 6\) aluminum bars for longitudinal reinforcement in the model test, while maintaining a protective layer thickness of 10 mm. The tie reinforcement comprised two \(\phi 1\) helical wires with a 125 mm spacing. Based on the calculated reinforcement for the anti-slip short pile, we completed the arrangement of the aluminum bar cage. Figure 4 depicts the reinforcement configuration for the anti-slip pile, ensuring compliance with the similarity conditions for the model test. \[fp=\frac{qpLp^{4}}{8 Eplp} \tag{18}\]3 Anti-slip short pile reinforcement diagram. Following the principles of similarity theory and the deflection equation for anti-slip piles, the model test attained similarity conditions with a fundamental geometric similarity ratio \(C_{1}\) = 20 and a fundamental stress similarity ratio \(C_{0}\) = 20.