# A Study on the Vertical Bearing Characteristics of Screw Piles in Permafrost Regions
## 4 Vertical Bearing Capacity Calculation Method  
The vertical bearing capacity of ordinary cast-in-place piles in permafrost regions is often estimated using the Chinese code \"Code for Design of Building Foundation in Permafrost Regions\", and its estimation formula is as follows [22]:  
\[R_{1}=q_{\text{fp1}}A_{\text{P}}+\text{U}_{\text{P1}}\sum_{i=1}^{n}f_{ci}l_{i} +\text{U}_{\text{P2}}\sum_{j=1}^{n}q_{sj}l_{j} \tag{2}\]  
where \(R_{1}\) represents the vertical bearing capacity of a single pile; \(q_{\text{fp1}}\) denotes the bearing capacity of the permafrost layer at the pile's end (kPa); \(A_{\text{P}}\) represents the pile's bottom area; \(U_{\text{P1}}\) indicates the circumference of the outside diameter around the pile;\(f_{ci}\) denotes the freezing strength of layer \(i\) in frozen soil; \(U_{\text{P2}}\) represents the circumference of the inner diameter around the pile; and \(q_{sj}\) denotes the friction force of the soil around the pile in the j layer. When the melting layer is intense, frost-heaving soil or extreme frost-heaving soil  
Figure 12: Comparison of load-settlement curves and equivalent friction resistance of different piles.  
produces a negative friction force around the pile, and the negative value is taken into the calculation, which is generally 10 kPa; \(l_{i}\), \(l_{j}\) indicate the length of each section divided by the soil layer; \(m\) represents the number of layers of permafrost; and \(n\) denotes the number of layers of the seasonal melt layer.  
Due to the mechanical interaction between the pile thread and the soil, the shear strength of the permafrost determines the bearing capacity of the pile foundation, and the shear strength of the frozen soil is greater than the freezing strength of the pile-soil contact surface [8,9]. Therefore, the method used to estimate the vertical bearing capacity of the pile foundation by using the freezing force of the soil and the pile's body in the design code [22] for building a foundation in a frozen soil region is not suitable for the drilled screw pile. Figure 13 depicts the schematic diagram of the calculation method of the code, according to the results of the model test and the numerical analysis; the revised formula is as follows:  
\[R_{2}=q_{\text{fp2}}A_{\text{p}}+\text{U}_{\text{P1}}\sum_{i=1}^{n}\tau_{ci}l_ {i}+\text{U}_{\text{p2}}\sum_{j=1}^{n}q_{sj}2l_{j} \tag{3}\]  
where \(R_{2}\) represents the vertical bearing capacity of a single pile; \(q_{\text{fp2}}\) indicates the bearing capacity of the permafrost layer at the pile's end (kPa); \(\tau_{ci}\) denotes the shear strength of layer \(i\) in frozen soil; \(U_{\text{p2}}\) represents the circumference of the inner diameter around the pile; and \(q_{sj2}\) represents the friction force of the soil around the pile in layer \(j\). When the melting layer is strong, frost-heaving soil or extremely strong frost-heaving soil produces a negative friction force around the pile, and the negative value is taken into the calculation, which is generally 10 kPa.  
Figure 14 indicates the comparison between the ultimate bearing capacity obtained by the model test, the numerical simulation, and the calculated value. The equivalent frictional resistance obtained from the model test presents an uneven distribution. Generally, the lateral resistance calculated by the modified specification is close to the test result. The distribution trend of the simulated friction resistance is obvious. The equivalent friction resistance of the top and bottom sides of the thread is much greater than the calculated value according to the revised code. The calculated value of the middle section is consistent with the revised code, indicating that the calculated result of the revised code is safe and  
Figure 13: A schematic diagram of the calculation method of the code.  
is suitable for estimating the vertical bearing capacity of drilled, cast-in-place piles in permafrost regions.