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In ocean engineering, pile sliding often occurs in the driving process of large-diameter pipe piles and will affect the engineering quality, so accurate pile sliding interval is necessary. According to the stress situation of steel pipe pile out of actual engineering, the causes of pile sliding are analysed. Using the static equilibrium equation, the mud depth at which the pipe pile may slip is calculated. The influence of pile siding friction was considered when calculating the second pile sliding, and the pile siding friction is divided into three influential areas. Using integrating method, the work done by pile resistance is calculated. Combined with the working principle and power principle, the energy transformation equation of the pipe pile in the process of sliding is obtained, and the sliding length and interval of the pile are calculated. A comparison between the measured results and the real case calculation was conducted using this new method. The comparison indicated that the total relative errors in pile sliding interval are 8% to 16%, and the new method has high accuracy. The results of the new method are in accord with the measured data, which can provide a reference for predicting the interval of pile sliding in the project.

As a structure providing production and living facilities, the offshore platform integrates drilling, transportation, construction, observation, and navigation. The pile foundation construction usually uses large-diameter and super-long steel pipe piles, and the pipe piles are driven into the seabed soil layer along the pipe by a hydraulic piling hammer. In the process of piling, when steel pipe piles encounter soft soil layers in marine soil layers, pile sliding often occurs due to the decrease of pile end resistance and pile side friction resistance. Slip pile not only affects the quality of pile formation and the bearing capacity of pile foundation, but also makes more errors in the actual penetration of pile and the design elevation of pile foundation.

In recent years, scholars at home and abroad have carried out a series of studies on pile sliding, such as Guo and others [

Firstly, the reasons for the sliding of large-diameter steel pipe piles of the offshore platform are analysed, and then the relationship between the ultimate bearing capacity of the foundation and the pile ends resistance is calculated by considering the influence of sliding piles of the pile side friction resistance of different depths. Then, a new algorithm for the sliding interval of large-diameter steeled pipe piles is established by using the static balance and function principle, and the rationality and reliability of the algorithm are verified through the comparative analysis of engineering examples.

Engineering practice shows that [

When the steel pipe pile has just entered the soil layer on the ocean surface, due to the weak bearing capacity of the soil layer, the pile will freely penetrate into the soil layer to a certain depth without hammering the pile hammer. When the pile enters the hard soil layer, the pile end resistance and side friction resistance become larger, and the steel pipe pile gradually penetrates into the soil under the action of hammering. When the pile enters the soft clay layer, the pile end resistance decreases and the pile side friction resistance is not enough to bear the quality of the pile and the pile hammer. At this time, the pile will penetrate into the soil layer without hammering; i.e., the pile body will slip. When the friction resistance of the pile entering the hard soil layer or the pile side increases to a certain value, the sliding of the pile stops. As the pile continues to penetrate, although the side friction area increases, the side friction of the pile actually decreases due to the remolding of the soil. Therefore, when entering the soft soil layer again, the phenomenon of secondary pile sliding will occur, and Figure

Schematic diagram of pile-run phenomenon.

When the total soil resistance of the pile body meets one of the following conditions, it is possible to slip the pile:

The pile end resistance of large-diameter steel pipe pile in the process of pile sliding can be obtained by calculating the soil resistance of the annular pile end. Due to the different properties of soil layers, noncohesive soil and cohesive soil layers adopt different formulas to calculate pile tip resistance. For noncohesive soil such as sand, the resistance at the pile end is calculated by formula of Berezantzev [_{u} in sandy soil layer is_{u} is the pile end resistance, kPa;_{q} and_{r} are the ultimate bearing capacity coefficients of the foundation, obtained from internal friction angle_{D} is effective overburden pressure at the base level of the pile, kPa;^{3}.

Ultimate bearing capacity coefficient of foundation.

| 0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 |

| ||||||||||

| 0 | 0.51 | 1.20 | 1.80 | 4.0 | 11.0 | 21.8 | 45.4 | 125 | 326 |

| 1.0 | 1.64 | 2.69 | 4.45 | 7.42 | 12.7 | 22.5 | 41.3 | 81.3 | 173.3 |

For cohesive soil such as clay, the annular section at the bottom of the pile provides little bearing capacity for the foundation. According to API specifications, it can be calculated by_{u}=_{r}_{u}. Som and Das [_{r} of 9 is more suitable in viscous soil through experiment and analysis, so the pile end resistance in viscous soil is_{u} is the undrained shear strength, kN/m^{2}.

Through the analysis of pile sliding phenomenon, it can be seen that the soil at the bottom of the pile will undergo shear failure during the process of pile penetration into the soil, the soil will form a remodelled area, and the soil strength will change accordingly [

Dover and Davidson [_{0} is the overburden pressure of the soil layer, kN/m^{2};

The calculation of friction resistance of steel pipe pile in clay layer also needs to reduce the strength of soil. Li [

Change of unit friction resistance.

As shown in Figure

Combined with the above considerations, when the steel pipe pile slips for the first time, the dynamic side friction of the pile can be calculated by the modified API method, and the calculation formula is_{u} is the undrained shear strength, kN/m^{2}. When_{u}≥72kpa, _{u}<72kPa,

For the case of secondary sliding of steel pipe piles, when calculating the dynamic side friction of piles in clay layer, it is necessary to consider the influence of the first sliding of piles on the side friction of piles, and according to the different degree of influence, the interval of pile penetration depth is divided into three influence zones, namely, fully affected area, semi-fully affected area, and no affected areas.

_{d} is the dynamic side friction in clay layer, kN, and f is the static side friction, kN.

_{end}>0.44, the designed depth of pile penetration is small, the design depth of pile driving distance after pile sliding is small, and the influence of subsequent pile driving on soil properties is small; the modified API method can still be used for calculation.② If_{end}<0.44, when the designed depth of mud entry is large, the subsequent piling will have a great impact on the soil properties, and the formula for calculating the dynamic side friction resistance at this time is as follows.

_{u}≥72kPa, _{u}<72kPa,

Based on the analysis of pile sliding mechanism, the calculation process of the existing pile sliding interval algorithm is improved. First, the pile end resistance is obtained by using Berezantzev's formula, and then the friction resistance is calculated by using different reduction factors in different influence areas. In sandy soil, the friction resistance of the pile side is calculated by conventional methods. Based on the dynamic process of pile sliding, a new algorithm of large-diameter steel pipe pile sliding interval is established by using static balance and functional principles.

When the steel pipe pile penetrates into the marine soil layer, the pile will be affected by the hammering force of hydraulic hammer, its own gravity, buoyancy, pile end resistance, and pile side friction. According to dynamic experience, when the hydraulic hammer blows the pipe pile, the power of the pipe pile and the hydraulic hammer is regarded as 1.2 times that of the gravity_{1}_{2} of the pile and the hydraulic hammer [

With the progress of sliding pile, the speed of steel pipe pile will gradually decrease to zero under the action of soil resistance and buoyancy, the kinetic energy of pile will dissipate in overcoming soil resistance and buoyancy to do work, so the energy equation can be listed according to the functional principle, and the length of sliding pile can be calculated. The formula for calculating the work done by the friction force on the pile side during pile sliding is_{mj} is the friction force of layer_{mj} is the friction force of the j-layer soil in the sliding pile interval, kN; z is the sliding distance of each layer of soil in the sliding pile interval, m.

According to the integral calculus method,_{mj} is a piecewise function in the sliding pile interval, so the general formula for calculating the dynamic friction resistance between clay and sand layers in the sliding pile interval is as follows:_{md} is the friction force of the_{ms} is the friction force of layer_{j-1} is the overburden pressure of layer_{j} is the severe degree of sand in layer^{3};_{j} is the overburden pressure of layer

In the process of pipe sliding the work done by the pile end resistance can be obtained by integrating the other columns of Berezantzev’s formula, and the calculation formula is as follows:

The buoyancy_{f} received by the steel pipe pile will gradually increase with the progress of the sliding pile, so the calculation method of the work ^{3}, and g is the gravity acceleration, m/s^{2}.

When hydraulic hammer hammers a steel pipe pile, there will be energy dissipation, usually corrected by using the coefficient, so the energy of the pile and hammer at the beginning of sliding pile is

According to (

According to the engineering data collected during the construction of Liwan pile foundation platform in the South China Sea, reasonable soil parameters are selected, and the new algorithm is used to calculate the pile sliding interval of steel pipe piles. The calculation results are compared and analysed with the actual pile sliding interval, and the rationality of the new algorithm is verified through the comparison results.

The pile foundation platform has 16 steel pipe piles, which are evenly distributed on the four corners of the pile foundation platform. Each steel pipe pile weighs 643.9kg and has a diameter of 2.74m and a pile length of 158m. The model of hydraulic hammer is MHU1200s, and the rated output energy is 1200kJ. In order to ensure the same soil properties around steel pipe piles, four steel pipe piles on one corner of the platform were selected for calculation and analysis. Through the analysis of soil parameters, it can be seen that the soft and hard soil layers of the soil layer, where the steel pipe pile is located, alternate, and the shallow soil layer has a long clay layer, so it is easy to slip the pile. At the soil depths of 58.8m and 108m, the soft clay layer appears again; at this time, it is likely that the secondary slip pile or even the tertiary slip pile will occur. The soil parameters of the soil layer where the steel pipe pile is located are listed in Table

The parameters of soil layers and calculation results of soil parameters.

number | property | thickness/m | cohesion/kPa | friction angle/(°) | unit weight/kN·m^{−3} | floor elevation/m | pile end resistance/kN | dynamic friction resistance/kN | static friction resistance/kN |

| |||||||||

1 | medium dense fine to coarse sand | 2.4 | 0 | 39 | 8.5 | 3.0 | 3291.7 | 39 | / |

2 | soft to hard clay | 7.9 | 35 | 0 | 8.9 | 10.9 | 259.9 | / | 1024.1 |

3 | dense silt | 2.3 | 0 | 37 | 8.9 | 13.2 | 5944 | 112.3 | / |

4 | dense sandy silt and hard clay interbedded | 7.8 | 70 | 0 | 8.6 | 21.0 | 519.8 | / | 1644.2 |

5 | hard silty clay | 3.6 | 50 | 0 | 9.2 | 24.6 | 371.25 | / | 411.9 |

6 | dense silty fine sand | 8.4 | 0 | 39 | 8.5 | 33.0 | 9084.6 | 271.7 | / |

7 | dense silty fine sand | 20.3 | 90 | 0 | 8.3 | 53.3 | 668.3 | / | 5501.6 |

8 | hard silty clay | 6.1 | 80 | 0 | 9.0 | 59.4 | 594 | / | 1447.9 |

9 | hard silty clay | 5.4 | 0 | 36 | 8.6 | 64.8 | 15598.1 | 582.7 | / |

10 | hard clay | 11.4 | 100 | 0 | 8.8 | 76.2 | 742.5 | / | 3389.1 |

11 | dense sandy silt | 3.4 | 0 | 36 | 8.3 | 79.6 | 13963.5 | 717 | / |

12 | hard silty clay | 29.3 | 120 | 0 | 8.5 | 108.9 | 891 | / | 10587.5 |

13 | dense sandy silt | 2.9 | 0 | 36 | 8.5 | 111.8 | 2655.4 | 1394.5 | / |

14 | hard clay | 19.6 | 160 | 0 | 9.0 | 131.4 | 1188 | / | 9443 |

Combined with the soil parameters selected in the actual project, the pile end resistance, sand dynamic side friction resistance, and clay static friction resistance of each layer of soil in the pile driving process of steel pipe piles are calculated using (

According to the calculated pile end resistance and pile side friction of each soil layer in Table

Comparison between theoretical and practical pile-run interval.

From the comparison results, it can be seen that the depth of pile entry and the interval of the first two pile slips are basically consistent with the actual engineering situation. There are some deviations in the calculation of the third pile sliding interval because the second pile sliding also affects the soil mass and changes the pile side friction, but the third pile sliding interval is smaller than the theoretical calculation interval length and within the safe range of pile foundation engineering, so the theoretical pile sliding interval can still provide a reference for the design of pile foundation and also verify the theory that the calculation of the pile sliding interval needs to consider the influence of the pile sliding on the soil mass, so the new algorithm and the traditional method are more consistent with the actual pile sliding interval and have higher accuracy. The pile sliding interval obtained by the new algorithm is basically consistent with the actual pile sliding interval, and the rationality of the new algorithm is verified.

Through the analysis and research on the process of pile sliding and its causes, the conclusions are as follows:

(

(

(

The data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest regarding the publication of this paper.

This study was financially supported by the National Natural Science Foundation of China (no. 41372288) and the Project of Science and Technology Innovation Fund for graduate students of the Shandong University of Science and Technology (no. SDKDYC180212).