/ / Article

Research Article | Open Access

Volume 2019 |Article ID 2638520 | https://doi.org/10.1155/2019/2638520

Zhijun Zhou, Yaqin Dong, Peijun Jiang, Dandan Han, Tong Liu, "Calculation of Pile Side Friction by Multiparameter Statistical Analysis", Advances in Civil Engineering, vol. 2019, Article ID 2638520, 12 pages, 2019. https://doi.org/10.1155/2019/2638520

# Calculation of Pile Side Friction by Multiparameter Statistical Analysis

Revised13 May 2019
Accepted03 Jun 2019
Published18 Jun 2019

#### Abstract

In this paper, a static load test and a multiparameter statistical analysis method are used to study the value of pile side friction in different soil layers in a loess region. Currently, static load testing is the most commonly used method to determine the bearing capacity of pile foundation. During the test, a vertical load is applied at the top of the pile, the data under each load level are recorded, and a Q-S curve is drawn to obtain the ultimate bearing capacity of a single pile. Reinforcement stress gauges are installed at different sections of the pile body, and then the axial force and the pile side friction of each section are calculated. Few studies have investigated the calculation of pile side friction in different soil layers using the multiparameter statistical analysis method. Obtaining accurate results using this method will provide an important supplement to the calculation of pile side friction and will also be conducive to the development of theoretical calculation of pile side friction. Therefore, taking Wuding Expressway project in loess region as an example, the lateral friction resistance of six test piles is studied through static load testing and multiparameter statistical analysis. The multiparameter statistical analysis method is compared with the static load test results, and the error is controlled within 20%. The results show that the calculation results of multiparameter statistical analysis essentially fulfill engineering requirements.

#### 1. Introduction

Loess sediment covers a large part of the globe, accounting for one-tenth of the land area worldwide. Loess is prevalent in China, with complete strata and heavy thickness, covering an area of approximately 630,000 km2 [1, 2]. Loess is a yellow silt sediment which was mainly transported by wind during the Quaternary period. It is rich in carbonate, with large voids, obvious vertical joints, and generally low groundwater level [3, 4]. With the continuous development of China’s economy, the traffic in loess areas is developing rapidly, along with increased construction of large highways and bridges .

At present, pile foundation is the most commonly used foundation form in highway bridge construction, and it is a durable and effective infrastructure . In the loess region of Shaanxi Province, bored cast-in-place piles are widely used due to their well-developed construction technology and high bearing capacity . Most of the piles are 30–70 m in length and more than 1 m in diameter. Friction piles or end-bearing friction piles are also commonly used. For long piles, the frictional resistance of the pile side accounts for more than 80% of the bearing capacity of piles, and for short piles, the resistance generally accounts for more than 60% . Therefore, the calculation of lateral resistance in loess areas is of great significance to the construction of highway bridges in such areas of China [27, 28].

The multiparameter statistical analysis method collects data from many test piles and establishes the relationship between pile side friction, cohesion, and the internal friction angle of the soil layer [39, 40]. However, few studies have been carried out to calculate pile side friction by the multiparameter statistical analysis method. Therefore, taking Wuding Highway in the Loess Plateau as an example, this paper carries out static load tests on six test piles and measures the size and distribution of pile side friction. The pile side friction in different soil layers is then calculated using the multiparameter statistical analysis method. Finally, the two results are compared. Obtaining a reasonable result using this method will provide an important supplement to the calculation of pile side friction, and it will also be conducive to the development of theoretical calculation of pile side friction.

#### 2. Test Site Engineering

Wuding Expressway is located within Yan’an City and Yulin City in Shaanxi Province, China (Figure 1). It starts from the east of Wuqi County, ends at Shijingzi, Southeast of Dingbian County, and is approximately 922.17 km long. The abutments on both sides are located in the Loess Lianghe subarea, and the topography of the abutment area is relatively small. The elevation of the ground level is between 1629.60 m and 1644.59 m, and the relative elevation difference is approximately 14.99 m. The test site shown in Figure 1 is situated at the separated intersection of Sunkelan Village, Yangjing Town, and Dingbian County. The topographic fluctuation of the test site is small, there is no surface water, the groundwater is very deep, and no groundwater is present in the process of drilling. The strata of the test site consist of the following:(1)Loessial soil (): the soil is brown-yellow, relatively uniform, contains macropore, wormhole, plant rhizome, and a small amount of gravel and hard plastic.(2)Old loess (): the soil is brown and yellow and relatively noncomplex. A small amount of hyphae is present in the soil, accompanied by wormholes, pinholes, some shellfish, and hard plastic.

#### 3. Test Contents

##### 3.1. Indoor Test

Laboratory testing of soils in the test area was mainly comprised of a moisture content test (Figure 2(a)), a compression test (Figure 2(b)), and a direct shear test (Figure 2(c)). The drying method was used in the soil moisture content test, and the soil void ratio was obtained by the compression test. Through analyzing the data from the moisture content and compression tests, the stratum characteristics and the main physical properties of the soil layer in the test area were obtained, as shown in Table 1.

 Soil layer division Depth (m) Layer thickness (m) Density (g/cm3) Water content (%) Void ratio Liquid index Compression coefficient (MPa−1) Loessial soil () 0∼6.5 1.8∼6.5 1.68 16.3 0.883 0.37 0.35 Old loess () 6.5∼50 24∼43.5 1.85 7.9 0.586 0.26 0.12

Cohesion and internal friction angle are important parameters used in this paper. Therefore, 34 groups of samples were tested by the direct shear test, including eight groups of loessial soil samples and 26 groups of old loess samples. In the direct shear test, the upper and lower boxes were aligned, fixed pins were inserted, and the pervious stones and filter paper were placed in the lower boxes. The knife edges of the ring knife with samples were placed upward, the knife back was downward, and the cutting box mouth aligned. The filter paper and the upper pervious stones were then placed, and the samples were pushed into the shear box slowly. Following this, the ring knife was removed, and the force transfer cover plate was added. Sliding steel balls were then installed, along with the shear box and force measuring ring. A preload of 0.01 was applied, the handwheel was rotated, and the dial reading of the force measuring ring was zeroed. After applying the vertical pressure, the fixed pin was pulled out immediately, the stopwatch was commenced, and the handwheel was rotated at a uniform speed of 0.8 mm/min (shear displacement was 0.2 mm per rotation cycle) so that the specimen was sheared and destroyed within 3–5 min. With every turn of the handwheel, the scale reading in the measuring ring was recorded once until soil sample shear failure. The calculated cohesive force and internal friction angle are provided in Table 2.

 Soil layer division Number of samples Cohesive force (kPa) Internal friction angle (°) Maximum Minimum Average Maximum Minimum Average Loessial soil () 8 8.3 5.4 6.8 29.4 25.9 28.4 Old loess () 26 43.0 11.8 30.5 32.9 18.6 25.8

#### 4. Static Load Test Result Analysis

##### 4.1. Settlement Calculation of Pile Top

The bearing capacity of multiple test piles of the same test site engineering and same size was varied, and the average value was taken to carry out static load test result analysis [39, 40]. Four displacement meters were installed to measure the settlement of the pile top under different loads in real time, and then the average settlement of four pile tops was taken as the settlement of the pile top under different loads.

The calculation results are provided in Table 3. The Q-S curve is formulated by calculating the settlement value of the pile top. The Q-S curve is an intuitive manifestation of the loading process of pile static load testing, as shown in Figure 7. Analysis of Figure 7 shows that the settlement of the test pile increases suddenly during the loading process. The Q-S curve shows a sharp drop point, which can illustrate the ultimate bearing capacity of the pile. The ultimate bearing capacity of the test pile is 9,000 kN.

 Serial number Load (kN) Loading time (min) Settlement (mm) Loading time at this level (min) Accumulated time (min) Settlement at this level (mm) Accumulated settlement (mm) 1 2,000 120 120 0.2050 0.2050 2 3,000 120 240 0.3625 0.5675 3 4,000 120 360 0.3800 0.9475 4 5,000 120 480 0.4375 1.3850 5 6,000 120 600 0.0700 1.4550 6 7,000 150 750 0.8325 2.2875 7 8,000 150 900 1.1550 3.4425 8 9,000 150 1050 3.7850 7.2275 9 10,000 150 1200 14.7425 21.9700 10 11,000 120 1320 20.7725 42.7425 11 12,000 150 1470 30.1241 72.8666

##### 4.3. Pile Side Friction Calculation

In the course of the test, the lateral friction resistance between two adjacent sections can be considered approximately equal to the variation of the axial force of the pile body between the sections [27, 4750]. Therefore, the formula for calculating the side friction resistance of the pile is as follows:where U is the perimeter of the pile body, Qi−1 is the axial force value at section i − 1, Qi is the axial force value at section i, and li is the height between the upper and lower sections. The pile side friction curve is formulated and is presented in Figure 9. As shown in Figure 9, the pile side friction increases gradually in the range of 0 m∼11 m, reaches peak value at 11 m, and then decreases gradually. This is because during the load transfer process, as the depth increases, the pile side friction resistance gradually works and reaches the limit value at 11 m. And then the pile top load begins to be mainly borne by the pile tip resistance, and the pile side frictional resistance decreases gradually.

#### 5. Multiparameter Statistical Analysis

Statistical analysis methods include two kinds. The first is the trial algorithm (interpolation method), in which the maximum and minimum values given by the original code are used for trial calculation and the value of pile side friction is adjusted according to the results of the trial calculation. The existing code in China  adopts this trial algorithm for analysis [40, 52]. The second method used is least squares statistical analysis, in which the number of classified soil layers with similar geological characteristics (age, stratum, and genesis) is taken as the number of unknown parameters. As the total lateral friction of each test pile can be expressed by the lateral friction of each layered soil, each test pile can be listed as an equation. When the number of test piles is equal to the number of layers, the equation system can be solved. When the number of test piles is larger than the number of layers, the least squares method can be used to simplify the equation system so that the number of equations is the same as the number of layers and the unknown value can be obtained and then substituted. The lateral friction of piles can be calculated using formula (6) .

##### 5.1. Basic Equations

According to the distribution of soil layers and the total resistance of each pile which is equal to the sum of the lateral resistance of each layered soil, the lateral resistance equation of each test pile can be determined [39, 40]:where Qf is the total frictional resistance of the pile side, U is the circumference of the pile, qsi is the unit surface friction resistance in the soil layer, li is the pile length of each soil layer, and m is the soil layer number.

According to the relationship between cohesive force, internal friction angle of shear strength index, and frictional resistance, the following equation can be formulated :where a and b are the empirical coefficients, based on existing results [39, 40], a and b should be between 0 and 1. σi is the average effective weight of each layer of soil, and Fi is the empirical coefficient of pile side friction in different soil layers.

Substitute equation (6) into (5), and make

Equation (7) can be simplified as follows [39, 40]:

Supposing that there are n test piles in the project, the soil layer is divided into m layers. If n > m, the equation can be solved. The following formula can thus be obtained from formula (9) [39, 40]:

In this paper, the principle of the least squares method is applied to the calculation of lateral friction of piles. By using the principle of the least squares method, the equations in (10) can be optimized into m standard equations (13) [39, 40]. The specific optimization process is as follows:(1)Construct the error function(2)To minimize the error value, make(3)The optimized standard equations are as follows:

By solving the formulas in (13), the empirical coefficients of different soil layers Fi can be obtained. However, two unknown empirical coefficients a and b remain in formula (13). According to the existing results [39, 40], a and b are between 0 and 1. Therefore, it is necessary to assume there are different combinations of a and b to obtain different combinations of Fi. Among the Fi values of different combinations, a set of values should be chosen as the optimal solution for formula (13), so the standard deviation σ of the formula should be calculated according to the following formula [39, 40]. When the standard deviation σ is the minimum, a and b are the most appropriate values to get the optimal solution Fi [39, 40]:

#### 6. Result Analysis of Multiparameter Statistical Analysis

According to the basic principle of multiparameter statistics and the pile test data collected above, there are six test piles and two layers of soil on the side of the pile. Six conditional equations (15) can then be listed from formula (10):

There are six equations and two unknown parameters in this system. The number of equations is more than the unknown number, so it can be solved by the least squares method. By using the principle of least squares, the equations in (15) can be optimized to two standard equations as follows:

The equations in (16) refer to the equations of F1 and F2. F1 and F2 are the empirical coefficients of pile side friction in different soil layers. In the process of solving, it is necessary to assume different combinations of a and b to get different Fi. Their standard deviations can then be calculated according to formula (14), and the optimal solution Fi can be determined by taking the values of a and b when the standard deviation σ is the smallest. By changing combinations of a and b, the above calculation methods for standard deviation is compiled into a MATLAB program, and the standard deviation σ under different combinations of a and b is obtained, as shown in Table 4.

 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 123.17 117.08 111.25 105.7 100.53 95.760 97.668 100.15 102.75 0.2 124.78 118.71 112.88 107.33 102.10 97.26 100.10 102.63 105.27 0.3 126.39 120.34 114.52 108.96 103.71 98.80 102.62 105.19 107.85 0.4 128.01 121.9 116.18 110.62 105.33 100.38 105.22 107.82 110.50 0.5 129.62 123.64 117.85 112.29 106.98 101.99 107.89 110.51 113.20 0.6 131.25 125.30 119.53 113.97 108.66 103.63 110.64 113.26 115.95 0.7 132.87 126.26 121.22 115.67 110.35 105.29 113.43 116.06 118.74 0.8 134.50 128.62 122.90 117.38 112.07 106.99 116.29 118.91 121.57 0.9 136.12 130.30 124.62 119.11 113.80 108.71 119.18 121.79 124.44

The results show that the minimum standard deviation is σ = 95.76 when a = 0.1 and b = 0.6. Then, F1 = 31.4 and F2 = 38.2 can be obtained by solving the equations in (16). The calculated parameters are replaced by formula (6), in which the internal friction angle and cohesion of each layer of soil is averaged , as shown Table 2. For example, the calculated values of pile side friction at 6.5 m pile depth and at 24.5 m pile depth are as follows:(1)Loessial soil ():(2)Old loess ():

Because the size of the six test piles are the same and they are located in the same project, the weighted average value of pile side friction of different soil layers under the maximum loading value 12,000 kN in static load test is taken as the measured value, and the calculation process is as follows:(1)Loessial soil ():(2)Old loess ():

Similarly, the calculation of the pile side friction resistance of each soil layer is also a weighted average. The calculated values are compared with the measured values of different soil layers in the static load test, and the error is provided in Table 5. According to Table 5, it is concluded that the error between the two methods is within 20%. If the parameters are reasonable, the calculation results of the multiparameter statistical analysis method can largely meet the engineering requirements.

 Soil classification Layer thickness (m) Measured value (kPa) Calculated value (kPa) Error (%) Loessial soil () 6.5 54 53 1.85 Old loess () 18.5 91 80 12.09

When calculating pile side friction by the multiparameter statistical analysis method, without considering the change of shear strength index along the pile depth in the same soil, the average value of them is used to calculate pile side friction . The calculation results are shown in Figure 10. It can be seen from Figure 10 that the pile side friction of the same soil layer varies little along the pile depth, while the pile side friction of different soil layers varies obviously along the pile depth. Therefore, in the multiparameter statistical analysis method, without considering the change of the shear strength index of the same soil layer along the pile depth, the pile side friction resistance of the same soil layer changes very little, while the shear strength index of different soil layers is different, and the pile side friction resistance of different soil layers changes obviously along the pile depth.

#### 7. Conclusions

In this paper, static load testing was carried out on the six test piles, and the size and distribution of pile side friction was measured. Pile side friction in different soil layers was then calculated using the multiparameter statistical analysis method. The main findings are summarized as follows:(1)The static load test results show that the pile side resistance and pile tip resistance are not entirely synchronized to the maximum. In the process of pile top load transfer, the resistance of pile side occurs prior to the resistance of the pile tip. As the loading continues to increase, the pile side resistance is fully exerted, the pile end resistance increases significantly, and the pile side frictional resistance first increases and then decreases from top to bottom.(2)The multiparameter statistical analysis method based on the shear strength index can calculate the pile side friction of different soil layers in loess areas. If the parameters are reasonable, the error between the calculated value and the measured value of the static load test method can be controlled within 20%.(3)In the existing Chinese code , the value of pile side friction is determined by the type of pile and soil parameter index (void ratio and liquid index). This paper calculated pile side friction by the multiparameter statistical analysis method. It was found that pile side friction is related not only to the type of pile and soil parameter but also to the shear strength index.

#### Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

#### Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

#### Acknowledgments

This research was funded by the National Key R&D Program of China (no. 2018YFC0808606) and the Project on Social Development of Shaanxi Provincial Science (nos. 2018SF-378 and 2018SF-382).

1. J. X. Lai, X. L. Wang, J. L. Qiu et al., “Extreme deformation characteristics and countermeasures for a tunnel in difficult grounds in southern Shaanxi, China,” Environmental Earth Sciences, vol. 77, no. 19, pp. 1–14, 2018. View at: Publisher Site | Google Scholar
2. J. Lai, J. Qiu, H. Fan et al., “Fiber bragg grating sensors-based in situ monitoring and safety assessment of loess tunnel,” Journal of Sensors, vol. 2016, Article ID 8658290, 10 pages, 2016. View at: Publisher Site | Google Scholar
3. Y. Zhang, Z. Song, X. Weng, and Y. Xie, “A new soil-water characteristic curve model for unsaturated loess based on wetting-induced pore deformation,” Geofluids, vol. 2019, Article ID 5261985, 13 pages, 2019. View at: Publisher Site | Google Scholar
4. P. F. Li, K. Y. Chen, F. Wang, and Z. Li, “An upper-bound analytical model of blow-out for a shallow tunnel in sand considering the partial failure within the face,” Tunnelling and Underground Space Technology, vol. 91, pp. 1–12, 2019. View at: Publisher Site | Google Scholar
5. Z. Zhou, J. Lei, S. Shi, and T. Liu, “Seismic response of aeolian sand high embankment slopes in shaking table tests,” Applied Sciences, vol. 9, no. 8, p. 1677, 2019. View at: Publisher Site | Google Scholar
6. Z. J. Zhou, C. N. Ren, G. J. Xu et al., “Dynamic failure mode and dynamic response of high slope using shaking table test,” Shock and Vibration, vol. 2019, Article ID 4802740, 19 pages, 2019. View at: Publisher Site | Google Scholar
7. L. M. Duan, Y. H. Zhang, and J. X. Lai, “Influence of ground temperature on shotcrete-to-rock adhesion in tunnels,” Advances in Materials Science and Engineering, vol. 2019, Article ID 8709087, 12 pages, 2019. View at: Publisher Site | Google Scholar
8. L. M. Duan, W. S. Lin, J. X. Lai, and P. Zhang, “Vibration characteristic of high-voltage tower influenced by adjacent tunnel blasting construction,” Shock and Vibration, vol. 2019, Article ID 8520564, 16 pages, 2019. View at: Publisher Site | Google Scholar
9. X. L. Luo, X. Meng, W. J. Gan, and Y. H. Chen, “Traffic data imputation algorithm based on improved low rank matrix decomposition,” Journal of Sensors, vol. 2019, Article ID 7092713, 10 pages, 2019. View at: Google Scholar
10. X. Liu, Q. Fang, D. Zhang, and Z. Wang, “Behaviour of existing tunnel due to new tunnel construction below,” Computers and Geotechnics, vol. 110, pp. 71–81, 2019. View at: Publisher Site | Google Scholar
11. Q.-Q. Zhang, S.-W. Liu, S.-M. Zhang, J. Zhang, and K. Wang, “Simplified non-linear approaches for response of a single pile and pile groups considering progressive deformation of pile-soil system,” Soils and Foundations, vol. 56, no. 3, pp. 473–484, 2016. View at: Publisher Site | Google Scholar
12. Q.-Q. Zhang and Z.-M. Zhang, “A simplified nonlinear approach for single pile settlement analysis,” Canadian Geotechnical Journal, vol. 49, no. 11, pp. 1256–1266, 2012. View at: Publisher Site | Google Scholar
13. X. B. Yue, Y. L. Xie, H. G. Zhang et al., “Study on geotechnical characteristics of marine soil at Hongkong-Zhuhai-Macao tunnel,” Marine Georesources and Geotechnology, vol. 37, no. 8, pp. 1–12, 2019. View at: Publisher Site | Google Scholar
14. X. L. Wang, J. X. Lai, R. Garnes, and Y. B. Luo, “Support system for tunnelling in squeezing ground of qingling-daba mountainous area: a case study from soft rock tunnels,” Advances in Civil Engineering, vol. 2019, Article ID 8682535, 17 pages, 2019. View at: Publisher Site | Google Scholar
15. Z.-F. Wang, S.-L. Shen, and G. Modoni, “Enhancing discharge of spoil to mitigate disturbance induced by horizontal jet grouting in clayey soil: theoretical model and application,” Computers and Geotechnics, vol. 111, pp. 222–228, 2019. View at: Publisher Site | Google Scholar
16. M. F. Chang and B. B. Broms, “Design of bored piles in residual soils based on field-performance data,” Canadian Geotechnical Journal, vol. 28, no. 2, pp. 200–209, 1991. View at: Publisher Site | Google Scholar
17. C. S. Chen and L. C. Hiew, “Performance of bored piles with different construction methods,” Proceedings of the Institution of Civil Engineers-Geotechnical Engineering, vol. 159, no. 3, pp. 227–232, 2006. View at: Publisher Site | Google Scholar
18. V. M. Mamonov, A. M. Dzagov, and P. M. Ermoshkin, “Bearing capacity of bored-cast-in-place piles made from concretes having different compositions,” Soil Mechanics and Foundation Engineering, vol. 26, no. 1, pp. 1–6, 1989. View at: Publisher Site | Google Scholar
19. A. M. Rybnikov, “Experimental investigations of bearing capacity of bored-cast-in-place tapered piles,” Soil Mechanics and Foundation Engineering, vol. 27, no. 2, pp. 48–52, 1990. View at: Publisher Site | Google Scholar
20. M. G. Zertsalov, M. V. Nikishkin, and I. N. Khokhlov, “On the calculation of bored piles under axial compressive loads in rocky soils,” Soil Mechanics and Foundation Engineering, vol. 54, no. 3, pp. 143–149, 2017. View at: Publisher Site | Google Scholar
21. Q. Zhang, Z. Zhang, F. Yu, and J. Liu, “Field performance of long bored piles within piled rafts,” Proceedings of the Institution of Civil Engineers-Geotechnical Engineering, vol. 163, no. 6, pp. 293–305, 2010. View at: Publisher Site | Google Scholar
22. N. F. Ismael, “Axial load tests on bored piles and pile groups in cemented sands,” Journal of Geotechnical and Geoenvironmental Engineering, vol. 127, no. 9, pp. 766–773, 2001. View at: Publisher Site | Google Scholar
23. J. Lai, H. Liu, J. Qiu, and J. Chen, “Settlement analysis of saturated tailings dam treated by CFG pile composite foundation,” Advances in Materials Science and Engineering, vol. 2016, Article ID 7383762, 10 pages, 2016. View at: Publisher Site | Google Scholar
24. Y. Lei, J.-F. Yin, Q.-N. Chen, and Y.-X. Liu, “Experimental study on the rock-socketed segment of pile and analysis of its load-bearing characteristics,” Journal of Highway and Transportation Research and Development (English Edition), vol. 11, no. 3, pp. 54–61, 2017. View at: Publisher Site | Google Scholar
25. R. Nazir, H. Moayedi, M. Mosallanezhad, and A. Tourtiz, “Appraisal of reliable skin friction variation in a bored pile,” Proceedings of the Institution of Civil Engineers-Geotechnical Engineering, vol. 168, no. 1, pp. 75–86, 2015. View at: Publisher Site | Google Scholar
26. C. W. W. Ng, T. L. Y. Yau, J. H. M. Li, and W. H. Tang, “Side resistance of large diameter bored piles socketed into decomposed rocks,” Journal of Geotechnical and Geoenvironmental Engineering, vol. 127, no. 8, pp. 642–657, 2001. View at: Publisher Site | Google Scholar
27. Z. J. Zhou, S. S. Zhu, X. Kong et al., “Optimization analysis of settlement parameters for postgrouting piles in loess area of Shaanxi, China,” Advances in Civil Engineering, vol. 2019, Article ID 7085104, 11 pages, 2019. View at: Publisher Site | Google Scholar
28. J. X. Lai, H. Q. Liu, J. L. Qiu et al., “Stress analysis of CFG pile composite foundation in consolidating saturated mine tailings dam,” Advances in Materials Science and Engineering, vol. 2016, Article ID 3948754, 12 pages, 2016. View at: Publisher Site | Google Scholar
29. J. D. Geddes, “Stresses in foundation soils due to vertical subsurface loading,” Géotechnique, vol. 16, no. 3, pp. 231–255, 1966. View at: Publisher Site | Google Scholar
30. Y. Fang, Z. Chen, L. Tao et al., “Model tests on longitudinal surface settlement caused by shield tunnelling in sandy soil,” Sustainable Cities and Society, vol. 47, Article ID 101504, 2019. View at: Publisher Site | Google Scholar
31. I. Said, V. De, and R. Frank, “Axisymmetric finite element analysis of pile loading tests,” Computers and Geotechnics, vol. 36, no. 1-2, pp. 6–19, 2009. View at: Publisher Site | Google Scholar
32. I. J. Johannessen and L. Bjerrum, “Measurement of the compression of a steel pile to rock due to settlement of the surrounding clay,” in Proceedings of the 6th International Conference on Soil Mechanics and Foundation Engineering, pp. 261–264, Montreal, Canada, September 1965. View at: Google Scholar
33. B. H. Fellenius and B. B. Broms, “Negative skin friction for long piles driven in clay,” in Proceedings of the 7th International Conference on Soil Mechanics and Foundation Engineering, pp. 93–98, Mexico City, Mexico, August 1969. View at: Google Scholar
34. M. H. Zhao, X. J. Zou, and Q. J. Liu, “Experimental study on vertical bearing capacity of large diameter and super long cast-in-place piles in Dongting Lake soft soil area,” China Civil Engineering Journal, vol. 37, no. 10, pp. 63–67, 2004. View at: Google Scholar
35. C. F. Zhao, J. Li, Z. X. Qiu et al., “Experimental study on load transfer characteristics of large diameter and super long bored piles in guangdong area,” Journal of Rock Mechanics and Engineering, vol. 34, no. 4, pp. 849–855, 2015. View at: Google Scholar
36. X. W. Wang, N. G. Yi, and S. P. Zhang, “Static loading test of the end-bearing pile under the side friction action,” Applied Mechanics and Materials, vol. 353–356, pp. 974–978, 2013. View at: Publisher Site | Google Scholar
37. Q.-Q. Zhang, Z.-M. Zhang, and S.-C. Li, “Investigation into skin friction of bored pile including influence of soil strength at pile base,” Marine Georesources & Geotechnology, vol. 31, no. 1, pp. 1–16, 2013. View at: Publisher Site | Google Scholar
38. S.-C. Li, Q. Zhang, Q.-Q. Zhang, and L.-P. Li, “Field and theoretical study of the response of super-long bored pile subjected to compressive load,” Marine Georesources & Geotechnology, vol. 34, no. 1, pp. 71–78, 2014. View at: Publisher Site | Google Scholar
39. Z. H. Chen and D. Z. Gao, “Finding the ultimate lateral friction of pile side layered soil by multi parameter optimal solution,” Engineering Investigation, vol. 1988, no. 5, pp. 15–20, 1988. View at: Google Scholar
40. X. M. Lou, C. F. Zhao, G. Chen et al., “Statistical analysis of parameters for calculating lateral friction of precast pile soft clay with shear strength index,” Rock and Soil Mechanics, vol. 31, no. S2, pp. 354–359, 2010. View at: Google Scholar
41. Ministry of Transportation of the People’s Republic of China, Technical Specification for Construction of Highway Bridges and Culverts JTG/T F50-2011, People’s Transportation Publishing House, Beijing, China, 2011.
42. Ministry of Housing and Urban-Rural Construction of the People’s Republic of China, Technology Specification of Building Pile Foundation Testing JGJ 106-2014, China Architecture & Building Press, Beijing, China, 2014.
43. J. Qiu, Y. Qin, Z. Feng, L. Wang, and K. Wang, “Safety risks and protection measures for the city wall during the construction and operation of Xi’an metro,” Journal of Performance of Constructed Facilities, vol. 33, no. 5, p. 12, 2019. View at: Google Scholar
44. C. F. Zhao, J. Lu, Q. C. Chao et al., “Experimental study on layered load transfer characteristics of large diameter and deep bored piles,” Journal of Rock Mechanics and Engineering, vol. 28, no. 5, pp. 1020–1026, 2009. View at: Google Scholar
45. Ministry of Housing and Urban-Rural Construction of the People’s Republic of China, Code for Design of Concrete Structures GB 50010-2010, China Architecture & Building Press, Beijing, China, 2010.
46. F. J. Chen, J. L. Ma, L. Zhu et al., “Analysis of pile side friction and pile end resistance of high speed railway bridges,” Railway Engineering, vol. 6, pp. 41–43, 2013. View at: Google Scholar
47. Z. M. Zhang and Q. Q. Zhang, “Experimental study on the bearing behavior of post-grouting piles,” Journal of Rock Mechanics and Engineering, vol. 28, no. 3, pp. 475–482, 2009. View at: Google Scholar
48. Z. M. Zhang, Q. Q. Zhang, and F. Yu, “A destructive field study on the behavior of piles under tension and compression,” Journal of Zhejiang University-Science A, vol. 12, no. 4, pp. 291–300, 2011. View at: Publisher Site | Google Scholar
49. Y. Q. Wang, H. T. Chang, J. Y. Wang, and X. L. Shi, “Countermeasures to prevent collapse during the construction of road tunnel in fault zone: a case study from the Yezhuping tunnel in South Qinling China,” Environmental Earth Sciences, vol. 78, no. 606, pp. 1–14, 2019. View at: Google Scholar
50. Y. Zheng, J. Xiong, T. Liu, and X. Yue, “Performance of a deep excavation in Lanzhou strong permeable sandy gravel strata,” Arabian Journal of Geosciences, vol. 12, no. 16, p. 12, 2019. View at: Google Scholar
51. Ministry of Construction of the People’s Republic of China, Technical Specification for Building Pile Foundation JGJ94-2008, China Architecture & Building Press, Beijing, China, 2008.
52. Y. K. Hong, X. M. Lou, and Q. H. Chen, “Statistical analysis of vertical bearing capacity parameters of driven precast reinforced concrete piles,” Journal of Geotechnical Engineering, vol. 15, no. 1, pp. 53–59, 1993. View at: Google Scholar

#### More related articles

We are committed to sharing findings related to COVID-19 as quickly as possible. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. Review articles are excluded from this waiver policy. Sign up here as a reviewer to help fast-track new submissions.