Performance of X-Section Concrete Pile Group in Coral Sand Under Vertical Loading

To reveal the bearing capacity of the X-section pile group in coral sand, a series of model load tests are conducted. The testing results are presented as load-settlement curves, pile-soil stress ratios, distributions of side friction and axial force, and load-sharing ratio between side and tip resistances. The reliability and accuracy of the numerical simulation model are verified by comparing the results of the model test. Comparative analysis between X-section and circular section piles with the same cross-sectional area indicates that the bearing capacity of the X-section pile group is much larger than that of the circular pile group. The axial force of X-section piles is smaller while the peak skin friction is larger than that of circular piles at the same depth. The skin friction of the core pile is the largest, followed by the side pile and the corner pile is the smallest when the load is relatively small; however, it is converse when the load is larger than 10 kN. Compared with piles in silica sand, the pile in coral sand has a lower bearing capacity, and the sand breakage leads to the steep drop failure of pile foundation. Moreover, pile positions under the raft have less effect on the load-share differences among corner, side and core piles in coral sand. This study provides a reference for the construction of pile foundations in coral sand.


Introduction
With current demands of marine resources and developments of the ocean high-tech, more and more structures and buildings need to be constructed on the island that is rich in coral sand all over the world (Wang et al., 2011). As one of the special soils, the irregular shape, high porous, and fragile properties of coral sands result in the high compressibility and low bearing capacity of coral sand foundation (Murff et al., 1987;Lv et al., 2018). Based on the fact that piles have a great advantage in improving the bearing capacity of weak soil (Cui et al., 2018;Li and Gao, 2019;Luan et al., 2020), pile foundations in coral sands are widely used. However, the bearing characteristic of piles in coral sand shows significant differences from that in quartz sand (Chin and Poulos, 1996). The existing data suggest that the side friction of piles in coral sand is relatively low due to the particle breakage along the side of piles (Shahnazari and Rezvani, 2013). As one of the feasible ways to improve the bearing capacity of pile, special shaped piles such as the rectangular pile, H-section, L-section, Y-section pile, I-section, barrette, tapered pile, belled pile, squeezed branch pile, and pipe pile could be selected (Seo et al., 2009;Chen et al., 2009;Lv et al., 2016;Ding et al., 2020;Wu et al., 2020).
As one new pile type, the X-reinforced concrete pile is a kind of energy saving and emission-reducing pile foundation technology (Liu, 2007;Lv et al., 2011), which has been widely used in high-speed railway and other projects of soft foundation reinforcement. The bearing capacity of X-shaped piles is larger than that of circular piles under equal crosssectional area. However, the bearing performance of X-section pile is more complex than that of a circular pile. Researchers have carried out a series of tests to study the load transfer mechanism of X-section piles Lv et al., 2014). Full-scale model tests on the vertical load of single piles with X-section pile have been carried out (Wang, et al., 2010;Zhang et al., 2011Zhang et al., , 2014. The uplift resistance of X-section pile has been studied by means of full-scale model test and finite element analysis Kong et al., 2012). The effect of cross section form on the distribution of side friction and end resistance is also revealed. Compared with circular pile with equal crosssectional area, X-section pile has better flexural and horizontal load resistance (Zhang et al., 2013;Liu et al., 2020). The results show that X-section pile has higher anti-drawing characteristics, and under the action of the upward pullout force. Furthermore, property and load transfer mechanism of cast-in-situ X-pile single pile composite foundation has been studied Lv et al., 2016). Results show that the pile soil load sharing of X-shaped pile is more reasonable than that of the circular pile. Therefore, the Xsection pile characterized with high side friction can be used to improve the bearing capacity of pile foundation in coral sand.
In this study, compared with circular piles with equal cross-sectional area, the single X-section piles and group Xsection piles are studied by model tests. The load-sharing of pile and soil, load-sharing of side resistance and tip resistance of the X-section pile are analyzed. Furthermore, compared with piles in silica sand, the load transfer mechanism of pile group is revealed from the bearing performance difference in corner piles, side piles, and center piles based on the peculiarity of coral sand. This study can be used as a reference for the design of pile in coral sand.

Equipment and the ground soil
The model test apparatus consists of a model tank, a loading system and a measuring system. The layout of piles and apparatus is displayed in Fig. 1. The size of the model tank is 1 m×0.8 m×0.8 m (length×width×height). Fig. 1a shows that the loading system consists of a reaction beam and a jack that can display the oil pressure. The measuring system consisted of a data acquisition system, dial indicators and strain gauges that were pasted on the side of piles. The error of the force applied by the jack is 3%, and the accuracy is 0.01 mm for dial gages. Before the loading of piles, a raft was placed on the top of piles. The settlement of piles was measured by the dial indicator and the vertical strain along piles was recorded by the data acquisition system (Qu et al., 2020). Fig. 1b displays that pile groups and the raft are placed in the center of the model tank to ensure the uniformity of the applied force. Ground soils used in the model tank are silica sand and coral sand, respectively. Basic parameters of the two kinds of sands used in this test are shown in Table 1. The relative density of sand is controlled by the sand-rain method, and the relative density of sand in the model tank is checked by sampling tests.

Model pile and the loading procedure
The mold to fabricate the X-section pile is shown in Fig. 2a. The length of the X-section pile is 700 mm and the buried depth of piles is 500 mm, and the sectional dimen-   Fig. 2b. The X-section pile is fabricated by inserting the reinforcement cage (composed of four #12 steel wire, #18 at 20 stirrups along the pile model) and filling the C32.5 concrete (cement : sand : stone : water= 1 : 1.11 : 2.72 : 0.38) into the mold. Circular piles, which have the same sectional area to the X-section pile (diameter of 4 cm), are used as contrasts.
The slow maintain load method is adopted in the pile load test. Each grade of load accounts for 10% of the total load, and the load duration of grade of load is half an hour. The preload is 15% of the estimated bearing capacity of model pile, and the preloading time is 12 h. Load test termination criteria is based on JGJ94-2008JGJ94- (2008.

P−S curves of pile foundation
The load−displacement curves (P−S curves) of the single-pile, the 4-pile and the 9-pile groups are shown in Fig. 3. The pile spacing under raft is 3D 0 , 4D 0 for pile in 4pile and 9-pile groups, respectively. All curves show that the displacement increases with increasing load, and presented the steep drop model. For the single piles, the difference of curves between circular pile and X-section pile is relatively small, and the bearing capacity of single piles is only about 0.8 kN in coral sand. For pile groups, the bearing capacity of X-section pile groups is much larger than that of circular pile groups and the increment increases with the increasing pile numbers. This is because the pile−soil interaction is improved with the increasing of pile numbers (higher soil density) (Qu et al., 2017). At the same time, the efficiency of the X-section pile raft foundation is much larger than that of the single raft. Results indicate that the bearing capacity of X-section pile raft foundation is much larger than that of the circular pile raft foundation. Compared with the same single piles in the silica sand (green curves in Fig. 3), the bearing capacity of piles in coral sand is much smaller than that in silica sand. Moreover, the P−S curves of pile in coral sand present a steeper drop failure mode, which is related to the breakage of coral sand along the side of the pile. Different from the pile model test in silica sand, a sudden settlement of pile is observed for the pile in coral sand, especially when a large load is applied. Fig. 4 shows the axial force of the X-section piles and the circular piles, respectively. The figures show that the axial force distribution of the X-section pile is basically similar with that of the conventional circular pile, reduced with the depth under loads. When the load is smaller than 0.5 kN, the reducing trend of axial force is sharp for all the X-section and circular piles but is relatively flat for circular pile when the load is larger than 0.5 kN. The phenomenon indicates that the X-section pile bears more loads using the side friction of piles.

Axial force
To show the detailed axial force distribution difference between circular piles and X-section piles, the axial force under the low load not larger than (≤) 0.5 kN and high load larger than 0.5 kN are presented in Fig. 5, respectively. Fig. 5 shows the axial force of X-section piles is obviously smaller than that of circular piles under the same load.  PENG Yu et al. China Ocean Eng., 2020, Vol. 34, No. 5, P. 621-630

Skin friction
The skin frictions of X-section pile and circular piles are shown in Figs. 6a and 6b. The side friction of piles increased with increasing load; under the load not larger than 0.4 kN, the increment is large but it is small when the load is larger 0.4 kN. To show the detailed side friction difference between circular piles and X-section piles, side friction distributions under the low load and high load are presented, respectively in Fig. 7. Under the low load not larger than 0.4 kN, the skin friction of X-section pile is smaller than that of circular piles due to the higher lateral surface area to share the load. Under the high load larger than 0.4 kN, the peak skin friction of X-section pile is shallower than that of circular piles, which indicates that the X-section pile has higher bearing potential than circular pile does.

Load-sharing of pile side and pile end
In Fig. 8, the total load of X-section pile consists of side resistance and tip resistance, and the pile-bearing load was developed by side resistance and tip resistance. The loadsharing of side resistance decreases with increasing load, which demonstrates that more load distributes to the tip resistance with the higher load. When the load increases to about 0.8 kN, the load-sharing of side resistance and tip resistance is nearly equal. The load-sharing of side resistance for the X-section pile is about 10% larger than that of the   circular pile. Therefore, the settlement of X-section pile is smaller than that of the circular pile (as shown in Fig. 3). The higher load-sharing of side resistance for the X-section pile demonstrates that the bearing capacity of the X-section pile is larger than that of the circular piles.
3.3 Pile shape effects on the stress of the pile group in model test 3.3.1 Axial force and side friction of pile in the 4-pile group Fig. 9 shows the distributions of axial force and side friction along the depth of pile in the 4-pile group. Fig. 9a shows that the axial force of X-section piles is obviously smaller than that of circular pile under the same loads. Fig. 9b shows that the side friction of X-section piles at the top and tip of piles is obviously larger than that of circular pile under the same load. The phenomenon indicates that the X-section pile in pile group has more bearing potential than circular pile does.

Load-sharing of side resistance and tip resistance in pile groups
The load-sharing of side resistance and tip resistance in the X-section pile groups and circular pile groups is shown in Fig. 10. As seen from the figure, the load-sharing of side resistance decreases with the increasing load, which demonstrates that more load distributes to the tip resistance with higher load. When the load increases to about 4 kN, the load-sharing of side resistance and tip resistance are beginning to stabilize for pile in coral sand. Compared with circular pile, the higher load-sharing of side resistance for the Xsection pile group means that the settlement of X-section piles is smaller under the same loading applied on the circular pile. Compared with the load-sharing of side resistance and tip resistance of single piles (Fig. 8), the load-sharing of side friction in the X-section pile group is larger than that in single piles. This higher load-sharing in pile group demonstrates that the side friction advantage of X-section pile could work better in pile groups.
Compared with the load sharing percentage of X-section pile in silica sand (green curves in Fig. 10), the load   sharing percentage of X-section pile in coral sand decreased sharply with the increase of the vertical load. The phenomenon is related to the breakage of coral sand along the side of piles, which sharply decreased the side friction around the pile. In this pile model test, the axial force usually suddenly drops and is difficult to maintain stability. Curves in Fig. 10 also show that the ultimate load sharing percentage of side friction for piles in coral sand is obviously smaller than that in silica sand.

Numerical model and parameters
In the simulation, the X-section pile group under the raft is modeled as an isotropic linear elastic model. Soils are modeled as a Mohr−Coulomb model. The interfaces of the pile-soils are modeled as a Coulomb sliding model, in which the friction coefficient of the pile-soil interface is assumed to be the same as that of the soil in tests. The upper boundary condition is assumed to be a free boundary; the side boundary condition is assumed to be a level-direction sliding support; and the bottom boundary condition is assumed to be a vertical-direction sliding support. Parameters used in numerical simulation models are shown in Table 2. The soil parameters are similar to those in model tests.

Verification of the numerical model
To verify the numerical simulation model in the PLAX-IS software, the comparative analysis is adopted based on the model test condition. The soil properties and pile parameters are the same as the results by the model test. Fig. 11 shows the comparison load-displacement curves (P−S curves) of the numerical simulation and model test results. The pile spacing is 4D 0 for piles in the 9-pile group in this numerical simulation. All curves show that the displacement increases with increasing load, and presents the steep drop failure mode. For the single piles, the curves of numerical simulation and model test matched well. For the P−S curves of the 4-pile and 9-pile groups, curves have not overlapped but are relatively close to the model test results. Fig. 12 shows the comparative axial force and side friction curves in the numerical simulation and the model tests. The numerical simulation results matched well with those of the model test results. Comparison results indicate that the analysis obtained from the numerical simulation of X-section pile groups is reliable and accurate. Fig. 13 shows the axial force of the X-section piles under different positions under the raft. The figures show that the axial force distribution of corner piles, side piles and core piles decreases with depth under different loads. For the corner pile, as the increase of the load, the increment of axial force is relatively large when the load is not larger than 4.56 kN and is relatively small when the load is larger than 4.56 kN. For the core pile, however, the increment of axial force is relatively small when the load is not larger than 4.56 kN while it is relatively large when the load is larger than 4.56 kN. The increment of axial force is relatively homogeneous for the side pile. Besides, the decrease of the axial force at deep location is relatively small for the corner pile compared with that of the side and core piles.

Pile position effects on axial forces of X-section pile
To show the detailed performance of axial force distribution among corner piles, side piles and core piles, the relationships between axial force and vertical load under different depths are shown in Fig. 14. At the same depth, the axial force of X-section piles from large to small is core piles, side piles and corner piles, respectively when the load smaller than 9 kN. However, the axial force of X-section piles from large to small are corner piles, side piles and core piles, respectively when the load is larger than 10 kN. Fig. 15 shows the skin friction of X-section pile under different positions of the raft. The skin friction is the largest at the middle part and relatively small at the top and tip parts of each corner, side and core piles. For the corner pile, the largest skin friction is located at about 25 cm depth of  However, the increment of the skin friction is very small under the load larger than 8.56 kN. This phenomenon might be explained by the reason that after the load is larger than 8.56 kN, the pile groups are beginning to fail. Besides, the largest skin friction in each pile position indicates that we can design piles with varying lengths to reduce the construction cost in coral sand.

Load transfer mechanism under the pile raft
The relationship between the skin friction and settlement could be used to reflect the bearing characteristics of the pile group. Fig. 16 shows the shape of settlement-side friction curves is basically similar to load−displacement curves and presents the steep drop model with increasing load. The phenomenon is also related to the breakage of coral sand along the pile, which decreases the side friction along the pile sharply. In the pile model test, the axial force usually drops suddenly with an obvious particle breakage noise and is difficult to maintain stability. Before the settlement of about 2 mm, the values of the skin friction of Xsection piles from large to small are corner piles, side piles, and core piles. However, the order of skin frictions is adverse under the settlement larger than 2 mm. With the increase of load, the core piles play a more important role in bearing load. η As mentioned above, the bearing performance of pile in different positions under rafts is different; therefore, the load share of each pile under the raft is different. In the 9pile group, there are three kinds of position piles (corner, side, and core piles). The load relative value reflected the load share of each position pile and the equation is calculated as follows: (1) is the load of each single position pile; , the average ultimate bearing capacity of piles; n, the pile number of pile group. Fig. 17 shows that with the increase in load, the load sharing of the corner pile decreases obviously while the load sharing of side pile and core pile increases. When the load is small, the load sharing from large to small is the corner pile (1.15), edge pile (0.902), and core pile (0.79); when the load increases to 8.56 kN, the load sharing from large to small is the side pile (1.03), corner pile (0.98), and core pile (0.95). When the load exceeds 9.06 kN, the load sharing from large to small is the core pile (1.15), side pile (1.05), and corner pile (0.91). In conclusion, with the increase of load for the X-section 9-pile group in coral sand, the main force is transferred from the corner pile to the inside side pile and then to core piles.
Compared with the load sharing of X-section pile in the silica sand (green curves in Fig. 17), the load sharing of the pile in coral sand is quite stable with the increase of vertical load (especially for the core pile). This indicates that the pile position effect on the bearing performance of piles under the raft is relatively small. The phenomenon is related to, compared with the easy-sliding silica sand, the coral sands characteristic with high angularity and rich cavity, Fig. 11. Comparison of load-displacement curves between numerical simulation and model test. PENG Yu et al. China Ocean Eng., 2020, Vol. 34, No. 5, P. 621-630 627 which impedes the slide among sand (high friction). Since the pile position effect on the bearing performance in the sand is highly relying on the slide of sand around piles, the pile position effect on the performance difference among the core pile, side pile, and corner pile is relatively small for piles in coral sand.

Conclusions
The bearing performance of X-section pile in coral sand has been studied by a series of model tests and numerical analyses. Compared with piles in silica sand, the results of single and group piles in coral sand are interpreted. The following conclusions can be drawn.
(1) The bearing capacity of the X-section pile in coral sand is larger than that of the circular pile under the same cross-sectional area. Compared with the same model pile in silica sand, the bearing capacity of piles in coral sand is smaller due to the particle breakage of coral sand which leads to the steep drop failure of the pile.
(2) Compared with that of circular piles, the axial force of X-section piles is obviously smaller while the peak skin friction is larger. The higher load-sharing of side resistance to total resistance in pile groups demonstrates that the side friction of X-section pile is strengthened obviously with the increasing number of piles.
(3) The numerical simulation results agree well with the model test results. At the same depth, core piles and corner piles have the largest and smallest axial force respectively, and the axial force of side piles is in between, when the load is smaller than 9 kN. The location of the peak skin friction of corner pile is deeper than that of the side and core piles and the increasing skin friction is relatively small when the increased load is larger than 8.56 kN.
(4) The relationship between the side friction and settlements is basically similar to the relationship between load and displacement, presented the steep drop model with increasing load. With the increase of the load, the dominating load-sharing transforms from the corner piles to side piles and finally to core piles. Compared with the pile in silica sand, the pile positions under the raft have less effect on the load-share differences among the corner, side and core piles.