Experimental study on negative skin friction characteristics of double-sleeve pile

Abstract

Pile foundation structures are widely used in the construction of high-piled wharves in coastal soft soil areas due to their excellent adaptability to such environments. However, the extensive, deep backfilling involved in constructing these wharves can easily induce negative skin friction (NSF) on the piles, resulting in safety issues such as excessive settlement during the service life of the structures. This paper presents an indoor model experiment to examine the distribution of the THE NSF under varying pile-top loads and surcharge effects on single pile and double-sleeve pile foundations. The potential of double-sleeve pile foundations to mitigate the NSF was also explored. The results show that the axial force within the double-sleeve pile’s protected section remains essentially stable, though it is affected by the surface surcharge in the unprotected section. Time effect is exhibited both for the axial force and the NSF, gradually increasing over time. Compared to single piles, double-casing pile foundations can effectively isolate the down drag load caused by surrounding soil settlement, thereby reducing or eliminating the NSF on the pile sides.

Introduction

In the context of rapid global maritime development and increasing worldwide freight volumes, numerous coastal engineering structures, such as ports and terminals, are being constructed on soft soil. Pile foundation systems are extensively employed in offshore infrastructure projects due to their adaptability to such geological conditions. Nevertheless, these soil layers, characterized by high water content, high compressibility, and susceptibility to thixotropic changes, are prone to consolidation settlement when subjected to the loads from stone dumping and backfilling operations. Pile foundations in silty soft soil regions often encounter the NSF on the pile sides due to large-scale deep backfilling, leading to excessive settlement and damage to wharf structures. Consequently, mitigating the NSF resistance in piles has become a critical challenge in applying pile foundations to under-consolidated clayey sites.

The concept of THE NSF in pile foundations was first introduced in the 1930s by Terzaghi, who provided simple calculation formulas. Over the years, numerous researchers have conducted in-depth studies on the NSF of pile foundations, focusing primarily on four aspects: field testing, indoor model testing, numerical simulations, and theoretical research. Concurrently, some scholars have conducted a series of studies in various areas such as under-consolidated soft soil regions, reclaimed land areas, regions with fluctuating groundwater levels, collapsible loess regions, and permafrost zones. These studies have provided substantial technical support for engineering design and construction.

Indoor model testing is a commonly method for studying the NSF on pile foundations. Numerous researchers have investigated the mechanical characteristics of piles, settlement changes, and consolidation settlement of the surrounding soil. Leung et al.¹ conducted centrifuge model tests to thoroughly investigate the effects of axial loading on the load transfer characteristics along the pile due to locked-in the NSF in consolidating clay. This research identified the influence of pile tip conditions (end-bearing or rock-socketed), the length of rock-socket, and the magnitude of load applied to the pile. Zhang et al.² carried out a model test on the NSF for super-long piles, deriving the temporal variation of the NSF and pile tip resistance, and inferring the location and changes of the neutral point from the pile axis force curve. Huang et al.³ performed experimental studies on pile body stress, pile-top displacement, and layered settlement of soil under different surcharge levels, discussing the depth of the neutral point and the group effect of the NSF. Huang et al.⁴ designed and conducted model tests on the NSF of pile groups in sandy soil, studying the pile body stress, pile-top displacement, and layered settlement of soil under different surcharge loads. Kog⁵ carried out a series of centrifuge tests on axially loaded piles in consolidated layered soils to better understand the impact of the NSF on pile settlement and the position of the neutral plane. Mashhour and Hanna⁶ presented the results of experimental research on end-bearing piles in collapsible soils, aiming to measure soil collapse before submersion and during submersion, as well as related resistance loads on the piles. Wang et al.⁷ utilized centrifuge model tests to simulate different pile spacings in pile raft composite foundations and pile geogrid composite foundations for high-speed railway rigid piles to study the time effect of the NSF. In their studies, a series of regularities regarding the NSF are also obtained. Zhang et al. ⁸ analyzed the impact of the groundwater level on the bearing characteristics of pile groups through a series of model tests, examining the changes in the pile axial force, the NSF, settlement, and pore-water pressure in soils.

In terms of field experiments, Junyoung et al.⁹ conducted foundational research on a pile-soil system, and the NSF in soft soil through long-term field was measured. Wu et al.¹⁰ built upon existing research and established a calculation method for the pile-soil shear displacement based on the monitoring results of pile strains and soil settlement during field tests.

In the realm of numerical simulation, Zhou and Wu¹¹ analyzed the characteristics of the NSF in long tubular piles within deep soft soil foundations through three-dimensional finite element numerical simulations. Chen et al.¹² proposed a calculation method for the NSF of piles in layered soil based on pile-soil interaction, employing consolidation theory and the finite difference method to conduct numerical research under two loading conditions of surcharge on the surrounding soil. Liu et al.¹³ established a two-dimensional axisymmetric model in the finite element program ABAQUS. The finite element analysis on the NSF of a single pile under different conditions was performed. Through systematic parameter analysis, various factors such as consolidation time, pile-soil interface properties, lateral earth pressure coefficient, ultimate pile-soil displacement, surcharge strength, and soil stiffness affecting the neutral plane and distribution of the NSF along the length of the pile were studied. Zhou and Lai¹⁴ used a two-dimensional particle flow program to numerically simulate soil-pile interactions under surface loads. The variation in the NSF in end-bearing piles under flexible distributed loads was also investigated. Morsy¹⁵ employed an axisymmetric finite element model to analyze the problem of the NSF in pile-soil interactions. An extensive parametric analysis was conducted to examine the impact of different factors on the performance of floating piles under downdrag forces. Chiou and Wei¹⁶ established a numerical mechanical flow analysis model based on effective stress using the ABAQUS software. By applying the modeling method to field model tests described in the literature, they verified the appropriateness of their modeling approach.

In terms of theoretical research, Comodromos and Bareka¹⁷ aimed to evaluate the impact of the NSF on pile foundations through three-dimensional nonlinear analysis of single and group piles. Chen et al.¹⁸ presented numerical solutions for the development of the NSF in piles within nonlinearly consolidating soil under different pile-top loading conditions, and also established a hyperbolic interface model that considers the development of shear strength at the pile-soil interface during soil consolidation and unload processes. Based on the concentric circle shear theory, Kong et al.¹⁹ proposed a simplified method for analyzing the NSF calculation of special-shaped piles considering pile-soil interaction. The accuracy of the proposed simplified method was verified using a numerical simulation model under the same conditions. Wu et al.²⁰ derived a semi-analytical solution to predict the development of the NSF in piles caused by the consolidation of newly filled soil in reclaimed land areas. The entire fill consolidation process was simulated by coupling a one-dimensional consolidation model before pile driving with a two-dimensional consolidation model.

In research on the mitigation of the NSF on pile sides, Xing and Liu²¹ conducted multi-pile immersion tests in the Lanzhou region and analyzed the factors affecting the NSF in pile foundations in collapsible loess areas. They concluded that an increase in the natural water content and dry density reduced the collapsibility of the loess, rate of immersion settlement, and the NSF on the piles. They suggested that, in engineering applications, the adverse effects of the NSF on pile foundations could be reduced by pre-wetting and surcharging to improve the collapsibility of loess. Shin et al.²² proposed an insertable component within the pile to respond to ground deformation. A series of model tests were also conducted to verify the performance of the component. Chai et al.²³ conducted a series of non-immersion and immersion tests to study the settlement, axial force, and lateral skin friction of piles with steel casings in loess under controlled conditions. The results showed that the presence of steel casing reduced the damage to pile foundations in collapsible loess, thereby providing theoretical support for the application of piles in loess areas.

Although extensive research has been conducted on the issue of the NSF in pile foundations, focusing primarily on the impact of different surrounding soils and loading methods on the characteristics of the NSF, there remains a significant gap in research on reducing the NSF resistance in double-sleeve pile foundations. Experimental verification of the applicability of double-sleeve piles in coastal muddy terrains is also limited.

This study takes place against the backdrop of a wharf construction project in Wenzhou, Zhejiang. It primarily conducts experimental research on the NSF characteristics of double-sleeve pile foundations. Comparison of the mechanical characteristics between single pile and double-sleeve pile foundations is also conducted. The study explores variations in the neutral point position of double-sleeve pile foundations and analyzes the impact of time on their mechanical characteristics.

Description of test

Model box and model piles

In this experiment, a cubic steel box with dimensions of 1.8 × 1.8 × 1.5 m (length × width × height) was used. Steel strips, each 10 mm thick, were welded to the box for reinforcement. To facilitate soil statured and drainage, four valves were designed at the bottom of the box, positioned 0.1 m from the edge along the length. Additionally, the inner surfaces of the box were uniformly coated with paint to reduce friction between the soil and the box walls.

As shown in Fig. 1, the indicators are fixed at the H-beam with the magnetic supports. The fixation depths of the indicators can be adjusted with two steel arms. The steel arms are connected by the universal joint shaft, so that the indicators can be located with a designed depth and direction. To ensure its stability, the values of the indicators remain constant in 10 min before recording. Furthermore, the changes in displacement are obtained by the difference between the two readings.

Fig. 1.

Fixation of dial indicators.

The model piles were made of organic glass, each 95 cm long with a diameter of 30 mm. The elastic modulus of the organic glass was 3 × 10⁶ kPa. The 45 cm-length outer sleeve was also made of organic glass, with a diameter of 42 mm and a wall thickness of 2 mm. The model piles and the sleeves are roughed to increase the friction of the surfaces, as shown in Fig. 2. In this experiment, four groups of piles were symmetrically arranged within the model box. Two groups consisted of single piles and the other two were double-sleeve piles. To better simulate the interaction between the piles and soil particles, both the model piles and sleeves were rubbed using 240-grit sandpaper before testing, creating a more significant friction effect.

Fig. 2.

Schematic of pile and sleeve.

As mentioned above, the organic glass rod is used in this test. However, the surface of organic glass is very smooth, and the friction at the test pile is small. Thus, the surfaces of the test piles were roughed by the sandpaper to increase the friction. For the same reason, the outside and inside surfaces of the sleeves were roughened.

Soil types

Due to the significant influence of the silt on the NSF at the pile, the silty soil used in the laboratory model test was sourced from an engineering site in Wenzhou, China, as shown in Fig. 3. According to a geological survey, five soil types are present at the site. The initial height of the silt layer was designed to be 19.9 m, which increased during the service life of the structure. The sediment siltation accumulates at a rate of 1.2 m per year, indicating significant drag on the pile foundation due to the silt. The silt used in this test was taken from the engineering site, as shown in Fig. 4. During the transportation, the silt is reserved in buckets with the PVC film covered to prevent water evaporation.

Fig. 3.

Schematic diagram of the project site.

Fig. 4.

On-site sampling of silt.

In view of the soils at offshore areas are saturated, the physical and mechanical parameters of the soils are also test under a saturated condition, as shown in Table 1. Three types of soil—pebbles, sand, and silt—were layered in the model box. The heights of the silt, sand, and pebble layers were 60 cm, 20 cm, and 60 cm, respectively.

Table 1.

Parameters of soils^a.

Type	Value
Water content of silt, W1 (%)	63.2
Water content of sand, W2 (%)	12.3
Water content of pebble-sand, W3(%)	10.7
Unit weight of silt, γ1 (kN/m3)	17.2
Unit weight of sand, γ2 (kN/m3)	15.9
Unit weight of pebble-sand, γ3 (kN/m3)	22.4
Void ratio of silt, e1	1.62
Void ratio of sand, e2	0.64
Void ratio of pebble-sand, e3	0.58
Liquidity index of silt, IL	1.55
Compression modulus of silt, Es (MPa)	2.09
Specific gravity of sand, Gs	2.45
Maximum dry density of sand, ρdmax (g/m3)	1.72
Minimum dry density of sand, ρdmin (g/m3)	1.38

^aThe geotechnical test is conducted in accordance with the JB/T 50123–2019 ²⁴.

Pile installation and load condition

The piles and the sleeves are assembled as a part before the soils filling. With the purpose to fixation, the 6 mm-gap between the pile and the sleeve is filled with iron wire. The iron wire is selected due to its lightweight and flexibility. Also, the iron wire will not occupy much space, and the silt can flow into the gap easily. After the double-sleeve pile installation, the iron wire is taken from the gap carefully. The location of the iron wire will be occupied with the silt soon. When worked as an end-bearing pile, the depth of the pile end entering the sand is designed in accordance with the corresponding the standard²⁵.

Subsequently, sand was introduced into the model box to a depth of 20 cm and compacted. The relative density D_r of 0.65 is determined by the geological survey report of the project. The targeted relative density ρ_d of the sand layer is achieved by a small manual compactor. According to the Eq. (3), the dry density at the relative density D_r of 0.65 can be obtained as 1.58 g/cm³. The maximum dry density ρ_dmax and the minimum dry density ρ_dmin are 1.72 and 1.38, respectively. Therefore, each layer was compacted at 200-mm thickness using a sand mass of 455 kg, calculating by Eq. (2).

$$D_r=\frac{({\rho }_d-{\rho }_{dmin}){\rho }_{dmax}}{({\rho }_{dmax}-{\rho }_{dmin}){\rho }_d}$$ 1

$${\rho }_d=\frac{m}{V_0}$$ 2

where V₀ is the volume corresponding to a 20 cm-height of the model box. It should be point out that the relative density in this test should be slightly higher than 0.65, as not considering the volume of piles. After that, the water was added by the four valves at the bottom of the model box, and the water level is flush with the sand surface. The sand is soaked to simulate ocean environment. Besides, the settlement marks were embedded at a depth of 15 cm within the sand layer. Finally, the silt was filled to a depth of 0.6 m, with settlement marks embedded at depths of 0.4 m, 0.3 m, and 0.2 m, respectively.

For the installation of the double-sleeve pile, a pile and a sleeve are assembled as a part in advance. It is worth mentioning that the gap between the pile and the sleeve is 6 mm, which is filled with iron wire. The iron wire is selected due to its lightweight and flexibility. Also, the iron wire will not occupy much space, and the silt can flow to the gap easily. After the double-sleeve pile installation, the iron wire is taken from the gap carefully. The location of the iron wire will be occupied with the silt soon.

Previous studies have demonstrated significant effects of particle size on the bearing capacity and friction resistance of piles, which were considered in this test. The soil particle size was smaller than 0.075 mm, and the ratio of the pile diameter to the soil particle diameter was greater than 23. The minimum distance between two piles were eight times the pile diameter D, and the minimum distance from the pile side to the box wall was greater than 8D. The distance from the pile end to the inner surface of the model box was 55 cm, which was 18 times the pile diameter. Therefore, boundary effects can be considered negligible in this experiment. Schematics of the single and double-sleeve pile models were illustrated in Fig. 5. In addition, a cap was fixed on the pile top for convenient loading.

Fig. 5.

Schematic of single and double-sleeve pile model.

Subsequently, the soil-pile model was left to settle for seven days to ensure stable soil settlement before loading. The uniformity of the gap between the sleeve and pile was also examined. To minimize the number of pores and cavities between the sleeve and the pile, the silt was manually vibrated using a steel bar. Then, loads were applied sequentially at the pile head and surrounding soil surface. The loading method at the pile top was based on JGJ94-2008, and a slow loading rate was adopted. Constant weights were used for both the pile head and surcharge loadings. Compared with a hydraulic loading system, the stability of constant weights is superior, allowing for a more flexible arrangement of data collection. Iron blocks of different weights were placed on the pile caps at intervals of 10 min. During surcharge loading, concrete blocks weighing 2.53 kg each were used. Two layers of concrete blocks were placed at each loading level, providing a pressure of 2.64 kPa at the soil surface. Three loading levels, providing a total pressure of 7.92 kPa, were applied during the test. Figure 6 exhibits the step-by-step loading process on the soil surface. It is noted that the uniformity of the pressure distributed on the soil surface should be carefully considered in this test. For this purpose, the bricks are placed at the planks on the soil surface to provide the pressure as uniformly as possible.

Fig. 6.

Step-by-step loading at soil surface.

Fiber Bragg gratings (FBG) measurement

The FBGs are calibrated before the test. The FBGs are produced by Jemetech Company, China. The performances of the FBGs are shown in Table 2. The FBGs are installed at the model pile and subjected to the calibration by the tensile test. The universal hydraulic testing machine can provide tensile loads in two ways: one is the displacement loading, and the other is the force loading. The loading scheme is designed as shown in Table 3. To observe the accuracy and reliability of the FBGs, the relationship between stress and strain should be linear for the model pile during the tensile test. According to Hooke’s law, the linear behavior exists below 70 kN-force for the organic glass rod. Therefore, the maximum tensile force is determined as 50 kN in this test.

Table 2.

Basic parameters of FBG in this test.

Item	Details
Wavelength tolerance	± 0.3 nm
Length of grating area	15 mm
Maximum pulling force	100 kPa
Working temperature	− 20 to 120℃

Table 3.

Basic parameters of FBG in this test.

Loading order	Tensile loads (kN)
1	20
2	30
3	40
4	50

Typical relationship between the wavelength and the force is shown in Fig. 7. The coefficient of determination R² is nearly 1, indicating a good linear fitting of the force and the wavelength. Therefore, it can be concluded that the FBGs used in this study is reliable and accurate.

Fig. 7.

Typical calibration curve of FBG.

The axial forces of the test piles were measured using FBGs. Small grooves were symmetrically cut on opposite sides of the test piles for the installation of FBGs. Acrylic adhesive was used to secure the FBGs in place. The installation sites of the FBGs ranged from a depth of 8 cm to 85 cm along the length of the pile, with intervals of 11 cm. A total of 16 FBGs were installed on each pile. The arrangement of the FBGs on the pile is shown in Fig. 8.

Fig. 8.

Illustration of FBGs location at model pile.

The strain of the pile, measured using FBGs, is used to calculate both the axial force and the friction resistance at the measurement point. The axial force on the pile is calculated as follows:

$$Q=E\times \epsilon \times A$$ 3

where Q is the axial force of the pile, E is the elastic modulus of the pile, ε is the strain measured by the FBGs, and A is the cross-sectional area of the pile.

Furthermore, the friction resistance is derived from the mechanical equilibrium equations, which can be expressed as follows:

$$\overline{q}=\frac{Q_{_i^{}}^{}-Q_{i-1}}{\pi d\mathrm{\Delta }l}$$ 4

Where $\overline{q}$ is the friction resistance at the test point, Q_i and Q_i-1 denote the axial forces at adjacent FBGs, and $\mathrm{\Delta }l$ represents the distance between these FBGs, with d being the pile diameter.

Experimental results and analysis

Changes in soil settlement

Figure 9 illustrates the trend of soil settlement at different depths over time. The settlement at depths of 20, 30, and 40 cm increased gradually, with greater settlement observed closer to the surface. At a depth of 75 cm, only a slight increase in settlement was noted over time. The degree of compaction, an important parameter affecting soil consolidation, is influenced by soil type, moisture content, and compaction level. In this experiment, the 0–60 cm soil layer, consisting of silty clay, experienced increased overburden pressure with depth, leading to higher compaction degrees and reduced settlement. The 60–80 cm soil layer, composed of sandy soil located at a deeper level, exhibited a much higher degree of compaction compared to the silt layer, showing almost no change in settlement as depicted in the figure.

Fig. 9.

Soil settlement with time.

Figure 10 presents the distribution of settlement rates for different soil layer depths within 383 h. Generally, the closer the silty layer is to the surface, the higher the settlement rate. Within the first 0–200 h, the settlement rate of the silty soil decreased slowly and stabilized after 200 h, reflecting the time effect on the consolidation settlement rate of the silty soil, which decreases gradually over time. The sandy soil layer showed almost no settlement, with a settlement rate close to 0.

Fig. 10.

Settlement rate of soil with time.

Axial force distribution on single pile

Figure 11a, b show the distribution of the axial force in the pile body under different surface loads when vertical loads of 246 N and 529 N, respectively were applied to the pile top. It is evident that with only the pile-top load, the axial force in the pile body decreased gradually with increasing depth. Upon initiating the surface load on the soil, the curve representing axial force distribution in the pile changed significantly, typically assuming a right-leaning "D" shape with smaller axial forces at the top and bottom and larger values in the middle, showing a pattern of first increasing then decreasing. As the load on the soil increased, the curve shifted further to the right. The axial force at each depth in the pile rose, indicating a positive correlation between the magnitude of the axial force and the soil load. Under most conditions, the maximum axial force occurred at an entry depth of 41 cm, beyond which the axial force rapidly decreased with depth. After 73 cm, the axial force declined slowly, with a relatively flat curve, similar to the trend observed when only the pile-top load was applied. This indicates a positive correlation between the magnitude of the soil load and the axial force at various depths in the pile.

Fig. 11.

Axial force of ordinary pile under pile top loads.

Additionally, we note that under a pile-top load of 529 kN and a soil load of 2.64 kPa, the maximum axial force in the pile occurs at 30 cm, with a slight reduction at 41 cm compared to the 30 cm mark. Under the same pile-top load, the maximum axial force under soil loads of 5.28 kPa and 7.92 kPa occurs at 41 cm. When the soil load is 2.64 kPa and the pile-top load is 246 kN, the position of the maximum axial force remains at 41 cm. This phenomenon indicates that increasing the pile-top load can cause a slight upward shift in the position of the maximum axial force in the pile. Therefore, applying a larger load to the pile top without protective measures around the pile is not suitable for reducing the NSF in the pile.

In a study by Chiou and Wei¹⁶, it was reported that the pile-top load significantly reduces the depth of the neutral plane. This was only observed in this experiment when the pile-top load was relatively large and the surface load on the soil was small. In the study by Chai et al.²³, where the soil was collapsible, for unprotected model piles under waterlogging conditions and without additional surface loads on the soil, the axial force curve with depth also exhibited a “D” shaped distribution. With a larger pile-top load, the position of the neutral point shifted slightly upwards. However, after additional surface loads on the soil, the distribution of axial force in the pile remained “D” shaped. Under the same pile-top load, the axial force continued to increase as the additional load increased. With a larger pile-top load, the position of the neutral point remained unchanged; however, with a smaller pile-top load, the position of the neutral point began to move downwards as the additional load increased. The patterns presented by the pile-top and surface loads on the soil in their study were generally consistent with those found in this experiment.

In addition, the allowable bearing capacity of the model pile should be analyzed by two aspects: the pile settlement and pile damage. The purpose of this study is to obtain the regularity of the NSF at different loading conditions. Also, the protective effect of the pile sleeve is another objective of this study. The largest load at the pile top can be calculated as 748.76 kPa, which is much less than the damage strength of the pile. Although the settlement might be large for the model piles, the regularity obtained is still valuable and meaningful.

Skin friction of single pile

The skin friction resistance of single pile as shown in Fig. 12. When only the top load of the pile was applied, the skin friction experienced by the pile was entirely positive. This indicates that under the sole action of the top load, the settlement of the soil due to its own weight was minimal, and the settlement of the pile body exceeded that of the adjacent soil, hence no significant NSF occurred. The skin friction curves fluctuated under both top load conditions, with gentler fluctuations observed when the top load was 246 kN. This variation is a consequence of the differing layered properties of the soil, as well as variations in density and compactness within each layer.

Fig. 12.

Friction distribution of pile under different vertical loads.

Moreover, when the soil was subjected to surcharge loads, a noticeable change in the skin friction of the pile body was observed. The overall trend indicates that the NSF increases with the depth of the pile foundation, peaking at 20 cm before gradually diminishing and reaching zero near the 40–50 cm. With increasing depth, positive skin friction developed, peaking at 75 cm, and then sharply declined until it approached zero at the bottom. When the top load remained constant and the surcharge load on the soil increased, most measurement points on the pile body experienced a slight increase in the NSF, and the neutral point shifted slightly downwards with the increased surcharge load. Conversely, when the soil load was constant and the top load increased, the neutral point shifted slightly upwards. The external load is the primary factor affecting the depth of the neutral point. The maximum NSF occurred at 19 cm, and the maximum positive skin friction was at 73 cm; these two points were located in the silt and sand layers, respectively. This phenomenon occurs because the upper silt layer is significantly affected by the surface surcharge, resulting in substantial settlement and drag load, which causes the NSF on the pile sides. The settlement in the sand and gravel layers beneath the pile is minimal, leading to positive skin friction.

Zhao et al.²⁶ studied loess with collapsibility and observed two neutral points when only the top load was present and the soil was wetted. The distribution of the pile skin friction resistance above the second neutral point was broadly consistent with that observed in this experiment. The soil profile used in this study consisted of silt-sand-gravel systems, where the silt properties were similar to those of collapsible loess, but the gravel layer lacked collapsibility. Hence, no second neutral point appeared near the bottom of the pile. Chai et al.²³ also conducted research using collapsible loess and found that when both the top load and surface surcharge were present and the soil was wetted, the distribution curve of skin friction for non-protected piles had only one neutral point. The NSF distribution largely matched the results of this experiment, confirming similar behaviors under comparable conditions.

Axial force distribution of double-casing pile

The distribution of the axial force in the pile body under various top loads for the double-casing piles is depicted in Fig. 13. As shown in Fig. 13a, with a top load of 221 N, the axial force within the protected section of the casing remains essentially constant. In the unprotected section, the axial force gradually diminishes under soil loads of 2.64 kPa or 5.28 kPa. However, at a soil load of 7.92 kPa, the axial force initially increases and then decreases in this region. It is suggested that there is an area where pile settlement is less than the consolidation settlement of the soil, resulting in the presence of the NSF on the pile sides. For surface loads of 2.64 kPa and 5.28 kPa, the axial force along the protected section is essentially unchanged, consistent with only applied top load of 221 N. In unprotected section, the axial force continues to decrease. At the soil surface load of 7.92 kPa, the axial force within the protected pile region equals the top load. In the unprotected region, it initially rises then falls, with the maximum value occurring near a depth of 63 cm. As shown in Fig. 13b, with a top load of 517 N, irrespective of the soil load, the axial force within the protected area of the outer casing remained constant along the depth. In the unprotected section, the axial force gradually decreased with depth. Comparing Fig. 13a, b, it is evident that increasing the top load of the pile with additional outer casing protection effectively reduces the NSF on the side of the pile.

Fig. 13.

Friction distribution of double-sleeving pile under different vertical loads.

Concurrently, as shown in Fig. 11a, in the absence of casing protection, the axial force at a depth of 63 cm was approximately 120 N when only subjected to the top load. Upon the application of surcharge loads to the soil, the axial force at this point significantly increased. With a mere load of 2.64 kPa, the value exceeds 320 N, nearly doubling. Conversely, in Fig. 11a, at a soil load of 7.92 kPa, the axial force measures around 250 N, which is less than a 0.7-fold increase compared to the 150 N when solely the top load is applied. Therefore, it can be inferred that the protective casing offers substantial protection to the pile body beneath the protected section. Considering this phenomenon, in practical engineering scenarios where the surrounding soil loads are modest, it may be feasible to reduce the length of the protective casing to conserve materials.

Skin friction of double-sleeve pile

The distribution of the NSF along the shaft of the double-casing pile under different top loads is illustrated in Fig. 14. When only the load was applied at the top of the pile, no NSF was generated. In the protected section of the double sleeve, skin friction was essentially zero. However, in the unprotected section, skin friction occurred. The curve fluctuated more pronounced as the top load on the pile increased. This phenomenon was due to the varying physical properties and settlement amounts of the soil in different layers.

Fig. 14.

Friction resistance distribution of double-sleeve pile under different vertical loads.

Under the two different pile-top load conditions, after applying a load on the soil surface, the axial force distribution in the protected section of the sleeve remained essentially unchanged. In the unprotected section with a pile-top load of 221 N, when the soil surcharge is 2.64 kPa and 5.28 kPa, the axial force curve gradually shifts overall to the left. At 83 cm depth, the data point shifted to the right along with the load increases, showing an increase in skin friction compared with when no soil surcharge was applied. When the soil surcharge is 7.92 kPa, the upper part of the curve exhibiting NSF in the unprotected section shifts to the left. From 74 cm depth, the curve shifts overall to the right, resembling the scenario in Fig. 12 where no casings were used for protection. The distribution of skin friction after the addition of steel casings in the study by Chai et al.²³ is fundamentally consistent with the results of this experiment.

In the unprotected section with a pile-top load of 517 N, no NSF occurred along the pile shaft under any of the three surcharge conditions. When the surcharge is 2.64 kPa, the upper half of the curve in the unprotected section shifts overall to the left, following a trend consistent with that of the soil before any load was applied. It is indicated that the influence of the surcharge on the skin friction of the pile is still relatively small. After a depth of more than 74 cm, the skin friction of the pile increased significantly compared with the situation without a surcharge, with the maximum value occurring at the bottommost measuring point. When the surcharge is 5.28 kPa, the impact of the surcharge on the skin friction grows. The curve of the unprotected section becomes nearly smooth without severe fluctuations, with the skin friction gradually increasing with depth. The maximum resistance located at the bottom. When the surcharge was 7.92 kPa, the effect of the surcharge on the lateral skin friction was the most significant, with the curve of the unprotected section being very smooth and following a trend similar to that when the surcharge was 5.28 kPa.

Time effect analysis

Figure 15 presents the distribution curves of the axial force in double-sleeve piles with depth over different time periods. In Fig. 15a, with a top load of 221 N, the change in axial force within the 0–41 cm depth remained minimal over time, consistently around 221 N. Between 41 and 63 cm depths, there was a trend of gradual increase with accumulated time. After 96 h, the increasing rate of the axial force diminished, resulting in nearly overlapping curves at 96 h, 168 h, and 216 h. This suggests that over time, the consolidation settlement of the surrounding soil exceeded the displacement settlement of the pile, and the soil settlement stabilized after a certain period. In Fig. 1b, with a top load of 517 N, the curve of the axial force variation remains largely unchanged in the upper part. After that, a slow decreasing trend of the axial force can be observed.

Fig. 15.

Distribution of axial force along double-sleeve pile with accumulated in time.

Figure 16 shows the distribution curves of the axial force at various test points along the double-sleeve pile with depth over different time periods. In Fig. 16a, with a top load of 221 N, the axial force at test points not exceeding 63 cm depth increased with time from 0 to 100 h and remained essentially constant thereafter. The test point at 74 cm depth showed a positive correlation with time, with the rate of increase declining between 150 and 216 h. Other depths showed a slight increase in axial force over time. In Fig. 16b, under the 517 N top load condition, the axial force at test points not exceeding 52 cm depth remained stable over time, with nearly overlapping curves. Beyond 63 cm depth, the axial force gradually increased with time. This suggests that the greater the top load of the pile, the shorter is the time required for the axial force in the silt layer to stabilize, and the longer is the time required for the axial force in the sand layer to stabilize.

Fig. 16.

Axial force of double-sleeve pile with accumulated in time.

The variation in skin friction of the double-casing pile foundation over time is shown in Fig. 17. Under the same accumulated time, the NSF of the pile under the 221 N top load was greater than that under the 517 N top load. In Fig. 17a, under the 221 N top load, the skin friction is positive from 0 to 41 cm depth, with little change in the curves over time. Negative friction resistance begins to occur after 41 cm, increasing continuously with time from 41 to 65 cm, and the neutral point is located near 65 cm and gradually moves downward with time. In addition, the NSF still occurs outside the casing. The vertical capacity of pile will be weakened as the appearance of the NSF. Thus, a longer casing is recommended to achieve a higher vertical capacity of the pile. With a top load of 517 N, the neutral point is situated near 50 cm as shown in Fig. 17b, and the patterns of skin friction change are consistent under both conditions.

Fig. 17.

Friction resistance of double-sleeve pile with accumulated in time.

Zhang et al.² also found that the negative friction resistance of ultra-long piles in silt exhibited significant time effects, with the negative friction resistance of the pile body gradually increasing and stabilizing as the surrounding soil consolidated and settled. This effect was also reflected at the neutral point’s depth, which gradually decreased with time and ultimately remained stationary at a certain depth. Wang et al.⁷ arrived at similar conclusions regarding the negative friction resistance and neutral point, showing time effects that were essentially identical to those observed in this experiment.

Discussion

The data for a single pile were interpolated to obtain the lateral friction resistance of a single pile when the pile-top load Q = 517 N. Figure 18 shows a comparative analysis of the negative friction resistance experienced by single piles and double-sleeve piles. As illustrated in Fig. 18, with a larger top load, the negative friction resistance is almost negligible. This phenomenon demonstrates that the double-casing structure can effectively isolate the negative friction resistance on the pile side, thereby playing a protective role in the pile foundation.

Fig. 18.

Comparison analysis of frictional resistance between single pile and double-sleeve pile. The S, D, p and s means single pile, double-sleeve pile, pile top loads and surcharge loads, respectively.

Compared to other research aimed at reducing the negative friction resistance, Xing and L. Liu²¹ proposed that overloading and pre-wetting can enhance the collapsibility of loess, thereby reducing the adverse effects of negative friction on pile foundations. In their study, the negative friction resistance experienced by Pile No. 9, which had a lower collapsibility, was reduced by 45% compared with that of the highly collapsible Pile No. 7. Chai et al.²³ conducted experiments on negative friction resistance of piles in collapsible loess areas. It is demonstrated that the addition of a steel casing virtually eliminated negative friction resistance around the pile, significantly reducing the negative friction experienced by the pile body.

Shawky et al.²⁷ investigated the reduction effects of three different technical methods on negative friction resistance. The regularity of the NSF distributed along the pile inside the sand socket are numerically studied. The NSF mitigating effects of the sand socket are compared with the sleeve, as shown in Fig. 19. Skin friction is normalized both for the sand socket pile and the double-sleeve pile for the convenience of analyzing. Also, the length of the double socked pile is linearly scaled according to the length of the double-sleeve piles. In the case of the sand socket pile, a single soft clay layer distribution is arranged. It is shown that a better protection of the sand socket is obtained nearby the soil surface, as less negative skin friction occurs along the pile length of 0 ~ 20 m. When the pile length is larger than 40 m, the negative skin friction disappears for the double-sleeve pile. The skin friction increases significantly, which contributes to improving the vertical bearing capacity. In contrast, the negative skin friction extensively distributed along the sand socket pile, due to the greater depth of the soft clay.

Fig. 19.

The mitigating of NSF by double-sleeve.

Through this model experiment, it was evident that the skin friction of the pile body protected by the sleeve was smaller and remained essentially unchanged, proving the effectiveness of the double-sleeve structure. This experiment demonstrated that the soil layer properties, pile foundation loads, and surcharge have a significant impact on the skin friction around the pile, and further obtained the variation patterns of the pile foundation skin friction under different conditions. In contrast, the soil layer design used in this experiment is common in coastal areas, providing theoretical support for engineering applications of double-casing piles in coastal regions.

Conclusions

Based on model tests of conventional single piles and double-casing piles, this study investigated the variation patterns of the axial force and negative friction resistance along the pile under different conditions in soft silty soil and explored the time effect on the negative friction resistance. A comparative analysis of the mechanical characteristics of conventional single and double-sleeve piles was conducted. The main conclusions are as follows:

• (1) Through long-term cumulative monitoring of soil settlement, it was found that the settlement amount of soil at different depths gradually increased over time, with the rate of settlement decreasing and eventually stabilizing.

• (2) As the surcharge on the soil surface increased, the axial force and negative friction resistance along the single pile continuously increased, with the neutral point moving downward. When the soil surface surcharge was constant, an increase in the surcharge at the pile top led to a decrease in the additional axial force, causing the position of the neutral point to rise.

• (3) For the double-sleeve pile, the axial force remained unchanged within the protected section. For the unprotected section, the axial force along the depth of the pile gradually decreased under the action of the surcharge. When the surcharge was large, the axial force showed a trend of initially increasing and then decreasing, resulting in negative friction resistance. Owing to the time effect in soil settlement consolidation, both the axial force and lateral friction resistance of the pile gradually stabilized over time.

• (4) By comparing the axial force and lateral friction resistance of conventional single piles, it was evident that the use of an outer casing in double-casing pile foundations effectively mitigated the negative friction resistance by isolating the settling action of the soil. Therefore, in regions with thick soft soil, particularly in coastal silty land areas, double-casing pile foundations can be used to overcome negative friction resistance, providing a safety guarantee for engineering construction.

Author contributions

The authors confirm contribution to the paper as follows: study conception and design: Nie Zhichao, Chen Zhihua; data collection: Cao Yang, Wang Lu; analysis and interpretation of results: Liu Xianpeng; draft manuscript preparation: Wang Lu. All authors reviewed the results and approved the final version of the manuscript.

Data availability

All data generated or analysed during this study are included in this published article land its supplementary information files.

Declarations

Competing interests

The authors declare no competing interests.