Investigation and numerical simulation study on the vertical bearing mechanism of large-diameter overlength piles in water-enriched soft soil areas

: With the development of urbanization, there is an increasing demand for higher land utilization rates, leading to the emergence of high-rise residential and commercial complexes. Additionally, in coastal areas, the presence of soft soil and low bearing capacity of the foundation necessitate higher foundation bearing capacity. Large-dia-meter, super-long piles have been widely employed in engineering projects to address these challenges e ﬀ ectively. This study analyzes their vertical bearing characteristics through ﬁ eld load tests and determines vertical load distribution and transfer mechanisms by using Brillouin Optical Time Domain Re ﬂ ectometry. A numerical computation and analysis method based on PLAXIS 3D was established, examining the e ﬀ ects of parameters such as pile diameter, length, and soil modulus on the vertical bearing characteristics. Results indicate that large-diameter, super-long piles mainly bear loads through side friction, with the tip bearing less load. As load levels increase, axial force increases linearly above 40 m depth and becomes nonlinear below. Frictional resistance is signi ﬁ cant below 40 m at 3,700 kN load. Parameter analysis shows that increasing pile length and diameter enhances bearing capacity, suggesting this method to improve pile foundation capacity in engineering.


Introduction
In accordance with statistical data, China witnesses the annual installation of more than 10 billion linear meters of pile foundations, emphasizing the magnitude of this crucial engineering practice.Pile foundations exhibit distinct bearing capacity features in different geological strata.The manifestation of both lateral and end-bearing resistance is correlated with variables encompassing pile length, pile diameter, and pertinent soil properties.In recent years, as building heights and structural loads have continued to surge, the pile top is subjected to increasingly substantial loads.This necessitates an expansion of pile dimensions, both in terms of length and diameter, to attain higher bearing capacities.Therefore, the bearing capacity of large-diameter and super-long piles is gradually emerging in engineering.The eastern region of China experiences a typical subtropical monsoon climate characterized by abundant rainfall and high levels of soil moisture.As a result, the predominant soil type in this area is soft soil enriched with water.Therefore, investigating the bearing capacity of large-diameter super-long piles in deep soft soil holds substantial practical significance for engineering applications.
Numerical simulation offers cost-effective and versatile advantages in simulating various scenarios.Over the past 5 years, some researchers [1][2][3][4][5][6][7] utilized numerical simulation software such as Marc, Abaqus, and FLAC 3D to simulate the load-bearing characteristics of large-diameter piles.They developed several computational models, including a vertical load-carrying capacity model for rocksocketed piles based on pile-side friction softening and a three-dimensional pile-soil model in rectangular coordinates, yielding valuable insights [8][9].However, the applicability of these numerical analysis findings in deep soft soil regions remains to be validated through field experiments.
Many scholars have conducted experimental studies on the geological and technical characteristics of soft soils.Some researchers [9][10][11][12] have investigated the properties of soft soils through indoor triaxial tests, direct shear tests, and other methods, exploring variations in shear strength with depth, as well as the effects of complex stress paths.They have also developed two-dimensional soft soil foundation models, enhancing nonlinear consolidation models.Focusing on the characteristics of soft soils in Fujian Province, Ouyang et al. [13] conducted a detailed statistical analysis on experimental data from Fuzhou Metro Line 2, revealing that under consolidated undrained conditions, the shear strength of soft soil exhibited a negative nonlinear correlation with natural moisture content, natural void ratio, liquidity index, and compression coefficient, while showing a positive linear correlation with compression modulus.Xie et al. [14] found that the consolidation yield stress in Fuzhou soft soil layers increased with depth.Different depths exhibited similar consolidation yield pressures and effective overburden pressures, with an over-consolidation ratio of around 1, despite no significant correlation with depth for compression modulus, liquid limit, and plastic limit.
At the same time, within the field of civil engineering scholarship, significant field investigations have been undertaken to examine the bearing characteristics of large-diameter, super-long piles.In the field of civil engineering, a considerable number of field experiments have been conducted concurrently to investigate the load-carrying characteristics of large-diameter, super-long piles.Early researchers [15][16][17] conducted experimental studies on various types of such piles, aiming to determine parameters such as failure moment, ultimate bearing capacity, and load-settlement curves in soft soil, thus obtaining preliminary insights into the failure modes and load-carrying properties of these piles.Subsequently, Vijayakanthan et al. [18], through centrifuge model testing, extensively discussed the influence of embedment depth on the flexural performance of large-diameter piles.Their findings revealed that increasing the embedment depth enhances both lateral and flexural resistance, particularly for piles with relatively shallow embedment depths.Ma et al. [19], through field static loading tests on ultra-long large-diameter bored piles, derived the loadcarrying capacity and settlement patterns of such piles under vertical loading in the region.Yan-Cheng [20] and colleagues, combining numerical simulations with field experiments, conducted a comprehensive investigation into the complex load-carrying performance of drilled shafts under vertical loading.They validated their numerical models by verifying measured load-displacement curves obtained from self-balancing field tests.Other researchers have also conducted experimental studies on the vertical load-bearing characteristics of large-diameter, super-long piles.These studies include but are not limited to research on the load-bearing characteristics of large-diameter, super-long prestressed concrete piles in silty soil foundations [21] and centrifuge tests on the monotonic and cyclic lateral characteristics of large-diameter slender piles in sandy soil [22].These experiments have targeted various soil environments and materials, yielding some results [23][24][25][26][27][28].However, there is still a gap in research on the vertical load-bearing mechanisms of large-diameter, super-long piles in saturated soft soils.
The length and diameter of piles exert significant influence on the load-carrying characteristics of large-diameter, super-long piles.Pile length affects the stiffness of the pilesoil system, thereby influencing the distribution of lateral soil resistance [29].While increasing pile length may enhance its bearing capacity to some extent, it can also markedly affect pile deformation, potentially deviating from deformation requirements.Within a certain range of pile lengths, increasing pile diameter can enhance the pile's bearing capacity.However, there exists an optimal pile diameter beyond which the ultimate bearing capacity does not significantly improve.Moreover, in practical engineering, longer pile lengths and larger diameters entail higher construction costs [30][31][32][33][34]. Thus, optimizing the cost-effectiveness of large-diameter, super-long piles and selecting appropriate pile lengths and diameters are critical considerations in engineering projects.
Currently, scholars have conducted a series of model tests and field experiments on various pile types, including driven cast-in-place piles, precast reinforced concrete (PHC) piles, and steel pipe piles, to investigate the vertical load-carrying performance of large-diameter piles.These studies have yielded valuable insights into the load transfer mechanisms of these piles.However, research on the numerical methods and analyses regarding the vertical load-carrying characteristics of large-diameter, super-long piles in deep soft soil remains incomplete.Parameters such as pile diameter and length significantly influence the vertical load-carrying capacity of large-diameter, super-long piles.Therefore, further numerical analyses are required to supplement existing research and provide a comprehensive understanding of the factors affecting their performance.
This article comprehensively elaborates the research content, experimental methodology, test process, and findings gained from the on-site trial of the vertical bearing characteristics of cast-in-place piles subjected to static load conditions.By the loading of a single pile, experimental results were obtained, which showed the distribution curve of axial force, side friction resistance, and pile tip resistance exhibited by the subjected test pile.The results of the distribution map are analyzed, and the vertical load transfer law of the test pile in soft soil enriched with water area is obtained.A Plaxis3D model was established, and parameter analysis was conducted to ascertain the influence of factors such as pile length and diameter on the vertical bearing capacity of the piles.

Field test
This trial is grounded in the Fuzhou Metro Smart Park project, an urban infrastructure within Fuzhou, which is situated at the Henggang depot of the Fuzhou Rail Transit Line 6.It is positioned within the geographical confines delineated on the south of Mazhang Road and the northeast of Lianbing Port.
The Henggang depot is characterized by its predominant double-component structure, concluding both an operational sector and a maintenance sector.The present test unfolds within the region of the depot's Metro section, wherein the foundational infrastructures are road tracks.
To confirm the load distribution of the test pile, this study employs distributed optical fiber monitoring technology.In contrast to conventional methodologies, optical fiber detection technology offers distinct advantages, including enhanced monitoring precision, durability, straightforward installation, and better stability.This technology enables precise measurement of axial force and pile side friction during the loading procedure, with the aim of offering valuable results to inform the design and construction of engineering pile foundations.
Brillouin scattering [30] is subject to the influence of both strain and temperature variations.When changes in temperature or the imposition of axial strain occur along the optical fiber, they produce a corresponding drift in the frequency of the backscattered Brillouin light within the fiber.This frequency shift has a linear correlation with variations in fiber strain and temperature.Consequently, by measuring the frequency shift of backscattered Brillouin (ν B ), the distribution information of temperature and strain along the optical fiber can be obtained.The fundamental principle existing in the strain in Brillouin Optical Time-Domain Reflectometry (BOTDR) is visually delineated in Figure 1.
The linear relationship between Brillouin frequency shift and fiber strain is shown in Figure 2. The slope of the linear relationship depends on the wavelength of the probing light and the type of optical fiber employed, necessitating calibration prior to experimentation.
The strain and Brillouin frequency shift of optical fibers can be expressed as follows: is the drift of the Brillouin frequency at a strain of; v B (0) is the drift of the Brillouin Large-diameter overlength piles in water-enriched soft soil areas  3 frequency at strain 0; approximately 493 MHz (/% strain); ε is the strain of the optical fiber.
The BOTDR equipment used in this testing is the AV6419 Optical Fiber Strain Distribution Analyzer developed by the 41st Research Institute of China Electronics Technology Group Corporation.
For the on-site test, strain-sensing optical cables and temperature-sensing optical cables were deployed on the test pile to facilitate optical fiber sensing evaluation.The sensor cables embedded in piles include Steel Rope Sheathed Sensor Cables (GS) and Fixed Point Sensor Cables (DD).GS boasts excellent mechanical properties and high resistance to tensile and compressive forces, making it suitable for various harsh conditions.DD features a unique internal fixed-point design that enables non-continuous, non-uniform strain to be measured in a segmented and homogenized manner, making it ideal for monitoring large deformations.Table 1 presents the types and main performance parameters of these two sensor cables.
Directly laying bare optical fibers on the surface of cast-in-place piles renders them vulnerable to breakage and the subsequent loss of their testing functionality.Therefore, during the trial, the optical fibers have undergone specialized treatment, and empirical evidence has demonstrated that this treatment significantly enhances their tensile strength, resistance to bending, resilience to impact, and fireresistant capabilities.These improvements have been achieved without compromising the fibers' sensing properties.Specific details about the optical fiber sensors are presented in Figure 3, where red markings indicate the strain-sensing optical cables, and blue markings represent the temperature-sensing optical cables.Information regarding the bundling of optical fibers and their placement within the reinforcement cage can be found in Figures 4 and 5.
To safeguard the optical fibers against potential damage at the pile head and the pile bottom, protective conduits have been employed to shield the optical fibers.Further details can be found in Figures 6 and 7.
The optical fiber is positioned alongside the primary reinforcement elements within the reinforcement cage.To   comprehensively appraise the strain distribution within the pile structure, a U-shaped configuration has been employed following research deliberations.This design ensures the optical fiber remains linear and uncurled during the installation process, as shown in Figure 8.

Calculation principles and methods
The scattering light offset measured by the instrument is used to obtain the axial compressive strain of the optical     Large-diameter overlength piles in water-enriched soft soil areas  5 fiber along the pile's length.Since the optical fiber is fixed within the concrete of the pile, under static loading pressure, these two should change synchronously.The axial compressive strain ε(Z) of the pile body concrete, as measured by the instrument, corresponds to the optical fiber's axial compressive strain.Therefore, the axial force σ(Z) in the pile body is given by: where E c represents the elastic modulus of the pile body concrete, the axial force Q(Z) in the pile body is given by: The fundamental differential equation for load transfer in piles is as follows: where q s (Z) represents the pile side friction; Q(Z) denotes the axial force within the pile; and U signifies the circumference of the pile.
where ΔQ(Z) represents the change in axial force between two cross-sections of the pile; ΔZ is the difference in depth between two cross sections of the pile.
Organizing the above equation results in: where Δε represents the change in axial strain between two cross-sections of the pile within a certain soil layer.By utilizing the above equations, calculations can be performed to obtain the strain distribution along the pile, subsequently providing the distribution of pile axial force and pile side friction.These distributions are essential for generating axial force and pile-side friction diagrams.
By correlating the pile head settlement with the applied loads, it is possible to derive the load-settlement curve for the pile under various loading conditions.Furthermore, using the end strain values, it is feasible to determine the end resistance and, consequently, establish the load-sharing ratio between pile side friction and pile end resistance.

Numerical simulation
Using PLAXIS 3D software, a numerical model was established as shown in Figure 9.According to the site investigation report, the soil layers' thickness and material properties were defined.The eight soil layers were categorized into seven soil types.
For the numerical simulation, the soil models were assigned based on their characteristics as follows: 1. Fill soil, silt, and silty clay were modeled using the HSS small-strain model.2. Medium sand and gravelly sand were modeled using the Mohr-Coulomb model.3. Completely weathered granite and highly weathered granite were modeled using the linear elastic model.
Specific material parameters are provided in Tables 2  and 3.
A model pile is established at the center of the soil mass using the cylinder command, as illustrated in Figure 10.The pile material is modeled as a linear elastic non-porous constitutive model.Based on actual engineering conditions, the concrete of the pile has a strength grade of C35, with an elastic modulus of 3 GPa, a Poisson's ratio (υ) of 0.19, and a   In the mesh options, medium density is selected for element distribution and the enhanced mesh refinement option is enabled.The numerical simulation model is shown in Figure 11.
Construction is carried out in stages.In the initial stage, the calculation type is set to the K0 process.The pile foundation model is not selected, and soil equilibrium is awaited.Other settings remain at their default values.In the subsequent step, the interaction between the pile and the soil is activated, the pile model is embedded, the specified concrete material is selected, and surface loads are applied.Subsequent loading is performed incrementally until reaching 7,400 kN, with displacement not reset at each step.

Results and discussion
Based on the aforementioned experimental and numerical simulation methods, we have obtained several results.The following sections present the experimental and numerical simulation results, followed by a discussion of the experimental findings.

Field test 3.1.1 The optical fiber monitoring results
In this fiber optic monitoring setup, optical fibers were arranged in a U-shape, with fibers located on the left side of the pile body near the lead side and the other end on the right side of the pile body.As mentioned in the previous section, the axial force of the pile body can be calculated based on strain variations.The measured strain data and the calculation of frictional resistance are presented in Appendix A.

Temperature change curve
The temperature change distribution curve is ascertainable through the temperature sensor, shown in Figure 12.
Throughout the loading process, temperature variations oscillate within the narrow range of −1 to 1°C, exhibiting minimal fluctuations.Consequently, when assessing the factors influencing optical fiber strain, the impact resulting from temperature variations can be disregarded.

Load-settlement curve
As depicted in Figure 13, the global curve demonstrates a gradual and predominantly linear transformation, devoid   Large-diameter overlength piles in water-enriched soft soil areas  7 of a conspicuous abrupt decline, confirming that the model pile does not achieve its ultimate bearing capacity when subjected to the maximum load.

Pile shaft axial force
A U-shaped arrangement is employed in the optical fiber monitoring setup.The optical fiber is located proximate to the leading edge positioned on the left side of the pile body, while the opposite end is situated on the right side of the pile body.By assessing strain variations, the axial force acting upon the pile body can be calculated.Consequently, axial force distribution profiles on both the left and right sides of the pile body have been obtained, as depicted in Figures 14 and 15.
Based on the conducted test, the load transfer mechanism of super-long cast-in-place piles can be elucidated.At a consistent depth, the axial force within the pile amplifies in concurrence with the increment in applied load.Simultaneously, it experiences a reduction longitudinally along the pile's length.When the burial depth is above 40 m, the axial force alteration conforms to an approximately linear pattern.As the pile traverses into sandy soil layers, there is an obvious surge in the frictional coefficient, resulting in an escalation of pile side friction and marked variations in axial force, with a concurrent attenuation in the slope of the curve.Upon piercing rock strata, for piles exceeding 50 m in depth, the lower rock stratum plays an additional end-bearing role, leading to a diminishment in    pile side friction and a gradual decrease in the rate of axial force change.For piles buried to depths exceeding 55 m, the axial force represents only about 15% of the load at the pile's top.This underscores the dominant contribution of pile side friction in the bearing load, with the load shared by the pile's end-bearing layer being comparatively less.
The decay rate of the axial force within the pile shaft is closely linked to the applied load at the pile's top.When subjected to small loads, the axial force represents an approximately linear trend.This phenomenon arises from the limited pile-soil displacement, wherein the pile side friction remains below its peak capacity.Consequently, the axial force attenuation within the pile shaft progresses at a comparatively slower pace, and no discernible attenuation disparity between soil strata is apparent, resulting in an almost linear axial force curve.
In contrast, when the applied load at the pile's top surpasses the threshold of 4,440 kN, the pile side friction progressively attains its full effectiveness.So in comparison to the conditions involving smaller loads, the decay of the axial force within the pile shaft accelerates.

Pile side friction
The distribution pattern of pile side friction is graphically represented in Figures 16 and 17.Additionally, the layered distribution of pile side friction is illustrated in Figures 18  and 19, while the distribution curve detailing pile end resistance is presented in Figures 20 and 21.
At pile summit loads of 1,440, 2,220, and 2,960 kN, the lateral friction distributed along the length of the pile exhibits a gradual reduction.This behavior stems from the progressive transmission of deformation from the upper regions of the pile downwards.As a result, the relative displacement trend between the upper portion and the surrounding soil, especially within regions buried beyond a depth of 40 m, surpasses the section buried at depths less than 40 m.This discrepancy contributes to the gradual diminution of lateral friction along the pile's length.
However, when the applied load exceeds 3,700 kN, the frictional resistance within the strata situated at a burial depth of 40 m or exceeding plays an increasingly significant role.Resulting lateral frictional resistance in the lower sections of the pile increases apparently.The magnitude of frictional resistance is essentially tied to the applied load, and the geotechnical properties of the soil layers also significantly influence the manifestation and variations of frictional resistance.An analysis of the test findings reveals that when the applied load exceeds 3,700 kN, the lateral frictional resistance within the upper section of the pile (situated at a depth less than 40 m) surpasses that within the lower pile sections (situated at a depth greater than 40 m).This observed discrepancy can be attributed to the specific characteristics of the underlying soil stratum, which leads to the pile's lateral frictional resistance in sandy soil exceeding that in soft soil.The peak lateral friction is manifest within the (muddy) gravel sand layer, attaining a maximum lateral friction value of 51.78 kPa.
As the applied load escalates, there is a concomitant increase in the pile end resistance.However, the percentage of the total load attributed to pile-end resistance experiences a gradual reduction, signifying a diminishing role of pile-end resistance.Super long piles primarily rely on side friction to bear the primary load, with a significant proportion of the load being allocated to pile side friction.

Model validation 3.2.1 Load-displacement curve
A comparison of the load-settlement curves obtained from numerical simulation and experiments (as shown in Figure 22)    is presented.From the figure, it can be observed that the numerical simulation load-settlement curve exhibits a good similarity with the experimental load-settlement curve, indicating the reasonability of the model and soil parameters established in the numerical simulation.Since the entire simulation process did not reach the ultimate bearing capacity, the load-settlement curve appears to be nearly linear without any nonlinear portions, aligning well with the experimental conditions.

Distribution of pile axial force
From Figure 23, the axial force gradually decreases along the length of the pile, with an abrupt change in axial force occurring at a depth of 40 m.In the lower portion of the pile, the rate of axial force change is higher than that in the upper section.This phenomenon can be attributed to the fact that the soil composition below 41.3 m consists of sand and rock layers, leading to an increase in side friction.The increased side friction not only provides lateral resistance but also contributes to the upward end bearing capacity, resulting in a more significant change in axial force.
This observation is in good agreement with the experimental results, further confirming the correctness of the model setup.

Lateral pile friction
Using the loading conditions of 4,440 and 5,180 kN, a comparison was made between the lateral pile friction distributions obtained from the experiments and those obtained through numerical simulations (Figure 24).The trends in lateral friction obtained from numerical simulations are in good agreement with the experimental results, with the maximum lateral friction occurring in the gravelly sand (with clay) layer.This further validates the reliability of the model.

Parameter analysis 3.3.1 Pile length
The performance of large-diameter and ultra-long piles in soft soil regions, particularly the influence of pile length on  both side and end resistances, is a crucial aspect of geotechnical engineering.In practical applications, the design of pile lengths is tailored to meet specific load-bearing requirements.This section employs the PLAXIS 3D numerical simulation software to delve into the repercussions of varying pile lengths on vertical load-bearing capabilities.The objective is to furnish valuable insights for the strategic management of future construction endeavors and to serve as a foundational reference for subsequent research endeavors.
While maintaining consistent soil parameters, the experiment systematically alters the pile length, ranging from 58.9 to 83.9 m.This deliberate variation enables the examination of load-settlement characteristics and load-sharing percentages, thereby unraveling the nuanced impact of changing pile lengths on the load-bearing performance of large-diameter and ultra-long piles.
By progressively escalating the applied load within the model, load-displacement curves for diverse pile lengths are obtained, as depicted in Figure 25.The overarching linearity of these curves suggests that the ultimate bearing capacity has not been attained.Notably, as the load intensifies, the gradual change characteristics become more pronounced, signifying an incremental surge in ultimate bearing capacity.This phenomenon is expounded by the diminishing mobilization of side friction and the concomitant deformation of the soil beneath the pile with increasing pile length.
When the pile length is 78.9 and 83.9 m, the two curves are essentially superimposed when the load is less than 4,440 kN, with a minimal difference.As the load exceeds 4,440 kN, the settlement difference gradually increases, but it is significantly less pronounced compared to the range of pile lengths from 53.9 to 83.9 m.This indicates that settlement tends to stabilize with the increasing pile length, suggesting the presence of a critical pile length.Beyond this critical length, further increases in pile length do not induce additional settlement changes.Therefore, in the design of large-diameter and ultra-long piles, solely increasing pile length is insufficient to control settlement; other factors must be considered to enhance the pile's ultimate load-bearing capacity.
Crucially, the analysis underscores the presence of a critical pile length, beyond which further elongation yields diminishing returns in terms of settlement variation.Consequently, the design strategy for large-diameter ultra-long piles necessitates a holistic approach that transcends the mere elongation of pile length, emphasizing the imperative to enhance the   pile's ultimate bearing capacity through alternative engineering measures.This discernment is integral for informing optimal engineering decisions in the realm of geotechnical design and construction.
Under the influence of various load levels, as depicted in Figures 26 and 27, the load-sharing ratio between side friction resistance and end-bearing resistance for different pile lengths is delineated.Across all pile lengths, the predominance of side friction resistance in large-diameter ultra-long piles exceeds 89.5%, indicative of their friction pile behavior.The overall load-sharing ratio curve manifests a non-linear trend, characterized by a rapid evolution in the load-sharing ratio when the load is below 3,700 kN, accompanied by a gradual augmentation in end-bearing resistance.Conversely, when the load surpasses 3,700 kN, the load-sharing ratio curve tends towards stabilization, denoting the near-complete mobilization of side friction resistance.
With consistent load levels, an elongation in pile length correlates with a heightened proportion of side friction resistance relative to the load, juxtaposed with a diminishing proportion of end-bearing resistance, thereby impeding load transmission to the pile base.Below the 3,700 kN threshold, variations in load-sharing ratio relative to pile length are marginal, owing to minimal pile-soil sliding tendencies and underutilization of pile-side friction resistance.Notably, as the pile length exceeds 78.9 m under loads surpassing 3,700 kN, the reduction in end-bearing resistance sharing remains uniform at approximately 2%, demonstrating a diminishing rate with further elongation, falling below 1%.This delineates the existence of a critical threshold for side friction resistance, beyond which additional increments in pile length yield no substantial augmentation in its proportional sharing.
Consequently, a critical depth is identified where the side friction resistance fully shoulders the load, coupled with minimal relative displacement between the pile and surrounding soil near the pile's end.At this juncture, further extensions in pile length exhibit negligible impact on the load-sharing ratio curve.

Pile diameter
In the scenario where soil parameters remain constant, the effects of varying pile diameters (0.4, 0.8, 1.2, and 1.6 m) on load-settlement curves and load-sharing percentages were investigated to explore the impact of pile diameter changes on pile-bearing performance, particularly in the context of large-diameter and ultra-long piles in deep soft soil.
Load-displacement diagrams were obtained for each pile diameter (D = 0.4 m, D = 0.8 m, D = 1.2 m, and D = 1.6 m) by incrementally applying loads in the established model, as depicted in Figure 28.The graphs reveal that, under the same load level, the pile head displacement gradually decreases with increasing pile diameter.Moreover, with larger loads, the reduction in pile head displacement becomes more pronounced.As the pile diameter increases, the load-displacement curves exhibit a more pronounced quasi-linear behavior, approaching a linear trend.The abscissa of the slope inflection point of the load-displacement curve gradually increases with the pile diameter, indicating an increase in the ultimate bearing capacity of the pile.This suggests that an increase in pile diameter results in an augmentation of both the base and side areas of the pile, contributing to higher lateral  frictional resistance and, consequently, an enhanced bearing capacity.
Based on the numerical simulation results, the distribution of pile side frictional resistance and pile tip resistance under load is illustrated in Figures 29 and 30.
It is evident from the figures that, for all pile diameters, the lateral frictional resistance of the ultra-long piles plays a predominant role in the pile foundation bearing capacity.Under a 1,440 kN load, the proportions of lateral frictional resistance to the total load for different pile diameters are 90.74,87.95, 85.72, and 83.91%, respectively.This indicates that with larger pile diameters, the initial proportion of load carried by tip resistance is greater.
As the loading progresses, the distribution pattern of the load-sharing curve exhibits distinct characteristics based on the pile diameter.Larger pile diameters result in a faster increase in the lateral frictional resistance contribution to the load-sharing curve.This is attributed to the increased pile-soil contact area with the larger pile diameter, leading to a corresponding acceleration in the rate of increase of lateral frictional resistance with the applied load.
The ratio of lateral frictional resistance sharing gradually rises and then levels off.With larger pile diameters, the abscissa of the turning point on the curve representing the proportion of lateral frictional resistance increases, indicating a greater elevation in the curve.This is because, when lateral frictional resistance is fully mobilized, the load value increases with the pile diameter, and with complete mobilization, larger pile diameters result in a higher proportion of lateral frictional resistance, which assumes a greater share of the load-carrying function.

Conclusions and limitations 4.1 Conclusions
In this article, the strain within the pile body is quantified via optical fiber monitoring technology.By establishing the correlation between strain and axial force, as well as strain and pile side friction, the distributions of pile shaft axial force and pile side friction are computed.Subsequently, the axial force and side friction along the pile shaft are depicted by plotting graphical representations, gaining the load transfer characteristics within the pile shaft.
The following conclusions have been primarily derived: (1) Field experiments have revealed the load transfer patterns within the pile shaft: the axial force demonstrates a non-linear variation with increasing depth, its rate of change being dependent on soil properties; lateral frictional resistance predominantly carries the load in large-diameter super long piles, with the end section bearing a minor load, indicative of the friction pile behavior.
(2) For super-long piles, the side friction gradually becomes effective from the pile top and activates earlier than the end-bearing resistance.When the load is substantial, the end-bearing resistance starts to take effect, and the side friction is fully mobilized.The upper portion of the pile bears a significant load, while the axial force in the lower portion is much smaller.Therefore, in pile foundation design, it is feasible to optimize the reinforcement ratio based on the axial force distribution along the pile shaft, thereby conserving resources.(3) The load transfer mechanism of super-long piles simulated using PLAXIS 3D closely aligns with the results from static load tests on test piles, confirming the validity and feasibility of using PLAXIS 3D to simulate the behavior of large-diameter, super-long piles.Analysis of the load-settlement curve, axial force distribution curve, and pile side friction curve revealed the characteristic bearing behavior of large-diameter, super-long piles in this region.(4) Through a controlled variable analysis of different factors affecting the load-bearing behavior curves of piles, it was determined that increasing pile length and diameter can significantly enhance the bearing capacity of pile foundations.However, there exist critical lengths and diameters beyond which no further significant improvements are observed.Therefore, in practical engineering applications, it is crucial to comprehensively consider all factors and select the optimal length-to-diameter ratio to maximize bearing capacity and minimize costs.

Limitations and prospects
This article conducts a study on the vertical bearing characteristics of large-diameter and ultra-long concrete piles in deep soft soil areas based on experiments combined with numerical simulations.However, due to limitations in experimental conditions, cost, and research capabilities, there remain several unresolved issues in this study.The author believes that further improvement and exploration are needed in the following aspects: 1.In practical engineering applications, pile foundations often appear in the form of pile groups.Subsequent research could focus on the spacing between pile groups and the effects of high and low pile caps on the bearing characteristics.This would facilitate the practical application of large-diameter and ultra-long piles in deep soft soil areas.2. Soft soils, characterized by high porosity and strong permeability, exhibit increased pore pressure and lateral squeezing forces under load, especially in the presence of water.This can lead to horizontal displacement and disturbance settlement of the soft soil, affecting the vertical bearing capacity of the piles.However, this study's numerical simulation neglects pore water, making it not universally applicable to all practical engineering scenarios.Subsequent research should focus on further investigating the vertical bearing characteristics of large-diameter and ultra-long concrete piles containing pore water in deep soft soil conditions.
Appendix A

Figure 1 :
Figure 1: Schematic diagram of strain measurement for BOTDR (image source from the internet).

Figure 2 :
Figure 2: The linear relationship between Brillouin frequency shift and strain.
weight (γ) of 22 kN m − ³.The pile is discretized into faces, and a normal interface is established on the pile sides.The material parameters of this interface are set to vary with the soil properties to simulate the interaction between the pile and the soil.A surface load is applied at the top plane of the pile in increments.All other parameters are set to the system's default values.

Figure 10 :
Figure 10: Pile setting and creation of pile-soil interaction surface.

Figure 12 :
Figure 12: Temperature distribution curve of pile body.

Figure 14 :
Figure 14: Distribution curve of axial force on the left side of the pile.

Figure 15 :
Figure 15: Distribution curve of axial force on the right side of a pile.

Figure 16 :
Figure 16: Distribution curve of left side friction resistance of pile.

Figure 17 :
Figure 17: Distribution curve of friction resistance on the right side of a pile.

Figure 18 :
Figure 18: Distribution curve of layered lateral friction resistance on the left side of the pile body.

Figure 19 :
Figure 19: Distribution curve of layered lateral friction resistance on the right side of the pile body.

Figure 20 :
Figure 20: Left pile end resistance distribution curve.

Figure 21 :
Figure 21: Distribution curve of resistance at the right pile end.

Figure 24 :
Figure 24: Comparison of experimental and numerical simulation lateral pile friction distributions.

Figure 26 :
Figure 26: Curve of side friction resistance sharing.

Figure 29 :
Figure 29: Curve of side friction resistance sharing.

Table 1 :
The types and main performance parameters of these two sensor cables optic cable name Model Cable diameter (mm) Maximum loss (dB km −1 ) Allow tension (N) Net weight (kg km −1 )

Table 2 :
HSS small strain model parameters

Table A1 :
Calculation values of friction resistance of piles