Study on the Bearing Capacity of Extra-Large-Diameter Piles in Complex and Thick Lacustrine Deposits

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have examined the bearing performance of large-diameter and ultra-long piles in layered soils via in-situ test and FEA. There are still some important points to be addressed:

(1) The authors should explained why the shaft friction exhibited such a complicated pattern. In the meantime, they should make a comparision with other kinds of piles and other publications such as "comparative investigation of axial bearing performance and mechanism of continuous flight auger pile". Also, they should delineate how they measured these profiles and what technique have they used?

(2) The authors should summarize the parameters used in the FEA as a table.

(3) How many conditions have the authors tested via FEA. Please also give a summarizing table and make a comparison.

(4) How did the authors calibrate the parameters in the simulations? In the meantime, how did the authros set the soil-pile interfacial model? That is very important to the results.

(5) I don't like the way of writing in 276-272. Please make a change. Also the way in line 338-343.

(6) How about the responses of shaft friction and tip resistance in the FEA. Please provide and make a comparion with the experimental observations.

(7) Indeed, I don't think FEA can reveal the mechanism of bearing performances of ultra-long piles and other kinds of foundation. The authors can applied DEM simulation and a section of discussion can be added. For instance, "numerical investigation of morphological effects on crushing characteristics of single calcareous sand particle by finite-discrete element method" can help understanding the soil-pile interaction at the microscale.

(8) There are some typos in the paper. The English wirting should be improved as well.

 

Author Response

Thank you for your insightful comments and useful suggestions for improvement. We have carefully considered your comments and suggestions for changes of the manuscript.

Comments 1:The authors should explained why the shaft friction exhibited such a complicated pattern. In the meantime, they should make a comparision with other kinds of piles and other publications such as "comparative investigation of axial bearing performance and mechanism of continuous flight auger pile". Also, they should delineate how they measured these profiles and what technique have they used?

Response 1:Agree.

We have added the relevant content.

• Line 503-523:The lateral friction resistance along the pile exhibits a multi-peak distribution pattern, first increasing, then decreasing, followed by another increase and subsequent decrease. This phenomenon is primarily attributed to the interlayer variability in the properties of the foundation soil. The study area predominantly exhibits complex interlayered distribution, resulting in loose upper soil structures that provide limited lateral friction resistance. As depth increases, the physical and mechanical properties of the foundation soil gradually improve, enabling the pile side friction resistance to progressively take effect. Furthermore, the contribution of lateral friction varies asynchronously across different soil layers: under light loads, upper layers initially bear and transmit the load, causing lateral friction in this zone to peak. However, by the time the load reaches the lower pile section, the residual load has relatively diminished, leading to a gradual decrease in lateral friction. As load increases, lateral friction resistance in all soil layers is fully mobilized. However, due to variations in soil properties, the lateral friction resistance borne by each layer differs. With further load increase, lateral friction resistance in the lower soil layers is gradually activated, causing the distribution curve to transition from a “hump-shaped” profile to a flatter form. If the load level continues to rise, the lower portion of the pile-side friction distribution curve gradually extends, indicating the progressive contribution of friction near the pile tip. Simultaneously, the pile-side friction in the upper portion of the pile body approaches its ultimate state, accompanied by varying degrees of softening phenomena.
• Line540-570:Field performance data for various pile types in China were collected from literature sources for further comparative analysis [51-53].ee Table 1.

Table 1. End Resistance and Lateral Resistance for Different Pile Types.

Pile type	Pile length/m	Pile diameter/mm	Ultimate Load/kN	Cumulative settlement value/mm	Terminal resistance ratio/%	Lateral resistance ratio/%
SJ-1	43	1000	22800	21.84	3.2	96.8
T1	98	1000	28800	107.33	7.8	92.2
SD2Bottom-expanded pile	7	2800	9600	2.20	88.4	11.6
Wedge pile	8.2	600	2650	18.83	22.3	77.7
End-bearing friction pile	7.1	800	1575	50.16	66.66	33.4
Pure friction pile	6.3	800	720	-	0	100
Large-diameter enlarged-diameter piles	16	1000	8300	2.53	-	-
Constant-cross-section pile	23	1000	7000	50.05	-	-
Drilled Piles	35	1000	10000	-	52	47.5
PHC pil	35	600	3600	-	-	-

As shown in Table 1, under identical conditions, the bearing capacity decreases and settlement increases in the following order: enlarged-base piles → wedge piles → end-bearing friction piles → pure friction piles. Large-diameter piles exhibit a significantly higher proportion of lateral resistance.

For T1, SJ-1, and pure friction piles, lateral resistance accounted for ≥92.2% while end resistance was ≤7.8%. These designs rely primarily on lateral friction between the pile body and soil layers, making them suitable for soft soil conditions. Bearing capacity is enhanced through “long pile length + large lateral area” configurations: T1 pile length 98m, ultimate load 28800kN; SJ-1 piles (43m long, ultimate load 22,800 kN) validate that “longer piles yield more significant lateral resistance contributions.”

SD2 enlarged-base piles (end resistance 88.4%) and end-bearing friction piles (end resistance 66.66%) relies primarily on end bearing force, suitable for scenarios where pile tips can penetrate hard rock/dense soil layers. Despite its 7m length, the SD2 achieves a ultimate load of 9600kN through its enlarged base structure, highlighting that “end resistance efficiency far exceeds lateral resistance.”

Wedge piles (lateral resistance 77.7% + end resistance 22.3%) and bored cast-in-place piles (end resistance 52% + lateral resistance 47.5%) exhibit synergistic effects between lateral and end resistance, making them suitable for conventional engineering scenarios in moderately dense strata (neither pure soft soil nor hard rock).

In summary, the bearing characteristics of ultra-long piles in complex, thick lacustrine deposits revealed in this study align with fundamental commonalities across pile types while exhibiting unique distribution patterns due to the depth effect of ultra-long piles, interactions within complex lacustrine strata, and specialized construction techniques. These findings not only fill a gap in existing pile type comparison studies regarding the “ultra-long + complex stratum” scenario but also provide data support for the differentiated optimization of bearing capacity design methods across pile types.

• Line 441-450:The pile-side friction distribution curve is calculated based on the variation of axial force along the pile length under various load conditions. Axial force refers to the force generated along the longitudinal axis of the pile when subjected to external loads. CTY-202 vibrating-wire strain gauges are installed within the pile body. Based on these strain gauges, axial force sensors embedded at interfaces of different soil layers within the pile body provide segmented axial force measurements along the depth. This enables the determination of deformation at each pile cross-section under various load levels, thereby allowing calculation of axial force at each location within the pile. The axial force detection results for each section of the T1, T5, and T6 test piles are detailed in Table 1-3.

Table 1. Axial Force in Pile Body of Pile T1.

Depth Range （m）	Pile-top pressure（kN)
	6400	9600	12800	16000	19200	22400	25600	28800
A	6400	9600	12800	16000	19200	22400	25600	28800
B	6342	9536	12714	15901	19105	22289	25480	28645
C	4213	5462	6345	7235	8876	9884	11246	13678
D	3587	4876	5426	6976	7459	8567	9876	10123
E	2563	3589	3758	4657	5012	6124	7123	7569
F	1785	2896	3241	3789	4016	4987	5876	6012
G	1042	1987	2300	2578	3459	4356	5236	5412
H	324	546	786	1214	1358	1657	1986	2237

Table 2. Axial Force in Pile Body of Pile T5.

Depth Range （m）	Pile-top pressure（kN)
	6400	9600	12800	16000	19200	22400	25600	28800
A	6400	9600	12800	16000	19200	22400	25600	28800
B	6200	9500	12700	15800	19000	22400	25300	28600
C	3300	5700	7800	9900	12690	14700	16500	18900
D	2200	4890	6600	8480	9800	11370	13200	14600
E	1700	4680	6400	8200	9500	10930	12000	13200
F	980	2930	4500	6200	6900	7980	8700	10500
G	460	1740	3200	4400	5200	6100	7000	8200
H	280	360	440	520	580	680	770	840

 

Table 3. Axial Force in Pile Body of Pile T6.

Depth Range （m）	Pile-top pressure（kN)
	6400	9600	12800	16000	19200	22400	25600	28800
A	6400	9600	12800	16000	19200	22400	25600	28800
B	6360	9540	12720	15900	19080	22260	25440	28614
C	6134	9314	12465	15589	18712	21836	24959	28076
D	3890	7070	9941	12503	15066	17628	20190	22747
E	3008	6188	8949	11291	13633	15975	18317	20653
F	1708	4888	7487	9504	11521	13538	15555	17566
G	1423	4002	6489	8285	10080	11876	13671	15460
H	54	112	187	256	280	278	527	770

 

Comments 2:The authors should summarize the parameters used in the FEA as a table.

Response 2:Added.

Line 629：Simulation parameters are presented in Table 3 .

Table 3. Finite Element Simulation Parameter.

Material Type	γ(kN/m-³)	E/Mpa	ν	C/（kpa）	φ /（°）	Constitutive model
clay	19.0	6.19	0.3	87.6	8.4	Mohr-Coulomb
Peaty soil	15.3	5.43	0.25	60.9	9.1	Mohr-Coulomb
C40	24.5	33.5	0.2	-	-	Elastic Model

Comments 3:How many conditions have the authors tested via FEA. Please also give a summarizing table and make a comparison.

Response 3:Added.

Line 769-781:A total of ten operating conditions were simulated, as shown in the table below.

4.4. Summary

This study simulated a total of ten scenarios, analyzing three conditions for soft layer thickness and pile length, and four conditions for pile diameter. The summary table is as follows.

Table 8. All operating conditions for finite element analysis testing.

Operating Condition Number	Pile length/m	Pile diameter/m	Thickness of rock and soil mass/m	Thickness of the weak layer/m	Settlement/mm	Pile tip resistance /kN
A1	98	0.5	108	40	1470	386.51
A2	98	0.5	108	30	1483	394.96
A3	98	0.5	108	10	1380	330.00
B1	108	1.0	118	118	163.6	102.93
B2	98	1.0	108	108	153.0	106.42
B3	88	1.0	98	98	134.77	67.80
C1	98	2.0	108	108	69.2	193.34
C2	98	1.5	108	108	91.4	141.11
C3	98	1.0	108	108	151.1	106.42
C4	98	0.5	108	108	444.5	59.78

Table 8 indicates that the final settlement value increases with the thickness of the weak layer and with the pile length, but decreases with the pile diameter. This clearly demonstrates the influence of these factors on the bearing capacity of extra-long, large-diameter piles. Pile tip resistance first increases and then decreases as the thickness of the weak layer and the pile length increase, indicating the existence of critical weak layer thickness and critical pile length. Conditions B2 and C3 share identical simulation parameters. Simulation results show identical pile tip resistance, with only a 2.1 mm difference in ultimate settlement.

Comments 4:How did the authors calibrate the parameters in the simulations? In the meantime, how did the authros set the soil-pile interfacial model? That is very important to the results.

Response 4:Added.

Line 622-628:Parameter Calibration: We calibrated simulation parameters by integrating laboratory test data with field measurement results. For soil parameters, we referenced triaxial compression and consolidation test results from soil samples collected at the test site. For pile material parameters, we utilized mechanical property test results from actual pile materials. We iteratively adjusted parameters until simulation results matched preliminary test data (e.g., load-settlement curves for typical piles) within an acceptable error range (less than 5%).

Line 630-648:Pile-soil interface model: When simulating pile-soil interaction, interface elements are employed to represent this process, with the mechanical properties of the interface material adhering to Coulomb's friction law. To account for friction variations at the pile-soil interface across different soil layers, three parameters are defined: ultimate shear force, shear stiffness modulus, and normal stiffness modulus. The ultimate shear force value is determined based on the ultimate lateral resistance. The shear stiffness modulus, representing the elastic parameter for tangential sliding of the interface element, is typically set at 15–20 times the elastic modulus of the adjacent soil layer. The normal stiffness modulus corresponds to the elastic properties of the interface element in both engaged and disengaged states along the normal direction, generally set at 10 times the shear stiffness modulus of the soil. In this simulation, the ultimate shear force is set to 16,000 kN, the shear stiffness modulus is taken as 15 times the soil layer's elastic modulus (800,000 kN), and the normal stiffness modulus is set to 10 times the soil shear stiffness modulus (8,000,000 kN). The model disregards loading apparatus settings and ignores energy dissipation during reaction transmission and other interference factors. Vertical forces are converted into surface loads and uniformly applied to the pile cap. For compression piles, the uniformly distributed load on the pile cap is set to 32,000 kPa. Load application is divided into 10 steps to simulate the graded loading process in static load tests.

Comments 5:I don't like the way of writing in 276-272. Please make a change. Also the way in line 338-343.

Response 5:Changed.

 

Line 688 : Figure 14: Load-Settlement Curves for Different Weak Interlayer Thicknesses

Line 689-691: As shown in Figure 15, the influence of weak layer thickness on the pile - end bearing capacity is illustrated as follows:

At 40 m, pile-end resistance is 386.5 kN (1.34% of the pile-top load);

Line 753-758: The load - settlement (Q - s) curves for piles with different diameters (Figure 3.5) illustrate that under the same load, the pile - top displacement reduces with the increase in pile diameter, and this reduction is more pronounced at higher loads. An increase in pile diameter not only makes the Q - s curves exhibit a more linear trend but also enhances the ultimate bearing capacity. This is because a larger pile diameter leads to an increase in both the base area and the side area, which in turn improves the shaft friction resistance.

Comments 6:How about the responses of shaft friction and tip resistance in the FEA. Please provide and make a comparion with the experimental observations.

Response 6:Added.

Line 657-665:The measured pile tip resistance was 2437 kN, while the finite element analysis yielded 2637 kN—an increase of 200 kN over the measured value, representing an error of 8.2%. The lateral resistance of the pile body is relatively complex, and the finite element observation results showed poor agreement with experimental observations. Therefore, this paper only compares settlement and tip resistance.

 

Figure 12. Pile-Soil Displacement Cross-Section Contour Map and Simulated Pile Tip Resistance Contour Map.

Comments 7:Indeed, I don't think FEA can reveal the mechanism of bearing performances of ultra-long piles and other kinds of foundation. The authors can applied DEM simulation and a section of discussion can be added. For instance, "numerical investigation of morphological effects on crushing characteristics of single calcareous sand particle by finite-discrete element method" can help understanding the soil-pile interaction at the microscale.

Response 7:We sincerely appreciate your valuable insights regarding the selection of numerical methods and the depth of mechanism analysis in this study. Your suggestion to incorporate Discrete Element Method (DEM) simulations to complement the micro-scale pile-soil interaction analysis has been thoroughly discussed by our team.

After repeated deliberation by our team, we conclude that the current finite element analysis (FEA) approach remains sufficient to meet the core objectives of this study. Our focus lies on quantifying the overall patterns and influencing factors of the bearing capacity of extra-long piles at the macro level—such as the load-settlement relationship—rather than the micro-scale mechanisms of particle interactions. The existing FEA model, validated with field load test data, accurately characterizes the macroscale bearing mechanism and aligns closely with the core research questions.

Regarding the DEM simulations and related literature you mentioned, we acknowledge their significant value in micro-mechanism research. However, considering: 1. The scope and focus on core objectives of this study, incorporating DEM would excessively broaden the research scope and divert attention from the primary focus on macro-scale bearing capacity; 2. DEM simulations require substantial additional work, including parameter calibration and mesh sensitivity analysis, which the current research data and timeframe cannot sufficiently support. Therefore, we have not incorporated DEM simulations into the revised manuscript. However, we have added a new section titled “Research Limitations and Future Prospects” in the Discussion, explicitly stating that “future studies may further explore the influence of micro-scale pile-soil interactions on macro-scale bearing capacity using DEM,” thereby providing a reference for subsequent research in this direction. We sincerely appreciate your understanding and expert guidance. Your feedback has helped us clarify the research boundaries and future directions, significantly enhancing the rigor of the manuscript.

Comments 8:There are some typos in the paper. The English wirting should be improved as well.

Response 8:Agree.

Thank you for your valuable feedback. We apologize for the typographical errors and language issues in the manuscript. We have carefully revised the paper and corrected all identified typographical mistakes. Additionally, we have improved the English writing throughout the manuscript for better clarity and readability. We believe these revisions enhance the overall quality of the paper.

We appreciate your understanding and hope the revised version meets the required standards.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The reviewed paper is dedicated to the study on the bearing capacity of extra-large diameter piles in complex and thick Lacustrine deposits. Three test piles with a diameter of 1m and lengths of 98 m, 93 m, and 92 m respectively were taken as the research objects. The bearing characteristic parameters were obtained through static load tests, and the influence laws of parameters such as the thickness of the weak layer, pile length and pile diameter in the peat soil layer were analyzed in combination with numerical simulation.

After introduction to the resaerch subject, Authors presented experimental observations and tests results. Based on the parameters of test pile T1, for calculation and combining with field static load tests, the Mohr-Coulomb constitutive model was taken into account for the soil, while the pile was simulated using beam elements. Model validation and parametric analysis are also presented in the paper. At the end of all analyses carried out by the Authors, five conclusions are presented, among others, the conclusion about influence of pile diameter on its bearing capacity. Authors mentioned that larger diameter increase both the pile base area and lateral surface area, thereby boosting lateral friction resistance. As pile diameter increases, settlement at the pile top gradually flattens and decreases. A critical pile diameter exists beyond which further increases have negligible impact on bearing capacity. Pile tip bearing capacity increases with pile diameter.

The reviewed paper is interesting and original because there is a real analyzed situation in which the length of piles is equal around 90-100 meters.

The paper is well organized, after introduction main subject is clear explained and presented by the Authors, and the main conclusions are shown. It is worth to noticed that the 3-D numerical model of pile foundations established based on static load tests demonstrated a discrepancy of only 1.27 mm between simulated and measured values, validating the model's validity. Test results indicate that all ultra-long test piles exhibit end-bearing friction characteristics.

Finally, the Reviewer suggests only to change the description for Figure 3 -

there is written: Figure 3. This is the curve showing the variation of the shaft friction of three test piles with the soil burial depth, while it could be written: Figure 3. The curve showing the variation of the shaft friction of three test piles with the soil burial depth.

The reviewed paper will be interesting for the readers, so in the reviewer's opinion it should be prepared for publication in INFRASTRUCTURES.

 

The research presented by the Authors will give the answer for the problem about the influence mechanism of complex and thick Lacustrine sedimentary strata on the bearing performance of large diameter and ultra-long piles. Taking into account the experimental piles results, numerical simulations were carried out in view of the special engineering properties of peat soil in the strata.

Considering the experimental results and numerical simulations of large-diameter and ultra-long piles, the reviewer can confirm the originality of the research. Piles of such large diameter and ultra-long piles are rarely constructed and field-tested.

Thanks to this work, researchers can directly apply the results and conclusions to their practice and to numerical modeling of soil-pile interactions. Additionally, it is worth noting that the authors proposed two models for numerical simulations: a Mohr-Coulomb model for the soil and beam elements for the pile.

There is no need to make any improvements to this article. The authors could use different models to analyze soil-pile interactions when the subsoil consists of other soil types (without peat).

The authors' conclusions are supported by experimental and numerical simulation results. They are directly related to the results presented in the chapters of the reviewed work.

The list of sources is sufficient. All sources are cited in the text. They are mainly from the last 10 years.

All tables and figures are essential to the text. The reviewer suggests adding units [mm] for the settlements given in Tables 2, 3, and 4.

Author Response

Thank you very much for your positive evaluation and valuable feedback on our manuscript. We greatly appreciate your recognition that no further improvements are needed. Your affirmation encourages us a lot, and we will follow the journal’s subsequent procedures closely.

Again, thank you for your time and efforts in reviewing our work.

Comments 1:there is written: Figure 3. This is the curve showing the variation of the shaft friction of three test piles with the soil burial depth, while it could be written: Figure 3. The curve showing the variation of the shaft friction of three test piles with the soil burial depth.

Yes, it has been changed.

Line 453-454:Figure 8. the curve showing the variation of the shaft friction of three test piles with the soil burial depth.

 

Comments 2:The reviewer suggests adding units [mm] for the settlements given in Tables 2, 3, and 4.

Added.

Line 596、626、660:

Table3. Simulated Single Pile Static Load Test Data for Different Weak Layer Thicknesses.

Weak Interlayer Thicknesses of 40m		Weak Interlayer Thicknesses of 30m		Weak Interlayer Thicknesses of 10m
Load/kN	Settlement/mm	Load/kN	Settlement/mm	Load/kN	Settlement/mm
0	0	0	0	0	0
6400	62	6400	61	6400	58
9600	150	9600	148	9600	142
12800	250	12800	253	12800	243
16000	370	16000	372	16000	360
19200	500	19200	503	19200	480
22400	640	22400	644	22400	610
25600	770	25600	794	25600	750
28800	940	28800	953	28800	890
32000	1470	32000	1483	32000	1380

Table 4. Simulated Single Pile Static Load Test Data for Different Pile Lengths.

L=108m		L=30m		L=10m
Load/kN	Settlement/mm	Load/kN	Settlement/mm	Load/kN	Settlement/mm
0	0	0	0	0	0
2880	10.9	2880	10.7	2880	9.3
5760	22.1	5760	21.9	5760	18.7
8640	35.1	8640	34.6	8640	29.3
11520	49.9	11520	48.6	11520	41.5
14400	66.1	14400	63.7	14400	54.9
17280	83.5	17280	79.8	17280	69.2
20160	102.1	20160	96.9	20160	84.4
23040	121.7	23040	114.8	23040	100.5
25920	142.2	25920	133.6	25920	117.3
28800	163.6	28800	153	28800	134.77

Table 5. Simulated Single Pile Static Load Test Data for Different Pile Diameters.

D=0.5m		D=1.0m		D=1.5m		D=2.0m
Load/kN	Settlement/mm	Load/kN	Settlement/mm	Load/kN	Settlement/mm	Load/kN	Settlement/mm
0	0	0	0	0	0	0	0
2880	15.6	2880	10.3	2880	8.1	2880	6.6
5760	37.6	5760	20.9	5760	16.2	5760	13.3
8640	67.2	8640	33.2	8640	24.3	8640	20
11520	103.3	11520	46.9	11520	32.8	11520	26.6
14400	145	14400	61.7	14400	41.8	14400	33.3
17280	191.7	17280	77.7	17280	51.2	17280	40.2
20160	243.1	20160	94.7	20160	60.9	20160	47.3
23040	298.5	23040	112.7	23040	70.8	23040	54.5
25920	357.8	25920	131.5	25920	81	25920	61.8
28800	444.5	28800	151.1	28800	91.4	28800	69.2

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1. It is recommended to supplement the calculation method for bearing capacity and compare the calculated values with experimental data, values from different national codes, and other theoretical calculations to make the paper more comprehensive.
2. In the paper, the Q-s curves of T1, T5, and T6 are almost identical, and the ultimate bearing capacities at the inflection points are roughly equal. However, the side resistance curves of each pile differ significantly. Does this indicate that the soil layer distribution affects the distribution of pile side resistance but has little impact on the ultimate bearing capacity?
3. In Figure 4, the curve for T6 shows a sudden and sharp decrease in the pile tip load, which contradicts the corresponding data for T6 in Figure 3.
4. There are issues with incorrect labeling in the paper. The numbering of figures and tables, as well as the citation format, need to be unified. For example, there are two "(b)" labels in Figure 3.
5. The clarity of the numerical simulation cloud images is relatively low, such as in Figure 11.
6. It is recommended to supplement the construction process and quality control measures for the test piles, as these factors significantly affect the side friction resistance.
7. It is suggested to include photos of the field tests, such as the loading setup and testing instruments, to enhance credibility.
8. The paper needs to cite more influential recent research findings in the field.

 

Author Response

We sincerely thank you for your valuable comments and constructive suggestions, which have significantly enhanced the quality and rigor of this manuscript. We have carefully addressed each comment and summarize the main revisions and responses as follows.

Comments 1:It is recommended to supplement the calculation method for bearing capacity and compare the calculated values with experimental data, values from different national codes, and other theoretical calculations to make the paper more comprehensive.

Response 1:Added.

Line 571-607:3.4. Single Pile Bearing Capacity Prediction

Cast-in-place piles are widely used in foundation engineering, and accurately predicting their vertical compressive bearing capacity is a core research topic for ensuring project safety and economic efficiency. However, in-situ load tests face significant challenges due to the complex interaction of geological conditions, construction disturbances, and other factors, making precise control of test conditions difficult. Furthermore, most tests cannot reach the failure state of the test pile due to loading limitations, making it challenging to accurately determine the ultimate vertical compressive bearing capacity of a single pile. This issue significantly constrains the reliability of engineering design. To address this, this paper proposes a collaborative “field test - mathematical model” bearing capacity prediction method: using field measurement data as a foundation, it incorporates widely validated mathematical models to assist in calculating ultimate bearing capacity. By cross-validating results from both technical approaches, it effectively compensates for the limitations of relying solely on either field tests or model predictions. This approach provides a more scientific quantitative basis for pile foundation design in practical engineering, offering significant guidance for enhancing structural safety and optimizing construction costs. From existing mature models, this paper selects four well-validated and highly applicable models, specifically as follows:

• Hyperbolic Model
• Double-break model
• Linear model
• Triple-Line Model

This study compares the on-site static load test results with the four mathematical models to evaluate their predictive capabilities. The accuracy and feasibility of the prediction models are validated through fitting results. Test pile T1 was selected for fitting, and the obtained fitting results were verified against the loading values corresponding to the maximum settlement during the test. The results are shown in Figure 10 and Table 2.

Table 2. Comparison Table of Four T1 Test Pile Models with Actual Load-Settlement Data.

Load/(kN)	Actual Settlement/mm	Hyperbolic Model Settlement/mm	Linear Model Settlement/mm	Triple-Line Model Settlement/mm/mm	Double-Hedged Model Settlement/mm
0	0	0	-7.31	0	0
6400	9.31	3.47	4.95	7.68	7.79
9600	12.78	5.77	11.09	11.52	11.69
12800	15.58	8.63	17.22	15.35	15.58
16000	18.51	12.28	23.35	19.19	19.33
19200	23.03	17.11	29.48	23.03	23.07
22400	26.82	23.79	35.61	38.47	26.82
25600	30.57	33.65	41.74	53.91	46.14
28800	36.62	49.63	47.87	69.35	65.47
32000	84.79	80.06	54.01	84.79	84.79

 

 

Figure 10. Comparison Chart of Four T1 Test Pile Models with Actual Measurement Curves.

As shown in Figure 10 and Table 1, the hyperbolic model provides a closer fit to the measured load values. Therefore, selecting the hyperbolic model enables more accurate prediction of the ultimate compressive bearing capacity of individual cast-in-place piles.

Comments 2:In the paper, the Q-s curves of T1, T5, and T6 are almost identical, and the ultimate bearing capacities at the inflection points are roughly equal. However, the side resistance curves of each pile differ significantly. Does this indicate that the soil layer distribution affects the distribution of pile side resistance but has little impact on the ultimate bearing capacity?

Response 2:yes, the total ultimate bearing capacity consists of two components: total lateral friction resistance and total end resistance.

For test piles (T1, T5, T6) in the same site with identical diameters, lengths, and construction methods, even if the soil layers along the pile shaft vary (e.g., differing thicknesses and burial depths of hard soil layers), their total ultimate bearing capacities are likely to be similar provided the following conditions are met: (1) Identical and stable bearing layer at the pile tip: All three piles rest on a bearing layer with similar properties and high bearing capacity at their tips. This implies their end resistance is essentially the same. (2) Similar “total strength envelope” of the surrounding soil: Despite differing soil distributions, the sum of lateral friction resistance from the pile top to the pile bottom is comparable across all soil layers. That is, the total of “soil friction resistance in soft soil + soil friction resistance in hard soil” is roughly equivalent. (3) The pile length and diameter are nearly identical: This ensures equal pile-soil contact area. Under these conditions, the pile's bearing capacity behaves more as a “monolithic unit.” The load-settlement relationship (Q-s curve) is primarily governed by this “monolithic” bearing capacity, resulting in similar curves and inflection points for all three piles.

Lateral friction develops in a layered, asynchronous manner and is closely related to relative pile-soil displacement. If the upper part of the pile is soft soil and the lower part is hard soil, the upper soft soil will initially exert a smaller friction resistance during the early loading phase. As settlement increases, the lower hard soil gradually begins to exert its high friction resistance. Conversely, if the upper portion consists of hard soil and the lower portion of soft soil, the upper hard soil will exert significant lateral friction early in loading, while the lower soft soil may never fully contribute. The resulting lateral friction-depth curves will exhibit distinctly different patterns: one may show “small at top, large at bottom,” while the other may display “large at top, small at bottom.” The lateral friction curve is calculated from the axial force measured by strain gauges embedded in the pile shaft. It clearly reveals how the load is transmitted downward along the pile. Different soil layer distributions result in distinct load transmission paths and patterns, leading to significant differences in the measured curves.

Therefore, under the specific conditions of this project, the distribution of soil layers primarily shapes the distribution pattern of lateral friction resistance, while having a relatively minor impact on the ultimate bearing capacity of the pile.

Comments 3:In Figure 4, the curve for T6 shows a sudden and sharp decrease in the pile tip load, which contradicts the corresponding data for T6 in Figure 3.

Response 3:Yes, it has been changed.

We sincerely apologize for the inconsistencies in the figures pointed out by the reviewers. Upon verification, this issue stemmed from an input error during data processing, which was due to our oversight. We have now rechecked the original data, corrected the erroneous entries, and ensured the updated figures are logically consistent and accurately support the paper's conclusions (the revised figures are included as supplementary materials/annotated at the corresponding locations in the revised manuscript). Moving forward, we will strengthen our multi-step verification processes for data entry to prevent recurrence of such issues. We once again express our gratitude to the reviewers for their valuable feedback, which has helped us refine our research findings.

Line 525:

          

Comments 4:There are issues with incorrect labeling in the paper. The numbering of figures and tables, as well as the citation format, need to be unified. For example, there are two "(b)" labels in Figure 3.

Response 4:Yes, it has been changed.

Line 453-457:

(a) T1 pile	(b) T5 pile

 

(c) T6 pile

 

Figure 3. the curve showing the variation of the shaft friction of three test piles with the soil burial depth.

Comments 5:The clarity of the numerical simulation cloud images is relatively low, such as in Figure 11.

Response 5:Okay, optimized.

Line 698、733、767:

(a)Condition 1	(b)Condition 2	(c)Condition 3

Figure 15. Contour Map of Pile Tip Bearing Capacity at Load Termination for Different Weak Layer Thicknesses.

(a)L=108m	(b)L=98m	(c)L=88m

 

Figure 17. Contour Map of Pile Tip Bearing Capacity at Termination of Loading for Different Pile Lengths.

(a)	(b)	(c)	(d)

Figure 19.  Contour Map of Pile Tip Bearing Capacity at Termination of Loading for Different Pile Diameters.

Comments 6:It is recommended to supplement the construction process and quality control measures for the test piles, as these factors significantly affect the side friction resistance.

Response 6:Added.

Line 210-411:2.3. Test Pile Construction Process and Quality Control

2.3.1. Test Pile Construction Process

(1) Site Hardening: To ensure drilling operations meet verticality requirements and mitigate adverse weather impacts during the rainy season, the construction site underwent hardening treatment, providing a stable foundation for subsequent work.

(2) Pile Body Precision Positioning Process: During site hardening, a “non-repeat staking device” was simultaneously installed. Subsequently, the steel casing was positioned and installed using ICE equipment. After casing installation, re-measurement and verification were conducted. Once the position was confirmed accurate, the drilling rig was positioned and centered (see Figure 4 (a)for details).

(3) Verticality Control for Hollow Pile Sections: With hollow pile sections ranging from 18 to 20 meters in length, to ensure verticality compliance and minimize displacement deviation at the designed pile cap, the ICE vibratory hammer was fixed to the frame of the three-axis mixing pile machine. A 20-meter steel casing was lowered for auxiliary control, leveraging the site hardening to maintain a level pile foundation working surface.

(4) Borehole Formation Method Selection: Rotary drilling rigs were used for pile foundation formation in the basement and auxiliary tower areas. Due to the presence of hard plastic silty clay beneath the main tower, conventional rotary drilling rigs faced significant challenges. Therefore, a combined formation method using both rotary drilling rigs and conventional rotary drilling rigs was adopted (see Figure4(b)for details).

 

(a) Hardened ground and pre-installed steel casings   (b)Borehole Formation Process

Figure 4. Site Construction Drawings

(5) Control Measures for Preventing Omissions and Errors in Pile Driving: Given the large number of piles, significant variations in specifications, and extended construction period, omissions or errors in pile driving are prone to occur during construction. Therefore, a daily verification mechanism is implemented. Each crew's management personnel will conduct item-by-item verification of the number of piles completed that day to ensure no omissions or sequence errors in pile construction.

(6) Pile Verticality Assurance Measures: As this project involves extra-long piles where verticality directly impacts quality, ultrasonic detectors will be used to conduct specialized verticality inspections on each pile after boring. Should any pile fail to meet design verticality standards, the borehole will be immediately backfilled with C15 concrete. Secondary boring operations will resume only after a specified interval.

(7) Targeted Mud Mixing: The construction site contains multiple thick silt layers, which impose stringent requirements on borehole quality and sediment control, thereby demanding strict mud performance standards. Consequently, specialized mud mixing tests must be conducted prior to formal drilling to determine suitable mud parameters that meet construction needs (see Figure 5 for details).

 

Figure 5. Drilling Fluid Mixing Test.

Reinforcement Cage Hoisting and Alignment: Due to the extra-long pile length, the hoisting operation and alignment quality of the reinforcement cage are critical. To ensure quality and shorten construction time, a two-section hoisting and alignment technique was adopted (Figure 6).

 

Figure 6. Hoisting and aligning steel reinforcement cages.

(9) Pile-Bottom Sediment Control Measures: The piles in this project are extra-long and must traverse multiple layers of silty sand, making sediment removal at the pile base particularly challenging. To address this, a dual-process approach combining a mud desander with air-lift reverse circulation hole cleaning technology was employed. This synergistic method precisely controls the thickness of sediment at the pile base to meet design requirements.

(10) Concrete Pouring Quality Assurance: Given the large diameter and extreme length of the piles, the concrete pouring volume is substantial with significant pouring depth, necessitating underwater pouring techniques. To ensure pouring quality, all equipment used is brand-new, and the pouring conduits are reinforced. This effectively prevents accidents such as conduit bursts or collapses during pouring, ensuring the smooth progression of concrete pouring operations.

(11) Pile-Base Grouting Quality Control: The main and auxiliary tower piles are designed with high bearing capacities. Relying solely on lateral friction resistance cannot meet design standards, necessitating pile-base grouting to enhance overall bearing capacity. To guarantee grouting effectiveness, threaded connections were used for grouting pipes, with PTFE tape wrapped around threaded sections to prevent cement slurry leakage. Additionally, grouting pipes were extended 50 cm beyond the rebar cage to ensure effective penetration into the soil layer. Check valves employed a triple-protection design featuring wooden plugs, metal check valves, and rubber check valves.

(12) Grouting Process Parameter Settings: Low-pressure, low-flow grouting equipment was selected, employing a two-stage grouting method. The initial grout volume constituted 60% of the total, with a 2-3 hour interval between stages. Grouting flow was strictly maintained below 50 L/min throughout the process.

2.3.2. Quality Control Measures

(1) Casing Fabrication and Installation

① Steel casings shall be fabricated from Q345 grade steel (to enhance reusability), with individual lengths of 10m. Joints shall undergo butt welding followed by reinforcement with a 200mm-wide steel plate of matching thickness welded around the exterior of the joint. ② Secure the ICE vibratory hammer to the triaxial mixing pile rig frame. Coordinate with the crane operator and ICE dedicated operator to clamp the top of the steel casing with ICE clamps and lift it off the ground. ③ After positioning the steel casing directly above the pile location and completing alignment, activate the ICE vibratory hammer. Slowly vibrate the steel casing downward to the design elevation. During vibration, two monitors positioned at 90° angles set up a theodolite aimed at the steel casing to continuously monitor its verticality. Immediate correction is made upon detecting any deviation.

(2) Drilling for Boreholes

① For the upper open pile section, a rotary drilling rig creates the borehole to the bottom of the casing. Ultrasonic equipment is then used for the first verticality inspection of the casing. The steel casing overlay section is constructed using dry drilling. ② For the lower effective pile length section:    - Initial boring is performed using a rotary drilling rig.    - After penetrating the ⑥1 layer of silty clay, switch to a positive circulation drilling rig to continue boring to the bottom.    - The mud mixture used for boring must be configured based on test boring data, including mixture ratios and air pressure adjustment parameters.

(3) Mud Preparation

Prepare sodium carboxymethyl cellulose (CMC) mud using clean water, bentonite, and soda ash, controlling performance parameters as follows: density 1.06–1.10 g/cm³, viscosity 23–28 s, with soda ash dosage at 5% of bentonite quantity. During drilling, maintain mud density at 1.10–1.25 g/cm³ and viscosity at 23–28 s to ensure borehole stability and secondary hole cleaning. Simultaneously control pH at 8–9 to maintain alkalinity and enhance clay dispersion.

(4) Mud Circulation System Setup

To achieve civilized construction practices, prevent secondary pollution, accelerate construction progress, and reduce costs, a dedicated mud circulation system is installed based on project characteristics and technical requirements. This ensures stable mud supply throughout the borehole formation process.

(5) Reinforcement Cage Fabrication and Hoisting

① To prevent stirrups from scraping the borehole wall during cage hoisting, centering supports are installed on the cage exterior (serving both centering and wall protection functions). These centering brackets are fabricated from Φ25 main rebars spaced at 3m intervals (twice the spacing of the reinforcement hoops). ② Grouting pipes are installed for all main tower piles. To prevent bending, deformation, or damage to the reinforcement cage and grouting pipes during hoisting, sectional reinforcement cages are lifted using a dual-crane hoisting method. Lifting points are strategically positioned based on the cage's length and center of gravity. ③ To enhance construction efficiency, reduce on-site cage jointing time, and minimize interference from overlapping equipment operations, one large tower crane is positioned at the main tower center. This crane handles cage transportation while also undertaking construction material transport tasks.

(6) Reverse Circulation Hole Cleaning

Due to equipment limitations and engineering geological conditions, placing the reinforcement cage is time-consuming. Therefore, after hoisting the cage, a pneumatic lifting device is used for secondary hole cleaning and debris removal at the bottom to ensure the thickness of bottom sediment meets design and specification requirements.

(7) Concrete Pouring

Concrete preparation must be completed 2 hours in advance. Pouring operations commence immediately after successful hole cleaning inspection to prevent sediment thickening due to prolonged delays. The initial pour volume is controlled to ensure the bottom of the chute is buried ≥2.5m in concrete, set at 2m³. The final pour elevation is 5% of the pile length above the designed pile cap (with the main tower pile final pour elevation set at 3.9m above the designed pile cap). The final concrete placement elevation must be precisely controlled using specialized measuring tools to prevent material waste from excessive elevation or non-compliance with design requirements due to insufficient elevation.

2.3.3. Influence of Construction Factors on Pile-Side Friction Resistance

(1) Casing Fabrication and Installation: Ensuring Initial Pile-Soil Interface Contact Quality

Steel casings are fabricated from Q345 steel with double-welded reinforcement (to prevent deformation). During vibratory driving, real-time verticality control using a theodolite prevents casing displacement that could cause borehole wall collapse or soil disturbance. If casing inclination or joint leakage occurs, it leads to loosening of the borehole wall soil, directly reducing the effective contact area between pile and soil and resulting in friction loss.

(2)Drilling and Mud Control: Stabilizing Interface Soil Strength

The upper section employs dry drilling with a hollow pile, while the lower section combines rotary drilling with positive circulation drilling to minimize soil disturbance. Improper drilling techniques can compromise borehole wall integrity and reduce soil strength, decreasing friction resistance by over 20%. CMC drilling fluid (density 1.06–1.25 g/cm³, viscosity 23–28 s) prevents borehole collapse through wall protection. Its alkaline environment (pH=8–9) enhances clay dispersion, forming a dense mud cake on borehole walls—preventing soil loss while strengthening bond strength between the pile and soil. Experiments demonstrate that this parameter mud can increase friction resistance by 10%–15% compared to conventional mud.

(3) Verticality of Reinforcement Cage Hoisting Relative to Pile Body: Ensuring Uniform Friction Force Transmission

A Φ25 centering bracket is installed on the outer side of the reinforcement cage (spaced 3m apart) to prevent stirrups from scraping the borehole wall during hoisting, which could cause soil loss and local friction failure. Dual-crane lifting with precision lifting point design prevents cage deformation, ensuring pile verticality—a 1% pile inclination causes uneven lateral friction distribution along the pile length. Localized stress concentration leads to premature friction failure, reducing overall bearing capacity by 8%–12%. Ultrasonic full-pile verticality inspection eliminates “skewed pile” issues: For every 0.5% deviation in verticality of extra-long piles, average friction loss reaches approximately 5% (based on relevant research in the “Technical Specifications for Building Pile Foundations” JGJ94). This demonstrates the critical impact of verticality control on friction resistance.

(4) Borehole Cleaning and Concrete Pouring: Preventing the Formation of “Ineffective Interfaces”

Air-lift reverse circulation secondary cleaning removes loose soil debris from the borehole bottom and walls. If sediment thickness exceeds 50mm, it forms a “buffer layer” at the pile base, creating gaps in the bond interface between the pile and soil. This prevents effective transmission of lateral friction resistance. Standards require sediment thickness ≤100mm for normal friction force transmission. This project directly ensures friction force transfer efficiency by controlling sediment within design limits through hole cleaning. Thickened concrete casing + initial filling volume ≥ 2m³ (with casing buried ≥ 2.5m) prevents concrete segregation or water ingress into the borehole caused by casing rupture: Segregated concrete reduces the pile surface roughness, diminishing friction with the soil; Water ingress into the borehole wall softens the surrounding soil (especially silty sand layers), reducing the soil's shear strength and consequently decreasing friction resistance by 10%–25%.

(5) Pile-Base Grouting: Indirectly Optimizing Friction Resistance Performance Environment

The main tower piles enhance pile-bottom bearing capacity through grouting at the pile base (using threaded connections + PTFE tape for leak prevention and triple check valves for pressure control). Simultaneously, the grouting pressure causes the pile body to float slightly upward, promoting tighter contact between the soil around the pile and the pile body itself. This effectively “compacts” the pile-soil interface, indirectly increasing friction resistance by approximately 5% to 8%. If grouting pipe leakage causes insufficient pressure, this “compaction effect” cannot be achieved, resulting in a corresponding loss of friction resistance.

The aforementioned construction measures directly or indirectly control the key factors influencing pile-side friction resistance across four dimensions: interface integrity (casing, hole cleaning), soil strength (mud, hole formation), transmission uniformity (verticality, reinforcement cage), and additional optimization (grouting). Engineering practice demonstrates that inadequate control in any single aspect—such as casing inclination, drilling fluid instability, or pile deviation—can significantly reduce friction resistance (typically by 10%–30%) and even result in substandard pile bearing capacity. By implementing the targeted measures outlined above, the efficiency of lateral friction can be enhanced to over 90% of the design value. This fully demonstrates that these construction factors exert a decisive and significant influence on lateral friction.

Comments 7:It is suggested to include photos of the field tests, such as the loading setup and testing instruments, to enhance credibility.

Response 7:Added.

Line 191-209:A schematic diagram of the reaction device is shown in Figure 2.

 

Figure 2. Diagram of Reaction Device.

The test loading method employed the “slow load maintenance method.” Test piles were loaded in nine stages, with each stage applying 1/10th of the estimated ultimate bearing capacity (3200 kN). The initial loading value was 6400 kN, and the maximum loading capacity reached 32000 kN. The static load field test is shown in Figure 3.

 

Figure 3. Static load test stacking diagram.

 

Comments 8:The paper needs to cite more influential recent research findings in the field.

Response 8:Added.

Line 67-128:Xiao Li et al. [17] analyzed and summarized the strain distribution, Poisson's ratio variation, axial force transfer, lateral resistance performance, and compression deformation patterns of large-diameter ultra-long piles based on the Ningbo LNG project. They concluded that ultra-long rock-embedded piles exhibit a bearing characteristic of “lateral resistance dominance with delayed end resistance,” quantitatively revealing the nonlinear relationship between pile-side friction resistance and relative pile-soil displacement. Duan Chang et al. [18] established a relationship between the uniaxial compressive strength of intact coral reef limestone and the ultimate lateral friction resistance and end resistance of piles. Based on field static load tests and core drilling tests of post-grouted rock-embedded cast-in-place piles, they proposed a calculation method for the bearing capacity design of such piles in coral reef limestone formations. Jin Ruibao et al. [19] investigated the effects of grouting methods and volumes on the vertical bearing capacity of large-diameter, extra-long piles in clayey soils based on static load tests. Results indicated that post-grouting significantly enhanced the ultimate bearing capacity of model piles while reducing pile-head settlement. He et al. [20] established a numerical model for extra-long piles based on Green-Lagrange strain theory, validated through field tests. They systematically investigated bearing characteristics under uniaxial and combined loads, revealing a complex sequence of failure modes. Tan et al. [21] proposed a novel machine learning (ML) approach coupling the extreme gradient boosting (XGBoost) algorithm with the state-of-the-art student-based optimization method (SPBO) to predict pile resistance. Results demonstrated that the proposed SPBO-XGBoost model outperformed all other models in prediction accuracy and reliability. Hu et al. [22] conducted in-situ static load tests on three ultra-high-rise, large-diameter, extra-long rock-anchor bored cast-in-place piles (LSRBP). They analyzed the effects of composite excavation and combined grouting on pile response, along with the optimization benefits of combined grouting. Results indicated that composite excavation enhances construction efficiency but compromises borehole quality and reduces LSRBP bearing capacity, while combined grouting compensates for this deficiency. Elsawwaf A et al. [23] proposed a hybrid method combining three-dimensional finite element (FE) modeling with evolutionary polynomial regression (EPR) based on a multi-objective genetic algorithm (MOGA) to predict the lateral bearing capacity of short straight piles and stepped conical piles in non-cohesive soils. Gao et al. [24] evaluated the effects of different additives (sodium carbonate, carboxymethyl cellulose, polyacrylamide, and barite powder) on modified mud properties and microstructure, determining optimal additive ratios. SEM tests revealed these additives produced denser mud cake structures, enhancing wall protection and filtration/loss reduction effects. Based on Randolph's research on pile resistance in homogeneous soils, Xiao et al. [25] proposed a novel, scientifically accurate three-stage analytical method for predicting pile settlement. Xu et al. [26] discovered through centrifuge model tests and finite element simulations that the unit external friction force propagates downward along the pile shaft and varies linearly with depth; while the unit internal friction force activates within a five-diameter (5D) zone above the pile tip and exhibits an exponential distribution with depth. They subsequently proposed a correction method to determine the unit internal sliding friction coefficient for open-ended single pile foundations, enabling precise assessment of their axial ultimate bearing capacity. Yuan et al. [27] conducted a series of centrifugal vibration table tests on large-diameter monopiles at scour locations, revealing that scour exerts a more pronounced influence on the higher-order modal frequencies of OWT systems. He Wentao et al. [28] investigated the seismic response of OWTs supported by single piles using advanced soil models. Results indicate that contributions from higher vibration modes become increasingly significant for large wind turbines, with soil-structure interaction playing a crucial role in dynamic response. Mozaffari N et al. [29] proposed a novel design model for large-diameter single piles, capable of accurately predicting pile behavior under lateral loads. Atroush A M et al. [30] rigorously evaluated machine learning (ML) and deep learning (DL) techniques. They found that while ML methods outperform traditional approaches in predicting pile lateral behavior, their “black-box” nature and reliance on data-driven insights yield results reflecting statistical robustness rather than clear geotechnical insights. Wan H Z et al. [31] investigated the effect of combined end-side grouting on the bearing capacity of large-diameter rock-bearing bored piles in highly weathered rock formations. Results demonstrated that combined grouting significantly enhanced the lateral and end resistance of bored piles, substantially increased bearing capacity, and effectively controlled settlement.

Line 853-886:

1. Xiao Li, Du Fenglei, Zhao Mingrui, et al. Field Test Study on Bearing Capacity and Deformation Characteristics of Large-Diameter Ultra-Long Rock-Embedded Piles [J/OL]. Chinese Journal of Geotechnical Engineering, 1-9 [2025-10-14].
2. Duan Chang, Wan Zhihui, Dai Guoliang, et al. Experimental Study on Basic Properties of Coral Reef Limestone and Vertical Bearing Characteristics of Post-Grouted Rock-Embedded Piles [J]. Journal of Rock Mechanics and Engineering, 2025, 44(03):721-736.
3. Jin R, Guo F, Xu N, et al. Laboratory Model Test Study on Bearing Characteristics of Super-Long and Large-Diameter Post-Grouting Piles in Clay Stratum[J]. Buildings, 2025, 15 (17):3038-3038.
4. He L, Liu X, Xie Y, et al. Study on complex failure modes of super-long piles in deep-water and soft-clay seabed under multiple combined loads[J]. Ocean Engineering, 2025, 336121806-121806.
5. Tan N, Duy-Khuong L, Q. T H, et al. Soft computing for determining base resistance of super-long piles in soft soil: A coupled SPBO-XGBoost approach[J]. Computers and Geotechnics, 2023, 162.
6. Tao H, Guoliang D, Zhihui W, et al. Field study of the effects of composite excavation and combined grouting on the response of large-diameter and superlong rock-socketed bored piles[J]. Acta Geotechnica, 2023, 19(4):1853-1871.
7. Elsawwaf A, Naggar E H, Choksi A F, et al. Predicting the lateral capacity of short step-tapered and straight piles in cohesionless soils using an FE-AI hybrid technique[J]. Ocean Engineering, 2025, 338121941-121941.
8. Qiang G, Qingliang H, Jian Z, et al. Experimental study on wall-protecting mud modification of super-long bored piles in the alluvial plain region of the Yellow River[J]. Construction and Building Materials, 2023, 368.
9. Kevin X, Shihong G, Jianghai W, et al. Three-Stage Analysis Method for Calculating the Settlement of Large-Diameter Extralong Piles[J]. International Journal of Geomechanics, 2023, 23(3).
10. Xu Z, Liang C, Jiang Y, et al. A correction method for unit internal skin friction of super-large diameter open-ended monopiles in clay[J]. Ocean Engineering, 2025, 337121891-121891.
11. Yuan Z, Liang F, Zhang H. Centrifuge model tests on scoured offshore wind turbines with large-diameter semi-rigid monopiles[J]. Soil Dynamics and Earthquake Engineering, 2025, 194109348.
12. He W, Takahashi A. Dynamic response analysis of monopile-supported offshore wind turbine on sandy ground under seismic and environmental loads[J]. Soil Dynamics and Earthquake Engineering, 2025, 189109105-109105.
13. Mozaffari N, Mesgarnejad A, Jhita P, et al. Extended Winkler Model for design of offshore wind turbine large diameter monopiles[J]. Ocean Engineering, 2024, 313(P3):119619-119619.
14. Atroush A M, Aboelela A, Hemdan D E E. Beyond p-y method: A review of artificial intelligence approaches for predicting lateral capacity of drilled shafts in clayey soils[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2024, 16(9):3812-3840.
15. Wan H Z, Duan C, Hu T, et al. Field Study on Bearing Capacity of Large-Diameter Rock-Socketed Bored Piles with Combined Grouting in Highly Weathered Rock Layers[J]. Rock Mechanics and Rock Engineering, 2024, 57(10): 8701-8722.

 

 

 

 

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The author have well reply my comment 7. Please revise and reconsider the work like "Numerical investigation of morphological effects on crushing characteristics of single calcareous sand particle by finite-discrete element method" and others. 

Author Response

Comments 1: Please revise and reconsider the work like "Numerical investigation of morphological effects on crushing characteristics of single calcareous sand particle by finite-discrete element method" and others.

Response 1: Added. We have added a chapter on discrete element method simulation and included a discussion section. Line 739-675:3.2.Discrete Element Simulation The currently prevalent macro-scale finite element analysis method can determine the bearing capacity and deformation characteristics of piles. However, due to the complexity of the pile-bottom environment and variations in soil displacement, macro-scale simulations cannot accurately reflect the micro-scale movement patterns of soil particles. In contrast, the discrete element method, which treats soil particles as discrete units, can reasonably describe the displacement and deformation patterns of pile-soil interaction. 3.2.1.Particle Flow Model Construction Using discrete element software, particle flow code was developed. After trial calculations, matching particle and wall parameters were selected to construct a computational model suitable for numerical simulation. The contact model employed linear contact, with ball elements simulating soil particles, wall elements simulating soil boundaries, and ball elements simulating pile foundations. Graded soil particles were used for the soil sample, as shown in Figure 1(a). The simulated displacement of soil around the pile, as shown in Figure1(b), is 107.01 mm, while the measured settlement is 107.33 mm. The error is negligible. Therefore, the established model is suitable for analysis.             (a)   (a) (b)              Figure 1.Pile-Soil Model and Pile-Surrounding Displacement Contour Map 3.2.2Micro-parameter calibration The relationship between granular flow micromechanical parameters and soil macromechanical parameters was established through matching calculations or numerical simulation tests. Combined with laboratory geotechnical tests, a trial-and-error approach was employed to calibrate the microparameters of discrete particles. This yielded the normal stiffness and shear stiffness of soil particles, the normal stiffness and shear stiffness of piles and model box walls, as well as the friction coefficients of particles and walls. Peat soils are formed by particles, while piles are formed by walls. Results are shown in Table 3. The specific calibration process is referenced in the literature. Basic parameters of the granular flow model are presented in Table 1. Table 1.Microscopic Parameter Calibration Values for Discrete Element Models. Model Particle density E/pa Kn/ks fc v R n Particle-Particle 2830 2×109 2 0.8 0.6 0.2 0.15 Particle-Wall - 2×109 2 2.5 0.6 - - 3.2.3 Application of Pile Loads Currently, due to computational limitations, only single-pile stress analysis is conducted. Lateral pressure from surrounding soil is simulated using wall elements. Vertical loads and lateral pressures are applied through servo control, with the servo control program written in FISH language. After generating the friction pile model, confining pressure is first applied to bring the pile to its initial state upon construction completion. Next, a rigid wall element with a diameter of 0.5m is controlled to simulate loading plate application onto the pile body. This replicates the graded loading process of a load test, synchronizing the target pressure with the graded loading stages of the load test. When the target pressure is reached, the wall stops moving, thereby halting the loading process. Due to computational limitations, only single-pile stress analysis is currently performed. Lateral pressure from surrounding soil is simulated through wall element loading. Vertical loads and lateral pressures are applied via servo control. The servo control program is written using the FISH language. After generating the friction pile model, confining pressure is first applied to bring the pile to its initial state upon construction completion. Then, a rigid wall element with a diameter of 0.5m is controlled to simulate the loading plate applying load to the pile body. This simulates the graded loading process of the load test, achieving synchronization between the target pressure and the graded load of the load test. When the target pressure is reached, the wall stops moving, thereby ceasing loading. 3.2.4.Comparison of Applicability Between Two Numerical Methods The finite element method (FEM) and discrete element method (DEM) each possess distinct advantages in studying pile foundation bearing capacity. FEM, based on continuum mechanics theory, excels at analyzing overall bearing characteristics and stress distribution with high computational efficiency, yet struggles to capture micromechanical interactions between particles surrounding the pile. DEM realistically describes particle rearrangement and interface slip processes, making it suitable for revealing friction mobilization and localized failure mechanisms, but it involves substantial computational demands and exhibits pronounced scale effects. Overall, FEM is suitable for macroscopic analysis, while DEM is better suited for studying microscopic mechanisms. Combining both methods enables multiscale characterization of the bearing behavior of extra-long, large-diameter friction piles.   Line 946-857:4.2Influence Analysis of Parameters Based on Discrete Element Simulation 4.2.1. Influence of Peat Soil Thickness To investigate the influence of peat interlayers in lacustrine sedimentary strata on ultra-long large-diameter friction piles, the original model was modified as follows: soil layer thickness set to 196 m, pile length to 98 m, and pile radius to 0.5 m. For computational convenience, only three soil layers were retained while other parameters remained unchanged. Specific working conditions are detailed in Table 10. Figure 21 presents the load-settlement curve contour plot.       Table 2. Parameters for Different Working Conditions.   Soil layer Thickness/m Working Condition 一 二 三 四 ⑩Clay 88.2 78.4 68.6 58.8 ⑨2Peaty soil 19.6 39.2 58.8 78.4 ⑩Clay 88.2 78.4 68.6 58.8       (a)Condition 1 (b)Condition 2     (a)Condition 3 (b)Condition 4 Figure 2. Stratigraphic Thickness Load Settlement Curve Cloud Map for Different Weak Layers. As shown in Figure 2, the curve profiles exhibit consistent trends with increasing thickness of the weak soil layer. However, under identical loading conditions, it is evident from the graph that thicker weak layers result in correspondingly greater settlement values. 4.2.2. Influence of Pile Length in Peaty Soils Establish discrete element models for friction piles with pile lengths of 88m, 108m, and 118m in peat soil layers to investigate the effect of pile length on the vertical bearing characteristics of friction piles, while keeping other pile design parameters constant. Figure 22 shows the vertical displacement of the soil around the pile.       (a)L=118m (b)L=108m (c)L=88m Figure 3. Displacement Contour Map of Soil Around Piles at Different Pile Lengths During Termination of Loading. As shown in Figure 3, the displacement of friction piles increases with pile length, reaching 0.64m, 0.61m, and 0.31m respectively, consistent with the results obtained from finite element simulations. Specifically, pile settlement increases with pile length. As pile length increases, the displacement of soil particles within the pile body also increases. However, once the pile reaches a critical length, further increases in pile length have a negligible effect on improving the bearing capacity of the pile foundation. 4.2.3. Influence of Pile Diameter in Peat Soil Establish discrete element models for four friction piles with diameters of 1m, 1.5m, and 2m in peat soil layers to investigate the influence of pile diameter on the vertical bearing characteristics of friction piles, while keeping other pile design parameters constant. Figure 23 shows the vertical displacement of the soil around the pile.       (a)D=2.0m (b)D=1.5m (c)D=1.0m Figure 4. Displacement Contour Maps of Soil Around Piles at Different Diameters During Termination of Loading. As shown in Figure 4, As the pile diameter increases, the displacement of soil particles in the friction pile decreases to 0.32 m, 0.28 m, and 0.197 m, respectively, consistent with the results obtained from finite element simulations. 4.2.4. Summary A total of ten working conditions were simulated. Three working conditions were analyzed for pile length and pile diameter, while four working conditions were analyzed for soft layer thickness. The summary is presented in Table 11. Table 3. All operating conditions for finite element analysis testing. Operating Condition Number Pile length/m Pile diameter/m Thickness of rock and soil mass/m Thickness of the weak layer/m A1 98 1.0 196 19.6 A2 98 1.0 196 39.2 A3 98 1.0 196 58.8 A4 98 1.0 196 78.4 B1 118 1.0 196 196 B2 108 1.0 196 196 B3 88 1.0 196 196 C1 98 2.0 196 196 C2 98 1.5 196 196 C3 98 1.0 196 196 According to the results obtained from the discrete element model simulation, the conclusions reached are consistent with those from the finite element simulation. 4.Discussion This study combines finite element modeling (FEM) with discrete element modeling (DEM) to analyze the bearing characteristics of ultra-long, large-diameter piles in complex geological formations. Key findings reveal that finite element simulations demonstrate increased pile bearing capacity with larger pile diameters and greater pile lengths. while discrete element modeling further reveals that soil particle displacement around the pile exhibits a “superficial dispersion and deep aggregation” pattern as pile diameter and length increase. The results from both simulation methods corroborate each other, quantifying the influence of pile diameter from a macromechanical perspective while elucidating the underlying mechanisms at the microscopic particle level. This provides multidimensional support for related engineering design and theoretical research. Regarding the complementarity of simulation methods: Finite element simulation, leveraging its efficiency in modeling continuous media, precisely captures the macro-mechanical response between pile foundations and soil. As pile diameter increases, both pile stiffness and bearing area grow synchronously, leading to more uniform stress distribution within the pile and surrounding soil while mitigating stress concentration—consistent with predictions from soil mechanics' continuous medium theory. Discrete element simulation, however, overcomes the limitations of the continuous medium assumption by clearly revealing the microscopic movement patterns of soil particles: at small pile diameters (<800 mm), the compaction effect of pile penetration on surrounding particles is concentrated near the surface, leading to high particle dispersion and disordered displacement; When the pile diameter increases to 1000 mm, the squeezing stress propagates deeper, forming an ordered stress system among particles with a significantly reduced displacement range. This microscopic mechanism also provides a rational explanation for the macroscopic phenomenon of the “critical bearing capacity threshold” observed in finite element simulations. The combination of these two methods achieves dual verification through “macroscopic mechanical quantification + microscopic mechanism analysis,” avoiding the potential limitations of a single simulation approach. The limitations of this study must be objectively stated: the simulation process did not account for the nonlinear rheological properties of the soil or damage effects during pile construction, and the particle model in the discrete element simulation simplified the complex composition of actual soil. Furthermore, the simulation was limited to a single soil type (peaty soil) and did not address composite soils or special geological conditions. Future research should incorporate soil rheological constitutive models, optimize discrete element particle parameters, and extend simulations to diverse geological scenarios. Integrating field prototype experiments to validate results will further enhance the accuracy of this simulation method in pile foundation engineering. In summary, this study employs a synergistic analysis of finite element and discrete element simulations to clarify the influence patterns of pile length, pile diameter, and soft layer thickness on macro- and micro-scale mechanical responses of pile foundations. The findings not only provide multidimensional data support for optimizing pile diameter design but also establish a reference paradigm for applying the “finite element-discrete element coupled simulation method” in similar engineering problems. This holds significant theoretical value and practical significance for enhancing the scientific rigor and safety of pile foundation engineering design.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors The author provided a very good response to my question, and the revisions are thorough. I recommend accepting it in its current form.

Author Response

Thank you very much for your positive feedback and valuable recognition of my response. I greatly appreciate your thorough review and constructive evaluation. I will proceed with the current version as you recommended.

Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

It seem that the authors did not fully understand my comment. Please revise and consider the publication like "Numerical Investigation of Morphological Effects on Crushing Characteristics of Single Calcareous Sand Particle by Finite-Discrete Element Method" and others (e.g., 10.1016/j.powtec.2023.119204).  I would like to give them one chance to revise.