Numerical Investigation of Large-Diameter Bored Piles under High-Strain Dynamic Testing: A Case Study in New Alamein City

Round 1

Reviewer 1 Report

The study mainly discusses the numerical investigation of large-diameter bored piles under High Strain Dynamic Testing (HSDT), with a case study conducted in New Alamein City. It aims to analyze the performance and dynamic behavior of large-diameter bored piles under axial compressive impact force using a numerical approach. In contrast to traditional Static Load Testing (SLT), the research examines the time and cost efficiency of HSDT. The research uses 2D axially symmetric non-linear finite element modeling (FEM) with the software Plaxis 2D, incorporating Mohr-Coulomb and Hardening Soil small-strain models to simulate soil response. I recommend a major revision, and here are my suggestions for changes and questions:

1. How was the FEM model calibrated to ensure the authenticity of simulation results?

2. Can you provide a more detailed justification for the specific soil models used in the simulation?

3. Are dynamic pile-soil interactions, including possible strain-rate effects on soil behavior, adequately represented in your models?

4. Can you provide more information on the validation process of numerical findings besides the use of the Modified Unloading Point (MUP) method?

5. How accurately does the numerical model predict load-displacement behavior compared to field test results?

6. What is the influence of pile cushion properties on the impact force-time history, and how is this accounted for in the model?

7. What are the limitations of the approach used in the study, and how could they affect the outcomes?

Quite good.

Author Response

Reply for Reviewers Comments for the Paper

“Numerical Investigation of Large-Diameter Bored Piles Under High Strain Dynamic Testing; A Case Study in New Alamein City”

Tarek N. Salem, Ahmed S. El-Saei, Katarína Krajníková, Dušan Katunský, Rana Hassan

               The authors express gratitude and appreciation for the reviewers' effort and time. We respectfully received their comments and valuable recommendations, which greatly enhanced the manuscript's clarity and helped accurately present the work's novelty. Please note that the revised manuscript marked most of the changes in yellow. Our response to each comment is shown below.

Reviewer #1

The study mainly discusses the numerical investigation of large-diameter bored piles under High Strain Dynamic Testing (HSDT), with a case study conducted in New Alamein City. It aims to analyze the performance and dynamic behavior of large-diameter bored piles under axial compressive impact force using a numerical approach. In contrast to traditional Static Load Testing (SLT), the research examines the time and cost efficiency of HSDT. The research uses 2D axially symmetric non-linear finite element modeling (FEM) with the software Plaxis 2D, incorporating Mohr-Coulomb and Hardening Soil small-strain models to simulate soil response.

Authors: Thank you for the comprehensive summary.

I recommend a major revision, and here are my suggestions for changes and questions:

Authors: All recommendations and suggestions for changes are taken into consideration very carefully.

1. How was the FEM model calibrated to ensure the authenticity of simulation results?

Authors: The studied site, as described in Section 2, contains the collaborative data of the soil profile, field Static Load Testing (SLT), field High Strain Dynamic Testing (HSDT), and a sample of this data, as shown in Figure 1 below.

Figure 1. Measured force F(t) response and measured Zv(t) (velocity times impedance) wave response.

            To accurately simulate the response of the soil to static and dynamic impact loading developed by static and dynamic load testing, the model geometry is adjusted to eliminate boundary effects on the results (as described in Section 3.1). Subsequently, the calibration technique is performed on the developed numerical model (FEM-Plaxis 2D) as follows (Figure 2):

Figure 2. Flowchart of the verification process of the developed numerical model (FEM-Plaxis 2D) against the field test records.

• Soil investigation input, i.e., determining initial soil parameters for each layer.
• Performing the dynamic modeling of the High Strain Dynamic Testing (HSDT), i.e., dynamic response.
• Collect calculated Force (F) and Velocity x Impedance (v) signals.
• Match the derived signals with the field record.
• A signal-matching procedure verifies the dynamic response of the developed numerical model. A set of parameters is varied and adjusted, including soil-pile interface parameters such as deformation characteristics and shear strength. As shown in Table 1, the adopted parameters from the signal-matching process are also assessed and matched to the ground or soil parameters obtained from the site investigation data.
• Derive the load-settlement curve from dynamic measurements using the Modified Unloading Point (MUP) method (hyperbolic approximation).
• Conduct the static modeling of the Static Load Test (SLT).
• Compare Load-Settlement Curve Results for Both Dynamic and Static Modeling (FEM) Against Field Measurements.

The authors recommend replacing Figure 5a, which depicts the modeling procedures of the developed FEM, with Figure 2, which illustrates the verification process of the developed FEM against field test records and provides a clearer calibration process.

2. Can you provide a more detailed justification for the specific soil models used in the simulation?

Authors: For dynamic and static loading simulations, the Mohr-Coulomb (MC) model is used to characterize the nonlinear response of the upper layers from large strains to small ones. On the other hand, the lower layer at the toe is modeled using the Hardening Soil model with small-strain stiffness (HS-small), which is a suitable constitutive soil model to capture the small strain (e.g., hysteretic damping) response. The MC model directly predicts wave velocities (i.e., compression and shear waves) in the soil deposit. In contrast to the MC model, the HS-small model wave velocities are unclear because they vary due to the stress-dependent stiffness. In addition, the MC soil model is better for presenting the actual field measurement, as shown in the verification results.

The authors provide more details for the constitutive soil model, HS-small, in the revised manuscript. (Kindly see page 6, section 3.4, L251-258)

3. Are dynamic pile-soil interactions, including possible strain-rate effects on soil behavior, adequately represented in your models?

Authors: In soil dynamics, small-strain stiffness has been a well-known phenomenon for a long time. In static analysis, the findings from soil dynamics have long been considered not to be applicable. Seeming differences between static and dynamic soil stiffness have been attributed to the nature of loading (e.g., inertia forces and strain rate effects) rather than to the magnitude of applied strain which is generally small in dynamic conditions (earthquakes excluded). As inertia forces and strain rate have only little influence on the initial soil stiffness, dynamic soil stiffness and small-strain stiffness can in fact be considered as synonyms (Benz, 2007; Plaxis 2D, 2022).

The authors use the HS-small, which has almost entirely the same parameters as the HS model. In fact, only two additional parameters are needed to describe the variation of stiffness with strain (Plaxis 2D, 2022):

• The initial or very small-strain shear modulus G₀.
• The shear strain level g₇ at which the secant shear modulus G_s is reduced to about 70% of G₀ (as depicted in Figure 3 below).

Figure 3. Secant and tangent shear modulus reduction curve

During unloading and reloading, the standard hardening soil model indicates elastic material behavior. However, soils can be regarded as purely elastic, in which the characteristic strain range is very small. Increases in strain amplitude cause a nonlinear decrease in soil stiffness. Figure 4 depicts an example of a stiffness reduction curve, as well as the typical shear strains that can be measured close to geotechnical structures and the appropriate strain ranges of lab tests.

Figure 4. Characteristic stiffness-strain behavior of soil with typical strain ranges for laboratory tests and structures (after Atkinson & Sallfors,1991).

The dynamic modulus of elasticity is defined to estimate the initial shear modulus (Go) by applying the chart developed by Alpan (1970). Hence, the adopted static soil modulus of elasticity, that is, E_dynamic » 2 E_static (as depited in Figure 5). The shear strain (g_0.7) is adopted at 8x10⁻⁴ for the calcareous claystone fragment layer (at the pile tip) to assess the impact of the small-strain parameters of the HS-small model on the measured velocity at the transducer location (at the pile head) (Kindly see page 7, section 3.4, L250-272).

Figure 5. Relation between dynamic (E_dynamic = E₀) and static soil stiffness (E_Static ≈ E_ur) after Alpan (1970).

In the case of dynamic applications using the MC model, alternative and additional parameters may be used to accurately define the dynamic stiffness based on wave velocities (i.e., Compression wave velocity and Shear wave velocity). This generally requires a much larger small strain stiffness rather than a stiffness at engineering strain levels.

Therefore, the numerical simulations accurately present the dynamic soil-pile interaction, as illustrated above. Also, the interface stiffness is derived from the deformation characteristics of the adjacent soil media at each stratum (Kindly see page 6, section 3.2 L222-226).

4. Can you provide more information on the validation process of numerical findings besides the use of the Modified Unloading Point (MUP) method?

Authors: As the study approaches (as shown in Figure 2), the authors clarify the modeling procedure for the interpreted analysis of CAPWAP software (as summarized in Figure 6).

The soil resistance determined using numerical modeling of the HSDT is the total compressive resistance, which includes both dynamic and static resistances. Additional analysis is required to separate the effects of dynamic soil-dependent behavior from the predicted total resistance, and subsequently, the mobilized static resistance is acquired, i.e., the calculated load-settlement response. Hence, the MUP is employed to interpret the dynamic responses measured from the FEM modeling to derive the calculated load-settlement curve. As CAPWAP software, the static numerical analyses, SLT, are performed using the adopted and matched soil deposit parameters (as shown in Table 1) acquired from the specific signal-matching technique. Then, a comparison is performed between the predictions of the static numerical model (FEM), the MUP, and the CAPWAP (real HSDT) against the results of real SLT. The revised manuscript clarifies these comparisons in more detail (Kindly see page 16-17, section 7.3, L513-538).

Figure 6. Flowchart showing the general approach to closed-form analysis of dynamic load testing (CAPWAP).

5. How accurately does the numerical model predict load-displacement behavior compared to field test results?

Authors: The ultimate static resistance predicted through CAPWAP (field HSDT) is approximately 5% higher than the static modeling (FEM), and both final displacement difference percentage is 11%. The difference between the measured SLT settlement and the computed HSDT is mainly due to the differences between the actual performance of each test. The concept in an induced dynamic test deformation due to the HDST is totally different from the concept of settlements induced by a gradually increasing static loads. In comparison to the field SLT results, the MUP determines the mobilized static pile resistance and load-settlement response with relatively large differences. Nevertheless, the highest measured settlement during SLT is 11.43 mm, whereas the computed value from the MUP is 7.01 mm, with a difference of nearly 39%. It is noted that the varied loading rates (Rizvi et al., 2022) may be associated with the difference in FEM and CAPWAP results compared to the field SLT. In addition, the deformation characteristics and shear strength parameters derived from the signal-matching analysis for both FEM and CAPWAP may be slightly lower than the ground or soil investigation data.

6. What is the influence of pile cushion properties on the impact force-time history, and how is this accounted for in the model?

Authors: The pile cushion comprises various materials, including hardwood, masonite fiber plates, and other artificial materials affecting cushion stiffness. Moreover, the pile cushion material thickness, cross-sectional area, and elastic modulus also affect the equivalent stiffness (k).

The cushion stiffness, k, governs the impact force's duration and amplitude at the pile top. The cushion stiffness is calculated through equation (8). The applied force responses are calculated using equations (7)–(15). Figure 7 indicates the impulse force-time response developed at different cushioning stiffnesses (k) considered in the dynamic analysis (i.e., parametric study): k = 500, 800, 1,012.5, 1,200, and 1,500 MN/m.

Figure 7. Shape of force pulses developed at different cushion stiffness (k).

7. What are the limitations of the approach used in the study, and how could they affect the outcomes?

Authors: Limitations of the research approach are listed below:

• However, the study approach may not be applicable to fine-grained soil formation; more investigations are required to assess the performance of bored large-diameter piles installed in cohesive soil under the HSDT. Moreover, the bored piles installed in coarse-grained soil formations need more exploration.
• The result may only be accurate if it is within the developed guidelines and design procedures for the HSDT to perform on bored piles effectively. Table 1 shows the study characteristics of adequate HSDT on bored piles, along with the lower and upper limits, average value, and standard deviation.

Table 1. Limitations of the execution of adequate HSDT on bored piles.

Author Response File: Author Response.pdf

Reviewer 2 Report

In Line 146, what did authors mean by "the studied tower code is LD-04".

In Section 3.2, simulation of interaction between the soil deposit and the bored pile should be explained in details.

In Line 251, why was soil damping ration assumed 5%. According to Table 1, for different soil layers this assumption was considered.

In Section 3.5, what criteria were used to determine mesh size.

In Section 4, how did the authors obtain Equation 4?

In Section 4, what is the difference between Equation 10 and Equation 11.

In Figure 4, how did the authors measure the impact load. The specification of sensors and sampling rate of measured data should be explained.

What is B parameter in Equation 13?

How was the Zv was obtained from measurement in Figure 5a?

Differences between results indicated in Figure 7a should explained in details.

Differences between results indicated in Figure 7b should explained in details.

In Figure 10a, how was static mobilized resistance derived?

In Line 190, "For SLT modeling, the extreme horizontal (at the bottom) and vertical boundaries are constrained." The sentence should be revised grammatically.

Author Response

Reply for Reviewers Comments for the Paper

“Numerical Investigation of Large-Diameter Bored Piles Under High Strain Dynamic Testing; A Case Study in New Alamein City”

Tarek N. Salem, Ahmed S. El-Saei, Katarína Krajníková, Dušan Katunský, Rana Hassan

               The authors express gratitude and appreciation for the reviewers' effort and time. We respectfully received their comments and valuable recommendations, which greatly enhanced the manuscript's clarity and helped accurately present the work's novelty. Please note that the revised manuscript marked most of the changes in yellow. Our response to each comment is shown below.

Reviewer #2

The authors acknowledge that the improvement of the manuscript is due to the efforts of the reviewers and their valuable recommendations. All comments and suggestions are taken into consideration very carefully. Many thanks and appreciation!

In Line 146, what did authors mean by "the studied tower code is LD-04".

Authors: The tower is entitled “NORTH EDGE TOWERS—NEW ALAMEIN (LD 04)” and is one of the series of towers owned by the Ministry of Housing, Utilities, and Urban Development. (Kindly find the link below that contains the LD-04 tower details: https://www.siac.com.eg/?q=experience-sectors/building/north-edge-towers-new-alamein-ld-04)

In Section 3.2, simulation of interaction between the soil deposit and the bored pile should be explained in details.

Authors: The numerical simulation of the soil deposit and the bored pile interaction, i.e., the interface elements, has been added in more detail in the revised manuscript. (Kindly see page 5-6, section 3.2, L222-226)

In Line 251, why was soil damping ratio assumed 5%. According to Table 1, for different soil layers this assumption was considered.

Authors: The soil damping ratio is assumed to be 0.05, considering engineering practice values and consistently matching with the numerical model predictions to the measured field responses (i.e., force and velocity time impedance (Zv) records). Moreover, from Table 2, it is evident that a typical damping ratio (x) is 0.05 for internal damping in soils.

Table 2. Some Typical Values of Internal Damping in Soils (Richart et al., 1970).

In Section 3.5, what criteria were used to determine mesh size.

Authors: The soil deposit and the pile are modeled using 15-node triangular elements. The element size is mainly controlled by the time-step size along with structural objects, soil medium, applied loads, and boundary conditions were considered during the mesh generation process. The whole mesh is subdivided into three zones (as depicted in Figure 2c). The mesh discretization is refined directly close to the bored pile, and the local refinement decreases farther away from the bored pile. The whole meshing discretization is developed using coarse, medium, and fine conditions. Regarding the computational requirements and accuracy, the load-settlement curve and the predicted velocity-time response curve at the top of the tested pile are employed as the mesh convergence criterion. In the analysis, the additional option of global refinement mesh is utilized to supply a good-quality mesh for every geometry, which also takes into account the necessary mesh refinement around structural elements and loads. (Kindly see page 6, section 3.2, L227-230)

In Section 4, how did the authors obtain Equation 4?

Authors: Clough and Penzien (1975) first obtained the impact force on the pile top when the free drop hammer impacts the elastic pile top; this approach is also employed in this paper. The physical model of dynamic pile hammering developed by Chen et al. (2003) (as depicted in Figure 3a) is utilized in this study. The procedures for this approach are discussed in detail elsewhere (Chen et al., 2003; Wang et al., 2022).

In Section 4, what is the difference between Equation 10 and Equation 11.

Authors: The authors apologize for this mistake that occurred during the editing of the manuscript according to the journal template. The correct equation has been added to the revised manuscript. Thanks for grabbing our attention! (Kindly see page 10, section 4, L321)

In Figure 4, how did the authors measure the impact load. The specification of sensors and sampling rate of measured data should be explained.

Authors: The calculated and measured force-time responses F(t) are developed from the calculated and measured strain ε(t) respectively, at the stress point (FEM) and the strain transducer, both at the same elevation at the pile head, using equation (20) (Kindly see page 15, section 7.2, L456-460). The revised manuscript clarifies the strain transducer and accelerometer sensor specifications, as well as sampling rate, in greater detail (Kindly see page 4, section 2, L172-177).

What is B parameter in Equation 13?

Authors: The B factor represents the hyperbola formula's parameter. Also, referring to Holscher et al. (2011), this parameter has no more definition.

How was the Zv was obtained from measurement in Figure 5a?

Authors: In practice, velocity v(t) is the particle velocity determined by integrating accelerometer records at the top of the pile with respect to time, t as per equation:

The pile impedance Z (dynamic stiffness) is based upon the material properties and the pile material density, as per equation (19). Both the calculated and measured Zv(t) waves are derived from the multiplication of the velocity-time response and the impedance Z (Kindly see page 14-15, section 7.2, L448-458).  

Differences between results indicated in Figure 7a should explained in details.

Authors: The results, as shown in Figure 7a, have been clarified (Kindly see page 16-17, section 7.3, L503-506; L525-527).

Differences between results indicated in Figure 7b should explained in details.  

Authors: The results, as shown in Figure 7b, have been clarified (Kindly see page 17, section 7.3, L533-536).

In Figure 10a, how was static mobilized resistance derived?

Authors: The derived static mobilized resistance through the MUP method at the unloading point (i.e., zero-instant velocity) can be estimated from the static soil response and the dynamic response (i.e., inertia force) as per equations (16)-(18) (Kindly see page 13, section 6, L384-420). In addition, Figure 8 illustrates the calculated load-settlement curve from the MUP approach for different drop heights.

Figure 8. The load-settlement curve derived from the MUP method for different drop heights.

In Line 190, "For SLT modeling, the extreme horizontal (at the bottom) and vertical boundaries are constrained." The sentence should be revised grammatically.

Authors: Thanks for the notice! That has been modified (Kindly see page 4-5, section 3.1, L201-202).

Author Response File: Author Response.pdf

Reviewer 3 Report

The bearing capacity of bored piles with large-diameter is an important topic in geotechnical engineering. High-Strain Testing can provide a unique alternative technique to traditional Static Load Testing (SLT) for determining the static compressive resistance of the bored piles, and HSDT is widely utilized in the bearing capacity testing of bored piles. This article numerically explores the performance of large-diameter bored piles during the HSDT and understands their dynamic behavior under an axial compressive impact force. The work is nice and should be interested to the readers of Buildings. Comments on this article are summarized as:

(1)   Line 17, the authors mentioned ‘The tested pile is 1.20 m diameter’. What diameter of pile foundation can be called a large diameter pile?

(2)   What pile forming process is used for the testing pile in this article? What is the quality of its pore formation?

(3)   Lines 213-214, why the global refinement mesh is utilized?

(4)   Lines 320-321, the authors mentioned, ‘Consequently, the system damping ratio no longer remains constant’. What is its specific pattern of change?

(5)   What is the reason for that the results in Figure 5b are not completely consistent?

(6)   Some relevant works should be considered during the revision, such as, Theoretical analysis of dynamic performance of concrete-filled steel tube pile under vertical load, Theoretical model for investigating three-dimensional effect in integrity test of open-end pipe piles, Horizontal vibration characteristics of pile groups in unsaturated soil considering coupled pile-pile interaction, A review of pile foundations in viscoelastic medium: dynamic analysis and wave propagation modeling.

The English quality of this manuscript is good.

Author Response

Reply for Reviewers Comments for the Paper

“Numerical Investigation of Large-Diameter Bored Piles Under High Strain Dynamic Testing; A Case Study in New Alamein City”

Tarek N. Salem, Ahmed S. El-Saei, Katarína Krajníková, Dušan Katunský, Rana Hassan

               The authors express gratitude and appreciation for the reviewers' effort and time. We respectfully received their comments and valuable recommendations, which greatly enhanced the manuscript's clarity and helped accurately present the work's novelty. Please note that the revised manuscript marked most of the changes in yellow. Our response to each comment is shown below.

Reviewer #3

The bearing capacity of bored piles with large-diameter is an important topic in geotechnical engineering. High-Strain Testing can provide a unique alternative technique to traditional Static Load Testing (SLT) for determining the static compressive resistance of the bored piles, and HSDT is widely utilized in the bearing capacity testing of bored piles. This article numerically explores the performance of large-diameter bored piles during the HSDT and understands their dynamic behavior under an axial compressive impact force. The work is nice and should be interested to the readers of Buildings.

Authors: Thanks for the comprehensive summary and the kind words.

Comments on this article are summarized as:

Authors: All comments and suggestions are taken into consideration very carefully.

(1)   Line 17, the authors mentioned ‘The tested pile is 1.20 m diameter’. What diameter of pile foundation can be called a large diameter pile?

Authors: O’Neil and Reese (1999) defined large-diameter piles as those with diameters larger than 760 mm. According to the Egyptian Code of Practice (ECP) for Soil Mechanics and Foundation Design and Construction, 202/4, bored piles with diameters larger than 600 mm are considered large-diameter piles.

(2)   What pile forming process is used for the testing pile in this article? What is the quality of its pore formation?

Authors: The test pile is a cast-in-situ concrete bored pile. The forming technique is according to the Egyptian Code of Practice (ECP) for Soil Mechanics and Foundation Design and Construction, 202/4, and Drilled Shafts Construction Procedures and LRFD Design Methods (FHWA NHI-18-024).

The steps in the process of constructing a bored pile (i.e., drilled shaft) using drilling fluids (bentonite) for boring side stability are summarized as follows:

1. Excavate the hole while maintaining a positive fluid head pressure at all times.
2. Clean the hole and prepare for concrete by removing any loose debris from the base of the excavation and by cleaning the fluids to remove excessive suspended materials.
3. Inspect the excavation to ensure that the base is sound and the fluid is reasonably clean.
4. Place the reinforcement.
5. Place the concrete using a tremie, minimizing the exposure of the concrete to the drilling fluid by maintaining embedment of the tremie below the rising surface of fresh concrete Extract any temporary casing as necessary and clean the top of the concrete surface in preparation for the connection to the structure.

The tested piles are formed with high quality; the pile integrity through the Field HSDT test is good, and matching dynamic responses with the numerical simulation also indicated the high quality of the boring technique.

(3)   Lines 213-214, why the global refinement mesh is utilized?

Authors: Besides, the whole mesh is segmented into three zones (i.e., local refinement) as depicted in Figure 2c; the additional option of global refinement mesh provided by PLAXIS is utilized to supply a good-quality mesh for every geometry, which also considers the necessary mesh refinement around structural elements and loads. 

(4)   Lines 320-321, the authors mentioned, ‘Consequently, the system damping ratio no longer remains constant’. What is its specific pattern of change?

Authors: The system's damping (x) is calculated through equation (11), which depends on the pile's elasticity modulus and cross-sectional area. The authors expect a slight reduction of impact force to occur, as shown in Figure 4b, which indicates either the pile impedance (Z) is not uniform due to the pile head being affected (i.e., damaged) from the impact; hence, the damping of the system is no longer a constant value.

(5)   What is the reason for that the results in Figure 5b are not completely consistent?

Authors: The authors conduct the best matching of dynamic responses through numerical modeling to the field records. Several factors affect the strain wave propagating through the pile, such as the soil layer properties, soil-pile interface element, mesh size, time step, and damping. In practice, the damping could be a significant contributing factor. However, actual damping could not be accurately calculated due to the large stiffness between the different soil layers along the pile length.

(6)   Some relevant works should be considered during the revision, such as, Theoretical analysis of dynamic performance of concrete-filled steel tube pile under vertical load, Theoretical model for investigating three-dimensional effect in integrity test of open-end pipe piles, Horizontal vibration characteristics of pile groups in unsaturated soil considering coupled pile-pile interaction, A review of pile foundations in viscoelastic medium: dynamic analysis and wave propagation modeling.

Authors: These references are added to the literature and highlighted in the references section (Kindly see page 3, section 1, L129-139).

References:

Alpan, I., 1970. The geotechnical properties of soils. Earth-Science Rev. 6, 5–49. https://doi.org/https://doi.org/10.1016/0012-8252(70)90001-2

Benz, T., 2007. Small-Strain Stiffness of Soils and its Numerical Consequences, University of Stuttgart.

Chen, R.P., Wang, S.F., Chen, Y.M., 2003. Study on pile drivability with one dimensional wave propagation theory. J. Zhejiang Univ. Sci. 4, 683–693. https://doi.org/10.1631/jzus.2003.0683

Clough, R.W., Penzien, J., 1975. Dynamics of structures. McGraw-Hill.inc, New York.

Holscher, P., Brassinga, H., Brown, M., Middendorp, P., Profittlich, M., Tol, F.A. Van, 2011. Rapid load testing on piles: Interpretation guidelines. FL: CRC Press, Boca Raton.

O’Neil, M.W., Reese, L.C., 1999. Drilled shafts: Construction procedures and design methods. United States. Federal Highway Administration. Office of Infrastructure.

Plaxis 2D, 2022. Material Models Manual.

Richart, F.E., Hall, J.R., Woods, R.D., 1970. Vibrations of soils and foundations.

Rizvi, S.M.F., Wang, K., Jalal, F.E., 2022. Evaluating the response of piles subjected to static and multiple dynamic axial loads. Structures 40, 187–201. https://doi.org/10.1016/j.istruc.2022.04.019

Wang, F., Wang, P. fei, Lyu, Z. da, Zhao, Z., Ma, B. han, 2022. Dynamic response of super-large-diameter steel casing under axial impact load. Ocean Eng. 244, 110249. https://doi.org/10.1016/j.oceaneng.2021.110249

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The revised manuscript has been greatly improved and can be considered for publication.

Reviewer 2 Report

All my comments have been addressed.