Numerical and Experimental Evaluation of Axial Load Transfer in Deep Foundations Within Stratified Cohesive Soils

Abstract

This study presents a numerical and experimental evaluation of axial load transfer mechanisms in deep foundations constructed in stratified cohesive soils in İzmir, Türkiye. A full-scale bi-directional static load test equipped with strain gauges was conducted on a barrette pile to investigate depth-dependent mobilization of shaft resistance. A finite element model was developed and calibrated using field-observed load–settlement and strain data to replicate the pile–soil interaction and deformation behavior. The analysis revealed a shaft-dominated load transfer behavior, with progressive mobilization concentrated in intermediate-depth cohesive layers. Sensitivity analysis identified the undrained stiffness (E_u) as the most influential parameter governing pile settlement. A strong polynomial correlation was established between calibrated E_u values and SPT N₆₀, offering a practical tool for preliminary design. Additionally, strain energy distribution was evaluated as a supplementary metric, enhancing the interpretation of mobilization zones beyond conventional stress-based methods. The integrated approach provides valuable insights for performance-based foundation design in layered cohesive ground, supporting the development of site-calibrated numerical models informed by full-scale testing data.

1. Introduction

The design and performance evaluation of deep foundations in stratified cohesive soils—especially in seismically active regions—demand a comprehensive understanding of soil–structure interaction beyond traditional force-based methodologies. While conventional approaches often emphasize ultimate capacity, they frequently neglect deformation behavior, mobilization sequences, and serviceability thresholds under working loads [1,2,3]. These limitations are particularly critical in layered or low-permeability cohesive soils, where progressive displacement governs axial resistance rather than instantaneous strength.

To address these shortcomings, performance-based design (PBD) frameworks have gained traction, integrating site investigations with full-scale load testing and instrumentation to inform decision-making through deformation characteristics and serviceability performance [4,5]. Recent advancements underscore the importance of evaluating the full load–settlement response rather than focusing solely on ultimate capacity [6], demonstrating that a more comprehensive interpretation of load–settlement behavior provides valuable insights into shaft and base resistance mobilization, with direct implications for serviceability design. Similarly, recent contributions [7] highlight that stratification effects critically impact foundation response, particularly under seismic and cyclic loading conditions.

Empirical design tools—such as idealized t–z and q–z curves—remain widely used but fail to capture depth-dependent stress redistribution and nonlinear behavior under complex field conditions [8,9,10].

Recent developments in numerical modeling, particularly finite element methods (FEM), enable advanced simulations of soil–structure interaction under complex loading scenarios [11]. Nevertheless, the predictive reliability of these models is contingent upon accurate calibration of soil stiffness, interface behavior, and constitutive parameters. Large-scale evaluations by [12] further demonstrated the considerable variability in numerical performance predictions, supporting the need for full-scale testing calibration in stratified cohesive soils.

Complementing numerical simulations, full-scale axial load tests with strain gauges have become essential for evaluating shaft and end-bearing mobilization mechanisms. Depth-wise strain data provide insight into stress transfer and friction mobilization—particularly important for barrette piles, whose non-cylindrical geometry induces anisotropic stress fields [13,14,15,16,17]. Experimental works further indicate significant shaft resistance variability depending on test type [18], and equivalent curve transformations require careful calibration to avoid underestimation [19,20]. These insights support the combined use of experimental data, advanced numerical modeling, and probabilistic assessment for more robust foundation design.

In light of these developments, this study presents a performance-based evaluation framework for a full-scale barrette foundation constructed in İzmir, Türkiye, where stratified cohesive soils and seismic demand pose significant geotechnical challenges. The methodology integrates:

• Bi-directional static load testing with strain gauges;
• FEM simulations;
• A strain energy–based interpretation of load transfer.

The study aims to:

• Calibrate stiffness and interface behavior using field-measured strain profiles;
• Identify energy concentration zones and mobilization patterns;
• Develop a practical E_u–N₆₀ correlation for preliminary design;
• Provide insights for site-specific performance-based design in complex soils.

By integrating strain energy-based performance indicators alongside conventional force–deformation metrics, this study advances a more physically grounded understanding of load mobilization, particularly for non-conventional foundations like barrette piles. The proposed framework combines full-scale load test data and strain energy analysis to develop a site-specific E_u–N₆₀ correlation, providing a practical tool for deformation-driven preliminary design in stratified cohesive soils.

2. Experimental Setup and Field Organizations

In this section, the geotechnical characteristics of the study area and the details of the full-scale axial load testing are presented to establish a robust foundation for subsequent numerical modeling and performance-based evaluations.

2.1. Site Characterization

A thorough understanding of subsurface conditions is vital for the reliable design of deep foundations, particularly in seismically active and geologically heterogeneous regions. At the study site in İzmir, Türkiye, a comprehensive geotechnical investigation program was undertaken to characterize soil stratigraphy and evaluate the variability of mechanical properties relevant to axial pile behavior.

The investigation scope included 7 rotary boreholes extending to depths of up to 110 m, MASW surveys, PS-logging, and detailed laboratory analyses. A summary of the site stratigraphy and average geotechnical properties is presented in

Table 1. Idealized soil profile.

Layer	Depth (m)	Soil Description	SPT N30 (avg.)	Vs (m/s)
1	0–6	Fill: rubble, gravel, construction debris	—	—
2	6–18	Organic-rich clay, silt, and sand (Holocene)	18	180–218
3	18–44	Silty clay with intermittent sand lenses	25	182–244
4	>44	Dense silty sand and gravel (cemented zones)	40	200–600

.

Shear wave velocity measurements ranged from 180 to 600 m/s across the profile, indicating a transition from soft to stiff materials with depth. The water table was observed between 2.5 and 11.0 m.

Figure 1 illustrates the variability in SPT N-values with depth, highlighting zones of weak cohesion in the upper 45 m and the onset of stronger granular layers below.

A strong correlation was observed between fines content (percent passing No. 200 sieve) and the plasticity index (PI), particularly within the soft cohesive layers found at depths of 6–18 m. These data, visualized in Figure 2, underscore the presence of low-permeability, highly compressible clays—critical factors for interpreting shaft resistance mobilization and drainage behavior during pile installation and loading.

2.2. Full-Scale Axial Load Testing

To assess axial performance under site-specific conditions and calibrate numerical models, two full-scale static load tests were conducted at the study site: one on a rectangular barrette pile and another on a conventional bored pile. The barrette pile measured 0.80 × 2.80 m in cross-section and extended to 60.0 m depth, while the bored pile had a 1.20 m diameter and 50.0 m length. Both tests were performed within the same geotechnical zone to ensure comparable subsurface conditions. The barrette was tested using bi-directional loading [21], while the bored pile followed a top-down loading procedure [22].

2.2.1. Instrumented Barrette Pile—Bi-Directional Load Test

The barrette pile was instrumented with ten vibrating wire strain gauges (SG1–SG10) along the shaft and LVDTs at the pile head and shaft to monitor settlement and displacement. This configuration enabled clear separation of shaft and base resistance contributions and allowed a detailed evaluation of load transfer in stratified cohesive soils.

A hydraulic jack was installed at a depth of 40.35 m, dividing the pile into upper and lower segments for bi-directional loading. Figure 3a shows the instrumentation layout and Figure 3b shows the internal configuration of the barrette pile.

The load–settlement response (Figure 4) displayed nonlinear deformation beyond 30,000 kN, marking plastic behavior in deeper strata. The maximum applied load was 45,000 kN, with 50 mm of settlement.

Serviceability limit state (SLS) settlements for deep foundations typically range from 10 mm to 25 mm, depending on the structural tolerance and subsoil stiffness, as supported by Eurocode-based guidelines and recent reliability-based design studies [23,24]. In this study, a conservative threshold of 10 mm was selected. The measured settlement remained below 10 mm up to a load of 20,000 kN, with 6.0 mm observed at 15,000 kN. Thus, the SLS capacity of the barrette pile was defined as 20,000 kN, satisfying serviceability requirements under working load conditions.

Axial microstrain measurements obtained from the ten strain gauges revealed a depth-dependent distribution of mobilized stresses. According to the manufacturer calibration certificates, the maximum non-linearity error of the installed strain gauges ranges between 0.11% and 0.28% of the full scale, corresponding to approximately ±2–6 με measurement uncertainty depending on gauge capacity. This level of measurement accuracy was considered during both strain interpretation and the subsequent calibration of numerical models. The peak strain (−269 µε) was recorded at a depth of 42.35 m, indicating maximum shaft resistance at this level (

Table 2. Axial microstrain values (µε) measured by strain gauges (SG1–SG10) installed along the barrette pile shaft.

SG No	Depth (m)	Microstrain (µε)
SG-1	−60.40	−56
SG-2	−55.75	−116
SG-3	−48.35	−176
SG-4	−42.35	−269
SG-5	−38.35	−258
SG-6	−30.30	−240
SG-7	−24.25	−141
SG-8	−17.25	−89
SG-9	−10.10	−31
SG-10	−5.10	−11

). Strain values increased from the pile head to deeper layers, confirming significant resistance mobilization within stiff cohesive strata (Figure 5).

Based on the interpreted microstrain data, unit shaft resistance values (Qs) were estimated at various depths (

Table 3. Depth-wise unit shaft resistance (Qs) calculated from strain gauge data.

Depth (m)	Qs (kPa)
0–10	20
10–15	60
15–25	90
25–35	115
35–40	120
40–50	120
50–60	140

). The results indicated a clear trend of increasing resistance with depth, particularly below 25 m, consistent with the presence of overconsolidated or cemented cohesive soils.

2.2.2. Conventional Bored Pile—Top-Down Axial Test

The bored pile was tested using a conventional top-down axial compression setup with four reaction piles. The load–settlement curve, shown in Figure 6, displayed a predominantly elastic response up to 13,500 kN of applied load. Maximum settlement was 9.75 mm, with approximately 2.2 mm of residual settlement upon unloading. While the test confirmed adequate bearing capacity, the relatively lower mobilized strain and settlement suggest a shallower activation of shaft resistance compared to the barrette.

The observations from both load tests provide critical benchmarks for evaluating the axial behavior of deep foundations and serve as reference points for the numerical model calibration and validation discussed in the following section.

3. Results and Discussion

This section presents a comprehensive evaluation of the barrette pile behavior under axial loading by integrating numerical simulations with field-monitored data. Beyond conventional load–settlement comparisons, the analysis incorporates advanced performance indicators such as strain energy distribution, interface mobilization intensity, and empirical stiffness correlations (e.g., Eu–N60). The calibrated model is further employed to explore parametric sensitivity, enabling a deeper understanding of stress transfer mechanisms and deformation behavior in layered cohesive soils.

3.1. Numerical Model Development

A finite element model was developed in PLAXIS 2D [25] to simulate the axial behavior of the barrette pile under realistic field conditions. The modeling framework consisted of (i) model geometry and boundary condition definition, (ii) preliminary parameter estimation from in situ and laboratory tests, and (iii) calibration using field-monitored load–settlement and strain gauge responses. Sensitivity analyses were also conducted to identify key geotechnical parameters influencing pile–soil interaction.

3.1.1. Model Setup

The numerical model was developed using an axisymmetric formulation to simulate the vertical response of the test piles. Although barrette piles have a rectangular shape, an equivalent circular section was adopted based on equal-perimeter principles to ensure comparable shaft–soil interface length and friction mobilization. This approach is widely accepted in geotechnical modeling and validated by previous studies [26,27], showing negligible error in settlement and capacity predictions under vertical loading. Moreover, axisymmetric FEM applications have demonstrated good agreement with pile loading tests when interface and stratification effects are properly incorporated [28].

The mesh employed 15-node triangular elements with local refinement around the pile–soil interface to capture stress concentrations. Four stratified soil layers were modeled, each with distinct stiffness and strength parameters derived from site investigations and calibrated via back-analysis.

A mesh sensitivity analysis was performed by varying element sizes from 2.15 m to 12.9 m (

Table 4. Effect of mesh discretization on pile head displacement under static axial loading.

Analysis ID	Element Dimension (m)	Pile Head Displacement (mm)	% Difference vs. Base
Base Model	6.46	35.95	—
1	2.15	33.48	−6.87%
2	3	33.64	−6.43%
3	4.31	34.2	−4.87%
4	8.6	36.33	1.06%
5	12.9	38.59	7.34%

). Finer meshes (2.15–3.00 m) reduced pile head settlement by 6–7%, while coarser meshes (>8.6 m) led to overestimation. A characteristic element size of ~3 m was adopted to ensure mesh-independent results with efficient computation.

Boundary conditions included fully fixed base nodes and horizontally fixed, vertically free lateral boundaries. Axial loads were incrementally applied at the pile head.

The model domain extended 100 m for the barrette pile and 85 m for the bored pile, with a lateral width of 20 D (~40 m) and a depth of 1.5 L (~100 m). This setup exceeds the commonly recommended 6–8 D width threshold [29,30] and was validated via sensitivity analysis, showing minimal boundary effects under static loading.

To confirm domain adequacy, additional sensitivity analyses varied the width (40–120 m) and depth (80–150 m). As shown in

Table 5. Sensitivity analysis of domain dimensions on pile head settlement.

Analysis ID	Width (m)	Depth (m)	Domain Width (D)~	Depth (L)~	Pile Head Displacement (mm)	% Difference vs. Base
Base Model	40	100	20 D	1.6 L	35.95	—
1	60	100	30 D	1.6 L	36.16	0.58%
2	20	100	10 D	1.6 L	33.94	−5.59%
3	40	150	20 D	2.5 L	36.9	2.64%
4	40	120	20 D	2.0 L	36.4	1.26%
5	40	80	20 D	1.3 L	34.44	−4.20%

, pile head displacements differed by ±5% relative to the base model, confirming that an 80 m width (1.3 L) and 100 m depth (1.6 L) are sufficient to avoid boundary influence.

Interface elements were incorporated along the pile–soil boundary to simulate shaft interaction. Interface strength was defined using the R_inter reduction factor, applying undrained shear strength (c_mob) under total stress conditions in accordance with standard axial loading practice [31]. Figure 7 shows the final mesh configuration of both models.

3.1.2. Initial Parameter Estimation and Model Calibration

An accurate definition of geotechnical parameters is critical for the reliability of finite element simulations in deep foundation and excavation analyses. In this study, a hybrid calibration approach was adopted: initial estimates of soil stiffness and shear strength were derived from site-specific geotechnical investigations, and subsequently refined using field-monitored deformation data.

Given the short-term nature of axial pile loading and the low permeability of cohesive soils, excess pore pressures generated during shearing do not dissipate promptly. Thus, undrained conditions govern the soil response, making total stress analysis more appropriate for simulating field behavior.

Accordingly, the Hardening Soil model under undrained conditions was employed to realistically capture both the small-strain stiffness and strain-dependent non-linear settlement behavior observed during static load testing. This modeling approach is consistent with recent studies, where the Hardening Soil model successfully captured nonlinear load–settlement behavior of deep foundations under undrained conditions validated by full-scale load tests [32].

For longer-term service conditions, however, partially drained behavior may become relevant, particularly within transition layers comprising silty or organic-rich soils (Layer 2 and local lenses within Layer 3). While these effects are not expected to influence the short-term static test results presented herein, they may lead to reduced settlement magnitudes or increased base resistance over time, which could be captured through coupled consolidation analyses in future investigations.

Initial undrained stiffness (E_u) and shear strength (c_u) values were estimated from SPT-N₆₀ data using established empirical correlations [33,34], with adjustments based on plasticity index (PI), following practices by [35]. The adopted parameters are summarized in

Table 6. Preliminary estimation of soil parameters based on SPT and index test data.

Layer	Depth (m)	Soil Description	N60	PI	f1 (Stroud)	cu (kPa)	Eu (MPa)	Es (MPa)
1	0–6	Fill with some sand/clay inclusions	10	25	4.5	45	12	10
2	6–18	Organic-rich clay/silt/sand (Holocene)	18	20–35	~4.5	81	18–21.6 (avg. 19.8)	13.86
3	18–44	Silty clay with sand lenses	25	10–25	~6.0	150	25–30 (avg. 27.5)	22
4	>44	Dense silty sand and gravel (cemented)	40	<10	~4.2	168	40–48 (avg. 44.0)	35.2

.

3.1.3. Sensitivity Analysis of Geotechnical Parameters

A parametric sensitivity analysis was conducted to identify dominant input parameters affecting pile settlement behavior and to support model calibration within the FEM framework [36,37].

The analysis focused on three parameters with direct influence on soil deformability and interface behavior:

• The reference stiffness modulus (E₅₀);
• Undrained shear strength (c_u);
• The pile–soil interface reduction factor (R_inter).

A one-at-a-time (OAT) variation method was employed, where each parameter was increased independently by +25%, +50%, and +100% from its baseline value, while the others were held constant. The output variable of interest was the pile head settlement at the final loading stage, which reflects the overall structural response and is directly comparable to field measurements [38].

The normalized sensitivity index (Si) was used to quantify parameter influence, allowing for direct cross-comparison, following established formulations [39,40].

Sensitivity indices were calculated for each soil layer to evaluate stratigraphic effects. The results are shown in Figure 8, which presents a tornado diagram ranking the relative influence of parameters across layers.

• E₅₀ in Layers 1 and 3 was found to be the most influential.
• c_u had a moderate impact, especially at deeper layers.
• The negligible influence of R_inter suggests that interface friction variability plays a limited role in settlement response under static loading conditions for the analyzed soil profile.

Overall, the tornado diagram highlights that stiffness controls settlement behavior, especially in the upper and mid-depth layers, guiding the calibration priorities in performance-based design.

In contrast, c_u becomes significant mainly under near-failure conditions or where full shaft resistance is mobilized. Since static load tests often operate in the small-to-moderate strain range, E₅₀ dominates the response. These findings are consistent with prior research [41], which highlights the dominant role of stiffness in early settlement behavior. This is also reflected in the strain gauge measurements obtained in this study, where axial strains predominantly remained within the small-strain range under test conditions, further supporting the controlling influence of E₅₀ on early settlement behavior.

The analysis revealed the following layer-wise effects on the pile settlement response:

• Layer 1 (0–6 m): Directly controls initial settlement response due to surface compressibility.
• Layer 3 (18–44 m): Corresponds to peak shaft resistance zone; highly influential.
• Layer 2 (6–18 m): Acts as a transition zone; minimal impact on total settlement.
• Layer 4 (>44 m): Stronger soil with limited mobilization; less impact.

These trends align with observations by [42,43], who also emphasized that upper and intermediate cohesive layers dominate the settlement response in stratified soil profiles.

3.2. Numerical Model Validation and Shaft Behavior Assessment

This section focuses on validating the finite element model through comparison with field measurements and analyzing the depth-wise mobilization of shaft resistance, displacement distribution, and overall load transfer characteristics in stratified cohesive soils.

3.2.1. Model Calibration and Load–Settlement Validation

Following the sensitivity analysis presented in Section 3.1.3, the finite element model was calibrated by adjusting the undrained stiffness modulus (E_u) for each stratified soil layer based on load–settlement test data [44]. The final calibrated E_u values are presented in

Table 7. Final calibrated undrained moduli.

Layer	Depth (m)	Soil Description	Eu Initial (MPa)	Eu Calibrated (MPa)	Eu Ratio	Remarks
1	0–6	Fill with some sand/clay inclusions	12,000	20,000	1.67	Controls initial compression zone
2	6–18	Organic-rich clay/silt/sand (Holocene)	19,800	40,000	2.02	Transition layer, moderate effect
3	18–44	Silty clay with sand lenses	27,500	54,000	1.96	Peak shaft resistance zone
4	>44	Dense silty sand and gravel (cemented)	44,000	90,000	2.04	End-bearing resistance zone

.

The mobilized shear strength and vertical displacement contours from the final stage of the numerical simulation are presented in Figure 9. The results demonstrate the progressive mobilization of shaft resistance along the pile–soil interface and the corresponding settlement patterns in the surrounding soil, indicating a shaft-dominated load transfer mechanism consistent with field observations. The updated stiffness profiles, implemented within the Hardening Soil model, yielded a close agreement with field measurements, thereby confirming the suitability of both the calibrated parameters and the adopted constitutive model.

Simulated load–settlement curves showed strong agreement with field data for the bored pile, particularly in the elastic-to-plastic transition range (Figure 10). The numerical model accurately captured both the initial stiffness and ultimate response, with minor underestimation near failure load attributed to interface idealizations.

To complement the axisymmetric model validation and examine the geometric influence of the barrette cross-section, an additional 3D finite element model was developed in PLAXIS 3D using the same calibrated soil stiffness and interface parameters derived from 2D analysis (Table 5). The 3D model employed the exact 0.80 m × 2.80 m rectangular cross-section, with boundary conditions and mesh refinement strategies matching the 2D setup. Surface loading was applied to replicate the field test load increments.

Figure 11 shows the total vertical displacement contours from the 3D analysis, illustrating both the global settlement distribution within the soil domain and the localized deformation along the pile shaft. The 3D simulation confirmed a shaft-dominated mechanism, with greater stress redistribution around the wider faces of the barrette pile and reduced settlements compared to 2D predictions.

For direct comparison, Figure 12 presents load–settlement curves from field testing, 2D, and 3D models. At 40,000 kN:

• Field test settlement = 26 mm;
• Calibrated 2D model settlement = 29.02 mm (+11.6% difference);
• Three-dimensional model settlement = 23 mm (−11.5% difference).

These results indicate that both models remain within acceptable limits (±12%), with the 2D model marginally overestimating and the 3D model slightly underestimating the settlements.

Overall, the 2D axisymmetric model proves sufficient for evaluating global axial behavior, while the 3D model offers refined insight into localized stress redistribution and cross-sectional influence. Combined, they support a robust and efficient modeling strategy within a performance-based design framework.

3.2.2. Mobilized Shaft Resistance and Displacement Interpretation

To validate the numerical simulation, mobilized shaft resistance (Qs) from strain gauge data was compared with mobilized shear stress (τ_mob) calculated from interface elements in the axisymmetric model.

Table 8. Comparison of numerical and field-derived shaft resistance.

Depth Range (m)	Qs from Strain Gauge (kPa)	τmob (Avg. Numerical Model) (kPa)
0–10	20	~47
10–15	60	~76
15–25	90	~144
25–35	115	~142
35–40	120	~139
40–50	120	~162
50–60	140	~163

summarizes the depth-wise comparison of τ_mob and back-analyzed Qs values along the barrette pile.

Figure 13 shows the depth-wise comparison of τ_mob and strain gauge-derived Qs, both indicating progressive shaft resistance mobilization with increasing depth and soil stiffness. Peak τ_mob values were observed below 40 m, corresponding to the cemented silty sand/gravel layer, consistent with [45]. Numerical results represent upper-bound mobilization, while field data likely reflect partial mobilization due to measurement limitations, highlighting the necessity of proper interface calibration (e.g., R_inter factors). Similar depth-dependent trends and calibration importance were also noted by [31] for pile foundations in layered soils.

In addition to static τmob–Qs comparisons, incremental mobilization behavior was evaluated under increasing load levels (Figure 14), further detailing depth-wise stress transfer patterns. The following observations were made:

• Limited shear mobilization at low load levels (<25% of maximum load), predominantly in soft cohesive upper layers;
• Progressive frictional resistance activation in intermediate depths (50–75% of maximum load);
• Full mobilization of shaft resistance in the stiffer, deeper layers under ultimate load (100%).

To further interpret interface behavior, the relative displacement profile (|u_rel|) between pile and soil was examined (Figure 15), providing additional insight into local slip patterns along the pile–soil interface.

As shown in Figure 15, relative displacement (|u_rel|) peaks within the upper 20–30 m and gradually decreases with depth. This suggests that significant interface movement occurs in the soft upper strata, especially near the pile head (0–10 m), where large deformations are accompanied by limited shear stress mobilization. In contrast, τ_mob reaches its maximum between 20 and 40 m, corresponding to stiffer cohesive layers where relative displacement is moderate but shear transfer is most effective. Below ~45 m, both |u_rel| and τ_mob decrease considerably, indicating limited load transfer in deeper strata. These findings highlight the importance of combining displacement- and stress-based assessments to capture load transfer mechanisms in layered cohesive soils.

3.2.3. Overall Load Transfer Mechanism

This section outlines the methodology for evaluating axial load distribution along the pile shaft and base using the mobilized shear stress profile (τ_mob) obtained from numerical simulations.

Both numerical results and full-scale load testing confirmed a shaft-dominated behavior, with approximately 92% of the total axial capacity (~41,400 kN) mobilized through shaft friction and only 8% (~3600 kN) via end bearing (Figure 16). This trend is typical for deep foundations in cohesive strata, where base resistance is limited by low stiffness and delayed mobilization under undrained conditions [4].

The large L/B ratio (~75) and extensive shaft surface area of the barrette pile enhance frictional mobilization, with strain gauge data indicating peak mobilization between 15 and 40 m, coinciding with stiffer cohesive layers. These results underline the predominance of shaft resistance in barrette pile performance and justify conservative assumptions for base resistance under serviceability design.

In engineering practice, such conservatism is standard in cohesive profiles, especially where soil variability or delayed tip mobilization is anticipated.

3.3. Regression-Based Correlation Between Undrained Stiffness (Eu) and SPT-N₆₀ in Stratified Cohesive Soils

Recent studies have demonstrated the practical utility of SPT-N₆₀-based correlations for estimating undrained stiffness (E_u), particularly in stratified and data-limited cohesive soils. For instance, refs. [46,47,48,49] proposed and validated refined N₆₀–E_u relationships, showing reliable performance across various cohesive profiles. These studies collectively support the use of N₆₀ as a robust proxy for E_u in preliminary design stages, especially where site-specific data are scarce.

In this study, a site-specific E_u–N₆₀ correlation was developed based on calibrated E_u values from back-analysis and corrected SPT-N₆₀ values from four stratified soil layers. The regression analysis (Figure 17) revealed a strong relationship (R² > 0.98), with a second-order polynomial providing a superior fit, particularly at higher N₆₀ values where stiffness increases nonlinearly due to cementation or overconsolidation:

$$E_u=35.44N_{60}+12.64{N_{60}}^2+1.294$$

(1)

The polynomial model prevents underestimation in stiffer layers and aligns well with full-scale mobilization behavior. The derived correlations align well with the established geotechnical literature. For instance, ref. [50] reported stiffness ratios of 15–40 × N₆₀, while ref. [51] suggested 25–75 × N₆₀ for cohesive deposits. The current findings generally fall within or slightly above these ranges, particularly at greater depths where cemented silty sand mixtures prevail.

To complement the regression calibration, a layer-wise variability analysis was performed for SPT-N₆₀, fines content (No. 200), and plasticity index (PI).

As illustrated in Figure 18, Coefficient of Variation (CoV) values exhibit a broad range across stratified layers. The highest CoV values (up to 50–80%) are observed in the upper fill and transitional layers (0–18 m), reflecting significant heterogeneity.

The results indicate that substantial within-layer variability exists across the stratified profile, with CoV values ranging from 25% to 50%, and peak scatter observed within the upper fill and transitional layers (Layers 1–2). This quantification of variability underlines the inherent heterogeneity present in the site conditions.

Despite this inherent variability, the high R² values (>0.98) confirm the regression model’s robustness. This dual approach—regression calibration and variability quantification—enhances confidence in the derived E_u–N₆₀ correlation.

From a practical design standpoint, the site-calibrated empirical relationships established in this study provide a rational starting point for numerical modeling, facilitating more realistic input selection prior to any back-analysis or instrumentation-based refinements. The findings are particularly applicable to sites with comparable stratified cohesive profiles, whereas application to markedly different settings may require additional calibration

3.4. Strain Energy-Based Evaluation for Performance-Oriented Foundation Design

The bi-directional static load test facilitated the transition from conventional prescriptive approaches to a performance-based evaluation of deep foundations. Beyond classical load–settlement interpretations, strain gauge data were combined with numerical stress outputs to compute the strain energy distribution along the pile–soil interface. This energetic approach offers a physically consistent understanding of mobilized resistance zones and deformation mechanisms.

The strain energy density (U) was computed using the classical elasticity formulation, which accounts for both normal and shear stress–strain interactions [52].

$$U={\displaystyle \frac{1}{2}}\left({\sigma }_{xx}{\epsilon }_{xx}+{\sigma }_{yy}{\epsilon }_{yy}+{\tau }_{xy}{\gamma }_{xy}\right)$$

(2)

The total strain energy along the pile shaft was obtained by integrating element-wise energy density values from FEM analysis. As shown in Figure 19, the highest energy accumulation occurred between 18 and 44 m, corresponding to the main load transfer zone dominated by shear mobilization. Energy values were lower in the upper (0–18 m) and lower (44–60 m) sections, confirming shaft-dominated load transfer with limited base contribution. Cumulatively, ~80% of the total strain energy was mobilized within the upper 40 m, supporting the concept of an “effective shaft length” in serviceability design.

Figure 20 further decomposes the strain energy contributions, showing shear strain (γ_xγ) as the dominant component throughout the interface. Vertical strain (ε_γγ) remains negligible, while radial strain (ε_xx) exhibits localized peaks, likely due to confinement effects near stiffer zones.

A stratified summary of strain energy distribution is provided in

Table 9. Summary of strain energy concentration zones and load transfer characteristics.

Layer	Depth Range (m)	Soil Description	Strain Energy Density (avg, kPa)	Dominant Strain Mode	Load Transfer Type	Remarks
1	0–6	Fill with sand/clay inclusions	Very Low (~0.1–0.3)	γxγ (minor)	Negligible	Low stiffness and strength; minimal mobilization; strain energy accumulation negligible throughout the layer.
2	6–18	Organic-rich clay/silt/sand (Holocene)	Moderate (~0.4–0.7)	γxγ dominant	Partial shaft friction	Deformation is dominant; moderate shear mobilization observed; limited load transfer due to soft compressible nature.
3	18–44	Silty clay with sand lenses	High (~1.0–1.6)	γxγ >> εxx	Major shaft friction	Peak mobilization zone; high strain energy density with dominant shear deformation; key contributor to shaft resistance.
4	44–60	Dense silty sand and gravel (cemented)	Moderate–High (~1.2–1.5)	γxγ + εxx (confined zone)	Transition to base zone	Increased confinement effect near pile tip; εxx contribution rises; energy reduces gradually, indicating shaft-to-base transfer transition.

, highlighting layer-specific energy densities, dominant strain modes, and associated load transfer mechanisms. Notably, Layer 3 (silty clay with sand lenses) shows the highest energy density, aligning with peak shaft resistance, while Layer 4 presents moderate energy levels associated with confined deformation near the pile base.

These results are consistent with load test findings, indicating that ~92% of total capacity was mobilized via shaft resistance, with minimal end-bearing contribution. This supports the conservative design approach of emphasizing shaft resistance in stratified cohesive profiles.

In summary, the strain energy approach offers a quantitative and physically transparent method to assess pile performance. It enhances FEM interpretation, aligns well with field observations, and supports performance-based foundation design. The recent literature [53,54] further validates the use of energy-based metrics in identifying critical deformation zones in geotechnical practice.

4. Conclusions

This study developed a comprehensive performance-based evaluation framework for a full-scale instrumented barrette pile constructed in layered cohesive soils in İzmir, Türkiye. By integrating strain gauge measurements, bi-directional load testing, and finite element modeling, the research offers several novel insights into axial load transfer mechanisms and design optimization for deep foundations under complex ground conditions.

The key conclusions are as follows:

• Model Calibration and Load–Settlement Behavior: The finite element model calibrated using depth-wise undrained stiffness (E_u) captured the observed nonlinear load–settlement response with high accuracy. The calibrated parameters provided strong agreement in both the elastic and plastic deformation ranges for barrette and bored piles, validating the numerical approach and parameter selection.
• Shaft Resistance Mobilization: Comparative analysis of mobilized shear stress (τ_mob) from numerical simulations and shaft resistance (Qs) from strain gauge data revealed consistent depth-wise mobilization patterns. Maximum mobilization occurred between 15 and 40 m, coinciding with moderately stiff cohesive layers. The observed discrepancy between numerical and measured values highlights the importance of interface calibration and consideration of partial mobilization effects.
• Strain Energy Interpretation: The strain energy density distribution along the pile–soil interface effectively identified zones of active load transfer. Shear strain (γ_xγ) dominated the energy accumulation, particularly in mid-depth layers, confirming that interface shear governs the axial behavior in stratified profiles. This energy-based interpretation provided a physically consistent metric to complement conventional stress/displacement outputs.
• Empirical Stiffness Correlation: A site-specific empirical relationship between E_u and corrected SPT resistance (N₆₀) was developed with R² > 0.98. This correlation is consistent with the established literature (e.g., Kulhawy and Mayne, Hatanaka and Uchida) and offers practical utility for early-stage design in data-limited conditions.
• Implications for Design Practice: The dominant contribution of shaft friction (92%) relative to base resistance (8%) reinforces the conservative design approach of minimizing reliance on end bearing in cohesive soils. Based on the combined findings from field instrumentation, numerical analysis, and strain energy mapping, the following practical design implications are proposed for stratified cohesive ground conditions:
  • Shaft Length Optimization: At least 80% of cumulative strain energy was mobilized within the upper 70–75% of pile length, supporting the definition of an “effective shaft length” for serviceability limit state (SLS) checks.
  • Reduced Base Contribution in Design: Considering negligible strain energy accumulation at the pile toe, base resistance should be excluded or limited to a ≤10% contribution in axial design calculations under working loads.
  • Settlement Control Focus: Settlement performance should primarily be verified within identified high-energy zones (e.g., 15–40 m), which govern most of the axial deformation.
  • Design without Load Testing: In similar cohesive profiles, the findings may serve as preliminary design references, especially in data-limited projects, reinforcing the practicality of strain energy evaluation for early-stage design.

This structured approach directly links observed mobilization behavior to actionable performance-based design decisions, contributing to more rational and site-specific foundation engineering.

Overall, the integration of full-scale test data with numerical simulations and energy-based analysis advances the understanding of pile–soil interaction and provides a robust framework for site-calibrated foundation design.

In particular, this study presents two distinct contributions to current geotechnical practice: (i) the application of strain energy mapping to evaluate depth-wise load transfer mechanisms, which offers a more physically consistent understanding of mobilization behavior in layered cohesive soils, and (ii) the development of a site-specific empirical Eu–N60 correlation based on full-scale load testing, enabling more reliable preliminary design in data-limited conditions. These combined advancements address key gaps in existing methodologies and enhance the applicability of performance-based design (PBD) for non-conventional foundations like barrette piles.

Future work may focus on extending this methodology to alternative foundation geometries and time-dependent effects such as consolidation and creep. In addition, incorporating construction-induced variables—such as base cleaning efficiency, slurry effects, and concreting quality—into the modeling framework would enhance the realism of load transfer simulations and improve their representativeness under field conditions.