Experimental and Numerical Study on the Bearing Capacity of Tapered Piles in Sand Under Compressive Load

Experimental and Numerical Study on the Bearing Capacity of Tapered Piles in Sand Under Compressive Load | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Experimental and Numerical Study on the Bearing Capacity of Tapered Piles in Sand Under Compressive Load moein mohammadizadeh, mohsen mohammadizadeh This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5783847/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Deep foundations are widely recognized as one of the most effective methods for transferring surface loads to subsurface soil layers. While cylindrical piles are the conventional choice for deep foundations, tapered piles offer significant advantages in load transfer and material efficiency. This study investigates 12 types of tapered piles with varying characteristics in the loose and dense soils under static loading conditions in both loose and dense sands through laboratory experiments. The behavior of tapered piles is also modeled numerically using finite difference analysis, and the numerical results are validated against the experimental data. Additionally, a parametric analysis is conducted to evaluate the influence of design variables such as taper angle, pile length and sand relative density on the load-settlement behavior. The comparative analysis between tapered and cylindrical piles identifies an optimal taper angle for homogeneous sands, revealing that the bearing capacity decreases by 2.86 degrees with an increase in pile angle. Moreover, increasing the relative density of the soil results in a 2- to 3-fold improvement in the bearing capacity of the piles. Numerical Modelling Taper Piles Finite Difference Method Sands Laboratory Test Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 1. Introduction When shallow foundations are inadequate due to insufficient bearing capacity or excessive settlement, deep foundations, such as piles, offer a viable alternative [ 1 – 6 ]. Cylindrical or prismatic piles, characterized by a constant cross-sectional area along their length, are commonly employed in practice. In geotechnical engineering, the bearing capacity of piles is a critical consideration in foundation design [ 7 – 12 ]. Tapered piles serve several important functions. Firstly, they facilitate a more uniform load distribution along the pile's length, thereby reducing stress concentrations. Additionally, tapered piles can be more cost-effective than cylindrical piles, as they require less material while still providing the necessary bearing capacity [ 13 ]. Numerous laboratory and theoretical studies have been conducted to evaluate the efficiency of tapered piles [ 14 – 18 ]. For instance, some authors [ 19 , 20 ] have explored the compressive capacity of tapered piles in comparison to traditional cylindrical piles. Other researchers [ 21 – 24 ] have investigated small-scale models of tapered piles. Among the earliest analytical studies on tapered piles, Nordlund [ 25 ] demonstrated a significant increase in axial bearing capacity for bored tapered piles. Similarly, Meyerhof [ 26 ] found that frictional capacity can increase by a factor of 1.5 compared to prismatic piles when a single tapered pile in sandy soils is subjected to vertical loading. Rybnikov [ 27 ] compared the bearing capacities of cylindrical and bored tapered piles, discovering that, for piles with equivalent average volume and radius, tapered piles exhibited a 20–30% increase in bearing capacity. Notably, when tapered piles and cylindrical piles with similar radii were installed in sandy soils, the bearing capacity of the cylindrical piles was found to be 200–250% lower [ 28 ]. Kurian and Srinivas [ 29 ] conducted experimental tests on tapered piles to validate numerical models of their compressive behavior, finding that three factors contributed to increased capacity : enhanced side friction, a direct bearing of the pile sides, and increased vertical pressure. Wei and El Naggar [ 30 ] observed that the performance of pile material improved with the taper angle, primarily due to the load being transferred to a larger soil mass. Furthermore, during pile installation, the increased lateral earth pressure from radial soil compaction, improves frictional resistance. Khan et al. [ 31 ] examined the axial compressive capacity of full-scale drilled concrete tapered piles. Their results showed that, compared to straight piles of equal volume, tapered piles with taper angles ranging from 0.95 to 1.91 degrees exhibited a load-bearing capacity increase of up to 50%. Zhan et al. [ 32 ] investigated tapered piles under axial loading in the sand with low dilatancy using finite element modeling (FEM). They concluded that the optimal taper angle for piles ranges from 0.5 to 1.0 degrees. Additionally, the increase in radial stress with tapered piles mitigates the convex heave at the pile-ground interface. The rise in the normalized radial distance for tapered piles leads to a minimum threefold increase near the pile-ground interface compared to cylindrical piles, resulting in elevated radial stresses within the soil [ 33 ]. Hataf and Shafaghat [ 34 ] found that the optimal taper angle for a pile under the axial load in the sand is closely related to the soil's friction angle. Their study showed that, at the optimal angle, the increase in frictional bearing capacity outweighs the reduction in end bearing capacity .However, as the taper angle increases further, frictional bearing capacity continues to improve while end bearing capacity declines. When subjected to vertical loads, tapered piles exhibit a smaller increase in bearing capacity compared to cylindrical piles [ 35 ]. Vali et al. [ 36 ] evaluated the settlement and bearing capacity of embedded tapered piles using three-dimensional finite element analysis, revealing that increases in pile diameter have minimal impact on bearing capacity. Nasrollahzadeh and Hataf [ 37 ] conducted laboratory tests and numerical analyses on single and group tapered and cylindrical piles in sand. Their findings demonstrated that tapered piles, whether single or grouped, show enhanced bearing capacity compared to cylindrical piles. Initial research in this field primarily focused on the advantages of using tapered piles, with later studies indicating that these benefits are most pronounced up to a certain taper angle. However, previous research has not adequately explored the complex interaction between piles and soil in determining bearing capacity, particularly in relation to soil density. Although significant research has been conducted on piles, there remains a notable gap in understanding the combined effects of pile dimensions and soil type on pile behavior under external loads. The load-settlement behavior of both tapered and cylindrical piles is intricately linked to the flexibility of the entire system, which is influenced by the properties of the surrounding soil, the taper angle, and the dimensions of the pile. Moreover, both numerical and laboratory simulations have been used to study the behavior of piles under axial loading in the sand, highlighting the crucial importance of considering installation effects for accurate modeling. The present study, conducts both numerical and experimental investigations to assess the impact of the relative density of surrounding sands on the performance of tapered piles. Additionally, this study examines the influence of taper angle on the bearing capacity of tapered piles. To achieve this, 12 piles with varying lengths and taper angles were tested in two types of sandy soils, with different internal friction angles. The experimental procedure began by placing the piles in both loose and dense soils, followed by applying load and measuring the resulting settlement using a gauge positioned on top of the piles. The experimental procedures and tests were then simulated using the finite difference method in FLAC3D software[ 38 ], as detailed in Section 2 . The results of these simulations are presented Section 3 . The paper concludes with a discussion of the findings in Section 4 and conclusions in Section 5. 2. Materials and methods 2.1. Laboratory Investigation 2.1.1 Experimental Setup The experimental setup began with the preparation of the soil, which was poured into a cylindrical container with a height of 1800 mm and a diameter of 1200 mm. The container was divided into 12 sections, each 150 mm in height. The soil was carefully deposited using the sand raining technique, followed by compaction. The resulting relative density was approximately 84% for dense sand and 38% for loose sand. Twelve samples of concrete pile samples with varying taper angles were constructed, and their characteristics are detailed in Table 1 . The mechanical properties of the piles and surrounding soils are provided in Table 2 . When the length-to-diameter ratio exceeded 10, the pile exhibited friction pile characteristics, classifying it as a long pile[ 39 ]. In the pile naming convention, the first letter indicates whether the pile is tapered (T) or cylindrical (C), followed by numbers representing the radius for uniform piles and the two-sided radius for tapered piles. Table 1 The dimension of tapered piles used in this article Index Length (mm) Bottom diameter (mm) Top diameter (mm) Volume (Cm3) Taper angle (deg) C 20 500 40 40 628 0 T 31 500 20 60 680 2.29 C 40 − 1 500 80 80 2510 0 T 62 − 1 500 40 120 2720 4.57 C 30 800 60 60 2262 0 T 51 800 20 100 2597 2.862 C 50 800 100 100 6283 0 T 82 800 40 160 7037 4.289 C 40 − 2 1200 80 80 6032 0 T 62 − 2 1200 40 120 6534 1.91 C 60 1200 120 120 13572 0 T 93 1200 60 180 14700 2.862 Table 2 Properties of concrete and soils Material Behavioral model Elastic modulus (MPa) [E] Poisson's Ratio [ \(\:\varvec{v}\) ] Cohesion (KPa) [ \(\:\varvec{C}\) ] Bulk modulus (MPa) [k] Angle of shear resistance ( ͦ ) [𝜑] Shear modulus (MPa) [G] Density (Kg/m3) [ \(\:\rho\:\) ] D10 D30 D60 Concrete pile Elastic 25000 0.2 - 13.9 - 10400 2500 - - - Soft sand Mohr-Coulomb 20 0.3 1 16.67 28 7.7 1478 0.3 0.87 1.81 Dense sand Mohr-Coulomb 55 0.35 1 61.6 35 19.85 1928 0.194 0.34 0.483 Figure 1 . Grading curve of loose and dense sand. Figure 1 shows the soil aggregate distribution of the materials used in the tests. The soil's physical properties were determined using the California Bearing Ratio (CBR) test in accordance with ASTM standards [ 40 , 41 ]. The modulus of elasticity of the sandy soils was calculated using the following equation: Figure 2 . Schematic view of loading system. Figure 3 . Location settlement gauge on the head pile. Figures 2 and 3 illustrate the loading apparatus, where the distance from the loading point to the pile is three times the distance between the pile and the support. Figure 4 depicts the loading system, which increases the load incrementally. Two types of sand, dense and loose, were employed in this research, with the CBR test results presented in Fig. 5 . Figure 4 . loading system. Figure 5 . CBR Test Results. Physical model was carefully designed to avoid scale effects, particularly concerning the ratio of the pile diameter to the soil’s average particle size (D₅₀). According to Sedran et al.[ 42 ], this ratio should exceed 30 to minimize scale effects in piles under axial loading, a condition that was met in all models used in this research. 2.2. Numerical Investigation Numerical analysis is a widely used and cost-effective method for analyzing pile behavior, offering reliable prognostication capabilities. In this study, FLAC3D, a finite difference modeling software specifically designed for simulating material behavior under both static and dynamic conditions, was employed to analyze the behavior of tapered piles. FLAC3D is known for its flexibility in modeling and analyzing complex geotechnical problems. 2.2.1. Model Geometry The initial step in using FLAC3D involves creating the model geometry. Cylindrical shell elements were used to simulate the soil elements in this study. A 3D axisymmetric model was developed, utilizing a quarter-section of the geometry to simplify the analysis while maintaining accuracy. As illustrated in Fig. 6 , the numerical model is represented by the vertical axis of symmetry intersecting the longitudinal axis of the pile. A fine mesh was applied near the pile-soil interface to ensure precise modeling of the interaction. After establishing the soil geometry, contact elements were introduced at the interface between the pile and the soil, simulating the pile in its designated position. The vertical loading of the pile is influenced by the soil-pile interface elements, making accurate modeling of this interface crucial [ 43 ]. The interaction between the pile and surrounding soil is governed by Coulomb friction, shear bonding, and tensile forces [ 38 ]. The stiffness of the contact surface elements, including both vertical and shear stiffness, was determined based on the properties of the surrounding soil. In FLAC3D, the contact surface element is used to model potential slip or detachment at the pile-soil interface. Shear and normal stiffness were represented using springs attached to each node of the pile. Lateral motion and vertical displacement between the pile and the adjacent soil were modeled by normal and shear springs, respectively. The interface friction angle was assumed to be equivalent to two-thirds of the soil’s internal friction angle (𝜑), as suggested by Bahrami et al. [ 44 ]. The relationship between normal stiffness (kₙ)) and shear stiffness (kₛ) is defined as follows [ 38 ]: $${k_n}={k_s}=~\frac{{k+\left( {\frac{4}{3}G} \right)}}{{\Delta Z}}~ \times 10$$ 2 where, k and G represent the soil’s bulk modulus and shear modulus, respectively, these parameters are calculated using the following formulas: $$K=\frac{E}{{3\left( {1 - 2\nu } \right)}}$$ 3 $$G=\frac{E}{{2\left( {1+\nu } \right)}}$$ 4 ΔZ is the smallest dimension of the soil element at the surface of the contact element. Two types of interface elements were used to apply the load to the pile: one along the pile’s length and the other at the pile’s toe. For this study, the normal and shear stiffness (kₙ and kₛ) for loose sand were set at 2693 Mpa/m, while for dense sand, these values were 8806 Mpa/m. Figure 6 . 3D model of piles group foundation and soil. 2.2.2. Boundary Conditions Virtual boundaries were established at specific distances from the pile to ensure accurate simulation results. Two key factors guided the selection of these boundaries: first, the boundary must be far enough from the pile to avoid influencing the loading results; second, it should be positioned where the analyzed soil volume is minimized to reduce computation time. Based on these considerations and the analysis of pile behavior, the horizontal boundary was set at a distance of 30R (where R is the pile radius) from the center of the pile. For the vertical boundary, the distance was set at L + 15R, where L and R represent the average length and diameter of the pile, respectively. To prevent vertical displacement roller supports were applied at the vertical boundary The numerical model consisted of 10,582 grid points and 3,375 zones .All displacements at the model's base were constrained, while the vertical outer faces were fixed in both the X- and Y-directions. Along the symmetry axis, roller supports were placed perpendicular to the symmetry plane to ensure zero displacement in this direction, allowing movement along the plane's surface. Additionally, a free-surface condition was applied at the top of the model (Z = 0). 2.2.3. Constitutive Model and Materials Properties The Mohr-Coulomb constitutive law was employed to model the behavior of sandy soils in this analysis. This model is well-suited for studying pile behavior in sandy soils, as it captures the essential stress-strain characteristics of such materials. The key parameters required for this constitutive model include the internal friction angle (𝜑), shear modulus, bulk modulus, and dilatancy angle. The rupture envelope in this model is defined by a direct relationship between shear stress (τ) and normal stress(σ), as expressed which is in the following equation (Eq. 5): In this equation, σ represents the normal stress on the fracture surface, τ denotes the shear stress, and 𝜑 and c correspond to the soil's internal friction angle and cohesion, respectively, as depicted in Fig. 7 . Figure 7 . Stress field Direction of characteristics on Mohr's circle. 2.2.4. Loading Procedure Following the preparation of the model geometry, the pile was first balanced under its weight. Subsequently, an external load was applied to the pile. A downward velocity of 1×10 ⁻⁶ m/timestep was imposed on the nodes of the pile. The numerical model indicated that a specific number of steps were required for the unbalanced force to reach a minimal value and remain stablewithout significant fluctuations. This process also necessitated considerable time to propagate the load adequately throughout the model. Once the unbalanced force stabilized, the velocity of the nodes was maintained at a constant rate. Figures 8 and 9 illustrate of Z-displacement contours for the T31 and T93 piles, respectively. Figure 8 . Contour of z displacement (m) T31 pile. Figure 9 . Contours of z displacement (m) T93 pile. 2.2.5. Verification Rybnikov [ 27 ] conducted a study on bored-cast-in-place tapered piles in the Irtysh Pavlodar region (formerly part of the Soviet Union). The vertical bearing capacity of the pile was determined based on a settlement of 24 mm from the load-average settlement data. Table 3 presents the soil characteristics used in that study, where the soil profile consisted of three distinct layers. The load-settlement curves obtained from the experimental results (with bottom and top radii of 100 and 300, respectively) were compared with the finite difference analysis for verification. Table 3 Properties of concrete and soils Index Sandy loam Ordinary loam Sand Layer thickness (m) 5.8 2.1 2.4 Soil density (gr/cm3) 1.74 1.68 1.81 Angle of internal friction (deg) 19 18 32 Cohesion (MPa) 0.012 0.026 0.004 Elastic modulus (MPa) 20 20 26 Angle of dilation (deg) 12 12 14 As illustrated in Fig. 10 , the pile-bearing capacity determined in this study aligns closely with Rybnikov’s results, demonstrating a high degree of accuracy. The discrepancy between the experimental and numerical results is less than 5%, indicating strong consistency between the two methods, particularly at the initial stages where the curves closely match. Figure 10 . Comparison of tapered pile analysis result with Rybnikov's Test Site. 3. Discussion 3.1. Efficacy of Vertical Load on the Response of Piles In order to increase the accuracy of the experimental test results, the load tests performed on each pile, are repeated three times, and by taking an average, the results of each test are recorded. The tangent intersection method defines the vertical bearing capacity [ 31 ]. As shown in Fig. 11 , two tangential lines were drawn along the primary and secondary sections of the load displacement curve. The load corresponding to the intersection of these two lines was identified as the bearing capacity. The load-displacement curve is approximately linear, with a near-horizontal slope after reaching the ultimate failure load. Determining a pile's stiffness from the load-settlement curve involves analyzing the slope of the curve at various points. This analysis provides insights into the pile's early elastic behavior (Initial Tangent Stiffness), its average stiffness up to a particular load (Secant Stiffness), and its instantaneous stiffness at a specific load level (Tangent Stiffness). For this purpose, a Python code was developed, as detailed in Appendix 1. Figure 11 . Failure criterion (a) Tangant intersection method. Sensitivity analysis is essential for optimizing the design and performance of tapered piles. This analysis is particularly important for understanding the impact of variables such as pile taper angle, soil properties, and embedment depth. By examining how changes in these parameters influence stress distribution and deformation behavior, the design of tapered piles can be optimized for improved performance. The taper angle of a pile plays a crucial role in influencing load distribution and overall stability. A steeper taper angle can improve lateral resistance but may also increase bending moments at the pile head, potentially leading to greater structural demands. Deeper embedment generally improves load-bearing capacity; however, it may also result in increased deformation at the pile top due to soil constraints. Analyses indicate that variations in the friction angle of sands lead to significant differences in bearing capacities[ 45 ]. Figures 12 to 17 illustrate the applied forces and the induced settlements observed in both experimental and numerical analyses. The piles used in the static analysis under vertical loading were grouped into three categories based on height and geometry. The first, second, and third groups of piles had heights of 500 mm, 800 mm, and 1200 mm, respectively. Each group included both a short pile and a long pile. As shown in Figs. 12 and 13 , for a given load, tapered piles exhibit less settlement than cylindrical piles, and their bearing capacity increases with a steeper taper angle. This indicates that in scenarios where settlement must be minimized, such as in urban construction, tapered piles offer a more efficient solution than cylindrical piles. Figure 12 . Load-settlement curve of C20 & T31 piles in laboratory model tests & FDM analysis. Figure 13 . Load-settlement curve of C40-1 & T62-1 piles in laboratory model tests & FDM analysis. Moreover, in all cases, the bearing capacity is significantly higher in dense sandy soil compared to loose sandy soil. For instance, as shown in Fig. 14 which relates to piles in dense sandy soil, the bearing capacity of tapered piles with an average diameter of 60mm increased by approximately 18% according to numerical analysis and by 21% based on laboratory tests compared to cylindrical piles. It is important to note that the volume of the cylindrical piles is 3.5% less than that of the tapered piles. Figure 14 . Load-settlement curve of C30 & T51 piles in laboratory model tests & FDM analysis. Figure 15 . Load-settlement curve of C50 & T82 piles in laboratory model tests & FDM analysis. Figure 16 . Load-settlement curve of C40-2 & T62-2 piles in laboratory model tests & FDM analysis. Figure 17 . Load-settlement curve of C60 & T93 piles in laboratory model tests & FDM analysis. Furthermore, Fig. 15 illustrates that for piles with a diameter of 100 mm, despite the tapered pile's volume increasing by 5%, its bearing capacity when maintaining the same average diameter was reduced by 22.5% in the numerical analysis and by 24% in the laboratory test compared to cylindrical piles. In this instance, the taper angle was4.289 degrees. Figure 16 shows that as settlement values increase, the bearing capacity of the tapered pile also increases relative to the cylindrical pile, consistent with previous findings. However, as depicted in the Fig. 17 , when the T93 pile was placed in loose sandy soil, the tolerable load at the same settlement initially favored the tapered piles over the cylindrical ones. Yet, as the applied load increased, the load-bearing curve for the cylindrical pile eventually exceeded that of the tapered pile. 4. Conclusions The studies conducted indicate that when tapered piles with a taper angle of less than 2.29 degrees are placed in loose sandy soil, their bearing capacity exceeds that of cylindrical piles with the same average diameter. However, as the taper angle increases, even though the concrete volume increases, the bearing capacity tends to decrease. For tapered piles in dense sandy soil, bearing capacities were found to be greater than those of cylindrical piles with a constant average diameter when taper angles were1.91, 2.29, and 4.57 degrees. Conversely, for piles with taper angles of 4.29 and 4.57 degrees in loose sandy soil, the bearing capacities were lower than those of cylindrical piles with the same average diameter. An excessive increase in the taper angle, particularly beyond 2.86 degrees, results in a reduction of the pile head's effective area compared to cylindrical piles. This leads to a more pronounced taper shape, causing the pile to penetrate the soil like a wedge which in turn increases settlement and reduces bearing capacity. The numerical analyses closely align with laboratory test results, with an acceptable margin of error between the numerical and experimental bearing capacities. The mechanical properties of the soil are directly related to the selection of optimal taper angles for piles, with significant differences observed between the optimal taper angles for dense and loose sandy soil. Increasing the taper angle of the pile head up to a certain point improves the bearing capacity. However, exceeding this optimal taper angle results in a decrease in bearing capacity. As the taper angle increases, shaft load capacities improve, while base load capacities diminish due to the reduced contact area with the ground. The relative density of the soil is a critical factor that governs the base resistance. Declarations Author Contribution Moein.M. conceptualized the study, designed the experimental setup, and conducted laboratory investigations. Mohsen.M. performed numerical modeling using FLAC3D, analyzed computational results, and validated them against experimental data. Project administration, writing—original draft, supervision, and visualization were performed by Mohsen.M. Both authors jointly wrote the manuscript and reviewed the final submission. Acknowledgement The authors would like to thank and appreciate Dr. Reza Pourhosseini Ardekani as well as Dr. Kazem Barkhordari from the University of Yazd, Iran for providing the laboratory facilities of this university and their instructive guidance. References Azzam, W. and A. Basha, Utilization of micro-piles for improving the sub-grade under the existing strip foundation: experimental and numerical study. Innovative Infrastructure Solutions, 2018. 3 : p. 1-11. Mohammadizadeh, M. and M. Mohammadizadeh, Numerical Modeling of a Dynamic Pile–Soil Interaction in Layered Soil Media. GEO, 2016: p. 96. Mohammadizadeh, M., et al., The undrained vertical bearing capacity of skirted foundations located on slopes using finite element limit analysis. Innovative Infrastructure Solutions, 2023. 8 (4): p. 121. Mohammadizadeh, M., B. Nadi, and A. Hajiannia, Sensitivity analysis of a skirted circular foundation located on clay by stress characteristic method. Arabian Journal of Geosciences, 2023. 16 (12): p. 673. Mohammadizadeh, M., et al., Experimental and Numerical Evaluation Performance of Strip Foundation Reinforced with Steel Slag Columns Compared to Skirted Foundation. Indian Geotechnical Journal, 2024: p. 1-17. Mohammadizadeh, M., et al., Laboratory and numerical study of the behavior of skirted foundation located on a buried pipe under static axial loading. Amirkabir Journal of Civil Engineering, 2023. 55 (1): p. 3-18. Shafaghat, A. and H. Khabbaz, Recent advances and past discoveries on tapered pile foundations: A review. Geomechanics and Geoengineering, 2022. 17 (2): p. 455-484. Rodriguez Rincón, E., R.P.d. Cunha, and B. Caicedo Hormaza, Analysis of settlements in piled raft systems founded in soft soil under consolidation process. Canadian Geotechnical Journal, 2020. 57 (4): p. 537-548. Ateş, B. and E. Şadoğlu, Experimental and numerical investigation of load sharing ratio for piled raft foundation in granular soils. KSCE Journal of Civil Engineering, 2022. 26 (4): p. 1662-1673. Ateş, B. and E. Şadoğlu, Experimental investigation for group efficiency of driven piles embedded in cohesionless soil. KSCE Journal of Civil Engineering, 2023. 27 (12): p. 5123-5134. Ates, B. and E. ŞADOĞLU, Experimental investigation of optimum piles spacing for piled raft foundation in sandy soils. Teknik Dergi, 2021. 32 (1). Ateş, B. and E. Şadoglu, Experimental and numerical investigation for vertical stress increments of model piled raft foundation in sandy soil. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 2022. 46 (1): p. 309-326. Vijayan, C. and R. Ayothiraman, Review of the State-of-the-Art on Response on Tapered Piles to Different Loading Conditions. Indian Geotechnical Journal, 2024: p. 1-15. Ismael, N.F., Behavior of step tapered bored piles in sand under static lateral loading. Journal of geotechnical and geoenvironmental engineering, 2010. 136 (5): p. 669-676. Majumder, M. and D. Chakraborty, Bearing capacity of tapered piles in clay under undrained condition. International Journal of Geotechnical Engineering, 2018: p. 1-7. Sakr, M. and M.H. El Naggar, Centrifuge modeling of tapered piles in sand. Geotechnical testing journal, 2003. 26 (1): p. 22-35. Singh, S. and N.R. Patra, Axial behavior of tapered piles using cavity expansion theory. Acta Geotechnica, 2020. 15 (6): p. 1619-1636. Wang, J., et al., Vertical impedance of a tapered pile in inhomogeneous saturated soil described by fractional viscoelastic model. Applied Mathematical Modelling, 2019. 75 : p. 88-100. Liu, J., et al., Load transfer behaviour of a tapered rigid pile. Géotechnique, 2012. 62 (7): p. 649-652. Naggar, M.H.E. and M. Sakr, Evaluation of axial performance of tapered piles from centrifuge tests. Canadian Geotechnical Journal, 2000. 37 (6): p. 1295-1308. Lee, J., et al., Estimation of axial load capacity for bored tapered piles using CPT results in sand. Journal of geotechnical and geoenvironmental engineering, 2009. 135 (9): p. 1285-1294. Paik, K., J. Lee, and D. Kim, Axial response and bearing capacity of tapered piles in sandy soil. Geotechnical Testing Journal, 2010. 34 (2): p. 122-130. Sakr, M., M.H.E. Naggar, and M. Nehdi, Load transfer of fibre-reinforced polymer (FRP) composite tapered piles in dense sand. Canadian Geotechnical Journal, 2004. 41 (1): p. 70-88. Sakr, M.A., W.R. Azzam, and H.K. Kassim, Geotechnical behavior of a single pile in sand with varied cross-section geometries and construction techniques. Innovative Infrastructure Solutions, 2023. 8 (6): p. 169. Nordlund, R., Bearing capacity of piles in cohesionless soils. Journal of the Soil Mechanics and Foundations Division, 1963. 89 (3): p. 1-36. Mayerhof, G., Bearing capacity and settlemtn of pile foundations. Journal of Geotechnical and Geoenvironmental Engineering, 1976. 102 (ASCE# 11962). Rybnikov, A., Experimental investigations of bearing capacity of bored-cast-in-place tapered piles. Soil Mechanics and Foundation Engineering, 1990. 27 (2): p. 48-52. Zil'berberg, S. and A. Sherstnev, Construction of compaction tapered pile foundations (from the experience of the" Vladspetsstroi" trust). Soil Mechanics and Foundation Engineering, 1990. 27 (3): p. 96-101. Kurian, N.P. and M.S. Srinivas, Studies on the behaviour of axially loaded tapered piles by the finite element method. International journal for numerical and analytical methods in geomechanics, 1995. 19 (12): p. 869-888. Wei, J. and M.H. El Naggar, Experimental study of axial behaviour of tapered piles. Canadian Geotechnical Journal, 1998. 35 (4): p. 641-654. Khan, M.K., M.H. El Naggar, and M. Elkasabgy, Compression testing and analysis of drilled concrete tapered piles in cohesive-frictional soil. Canadian Geotechnical Journal, 2008. 45 (3): p. 377-392. Zhan, Y.-g., H. Wang, and F.-c. Liu, Numerical study on load capacity behavior of tapered pile foundations. Electronic Journal of Geotechnical Engineering, 2012. 17 : p. 1969-1980. Manandhar, S. and N. Yasufuku, Vertical bearing capacity of tapered piles in sands using cavity expansion theory. Soils and Foundations, 2013. 53 (6): p. 853-867. Hataf, N. and A. Shafaghat, Optimizing the bearing capacity of tapered piles in realistic scale using 3D finite element method. Geotechnical and Geological Engineering, 2015. 33 (6): p. 1465-1473. Mohammadizadeh, M. and M. Mohammadizadeh. Numerical Study of Tapered Piles in Sand . in International Congress and Exhibition" Sustainable Civil Infrastructures: Innovative Infrastructure Geotechnology" . 2017. Springer. Vali, R., et al., A three-dimensional numerical comparison of bearing capacity and settlement of tapered and under-reamed piles. International Journal of Geotechnical Engineering, 2019. 13 (3): p. 236-248. Nasrollahzadeh, E. and N. Hataf, Experimental and numerical study on the bearing capacity of single and groups of tapered and cylindrical piles in sand. International Journal of Geotechnical Engineering, 2019: p. 1-12. Itasca, F.D., Fast Lagrangian analysis of continua in 3 dimensions, Version 4.0. Minneapolis, Minnesota, Itasca Consulting Group, 2009. 438 . Zhu, H., et al., Assessment of Earth Retaining Performance for Long-Short Piles Composite Structures from Field Experiments and Numerical Analysis. Buildings, 2022. 12 (10): p. 1524. ASTM, D., Standard test method for CBR (California bearing ratio) of laboratory-compacted soils. Annual Book of ASTM Standards, 1883. 4 . Leask, A. NAASRA interim guide to pavement thickness design . in (paper to) National Local Government Engineering Conference, 1st, 1981, Adelaide, Australia . 1981. Sedran, G., D.F. Stolle, and R.G. Horvath, An investigation of scaling and dimensional analysis of axially loaded piles. Canadian geotechnical journal, 2001. 38 (3): p. 530-541. Jesmani, M., et al., Undrained vertical bearing capacity of piles located near soft clay slope. Journal of Engineering Research, 2015. 3 (3): p. 21-38. Bahrami, M., M.I. Khodakarami, and A. Haddad, Seismic behavior and design of strutted diaphragm walls in sand. Computers and Geotechnics, 2019. 108 : p. 75-87. Sakr, M.A., et al., Behavior of grouted single screw piles under inclined tensile loads in sand. EJGE, 2016. 21 (2016): p. 572-591. Additional Declarations No competing interests reported. Supplementary Files Appendix1.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5783847","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":406682478,"identity":"69913f0f-1938-4a26-bfd8-95f58c96427f","order_by":0,"name":"moein mohammadizadeh","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8ElEQVRIiWNgGAWjYFACHjDJ2AYkJBgbbIAkiVrSSNDSANFymLAW3fbeg59u5tjJ9vEffnjj447zif2zmw8+YKixicalxezMuWTp3G3Jxm0Mx4wtZ565nTjjzrFkA4ZjabkNuLTcyDEAamFObGNsMJPmbbud2HAjxwzkQnxajH/nbqtPbGNm/yb9t+1c4nwitJgBbTmc2MbGYybN2HYgcQNBLWfOmFnnbjtu3MbDU2zZ25ZsvPFGWrJBAj6/HO8xvp27rVp2fv/xjTd+ttnJzruRfPDBhxobnFowgCNYZQKxykHAnhTFo2AUjIJRMDIAAJRcYeh6bddIAAAAAElFTkSuQmCC","orcid":"","institution":"Islamic Azad University, Sirjan Branch","correspondingAuthor":true,"prefix":"","firstName":"moein","middleName":"","lastName":"mohammadizadeh","suffix":""},{"id":406682479,"identity":"5c60e75a-1af4-43c9-a564-977d14f7aabe","order_by":1,"name":"mohsen mohammadizadeh","email":"","orcid":"","institution":"Islamic Azad University, Sirjan Branch","correspondingAuthor":false,"prefix":"","firstName":"mohsen","middleName":"","lastName":"mohammadizadeh","suffix":""}],"badges":[],"createdAt":"2025-01-07 19:23:04","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5783847/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5783847/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":74931475,"identity":"d2ce13d9-5cee-432f-b410-a437781ce8a0","added_by":"auto","created_at":"2025-01-28 12:33:03","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":68958,"visible":true,"origin":"","legend":"\u003cp\u003eGrading curve of loose and dense sand.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5783847/v1/38a806ff67443783962af8d4.png"},{"id":74931160,"identity":"5a91b945-9eda-4529-9339-b19b75ae462c","added_by":"auto","created_at":"2025-01-28 12:25:03","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":113680,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic view of loading system.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5783847/v1/f138d677c8be1d2292de44a5.png"},{"id":74931155,"identity":"d70ebce4-38e4-40e2-ad02-184e1263f54f","added_by":"auto","created_at":"2025-01-28 12:25:03","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":861384,"visible":true,"origin":"","legend":"\u003cp\u003eLocation settlement gauge on the head pile.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5783847/v1/e695c79ba9391fb49a0cd3f6.png"},{"id":74931161,"identity":"e93b470f-547a-4d39-acf9-9ad893c694fa","added_by":"auto","created_at":"2025-01-28 12:25:03","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":759783,"visible":true,"origin":"","legend":"\u003cp\u003eloading system.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5783847/v1/b620f2feaf07791641903a11.png"},{"id":74931163,"identity":"2085ea78-b415-4249-80f0-b9e7d3c6d125","added_by":"auto","created_at":"2025-01-28 12:25:03","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":57407,"visible":true,"origin":"","legend":"\u003cp\u003eCBR Test Results.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5783847/v1/7798103131f6406df1e5abea.png"},{"id":74931180,"identity":"88d17fb2-a53e-44ae-aa67-7c9054c91383","added_by":"auto","created_at":"2025-01-28 12:25:04","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":199042,"visible":true,"origin":"","legend":"\u003cp\u003e3D model of piles group foundation and soil.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-5783847/v1/560ef8bc5f30503259ab212e.png"},{"id":74931201,"identity":"002b278b-fdf6-48db-bab5-494b073d4b0f","added_by":"auto","created_at":"2025-01-28 12:25:05","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":62406,"visible":true,"origin":"","legend":"\u003cp\u003eStress field Direction of characteristics on Mohr's circle.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-5783847/v1/cbf2bde9320f96a9af87691a.png"},{"id":74931157,"identity":"2b1885d5-e5ff-497c-94a9-08a2af184976","added_by":"auto","created_at":"2025-01-28 12:25:03","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":313873,"visible":true,"origin":"","legend":"\u003cp\u003eContour of z displacement (m) T31 pile.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-5783847/v1/cfe6d04b9140a49a322b7341.png"},{"id":74931172,"identity":"fe3667f4-498c-47ef-8301-ad7f94b6f246","added_by":"auto","created_at":"2025-01-28 12:25:04","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":340911,"visible":true,"origin":"","legend":"\u003cp\u003eContours of z displacement (m) T93 pile.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-5783847/v1/3c2c9f48247a33a01ff8efb1.png"},{"id":74931156,"identity":"ff2e70e7-0d71-4fe3-91df-dcd736e37c24","added_by":"auto","created_at":"2025-01-28 12:25:03","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":19712,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of tapered pile analysis result with Rybnikov's Test Site.\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-5783847/v1/370c4ecb340bb2e0cd12db43.png"},{"id":74932434,"identity":"919ec9d5-ffb9-44c9-8f12-dca18726fbf5","added_by":"auto","created_at":"2025-01-28 12:41:03","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":64675,"visible":true,"origin":"","legend":"\u003cp\u003eFailure criterion (a) Tangant intersection method.\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-5783847/v1/28217588f9104d14fe0241e2.png"},{"id":74931186,"identity":"22d635f3-44af-41da-ac1c-3dd0e511f212","added_by":"auto","created_at":"2025-01-28 12:25:04","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":51197,"visible":true,"origin":"","legend":"\u003cp\u003eLoad-settlement curve of C20 \u0026amp; T31 piles in laboratory model tests \u0026amp; FDM analysis.\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-5783847/v1/7636820e1122685f0d9731ea.png"},{"id":74931166,"identity":"e70294db-2793-452a-848d-196a9c29ab8a","added_by":"auto","created_at":"2025-01-28 12:25:03","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":48842,"visible":true,"origin":"","legend":"\u003cp\u003eLoad-settlement curve of C40-1 \u0026amp; T62-1 piles in laboratory model tests \u0026amp; FDM analysis.\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-5783847/v1/4ab0cba654a81c76ab179a59.png"},{"id":74931484,"identity":"c06563be-0907-4cf5-a323-3cde4742559b","added_by":"auto","created_at":"2025-01-28 12:33:04","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":46007,"visible":true,"origin":"","legend":"\u003cp\u003eLoad-settlement curve of C30 \u0026amp; T51 piles in laboratory model tests \u0026amp; FDM analysis.\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-5783847/v1/84ba47628e092d9000b00bfc.png"},{"id":74931175,"identity":"f2f04b75-d6ce-4eb6-809f-5fa3f5b39a0c","added_by":"auto","created_at":"2025-01-28 12:25:04","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":52924,"visible":true,"origin":"","legend":"\u003cp\u003eLoad-settlement curve of C50 \u0026amp; T82 piles in laboratory model tests \u0026amp; FDM analysis.\u003c/p\u003e","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-5783847/v1/7a13916b3c6d0d1ec41513d9.png"},{"id":74931491,"identity":"2a48a6ac-e724-4094-a2da-3c953b61796d","added_by":"auto","created_at":"2025-01-28 12:33:06","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":56344,"visible":true,"origin":"","legend":"\u003cp\u003eLoad-settlement curve of C40-2 \u0026amp; T62-2 piles in laboratory model tests \u0026amp; FDM analysis.\u003c/p\u003e","description":"","filename":"16.png","url":"https://assets-eu.researchsquare.com/files/rs-5783847/v1/35073efac59e0923fc7c57b1.png"},{"id":74931206,"identity":"a1d3e1ae-cb95-436b-a095-2f503fc1a0fb","added_by":"auto","created_at":"2025-01-28 12:25:05","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":45682,"visible":true,"origin":"","legend":"\u003cp\u003eLoad-settlement curve of C60 \u0026amp; T93 piles in laboratory model tests \u0026amp; FDM analysis.\u003c/p\u003e","description":"","filename":"17.png","url":"https://assets-eu.researchsquare.com/files/rs-5783847/v1/b684a6f0dd26fef3a79428a4.png"},{"id":74932880,"identity":"edabbf1a-ad08-4e7c-b63b-59e6a4c9e2a6","added_by":"auto","created_at":"2025-01-28 12:49:06","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4719511,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5783847/v1/697e4bbb-1ca4-42d2-92f2-94c9fadf239e.pdf"},{"id":74931154,"identity":"f5b859f3-0793-4560-a142-65e79a56bdce","added_by":"auto","created_at":"2025-01-28 12:25:03","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":14644,"visible":true,"origin":"","legend":"","description":"","filename":"Appendix1.docx","url":"https://assets-eu.researchsquare.com/files/rs-5783847/v1/411b99dff002a21141effb9d.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Experimental and Numerical Study on the Bearing Capacity of Tapered Piles in Sand Under Compressive Load","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eWhen shallow foundations are inadequate due to insufficient bearing capacity or excessive settlement, deep foundations, such as piles, offer a viable alternative [\u003cspan additionalcitationids=\"CR2 CR3 CR4 CR5\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Cylindrical or prismatic piles, characterized by a constant cross-sectional area along their length, are commonly employed in practice. In geotechnical engineering, the bearing capacity of piles is a critical consideration in foundation design [\u003cspan additionalcitationids=\"CR8 CR9 CR10 CR11\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Tapered piles serve several important functions. Firstly, they facilitate a more uniform load distribution along the pile's length, thereby reducing stress concentrations. Additionally, tapered piles can be more cost-effective than cylindrical piles, as they require less material while still providing the necessary bearing capacity [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eNumerous laboratory and theoretical studies have been conducted to evaluate the efficiency of tapered piles [\u003cspan additionalcitationids=\"CR15 CR16 CR17\" citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. For instance, some authors [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] have explored the compressive capacity of tapered piles in comparison to traditional cylindrical piles. Other researchers [\u003cspan additionalcitationids=\"CR22 CR23\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] have investigated small-scale models of tapered piles.\u003c/p\u003e \u003cp\u003eAmong the earliest analytical studies on tapered piles, Nordlund [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] demonstrated a significant increase in axial bearing capacity for bored tapered piles. Similarly, Meyerhof [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] found that frictional capacity can increase by a factor of 1.5 compared to prismatic piles when a single tapered pile in sandy soils is subjected to vertical loading. Rybnikov [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] compared the bearing capacities of cylindrical and bored tapered piles, discovering that, for piles with equivalent average volume and radius, tapered piles exhibited a 20\u0026ndash;30% increase in bearing capacity. Notably, when tapered piles and cylindrical piles with similar radii were installed in sandy soils, the bearing capacity of the cylindrical piles was found to be 200\u0026ndash;250% lower [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eKurian and Srinivas [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] conducted experimental tests on tapered piles to validate numerical models of their compressive behavior, finding that three factors contributed to increased capacity : enhanced side friction, a direct bearing of the pile sides, and increased vertical pressure.\u003c/p\u003e \u003cp\u003eWei and El Naggar [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e] observed that the performance of pile material improved with the taper angle, primarily due to the load being transferred to a larger soil mass. Furthermore, during pile installation, the increased lateral earth pressure from radial soil compaction, improves frictional resistance.\u003c/p\u003e \u003cp\u003eKhan et al. [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] examined the axial compressive capacity of full-scale drilled concrete tapered piles. Their results showed that, compared to straight piles of equal volume, tapered piles with taper angles ranging from 0.95 to 1.91 degrees exhibited a load-bearing capacity increase of up to 50%. Zhan et al. [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] investigated tapered piles under axial loading in the sand with low dilatancy using finite element modeling (FEM). They concluded that the optimal taper angle for piles ranges from 0.5 to 1.0 degrees. Additionally, the increase in radial stress with tapered piles mitigates the convex heave at the pile-ground interface. The rise in the normalized radial distance for tapered piles leads to a minimum threefold increase near the pile-ground interface compared to cylindrical piles, resulting in elevated radial stresses within the soil [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eHataf and Shafaghat [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e] found that the optimal taper angle for a pile under the axial load in the sand is closely related to the soil's friction angle. Their study showed that, at the optimal angle, the increase in frictional bearing capacity outweighs the reduction in end bearing capacity .However, as the taper angle increases further, frictional bearing capacity continues to improve while end bearing capacity declines. When subjected to vertical loads, tapered piles exhibit a smaller increase in bearing capacity compared to cylindrical piles [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. Vali et al. [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e] evaluated the settlement and bearing capacity of embedded tapered piles using three-dimensional finite element analysis, revealing that increases in pile diameter have minimal impact on bearing capacity. Nasrollahzadeh and Hataf [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e] conducted laboratory tests and numerical analyses on single and group tapered and cylindrical piles in sand. Their findings demonstrated that tapered piles, whether single or grouped, show enhanced bearing capacity compared to cylindrical piles.\u003c/p\u003e \u003cp\u003eInitial research in this field primarily focused on the advantages of using tapered piles, with later studies indicating that these benefits are most pronounced up to a certain taper angle. However, previous research has not adequately explored the complex interaction between piles and soil in determining bearing capacity, particularly in relation to soil density. Although significant research has been conducted on piles, there remains a notable gap in understanding the combined effects of pile dimensions and soil type on pile behavior under external loads. The load-settlement behavior of both tapered and cylindrical piles is intricately linked to the flexibility of the entire system, which is influenced by the properties of the surrounding soil, the taper angle, and the dimensions of the pile. Moreover, both numerical and laboratory simulations have been used to study the behavior of piles under axial loading in the sand, highlighting the crucial importance of considering installation effects for accurate modeling. The present study, conducts both numerical and experimental investigations to assess the impact of the relative density of surrounding sands on the performance of tapered piles. Additionally, this study examines the influence of taper angle on the bearing capacity of tapered piles. To achieve this, 12 piles with varying lengths and taper angles were tested in two types of sandy soils, with different internal friction angles. The experimental procedure began by placing the piles in both loose and dense soils, followed by applying load and measuring the resulting settlement using a gauge positioned on top of the piles. The experimental procedures and tests were then simulated using the finite difference method in FLAC3D software[\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e], as detailed in Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The results of these simulations are presented Section \u003cspan refid=\"Sec11\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The paper concludes with a discussion of the findings in Section \u003cspan refid=\"Sec13\" class=\"InternalRef\"\u003e4\u003c/span\u003e and conclusions in Section 5.\u003c/p\u003e"},{"header":"2. Materials and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003e2.1. Laboratory Investigation\u003c/h2\u003e\n \u003cdiv id=\"Sec4\" class=\"Section3\"\u003e\n \u003ch2\u003e2.1.1 Experimental Setup\u003c/h2\u003e\n \u003cp\u003eThe experimental setup began with the preparation of the soil, which was poured into a cylindrical container with a height of 1800 mm and a diameter of 1200 mm. The container was divided into 12 sections, each 150 mm in height. The soil was carefully deposited using the sand raining technique, followed by compaction. The resulting relative density was approximately 84% for dense sand and 38% for loose sand.\u003c/p\u003e\n \u003cp\u003eTwelve samples of concrete pile samples with varying taper angles were constructed, and their characteristics are detailed in Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. The mechanical properties of the piles and surrounding soils are provided in Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e. When the length-to-diameter ratio exceeded 10, the pile exhibited friction pile characteristics, classifying it as a long pile[\u003cspan class=\"CitationRef\"\u003e39\u003c/span\u003e]. In the pile naming convention, the first letter indicates whether the pile is tapered (T) or cylindrical (C), followed by numbers representing the radius for uniform piles and the two-sided radius for tapered piles.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eThe dimension of tapered piles used in this article\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eIndex\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eLength\u003c/p\u003e\n \u003cp\u003e(mm)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBottom diameter (mm)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eTop diameter (mm)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eVolume\u003c/p\u003e\n \u003cp\u003e(Cm3)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eTaper angle (deg)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC 20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e500\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e628\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eT 31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e500\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e680\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.29\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC 40\u0026thinsp;\u0026minus;\u0026thinsp;1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e500\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2510\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eT 62\u0026thinsp;\u0026minus;\u0026thinsp;1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e500\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e120\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2720\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.57\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC 30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e800\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2262\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eT 51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e800\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2597\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.862\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC 50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e800\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6283\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eT 82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e800\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e160\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7037\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.289\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC 40\u0026thinsp;\u0026minus;\u0026thinsp;2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1200\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6032\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eT 62\u0026thinsp;\u0026minus;\u0026thinsp;2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1200\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e120\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6534\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.91\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC 60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1200\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e120\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e120\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e13572\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eT 93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1200\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e180\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e14700\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.862\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"left\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\u0026nbsp;\u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eProperties of concrete and soils\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMaterial\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBehavioral\u003c/p\u003e\n \u003cp\u003emodel\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eElastic\u003c/p\u003e\n \u003cp\u003emodulus\u003c/p\u003e\n \u003cp\u003e(MPa)\u003c/p\u003e\n \u003cp\u003e[E]\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePoisson\u0026apos;s\u003c/p\u003e\n \u003cp\u003eRatio\u003c/p\u003e\n \u003cp\u003e[\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{v}\\)\u003c/span\u003e\u003c/span\u003e]\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCohesion\u003c/p\u003e\n \u003cp\u003e(KPa)\u003c/p\u003e\n \u003cp\u003e[\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{C}\\)\u003c/span\u003e\u003c/span\u003e]\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eBulk modulus\u003c/p\u003e\n \u003cp\u003e(MPa)\u003c/p\u003e\n \u003cp\u003e[k]\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAngle of shear\u003c/p\u003e\n \u003cp\u003eresistance\u003c/p\u003e\n \u003cp\u003e( ͦ )\u003c/p\u003e\n \u003cp\u003e[𝜑]\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eShear modulus\u003c/p\u003e\n \u003cp\u003e(MPa)\u003c/p\u003e\n \u003cp\u003e[G]\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDensity\u003c/p\u003e\n \u003cp\u003e(Kg/m3)\u003c/p\u003e\n \u003cp\u003e[\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\rho\\:\\)\u003c/span\u003e\u003c/span\u003e]\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eD10\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eD30\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eD60\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eConcrete\u003c/p\u003e\n \u003cp\u003epile\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eElastic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e25000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10400\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2500\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSoft sand\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMohr-Coulomb\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e16.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1478\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.81\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDense\u003c/p\u003e\n \u003cp\u003esand\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMohr-Coulomb\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e61.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1928\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.194\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.34\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.483\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. Grading curve of loose and dense sand.\u003c/p\u003e\n \u003cp\u003eFigure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e shows the soil aggregate distribution of the materials used in the tests. The soil\u0026apos;s physical properties were determined using the California Bearing Ratio (CBR) test in accordance with ASTM standards [\u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e41\u003c/span\u003e]. The modulus of elasticity of the sandy soils was calculated using the following equation:\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"left\" class=\"colspec\"\u003e\u003cimg src=\"data:image/png;base64,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\"\u003e\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e. Schematic view of loading system.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e. Location settlement gauge on the head pile.\u003c/p\u003e\n \u003cp\u003eFigures \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e illustrate the loading apparatus, where the distance from the loading point to the pile is three times the distance between the pile and the support. Figure \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e depicts the loading system, which increases the load incrementally. Two types of sand, dense and loose, were employed in this research, with the CBR test results presented in Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e. loading system.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e. CBR Test Results.\u003c/p\u003e\n \u003cp\u003ePhysical model was carefully designed to avoid scale effects, particularly concerning the ratio of the pile diameter to the soil\u0026rsquo;s average particle size (D₅₀). According to Sedran et al.[\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e], this ratio should exceed 30 to minimize scale effects in piles under axial loading, a condition that was met in all models used in this research.\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n \u003ch2\u003e2.2. Numerical Investigation\u003c/h2\u003e\n \u003cp\u003eNumerical analysis is a widely used and cost-effective method for analyzing pile behavior, offering reliable prognostication capabilities. In this study, FLAC3D, a finite difference modeling software specifically designed for simulating material behavior under both static and dynamic conditions, was employed to analyze the behavior of tapered piles. FLAC3D is known for its flexibility in modeling and analyzing complex geotechnical problems.\u003c/p\u003e\n \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e\n \u003ch2\u003e2.2.1. Model Geometry\u003c/h2\u003e\n \u003cp\u003eThe initial step in using FLAC3D involves creating the model geometry. Cylindrical shell elements were used to simulate the soil elements in this study. A 3D axisymmetric model was developed, utilizing a quarter-section of the geometry to simplify the analysis while maintaining accuracy. As illustrated in Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e, the numerical model is represented by the vertical axis of symmetry intersecting the longitudinal axis of the pile. A fine mesh was applied near the pile-soil interface to ensure precise modeling of the interaction. After establishing the soil geometry, contact elements were introduced at the interface between the pile and the soil, simulating the pile in its designated position. The vertical loading of the pile is influenced by the soil-pile interface elements, making accurate modeling of this interface crucial [\u003cspan class=\"CitationRef\"\u003e43\u003c/span\u003e]. The interaction between the pile and surrounding soil is governed by Coulomb friction, shear bonding, and tensile forces [\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e]. The stiffness of the contact surface elements, including both vertical and shear stiffness, was determined based on the properties of the surrounding soil. In FLAC3D, the contact surface element is used to model potential slip or detachment at the pile-soil interface. Shear and normal stiffness were represented using springs attached to each node of the pile. Lateral motion and vertical displacement between the pile and the adjacent soil were modeled by normal and shear springs, respectively. The interface friction angle was assumed to be equivalent to two-thirds of the soil\u0026rsquo;s internal friction angle (𝜑), as suggested by Bahrami et al. [\u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e]. The relationship between normal stiffness (kₙ)) and shear stiffness (kₛ) is defined as follows [\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e]:\u003c/p\u003e\n \u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e$${k_n}={k_s}=~\\frac{{k+\\left( {\\frac{4}{3}G} \\right)}}{{\\Delta Z}}~ \\times 10$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003ewhere, k and G represent the soil\u0026rsquo;s bulk modulus and shear modulus, respectively, these parameters are calculated using the following formulas:\u003c/p\u003e\n \u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e$$K=\\frac{E}{{3\\left( {1 - 2\\nu } \\right)}}$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e$$G=\\frac{E}{{2\\left( {1+\\nu } \\right)}}$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003e\u0026Delta;Z is the smallest dimension of the soil element at the surface of the contact element. Two types of interface elements were used to apply the load to the pile: one along the pile\u0026rsquo;s length and the other at the pile\u0026rsquo;s toe. For this study, the normal and shear stiffness (kₙ and kₛ) for loose sand were set at 2693 Mpa/m, while for dense sand, these values were 8806 Mpa/m.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e. 3D model of piles group foundation and soil.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e\n \u003ch2\u003e2.2.2. Boundary Conditions\u003c/h2\u003e\n \u003cp\u003eVirtual boundaries were established at specific distances from the pile to ensure accurate simulation results. Two key factors guided the selection of these boundaries: first, the boundary must be far enough from the pile to avoid influencing the loading results; second, it should be positioned where the analyzed soil volume is minimized to reduce computation time. Based on these considerations and the analysis of pile behavior, the horizontal boundary was set at a distance of 30R (where R is the pile radius) from the center of the pile. For the vertical boundary, the distance was set at L\u0026thinsp;+\u0026thinsp;15R, where L and R represent the average length and diameter of the pile, respectively. To prevent vertical displacement roller supports were applied at the vertical boundary\u003c/p\u003e\n \u003cp\u003eThe numerical model consisted of 10,582 grid points and 3,375 zones .All displacements at the model\u0026apos;s base were constrained, while the vertical outer faces were fixed in both the X- and Y-directions. Along the symmetry axis, roller supports were placed perpendicular to the symmetry plane to ensure zero displacement in this direction, allowing movement along the plane\u0026apos;s surface. Additionally, a free-surface condition was applied at the top of the model (Z\u0026thinsp;=\u0026thinsp;0).\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e\n \u003ch2\u003e2.2.3. Constitutive Model and Materials Properties\u003c/h2\u003e\n \u003cp\u003eThe Mohr-Coulomb constitutive law was employed to model the behavior of sandy soils in this analysis. This model is well-suited for studying pile behavior in sandy soils, as it captures the essential stress-strain characteristics of such materials. The key parameters required for this constitutive model include the internal friction angle (𝜑), shear modulus, bulk modulus, and dilatancy angle. The rupture envelope in this model is defined by a direct relationship between shear stress (\u0026tau;) and normal stress(\u0026sigma;), as expressed which is in the following equation (Eq.\u0026nbsp;5):\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAgEAAAA7CAYAAADimFmDAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAmSSURBVHhe7d09TFPdHwfwL/8wOJQwlMHaiWJpZEAJoQNpjKEmVlDi4AswAInigMujEOLAIAmJlrTo5KCYgFEC6mAoVqPYECUOJKUNA0mp1AELLAzYO2hicp7hz73pPa2VN1/63O8nuUN/5/a+gPF87z3nXgqEEAJERERkOP+TC0RERGQMDAFEREQGxRBARERkUAwBREREBsUQQEREZFAMAURERAbFEEBERGRQDAFEREQGxRBARERkUAwBREREBsUQQEREZFAMAURERAbFEEBERGRQDAFEREQGxRBARERkUAwBREREBsUQQEREZFAMAURERAbFEEBERGRQDAFEREQGxRBARERkUAwBBvPkyRPE43G5vCXxeBzBYFAuExFRnmIIMJChoSHY7XbY7Xa5aUvsdjssFguGhobkJiIiykMMAQYRiUQAAFVVVXLTtlRVVSGZTGrbIyKi/MUQYBCPHj1CdXW1XN6RxsZGTExMyGUiIsozDAF/iUgkgnfv3snlPRGJRPD58+cdDwPI7HY7FhYWeDeAiCjPMQT8JSYmJvask5aFQiE4nU6YTCa5aUdMJhOcTidCoZDcREREeYQh4C8QDAaxsLCAoqIiuWnXFEXBy5cv4XA45KZdcTgcmJ+fl8tERJRH8j4EdHV1oaCgQLeUlJT81lvViqJgbGwMDocj41jUpa2tTf4aVldXcfz4cTQ0NODJkycoKirC5OSk1q4oinZ+TqcTwWAQJSUl2jbLysqwuroKRVHQ19eHkpISHD9+HIqiaNtIpVL49OmT9vlHFEXB7du34XA44Pf7EYlE4HQ6UVBQkLFN1czMDFZXV+Xylk1OTsLv98vlrILBoHY8Tqfzt/5+iejX8Hg8mJmZQSKRyPg/s6CgAIlEAgMDAxgYGJC/Snskr0OA3+/H4OCgXMaRI0d+2a11maIoOHPmDJqbm7G4uCg3a86dOyeXYLFY8Pz5c7jdbgQCAQghcOrUKWDzmfzDhw8Dmx3548ePMTIygvX1dQQCAfh8PrhcLhQVFaGvrw81NTUYHh5GNBrVvQdgbW0NhYWFsFqtWk2mnsOLFy8wOTmJlpYWeL1ePH78GHNzc4hGo7hy5YruO1arFYWFhVhbW9PVfwW/34/W1lbcuHEDQghcuHCBQxFEea6zsxO9vb1wuVwAAK/XCyGEbrHZbOjp6QEAjI2NSVugvZC3IeDdu3ewWq0QQsDn86G1tVX7hzM1NZUx/t3W1paRMuUl29V6LmrnGY1GMTg4iFQqBSEEVlZW0NHRoX1O79xlqVQKX7580XXSq6ur8Hg8cLlc8Pv9MJlMsNvt2LdvH2w2GxwOB16+fInKykr4/X60tLSgvr4esVgMxcXF2L9/v24fuajnYLVaMTU1BbvdjtHRUdTU1GjvFDhy5AiSyWTWuwG/2uTkJG7evIk3b96gvr4e8Xgc4+Pjez68QUS/j9qhqwHgZ3p6etDb24tEIiE30S7lbQg4evQompqatDHvbFfa6UZGRjJSpryMjIzIX8tpenoab9++xfDwMK5evaoFD4vFgm/fvmVcPWcTDoexvr6u67ivX78OALh161bamv/ncrmgKAqWl5exuLiI6upq7dn/+fl5lJaW6uYWJJNJrK+vp21Bb3p6GtFoFP/88w+wGQpmZ2dRV1enW89qtWYEq/X1dSSTSV1tLymKgjt37qChoUE7R7vdjtnZ2R+GKiL6+/X29qKlpUVXC4VCuosy+cr/8uXL8Pl8uhrtXt6GAFU8HofZbMaxY8fkpl/u6dOncLvdWfddWVm5pavnWCwGl8sFi8UCbN4FmJmZQWdnp1ZLr1dWViIUCmFxcREmk0nrDNX2kydPZnTWP6J2sunDJ+pQQvrnaDSKyspK3Xd3Qr4bc/r0aXR3d+tq6jwHpIWsnwU8IsofiUQCS0tLWe8CqBdkXq8Xzc3NmJmZ0dpqa2vx+vVr3fq0e3kfAu7cubOlx9/kDijbsp3hgFydrnp3ItvVczp1vfQONhwOA0BGSh4dHcXGxgbq6uowPz8Pm82G7u5urT0cDmvt6axWK8xms66mUicNpp+D/DhhKBRCcXFxxvEAgNlszjnXQCbfjVHnNqTXlpaWtPATi8Vgs9n27CVHRPTnzc7OoqysTFez2Wx49eqV9rmnpwcnTpzAhw8ftNqBAwewtLTEIYE9ltchQO2IHQ4H4vE4bt++La+ikTugbMt2hgOKiopQWlqa9TG5rV7BxuNxLC8v6zruWCymWwebL/sZHx9HcXExsDkrX75TEIvFdjwhUj0HeShAHY9/9uyZbl9/kqIoeP/+vVwmIqIdyOsQsLa2ho2NDZw+fRoejwdNTU3yKr+MyWTCyZMn8fDhQ23sStl8zK69vR0+n++n49bJZBLfv3+HyWTCgwcPtPrGxoY26z4YDCIcDuPQoUNwuVwIhUIZV/zpdx6CwaDusb39+/fj+/fvWcfuLRYLXC6Xdg7qUIDFYkFfXx/a29sxPDyc9e8NqMe+nUmI2+VwOJBIJDA6Ogpshqa+vj4cPHhQXpWI/mM+fvyI2tpauUx7TeSxlZUVYbPZRE1NjZibm5Obf4v79+8Ls9ksAAiz2Sw6OjrE4uKivFpWgUBAmM1mMTg4KFKplBBCiFQqJdxutwCgnZdaKy8vFx6PR9hsNrGysqJtJ/3nkG3fra2twufzyWUhNvd37do17RwAiPLyct0xZRMIBITb7c65zs8EAoEfHpcq/efb0dGxq/0R0Z+3tLQk5K6nrKxM99nr9Qqv16urvX//PmM92r0CIYSQgwH9t/j9fszPz+cc7lAUBRcvXsT169ezXvnL1Jf8dHV1yU1ERDl5PB7dOwLGxsbQ3NystXu9Xu39ACr1hUFynXYnr4cDaGvq6urw9evXnE8qyE8F5CLPHSAi2o729nZtmA8AmpqadPOzsnX09+7dw9mzZ+Uy7RJDgAFUVVWhoqJC9yZBmfxUQC6pVAoVFRVbumNARCRT52+lPwKYy8DAAPr7+2Gz2eQm2iWGAINobGzExMSEXAZ2cGX/4sULNDY2ymUioi27e/cu+vv7fxoE1GGA3znx20g4J8BAhoaGdG8Y3IlIJIJwOIxLly7JTURElGcYAgwmGAxqfxNgu+LxOCKRCM6fPy83ERFRHmIIICIiMijOCSAiIjIohgAiIiKDYgggIiIyKIYAIiIig2IIICIiMiiGACIiIoNiCCAiIjIohgAiIiKDYgggIiIyKIYAIiIig2IIICIiMiiGACIiIoNiCCAiIjIohgAiIiKD+hdPQ227Ckfe8QAAAABJRU5ErkJggg==\"\u003e\u003c/div\u003e\n \u003cp\u003eIn this equation, \u003cem\u003e\u0026sigma;\u003c/em\u003e represents the normal stress on the fracture surface, \u003cem\u003e\u0026tau;\u003c/em\u003e denotes the shear stress, and 𝜑 and \u003cem\u003ec\u003c/em\u003e correspond to the soil\u0026apos;s internal friction angle and cohesion, respectively, as depicted in Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e. Stress field Direction of characteristics on Mohr\u0026apos;s circle.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e\n \u003ch2\u003e2.2.4. Loading Procedure\u003c/h2\u003e\n \u003cp\u003eFollowing the preparation of the model geometry, the pile was first balanced under its weight. Subsequently, an external load was applied to the pile. A downward velocity of 1\u0026times;10\u003csup\u003e⁻⁶\u003c/sup\u003e m/timestep was imposed on the nodes of the pile. The numerical model indicated that a specific number of steps were required for the unbalanced force to reach a minimal value and remain stablewithout significant fluctuations. This process also necessitated considerable time to propagate the load adequately throughout the model. Once the unbalanced force stabilized, the velocity of the nodes was maintained at a constant rate. Figures \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e and \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e illustrate of Z-displacement contours for the T31 and T93 piles, respectively.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e. Contour of z displacement (m) T31 pile.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e. Contours of z displacement (m) T93 pile.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e\n \u003ch2\u003e2.2.5. Verification\u003c/h2\u003e\n \u003cp\u003eRybnikov [\u003cspan class=\"CitationRef\"\u003e27\u003c/span\u003e] conducted a study on bored-cast-in-place tapered piles in the Irtysh Pavlodar region (formerly part of the Soviet Union). The vertical bearing capacity of the pile was determined based on a settlement of 24 mm from the load-average settlement data. Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e presents the soil characteristics used in that study, where the soil profile consisted of three distinct layers. The load-settlement curves obtained from the experimental results (with bottom and top radii of 100 and 300, respectively) were compared with the finite difference analysis for verification.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eProperties of concrete and soils\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eIndex\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSandy loam\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eOrdinary loam\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSand\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLayer thickness (m)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSoil density (gr/cm3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.81\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAngle of internal friction (deg)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e32\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCohesion (MPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.012\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.026\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.004\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eElastic modulus (MPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e26\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAngle of dilation (deg)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eAs illustrated in Fig. \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e, the pile-bearing capacity determined in this study aligns closely with Rybnikov\u0026rsquo;s results, demonstrating a high degree of accuracy. The discrepancy between the experimental and numerical results is less than 5%, indicating strong consistency between the two methods, particularly at the initial stages where the curves closely match.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e. Comparison of tapered pile analysis result with Rybnikov\u0026apos;s Test Site.\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"3. Discussion","content":"\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n \u003ch2\u003e3.1. Efficacy of Vertical Load on the Response of Piles\u003c/h2\u003e\n \u003cp\u003eIn order to increase the accuracy of the experimental test results, the load tests performed on each pile, are repeated three times, and by taking an average, the results of each test are recorded. The tangent intersection method defines the vertical bearing capacity [\u003cspan class=\"CitationRef\"\u003e31\u003c/span\u003e]. As shown in Fig. \u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e, two tangential lines were drawn along the primary and secondary sections of the load displacement curve. The load corresponding to the intersection of these two lines was identified as the bearing capacity. The load-displacement curve is approximately linear, with a near-horizontal slope after reaching the ultimate failure load. Determining a pile\u0026apos;s stiffness from the load-settlement curve involves analyzing the slope of the curve at various points. This analysis provides insights into the pile\u0026apos;s early elastic behavior (Initial Tangent Stiffness), its average stiffness up to a particular load (Secant Stiffness), and its instantaneous stiffness at a specific load level (Tangent Stiffness). For this purpose, a Python code was developed, as detailed in Appendix 1.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e. Failure criterion (a) Tangant intersection method.\u003c/p\u003e\n \u003cp\u003eSensitivity analysis is essential for optimizing the design and performance of tapered piles. This analysis is particularly important for understanding the impact of variables such as pile taper angle, soil properties, and embedment depth. By examining how changes in these parameters influence stress distribution and deformation behavior, the design of tapered piles can be optimized for improved performance.\u003c/p\u003e\n \u003cp\u003eThe taper angle of a pile plays a crucial role in influencing load distribution and overall stability. A steeper taper angle can improve lateral resistance but may also increase bending moments at the pile head, potentially leading to greater structural demands. Deeper embedment generally improves load-bearing capacity; however, it may also result in increased deformation at the pile top due to soil constraints. Analyses indicate that variations in the friction angle of sands lead to significant differences in bearing capacities[\u003cspan class=\"CitationRef\"\u003e45\u003c/span\u003e].\u003c/p\u003e\n \u003cp\u003eFigures \u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e to \u003cspan class=\"InternalRef\"\u003e17\u003c/span\u003e illustrate the applied forces and the induced settlements observed in both experimental and numerical analyses. The piles used in the static analysis under vertical loading were grouped into three categories based on height and geometry. The first, second, and third groups of piles had heights of 500 mm, 800 mm, and 1200 mm, respectively. Each group included both a short pile and a long pile.\u003c/p\u003e\n \u003cp\u003eAs shown in Figs. \u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e and \u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003e, for a given load, tapered piles exhibit less settlement than cylindrical piles, and their bearing capacity increases with a steeper taper angle. This indicates that in scenarios where settlement must be minimized, such as in urban construction, tapered piles offer a more efficient solution than cylindrical piles.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e. Load-settlement curve of C20 \u0026amp; T31 piles in laboratory model tests \u0026amp; FDM analysis.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003e. Load-settlement curve of C40-1 \u0026amp; T62-1 piles in laboratory model tests \u0026amp; FDM analysis.\u003c/p\u003e\n \u003cp\u003eMoreover, in all cases, the bearing capacity is significantly higher in dense sandy soil compared to loose sandy soil. For instance, as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e14\u003c/span\u003e which relates to piles in dense sandy soil, the bearing capacity of tapered piles with an average diameter of 60mm increased by approximately 18% according to numerical analysis and by 21% based on laboratory tests compared to cylindrical piles. It is important to note that the volume of the cylindrical piles is 3.5% less than that of the tapered piles.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e14\u003c/span\u003e. Load-settlement curve of C30 \u0026amp; T51 piles in laboratory model tests \u0026amp; FDM analysis.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e15\u003c/span\u003e. Load-settlement curve of C50 \u0026amp; T82 piles in laboratory model tests \u0026amp; FDM analysis.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e16\u003c/span\u003e. Load-settlement curve of C40-2 \u0026amp; T62-2 piles in laboratory model tests \u0026amp; FDM analysis.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e17\u003c/span\u003e. Load-settlement curve of C60 \u0026amp; T93 piles in laboratory model tests \u0026amp; FDM analysis.\u003c/p\u003e\n \u003cp\u003eFurthermore, Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e15\u003c/span\u003e illustrates that for piles with a diameter of 100 mm, despite the tapered pile\u0026apos;s volume increasing by 5%, its bearing capacity when maintaining the same average diameter was reduced by 22.5% in the numerical analysis and by 24% in the laboratory test compared to cylindrical piles. In this instance, the taper angle was4.289 degrees. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e16\u003c/span\u003e shows that as settlement values increase, the bearing capacity of the tapered pile also increases relative to the cylindrical pile, consistent with previous findings. However, as depicted in the Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e17\u003c/span\u003e, when the T93 pile was placed in loose sandy soil, the tolerable load at the same settlement initially favored the tapered piles over the cylindrical ones. Yet, as the applied load increased, the load-bearing curve for the cylindrical pile eventually exceeded that of the tapered pile.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4. Conclusions","content":"\u003cp\u003eThe studies conducted indicate that when tapered piles with a taper angle of less than 2.29 degrees are placed in loose sandy soil, their bearing capacity exceeds that of cylindrical piles with the same average diameter. However, as the taper angle increases, even though the concrete volume increases, the bearing capacity tends to decrease.\u003c/p\u003e \u003cp\u003eFor tapered piles in dense sandy soil, bearing capacities were found to be greater than those of cylindrical piles with a constant average diameter when taper angles were1.91, 2.29, and 4.57 degrees. Conversely, for piles with taper angles of 4.29 and 4.57 degrees in loose sandy soil, the bearing capacities were lower than those of cylindrical piles with the same average diameter.\u003c/p\u003e \u003cp\u003eAn excessive increase in the taper angle, particularly beyond 2.86 degrees, results in a reduction of the pile head's effective area compared to cylindrical piles. This leads to a more pronounced taper shape, causing the pile to penetrate the soil like a wedge which in turn increases settlement and reduces bearing capacity. The numerical analyses closely align with laboratory test results, with an acceptable margin of error between the numerical and experimental bearing capacities.\u003c/p\u003e \u003cp\u003eThe mechanical properties of the soil are directly related to the selection of optimal taper angles for piles, with significant differences observed between the optimal taper angles for dense and loose sandy soil. Increasing the taper angle of the pile head up to a certain point improves the bearing capacity. However, exceeding this optimal taper angle results in a decrease in bearing capacity. As the taper angle increases, shaft load capacities improve, while base load capacities diminish due to the reduced contact area with the ground. The relative density of the soil is a critical factor that governs the base resistance.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eMoein.M. conceptualized the study, designed the experimental setup, and conducted laboratory investigations. Mohsen.M. performed numerical modeling using FLAC3D, analyzed computational results, and validated them against experimental data. Project administration, writing\u0026mdash;original draft, supervision, and visualization were performed by Mohsen.M. Both authors jointly wrote the manuscript and reviewed the final submission.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThe authors would like to thank and appreciate Dr. Reza Pourhosseini Ardekani as well as Dr. Kazem Barkhordari from the University of Yazd, Iran for providing the laboratory facilities of this university and their instructive guidance.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eAzzam, W. and A. Basha, \u003cem\u003eUtilization of micro-piles for improving the sub-grade under the existing strip foundation: experimental and numerical study.\u003c/em\u003e Innovative Infrastructure Solutions, 2018. \u003cstrong\u003e3\u003c/strong\u003e: p. 1-11.\u003c/li\u003e\n \u003cli\u003eMohammadizadeh, M. and M. Mohammadizadeh, \u003cem\u003eNumerical Modeling of a Dynamic Pile\u0026ndash;Soil Interaction in Layered Soil Media.\u003c/em\u003e GEO, 2016: p. 96.\u003c/li\u003e\n \u003cli\u003eMohammadizadeh, M., et al., \u003cem\u003eThe undrained vertical bearing capacity of skirted foundations located on slopes using finite element limit analysis.\u003c/em\u003e Innovative Infrastructure Solutions, 2023. \u003cstrong\u003e8\u003c/strong\u003e(4): p. 121.\u003c/li\u003e\n \u003cli\u003eMohammadizadeh, M., B. Nadi, and A. Hajiannia, \u003cem\u003eSensitivity analysis of a skirted circular foundation located on clay by stress characteristic method.\u003c/em\u003e Arabian Journal of Geosciences, 2023. \u003cstrong\u003e16\u003c/strong\u003e(12): p. 673.\u003c/li\u003e\n \u003cli\u003eMohammadizadeh, M., et al., \u003cem\u003eExperimental and Numerical Evaluation Performance of Strip Foundation Reinforced with Steel Slag Columns Compared to Skirted Foundation.\u003c/em\u003e Indian Geotechnical Journal, 2024: p. 1-17.\u003c/li\u003e\n \u003cli\u003eMohammadizadeh, M., et al., \u003cem\u003eLaboratory and numerical study of the behavior of skirted foundation located on a buried pipe under static axial loading.\u003c/em\u003e Amirkabir Journal of Civil Engineering, 2023. \u003cstrong\u003e55\u003c/strong\u003e(1): p. 3-18.\u003c/li\u003e\n \u003cli\u003eShafaghat, A. and H. Khabbaz, \u003cem\u003eRecent advances and past discoveries on tapered pile foundations: A review.\u003c/em\u003e Geomechanics and Geoengineering, 2022. \u003cstrong\u003e17\u003c/strong\u003e(2): p. 455-484.\u003c/li\u003e\n \u003cli\u003eRodriguez Rinc\u0026oacute;n, E., R.P.d. Cunha, and B. Caicedo Hormaza, \u003cem\u003eAnalysis of settlements in piled raft systems founded in soft soil under consolidation process.\u003c/em\u003e Canadian Geotechnical Journal, 2020. \u003cstrong\u003e57\u003c/strong\u003e(4): p. 537-548.\u003c/li\u003e\n \u003cli\u003eAteş, B. and E. Şadoğlu, \u003cem\u003eExperimental and numerical investigation of load sharing ratio for piled raft foundation in granular soils.\u003c/em\u003e KSCE Journal of Civil Engineering, 2022. \u003cstrong\u003e26\u003c/strong\u003e(4): p. 1662-1673.\u003c/li\u003e\n \u003cli\u003eAteş, B. and E. Şadoğlu, \u003cem\u003eExperimental investigation for group efficiency of driven piles embedded in cohesionless soil.\u003c/em\u003e KSCE Journal of Civil Engineering, 2023. \u003cstrong\u003e27\u003c/strong\u003e(12): p. 5123-5134.\u003c/li\u003e\n \u003cli\u003eAtes, B. and E. ŞADOĞLU, \u003cem\u003eExperimental investigation of optimum piles spacing for piled raft foundation in sandy soils.\u003c/em\u003e Teknik Dergi, 2021. \u003cstrong\u003e32\u003c/strong\u003e(1).\u003c/li\u003e\n \u003cli\u003eAteş, B. and E. Şadoglu, \u003cem\u003eExperimental and numerical investigation for vertical stress increments of model piled raft foundation in sandy soil.\u003c/em\u003e Iranian Journal of Science and Technology, Transactions of Civil Engineering, 2022. \u003cstrong\u003e46\u003c/strong\u003e(1): p. 309-326.\u003c/li\u003e\n \u003cli\u003eVijayan, C. and R. Ayothiraman, \u003cem\u003eReview of the State-of-the-Art on Response on Tapered Piles to Different Loading Conditions.\u003c/em\u003e Indian Geotechnical Journal, 2024: p. 1-15.\u003c/li\u003e\n \u003cli\u003eIsmael, N.F., \u003cem\u003eBehavior of step tapered bored piles in sand under static lateral loading.\u003c/em\u003e Journal of geotechnical and geoenvironmental engineering, 2010. \u003cstrong\u003e136\u003c/strong\u003e(5): p. 669-676.\u003c/li\u003e\n \u003cli\u003eMajumder, M. and D. Chakraborty, \u003cem\u003eBearing capacity of tapered piles in clay under undrained condition.\u003c/em\u003e International Journal of Geotechnical Engineering, 2018: p. 1-7.\u003c/li\u003e\n \u003cli\u003eSakr, M. and M.H. El Naggar, \u003cem\u003eCentrifuge modeling of tapered piles in sand.\u003c/em\u003e Geotechnical testing journal, 2003. \u003cstrong\u003e26\u003c/strong\u003e(1): p. 22-35.\u003c/li\u003e\n \u003cli\u003eSingh, S. and N.R. Patra, \u003cem\u003eAxial behavior of tapered piles using cavity expansion theory.\u003c/em\u003e Acta Geotechnica, 2020. \u003cstrong\u003e15\u003c/strong\u003e(6): p. 1619-1636.\u003c/li\u003e\n \u003cli\u003eWang, J., et al., \u003cem\u003eVertical impedance of a tapered pile in inhomogeneous saturated soil described by fractional viscoelastic model.\u003c/em\u003e Applied Mathematical Modelling, 2019. \u003cstrong\u003e75\u003c/strong\u003e: p. 88-100.\u003c/li\u003e\n \u003cli\u003eLiu, J., et al., \u003cem\u003eLoad transfer behaviour of a tapered rigid pile.\u003c/em\u003e G\u0026eacute;otechnique, 2012. \u003cstrong\u003e62\u003c/strong\u003e(7): p. 649-652.\u003c/li\u003e\n \u003cli\u003eNaggar, M.H.E. and M. Sakr, \u003cem\u003eEvaluation of axial performance of tapered piles from centrifuge tests.\u003c/em\u003e Canadian Geotechnical Journal, 2000. \u003cstrong\u003e37\u003c/strong\u003e(6): p. 1295-1308.\u003c/li\u003e\n \u003cli\u003eLee, J., et al., \u003cem\u003eEstimation of axial load capacity for bored tapered piles using CPT results in sand.\u003c/em\u003e Journal of geotechnical and geoenvironmental engineering, 2009. \u003cstrong\u003e135\u003c/strong\u003e(9): p. 1285-1294.\u003c/li\u003e\n \u003cli\u003ePaik, K., J. Lee, and D. Kim, \u003cem\u003eAxial response and bearing capacity of tapered piles in sandy soil.\u003c/em\u003e Geotechnical Testing Journal, 2010. \u003cstrong\u003e34\u003c/strong\u003e(2): p. 122-130.\u003c/li\u003e\n \u003cli\u003eSakr, M., M.H.E. Naggar, and M. Nehdi, \u003cem\u003eLoad transfer of fibre-reinforced polymer (FRP) composite tapered piles in dense sand.\u003c/em\u003e Canadian Geotechnical Journal, 2004. \u003cstrong\u003e41\u003c/strong\u003e(1): p. 70-88.\u003c/li\u003e\n \u003cli\u003eSakr, M.A., W.R. Azzam, and H.K. Kassim, \u003cem\u003eGeotechnical behavior of a single pile in sand with varied cross-section geometries and construction techniques.\u003c/em\u003e Innovative Infrastructure Solutions, 2023. \u003cstrong\u003e8\u003c/strong\u003e(6): p. 169.\u003c/li\u003e\n \u003cli\u003eNordlund, R., \u003cem\u003eBearing capacity of piles in cohesionless soils.\u003c/em\u003e Journal of the Soil Mechanics and Foundations Division, 1963. \u003cstrong\u003e89\u003c/strong\u003e(3): p. 1-36.\u003c/li\u003e\n \u003cli\u003eMayerhof, G., \u003cem\u003eBearing capacity and settlemtn of pile foundations.\u003c/em\u003e Journal of Geotechnical and Geoenvironmental Engineering, 1976. \u003cstrong\u003e102\u003c/strong\u003e(ASCE# 11962).\u003c/li\u003e\n \u003cli\u003eRybnikov, A., \u003cem\u003eExperimental investigations of bearing capacity of bored-cast-in-place tapered piles.\u003c/em\u003e Soil Mechanics and Foundation Engineering, 1990. \u003cstrong\u003e27\u003c/strong\u003e(2): p. 48-52.\u003c/li\u003e\n \u003cli\u003eZil\u0026apos;berberg, S. and A. Sherstnev, \u003cem\u003eConstruction of compaction tapered pile foundations (from the experience of the\u0026quot; Vladspetsstroi\u0026quot; trust).\u003c/em\u003e Soil Mechanics and Foundation Engineering, 1990. \u003cstrong\u003e27\u003c/strong\u003e(3): p. 96-101.\u003c/li\u003e\n \u003cli\u003eKurian, N.P. and M.S. Srinivas, \u003cem\u003eStudies on the behaviour of axially loaded tapered piles by the finite element method.\u003c/em\u003e International journal for numerical and analytical methods in geomechanics, 1995. \u003cstrong\u003e19\u003c/strong\u003e(12): p. 869-888.\u003c/li\u003e\n \u003cli\u003eWei, J. and M.H. El Naggar, \u003cem\u003eExperimental study of axial behaviour of tapered piles.\u003c/em\u003e Canadian Geotechnical Journal, 1998. \u003cstrong\u003e35\u003c/strong\u003e(4): p. 641-654.\u003c/li\u003e\n \u003cli\u003eKhan, M.K., M.H. El Naggar, and M. Elkasabgy, \u003cem\u003eCompression testing and analysis of drilled concrete tapered piles in cohesive-frictional soil.\u003c/em\u003e Canadian Geotechnical Journal, 2008. \u003cstrong\u003e45\u003c/strong\u003e(3): p. 377-392.\u003c/li\u003e\n \u003cli\u003eZhan, Y.-g., H. Wang, and F.-c. Liu, \u003cem\u003eNumerical study on load capacity behavior of tapered pile foundations.\u003c/em\u003e Electronic Journal of Geotechnical Engineering, 2012. \u003cstrong\u003e17\u003c/strong\u003e: p. 1969-1980.\u003c/li\u003e\n \u003cli\u003eManandhar, S. and N. Yasufuku, \u003cem\u003eVertical bearing capacity of tapered piles in sands using cavity expansion theory.\u003c/em\u003e Soils and Foundations, 2013. \u003cstrong\u003e53\u003c/strong\u003e(6): p. 853-867.\u003c/li\u003e\n \u003cli\u003eHataf, N. and A. Shafaghat, \u003cem\u003eOptimizing the bearing capacity of tapered piles in realistic scale using 3D finite element method.\u003c/em\u003e Geotechnical and Geological Engineering, 2015. \u003cstrong\u003e33\u003c/strong\u003e(6): p. 1465-1473.\u003c/li\u003e\n \u003cli\u003eMohammadizadeh, M. and M. Mohammadizadeh. \u003cem\u003eNumerical Study of Tapered Piles in Sand\u003c/em\u003e. in \u003cem\u003eInternational Congress and Exhibition\u0026quot; Sustainable Civil Infrastructures: Innovative Infrastructure Geotechnology\u0026quot;\u003c/em\u003e. 2017. Springer.\u003c/li\u003e\n \u003cli\u003eVali, R., et al., \u003cem\u003eA three-dimensional numerical comparison of bearing capacity and settlement of tapered and under-reamed piles.\u003c/em\u003e International Journal of Geotechnical Engineering, 2019. \u003cstrong\u003e13\u003c/strong\u003e(3): p. 236-248.\u003c/li\u003e\n \u003cli\u003eNasrollahzadeh, E. and N. Hataf, \u003cem\u003eExperimental and numerical study on the bearing capacity of single and groups of tapered and cylindrical piles in sand.\u003c/em\u003e International Journal of Geotechnical Engineering, 2019: p. 1-12.\u003c/li\u003e\n \u003cli\u003eItasca, F.D., \u003cem\u003eFast Lagrangian analysis of continua in 3 dimensions, Version 4.0.\u003c/em\u003e Minneapolis, Minnesota, Itasca Consulting Group, 2009. \u003cstrong\u003e438\u003c/strong\u003e.\u003c/li\u003e\n \u003cli\u003eZhu, H., et al., \u003cem\u003eAssessment of Earth Retaining Performance for Long-Short Piles Composite Structures from Field Experiments and Numerical Analysis.\u003c/em\u003e Buildings, 2022. \u003cstrong\u003e12\u003c/strong\u003e(10): p. 1524.\u003c/li\u003e\n \u003cli\u003eASTM, D., \u003cem\u003eStandard test method for CBR (California bearing ratio) of laboratory-compacted soils.\u003c/em\u003e Annual Book of ASTM Standards, 1883. \u003cstrong\u003e4\u003c/strong\u003e.\u003c/li\u003e\n \u003cli\u003eLeask, A. \u003cem\u003eNAASRA interim guide to pavement thickness design\u003c/em\u003e. in \u003cem\u003e(paper to) National Local Government Engineering Conference, 1st, 1981, Adelaide, Australia\u003c/em\u003e. 1981.\u003c/li\u003e\n \u003cli\u003eSedran, G., D.F. Stolle, and R.G. Horvath, \u003cem\u003eAn investigation of scaling and dimensional analysis of axially loaded piles.\u003c/em\u003e Canadian geotechnical journal, 2001. \u003cstrong\u003e38\u003c/strong\u003e(3): p. 530-541.\u003c/li\u003e\n \u003cli\u003eJesmani, M., et al., \u003cem\u003eUndrained vertical bearing capacity of piles located near soft clay slope.\u003c/em\u003e Journal of Engineering Research, 2015. \u003cstrong\u003e3\u003c/strong\u003e(3): p. 21-38.\u003c/li\u003e\n \u003cli\u003eBahrami, M., M.I. Khodakarami, and A. Haddad, \u003cem\u003eSeismic behavior and design of strutted diaphragm walls in sand.\u003c/em\u003e Computers and Geotechnics, 2019. \u003cstrong\u003e108\u003c/strong\u003e: p. 75-87.\u003c/li\u003e\n \u003cli\u003eSakr, M.A., et al., \u003cem\u003eBehavior of grouted single screw piles under inclined tensile loads in sand.\u003c/em\u003e EJGE, 2016. \u003cstrong\u003e21\u003c/strong\u003e(2016): p. 572-591.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Numerical Modelling, Taper Piles, Finite Difference Method, Sands, Laboratory Test","lastPublishedDoi":"10.21203/rs.3.rs-5783847/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5783847/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDeep foundations are widely recognized as one of the most effective methods for transferring surface loads to subsurface soil layers. While cylindrical piles are the conventional choice for deep foundations, tapered piles offer significant advantages in load transfer and material efficiency. This study investigates 12 types of tapered piles with varying characteristics in the loose and dense soils under static loading conditions in both loose and dense sands through laboratory experiments. The behavior of tapered piles is also modeled numerically using finite difference analysis, and the numerical results are validated against the experimental data. Additionally, a parametric analysis is conducted to evaluate the influence of \u0026nbsp;design variables such as taper angle, pile length and sand relative density on the load-settlement behavior. The comparative analysis between tapered and cylindrical piles identifies an optimal taper angle for homogeneous sands, revealing that the bearing capacity decreases by 2.86 degrees with an increase in pile angle. Moreover, increasing the relative density of the soil results in a 2- to 3-fold improvement in the bearing capacity of the piles.\u003c/p\u003e","manuscriptTitle":"Experimental and Numerical Study on the Bearing Capacity of Tapered Piles in Sand Under Compressive Load","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-28 12:24:58","doi":"10.21203/rs.3.rs-5783847/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"b350fedc-c594-4fdf-9ee9-461a2c56a148","owner":[],"postedDate":"January 28th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-03-13T04:53:23+00:00","versionOfRecord":[],"versionCreatedAt":"2025-01-28 12:24:58","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5783847","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5783847","identity":"rs-5783847","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}