Performance Optimization of Piled Raft Foundations in Layered Soil under Uniform Vertical Loading Using Plaxis 3D

Piled raft foundations are composite foundations that combine piles and raft to support civil engineering structure and to reduce the settlement. Te data were obtained from Addis Ababa, Ethiopia. In this study, the efects of raft thickness, number of piles, pile length, spacing of piles, and pile diameter on the response of piled-raft foundations were investigated using the fnite element-based program Plaxis 3D for layered soils (medium to very stif high plastic silty clay and medium to very dense silty sand soil) subjected to uniform vertical loading. Te results showed that increasing the thickness of the raft from 0.7 m to 1.7 m reduced the diferential settlement by 78.21% when there were 16 piles. However, the maximum settlement also increased by 2.81%. Increasing the number of piles from 4 to 16 reduced the maximum settlement by 22.09% for a pile spacing of 4D. Moreover, increasing the pile length from 9m to 15 m contributed to a 19.49% reduction in the total settlement for a pile spacing of 5D. Terefore, the current study provides a useful framework for analyzing and designing large piled-raft foundations.


Introduction
Te rapid urbanization of recent decades has increased the need for large civil structures.However, many of these structures are being built on soft soil sites, which can result in ground settling, particularly in urban areas where there are few rock sites available.Given the strict safety regulations, the allowable diferential settlement of the structure in high-rise buildings is very small, despite the tremendous weight of the structure.Adequate foundations are essential to transfer loads from the superstructure to the substructure.
Buildings are constructed from the ground up, but if the foundation fails, the entire building could collapse or fail in many other ways.In cases where a heavy structure is built on weak soil, a shallow raft foundation may not meet the design criteria, necessitating load transmission to a deeper, more capable layer.Piled foundations have been developed to support the excessive loads caused by superstructures and to prevent excessive settlements [2].However, due to the loadsharing mechanism between piles, rafts, and soil, it is not feasible to construct foundations using only piles or rafts.Tis would lead to high construction costs and excessive settlement, respectively.Consequently, "Piled Raft Foundations," a combination of two distinct systems, have been created [3].Recently, piled raft foundations (PRFs) have become popular in high-rise and signifcant building designs for their efcient control of total and diferential settlement and their high bearing capacity [4].
In recent years, there has been an increased focus on the use of sustainability principles in engineering design.Piled raft foundations have been shown to ofer several benefts in this regard, including the use of less material than conventional foundations, reduced construction time and associated costs, and a smaller environmental impact.Additionally, the use of piled raft foundations can help to reduce the amount of excavation required, which can limit the impact on the environment and surrounding communities.As such, the use of piled raft foundations can be seen as a sustainable alternative to conventional foundation systems [5].
Poulos [6] studied the maximum total, diferential settlement, and ultimate load capacity for diferent loading scenarios, as well as the weight carried by each interacting component and various input parameters, particularly for the pile and the rafty, were analyzed.Analytical methods can be used to determine the behavior of piled raft systems, but these methods are often insufcient due to the complex three-dimensional interaction between the soil, raft, and pile.Terefore, numerical approaches are often utilized to solve these problems, particularly with the development of advanced understanding and high-performance computing tools.
Tere are three broad classes of numerical analysis methods for piled raft foundation systems: (1) simplifed calculation methods, (2) approximate computer-based methods, and (3) more rigorous computer-based methods.Among these methods, 3D linear/nonlinear fnite element or fnite diference methods are the most feasible [6].Nonlinear 3D fnite element and fnite diference analyses have been carried out recently.Nevertheless, diffculties in modeling the soil-structure interface persist as a challenge in this 3D fnite element and fnite diference analyses.
Te main difculty in applying numerical methods to piled raft foundation systems lies in selecting appropriate input parameters to provide efective output results.By performing a back analysis on well-documented case histories, the process of determining suitable values for these input parameters can be altered.In parametric analyses, diferent parameters are analyzed to investigate the behavior of piled raft foundation systems under axial loads.Many studies in the literature focused on the parameters, such as pile number, pile length, pile diameter, pile spacing ratio, pile location, pile stifness, load distribution, load level, raft thickness, raft dimensions, and soil type [7].
Te design of piled rafts primarily raises questions about the load distribution between the raft and piles, as well as the impact of extra pile support on absolute and diferential settlements [8].Another important factor in the design of piled raft foundations is the type of soil present at the site.Diferent soil types have varying characteristics that can impact the performance of the foundation.For instance, in soft soils, it may be necessary to increase the length or number of piles to ensure adequate support for the structure.Similarly, in areas with high water content, the soil may be susceptible to settlement and it may be necessary to increase the raft thickness to prevent diferential settlement.A thorough understanding of the soil conditions is therefore critical in the design and construction of piled raft foundations [9].
It is important to note that the behavior of piled raft foundations is still not fully understood, and there is ongoing research to better understand the interaction between the pile, raft, and soil.Recent studies have suggested that there may be a need to consider the infuence of factors such as pile spacing, pile arrangement, and soil-structure interaction on the behavior of piled raft foundations.In addition, further research is needed to evaluate the impact of these factors on the long-term performance of piled raft foundations [10].
Te fnite element method (FEM) serves as a formidable tool for modeling a diverse range of geotechnical challenges, from excavation and seismic analysis to slope stability analysis, foundation design, settlement, consolidation, and more [11].For instance, the fnite element method (FEM) was employed to address the excavation issue in references [11,12] and the consolidation settlement in reference [13].Te solutions of fnite element models were used to discuss the efects of these parameters.Parametric analyses of the piled raft were carried out using Plaxis 3D software.By varying the parameters, it is possible to understand how the behavior of piled raft foundation systems changed with diferent input values [14].In a study conducted by researchers [15], Plaxis 3D was utilized to carry out a parametric study investigating unconnected piled rafts in clayey soil.Te results of this study can be used to optimize design parameters and improve the performance of piled raft foundation systems.

Numerical Model
Te model comprises a soil continuum, a rectangular raft foundation (1.5 L r /B r , 10 m B r , and 15 m L r ), an interface component, and a 360 kPa UDL; a drained analysis was utilized since no water was encountered in boreholes.Te raft's edge lateral boundaries were set at twice the raft's width, limiting horizontal (but allowing vertical) soil displacement.
In a raft foundation, the pressure bulb size was up to double the raft's width, while in a pile group, it was formed at two-third of the pile length, resulting in a bottom soil boundary with a vertical distance equal to twice the raft's width plus two-third of the pile length [16].A global fne mesh was used for the soil domain, with an extremely fne mesh near structural components using a 0.25 coarseness factor as shown in Figure 1.Te piled raft examination involved three phases: initial, construction, and loading.Preliminary analysis showed the chosen lateral boundaries were adequate, as the observed plastic strain area in the soil equaled the raft's width (B r ) laterally from its edge.

Constitutive Modeling.
Te Mohr-Coulomb model, commonly employed in geotechnical works, requires a few input parameters such as cohesion, internal friction angle, Young's modulus, and Poisson's ratio which can be obtained from standard soil tests [17].Te soil was represented using 10-node tetrahedral elements, the raft used triangular plate elements, and the piles were modeled as embedded beam elements [10].Meshing results in each element have six degrees of freedom (three translational and three rotational).Te analyses account for defection due to shearing, bending, and axial forces, allowing plasticity if predefned limits are reached.

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Advances in Materials Science and Engineering Te load-bearing behavior of a piled raft is characterized by a complex soil-structure interaction between the piles, raft, and the subsoil [18].Te raft and piles remain elastic due to their higher modulus of elasticity compared to soil, making them linearly elastic.Tey are rigidly connected, and their interface is represented by the interface reduction factor (R inter ), which shows the interface strength as a percentage of adjacent soil's shear strength.Te raft-soil interface, considered a smooth contact with a R inter of 0.8, follows the Plaxis 3D manual's recommendations (0.8-1 for sand-concrete and 0.7-1 for clay-concrete interactions).Te soil-pile interaction is modeled using embedded interface elements of 3-node line elements with node pairs [19].Interface elements have zero thickness (h � 0), follow the Mohr-Coulomb failure criterion, and enable simulating displacement discontinuity between structural elements (raft and piles) and the soil mass.

Input Parameter for Numerical Analysis
2.2.1.Soil.Te analysis studied weak soil characteristics using a Mohr-Coulomb Elastoplastic medium and a twolayer subsoil (medium to very stif high plastic silty clay and medium to very dense silty sand soil) model for Addis Ababa's Bole Arabsa V (Figure 2), based on 280 borehole data extending 10 m and 15 m from the surface.No water table was considered as subsurface water was not encountered in the boreholes.Geotechnical parameters were sourced from collected data, and missing information was estimated using empirical equations derived from Standard Penetration Test (SPT) values.Young's modulus, cohesion, angle of friction, and Poisson's ratio were determined using methodologies from references [20][21][22].

Raft.
Te raft, a fat slab of consistent thickness on the ground had a smaller occupied volume than the soil mass.A rectangular raft foundation with a 1.5 length-to-width ratio (L r /B r � 1.5), a width of 10 m (B r ), and a length of 15 m (L r ) was modeled.Te initial raft thicknesses of 0.7 m, 1.2 m, and 1.7 m were determined using SAFE 20 software, which imported loads from the ETABS output, to resist punching forces.Relevant properties of the raft were gathered from prior publications.[23] guidelines, using diameters of 0.6 m, 0.8 m, and 1 m, and spacing of 3D, 4D, and 5D on the raft's shorter side, with 1.5 times that on the longer side.Pile lengths of 15 m, 12 m, and 9 m were examined to assess a settlement in large piled rafts (B r > L p ) [19,[24][25][26], where piles primarily reduce settlement.Pile numbers 4, 9, and 16 were tested in 2 × 2, 3 × 3, and 4 × 4 confgurations.

2.2.4.
Load.Te total load on the structural system is assumed to be evenly distributed across the raft's surface area, as is typical for a fexible raft but may result in non-uniform stress distribution due to diferential settlements [27].For this study, the load was obtained from ETABS output for a 12-story residential apartment, aligning with the Ethiopian Building Code Standard for buildings exceeding 36 meters or 12 foors [28,29].Although the uniform load assumption may not accurately refect actual conditions, it is acceptable for practical purposes [27].

Model Validation.
Tis study validates the modeling approach by comparing numerical fndings with references [16,17,30] on a 24 × 24 m, 2 m-thick square raft piled system, embedded in soft clay, supported by 16 piles, 1.0 m diameter, 15 m-long circular piles spaced 6D apart.Te foundation is subjected to a uniform vertical load, with soil and foundation parameters as detailed in Table 1. Figure 3 compares the load-settlement behavior of the piled raft using fnite diference analysis with the referenced fnite element analyses, fnding good agreement between the studies.

Parametric Study
A comprehensive parametric study investigated the behavior of piled raft (PR) foundations under vertical loading in layered soil, considering 3D interactions and variables like pile diameter, spacing, length, number, and raft thickness.Te study examined various foundation types such as PR and unpiled raft (UR) for drained soil conditions.Smaller dimensions were used to reduce storage and computational time, alongside common dimensions followed by researchers and standards.Te piled rafts, foundation, soil parameters, and geometric confgurations are presented in Figure 4 and Tables 2 and 3, respectively.

Unpiled Raft Behavior.
A 15 m × 10 m rectangular raft lies on a layered soil profle with a top layer of 5 m-thick silty clay and a lower layer of silty sand.Te raft thickness is important for unpiled raft foundations, as piled raft behavior depends on raft fexibility or stifness.Raft-to-soil stifness ratio (K_ rs ) is used to assess raft stifness, as shown in equation ( 1) [26].Higher raft thickness leads to increased K_ rs , with values below 0.001 indicating perfect fexibility, between 0.001 and 1 intermediate fexibility, and above 1 indicating perfect stifness.Te study calculates K_ rs values for raft thicknesses of 0.7 m (0.1311), 1.2 m (0.66), and 1.7 m (1.878), with the 0.7 m thickness being more fexible.Advances in Materials Science and Engineering Te raft foundation, subjected to a 360 kPa vertical load, Figure 5 shows increased maximum settlement with increasing thickness due to self-weight, while diferential settlement decreased as raft rigidity provided more even load distribution on the soil.A thicker raft can better handle vertical loads and minimize diferential settlement, which is crucial for structural stability and safety [16].Te observed phenomenon can be credited to the rigidity of the raft.An increase in raft thickness results in enhanced rigidity.

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According to Figure 5, there's a decrease in diferential settlement from 23 mm to 3.1 mm as the raft thickness swells from 0.7 m to 1.7 m.Tis lends itself to a more even distribution of load on the soil.Raft thickness must balance maximum settlement, diferential settlement, and foundation system stability.

Efect of Raft Tickness.
Te efect of raft thickness on settlement was investigated through varying raft thicknesses (0.7 m, 1.2 m, and 1.7 m), fxed pile length (9 m), pile diameter and spacing (0.8 m and 3 times of pile diameter), and applied loading (360 kPa).Maximum settlement increased with increased raft thickness for both piled and unpiled cases due to the increased self-weight of the raft.Piled rafts experienced lower maximum settlement compared to unpiled ones, thanks to shared loads between piles and raft, and increased stifness.Te number of piles also afected settlement values, with more piles providing better load distribution (Figure 7).Diferential settlements tended to decrease with increasing raft thickness for both piled and unpiled rafts due to their increased rigidity and even load distribution (Figure 8).However, the relationship between diferential settlement and the number of piles is complex, with values decreasing from 4 to 9 piles, but increasing from 9 to 16 piles, attributing to uneven load distribution among edge and center piles [16].Optimal piled raft performance requires careful consideration of pile arrangement and raft thickness.

Efect of Pile
Diameter.Tis study investigated the efect of pile diameter (0.6 m, 0.8 m, and 1.0 m) on the performance of piled rafts, maintaining a constant raft thickness of 0.7 m.Te maximum settlement, diferential settlement, and maximum bending moment were used as evaluation criteria.Results showed increased pile diameter decreased maximum settlement due to increased surface area, skin friction, and base resistance (reductions of 1.32%, 5.75%, and 6.27% for 4, 9, and 16 piles when diameter increased from 0.6 m to 0.8 m; and 5% and 4.03% for 4 and 9 piles when increased from 0.8 m to 1 m) (Figure 9).However, diferential settlement exhibited a more complex  Advances in Materials Science and Engineering pattern (Figure 10), infuenced by both pile diameter and number of piles, and attributed to the ratio of the pile group width to the raft width (B g /B r ).As pile diameter and the number of piles increased, group width increased, resulting in uneven load distribution and increased diferential settlement.
Te bending moment development in the piled raft system is crucial for structural design, with piled rafts experiencing both sagging and hogging moments.Plaxis 3D, the software used for the fnite element method, has an output feature that includes options for calculating both the bending moment and shear in the X and Y axes.Tis aids in identifying maximum negative and positive bending, which could potentially occur at diferent positions on the raft.Figure 11 shows that increasing the pile diameter leads to an increased negative bending moment for 16 piles due to larger contact areas and increased soil resistance.For 4-pile and 9pile confgurations, the behavior of the maximum negative bending moment varies, with the position for the development changing as pile diameter, spacing, and width of grouped piles increase.Te maximum positive bending moment is mainly infuenced by the raft's dimensions, In both cases, the moment value in the long axis is greater than that of the short axis in most conditions.

Efect of Pile Spacing.
Te investigation analyzed the efect of pile spacing (3D, 4D, 5D) on the performance of piled rafts with 4, 9, and 16 piles.Piles were 9 meters long, 0.6 meters in diameter, with a 0.7-meter-thick raft, and subjected to a 360 kPa load.Increasing pile spacing led to a decrease in maximum settlement (4.34%, 6.3%, and 3.36% reduction from 3D to 5D spacing for 4, 9, and 16 piles, respectively) (Figure 12) and afected diferential settlement diferently: inversely for 9 and 16 piles, and initially decreasing then increasing for 4 piles (Figure 13)).Tis is due to the expanded pile group area and load distribution changes as spacing increases.Overall, more piles resulted in reduced settlement; the 9-pile confguration had the best settlement reduction rate when spacing increased.

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Figure 14 shows that as pile spacing increases from 3D to 4D, the maximum negative moment decreases for four and nine piles but increases from 4D to 5D.Tis can be attributed to the combined efects of the width of the grouped pile (B g ) and the spacing of the piles.As the pile spacing and number of pile increases, width of the group piles increases, which results in a change in the position for the development of the maximum negative bending moment.Additionally, unlike the other two pile numbers (4 and 16), the center of the raft is supported by the piles in the case of a 9-pile number, further contributing to the observed behavior.However, when the pile number is 16, the maximum negative moment behaves diferently due to the decreased cantilever portion of the raft, leading to more load supported by piles.Te positive bending moment decreases with increasing pile spacing for four piles, increases for 16 piles, and varies for nine piles (similar to the case of pile diameter).

Efect of Pile
Length.Te study investigated the impact of pile length on the behavior of piled raft foundations, using a basic model with 9 piles of 9 m, 12 m, and 15 m lengths and various spacing confgurations.Te pile diameter was 0.6 meters, and the raft thickness was 0.7 meters, with an applied loading of 360 kPa.Increasing pile length decreases maximum settlement, for instance, Figure 15 shows that increasing pile length from 9 m to 15 m decreased maximum settlement from 123.6 mm to 108.8 mm under a uniform load of 360 kPa for a pile spacing of 3D, and diferential settlement varied depending on pile lengths, spacings, and soil layers (Figure 16).Longer piles transferring loads through silty clay to stifer silty sand increased diferential settlements, while pile spacing afected load distribution and diferential settlement, with closely spaced piles potentially leading to uneven support.
Findings show that increasing pile length from 9 m to 12 m reduces maximum settlement by 7.85%, 7.29%, and 11.14% for 3D, 4D, and 5D pile spacings, respectively, while increasing it from 12 m to 15 m results in declines of 4.4%, 9.32%, and 9.31%.5D spacing ofers the most signifcant reduction in maximum settlement with increasing pile length, but its diferential settlement is higher than 4D spacing and lower than 3D spacing.Terefore, considering both maximum and diferential settlement reductions can help choose the optimal pile spacing for specifc design requirements and soil conditions.
Figure 17 demonstrates the correlation between increasing pile lengths and the resulting changes in bending moments in raft foundations.A longer pile results in a higher negative bending moment due to enhanced stifness, resistance, and reduced defection.Conversely, maximum positive bending moments decrease with increased pile lengths as the load transfers deeper into the ground, allowing more efcient load distribution and reduced bearing pressure on the raft foundation.Tis variation in positive moments is infuenced by underlying soil properties and changing pile lengths.Additionally, smaller pile spacing leads to a reduced positive bending moment as the soil bears a greater load.In 5D spacing, the positive bending moment is greater on the shorter side due to the longer side spacing (S x ) being 1.5 times the shorter side spacing (1.5 S y ).As pile length increases, soil support for the raft reduces and the pile supports most of the load, increasing the positive bending moment on the shorter side compared to the longer side.

Efect of Number of Piles.
Te investigation of piled raft performance with models incorporating 4, 9, and 16 piles and 3D, 4D, and 5D pile spacing showed that both factors signifcantly impact maximum settlement and differential settlement (Figures 18 and 19).A fxed raft thickness (0.7 m), pile diameter (0.6 m), and length (9 m) were used, and the models were loaded with 360 kPa.Results showed a decreasing maximum settlement of 9.06%, 10.74%, Advances in Materials Science and Engineering and 10.93% from 4 to 9 piles for 3D, 4D, and 5D spacing, and 10.93%, 10.42%, and 8.12% for 9 to 16 piles.Incorporating numerous piles efectively difuses the raft's load, ensuring its equal distribution to the underneath soil and expanding the building's load over a larger area.Tis practice minimizes the risk of overloading the soil, thereby avoiding structural issues or settlement [31].Optimal spacing to reduce maximum settlement was found to be 4D, but differential settlement behavior varied, making careful consideration of both factors crucial in designing piled raft foundations.Bending moments were also impacted by pile spacing and numbers, in ways relating to the area (A g ) and width (B g ) of the pile group (Figure 20).As for the maximum positive bending moment, there is a decrease with an increasing number of piles when the pile spacing is 3D and an increase when the spacing is 5D, along both axes.However, for a pile spacing of 4D, the behavior is diferent, initially decreasing and then increasing as the number of piles increases.

Conclusion
Te following conclusions can be drawn from numerical analysis: (i) Te behavior of an unpiled rectangular raft foundation was signifcantly afected by the applied load and raft thickness.An increase in load resulted in greater settlement due to heightened soil compression, while a thicker raft could lessen diferential settlement by evenly spreading the load on the soil.Te diferential settlement decreased by 86.52% for unpiled, 37.26% for 4 piles, 61.9% for 9 piles, and 78.2% for 16 piles when raft thickness increased from 0.7 m to 1.7 m. (ii) Increasing raft thickness also led to a higher selfweight, contributing to a greater maximum settlement, which increased by 4.59% for unpiled, 9.55% for 4 piles, 9.79% for 9 piles, and 3.88% for 16 piles.Tus, it was essential to carefully determine the raft thickness to balance maximum and differential settlement, ensuring the overall stability and safety of the foundation system.(iii) A larger pile diameter greatly impacted piled raft's performance, reducing maximum settlement by 6.26% and 9.55% for 4 and 9 piles (0.6 m to 1 m) due to an increased surface area and base resistance.Diferential settlement and bending moments depended on factors like pile group to raft width ratio, pile spacing, and raft dimensions.(iv) Te research showed that pile spacing crucially afected piled raft foundations' settlement and bending moment, infuenced by factors like pile numbers and group pile width (B g ).Increased spacing (from 3D to 5D) led to reduced maximum settlement by 4.34%, 6.3%, and 3.36% for 4, 9, and 16 piles, respectively, while causing opposite efects on diferential settlement and complex impacts on bending moments.(v) Increasing pile length from 9 m to 15 m reduced maximum settlement by 11.9%, 15.93%, and 19.42% for pile spacings of 3D, 4D, and 5D, respectively.Diferential settlement varied with pile lengths and spacings while bending moments increased negatively and decreased positively with longer piles.Performance was infuenced by load distribution, foundation stifness, defection, and soil layer interactions.(vi) Te study on piled raft performance revealed the signifcant impact of pile number and spacing on maximum and diferential settlement.Increasing pile numbers from 4 to 16 reduced maximum settlement by 19%, 20.04%, and 18.17% for pile spacings of 3D, 4D, and 5D, respectively.However, diferential settlement varied with specifc pile spacing and number.Te area coverage of the pile group (A g ) also notably afected overall performance.Tus, engineers and designers had to carefully consider pile number and spacing to optimize performance and minimize settlements.(vii) A signifcant observation in this study, besides the parameters, was the impact of the ratio between the pile group width and the raft width (B g /B r ) on the diferential settlement and the bending moment of the raft.As the ratio of the pile group width to the width of the raft (B g /B r ) changed, both the differential settlement and the bending moment exhibited diferent behaviors.Terefore, the performance of piled rafts was mainly related to the area covered by the pile group (A g ).

Figure 3 :
Figure 3: Comparison of the current study's results and previous numerical studies on load-settlement behavior of piled raft.

Figure 4 :
Figure 4: Example of piled rafts considered for parametric analysis.

Figure 6 :Figure 7 :Figure 8 :
Figure 6: Settlement v s load of the unpiled and piled raft foundation.

Table 2 :
Material properties used in the parametric analysis.

Table 3 :
Geometric confgurations of the pile-raft model for parametric analysis.