# Improved Performance of Raft Foundation Using Detached Pile Columns in Loose Subsoil Conditions

Authors: Fekadu Melese
Journal: Advances in Civil Engineering
 (2022)

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## Abstract

Piles act as settlement reducers in case of connected piled-raft foundation and hence decrease the settlements of the raft. The design concept of the connected piled-raft foundations is to lessen the number of piles and utilize the bearing capacity of the system piled raft. Due to significant straining actions at the pile head-raft connection, an alternative technique is proposed to disconnect the piles from the raft. A granular layer (cushion) beneath the raft is incorporated. The disconnection has a beneficial effect on reducing axial load compared to connected piles. For small piled rafts, nonconnected piled rafts show less stiffness than connected piled rafts, and the soil is highly stressed and shows greater raft settlement. In the case of the large piled raft, nonconnected piled rafts show greater settlement efficiency. Cushion stiffness was realized to be more substantial for a nonconnected piled raft with shorter piles than one with longer piles. The results show that the load transfer mechanism in a nonconnected piled raft is mainly governed by the thickness and stiffness of the cushion layer and by the stiffness of the subsoil.


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## Body

## 1. Introduction

For given load circumstances, shallow foundations are acceptable foundations when suitable bearing stratum is present at a shallow depth. The use of deep foundations is required if the load from the structures would lead to excessive settlements. Conventionally piles are added for load bearing capacity and settlement reduction requirements. Most conventional projects rely on assuming that piles were designed to carry the entire load of the structures. In this case, a large number of piles were utilized. However, in a study [1], they discussed the idea of using a few piles to reduce the settlement to a required level and to improve the state of stress in the raft. The piles are therefore termed as “settlement reducers.” As the name indicates, the main purpose of introducing settlement reducer piles is to satisfy the settlement requirements. As mentioned in [2], to reduce settlements to a permissible value, usually a small number of piles are sufficient, and further addition of piles may result in only marginal further reductions in settlements. Conventionally, piles were designed to take all external loads [3], and there was a margin for the pile to reach either its geotechnical bearing capacity or its structural collapse load.In [4], it is considered that for competent design of rafts with settlement-reducing piles, 80% of the pile capacity mobilization can be assumed under working load. In this regard, a lower factor of safety can be applied to the geotechnical capacity of the piles, and the bearing capacity of the raft is adequate on its own. In usual cases, piles are cast monolithically with the rafts, called “connected settlement reducer piles.” Since few numbers of piles are adequate to reduce the settlement to permissible value [1] and however if these piles are connected to the raft, concentration of high axial stresses in the pile heads may develop and their load-carrying capacity will be governed by their structural capacities rather than by geotechnical capacity [5]. They often lead to significant straining actions at the pile head-raft connection.In a study conducted [5], it was identified the problems associated with structurally connected settlement reducing piles and clearly discussed alternative solutions, which is the adoption of nonconnected settlement reducer piles, known as nonconnected piled raft foundation (NC), in which the raft-pile connection is detached. In the case of a disconnected piled foundation system, there is no structural connection between the piles and the raft and the gap is usually filled with granular material (cushion). Some studies have been devoted to the effect cushion on the disconnected piled raft performance [6–9]. In [9], they investigated whether proper grading of the load transform platform can advance the axial stiffness of a disconnected piled raft foundation system.Several authors have recently presented results of numerical simulations [5, 6, 10–12] or 1g model tests concerning rafts on disconnected settlement-reducing piles [7] and multi−gcentrifuge tests [8, 9].Practically, recently in some projects, the piles are detached from the raft by a cushion layer, which creates a more uniform pressure distribution on the raft bottom and reduces constraint reactions in the soil, foundation, and superstructure. Among these, the foundation systems of the Rion Antirion Bridge in Greece [13] and the recently completed super long-span Izmit Bay bridge [14] consist of vertical inclusions (disconnected piles) to improve the shear resistance of the foundation soils and to minimize the hazards related to differential settlements, plus a gravel bed to limit the shear forces and moments transmitted between the superstructure and the foundation soils.In [7], they evaluated the effectiveness of nonconnected piles as a settlement reducer by subjecting small-scale nonconnected piled raft foundations to vertical loading. These piles were used as soil reinforcing elements instead of as structural elements. The result indicated that nonconnected piles were effective in reducing settlement and bending moments at the pile head.The load transfer mechanisms of a disconnected piled raft greatly differ from those of a raft with piles connected [15] because of the compressibility of the layer, which permits a relative raft-pile displacement. A relative downward displacement of the soil, with respect to the upper part of the pile, takes place and gives rise to negative skin friction [8]. Studies [7, 16] suggest that such a mechanism is influenced by the thickness and stiffness of the cushion layer and by the stiffness of the soil. A study [7] stated that a disconnected pile serves mainly as a reinforcement of the subsoil, enhancing the stiffness of an unpiled raft.A study conducted [17] experimentally studied the effectiveness of using both connected and nonconnected short piles to the raft on the behavior of an eccentrically loaded raft. The test indicates that the use of short piles near to the raft edges not only significantly enhances the raft bearing pressures but also leads to a reduction in raft settlements and tilts leading to an economical design of the raft.Many studies concerning the analysis of nonconnected piled raft foundations have been proposed by various researchers [5, 8, 17, 18]. However, most of them do not incorporate the effect of cushion and load sharing and carrying mechanisms of piles in a nonconnected piled raft foundation. In this research, the effects of variation in cushion thickness, pile number, raft thickness, cushion and subsoil stiffness on load sharing and settlement efficiency of nonconnected piles are studied in detail.


## 2. Load Transfer Mechanism

Nonconnected piles are partially loaded from the raft, which is an arching effect, and partially through the skin friction (negative) at the top part (Figure1). A study [19] stated that “arching” is the transfer of stress from a yielding part of a soil mass to adjoining less-yielding or restrained parts of the mass. Previous researchers [7, 12, 16, 20] have shown the development of skin friction distribution along the pile shaft. The maximum axial force (Nmax) found some depth below the pile head, as a consequence of the negative skin friction along the upper portion of the piles, whereas in connected piled raft foundation (PRF) it is found at the pile head.Figure 1
Negative skin friction in nonconnected piled raft foundation (NC).A study [7] investigated that negative skin friction governed the load transfer on the upper part of the piles, while positive skin friction governed the load transfer on the lower part of the piles. Similarly, it was [21] reported that the load carrying capacity of piles and rafts is complex due to interactions between the piles, the subsoil, and the raft (Figure 2). However, load sharing in a disconnected piled raft is even more complex due to the deformable cushion layer between the piles and the raft [12].Figure 2
Interactions between soil and structural members adopted from [12]. (a) PR. (b) DPR. (R = raft, P = pile, and S = soil).
(a)(b)Reference [7] reported that disconnected piles carry a load of 30–35% of the applied load. This is due to the detachment of piles from the raft; the piles did not receive the load directly. This amount of load sharing is similar to the 32% reported by [22] for design conditions that lead to an 80% mobilization of pile capacity.In [23], they quantitatively described the pile-subsoil relative displacement by introducing a normalized ratio as follows:(1)ξ=Ws−WpB∗100,where Ws, Wp, and B are subsoil, pile settlement, and the raft breadth, respectively. At the top parts of the piles, subsoil settlement in the nonconnected piled raft is larger than settlement of piles. The greater values of ξ means the larger relative pile-soil displacement and larger negative skin friction (NSF).


## 3. Finite Element Modelling

The finite element method has become popular in recent years in geotechnical engineering. A variety of finite element computer programs have been developed with a number of useful features and to suit different requirements [24]. The analysis method in this study refers to three-dimensional finite element methods (FEM) via PLAXIS 3D 2020 [25] connect edition software. Figure 3 shows finite element models for raft and nonconnected piles.Figure 3
Discretized volume raft and piles.


### 3.1. Pile Modelling Options in PLAXIS 3D

Two pile modelling alternatives were extensively compared by previous researchers [12, 26] using either volume element (3D) or embedded pile (EP) elements (1-D element). Figures 4(a) and 4(b) represent embedded and volume piles, respectively. In [27], they reported that 3D finite element analyses allow accounting geometrical irregularities and material nonlinearities. However, the large number of piles leads to computationally demanding models that may be beyond the capabilities of the code or simply take too long time to analyze [26].Figure 4
Embedded pile (a) and (b) volume pile.
(a)(b)The benefit of embedded piles is that piles can cross finite elements in any direction and do not influence the finite element mesh, so significant computational time can be saved [12, 25, 26, 28–30].Fully solid (volume element) approaches seem to be more realistic, as they do not introduce any specific assumptions on the structural behavior of the piles.The piled-raft foundation system is a 3D complex problem, which needs a 3D finite element method to be solved [26]. Consequently, 3D volume elements are used to model all structural elements in this research. This pile-soil interaction occurs at the true pile perimeter.


### 3.2. Mesh and Boundary Condition

From the edge of the raft, lateral soil domain boundaries of the model were placed at a distance of two and a half times the width of raft (2.5B) and restrained against horizontal translation (i.e., horizontal displacement) but with vertical translation (i.e., vertical displacement) of soil being allowed.As [31] investigated, the stress isobar in a raft foundation was formed up to twice the width of the raft (2∗Br), and in a pile raft, it was formed at two-third of the pile length (2/3∗Lp). Thus, the bottom soil boundary was at a vertical distance of twice the width of the raft plus two-third of the pile length (2∗Br+2/3∗Lp) and was restricted from both horizontal and vertical translations. Similarly, for mesh sensitivity analysis [31], the fine mesh was defined globally for the entire soil domain and the refined mesh was chosen in the vicinity of the structural elements.


### 3.3. Constitutive Modelling

The cushion layer and subsoil material are modelled by using hardened soil model material in a drained condition. Material properties used in this study were adopted from [26]. In this research, the finite element model in the PLAXIS 3D has been validated by comparing it with the reported results of [8]. Rafts of 7.5 m × 7.5 m size and 9 piles of 0.5 m in diameter with a length of 20 m were used in the study. The piles were spaced at five times of pile diameter (S=5Dp), and a distributed load of 1.22 MPa was uniformly applied on the foundation. The material properties of the soil, raft, and piles and their geometric configuration are given in Tables 1–3. The finite element model for validation is shown in Figure 5.Table 1
Raft and pile properties used in the validation [8].
MaterialYoung’s modulusE (MPa)Unit wt.γ (kN/m3)Poisson’s ratioνRaft30,000240.15Pile30,000240.15Table 2
Geometric configurations used in the validation [8].
GeometryModel dimension (mm)Prototype dimension (m)Raft width (B)1157.5Pile length (Lp)29219Pile diameter (Dp)80.5Pile spacing (S)38.52.5Thickness of cushion layer (hc)15.41Table 3
Cushion and subsoil properties used in the validation.
ParameterMaterial typeCushion layerFoundation soilC′ (kPa)00φ′ (0)3535γdry (kN/m3)16.6715.3E50ref (MPa)2015Eoedref (MPa)2015Eurref (MPa)6045m0.550.5Vur0.20.2Ψ (0)55KoNC1 − sinφ′1 − sinφ′OCR11Figure 5
Staged construction of FEM in PLAXIS 3D.Figures6 and 7 indicate that the finite element results are in rationally good agreement with those reported for nonconnected and raft foundations. As a study [31] investigated that for continuing the accuracy of the results, similar modelling steps have been followed to model the different foundation systems of the present study.Figure 6
Load settlement curve for validation of the nonconnected piled raft (9NC).Figure 7
Load settlement curve for validation of unpiled raft (UR).


## 3.1. Pile Modelling Options in PLAXIS 3D

Two pile modelling alternatives were extensively compared by previous researchers [12, 26] using either volume element (3D) or embedded pile (EP) elements (1-D element). Figures 4(a) and 4(b) represent embedded and volume piles, respectively. In [27], they reported that 3D finite element analyses allow accounting geometrical irregularities and material nonlinearities. However, the large number of piles leads to computationally demanding models that may be beyond the capabilities of the code or simply take too long time to analyze [26].Figure 4
Embedded pile (a) and (b) volume pile.
(a)(b)The benefit of embedded piles is that piles can cross finite elements in any direction and do not influence the finite element mesh, so significant computational time can be saved [12, 25, 26, 28–30].Fully solid (volume element) approaches seem to be more realistic, as they do not introduce any specific assumptions on the structural behavior of the piles.The piled-raft foundation system is a 3D complex problem, which needs a 3D finite element method to be solved [26]. Consequently, 3D volume elements are used to model all structural elements in this research. This pile-soil interaction occurs at the true pile perimeter.


## 3.2. Mesh and Boundary Condition

From the edge of the raft, lateral soil domain boundaries of the model were placed at a distance of two and a half times the width of raft (2.5B) and restrained against horizontal translation (i.e., horizontal displacement) but with vertical translation (i.e., vertical displacement) of soil being allowed.As [31] investigated, the stress isobar in a raft foundation was formed up to twice the width of the raft (2∗Br), and in a pile raft, it was formed at two-third of the pile length (2/3∗Lp). Thus, the bottom soil boundary was at a vertical distance of twice the width of the raft plus two-third of the pile length (2∗Br+2/3∗Lp) and was restricted from both horizontal and vertical translations. Similarly, for mesh sensitivity analysis [31], the fine mesh was defined globally for the entire soil domain and the refined mesh was chosen in the vicinity of the structural elements.


## 3.3. Constitutive Modelling

The cushion layer and subsoil material are modelled by using hardened soil model material in a drained condition. Material properties used in this study were adopted from [26]. In this research, the finite element model in the PLAXIS 3D has been validated by comparing it with the reported results of [8]. Rafts of 7.5 m × 7.5 m size and 9 piles of 0.5 m in diameter with a length of 20 m were used in the study. The piles were spaced at five times of pile diameter (S=5Dp), and a distributed load of 1.22 MPa was uniformly applied on the foundation. The material properties of the soil, raft, and piles and their geometric configuration are given in Tables 1–3. The finite element model for validation is shown in Figure 5.Table 1
Raft and pile properties used in the validation [8].
MaterialYoung’s modulusE (MPa)Unit wt.γ (kN/m3)Poisson’s ratioνRaft30,000240.15Pile30,000240.15Table 2
Geometric configurations used in the validation [8].
GeometryModel dimension (mm)Prototype dimension (m)Raft width (B)1157.5Pile length (Lp)29219Pile diameter (Dp)80.5Pile spacing (S)38.52.5Thickness of cushion layer (hc)15.41Table 3
Cushion and subsoil properties used in the validation.
ParameterMaterial typeCushion layerFoundation soilC′ (kPa)00φ′ (0)3535γdry (kN/m3)16.6715.3E50ref (MPa)2015Eoedref (MPa)2015Eurref (MPa)6045m0.550.5Vur0.20.2Ψ (0)55KoNC1 − sinφ′1 − sinφ′OCR11Figure 5
Staged construction of FEM in PLAXIS 3D.Figures6 and 7 indicate that the finite element results are in rationally good agreement with those reported for nonconnected and raft foundations. As a study [31] investigated that for continuing the accuracy of the results, similar modelling steps have been followed to model the different foundation systems of the present study.Figure 6
Load settlement curve for validation of the nonconnected piled raft (9NC).Figure 7
Load settlement curve for validation of unpiled raft (UR).


## 4. Parametric Study

The most important results discussed in this research are the load sharing ratio and the settlement reduction factor, also known as the settlement efficiency ratio. A study [31] defined the load-sharing ratio (αpr) as the ratio of the total load carried by the piles (Rpile) to the applied load (Rtotal) on the foundation. Rpile is the summation of the axial load carried by each pile at its head.(2)αpr=∑Rpile,iRtotal.In [8], they quantified the settlement performance of NC and PR foundations by means of the definition of the following settlement efficiency ratio:(3)η=wrUR−wrDPR/CPRwrUR,where wrUR and wrDPR/CPR are the settlements of the unpiled raft and disconnected/connected piled raft, respectively. Adding piles improves load-settlement behavior so that the values of wrDPR/CPR are always smaller than wrUR (i.e., 0≤η≤1). Therefore, larger values for the settlement efficiency ratio mean greater efficiency in reducing raft settlement [23].Figure8 shows the typical geometrical configuration for parametric study of unpiled raft (UR), nonconnected piled raft with 9 piles (9NC), and connected piled raft with 9 piles (9PR). Moreover, for nonconnected piled rafts with different cushion thickness, the following designation can be used. For example, 9NC1.0 refers to a nonconnected piled raft with a 9-number of piles and a cushion thickness (Hc) of 1 m. For the rest number of piles and cushion thickness, similar designations are used.Figure 8
Typical geometry for parametric study.Relevant material properties used in the research is summarized below in Tables4 and 5.Table 4
Material properties used for raft and piles.
MaterialYoung’s modulusE (MPa)Unit wt.γ (kN/m3)Poisson’s ratioνRaft30,000240.15Pile30,000240.15Table 5
Material properties used for cushion and subsoil layer stiffness variation [26].
ParameterUnitCushion (1)Cushion (2)Cushion (3)Cushion (4)Subsoil (1)Subsoil (2)Subsoil (3)γdrykN/m316.6718.521221515.516.5E50refMPa24406082131824EoedrefMPa24406082131824EurrefMPa72120180246395472m—0.550.60.650.650.50.530.55Vur—0.20.20.20.20.20.20.2φ′(°)32.5354243.5273334.5KoNC—0.4630.4260.3310.3120.50.4550.434Ψ (0)(°)2.551213.5034.5OCR—1111111PrefkPa100100100100100100100For parametric studies of cushion and subsoil stiffness variation, all material properties described in Table5 are used. However, for the rest of the analysis (Table 6), properties described as “cushion 3” and “subsoil 2” are used.Table 6
Summary of parametric study.
ParametersRaft dimensionsL∗W∗tSubsoil parameterE50ref (MPa)Cushion parameterPile group geometryThickness (m)E50ref (MPa)NpLpSp/DpPile length12∗12∗1182604, 971216205Pile spacing12∗12∗1182604, 9202, 3, 4, 5, 6, 7, 9Cushion thickness12∗12∗1180.511.522.53.0604, 5, 9205Subsoil and cushion stiffness12∗12∗1131824224, 40, 60, 829205Number of piles12∗12∗118260491625205Raft thickness12∗12∗trtr = 0.25–2.2518260975In the three-dimensional finite element model, boundaries of 60 m × 60 × 50 m are used. A uniformly distributed load of 500 kN/m2 will be used. The phases in staged construction are as follows:Initial phasePhase 1: installation of the pilesPhase 2: addition of cushion layer (only for nonconnected piled raft system)Phase 3: installation of the raftPhase 4: loading the pile raft system


### 4.1. Analysis and Discussion

This section discusses the effect of cushion thickness (Hc), cushion and subsoil stiffness, pile length (Lp), number of piles (Np) and raft thickness (tr) on settlement efficiency ratio (η), load sharing ratio (αpr), axial load distribution along pile length and differential settlement (ΔS/B). Therefore, the effect of these parameters on connected and nonconnected foundations are presented in the following sections.


### 4.2. Relative Raft-Soil Stiffness

The stiffness of the raft is the main factor that controls the performance of piled rafts; it influences the interactions of the raft with the piles and the soil [32]. The raft-soil relative stiffness (Krs) greatly influences the differential settlement of a piled raft foundation. As investigated by [33], the large raft stiffness, the small differential settlement of a piled raft, and vice versa. Therefore, raft thickness determination is very necessary. For rectangular rafts, [22] suggested the following equation to estimate the relative flexibility of raft:(4)Krs=5.57ErEs1−νS21−νr2BL0.5trL3,where Er and Es = Young’s modulus of the raft and the soil, respectively; νr and νS = Poisson’s ratio of the raft and the soil, respectively; B and L = breadth and length of the raft, respectively; and tr = thickness of the raft.According to [22], the raft is flexible when Krs ranges from 0.01 to 1.0. A study [33] recommended that rafts of Krs ranging between 5 and 10 are rigid. Furthermore, [34] suggested the ranges of fully flexible and fully rigid Krs to be 0.008 and 54, respectively. The effect of raft-soil relative stiffness shows a similar effect on both connected and nonconnected piled raft foundations, as shown in Figure 9. Figure 9(a) shows that the maximum settlement initially decreases with raft thickness (stiffness) and increases very slightly after reaching the limiting raft thickness (around Krs of 1.182 for 9NC1.0 and 3.988 for 9PR in this study), i.e., tr = 1.5 and tr = 1.25 m. This is because increasing the raft thickness beyond the limit (optimum thickness) gives excessive weight to the raft and leads to additional settlement [32]. As a comparison, normalized differential settlement (ΔS/B) and normalized maximum settlement (Smax/B) of nonconnected piled rafts are lower than connected piled rafts in the case of the large piled raft (Br/Lp > 1).Figure 9
Effect of raft-soil relative stiffness on (a) normalized differential settlement ΔS/Br (%) and (b) normalized maximum settlement Smax/Br (%).
(a)(b)However, as the raft thickness increases the normalized differential settlement (ΔS/Br (%)) of both nonconnected (NC) and connected piled raft (PR) significantly decreased (Figure 9(b)). But the rate of decrease in differential settlement seems to disappear at some specific Krs (around Krs of 3.988 in this study), i.e., tr = 1.5 m.Regarding this, it was recently [32] reported that stiffening the raft excessively may not guarantee the effective reduction of the differential settlement, especially when the piles are closely spaced. A similar finding has been also reported by [35, 36]. In [10], also studied that increasing the raft stiffness may be also useful in resisting the punching and shear. To sum up, increasing the raft stiffness is effective in primarily reducing the differential settlement.The raft thickness has a very small effect on the load carried by the nonconnected piles as shown in Figure10. However, for connected piles, as the raft-soil relative stiffness (Krs) increased (as raft thickness increase), the load sharing ratio of piles (αpr) decreased.Figure 10
Effect of raft-soil relative stiffness on a load sharing ratio of piles.Piles in a connected piled raft share a greater portion of the total load applied as compared to nonconnected piles due to the transfer of load from the raft to piles directly. However, in nonconnected cases, the insertion of the cushion layer changes the load transfer mechanisms of the foundation, as the cushion redistributes the load.Similar observations regarding the effect of raft thickness on the load sharing at small settlement levels are reported. A study [37] stated that raft thickness has a slight effect on the load sharing percentage of piled-raft foundations on sandy soil. Similarly, [33] pointed out that except for thin rafts, the load sharing between the raft and the piles is little affected by the raft-soil relative stiffness.


### 4.3. Effect of Cushion Thickness

To study the effect of variation in cushion thickness, a nonconnected piled raft (NC) was modelled with 4, 5, and 9 piles with a pile length of 20 m and a normalized spacing (S/D) of 5. As a comparison, a connected piled raft (PR) with 4, 5, and 9 piles has been modelled. For the NC case, the cushion thickness (Hc) of 0.5, 1.0, 1.5, 2.0, 2.5, and 3 m was varied for parametric studies. 4NC0.5 represents a nonconnected piled raft with 4 number of piles and a cushion thickness of 0.5 m, and a similar method for the remaining number of piles and cushion thicknesses. The effects of cushion thickness on the behavior of the NC foundation such as the settlement of the raft, pile axial force, and subsoil settlements in comparison with unpiled raft (UR) and PR foundation were analyzed.Figure11 shows variation in the subsoil settlement versus the cushion thickness. The result shows that the maximum settlement of the subsoil decreases with the increase of the cushion thickness. As compared to a raft without piles, a nonconnected piled raft with 3.0 m cushion thickness has a greater settlement reduction.Figure 11
Variation of normalized subsoil settlement with the cushion thickness.In Figure12, as the cushion thickness increases, the settlement efficiency ratio increases. However, the connected piled raft has a better performance. Increasing cushion thickness shows a marginal increase of settlement efficiency from 0.26 to 0.28. This result is in agreement with [9], who reported that the optimum thickness of the granular layer in the pile raft systems in sandy soil is suggested as 1.5 m.Figure 12
Comparison of settlement efficiency ratio of nonconnected piled raft (NC) of Np = 9 with cushion thickness (Hc) of 0.5 to 3.0 m and connected piled raft (PR) with Np = 9.Figure13 shows that the axial load at the pile head decreases as the thickness of the cushion increases. As the cushion thickness increases, the minimum force has been transferred to the piles. As [8, 16, 21] pointed out, for any cushion thickness (Hc) value, negative and positive skin friction, at z=zn the neutral plane is located, and maximum axial force is found at this point. As Figure Figure 13 shows, the position of the neutral plane tends to shift downwards as the thickness of the cushion (Hc) increases, while the maximum axial force (Nmax) in NC is always found to be lower than in connected piled rafts (PR). For PR cases, the maximum axial force (Nmax) formed in piles is higher than the piles in the NC case. This indicates that high stress concentration at the pile head is found when piles are connected to the raft.Figure 13
Variation of normalized axial force along the length of the corner pile with varying cushion. (a) Np = 4, (b) Np = 5, and (c) Np = 9.
(a)(b)(c)As described in Figure14, the cushion thickness increases, the load sharing percentage of piles increases up to Hc/Dp of 4. However, further increasing of the thickness is insignificant. It may be deduced that the load sharing between the cushion and the piles is affected by the thickness of the cushion.Figure 14
Variation of load sharing ratio of piles on cushion thickness.Beyond the state-of-the-art, practically many projects have been constructed with a cushion layer of 3 m depending on the site conditions. For example, the innovative foundation system of the Rion Antirion bridge [38] consists of three 90 m and one 80 m diameter piers and includes the use of up to 30 m long, 2 m diameter nonconnected steel piles to reinforce the weak foundation soils, designed with a 3 m cushion layer [13]. Similarly, ICEDA [39], which is a French project, was constructed with a 2.75 m cushion thickness under mat foundation for nuclear waste storage plants.ASIRI [15] recommends a cushion thickness of 0.4 to 0.8 m to design a raft, particularly intending to reduce bending moments. However, the thickness suggested by ASIRI [15] may be site-specific, particularly for raft bending moments. It did not address settlement efficiency, load sharing ratio of piles, and overall foundation performance. Similarly, [9, 40] reported that by increasing cushion thickness more than a certain value (about 1.5 m), the decreasing rate of raft settlement becomes very minimum and a further increase in cushion thickness will not be significant. Therefore, [11] concluded that economic analysis and technical conditions should be checked between thickening the cushion layer and strengthening the raft.


### 4.4. Cushion and Subsoil Stiffness Variation

The founding soil characteristics which are the cushion and subsoil stiffness slightly affect the load-bearing behavior of piled rafts [20]. Practice shows that the cushion layer inserted between the raft and piles can adjust the load-sharing ratios of piles and subsoil and enhance the strength of subsoil among piles [9, 15, 20]. To investigate the effect of cushion stiffness on the performance of the unconnected piled raft system, a wide range of values of stiffness was used. The length of piles was varied from 7 to 20 m, composing both small and large piled raft foundations. Material properties for cushion and subsoil stiffness variation are summarized in Table 7.(i)
Figure15(c) shows that increasing subsoil and cushion or load transfer platform (LTP) stiffness increases the settlement efficiency ratio (η). For subsoil stiffness (E50ref) of 13 MPa, increasing the cushion stiffness (E50ref) from 24 MPa to 82 MPa increases η value from 0.28 to 0.365. Similarly, for a cushion stiffness of 60 MPa, increasing subsoil stiffness from 13 MPa to 24 MPa increases the η by 77.4%.(ii)
With high cushion stiffness (E50ref = 82 MPa), the raft settlement of a connected piled raft has no significant difference with that of a nonconnected piled raft. For instance, for subsoil stiffness of 24 MPa and a 20 m pile length, the settlement efficiency (η) for the connected and nonconnected piled rafts is 0.648 and 0.635, respectively.(iii)
For a pile length of 14 m, a similar effect is pronounced (Figure15(b)). In a study [41], they grouped piled raft foundations into two broad categories of small (raft breadth to the pile length ratio, B/Lp < 1) and large piled rafts (B/Lp > 1). A square raft of width, B = 12 m was considered here. For large piled rafts, increasing the stiffness of the cushion decreases the settlement of nonconnected piled rafts (NC) even more than that of connected piled rafts (PR). Figure 15(a) indicates that the settlements of nonconnected piled rafts with B/Lp = 1.7 are lesser than the conforming cases for a connected piled raft. A similar result has been reported by [9].Table 7
Summary of parameters for subsoil and cushion stiffness effect.
Raft dimension (m)Raft thickness (m)Number of pilesCushion stiffness (E50ref) kN/m2Subsoil stiffness (E50ref) kN/m2Pile length (m)Output (response)12 × 121.5924,00040,00060,00082,00013,00018,00024,00071420Settlement efficiency ratioAxial force distributionLoad sharing ratioFigure 15
Effect of subsoil and cushion stiffness on settlement efficiency ratio (η) for 9NC1.0 (a) Lp = 7 m. (b) Lp = 14 m. (c) Lp = 20 m.
(a)(b)(c)In reference to Figure16(a)–16(d), cushion stiffness has a uniform effect on the pile response and causes a considerable increase in the pile load. Similarly, increasing the pile length from 7 to 20 m increases the pile load.Figure 16
Effect of cushion stiffness on typical corner pile axial force for subsoil E50ref = 18 MPa. (a) Lp = 7 m, (b) Lp = 14 m, and (c) Lp = 20 m. (d) The effect of subsoil and cushion stiffness on a load sharing ratio of piles (9NC1.0 and Lp = 20).
(a)(b)(c)The effect of changing the stiffness of the subsoil and cushion on the load sharing ratio of the piles is shown in Figure16(d). The load carried by the piles increases significantly with the increase in cushion stiffness. For subsoil stiffness of E50ref = 13 MPa, increasing cushion stiffness, E50ref from 24 MPa to 82 MPa increases the load sharing percentage of piles by 75%.


### 4.5. Effect of Pile Number

To analyze the influence of pile number, simulations were performed with 4, 9, 16, and 25 piles having a length of 20 m, anS/Dp of 5, and a square raft width of 12 m. For nonconnected piled raft foundations, a cushion thickness of 1.5 m was considered. Material properties of the subsoil and cushion are tabulated.In Table5, properties described as “cushion 3” and “subsoil 2” were used. Figure 17 shows a typical model configuration for parametric studies of pile number effects.Figure 17
Pile number configuration.Figure18 shows raft maximum settlement versus the number of piles for connected and nonconnected piled raft systems. The raft’s maximum settlement was reduced as the number of piles increased. As predicted, assessment of the following cases in Figure 18 shows a decrease in the rate of the raft settlement, which causes a minor difference in the settlement.Figure 18
Comparison of a normalized maximum settlement of raft for NC and PR with several piles (Lp = 20 m andS/Dp = 5).As shown in Figure19, increasing pile numbers from 4 to 9, 9 to 16, and 16 to 25 results in 14%, 15%, and 12% settlement reductions in the disconnected case. Similarly, for connected piled rafts, 22%, 32%, and 25%, respectively.Figure 19
Effect of pile number on settlement efficiency ratio for NC09/PR09, Lp = 20 m, andS/Dp = 5.The variation of the distribution of the axial force for 4, 9, 16, and 25 piles is shown in Figure20. It can be seen that the axial force along the pile decreased noticeably with increasing the pile number. For typical corner pile axial force distribution (Figure 20), as the pile number increases, the down-drag force decreases, and the lesser load is transferred to the piles.Figure 20
Number of piles effect on axial force distribution of corner piles for both connected and nonconnected piled raft (Lp = 20 m andS/Dp = 5).The connected piled raft with 4 piles of 20 m length takes about 58% more loads than the loads in the nonconnected piled raft, as shown in Figure21 and tabulated in Table 8. By increasing the number of piles from 16 to 25, the load sharing ratio of connected piled rafts increases by about 15%, while this value is more significant, nearly 32% for nonconnected piled rafts, similar to the values reported by [22]. As reported by [23], however, because the load sharing ratio for the nonconnected piled raft is much lower than that for the connected piled raft, it is not favorable to use a large number of them, and the limit of Np = 16 is suitable for both forms.Figure 21
Number of piles effect on a load sharing ratio of pile.Table 8
Tabulated value of number of piles effect on load sharing of foundation.
NpLoad sharing ratio of piles (%)NonconnectedConnected48.7520.87511.1625.55917.8741.241626.8164.052535.5473.58


## 4.1. Analysis and Discussion

This section discusses the effect of cushion thickness (Hc), cushion and subsoil stiffness, pile length (Lp), number of piles (Np) and raft thickness (tr) on settlement efficiency ratio (η), load sharing ratio (αpr), axial load distribution along pile length and differential settlement (ΔS/B). Therefore, the effect of these parameters on connected and nonconnected foundations are presented in the following sections.


## 4.2. Relative Raft-Soil Stiffness

The stiffness of the raft is the main factor that controls the performance of piled rafts; it influences the interactions of the raft with the piles and the soil [32]. The raft-soil relative stiffness (Krs) greatly influences the differential settlement of a piled raft foundation. As investigated by [33], the large raft stiffness, the small differential settlement of a piled raft, and vice versa. Therefore, raft thickness determination is very necessary. For rectangular rafts, [22] suggested the following equation to estimate the relative flexibility of raft:(4)Krs=5.57ErEs1−νS21−νr2BL0.5trL3,where Er and Es = Young’s modulus of the raft and the soil, respectively; νr and νS = Poisson’s ratio of the raft and the soil, respectively; B and L = breadth and length of the raft, respectively; and tr = thickness of the raft.According to [22], the raft is flexible when Krs ranges from 0.01 to 1.0. A study [33] recommended that rafts of Krs ranging between 5 and 10 are rigid. Furthermore, [34] suggested the ranges of fully flexible and fully rigid Krs to be 0.008 and 54, respectively. The effect of raft-soil relative stiffness shows a similar effect on both connected and nonconnected piled raft foundations, as shown in Figure 9. Figure 9(a) shows that the maximum settlement initially decreases with raft thickness (stiffness) and increases very slightly after reaching the limiting raft thickness (around Krs of 1.182 for 9NC1.0 and 3.988 for 9PR in this study), i.e., tr = 1.5 and tr = 1.25 m. This is because increasing the raft thickness beyond the limit (optimum thickness) gives excessive weight to the raft and leads to additional settlement [32]. As a comparison, normalized differential settlement (ΔS/B) and normalized maximum settlement (Smax/B) of nonconnected piled rafts are lower than connected piled rafts in the case of the large piled raft (Br/Lp > 1).Figure 9
Effect of raft-soil relative stiffness on (a) normalized differential settlement ΔS/Br (%) and (b) normalized maximum settlement Smax/Br (%).
(a)(b)However, as the raft thickness increases the normalized differential settlement (ΔS/Br (%)) of both nonconnected (NC) and connected piled raft (PR) significantly decreased (Figure 9(b)). But the rate of decrease in differential settlement seems to disappear at some specific Krs (around Krs of 3.988 in this study), i.e., tr = 1.5 m.Regarding this, it was recently [32] reported that stiffening the raft excessively may not guarantee the effective reduction of the differential settlement, especially when the piles are closely spaced. A similar finding has been also reported by [35, 36]. In [10], also studied that increasing the raft stiffness may be also useful in resisting the punching and shear. To sum up, increasing the raft stiffness is effective in primarily reducing the differential settlement.The raft thickness has a very small effect on the load carried by the nonconnected piles as shown in Figure10. However, for connected piles, as the raft-soil relative stiffness (Krs) increased (as raft thickness increase), the load sharing ratio of piles (αpr) decreased.Figure 10
Effect of raft-soil relative stiffness on a load sharing ratio of piles.Piles in a connected piled raft share a greater portion of the total load applied as compared to nonconnected piles due to the transfer of load from the raft to piles directly. However, in nonconnected cases, the insertion of the cushion layer changes the load transfer mechanisms of the foundation, as the cushion redistributes the load.Similar observations regarding the effect of raft thickness on the load sharing at small settlement levels are reported. A study [37] stated that raft thickness has a slight effect on the load sharing percentage of piled-raft foundations on sandy soil. Similarly, [33] pointed out that except for thin rafts, the load sharing between the raft and the piles is little affected by the raft-soil relative stiffness.


## 4.3. Effect of Cushion Thickness

To study the effect of variation in cushion thickness, a nonconnected piled raft (NC) was modelled with 4, 5, and 9 piles with a pile length of 20 m and a normalized spacing (S/D) of 5. As a comparison, a connected piled raft (PR) with 4, 5, and 9 piles has been modelled. For the NC case, the cushion thickness (Hc) of 0.5, 1.0, 1.5, 2.0, 2.5, and 3 m was varied for parametric studies. 4NC0.5 represents a nonconnected piled raft with 4 number of piles and a cushion thickness of 0.5 m, and a similar method for the remaining number of piles and cushion thicknesses. The effects of cushion thickness on the behavior of the NC foundation such as the settlement of the raft, pile axial force, and subsoil settlements in comparison with unpiled raft (UR) and PR foundation were analyzed.Figure11 shows variation in the subsoil settlement versus the cushion thickness. The result shows that the maximum settlement of the subsoil decreases with the increase of the cushion thickness. As compared to a raft without piles, a nonconnected piled raft with 3.0 m cushion thickness has a greater settlement reduction.Figure 11
Variation of normalized subsoil settlement with the cushion thickness.In Figure12, as the cushion thickness increases, the settlement efficiency ratio increases. However, the connected piled raft has a better performance. Increasing cushion thickness shows a marginal increase of settlement efficiency from 0.26 to 0.28. This result is in agreement with [9], who reported that the optimum thickness of the granular layer in the pile raft systems in sandy soil is suggested as 1.5 m.Figure 12
Comparison of settlement efficiency ratio of nonconnected piled raft (NC) of Np = 9 with cushion thickness (Hc) of 0.5 to 3.0 m and connected piled raft (PR) with Np = 9.Figure13 shows that the axial load at the pile head decreases as the thickness of the cushion increases. As the cushion thickness increases, the minimum force has been transferred to the piles. As [8, 16, 21] pointed out, for any cushion thickness (Hc) value, negative and positive skin friction, at z=zn the neutral plane is located, and maximum axial force is found at this point. As Figure Figure 13 shows, the position of the neutral plane tends to shift downwards as the thickness of the cushion (Hc) increases, while the maximum axial force (Nmax) in NC is always found to be lower than in connected piled rafts (PR). For PR cases, the maximum axial force (Nmax) formed in piles is higher than the piles in the NC case. This indicates that high stress concentration at the pile head is found when piles are connected to the raft.Figure 13
Variation of normalized axial force along the length of the corner pile with varying cushion. (a) Np = 4, (b) Np = 5, and (c) Np = 9.
(a)(b)(c)As described in Figure14, the cushion thickness increases, the load sharing percentage of piles increases up to Hc/Dp of 4. However, further increasing of the thickness is insignificant. It may be deduced that the load sharing between the cushion and the piles is affected by the thickness of the cushion.Figure 14
Variation of load sharing ratio of piles on cushion thickness.Beyond the state-of-the-art, practically many projects have been constructed with a cushion layer of 3 m depending on the site conditions. For example, the innovative foundation system of the Rion Antirion bridge [38] consists of three 90 m and one 80 m diameter piers and includes the use of up to 30 m long, 2 m diameter nonconnected steel piles to reinforce the weak foundation soils, designed with a 3 m cushion layer [13]. Similarly, ICEDA [39], which is a French project, was constructed with a 2.75 m cushion thickness under mat foundation for nuclear waste storage plants.ASIRI [15] recommends a cushion thickness of 0.4 to 0.8 m to design a raft, particularly intending to reduce bending moments. However, the thickness suggested by ASIRI [15] may be site-specific, particularly for raft bending moments. It did not address settlement efficiency, load sharing ratio of piles, and overall foundation performance. Similarly, [9, 40] reported that by increasing cushion thickness more than a certain value (about 1.5 m), the decreasing rate of raft settlement becomes very minimum and a further increase in cushion thickness will not be significant. Therefore, [11] concluded that economic analysis and technical conditions should be checked between thickening the cushion layer and strengthening the raft.


## 4.4. Cushion and Subsoil Stiffness Variation

The founding soil characteristics which are the cushion and subsoil stiffness slightly affect the load-bearing behavior of piled rafts [20]. Practice shows that the cushion layer inserted between the raft and piles can adjust the load-sharing ratios of piles and subsoil and enhance the strength of subsoil among piles [9, 15, 20]. To investigate the effect of cushion stiffness on the performance of the unconnected piled raft system, a wide range of values of stiffness was used. The length of piles was varied from 7 to 20 m, composing both small and large piled raft foundations. Material properties for cushion and subsoil stiffness variation are summarized in Table 7.(i)
Figure15(c) shows that increasing subsoil and cushion or load transfer platform (LTP) stiffness increases the settlement efficiency ratio (η). For subsoil stiffness (E50ref) of 13 MPa, increasing the cushion stiffness (E50ref) from 24 MPa to 82 MPa increases η value from 0.28 to 0.365. Similarly, for a cushion stiffness of 60 MPa, increasing subsoil stiffness from 13 MPa to 24 MPa increases the η by 77.4%.(ii)
With high cushion stiffness (E50ref = 82 MPa), the raft settlement of a connected piled raft has no significant difference with that of a nonconnected piled raft. For instance, for subsoil stiffness of 24 MPa and a 20 m pile length, the settlement efficiency (η) for the connected and nonconnected piled rafts is 0.648 and 0.635, respectively.(iii)
For a pile length of 14 m, a similar effect is pronounced (Figure15(b)). In a study [41], they grouped piled raft foundations into two broad categories of small (raft breadth to the pile length ratio, B/Lp < 1) and large piled rafts (B/Lp > 1). A square raft of width, B = 12 m was considered here. For large piled rafts, increasing the stiffness of the cushion decreases the settlement of nonconnected piled rafts (NC) even more than that of connected piled rafts (PR). Figure 15(a) indicates that the settlements of nonconnected piled rafts with B/Lp = 1.7 are lesser than the conforming cases for a connected piled raft. A similar result has been reported by [9].Table 7
Summary of parameters for subsoil and cushion stiffness effect.
Raft dimension (m)Raft thickness (m)Number of pilesCushion stiffness (E50ref) kN/m2Subsoil stiffness (E50ref) kN/m2Pile length (m)Output (response)12 × 121.5924,00040,00060,00082,00013,00018,00024,00071420Settlement efficiency ratioAxial force distributionLoad sharing ratioFigure 15
Effect of subsoil and cushion stiffness on settlement efficiency ratio (η) for 9NC1.0 (a) Lp = 7 m. (b) Lp = 14 m. (c) Lp = 20 m.
(a)(b)(c)In reference to Figure16(a)–16(d), cushion stiffness has a uniform effect on the pile response and causes a considerable increase in the pile load. Similarly, increasing the pile length from 7 to 20 m increases the pile load.Figure 16
Effect of cushion stiffness on typical corner pile axial force for subsoil E50ref = 18 MPa. (a) Lp = 7 m, (b) Lp = 14 m, and (c) Lp = 20 m. (d) The effect of subsoil and cushion stiffness on a load sharing ratio of piles (9NC1.0 and Lp = 20).
(a)(b)(c)The effect of changing the stiffness of the subsoil and cushion on the load sharing ratio of the piles is shown in Figure16(d). The load carried by the piles increases significantly with the increase in cushion stiffness. For subsoil stiffness of E50ref = 13 MPa, increasing cushion stiffness, E50ref from 24 MPa to 82 MPa increases the load sharing percentage of piles by 75%.


## 4.5. Effect of Pile Number

To analyze the influence of pile number, simulations were performed with 4, 9, 16, and 25 piles having a length of 20 m, anS/Dp of 5, and a square raft width of 12 m. For nonconnected piled raft foundations, a cushion thickness of 1.5 m was considered. Material properties of the subsoil and cushion are tabulated.In Table5, properties described as “cushion 3” and “subsoil 2” were used. Figure 17 shows a typical model configuration for parametric studies of pile number effects.Figure 17
Pile number configuration.Figure18 shows raft maximum settlement versus the number of piles for connected and nonconnected piled raft systems. The raft’s maximum settlement was reduced as the number of piles increased. As predicted, assessment of the following cases in Figure 18 shows a decrease in the rate of the raft settlement, which causes a minor difference in the settlement.Figure 18
Comparison of a normalized maximum settlement of raft for NC and PR with several piles (Lp = 20 m andS/Dp = 5).As shown in Figure19, increasing pile numbers from 4 to 9, 9 to 16, and 16 to 25 results in 14%, 15%, and 12% settlement reductions in the disconnected case. Similarly, for connected piled rafts, 22%, 32%, and 25%, respectively.Figure 19
Effect of pile number on settlement efficiency ratio for NC09/PR09, Lp = 20 m, andS/Dp = 5.The variation of the distribution of the axial force for 4, 9, 16, and 25 piles is shown in Figure20. It can be seen that the axial force along the pile decreased noticeably with increasing the pile number. For typical corner pile axial force distribution (Figure 20), as the pile number increases, the down-drag force decreases, and the lesser load is transferred to the piles.Figure 20
Number of piles effect on axial force distribution of corner piles for both connected and nonconnected piled raft (Lp = 20 m andS/Dp = 5).The connected piled raft with 4 piles of 20 m length takes about 58% more loads than the loads in the nonconnected piled raft, as shown in Figure21 and tabulated in Table 8. By increasing the number of piles from 16 to 25, the load sharing ratio of connected piled rafts increases by about 15%, while this value is more significant, nearly 32% for nonconnected piled rafts, similar to the values reported by [22]. As reported by [23], however, because the load sharing ratio for the nonconnected piled raft is much lower than that for the connected piled raft, it is not favorable to use a large number of them, and the limit of Np = 16 is suitable for both forms.Figure 21
Number of piles effect on a load sharing ratio of pile.Table 8
Tabulated value of number of piles effect on load sharing of foundation.
NpLoad sharing ratio of piles (%)NonconnectedConnected48.7520.87511.1625.55917.8741.241626.8164.052535.5473.58


## 5. Summary and Conclusions

Numerical modelling was used to evaluate the effectiveness of nonconnected settlement reducer piles under the raft foundation (NC) in terms of settlement efficiency ratio, load sharing ratio of piles, and axial load distribution along the pile length. This research also compares the performance of connected settlement reducer piles (PR) with nonconnected piles. As compared to a raft without piles (unpiled raft), a nonconnected piled raft shows greater settlement efficiency. It reduces the settlement by up to 40% for 16 nonconnected piles. The following conclusions can be drawn for conducted parametric studies:(i)
Nonconnected piled raft foundation system is likely to be governed by the interposed layer stiffness and thickness.(ii)
In the PR, the maximum load occurred at the top of the pile, and the axial load decreased with depth. It is also confirmed that the effect of negative skin friction of the NC, which changes the pile axial load distribution form.(iii)
By increasing the cushion stiffness, the ratio of the sum of pile loads to the total load increases. Also, parametric studies show that the lower the cushion stiffness, the deeper the location of the neutral plane.(iv)
For small piled raft (Br/Lp < 1), nonconnected piled rafts show less stiffness than connected piled rafts, and the soil is highly stressed and shows greater raft settlement. However, in the case of large piled rafts (Br/Lp > 1), nonconnected piled rafts show greater settlement efficiency.(v)
As the stiffness of the cushion layer increases from 24 MPa to 82 MPa, the total load carried by all piles decreases by 49%. Cushion stiffness was realized to be more substantial for a nonconnected piled raft with shorter piles than one with longer piles.(vi)
The effect of raft-soil relative stiffness shows a similar effect on both connected and nonconnected piled raft foundations. It shows that the maximum settlement initially decreases with an increase in raft-soil relative stiffness and increases very slightly after reaching the limiting raft thickness (aroundKrs of 1.182 for 9NC1.0 and 3.988 for 9PR in this study), i.e., tr = 1.5 and tr = 1.25 m.(vii)
However, as the raft thickness increased, the normalized differential settlement (ΔS/Br (%)) of both nonconnected (NC) and connected piled raft (PR) significantly decreased. But the rate of decrease in differential settlement seems to disappear at some specific Krs, around Krs of 3.988 (tr = 1.5 m) in this study. It can be concluded that increasing the raft thickness (stiffness) is effective, primarily, in reducing the differential settlement.(viii)
The raft-soil relative stiffness (raft thickness) has a small effect on the load carried by the nonconnected piles. However, for connected piles, as the raft-soil relative stiffness (Krs) increased (as raft thickness increased), the load sharing ratio of piles (αpr) decreased.


## 6. Recommendations

The research presented in this paper has confirmed the importance of the cushion layer between pile head and raft on the load settlement behavior of nonconnected settlement reducing piles under the raft foundation. The linear elastic (LE) and hardening soil (HS) models were employed for the analysis of the composite foundations and the simulation of the behavior of the cushion layer and subsoil. This research recommends the following aspects that require further examination:(1)
Further analysis may be carried out to investigate whether a combination of NC and PR proves to be economical. By providing a connected pile system at a critical location (critical location is to be identified through modelling or other appropriate method), the differential settlement can be reduced.(2)
Addition of reinforcement elements such as geogrid in the cushion layer of the nonconnected pile raft foundation may change the load transition mechanism and the portion of piles and raft from the total load.(3)
NC technique is more efficient when the foundation soil has high compressibility (soft soils). Also, it is suggested that the pile be embedded in a relatively hard layer to ensure its role as a settlement reducer.(4)
In this work, only static loading was considered. The effectiveness of the disconnection at the pile head and load transfer mechanism during dynamic loading needs further investigation. More research will be performed related to nonconnected piles, particularly on the subject of their use in seismic areas and for liquefaction mitigation.



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*Source: 4002545-2022-03-08.xml*