Next Article in Journal
Exploring the Barriers against Using Cryptocurrencies in Managing Construction Supply Chain Processes
Previous Article in Journal
Sneezing Aerosol Transport in an Indoor Farmers’ Market
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Buildings
Volume 12
Issue 3
10.3390/buildings12030356
buildings-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles thumb_up
...
Endorse textsms
...
Comment
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Numerical Analysis of Piled-Raft Foundations on Multi-Layer Soil Considering Settlement and Swelling

by
Muhammad Rehan Hakro
1,
Aneel Kumar
1,
Zaheer Almani
1,*,
Mujahid Ali
2,*,
Fahid Aslam
3,
Roman Fediuk
4,5,*,
Sergey Klyuev
6,7,*,
Alexander Klyuev
6 and
Linar Sabitov
7,8
1
Department of Civil Engineering, Mehran University of Engineering and Technology, Jamshoro 76062, Sindh, Pakistan
2
Department of Civil and Environmental Engineering, Universiti Teknologi PETRONAS, Bandar Seri Iskandar 31750, Perak, Malaysia
3
Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
4
Polytechnic Institute, Far Eastern Federal University, 690922 Vladivostok, Russia
5
Peter the Great St. Petersburg Polytechnic University, 195251 Saint Petersburg, Russia
6
Department of Theoretical Mechanics and Strength of Materials, Belgorod State Technological University Named after V.G. Shukhov, 308012 Belgorod, Russia
7
Kazan Federal University, 420008 Kazan, Russia
8
Kazan State Power Engineering University, 420066 Kazan, Russia
*
Authors to whom correspondence should be addressed.
Buildings 2022, 12(3), 356; https://doi.org/10.3390/buildings12030356
Submission received: 30 January 2022 / Revised: 28 February 2022 / Accepted: 2 March 2022 / Published: 15 March 2022
(This article belongs to the Section Construction Management, and Computers & Digitization)
Browse Figures
Versions Notes

Abstract

:
Numerical modelling can simulate the interaction between structural elements and the soil continuum in a piled-raft foundation. The present work utilized a two-dimensional finite element Plaxis 2D software to investigate the settlement, swelling, and structural behavior of foundations during the settlement and swelling of soil on various soil profiles under various load combinations and geometry conditions. The field and laboratory testing have been performed to determine the behavior soil parameters necessary for numerical modelling. The Mohr–Coulomb model is utilized to simulate the behavior of soil, as this model requires very few input parameters, which is important for the practical geotechnical behavior of soil. From this study, it was observed that, as soil is soft and has less stiffness, the un-piled raft was not sufficient to resists and higher loads and exceeds the limits of settlement. Piled raft increases the load carrying capacity of soil, and the lower soil layer has a higher stiffness where the pile rests, decreasing the significant settlement. Further, the effects of (L/d) and (s/d) of the pile and Krs on the settlement are also discussed, detailed numerically under different scenarios. The swelling of expansive soil was also simulated in Plaxis 2D with an application of positive volumetric strain. The above-mentioned parametric study was similarly implemented for the heaving of foundation on expansive soil.

1. Introduction

A piled raft foundation is a type of geotechnical foundation that consists of three components: the raft, the piles, and the soil domain [1,2,3]. The piles can be utilized to mitigate the raft foundations settlement [1,2]. Additionally, some studies indicated that the piles in the piled raft (Figure 1) may be used to support a portion of the superstructure’s load. Their relative stiffness determines the load distribution between the piles, raft, and earth. The piled raft can be categorized into small, piled rafts (Br < Lp) and large, piled rafts (Br > Lp) based on their dimensions [3,4]. The fundamental rationale for adding piles to a small, piled raft is to provide a sufficient safety factor against bearing failure [5]. However, piles are added to a huge, piled raft primarily to reduce settlement. One of the most significant aspects in foundation design is bearing capacity [6,7]. A change in the effective stress causes a change in the volume of saturated soils. When the effective stress rises, the volume of the soil decreases, and vice versa. Effective stress, on the other side, is insufficient to characterize the volume change of unsaturated soils [6,8].
Different definitions of effective stress have been proposed over the last six decades [8]. Compared to the approach based on net stress, the use of effective stress can guarantee smooth transitions between saturated and unsaturated soils that will be useful for the performed numerical studies.
An overview of the theoretical and practical evolution of piled raft foundations and their application to the mitigation of settling in high-rise buildings is provided by Katzenbach et al. [9]. Numerical modelling is used to investigate the behavior of a massive piled-raft foundation on clay soil. The results indicated that when the pile diameter and pile spacing was increased by 5 to 6 times, both the average settlement ratio and the differential settlement ratio reduced and increased, respectively [10].
The behavior of a structure under static or dynamic loading is influenced by the soil–structure interaction. It has an impact on the behavior of the soil as well as the response of the pile when loaded. The analysis is critical for improving structural safety under extreme loading circumstances by predicting more accurate structural behavior [11,12,13] The behavior of the soil–pile system is mostly nonlinear, which complicates the situation. The load is resisted in a laterally loaded pile by the soil–pile interaction effect, which is dependent on soil characteristics, pile material, pile diameter, loading type, and ground bed slope [14]. The settlement of a vertically loaded piled raft using a multiphase model that included soil–pile interaction was investigated by Bourgeois [15]. Modelling the behavior of the interface of unsaturated soils and structural elements such as piles requires a novel contact formulation.
The study of Oteuil [16] aimed to develop a framework for the axial and lateral capacity of bored piles analysis and design when only a few soil parameters are known. Numerical calculations support analytical methods in accordance with the relevant code of practice in the proposed methodology. The findings show that a resilient design can be obtained with only a few soil parameters: a conventional penetration test and a cone penetration test, as long as the analytical results are backed by numerical calculations.
Full-scale testing on piled foundations is time consuming and costly and may not be viable if long-term conditions need to be evaluated. In light of this, numerical modelling plays a critical role in determining if foundations are a viable alternative for inner city redevelopment [17,18,19,20]. A number of studies have been conducted on understanding the behavior of rafts and piled raft foundations [21,22,23,24,25,26,27], settlements of piled rafts [28,29,30,31,32,33,34], and bearing behavior [35,36,37,38,39]. However, this study focuses on the different geotechnical soil behavior such as multi-layer, vertical, and lateral swelling of expansive soils of foundations with different loading conditions and piles embedded in soil with varying soil stiffnesses. The Plaxis 2D FEM software (version V20, Bentley Systems, Exton, PA, United States) will be used in this study with the factors mentioned above to numerically determine the structural and geotechnical behavior of piled-raft foundation with settlement and swelling situations. The findings of this study are validated by measuring them to those of similar subgrade structures and geological conditions found in the literature.

2. Literature Review

2.1. Theoretical Background

Three main components comprise the piled raft foundation: the raft; the piles; and the foundation soil. The structure load is applied to the piled raft foundation, and the contact pressure balances the load between the raft and the soil and in part by the piles (QG). As a result, a coefficient αp is developed to describe the pile’s percentage of load using Equation (1) [35].
αp = QG/Q

2.2. Bearing Capacity of Un-Piled Raft

The ultimate load-bearing capacity of un-piled raft QUR is calculated from the theory of plasticity given by [40,41], as shown in Equation (2).
QUR = (cNc + qNq + 0.5BrγNγ)A
where γ is the soil’s unit weight, c is its cohesion, q is the vertical stress at the foundation level, and Nc, Nq, and N are the bearing capacity factors. Br is the width of footing. The final load-bearing capacity was equivalent to the load associated with w = 0.1. Br settlement was determined by Terzaghi [42,43]. However, various adjustment factors are required to account for the varying foundation parameters in this assessment.

2.3. Bearing Capacity of Single and Group Piles

The ultimate bearing capacity of a free-standing single pile QSP can be obtained using Equation (3).
QSP = fsAs + qbAb
where As and Ab denote the shaft and base areas of the pile, respectively, and fs and qb denote the average frictional resistance along the pile shaft and the end-bearing pressure.
For a group of piles, the ultimate capacity is computed by comparing each pile’s capacity to the total number of piles in the group, as defined by the formula as expressed in Equation (4) [44].
QGP = χnQSP
where n denotes the number of piles in the group, and χ is the group efficiency factor, which varies according to the pile type and soil type. Numerous experimental processes were conducted to determine the value of χ [45]. This group efficiency factor is often greater than unity in loose to medium-thick sand but is generally less than unity in clayey soils, and hence the influence of the efficiency factor on clayey soils is probably not very substantial. However, for design reasons, a value of unity is used for driven piles while lesser values are used for bored friction piles.
The piled raft foundation’s ultimate load-bearing capacity QPR can be calculated as the total of the capacity of the un-piled raft and pile group “expressed in terms of the capacities of individual piles”, as shown in Equation (5) [46,47].
QPR = QUR + QGP
QPR, QGP, and QUR denote the ultimate load-bearing capacity of a piled raft foundation, a single-pile-raft foundation, and an un-piled raft foundation, respectively [48,49]. As pile is installed, it may affect the soil properties and performance of the raft compared to an un-piled raft. Additionally, the piles that comprise a piled raft are influenced by the interaction of the heaps and the raft. As a result, a revision was proposed to Equation (6) by [46].
QPR = αURQUR + αGQGP
where αUR and αG are the coefficients determining the raft’s and pile group’s failure loads when combined in a piled raft. These variables contribute to the complexity of the load-bearing mechanism in a piled raft foundation. Because the load carrying capacity of a single pile and an un-piled raft are the only available parameters during the design stage, the prophecy of these coefficients is critical during the design, as shown in Equation (7), [44].
QUR = 2/3cNcscdcic + q(Nq − 1)sqdqiq
where QUR is the ultimate load-carrying capacity of a raft without any pile, c is the weighted cohesion of soil up to the depth equal to the width of footing. sc and sq are the bearing capacity correction factors for the shape; dc and dq are the bearing capacity correction factors for depth; and ic and iq are the bearing capacity correction factors for inclination [50].

3. Materials and Methods

The depth of drilling was 30 ft, and 2 bore holes were drilled, with the distance between the boreholes being 100 m. The number of bore holes was suggested from past studies and surveys for the study area. The drilling was conducted at Qasimabad, District Hyderabad, Sindh, Pakistan. The soil samples were collected as disturbed in nature. After the collection of soil samples, all the basic soil tests were conducted, such as soil classification, Atterberg limits, shear strength, and consolidation. This research endeavor employs a multi-phase methodology. The first phase involved determining the engineering characteristics of the soil to determine its strength parameters and then categorizing the soil accordingly. Figure 2 illustrates the laboratory work involved in Phase 1. In Phase 2, numerical analysis was used to assess how the footing behaved under various scenarios. Since the advent of Finite Elements methods, numerical methods have become the third pillar in understanding the responses of structures and the study of engineering problems, alongside theory and experiments.
Plaxis 2D was used to conduct numerical analyses. Plaxis establishes complete fixity at the geometry’s base and smooth conditions along its vertical sides, including the symmetric boundary. The vertical boundaries were adjusted to be free vertically and confined horizontally, while the bottom horizontal boundary was assumed to be fixed in both directions. Although the bearing layer extends to infinity, the soil domain beneath the pile is constrained for modelling purposes. The model was chosen following the problem specification. Given that the current study is attempting to determine the behavior of a piled raft with increasing complexity, the model must be computationally simple while still producing the desired results in a reasonable amount of time. The geometry of the model to be constructed in Plaxis 2D is illustrated in Figure 3.
The prime difference between those models is the efficacy with which the stress–strain behavior of the soil can be properly represented [51,52,53,54]. The material behavior of soil is simulated in this study utilizing the Mohr–Coulomb failure criterion and a linear elastic-perfectly plastic constitutive law. The Mohr–Coulomb model, which is commonly used in geotechnical modelling, has the benefit of requiring minimal input parameters, all of which can be obtained from normal soil tests [55,56,57,58,59,60]. The use of a more complicated constitutive model that takes nonlinear behavior into account will almost certainly necessitate the estimation of specific input parameters from atypical experiments. As a result, more input parameters will be examined, and their dependency will be less obvious. The numerical simulation analysis method used in this research drained conditions to determine the piled raft system [61,62,63,64,65].
The raft and piles are represented by an embedded beam element with a unique interface element. In this study, the raft and piles are simulated with a Linear Elastic Model. Due to their higher modulus of elasticity of foundation than the surrounding soil, these piles and rafts retain their elastic state. Between the raft and the pile heads, a rigid connection is contemplated. The following summarizes the analyses performed in this study.
Initial stage: Using the K0 technique, the soil domain is allowed to develop in situ stresses.
  • Stage 1: Installation of bored piles.
  • Stage 2: The raft is positioned on top of the piles. Additionally, interfaces are active. The model geometry is created in a structure phase, where the soil properties assign the model to each layer in the soil mode.
  • Stage 3: The vertical load is incrementally introduced. Finally, the full model is calculated.

4. Results and Discussion

4.1. Laboratory Testing

The results of geotechnical testing are given in Table 1 and Figure 4, with Atterberg’s limits, AASHTO, and USCS classifications for different depths. The cohesion 7 kPa to 25 kPa and angle of internal friction from 13° to 27°, as observed in Figure 5, depicts the changes of normal stress to shear stress. The modulus of the elasticity of the soil changed from 6000 to 9000 kN/m2, as mentioned in Table 2. The odometer tests performed and the stress and voids ratio variations are shown in Figure 5 and Figure 6, with the value of Cc as 0.0122, 0.0106, and 0.0197, respectively, at different depths also mentioned in Table 2.

4.2. Numerical Modelling

In Plaxis 2D, the raft modelled as a plate element and its properties are as given in the Table, while the pile properties are as in the embedded beam row. In this study, the effect of the number of piles, soil conditions, the end of pile at soil with varying stiffness, length of piles on settlement, and swelling of foundation were examined.
The value of Poisson’s ratio is normally taken as 0.5 and 0.3 for undrained and drained conditions, respectively, and the modulus of elasticity is from Table 3. The undrained shear strength is half of the unconfined compressive strength of soil [66,67,68]. The raft and pile structure properties are given in Table 4 and Table 5.

4.2.1. Numerical Modelling of Settlement

The length of a raft was 11 m and thickness 0.8 m, with the water level placed at near the ground level, representing field-like conditions such as having been obtained through boring. The effect of calculation-type plastic and consolidation is given in Figure 7, with an un-piled raft foundation. The uniformly distributed load (UDL) applied on the raft simulates the building load, with the value as 400 kN/m2. In the plastic calculation, the value of the settlement was higher compared to the consolidation settlement. From this, it can be concluded that the quick rate of loading of the settlement value was more than the slow rate of loading. The consolidation settlement should be considered for design purposes, such as for buildings designed for long periods. The effect of loading was recorded as being higher below the raft and decreased with depth.
The inclusion of piles beneath the raft not only improves the raft’s bearing capacity by assuming that the piles totally carry the load, but it also acts as “settlement reducers”, reducing the excessive settlement that would occur in the absence of piles in a piled raft foundation. Similar observations were recorded in their FEM-based study by [70], a numerical study on the effect of number of piles on the settlement of raft. However, this study focuses on soil and loading conditions [71,72,73,74]. The increase in the load increases the settlement, where with a load of 100 kN/m2 the settlement was recorded as 69.78 mm and with the pile-raft as 38.22 mm. The load of 200 kN/m2 and 400 kN/m2 produced 13.95 cm, 75.69 mm, and 36.34 and 24.06 cm without and with the pile raft. The settlement was higher at the center of raft; the maximum settlement value permitted for raft foundations on clay soil was 75–125 mm, while the maximum settlement value permitted for raft foundations on sand soil was around 50–75 mm. Each raft was loaded uniformly with a 400 kPa load. This amount of load was roughly similar to what a small to medium-sized building on the surface transfers to [75,76,77]. They applied load on the piled raft until 2% of the dimensions of the raft was increased in the numerical study by [28,78].
Thus, all these rafts with a load of 400 kN/m2 do not meet the settlement requirements for the raft footing. To address this issue, the next part of the study will consider piling installations as a more effective foundation choice for reducing settlement limits that exceed in this poor soil profile. Figure 8 and Figure 9 depict the settlements of the pile heads relative to the soil surface over time.
With a homogenous soil stratum with a pile-raft UDL of 200 kN/m2, the settlement was recorded as 74.59 mm and 33.55 mm with the end pile rested at the hard strata, with a modulus of elasticity as 40,000 kN/m2. In this study, the effect of raft thickness was also studied, and it was observed that, increasing the thickness of the raft from 0.8 m to 2 m, the settlement decreased from 75 mm to 40 mm. Similar effects were also noted by a numerical study, which stated that after a raft thickness of 2.5 m, there is little or no benefit in terms of the total and differential settlement decrease from increasing the raft thickness [79]. The inclusion of the raft over the piles minimizes the relative displacement of the piles and surrounding soils, resulting in a reduction in pile mobilization more in a piled raft system than a pile foundation, as in Figure 10, [44].
The influence of raft size on foundation settlement was investigated in this parametric study. Three different raft sizes were analyzed: 11 × 11 m2, 22 × 22 m2, and 33 × 33 m2, with a 1 m thickness. The margin of settlement as the raft size grows under the same applied load was the subject of this case study. The load applied to the raft was 200 kPa. The settlement was recorded as 75 mm and 130 mm on the raft sizes of 11 m and 30 m, and a similar pattern of settlement was recorded with the numerical modelling in ABAQUS by [80,81], but with load of 800 kPa.
The ratio of pile area (Ap) to raft area (Ar) was also studied, as shown in Figure 10, and from this it was observed that without significant effect of loading conditions, there has been much improvement in the reduction of the settlement of piled raft. Equation (8) calculated the raft-to-soil stiffness ratios for the raft models that were tested.
K rs = 4 3 π E r 1 − v s 2 E s B L t r L 3
where B and L signify the width and length of the raft, respectively, and tr signifies the thickness of the raft. Krs values between 0.01 and 10 and corresponds to rafts that are extremely flexible to extremely stiff [82].
The load-settlement curves for un-piled raft models with varying relative stiffnesses (Krs) was simulated in Plaxis 2D. An increase in raft-relative stiffness results in an increase in the load carrying capacity of an un-piled raft while decreasing settlement (e.g., at a 36 cm settlement, an increase in raft-relative stiffness from 0.47 to 5.65 results in an increase in raft load of 6.32%, while an increase in raft relative stiffness from 0.47 to 9.7 results in an increase in raft load of 9.12%). A square raft’s differential settlement is defined as the difference between the settlements at the raft’s center and mid-side positions [83]. The present tests reveal that the raft with Krs equal to 9.7 settled differentially. The raft with Krs = 9.7 is too rigid, according to the numerical and experimental study of [35,83,84,85].
The behavior of a combined piled raft owing to the application of vertical loads depends on the pile spacing, pile diameter (D), and raft thickness. When examining the response of any group pile or piled raft, the space between two piles becomes critical. The group interaction between the piles is a function of the pile spacing, and this interaction varies dramatically between closely spaced and widely spread pile groups.
For the behavior of a piled raft for vertical loads, a series of numerical studies are performed with different pile spacing, such as 3D, 4D, 5D, and 6D, where D is the diameter of piles, with different raft thickness, such as 1 m, 1.5 m, and 2 m, and with different pile diameters of 0.8 m, 1, and 2 m. The assumed geometry of the piled raft is illustrated in Table 6. As the spacing is increased, the settlement increased in the piled-raft foundation. The effect of pile spacing 3D, 4D, 5D, and 6D on the settlement mentioned in Table 6 had similar observations noted with the vertical loading of 300 kN/m2 in MIDAS GTS NX 3D in the study by Bandyopadhyay et al. [86].
In each parametric study, only one parameter was modified at a time, and all other parameters were set to their standard values. In this research, multi-layers on the settlement of piled-raft foundations were also studied, as shown in Figure 11, with the top layer having a low stiffness and the lower layer having a higher value of stiffness. This study compared the properties of two types of clay soils, namely soft clay and very stiff clay. As in the practice, the homogenous soil profile does not exist, so it is very important to give attention to this numerical study. Figure 12 shows the variation of load and settlement.
Figure 13 illustrates the variation in the settling of the rectangular pile with a pile depth for various values of the elastic moduli of the soil in the top and bottom layers while keeping the elastic moduli of the remaining layers constant. Figure 11 illustrates the variation in the settlement of the pile with pile depth for various values of the elastic moduli of the soil in the top layer under the floating base condition while keeping the elastic moduli of the remaining layers constant. The behavior of the pile in the layered soil strata for the floating pile condition seen in the figures can be explained by the fact that the variation in the elastic modulus of the soil between the top and bottom layers has a significant effect on the pile’s deformation.
For example, if elastic modulus values are between 2.5 MPa and 70 MPa, the normal range for cohesive soils and sands are used, and the top deformation of the pile decreases by about 23%, and the internal deformation decreases by about 28% in the earlier case, whereas in the latter case, the top deformation of the pile decreases by about 85%. Thus, by designing the bottom layer, it is possible to lessen the pile’s settlement; typically, sandy soils with SPT values of 50–80 can be used to achieve lower pile settlement values.
The preceding discussion implies that the bearing layer significantly influences the pile’s settlement, particularly for lower values of the bearing layer’s elastic modulus. It has been demonstrated in Figure 11 that the pile exhibits nearly rigid body motion, indicating that even if the pile is embedded in relatively strong soil layers (in terms of the elastic modulus) above the bearing layer, the pile’s settlement can be rather high. As appropriate care of the bearing area is almost unattainable, it is worth noting that the bearing layer should have a higher elastic modulus value than any other layer in the soil strata. A similar finding was also cited in the numerical modelling study of [79], and they also found that increasing the elastic modulus of the intermediate soil layers had a minor influence on the pile’s deformations. Additionally, the change in the pile’s internal deformation is minor. As a result, changes in the elastic moduli of the subsurface soil layers other than the top and bearing layers have had no effect on the pile’s settlement.
Es and a lower value of Krs relative stiffness decrease the settlement of piled raft. It is self-evident that as the stiffness of the bearing soil increases, so does the axial stress. For piles lying on rock-bearing soil, the axial stress along the pile varies according to the weight transferred to the pile tip, which is greater than the load given to the pile head. This may be a result of the bearing layer’s high stiffness, which prevents relative displacement in the lowest section of the pile, where positive skin friction is produced. The more embedment of piles in soil having a lower relative stiffness value increases the load carrying capacity, and thereby formulation of economic design, without increasing the thickness and length of the raft and piles individually, as evident from Figure 12. In this study, the effect L/D ratio on the settlement was also studied, and it was observed that the L/D ratio is effective in reducing the settlement of piled-raft foundation. This is consistent with the findings of Katzenbach et al. [9], who conducted theoretical assessments of rafts with varying numbers of piles to determine the effect on settlement [87].
Thus, the effect of the stiffness of the foundation soil is considered in this parametric analysis. Numerous numerical computations were run for reference foundation models with varying foundation soil elastic moduli to investigate the effect of foundation soil stiffness on load settlement behavior and axial stress along the piles.
The settlement of soft and very stiff clay was under a final load of 200 kPa. In general, it appears as though a tougher soil consistency results in less settlement and an increase in the thickness of the raft foundation. However, increasing the raft thickness had no discernible influence on the foundation’s settlement in stiff clay. The differential settlements of the piled-raft foundation system had varying raft thicknesses. The modelling demonstrates that increasing the thickness of the raft results in decreased settlement. For a foundation with a raft thickness of 1 m, the differential settlement was rather large. The settlement of the foundation was 75 mm in soft clay soil and 40 mm in very stiff clay soil.
The distribution of axial stress, which is a critical parameter in the design of piles from a capacity perspective, and the distribution of bending moment will influence the structural design provisions. It has been illustrated in Figure 13 that a change occurred in bending moment over the length of the raft, with the bending moment being greater with a piled raft foundation than with an un-piled raft, but with a significant reduction in settlement with a piled raft. A similar observation was also cited by Deb et al. [88].
Typically, the raft foundation is intended to withstand the highest bending moment and shear force values [89,90]. Thus, the maximum bending moment and maximum shear force values are considered in this investigation. As in Figure 14, Mmax is lower in the piled-raft foundation with a soft clay soil profile than in PRC with a stiff clay soil profile. The unequal length of pile increases the differential settlement and bending moment in the piled raft.

4.2.2. Numerical Modelling of Swelling

For observing the effect of swelling on the piled-raft foundation, the swelling applied to the soil cluster with a positive volumetric strain. The value of volumetric strain was determined from the swelling potential from laboratory tests.
In general, piles are designed to withstand a combined axial load and bending moment caused by lateral loads. Although the bending moment due to axial load is negligible, when the pile passes through a swelling layer, this portion experiences a greater bending moment, which is not the case when the pile group travels through a homogenous and non-swelling layer. The analysis was conducted on various piled raft systems while varying the vertical load to determine the influence of the vertical load on the swelling of piled-raft systems, as in Figure 15. It is shown in Figure 15 the effect of loading without consideration of swelling and the application of swelling in each layer of different depths. The thickness of the swelling clay layer (t) was varied to determine the influence of layer thickness on the displacement, and it was observed that as thickness (t) increased, the vertical swelling displacement increased. The embedded length ratio is (t1/L), where t1 is the thickness of the non-swelling layer, and in a (t1/L) ratio of 0.5 swelling, displacement decreased. The soil stiffness of the (t1) layer increased; the significant reduction in swelling was observed as shown in Figure 16. The upper swelling is described as an active zone, while lower bottom layer is a stable zone. To saturate the expansive soil within the model in 100 days, a saturated coefficient of permeability of 0.027 m/day was determined in the laboratory, but 0.27 m/day was used in simulation. This assumption is more realistic and compatible with field research [46]. The piles resting at the lowest layer with the highest stiffness and effect of lateral swelling on piles displacement are illustrated in Figure 17 and Figure 18, respectively. There were no significant changes in pile settlement because of lateral pressure on the pile because of the swelling of soil. The higher the loading, the higher the deflection at outer piles observed with the effect of swelling, with about 60 mm deflection. Outer piles were subjected to a higher deflection as compared to inner piles; this is illustrated in Figure 19.
The behavior of a pile over time in expansive soils is more intricate than the other characteristics discussed earlier. The critical issue is to establish the deformation function of the soil adjacent to the pile and then compute the pile’s axial force and deformation using the differential equation for pile–soil interaction. We approximate the behavior of soil expansion using Equation (9) [91]. The period for the swelling in the calculation phase was taken at 150 days, which is long enough to saturate the soil beneath the foundation. This time period for the calculation is quoted from the FEM and analytical study based on the Australian standards and formulas of [92]. Moreover, the formerly mentioned study was only applicable to slab for a uniformly distributed load of 6 kPa, but in this study the soil is subjected to loads from the construction of raft and pile to buildings loads for a decade, and after that the water conditions changed to being fully saturated. This will be better in simulating the actual field conditions for semi-arid regions.
s z , t = A · e − B / t − A · e − B / t h 0 · z             0 ≤ z ≤ h 0 0 , z > h 0
Tensile strains become increasingly insensitive to irrigation duration, as the swelling potential inside the expanding soil is depleted during saturation. If sufficient saturation time is allowed, the maximum stress will stabilize. As a result, the upward displacements first exhibit a high sensitivity to the entering water but thereafter exhibit decreasing sensitivity to the saturation.
The surface heave/swelling is modelled in this step for raising the water table to the whole soil model and the shear force/bending moment as in Figure 20 and Figure 21 due to the swelling of soil. The swelling of soil causes the significant changes in the bending moment shear forces of pile as compared to non-swelling soil. Therefore, the structural provision is very much necessary for the designing of piled raft. The increase in water level increases the horizontal and vertical displacement on the pile and raft. The swelling decreases with the increase of load.
The parametric study was also conducted to observe the effect of the diameter to length (d/L) ratio, from 0.01 to 0.06, and with the ratio of 0.05 there has been a 20% reduction in the heave of foundation rested on expansive soil. The slight variations in d/L ratio from the other studies, which are 0.04 and 0.03 [93,94], respectively, are due to geometry, soil and loading conditions.
To represent the stress-strain behavior, the Mohr–Coulomb model is a perfect linear elastoplastic model with five input parameters. This model has more applicability than other models due to its ease of formulation as well as the lower data input determined by simple tests. Problems such as soil-bearing capacity and slope stability can be readily designed with this model [95]. According to Chen et al. [96], the Mohr–Coulomb model could be used to obtain an initial estimate of deformations (order of magnitude). As for this current study, the ultimate object was to observe settlement with and without a piled raft, this model was the first choice.
Generally speaking, if progressive failure and the influence of pile penetration on the surrounding medium is the subject of investigation, models such as Mohr–Coulomb will not be an accurate choice, as important factors such as stress-induced anisotropy [96], principal stress rotation [97], and the generation of excess pore water pressure and the additional settlement due to the dissipation of the excess water pressure [98] cannot be considered in the analysis. The model has also limited applicability when over-consolidated clays, dense sandy soils, and the behavior under cyclic loads are studied.

5. Conclusions

To better understand the piled-raft foundation, numerical modelling was performed in Plaxis 2D to obtain more insight into the complex conditions that foundations may face in the design period. A parametric study was conducted and included loading conditions L/D, spacing, stiffness of soil, and raft thickness considering the settlement and swelling in individual cases.
  • The settlement decreased with an increase in the thickness of soil, but even increasing thickness, the structure load exceeded the ultimate settlement limits in soft soil. The piles with rafts satisfy the settlement requirements in the study area soil.
  • The more the embedment of pile in a stiffed layer, the lesser will be the settlement, as this approach will be more suitable as compared to increasing the thickness and length of raft and pile, respectively.
  • The variation in axial stress and bending moment in the region of the expansive soil layer indicates that the drag force generated by the shale layer influences the decline in the axial stress distribution. Regardless of its location, the drag force adds additional load to the pile. In other words, the segment of the pile that passes through the expansive layer is subjected to increased axial load. The presence of a non-swelling layer at the base of the pile reduces the halving of the foundation; however, the pile is subjected to more axial and bending moment.
  • The more the depth of expansive soil, more will be the heaving displacement of the foundation; however, this depends on the swelling of layer, which is saturated. Saturation turns depends on soil conditions such as the density and permeability of soil.
  • While designing a piled-raft system, the maximum bending moment created in the raft should be considered, as the bending was higher in the piled-raft foundation as compared to the raft foundation.

Author Contributions

Conceptualization, M.R.H., Z.A. and M.A.; methodology, M.A. and A.K. (Aneel Kumar); software, F.A., S.K. and A.K. (Alexander Klyuev); validation, A.K. (Aneel Kumar) L.S., R.F., M.A. and S.K.; formal analysis, M.A., M.R.H. and R.F.; investigation, R.F., F.A. and A.K. (Aneel Kumar); resources, M.R.H., S.K. and L.S.; data curation, A.K. (Aneel Kumar) and M.R.H.; writing—original draft preparation, M.R.H. and M.A.; writing—review and editing, M.A., R.F., S.K., F.A., A.K. (Alexander Klyuev) and L.S.; visualization, A.K. (Alexander Klyuev); supervision, Z.A.; project administration, M.A., Z.A., A.K. (Aneel Kumar) and R.F.; funding acquisition, R.F., S.K., A.K. (Alexander Klyuev), L.S. and F.A. All authors have read and agreed to the published version of the manuscript.

Funding

This paper has been supported by the Kazan Federal University Strategic Academic Leadership Program (PRIORITY-2030).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data will be available on a special request from the corresponding authors.

Acknowledgments

This work was realized in the framework of the Program «Priority 2030» on the base of the Belgorod State Technological University Named after V.G. Shukhov.

Conflicts of Interest

The authors declare no conflict of interest.

References

  1. Burland, J.; Burbidge, M.; Wilson, E.; Terzaghi, K. Settlement of Foundations on Sand and Gravel. Proc. Inst. Civ. Eng. 1985, 78, 1325–1381. [Google Scholar] [CrossRef]
  2. Ali, M.; Abbas, S.; Khan, M.I.; Gad, M.A.; Ammad, S.; Khan, A. Experimental Validation of Mander’s Model for Low Strength Confined Concrete Under Axial Compression. In Proceedings of the 2020 Second International Sustainability and Resilience Conference: Technology and Innovation in Building Designs (51154), Sakheer, Bahrain, 11–12 November 2020; pp. 1–6. [Google Scholar] [CrossRef]
  3. Mandolini, A.; di Laora, R.; Mascarucci, Y. Rational Design of Piled Raft. Procedia Eng. 2013, 57, 45–52. [Google Scholar] [CrossRef] [Green Version]
  4. Khan, M.I.; Sutanto, M.H.; Bin Napiah, M.; Zoorob, S.E.; Al-Sabaeei, A.M.; Rafiq, W.; Ali, M.; Memon, A.M. Investigating the Mechanical Properties and Fuel Spillage Resistance of Semi-Flexible Pavement Surfacing Containing Irradiated Waste PET Based Grouts. Constr. Build. Mater. 2021, 304, 124641. [Google Scholar] [CrossRef]
  5. Shaldykova, A.; Moon, S.-W.; Kim, J.; Lee, D.; Ku, T.; Zhussupbekov, A. Comparative Analysis of Kazakhstani and European Approaches for the Design of Shallow Foundations. Appl. Sci. 2020, 10, 2920. [Google Scholar] [CrossRef] [Green Version]
  6. Lee, L.M.; Kassim, A.; Gofar, N. Performances of Two Instrumented Laboratory Models for the Study of Rainfall Infiltration into Unsaturated Soils. Eng. Geol. 2010, 117, 78–89. [Google Scholar] [CrossRef]
  7. Du, D.; Zhuang, Y.; Sun, Q.; Yang, X.; Dias, D. Bearing Capacity Evaluation for Shallow Foundations on Unsaturated Soils Using Discretization Technique. Comput. Geotech. 2021, 137, 104309. [Google Scholar] [CrossRef]
  8. Wijaya, M.; Leong, E.C. Swelling and Collapse of Unsaturated Soils Due to Inundation Under One-Dimensional Loading. Indian Geotech. J. 2016, 46, 239–251. [Google Scholar] [CrossRef]
  9. Katzenbach, R.; Bachmann, G.; Boled-Mekasha, G.; Ramm, H. Combined Pile Raft Foundations (CPRF): An Appropriate Solution for the Foundations of High-Rise Buildings. Slovak J. Civ. Eng. SJCE 2005, 19–29. Available online: https://www.svf.stuba.sk/buxus/docs/sjce/2005/2005_3/file1.pdf (accessed on 29 January 2022).
  10. De Azevedo, A.R.; Klyuev, S.; Marvila, M.T.; Vatin, N.; Alfimova, N.; de Lima, T.E.; Fediuk, R.; Olisov, A. Investigation of the Potential Use of Curauá Fiber for Reinforcing Mortars. Fibers 2020, 8, 69. [Google Scholar] [CrossRef]
  11. Zhao, T.-H.; Wang, M.-K.; Hai, G.-J.; Chu, Y.-M. Landen inequalities for Gaussian Hypergeometric Function. Rev. Real Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 2021, 116, 53. [Google Scholar] [CrossRef]
  12. Nazeer, M.; Hussain, F.; Khan, M.I.; Rehman, A.U.; El-Zahar, E.R.; Chu, Y.-M.; Malik, M. Theoretical Study of MHD Electro-osmotically Flow of Third-Grade Fluid in Micro Channel. Appl. Math. Comput. 2021, 420, 126868. [Google Scholar] [CrossRef]
  13. Chu, Y.-M.; Shankaralingappa, B.; Gireesha, B.; Alzahrani, F.; Khan, M.I.; Khan, S.U. Combined Impact of Cattaneo-Christov Double Diffusion and Radiative Heat Flux on Bio-Convective Flow of Maxwell Liquid Configured by a Stretched Nano-Material Surface. Appl. Math. Comput. 2021, 419, 126883. [Google Scholar] [CrossRef]
  14. Kavitha, P.E.; Beena, K.S.; Narayanan, K.P. A review on soil–structure interaction analysis of laterally loaded piles. Innov. Infrastruct. Solut. 2016, 1, 14. [Google Scholar] [CrossRef] [Green Version]
  15. Bourgeois, E.; de Buhan, P.; Hassen, G. Settlement Analysis of Piled-Raft Foundations by Means of a Multiphase Model Accounting for Soil-Pile Interactions. Comput. Geotech. 2012, 46, 26–38. [Google Scholar] [CrossRef]
  16. Oteuil, A.; Oralbek, A.; Mukhamet, T.; Moon, S.-W.; Kim, J.; Tokbolat, S.; Satyanaga, A. Robust Analysis and Design of Bored Pile Considering Uncertain Parameters. Indian Geotech. J. 2022, 1–15. [Google Scholar] [CrossRef]
  17. Sheil, B. Numerical Simulations of the Reuse of Piled Raft Foundations in Clay. Acta Geotech. 2017, 12, 1047–1059. [Google Scholar] [CrossRef] [Green Version]
  18. Ali, M.; Room, S.; Khan, M.I.; Masood, F.; Memon, R.A.; Khan, R.; Memon, A.M. Assessment of Local Earthen Bricks in Perspective of Physical and Mechanical Properties Using Geographical Information System in Peshawar, Pakistan. Structures 2020, 28, 2549–2561. [Google Scholar] [CrossRef]
  19. Ali, M.; Masood, F.; Khan, M.I.; Azeem, M.; Qasim, M.; Ali, F.N. Evaluation of Flexible Pavement Distresses-A Case Study of Northern Bypass Peshawar, Pakistan. In Proceedings of the 2021 Third International Sustainability and Resilience Conference: Climate Change, Sakheer, Bahrain, 15 November 2021; pp. 399–404. [Google Scholar] [CrossRef]
  20. Amran, M.; Fediuk, R.; Murali, G.; Avudaiappan, S.; Ozbakkaloglu, T.; Vatin, N.; Karelina, M.; Klyuev, S.; Gholampour, A. Fly Ash-Based Eco-Efficient Concretes: A Comprehensive Review of the Short-Term Properties. Materials 2021, 14, 4264. [Google Scholar] [CrossRef]
  21. Berezantzev, V. Load Bearing Capacity and Deformation of Piled Foundations. In Proceedings of the 5th International Conference, ISSMFE, Paris, France, 17–22 July 1961; Volume 2, pp. 11–12. [Google Scholar]
  22. Burland, J. Shaft Friction of Piles in Clay—A Simple Fundamental Approach; Ground Engineering: London, UK, 1973; Volume 6, pp. 30–38. [Google Scholar]
  23. Poulos, H.G. Pile Behaviour—Theory and Application. Geotechnique 1989, 39, 365–415. [Google Scholar] [CrossRef]
  24. Poulos, H.; Small, J.; Chow, H. Piled Raft Foundations for Tall Buildings. Geotech. Eng. J. SEAGS AGSSEA 2011, 42, 78–84. [Google Scholar]
  25. Poulos, H.G.; Bunce, G. Foundation Design for the Burj Dubai–The World’s Tallest Building. In Proceedings of the 6th International Conference of Case Histories in Geotechnical Engineering, Arlington, VA, USA, 11–16 August 2008; Volume 1. [Google Scholar]
  26. Rabiei, M.; Choobbasti, A.J. Piled Raft Design Strategies for High Rise Buildings. Geotech. Geol. Eng. 2015, 34, 75–85. [Google Scholar] [CrossRef]
  27. Russo, G. Numerical Analysis of Piled Rafts. Int. J. Numer. Anal. Methods Geomech. 1998, 22, 477–493. [Google Scholar] [CrossRef]
  28. Balakumar, V.; Huang, M.; Oh, E.; Balasubramaniam, A. Effect of Intermediary Weak Layer on The Behaviour of Piled Raft. In Proceedings of the 20th SEAGC-3RD AGSSEA Conference, Jakartha, Indonesia, 6–7 November 2018. [Google Scholar]
  29. Chow, H.; Small, J. Behaviour of piled rafts with piles of different lengths and diameters under vertical loading. In Advances in Deep Foundations; Geo-Fronties Congress: Austin, TX, USA, 2005; pp. 1–15. [Google Scholar]
  30. Barreto, E.D.S.; Stafanato, K.V.; Marvila, M.T.; de Azevedo, A.R.G.; Ali, M.; Pereira, R.M.L.; Monteiro, S.N. Clay Ceramic Waste as Pozzolan Constituent in Cement for Structural Concrete. Materials 2021, 14, 2917. [Google Scholar] [CrossRef] [PubMed]
  31. De Azevedo, A.R.; Marvila, M.T.; Ali, M.; Khan, M.I.; Masood, F.; Vieira, C.M.F. Effect of the Addition and Processing of Glass Polishing Waste on the Durability of Geopolymeric Mortars. Case Stud. Constr. Mater. 2021, 15, e00662. [Google Scholar] [CrossRef]
  32. Gad, M.A.; Riad, A.M.; Nikbakht, E.; Ali, M.; Ghanem, G.M. Structural Behavior of Slender Reinforced Concrete Columns Wrapped with Fiber Reinforced Polymers Subjected to Eccentric Loads. In Proceedings of the 2020 Second International Sustainability and Resilience Conference: Technology and Innovation in Building Designs, Sakheer, Bahrain, 11–12 November 2020; pp. 1–5. [Google Scholar] [CrossRef]
  33. Ahmed, H.U.; Mohammed, A.A.; Rafiq, S.; Mohammed, A.S.; Mosavi, A.; Sor, N.H.; Qaidi, S.M.A. Compressive Strength of Sustainable Geopolymer Concrete Composites: A State-of-the-Art Review. Sustainability 2021, 13, 13502. [Google Scholar] [CrossRef]
  34. Ayoobi, N.; Sharifrazi, D.; Alizadehsani, R.; Shoeibi, A.; Gorriz, J.M.; Moosaei, H.; Khosravi, A.; Nahavandi, S.; Chofreh, A.G.; Goni, F.A.; et al. Time Series Forecasting of New Cases and New Deaths Rate for COVID-19 Using Deep Learning Methods. Results Phys. 2021, 27, 104495. [Google Scholar] [CrossRef]
  35. Lee, J.; Kim, Y.; Jeong, S. Three-Dimensional Analysis of Bearing Behavior of Piled Raft on Soft Clay. Comput. Geotech. 2010, 37, 103–114. [Google Scholar] [CrossRef]
  36. Reul, O.; Randolph, M.F. Design Strategies for Piled Rafts Subjected to Nonuniform Vertical Loading. J. Geotech. Geoenviron. Eng. 2004, 130, 1–13. [Google Scholar] [CrossRef]
  37. Reul, O. Numerical Study of the Bearing Behavior of Piled Rafts. Int. J. Géoméch. 2004, 4, 59–68. [Google Scholar] [CrossRef]
  38. Azareh, A.; Sardooi, E.R.; Gholami, H.; Mosavi, A.; Shahdadi, A.; Barkhori, S. Detection and prediction of lake degradation using landscape metrics and remote sensing dataset. Environ. Sci. Pollut. Res. 2021, 28, 27283–27298. [Google Scholar] [CrossRef]
  39. Darban, S.; Tehrani, H.G.; Karballaeezadeh, N.; Mosavi, A. Application of Analytical Hierarchy Process for Structural Health Monitoring and Prioritizing Concrete Bridges in Iran. Appl. Sci. 2021, 11, 8060. [Google Scholar] [CrossRef]
  40. Terzaghi, K. Theoretical Soil Mechanics; Wiley: New York, NY, USA, 1943. [Google Scholar]
  41. Manshadi, M.D.; Ghassemi, M.; Mousavi, S.; Mosavi, A.; Kovacs, L. Predicting the Parameters of Vortex Bladeless Wind Turbine Using Deep Learning Method of Long Short-Term Memory. Energies 2021, 14, 4867. [Google Scholar] [CrossRef]
  42. Cooke, R.W. Piled Raft Foundations on Stiff Clays—A Contribution to Design Philosophy. Geotechnique 1986, 36, 169–203. [Google Scholar] [CrossRef]
  43. Dehghani, E.; Ranjbar, S.; Atashafrooz, M.; Negarestani, H.; Mosavi, A.; Kovacs, L. Introducing Copula as a Novel Statistical Method in Psychological Analysis. Int. J. Environ. Res. Public Health 2021, 18, 7972. [Google Scholar] [CrossRef]
  44. Deb, P.; Pal, S.K. Analysis of Load Sharing Response and Prediction of Interaction Behaviour in Piled Raft Foundation. Arab. J. Sci. Eng. 2019, 44, 8527–8543. [Google Scholar] [CrossRef]
  45. Whitaker, T. Experiments with Model Piles in Groups. Geotechnique 1957, 7, 147–167. [Google Scholar] [CrossRef]
  46. Liu, Y.; Vanapalli, S.K. Prediction of Lateral Swelling Pressure Behind Retaining Structure with Expansive Soil as Backfill. Soils Found. 2018, 59, 176–195. [Google Scholar] [CrossRef]
  47. Poulos, H. Practical Design Procedures for Piled Raft Foundations, In Design Applications of Raft Foundations; Thomas Telford Publishing: London, UK, 2000; pp. 425–467. [Google Scholar]
  48. Zha, T.H.; Castillo, O.; Jahanshahi, H.; Yusuf, A.; Alassafi, M.O.; Alsaadi, F.E.; Chu, Y.M. A Fuzzy-Based Strategy to Suppress the Novel Coronavirus (2019-NCOV) Massive Outbreak. Appl. Comput. Math. 2021, 20, 160–176. [Google Scholar]
  49. Zhao, T.; Wang, M.; Chu, Y. On the Bounds of the Perimeter of an Ellipse. Acta Math. Sci. 2022, 42, 491–501. [Google Scholar] [CrossRef]
  50. Park, D.; Park, D.; Lee, J. Analyzing Load Response and Load Sharing Behavior of Piled Rafts Installed with Driven Piles in Sands. Comput. Geotech. 2016, 78, 62–71. [Google Scholar] [CrossRef]
  51. Rajesh, B.G.; Chukka, S.; Dey, A. Finite Element Modeling of Embankment Resting on Soft Ground Stabilized with Prefabricated Vertical Drains. Elastic 2018, 10, 6. [Google Scholar]
  52. Musarat, M.A.; Alaloul, W.S.; Rabbani, M.B.A.; Ali, M.; Altaf, M.; Fediuk, R.; Vatin, N.; Klyuev, S.; Bukhari, H.; Sadiq, A.; et al. Kabul River Flow Prediction Using Automated ARIMA Forecasting: A Machine Learning Approach. Sustainability 2021, 13, 10720. [Google Scholar] [CrossRef]
  53. Nafees, A.; Amin, M.N.; Khan, K.; Nazir, K.; Ali, M.; Javed, M.F.; Aslam, F.; Musarat, M.A.; Vatin, N.I. Modeling of Mechanical Properties of Silica Fume-Based Green Concrete Using Machine Learning Techniques. Polymers 2021, 14, 30. [Google Scholar] [CrossRef] [PubMed]
  54. Ebrahimi-Khusfi, Z.; Taghizadeh-Mehrjardi, R.; Roustaei, F.; Ebrahimi-Khusfi, M.; Mosavi, A.H.; Heung, B.; Soleimani-Sardo, M.; Scholten, T. Determining the Contribution of Environmental Factors in Controlling Dust Pollution during Cold and Warm Months of Western Iran Using Different Data Mining Algorithms and Game Theory. Ecol. Indic. 2021, 132, 108287. [Google Scholar] [CrossRef]
  55. Halder, P.; Manna, B. Performance Evaluation of Piled Rafts in Sand Based on Load-Sharing Mechanism Using Finite Element Model. Int. J. Geotech. Eng. 2020, 1–18. [Google Scholar] [CrossRef]
  56. Nafees, A.; Javed, M.F.; Musarat, M.A.; Ali, M.; Aslam, F.; Vatin, N.I. FE Modelling and Analysis of Beam Column Joint Using Reactive Powder Concrete. Crystals 2021, 11, 1372. [Google Scholar] [CrossRef]
  57. Zhao, T.; Khan, M.I.; Chu, Y. Artificial Neural Networking (ANN) Analysis for Heat and Entropy Generation in Flow of Non-Newtonian Fluid between Two Rotating Disks. Math. Methods Appl. Sci. 2021. [Google Scholar] [CrossRef]
  58. Iqbal, M.A.; Wang, Y.; Miah, M.M.; Osman, M.S. Study on Date–Jimbo–Kashiwara–Miwa Equation with Conformable Derivative Dependent on Time Parameter to Find the Exact Dynamic Wave Solutions. Fractal Fract. 2022, 6, 4. [Google Scholar] [CrossRef]
  59. Ghaemi, A.; Zhian, T.; Pirzadeh, B.; Monfared, S.H.; Mosavi, A. Reliability-Based Design and Implementation of Crow Search Algorithm for Longitudinal Dispersion Coefficient Estimation in Rivers. Environ. Sci. Pollut. Res. 2021, 28, 35971–35990. [Google Scholar] [CrossRef]
  60. Jabir, H.A.; Abid, S.R.; Murali, G.; Ali, S.H.; Klyuev, S.; Fediuk, R.; Vatin, N.; Promakhov, V.; Vasilev, Y. Experimental Tests and Reliability Analysis of the Cracking Impact Resistance of UHPFRC. Fibers 2020, 8, 74. [Google Scholar] [CrossRef]
  61. Banerjee, R.; Bandyopadhyay, S.; Sengupta, A.; Reddy, G.R. Settlement Behaviour of a Pile Raft Subjected to Vertical Loadings in Multilayered Soil. Géoméch. Geoengin. 2020, 17, 282–296. [Google Scholar] [CrossRef]
  62. Puri, A.; Oktavia, F.; Dharmowijoyo, D.B.E.; Ali, M. Prediction of Deflection of Single-pile Nailed-Slab by Using the Allowable Equivalent Modulus of Subgrade Reaction in Case of Additional Modulus from Modified Hardiyatmo Method. In Proceedings of the IOP Conference Series: Earth and Environmental Science, Surakarta, Indonesia, 24–25 August 2021; Volume 832, p. 012022. [Google Scholar] [CrossRef]
  63. Zhao, T.-H.; He, Z.-Y.; Chu, Y.-M. Sharp Bounds for the Weighted Hölder Mean of the Zero-Balanced Generalized Complete Elliptic Integrals. Comput. Methods Funct. Theory 2020, 21, 413–426. [Google Scholar] [CrossRef]
  64. Zhao, T.-H.; Wang, M.-K.; Chu, Y. Concavity and Bounds Involving Generalized Elliptic Integral of the First Kind. J. Math. Inequalities 2007, 701–724. [Google Scholar] [CrossRef]
  65. Haji-Savameri, M.; Norouzi-Apourvari, S.; Irannejad, A.; Hemmati-Sarapardeh, A.; Schaffie, M.; Mosavi, A. Experimental Study and Modelling of Asphaltene Deposition on Metal Surfaces with Superhydrophobic and Low Sliding Angle Inner Coatings. Sci. Rep. 2021, 11, 16812. [Google Scholar] [CrossRef]
  66. Skempton, A.W.; MacDonald, D.H. The Allowable Settlements of Buildings. In Proceedings of the Institution of Civil Engineers; ICE Publishing: London, UK, 1956; Volume 5, pp. 727–768. [Google Scholar]
  67. Janizadeh, S.; Pal, S.C.; Saha, A.; Chowdhuri, I.; Ahmadi, K.; Mirzaei, S.; Mosavi, A.H.; Tiefenbacher, J.P. Mapping the Spatial and Temporal Variability of Flood Hazard Affected by Climate and Land-Use Changes in the Future. J. Environ. Manag. 2021, 298, 113551. [Google Scholar] [CrossRef]
  68. Makul, N.; Fediuk, R.; Amran, M.; Zeyad, A.; Murali, G.; Vatin, N.; Klyuev, S.; Ozbakkaloglu, T.; Vasilev, Y. Use of Recycled Concrete Aggregates in Production of Green Cement-Based Concrete Composites: A Review. Crystals 2021, 11, 232. [Google Scholar] [CrossRef]
  69. Ural, N.; Gergin, A. Foundation design on problematic soils with high underground water level. Rev. Construccion. 2020, 19, 233–245. [Google Scholar] [CrossRef]
  70. Elarabi, H. Modelling of Piled Raft Foundation on Soft Clay. In Proceedings of the International Conference for Postgraduate Studies and Scientific Research, Khartoum, Sudan, 18–21 February 2012. [Google Scholar]
  71. Wulandari, P.S.; Tjandra, D. Analysis of Piled Raft Foundation on Soft Soil Using PLAXIS 2D. Procedia Eng. 2015, 125, 363–367. [Google Scholar] [CrossRef] [Green Version]
  72. Kalbasi, R.; Jahangiri, M.; Mosavi, A.; Dehshiri, S.J.H.; Ebrahimi, S.; Etezadi, Z.A.-S.; Karimipour, A. Finding the Best Station in Belgium to Use Residential-Scale Solar Heating, One-Year Dynamic Simulation with Considering All System Losses: Economic Analysis of Using ETSW. Sustain. Energy Technol. Assessments 2021, 45, 101097. [Google Scholar] [CrossRef]
  73. Kharun, M.; Klyuev, S.; Koroteev, D.; Chiadighikaobi, P.; Fediuk, R.; Olisov, A.; Vatin, N.; Alfimova, N. Heat Treatment of Basalt Fiber Reinforced Expanded Clay Concrete with Increased Strength for Cast-In-Situ Construction. Fibers 2020, 8, 67. [Google Scholar] [CrossRef]
  74. Fediuk, R.; Amran, Y.M.; Mosaberpanah, M.; Danish, A.; El-Zeadani, M.; Klyuev, S.; Vatin, N. A Critical Review on the Properties and Applications of Sulfur-Based Concrete. Materials 2020, 13, 4712. [Google Scholar] [CrossRef] [PubMed]
  75. Garcia, J.R.; de Albuquerque, P.J.R. Influence of Relative Stiffness on the Behavior of Piled Raft Foundations. Acta Scientiarum Technol. 2018, 40, 35209. [Google Scholar] [CrossRef]
  76. Zhao, T.-H.; Wang, M.-K.; Chu, Y.-M. Monotonicity and Convexity Involving Generalized Elliptic Integral of the First Kind. Rev. Real Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 2021, 115, 46. [Google Scholar] [CrossRef]
  77. Mala, A.; Sherwani, A.; Younis, K.; Faraj, R.; Mosavi, A. Mechanical and Fracture Parameters of Ultra-High Performance Fiber Reinforcement Concrete Cured via Steam and Water: Optimization of Binder Content. Materials 2021, 14, 2016. [Google Scholar] [CrossRef]
  78. Li, Y.; Moradi, I.; Kalantar, M.; Babadi, E.; Malekahmadi, O.; Mosavi, A. Synthesis of New Dihybrid Nanofluid of TiO2/MWCNT in Water–Ethylene Glycol to Improve Mixture Thermal Performance: Preparation, Characterization, and a Novel Correlation via ANN Based on Orthogonal Distance Regression Algorithm. J. Therm. Anal. Calorim. 2021, 144, 2587–2603. [Google Scholar] [CrossRef]
  79. Reddy, C.R.K.; Rao, T.G. Numerical Analysis of Piles in Layered Soils: A Parametric Study. Glob. J. Res. Eng. 2014, 14. Available online: https://www.engineeringresearch.org/index.php/GJRE/article/view/1212 (accessed on 29 January 2022).
  80. Susila, E.; Syahputra, M.Y.; Sahadewa, A.; Putri, K.M.E. An Evaluation of Pile-Raft Interaction in Cohesive Soils using 3D Finite Element Method. J. Eng. Technol. Sci. 2019, 51, 662. [Google Scholar] [CrossRef] [Green Version]
  81. Meiabadi, M.S.; Moradi, M.; Karamimoghadam, M.; Ardabili, S.; Bodaghi, M.; Shokri, M.; Mosavi, A.H. Modeling the Producibility of 3D Printing in Polylactic Acid Using Artificial Neural Networks and Fused Filament Fabrication. Polymers 2021, 13, 3219. [Google Scholar] [CrossRef]
  82. Hain, S.J.; Lee, I.K. The Analysis of Flexible Raft-Pile Systems. Geotechnique 1978, 28, 65–83. [Google Scholar] [CrossRef]
  83. El-Garhy, B.; Galil, A.A.; Youssef, A.-F.; Raia, M.A. Behavior of Raft on Settlement Reducing Piles: Experimental Model Study. J. Rock Mech. Geotech. Eng. 2013, 5, 389–399. [Google Scholar] [CrossRef] [Green Version]
  84. Lee, S.-H.; Chung, C.-K. An Experimental Study of the Interaction of Vertically Loaded Pile Groups in Sand. Can. Geotech. J. 2005, 42, 1485–1493. [Google Scholar] [CrossRef]
  85. Mohammadi, M.-R.; Hadavimoghaddam, F.; Pourmahdi, M.; Atashrouz, S.; Munir, M.T.; Hemmati-Sarapardeh, A.; Mosavi, A.H.; Mohaddespour, A. Modeling Hydrogen Solubility in Hydrocarbons Using Extreme Gradient Boosting and Equations of State. Sci. Rep. 2021, 11, 17911. [Google Scholar] [CrossRef] [PubMed]
  86. Bandyopadhyay, S.; Sengupta, A.; Parulekar1b, Y. Behavior of a Combined Piled Raft Foundation in a Multi-Layered Soil Subjected to Vertical Loading. Geomech. Eng. 2020, 21, 379–390. [Google Scholar]
  87. Singh, B.; Singh, N.T. Influence of Piles on Load-Settlement Behaviour of Raft Foundation. Int. J. Eng. Sci. Technol. 2011, 3, 8385–8394. [Google Scholar]
  88. Deb, P.; Pal, S.K. Structural and Geotechnical Aspects of Piled Raft Foundation through Numerical Analysis. Mar. Georesour. Geotechnol. 2021, 1–24. [Google Scholar] [CrossRef]
  89. Mali, S.; Singh, B. Behavior of Large Piled Raft Foundation on Different Soil Profiles for Different Loadings and Different Pile Raft Configurations. Innov. Infrastruct. Solut. 2019, 4, 8. [Google Scholar] [CrossRef]
  90. Mali, S.; Singh, B. 3D Numerical Modeling of Large Piled-Raft Foundation on Clayey Soils for Different Loadings and Pile-Raft Configurations. Stud. Geotech. Mech. 2020, 42, 1–17. [Google Scholar] [CrossRef]
  91. Zhang, C.-S.; Wang, Y.-H.; Xiao, H.-B.; Fan, Z.-H. Numerical Simulation of Soil-Pile Interaction in Expansive Soils Foundation. In Proceedings of the Soils and Rock Instrumentation, Behavior, and Modeling: Selected Papers from the 2009 GeoHunan International Conference, Changsha, China, 3–6 August 2009; pp. 99–105. [Google Scholar]
  92. Shams, M.A.; Shahin, M.A.; Ismail, M.A. Analysis and Modelling of Stiffened Slab Foundation on Expansive Soils. In International Congress and Exhibition Sustainable Civil Infrastructures: Innovative Infrastructure Geotechnology; Springer: Berlin/Heidelberg, Germany, 2017; pp. 250–261. [Google Scholar]
  93. Poulos, H.G.; Davis, E.H. Pile Foundation Analysis and Design; Wiley: New York, NY, USA, 1980; Volume 397. [Google Scholar]
  94. Xiao, H.-B.; Zhang, C.-S.; Wang, Y.-H.; Fan, Z.-H. Pile-Soil Interaction in Expansive Soil Foundation: Analytical Solution and Numerical Simulation. Int. J. Geomech. 2011, 11, 159–166. [Google Scholar] [CrossRef]
  95. Çelik, S. Comparison of Mohr-Coulomb and Hardening Soil Models Numerical Estimation of Ground Surface Settlement Caused by Tunneling. J. Inst. Sci. Technol. 2017, 7, 95–102. [Google Scholar] [CrossRef]
  96. Chen, S.-L.; Lee, S.-C.; Wei, Y.-S. Numerical Analysis of Ground Surface Settlement Induced by Double-O Tube Shield Tunneling. J. Perform. Constr. Facil. 2016, 30, 04016012. [Google Scholar] [CrossRef]
  97. Whittle, A.J. A Constitutive Model for Overconsolidated Clays with Application to the Cyclic Loading of Friction Piles. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, USA, 1987. [Google Scholar]
  98. Dou, J.; Chen, J.; Zhang, Z.-J. Influence of Large-Diameter Pipe Pile Driving on Surrounding Marine Soils and Adjacent Submarine Pipelines. Mar. Georesources Geotechnol. 2019, 39, 15–33. [Google Scholar] [CrossRef]
Buildings 12 00356 g001 550
Figure 1. Piled raft foundation (Qp = end bearing capacity of pile).
Figure 1. Piled raft foundation (Qp = end bearing capacity of pile).
Buildings 12 00356 g001
Buildings 12 00356 g002 550
Figure 2. Illustration of laboratory work: (a) shear strength test; (b) un-confined compression test.
Figure 2. Illustration of laboratory work: (a) shear strength test; (b) un-confined compression test.
Buildings 12 00356 g002
Buildings 12 00356 g003 550
Figure 3. Geometry of the pile-raft foundation (S = spacing (variable), Dia = variable, Length = 11 m).
Figure 3. Geometry of the pile-raft foundation (S = spacing (variable), Dia = variable, Length = 11 m).
Buildings 12 00356 g003
Buildings 12 00356 g004 550
Figure 4. Particle size distribution curve.
Figure 4. Particle size distribution curve.
Buildings 12 00356 g004
Buildings 12 00356 g005 550
Figure 5. Shear strength envelop (a) 0 to 5 ft (b) 6 to 10 ft.
Figure 5. Shear strength envelop (a) 0 to 5 ft (b) 6 to 10 ft.
Buildings 12 00356 g005
Buildings 12 00356 g006 550
Figure 6. Stress and voids ratio curves: (a) 0 to 5 ft and (b) 6 to 10 ft.
Figure 6. Stress and voids ratio curves: (a) 0 to 5 ft and (b) 6 to 10 ft.
Buildings 12 00356 g006
Buildings 12 00356 g007 550
Figure 7. 400 kN/m2 with (a) plastic analysis and (b) consolidation analysis.
Figure 7. 400 kN/m2 with (a) plastic analysis and (b) consolidation analysis.
Buildings 12 00356 g007
Buildings 12 00356 g008 550
Figure 8. 200 kN/m2 and raft and pile raft: (a) deformed mesh of raft, (b) contours of displacement raft, (c) deformed mesh piled raft, and (d) contours of displacement piled raft.
Figure 8. 200 kN/m2 and raft and pile raft: (a) deformed mesh of raft, (b) contours of displacement raft, (c) deformed mesh piled raft, and (d) contours of displacement piled raft.
Buildings 12 00356 g008
Buildings 12 00356 g009 550
Figure 9. 500 kN/m2 load, raft and pile raft: (a) deformed mesh of raft, (b) contours of displacement raft, (c) deformed mesh piled raft, and (d) contours of displacement piled raft.
Figure 9. 500 kN/m2 load, raft and pile raft: (a) deformed mesh of raft, (b) contours of displacement raft, (c) deformed mesh piled raft, and (d) contours of displacement piled raft.
Buildings 12 00356 g009
Buildings 12 00356 g010 550
Figure 10. Pile area/raft area (Ap/Ar) and effect on settlement.
Figure 10. Pile area/raft area (Ap/Ar) and effect on settlement.
Buildings 12 00356 g010
Buildings 12 00356 g011 550
Figure 11. Hard strata at bottom, raft and piled raft: (a) deformed mesh of raft, (b) contours of displacement raft, (c) deformed mesh piled raft, and (d) contours of displacement piled raft.
Figure 11. Hard strata at bottom, raft and piled raft: (a) deformed mesh of raft, (b) contours of displacement raft, (c) deformed mesh piled raft, and (d) contours of displacement piled raft.
Buildings 12 00356 g011
Buildings 12 00356 g012 550
Figure 12. Effect of multi-layer soil profile on settlement.
Figure 12. Effect of multi-layer soil profile on settlement.
Buildings 12 00356 g012
Buildings 12 00356 g013 550
Figure 13. Bending moment, un-piled and piled raft.
Figure 13. Bending moment, un-piled and piled raft.
Buildings 12 00356 g013
Buildings 12 00356 g014 550
Figure 14. Bending moment variation profile along length of raft.
Figure 14. Bending moment variation profile along length of raft.
Buildings 12 00356 g014
Buildings 12 00356 g015 550
Figure 15. Settlement to progressive swelling effect.
Figure 15. Settlement to progressive swelling effect.
Buildings 12 00356 g015
Buildings 12 00356 g016 550
Figure 16. Effect of stiffness of lowest bottom layer on swelling.
Figure 16. Effect of stiffness of lowest bottom layer on swelling.
Buildings 12 00356 g016
Buildings 12 00356 g017 550
Figure 17. Piles rest at lowest layer with higher stiffness.
Figure 17. Piles rest at lowest layer with higher stiffness.
Buildings 12 00356 g017
Buildings 12 00356 g018 550
Figure 18. Effect of lateral swelling on piles displacement.
Figure 18. Effect of lateral swelling on piles displacement.
Buildings 12 00356 g018
Buildings 12 00356 g019 550
Figure 19. Effect of lateral swelling on horizontal displacement.
Figure 19. Effect of lateral swelling on horizontal displacement.
Buildings 12 00356 g019
Buildings 12 00356 g020 550
Figure 20. Bending moment on pile due to lateral swelling.
Figure 20. Bending moment on pile due to lateral swelling.
Buildings 12 00356 g020
Buildings 12 00356 g021 550
Figure 21. Shear force variation on pile.
Figure 21. Shear force variation on pile.
Buildings 12 00356 g021
Table
Table 1. Soil properties.
Table 1. Soil properties.
Representative DepthLiquid Limit (LL)Plasticity Index (PI)AASHTO
Soil Group		USCS Soil Group Name (Symbol)Clay Content
0–10 ft26.7%11.765A-6 (Clayey Soil)Silty Clays (CL)10.2%
10–20 ft34.8%19.63A-6 (Clayey Soil)Silty Clays (CL)13.5%
20–25 ft38.7%14.2682A-6 (Clayey Soil)Silty Clays (CL)8.06%
25–30 ft36.8%12.38A-6 (Clayey Soil)Silty Clays (CL)11.6%
30–35 ft36.6%11.25A-6 (Clayey Soil)Inorganic Clayey Silts (ML)11.8%
Table
Table 2. Basic parameters of soil.
Table 2. Basic parameters of soil.
ParametersBore Hole Depth
(0 ft–5 ft)		Bore Hole Depth
(6 ft–10 ft)		Bore Hole Depth
(11 ft–20 ft)
Primary Compression Index (Cc)0.01220.01060.0197
Secondary Compression index (Cα)00.00343650
Swelling Index (Cs)0.00450.00450
Pre-consolidation Pressure (σ’c) (kN/m2)70825
Initial void ratio of clay layer (eo)0.3800.3530.433
Void ratio at the end of primary consolidation (ep)0.3630.3420.387
Unit Weight (γ) (kN/m3)19.2519.2718.65
Cohesion (c) (kN/m2)13.7347.84825.506
Internal angle friction (ϕ) (Degrees)182713
Modulus of Elasticity (E)600060009000
Analysis TypeDrainedDrainedDrained
Table
Table 3. Modulus of elasticity of soils/clays (data from Ref. [66]).
Table 3. Modulus of elasticity of soils/clays (data from Ref. [66]).
MaterialYoung’s Modulus E (kg/cm2)Poisson’s Ratio ν
Soft sensitive clays20–40 (500 su)
Firm to stiff clays40–80 (1000 su)0.4–0.5
Very stiff clays80–200 (1500 su)(undrained)
Table
Table 4. Properties of raft foundation as plate element (data from Ref. [69]).
Table 4. Properties of raft foundation as plate element (data from Ref. [69]).
ParameterValue
Thickness (d) (m)0.5
Material ModelElastic
EA (kN/m)6.0 × 106
EI (kN/m2/m)333.3 × 103
Weight (w) (kN/m/m)6
Poisson Ratio0.2
Table
Table 5. Properties of piled-raft foundation as embedded beam row (data from Ref. [69]).
Table 5. Properties of piled-raft foundation as embedded beam row (data from Ref. [69]).
Design ElementEmbedded Beam Row
Material ModelElastic
E (kN/m2)30.0 × 106
γ (kN/m3)0.150
D (d) (m)0.8
A (m2)0.5027
I (m4)0.02011
Lspacing (m)2.0
Tskin, start, max (kN/m)100
Tskin, end, max (kN/m)200
Fmax (kN)500
Table
Table 6. Pile spacing and settlement.
Table 6. Pile spacing and settlement.
Pile ConfigurationSettlement Corresponding to 200 kPa Vertical Load (mm)
Raft Only111
3D Spacing42
4D Spacing65
5D Spacing88
6D Spacing155
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Share and Cite

MDPI and ACS Style

Hakro, M.R.; Kumar, A.; Almani, Z.; Ali, M.; Aslam, F.; Fediuk, R.; Klyuev, S.; Klyuev, A.; Sabitov, L. Numerical Analysis of Piled-Raft Foundations on Multi-Layer Soil Considering Settlement and Swelling. Buildings 2022, 12, 356. https://doi.org/10.3390/buildings12030356

AMA Style

Hakro MR, Kumar A, Almani Z, Ali M, Aslam F, Fediuk R, Klyuev S, Klyuev A, Sabitov L. Numerical Analysis of Piled-Raft Foundations on Multi-Layer Soil Considering Settlement and Swelling. Buildings. 2022; 12(3):356. https://doi.org/10.3390/buildings12030356

Chicago/Turabian Style

Hakro, Muhammad Rehan, Aneel Kumar, Zaheer Almani, Mujahid Ali, Fahid Aslam, Roman Fediuk, Sergey Klyuev, Alexander Klyuev, and Linar Sabitov. 2022. "Numerical Analysis of Piled-Raft Foundations on Multi-Layer Soil Considering Settlement and Swelling" Buildings 12, no. 3: 356. https://doi.org/10.3390/buildings12030356

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop