Nonlinear 3D interactive analysis of superstructure and piled raft foundation

Engineering Structures 143 (2017) 204–218

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Engineering Structures journal homepage: www.elsevier.com/locate/engstruct

Nonlinear 3D interactive analysis of superstructure and piled raft foundation Junyoung Ko a, Jaeyeon Cho b, Sangseom Jeong c,⇑ a

Department of Civil, Environmental and Construction Engineering, Texas Tech University, 911 Boston Ave., Lubbock, TX 79409, USA Foundations and Geotechnics, Mott MacDonald, 8-10 Sydenham Road, Croydon CR0 2EE, UK c Department of Civil and Environmental Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea b

a r t i c l e

i n f o

Article history: Received 8 November 2016 Revised 7 March 2017 Accepted 12 April 2017

Keywords: Piled raft foundations Superstructure Iterative and interactive analysis Unified analysis

a b s t r a c t An interactive design method that takes into account the coupling between the stiffness of the superstructure, the piled raft and the soil has been proposed for analyzing the response of building structure. Special attention is given to consideration of interaction between the superstructure and the piled raft. And a series of numerical analysis is performed to validate the interactive analysis routine in comparison to the unified analysis method. Through the comparative studies, it is found that the iterative and interactive analysis gave similar results of settlement and raft bending moment compared with finite element analysis. And it is also found that the proposed design method considering interaction between superstructure and foundation is capable of predicting reasonably well the behavior of building structures. It can be effectively used to perform the design of a superstructure-piled raft foundation system. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction All over the world, an increasing need for optimized foundation design of the building structure is becoming an important issue in engineering practice. In the conventional design of pile foundations, the total load transmitted by the superstructure is carried by the piles, with any contribution of the raft (footing) being ignored. The piles are generally located on a regular grid pattern with the same diameter and length. According to most standards of pile design, identical piles must be designed with an adequate safety factor from 2 to 3. This requirement leads to a higher number and larger length of piles. Therefore, the pile foundation is more expensive and the settlement is unnecessarily small. In recent decades, the concept of piled raft has been used extensively in Europe and Asia and an increasing number of structures, especially buildings, have been founded on them [1–4] and piled rafts have proved to be an economical alternative to conventional pile foundations in circumstances in which the soil below the raft can provide significant bearing capacity and stiffness to supplement that of the piles. In the design of a building structure, the soil-structure interaction problem is an interdisciplinary field which involves structural and geotechnical engineering. In the traditional design practice,

⇑ Corresponding author. E-mail address: [email protected] (S. Jeong). http://dx.doi.org/10.1016/j.engstruct.2017.04.026 0141-0296/Ó 2017 Elsevier Ltd. All rights reserved.

the superstructure is typically analyzed without modeling the foundation-subsoil (i.e. fixed boundary or rigid base conditions) and the foundation is designed without considering the effect of the superstructure stiffness. It may result in overestimation of forces, the bending moment, and the settlement of the superstructure and foundation [5,6]. Nevertheless the traditional design approach is still dominant in engineering practice. This is because the analysis process is affected by many factors such as: column and wall geometry, design load, raft and pile group geometry, soil properties, and interaction between different structural elements. Accordingly, there is currently no practical method available to predict behavior of the entire structures due to the difficulty and uncertainty in quantifying these factors. Much work has been done to study the superstructurefoundation interaction problem by many researchers. In the early 1950s, Mayerhof [7] recognized the importance of superstructure-foundation-soil interaction. From then onwards, numerous studies have been carried out to quantify the effect of soil-structure interaction on the behavior of framed structure. Recently the possible unified structural-geotechnical models for the structure-foundation-soil system are reported. Lee and Brown [8] developed and analysis by treating the structure, foundation and soil system as an integral unit. Fraser and Wardle [9] used the finite element method to analyze a two bay portal frame on a layered cross-anisotropic elastic continuum. Viladkar et al. [10] also presented a new approach for the physical and material

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modeling of a space frame-raft-soil system. Hora [11] presented the computational methodology adopted for nonlinear soilstructure interaction analysis of an infilled frame-foundation-soil system. Most of the unified analysis based on the finite element method [12–15] provides versatile tools that are capable of modeling the superstructure, soil continuity, soil nonlinearity, soil-structure interface behavior, and 3-D boundary conditions. Therefore, it considers the structure-foundation-soil interaction automatically, while the traditional design method does not. However, the finite element method remains primarily a research technic due to the effort required in computation and in modeling the problem. Additionally, full 3D FE analyses were almost impossible for large scale of superstructure-foundation-soil systems. This is because it is too complicated and time consuming to simulate a soil-structure interaction problem as the entire building structure. Besides, the amount of results from the 3D FE analysis is huge but only a few data are of interest to the structural engineer. So for a practical design of a building structure, the design methods should be more simple and reliable, especially for cost-effectiveness. In this study, an interactive design method is proposed for the simplified interaction between the superstructure and a piled raft. It is intermediate in theoretical accuracy between a unified analysis and the conventional design approach. Additionally, the proposed method is necessary for the geotechnical engineer to form an understanding of the load transfer mechanism from the superstructure to the foundation. The overall objective of this study is focused on the application of the interactive design method for predicting behavior of entire building structures, and a series of numerical analysis is performed to validate the interactive analysis routine in comparison to the unified analysis method. For this purpose, the three-dimensional (3D) Finite-Element (FE) analysis has been carried out. For the unified analysis of superstructure and foundation, the numerical analyses were performed via the FE code PLAXIS 3D foundation [16], with column, floor and piled raft foundation systems.

(a) CSM boundary condition (proposed method)

2. New design method for piled rafts supported building structures To determine accurate deformations and internal forces in a building structure, it is necessary to account for the whole system response, including the superstructure, foundation, and soil. Such an accurate determination of the building response is necessary to make design decisions within the performance-based engineering framework. In this study, therefore, a new analysis methodology for superstructure-foundation-soil is proposed by considering coupled stiffness of foundation-soil and structure. 2.1. Idealization of superstructure Fig. 1(a) and (b) illustrate a numerical model of superstructure used in the proposed and conventional design method. A 3D FEM model to simulate the response of a superstructure under gravity load using MIDAS-CIVIL [17] is presented here. In the most generalized form, superstructure of the building frames may be idealized as three-dimensional space frame using two noded beam elements with six degrees of freedom per node. It is adopted for the beams and columns of superstructure and connections between beams and columns are treated as rigid. A four-node plate element with six degrees of freedom per node was used to model the slabs of the superstructure and the raft supporting the frame structure. The soil and pile head supporting at various node of the plate element are simulated by a series of equivalent and independent elastic springs with six degrees of freedom. The coupled stiffness matrix (CSM), [k]i, is of order 6
6, representing three spring

(b) Fixed boundary condition (conventional design) Fig. 1. Idealized 3D model of superstructure (MIDAS-CIVIL).

constants, three rotational constraints, and four coupling between spring and rotational constraints. The equilibrium equation at the pile head and soil in local coordinate system (u, v, w) is represented as follows;

2 6 6 6 6 6 6 6 6 4

K 11

0

0

0

0

0

k22

0

0

0

0 0

0 0

k33 0

0 k44

k35 0

0

0

k53

0

k55

0

k62

0

0

0

8 9 38 9 du > Fu > > > > > > > > > > > 7 > > > > > k26 7 > dv > Fv > > > > > > > > > > > > > 7< < = 0 7 dw Fw = 7 ¼ > 0 7 Mu > > au > > > > 7> > > > > > > > 7> > > > > > > > 5 0 > av > Mv > > > > > > > : ; : ; k66 i aw i Mw i 0

ð1Þ

where [k]i is the stiffness matrix of pile head and soil, {d}i is the vector of displacement, {a}i is the vector of rotation, {F}i is the vector of force, and {M}i is the vector of moment at the ith pile head and soil.

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2.2. Modeling of piled raft foundation The modeling of the piled raft foundation was performed using YSPR [5,6]. In the analytical approach, the individual piles are modeled using general beam-column elements and the soil below the raft is treated as a linear or nonlinear spring element. The soil at the individual piles is represented by load-transfer curves. The axial load transfer curves (t-z, q-z curves) are estimated using the equation developed by McVay et al. [18], the lateral load transfer curve (p-y curve) is used as an API model proposed by O’Neill and Murchison [19]. For the modeling of a flexible raft, threedimensional finite elements, such as four-node flat shell element was used. Fig. 2 shows the numerical model of the piled raft used in the present study. To consider the nonlinear load-displacement relationship at each pile head and soil (below the raft), an incremental secant modulus method developed by Won et al. [20] is used. From the process of incremental secant modulus method, the coupled stiffness matrix, [k]i (Eq. (1)), is estimated at each design load. The importance of soil-structure interaction (SSI) in the analysis and design of piled rafts has long been recognized by geotechnical engineers. As shown in Fig. 2, it is possible to consider several interactions of piled rafts in the proposed method. The pile-soil and raft-soil interaction were considered by a set of load-transfer curves. For the raft-soil-pile interaction, in this study a membrane-spring system was incorporated to involve the soil spring-coupling effects. The pile–soil–pile interaction that occurs in closely spaced piles can be taken into account by introducing a p-multiplier [21,22] for the soil reactions (p–y curves), group efficiency factor [23,24] for the side resistance (t-z curve) and end bearing resistance (q-w curve) for single piles. Therefore, the soil-foundation coupled stiffness matrix can be calculated by YSPR for CSM boundary condition. The detailed algorithm of YSPR was discussed in the previous researches by authors [5,6].

improved analytical method was proposed on the basis of idealization for the superstructure, and the soil-structure interaction solution techniques described in the previous section. The proposed interactive analysis which requires the cooperation of the structural and geotechnical engineer considers the interaction between superstructure-foundation and soil simultaneously. Fig. 3 shows a schematic diagram and skeleton flowchart of the proposed interactive analysis. It shows the dependences between the structural and geotechnical engineer and the dependence of the outcome of calculations on the information exchanged throughout the design procedure. The procedure of interactive analysis in this study includes the following steps: (1) The structural engineer computes the nodal reaction force of superstructure-foundation interface (raft) for a fixed boundary condition using the MIDAS-CIVIL program. (2) The geotechnical engineer applies the reaction force as the load condition of the foundation and constructs the CSM (coupled stiffness matrix) of soil and foundation using the YSPR program. (3) The CSM from step 2 is used as a boundary condition to perform the structural analysis and re-calculate the nodal reaction force at the interface using the MIDAS-CIVIL program. (4) The geotechnical engineer analyzes the behavior of the foundation and constructs the CSM under the load condition from step 3. (5) The calculation procedure, step 2–4, is iterated until the error between the behavior of the superstructure and foundation falls within a tolerance limit. This is done by checking the convergence of member forces and displacements at interface nodes. 3. Validation and application of the design method

2.3. Solution procedure

3.1. Problem description

A more rational design solution for the soil-structure interaction problem can be achieved with computational validity and accuracy by an appropriate analysis method. In this study, an

A series of numerical analyses were performed to validate the structural-analysis routine in the present method by comparison with the unified analysis (based on FE analysis) method. A fully

Fig. 2. Modeling of piled raft considering soil-structure interaction (YSPR).

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(a) Schematic diagram STEP-1 1) Analysis of superstructure in fixed boundary condition 2) Calculate reaction force of fixed boundary

Superstructure

Foundation

STEP-2 1) Construct the CSM of soil and foundation using reaction force 2) Design initial cross section of the foundation

STEP-5 1) Re-design cross section of the foundation 2) Re-construct the CSM of foundation-soil

STEP-3 1) Re-analysis of superstructure in CSM boundary condition 2) Calculate reaction force of CSM boundary

Iteration

STEP-4 1) Check the convergence of member force or displacement at superstructure-foundation interface 2) Evaluate stability of the foundation

No Yes

Superstructure design

Foundation design

(b) Flow chart Fig. 3. Interactive analysis between superstructure and foundation.

modeled superstructure-foundation-soil system was analyzed using the FE program PLAXIS 3D Foundation. A schematic representation of a building structure is shown in Fig. 4. Comparisons were made for the raft settlement, raft bending moment, settlement of superstructure along the A-A0 section and pile load distribution.

The analysis was carried out on a space frame (2bay)-piled raftsoil system with ten stories. The piles are 1 m in diameter and 10 m in embedded length. There are 25 identical vertical piles, which are spaced by 2.5 m (= 2.5D, where D is a pile diameter). A square raft has a width of 15 m with fixed pile head conditions. The columns are 3.5 m in length and 0.6 m in width. The mesh size, which

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The specified initial stress distributions should match with a calculation based on the self-weight of the material. After the initial step, the applied loading was simulated by a self-weight of superstructure. An analysis was carried out by assuming that the only vertical load was applied on the raft through the nine columns. Fig. 6 shows the construction stage-dependent development of load-settlement behavior of the piled raft foundation. After concreting the raft, the vertical load on the raft increased constantly until the completion of all construction stages. The pile, raft, column and slab are considered as linear-elastic material at all times, while for the surrounding soil layer the Mohr-Coulomb non-associated flow rule is adopted. The interface element modeled by the bilinear Mohr-Coulomb model is employed to simulate the pile–soil interface as discussed by Jeong et al. [25]. Table 1 summarizes the soil profile and the material properties used in this study. 3.2. Comparison with unified analysis

(a) Structure and subsurface soil profile

(b) Plan view of structure Fig. 4. Schematic diagram of a building structure.

minimizes the effect of the mesh boundary on the pile behavior, was 120D wide and 100D long. The raft and slab were modeled using plate elements and soil elements are 15-node wedge elements which are composed of 6-node triangular elements in the horizontal direction and 8-node quadrilaterals in the vertical direction. Each pile in a group is modeled with a massive circular pile composed of volume elements with an interface at the outside of the pile. Two node vertical and horizontal beam elements are used for the columns and beams respectively. At the left- and right-hand vertical boundaries, lateral displacements were restrained, whereas fixed supports were applied to the bottom boundaries. As mentioned above, the typical three-dimensional finite element mesh used for the unified analysis is shown in Fig. 5.

Fig. 7 shows the predicted responses of superstructure and piled raft foundation. Results from the analysis with fixed boundary conditions (i.e. the conventional design method) are also included for comparison. From a convergence check, it was found that the iteration procedure (1st–3rd CSM) of YSPR satisfied the convergence condition of raft settlement with those obtained from the MIDAS-CIVIL. As shown in Fig. 7(a), the proposed method accurately predicts the general trend of the values from the unified analysis when compared with the results from the fixed boundary. The analyses of the piled raft by the fixed boundary condition method produce large raft settlement of about 7.3–9.4% more than the results of the proposed solution. Compared to the unified analysis, the fixed boundary condition analysis shows a significant increase in settlement of about 28–42%. This is because the fixed boundary methods do not reflect the three-dimensional combination of stiffness due to piled raft-soil interaction, and thus, overestimate the reaction force as the load condition of foundation. Fig. 7(b) shows the predicted raft bending moment for the piled raft foundation. All of the methods predict the general trend of the values of the unified analysis reasonably well. However, the fixed boundary condition method exhibits a relatively larger bending moment of about 57% compared with the results of the proposed solution. This curve demonstrates the reductions in internal force by considering soil-structure interaction. Therefore, the proposed method may be more appropriate and realistic to represent foundation-soil behavior than the fixed boundary condition. As shown in Fig. 7(c), the magnitude of axial load is clearly related to the applied boundary condition and thus represents a significant reduction in axial load by considering foundation-soil stiffness, although the distributions in each pile show generally similar shapes in all cases. This clearly demonstrates that for the analysis results, the proposed method gives more realistic results for bearing behavior of piles, because the fixed boundary condition method does not consider soil-structure interaction and the proposed method does so using coupled stiffness matrix and iteration solution algorithm. Fig. 7(d) shows a comparison of the calculated settlement of the superstructure. The prediction of the fixed boundary condition method is much more conservative than that of 3D FE analyses and the proposed one. These results clearly demonstrate that the distribution pattern of the internal force and settlement is significantly dominated by boundary condition representing a foundation-soil interaction. The reason for this behavioral difference between the fixed boundary and CSM boundary is explained by the fact that the CSM boundary will produce more flexibility than the fixed boundary. In addition, the amount of redistribution of loads depends upon the rigidity of the structure and the load-settlement characteristics

J. Ko et al. / Engineering Structures 143 (2017) 204–218

209

Superstructure (10 stores, concrete frame) Foundation (5X5 Piled raft) 120m 100m

(a) Superstructure-foundation-soil system

Beam & Column (Beam element, 0.6X0.6m2) 35m Slab (Plate element, 10X10m2, thick.=0.2m)

Raft (Plate element, 15X15m2, thick.=1m)

Pile (Volume element, D=1m, L=10m)

(b) Modeling of superstructure-piled raft foundation Fig. 5. Typical 3D FE model for unified analysis.

of the soil [14]. Therefore, the conventional fixed boundary may not reflect the nature of the soil-structure interaction for the general case, and thus it requires validation before being used in engineering practice. As mentioned above, the boundary condition influences the load distribution and the settlement of the entire structure. In addition, the effect of the boundary condition, investigated by changing the stiffness of the foundation and superstructure, is shown in Fig. 8(a)–(d). In case 1, the elastic modulus of a piled raft is made 10 times larger (2.5
108 kPa) than that of the previous studies. In case 2, an elastic modulus is used 100 times larger (2.5
109 kPa) than that of previous case for modeling a piled raft similar to a fixed boundary condition. As expected, structural behavior was highly influenced by the different boundary conditions as the elastic modulus of foundation increased.

Fig. 8 shows the raft settlement, bending moment, superstructure displacement and computed reaction force. As the elastic modulus (E) of a piled raft increased, the difference between the results of the CSM boundary and those of case 1 and 2 increased and got near to the results of the fixed boundary condition. Especially, it is shown that similar trends are estimated between case 2 (100 times larger elastic modulus) and the fixed boundary condition. This comparative study suggests that the CSM boundary condition gives more flexible results for structural analysis, because of the difference in the modeling methods, whereby the CSM method model foundation-soil using stiffness matrices and the conventional method does so using the fixed boundary condition. From these analyses, it was concluded that the overall behavior of a structure is affected significantly by the boundary condition.

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Fig. 6. Calculated construction stage-dependent load-settlement behavior of piled raft.

4. Parametric study This section is focused on the effects of superstructurefoundation interaction on the behavior of building structure. Based on the comparative studies considered, soil-structure interactions have a great impact on the whole system response. To obtain detailed information on the effect of superstructure-foundation interaction, a series of numerical analysis of a building structure by using the present method were performed for different raft and slab thickness (or elastic modulus), pile configuration, pile lengths, pile diameters and column sectional area (or elastic modulus). 4.1. Effects of superstructure stiffness The effect of the superstructure stiffness on the behavior of foundation is investigated by changing the slab stiffness (thickness or elastic modulus) and the column stiffness (sectional area or elastic modulus). Fig. 9(a) shows the raft settlement with varying stiffness of a slab tslab. Three different stiffness (tslab = 0.2, 0.6 m and the elastic modulus of slab Eslab = 27,277 MPa = C35) are investigated. Except the stiffness of a slab, all other conditions are identical with the condition of validation case in the previous section. As shown in Fig. 9(a), the settlement of the foundation is clearly related to the applied stiffness of the superstructure and thus represents a

significant reduction in settlement with increasing stiffness of superstructure, although the distributions of settlement show generally similar shapes in all cases. However, the maximum settlement at the center of the raft is decreased to 5.3%. Bending moment distributions from the same analysis conditions are illustrated in Fig. 9(b). The increase in the thickness of slab from 0.2 m to 0.6 m resulted in a 20.3% decrease in the maximum bending moment. The estimated maximum bending moment in both the tslab = 0.2 m case and Eslab = C35 case showed similar maximum bending moment. Fig. 9(c) shows the load sharing ratio (apr) depending on the stiffness of the slab. The definition of load sharing ratio (apr) is the ratio of the sum of all pile loads to the total load of the foundation [26]. The load sharing ratio of the piles decreased with increasing stiffness of superstructure. This difference of the load sharing was caused by the contribution of the superstructure which was more efficient with increasing stiffness. Fig. 9(d) shows the settlement of foundation under the three different column stiffness (Breadth of column, Bcolumn = 0.6, 1.0 m and elastic modulus of column, Ecolumn = 27,277 MPa = C35). This curve demonstrates the reduction in settlement with increasing stiffness of column. Although the distributions of settlement show generally similar shapes in all cases, the maximum settlement at the center of raft is decreased to 5.6%. Thus, settlement reduction and increase in column stiffness should be thoroughly checked for a proper foundation design. Bending moment distributions from the same analysis conditions are illustrated in Fig. 9(e). The increase in the sectional area of column from 0.6
0.6 m2 to 1.0
1.0 m2 resulted in a 16.6% decrease in the maximum bending moment. The estimated maximum bending moment in both the sectional area 0.6
0.6 m2 case and the Ecolumn = C35 case showed similar maximum bending moment. Fig. 9(f) shows the load sharing ratio (apr) depending on stiffness of column. The load sharing ratio of the piles also decreased with increasing stiffness of column. It is also found that the settlement and bearing behavior of foundation changes with varying superstructure stiffness. From this comparative study, it is concluded that it is important to consider the stiffness of the superstructure. This can be explained by noting that the reason for reductions in settlement and load sharing of the piles with increasing stiffness of the superstructure. Additionally, with an increase in the stiffness of the superstructure, internal force of the foundation also decreased.

4.2. Effects of foundation-soil stiffness 4.2.1. Pile spacing Fig. 10(a) shows the settlement at the top of superstructure with varying a pile spacing, s. Three different pile spacing (s = 2.5D, 5D, and 6D; D: pile diameter, 1 m) are investigated. The distribution of the computed settlement was smaller at center of the slab than the side of slab, irrespective of pile spacing. This

Table 1 Material properties for unified analysis. Weathered soil

Soft rock

Hard rock

Raft

Pile

Column & slab

Unit weight, c (kN/m ) Young’s modulus, E (MPa)

19 50

23 500

26 2000

25

24.5

Cohesion of soil, c (kPa) Friction angle of soil, / (deg.) Poisson’s ratio, m Model

15 35 0.32 M.C.a

50 40 0.25

100 45 0.2

25 C30 = 24,645 C35 = 27,277 – – 0.18 L.E.a

– – 0.18

– – 0.18

3

a

Note: M.C. is Mohr Coulomb elasto-plastic model. L.E. is Linear Elastic Model.

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J. Ko et al. / Engineering Structures 143 (2017) 204–218 2000 Unified Analysis (PLAXIS 3D) Fixed Boundary (YSPR) 1st CSM (YSPR) 2nd CSM (YSPR) 3rd CSM (YSPR)

Unified Analysis (PLAXIS 3D) Fixed boundary (YSPR) 1st CSM (YSPR) 2nd CSM (YSPR) 3rd CSM (YSPR)

1500

Pile axial load (kN)

Raft settlement (mm)

0

-10

-20

1000

500

0

-30 -20

-10

0

10

0

20

5

10

(a) Raft settlement

20

25

(c) Pile axial load 10

1500 Unified Analysis (PLAXIS 3D) Fixed Boundary (YSPR) 1st CSM (YSPR) 2nd CSM (YSPR) 3rd CSM (YSPR)

1000

Unified Analysis (PLAXIS 3D) Fixed Boundary (Midas) 1st CSM (Midas) 2nd CSM (Midas) 3rd CSM (Midas)

0

Slab settlement (mm)

Raft bending moment (kN-m)

15

Pile number

Horizontal distance (m)

500

0

-500

-10

-20

-30

-40

-1000

-50

-1500 -20

-10

0

10

20

Horizontal distance (m)

(b) Raft bending moment

-15

-10

-5

0

5

10

15

Horizontal distance (m)

(d) Settlement of superstructure

Fig. 7. Computed response of superstructure and foundation behavior.

was due to the spacing of pile-column. When the pile-column spacing was zero (s = 5D), the computed settlement of superstructure was smaller than that from the others. In a situation where the pile-column spacing increased from 2 (s = 6D) to 5 (s = 2.5D), the settlement of the slab also increases. The reference design adopted by Yamashita et al. [27] involves the use of a pile below each column location. The present analyses have demonstrated that this solution fully satisfied the design requirements. Bending moment distributions from the same analysis conditions are illustrated in Fig. 10(b). In this figure, a positive value in the y-axis direction means sagging (concave) of the raft and a negative value means hogging (convex) of the raft. The increase in the pile spacing from 2.5 to 6 m resulted in a 74.5% decrease in the maximum sagging moment. On the other hand, with an increase in the pile spacing, the maximum hogging moment gradually increased. The axial forces of column are listed in Table 2. The maximum axial force is observed at the central column and it decreases significantly towards the outer columns. Axial forces of central column gradually reduce as pile spacing is increased and corresponding increase is found in the outer columns due to differential settlement. When differential settlement is small, less reduction of axial force at the side columns is observed. This is because of the transfer of axial force between central and outer columns due to differential settlements. Therefore, it could be said that redistribution of the forces in the column members is mainly

governed by the settlement of the foundation with varying of pile spacing. 4.2.2. Pile diameter Fig. 11(a) presents the settlement at the top of superstructure with varying a pile diameter (D). Three different pile diameters (D = 1.0, 1.5, and 2.0 m) are used. To clarify the effect of pile diameter, pile spacing was applied in same condition (s = 2.5 m). The increase in the pile diameter from 1.0 to 2.0 resulted in a 13% decrease in the maximum superstructure settlement. These results indicate an approximately linear decrease of the settlement with the pile diameter. The ratio of total pile cross sectional area to the plan area of the pile group increases (i.e. the ‘‘equivalent pier” becomes stiffer) and the foundation response becomes stiffer. Fig. 11(b) shows distribution of the computed settlement at the raft, based on the same analysis conditions. This curve demonstrates the 27% decreases in settlement with gradual increase of pile diameter. It should be noted that settlement of foundation induces a decrease in settlement of superstructure. Thus, settlement between superstructure and foundation should be thoroughly checked for a building design. Fig. 11(c) and (d) illustrate the distribution of bending moment in the slab and raft. In these figures, a positive value in the y-axis direction means sagging (concave) of the raft and a negative value means hogging (convex) moment. This indicates that the increase in the pile diameter under the same pile spacing has only a

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J. Ko et al. / Engineering Structures 143 (2017) 204–218 -10

-10 Fixed Boundary (YSPR)

-15

-15

Raft settlement (mm)

Raft settlement (mm)

3rd CSM (YSPR) Case 1 (YSPR) Case 2 (YSPR)

-20

-25

-20

-25

-30

-30 -20

-10

0

10

20

-20

-10

Horizontal distance (m)

0

10

20

Horizontal distance (m)

(a) Raft settlement 1500 3rd CSM (YSPR) Case 1 (YSPR) Case 2 (YSPR)

Fixed Boundary (YSPR)

1000

Raft bending moment (kN-m)

1000

500

0

-500

-1000

500

0

-500

-1000

-1500

-1500 -20

-10

0

10

20

-20

-10

Horizontal distance (m)

0

10

20

Horizontal distance (m)

(b) Raft bending moment 10

10

0

Slab settlement (mm)

Slab settlement (mm)

Fixed Boundary (Midas)

3rd CSM (Midas) Case 1 (Midas) Case 2 (Midas)

0

-10

-20

-10

-20

-30

-30

-40

-40 -15

-5

-10

5

0

10

15

-15

-5

-10

5

0

10

15

Horizontal distance (m)

Horizontal distance (m)

(c) Settlement of superstructure 10000

10000 3rd CSM Case 1 Case 2

Fixed Boundary

8000 node 41

6000 node 62 node 14

node 38

node 68

node 44

4000

node 71

Reaction force (kN)

8000

Reaction force (kN)

Raft bending moment (kN-m)

1500

node 41

6000 node 14

node 38

node 44

node 68

4000

node 71

2000

2000

0

0 0

9

18

27

36

45

54

63

72

81

0

9

18

Node number

27

36

45

54

Node number

(d) Reaction force at nodal point Fig. 8. Effect of boundary condition: stiff foundation.

63

72

81

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J. Ko et al. / Engineering Structures 143 (2017) 204–218

decrease 5.6%

(d)

(a)

decrease 20.3%

(b)

decrease 16.6%

(e)

32.22%

32.19%

30.08%

32.22%

32.20%

29.70%

tslab = 0.2m

stiff.slab = C35

tslab = 0.6m

Bcolumn = 0.6m

stiff.column = C35

Bcolumn = 1.0m

(f)

(c)

Fig. 9. Effect of superstructure stiffness.

marginal influence on the slab bending moment. On the other hand, the increase in the pile diameter from 1.0 to 2.0 m resulted in a 44% increase in the maximum sagging moment in the raft. Table 3 summarizes the axial forces in the column. The maximum axial force is observed at the central column and it decreases significantly towards the outer columns. Axial forces of central column gradually increase as pile diameter is increased and corresponding decrease is found in the outer columns due to differential settlement. In this analysis, an increase in the pile diameter below the column induced an increase in the axial force in the column. It is also found that the redistribution of the forces in the column members is mainly governed by the settlement of the foundation with varying of pile diameter.

4.2.3. Pile length The effects of pile length on the changes of superstructure and foundation behavior were investigated. Three different pile lengths (pile length, Lp = 10, 15, and 20 m) were considered in the analyses. As shown in Fig. 12(a), the magnitude of settlement is clearly related to the applied pile length and thus represents a significant reduction in settlement with increasing pile length. The increase in the pile length from 10 to 20 m resulted in a 28% decrease in the maximum settlement. Fig. 12(b) shows distribution of the computed settlement at the raft, based on the same analysis conditions. This figure also shows the effect of pile length on the foundation settlement.

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-20

Slab settlement (mm)

-25

-30

-35 s = 2.5D s = 5D s = 6D -40 -12

-6

0

12

6

Horizontal distance (m)

(a) Slab settlement

Slab bending moment (kN-m)

30

15

0

-15 s = 2.5D s = 5D s = 6D -30 -12

-6

0

6

12

Horizontal distance (m)

(b) Slab bending moment Fig. 10. Behavior of superstructure with pile spacing.

Fig. 12(c) and (d) illustrate the distribution of bending moment in the slab and raft. In these figures, a positive value in the y-axis direction means sagging (concave) of the raft and a negative value means hogging (convex) moment. This indicates that the increase

in the pile length has only a marginal influence on the slab bending moment. As expected, the increase in the pile length from 10 to 20 m resulted in a 22.6% decrease in the maximum hogging moment. However, with an increase in the pile length, the maximum sagging moment gradually increased. It can be concluded that the settlement behavior of superstructure is heavily dependent on foundation stiffness with varying spacing, diameter and length of pile. Relatively small effects were observed in the internal force of superstructure. Table 4 shows the axial forces of column. The maximum axial force is observed at the central column under a pile length Lp of 20 m and it decreases significantly towards the outer columns in all cases. Axial forces of central column gradually increase as pile length is increased and corresponding decrease is found in the outer columns due to differential settlement. Ideally more reduction of axial force with the increase of differential settlement under a same pile length since less load transfer will occur. These results suggest the importance of modeling the foundation and sub-soils with the superstructure in order to considering superstructurefoundation interaction. 4.2.4. Raft stiffness Based on the literature [28,29], the thickness of the raft foundation is usually determined by punching shear around column, contact pressure, foundation settlement, bending deflection, and raft and building bending moment. In order to quantify the change of superstructure behavior due to raft stiffness, four different raft stiffness (thickness of raft, tr = 0.5, 1.0, 4.0 m, and Young’s modulus of raft, Er = 27,277 MPa = C35) were considered. Fig. 13(a) shows the changes in slab settlement computed in this analysis. The results demonstrate that changes in superstructure settlement occurred when the stiffness of foundation changed. As shown in Fig. 13(b), the reduction in foundation settlement due to increase in the raft stiffness led to the reduction of settlement in the superstructure. It has been shown that for a relatively rigid raft (tr = 4 m), the distribution of settlement is more uniform than that for a flexible raft (tr = 0.5 m). The settlement behavior of the superstructure is heavily dependent on foundation stiffness with varying raft thickness and elastic modulus, as explained in previous section. Fig. 13(c) shows the development of bending moment in the slab. However, the computed bending moments in the slab were not comparable with changes in raft stiffness. On the other hand, a linear relationship was observed between the raft stiffness and raft bending moment. As shown in Fig. 13(d), the increase in the raft thickness from 0.5 to 4 m resulted in a 73.1% increase in the maximum hogging moment. These trends are very similar to the results from the previous work although the soil condition was considerably different. Table 5 shows the axial forces of column. The maximum axial force is observed at the central column under a raft thickness tr of 4 m. And axial forces of outer columns also increase significantly

Table 2 Axial force in columns with pile spacing. Pile spacing

Axial force of column (kN) Center

Corner

Side

2.5D

6839

5D

6575

6D

6516

2540 (62.8%) 2584 (60.7%) 2564 (60.7%)

4013 (41.3%) 4062 (38.2%) 4083 (37.3%)

Note: dc-s is center-side differential settlement. dc-c is center-corner differential settlement.

dc-s (mm)

dc-c (mm)

7

14

8

14

10

15

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J. Ko et al. / Engineering Structures 143 (2017) 204–218

30

Slab bending moment (kN-m)

Slab settlement (mm)

-20

-25

-30

-35 D = 1.0m D = 1.5m D = 2.0m

-40

15

0

-15 D = 1.0m D = 1.5m D = 2.0m

-30 -12

-6

0

12

6

-12

Horizontal distance (m)

0

12

6

Horizontal distance (m)

(a) Slab settlement

(c) Slab bending moment

-5

500

Raft bending moment (kN-m)

Raft settlement (mm)

-6

-10

-15

-20 D = 1.0m D = 1.5m D = 2.0m

-25

0

-500

-1000 D = 1.0m D = 1.5m D = 2.0m

-1500 -18

-9

0

9

18

-18

Horizontal distance (m)

-9

0

9

18

Horizontal distance (m)

(b) Raft settlement

(d) Raft bending moment

Fig. 11. Behavior of superstructure and piled raft foundation with pile diameters.

Table 3 Axial force in columns with pile diameters. Pile diameter

Axial force of column (kN) Center

Corner

Side

D = 1.0 m

6839

D = 1.5 m

6907

D = 2.0 m

6942

2540 (62.8%) 2532 (63.3%) 2528 (63.6%)

4013 (41.3%) 4003 (42.0%) 3999 (42.4%)

with increasing raft stiffness. Results showed that the stiffer the bearing layer or foundation, the more increase in column axial force at given analysis condition.

6. Conclusions The main objective of this study was to propose the new interactive design methodology for superstructure-foundation-soil system. A series of numerical analyses were conducted to investigate the effects of superstructure and foundation stiffness on behavior of building structure. The main characteristic of these analyses was to consider superstructure-foundation interaction. The validation of the proposed design method against 3D FE analysis is also

dc-s (mm)

dc-c (mm)

7

14

6

12

4

9

discussed. Based on the findings of this study, the following conclusions can be drawn: (1) An analysis using the conventional fixed boundary method produces a smaller foundation settlement than the results obtained based on the proposed method. From the results of the comparative studies, it is shown that the distribution pattern of the internal force and settlement of entire structure is significantly dominated by boundary condition representing a foundation-soil interaction. Therefore, the conventional fixed boundary may not reflect the nature of the soil-structure interaction for the general case, and thus it requires validation before being used in engineering practice.

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-15

30

Slab bending moment (kN-m)

Slab settlement (mm)

-20

-25

-30

-35 L = 10m L = 15m L = 20m

-40

15

0

-15 L = 10m L = 15m L = 20m

-30 -12

-6

0

12

6

-12

Horizontal distance (m)

0

12

6

Horizontal distance (m)

(a) Slab settlement

(c) Slab bending moment

0

1000

Raft bending moment (kN-m)

-5

Raft settlement (mm)

-6

-10

-15

-20 L = 10m L = 15m L = 20m

-25

500

0

-500

-1000 L = 10m L = 15m L = 20m

-1500 -18

-9

0

9

18

-18

-9

0

9

Horizontal distance (m)

Horizontal distance (m)

(b) Raft settlement

(d) Raft bending moment

18

Fig. 12. Behavior of superstructure and piled raft foundation with pile lengths.

Table 4 Axial force in columns with pile lengths. Pile length

Axial force of column (kN) Center

Corner

Side

Lp = 10 m

6839

Lp = 15 m

7057

Lp = 20 m

7329

2540 (62.8%) 2486 (64.8%) 2418 (67.0%)

4013 (41.3%) 4012 (43.1%) 4011 (45.3%)

(2) Additionally, it is found that the iterative and interactive analysis gave similar results of settlement and raft bending moment compared with finite element analysis. And it is also found that the interactive analysis method considering superstructure and foundation conditions is capable of predicting reasonably well the behavior of entire building structures. It can be effectively used to perform the design of a superstructure-piled raft foundation system. (3) From the parametric studies, it is shown that the effect of superstructure stiffness affects the behavior of the foundation. This can be explained by noting that the reason for

dc-s (mm)

dc-c (mm)

7

14

3

3

2

2

reductions in settlement and load sharing of pile with increasing stiffness of superstructure. Furthermore, the settlement behavior and force redistribution of superstructure is heavily dependent on foundation stiffness with varying spacing, diameter, length of pile and raft stiffness. Relatively small effects were observed in the internal force of superstructure. (4) The interaction of superstructure, its foundation and the subsoil may have important effects on the behavior of each component as well as on the overall building system. Thus, interaction effect between superstructure and foundation should be thoroughly checked for a design practice.

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30

Slab bending moment (kN-m)

Slab settlement (mm)

-10

-20

-30

-40

tr = 1m tr = 4m tr = 1m (C35) tr = 0.5m

-50

15

0

-15

tr = 1m tr = 4m tr = 1m (C35) tr = 0.5m

-30 -12

-6

0

6

12

-12

Horizontal distance (m)

-6

(a) Slab settlement

12

6

(c) Slab bending moment

-5

1500

Raft bending moment (kN-m)

-10

Raft settlement (mm)

0

Horizontal distance (m)

-15

-20

tr = 1m tr = 4m tr = 1m (C35) tr = 0.5m

-25

-30

0

-1500

-3000

tr = 1m tr = 4m tr = 1m (C35) tr = 0.5m

-4500 -18

-9

0

9

18

Horizontal distance (m)

-18

-9

0

9

18

Horizontal distance (m)

(b) Raft settlement

(d) Raft bending moment

Fig. 13. Behavior of superstructure and piled raft foundation with raft stiffness.

Table 5 Axial force in columns with raft stiffness. Raft stiffness

Axial force of column (kN) Center

Corner

Side

tr = 0.5 m

6927

tr = 1 m

6839

Er = C35

6839

tr = 4 m

7032

2637 (61.9%) 2540 (62.8%) 2538 (62.9%) 2405 (65.8%)

3894 (43.8%) 4013 (41.3%) 4015 (41.3%) 4098 (41.7%)

Acknowledgements The authors acknowledge support in this research for the National Research Foundation of Korea (NRF) (Grant Nos. 20110030040 and 2016R1A6A3A03010454). References [1] Cooke RW. Piled raft foundations on stiff clays: a contribution to design philosophy. Geotechnique 1986;36(2):169–203. [2] Katzenbach R, Arslan U, Moormann C. Piled raft foundations projects in Germany. In: Hemsley JA, editor. Design applications of raft foundations. Thomas Telford; 2000. p. 323–92.

dc-s (mm)

dc-c (mm)

12

18

7

14

6

14

1

2

[3] Poulos HG. Piled-raft foundation; design and applications. Geotechnique 2001;51(2):95–113. [4] Reul O, Randolph MF. Piled rafts in overconsolidated clay-comparison of insitu measurements and numerical analyses. Geotechnique 2003;53(3):301–15. [5] Jeong SS, Cho JY, Lim HS, Lee JH. Nonlinear 3D coupled analysis of piled raft foundations for high-rise building. In: Proceedings of the IS-Kanazawa. Kanazawa, Japan; 2012. p. 461–6. [6] Jeong SS, Cho JY. Proposed nonlinear 3-D analytical method for piled raft foundations. Comput Geotech 2014;59:112–26. [7] Mayerhof G. Some recent foundation research and its application to design. Struct Eng 1953;31(6):151–67. [8] Lee IK, Brown PT. Structures and foundation interaction analysis. J Struct Div ASCE 1972;11:2413–31. [9] Fraser RA, Wardle LJ. Numerical analysis of rectangular rafts on layered foundations. Geotechnique 1976;26(4):613–30.

218

J. Ko et al. / Engineering Structures 143 (2017) 204–218

[10] Viladkar MN, Noorzaei J, Godbole PN. Interactive analysis of a space frameraft-soil system considering soil nonlinearity. Comput Struct 1994;51:343–56. [11] Hora M. Nonlinear interaction analysis of infilled building frame-soil system. J Struct Eng 2006;33(4):309–18. [12] Agrawal R, Hora MS. Nonlinear interaction behaviour of plane frame-layered soil system subjected to seismic loading. Int J Struct Eng Mech 2012;11 (6):711–34. [13] Brown PT, Yu SKR. Load sequence and structure-foundation interaction. J Struct Eng 1986;112(3):481–8. [14] Dutta SC, Roy R. A critical review on idealization and modeling for interaction among soil-foundation-structure system. Comput Struct 2002;80:1579–94. [15] Nataralan K, Vidivelli B. Effect of column spacing on the behavior of frame-raft and soil systems. J Appl Sci 2009;9(20):3629–40. [16] PLAXIS Inc. PLAXIS 3D foundation user manual, version 2.0; 2008. [17] MIDAS Information Technology. MIDAS-CIVIL online manual. Korea; 2011. Available from . [18] McVay MC, Townsend FC, Bloomquist DG, O’Brien M, Caliendo JA. Numerical analysis of vertically loaded pile groups. In: Proceedings of found eng: current principles and practices. ASCE. New York; 1989. p. 675–90. [19] O’Neill MW, Murchison JM. An evaluation of p-y relationship in sands. A report PRAC82-41-1. The American Petroleum Institute; 1983. [20] Won JO, Jeong SS, Lee JH, Jang SY. Nonlinear three-dimensional analysis of pile group supported columns considering pile cap flexibility. Comput Geotech 2006;33:355–70.

[21] Brown DA, Reese LC, O’Neill MW. Cyclic lateral loading of a large-scale pile group. J Geotech Eng 1987;113(11):1326–43. [22] Lieng JT. Behavior of laterally loaded piles in sand-large scale model test [Ph.D. thesis]. Norwegian Institute of Technology; 1988. [23] O’Neill MW. Group action in offshore piles. In: Proceedings of specialty conference on geotechnical engineering in offshore practice, ASCE. Austin, TX; 1983. p. 25–64. [24] Vesic AS. Experiments with instrumented pile groups in sand. In: Deep foundation, ASTM, special technical publication, vol. 444; 1969. p. 172–222. [25] Jeong SS, Seo DH, Kim YH. Numerical analysis of passive pile groups in offshore soft deposits. Comput Geotech 2009;36:1164–75. [26] Katzenbach R, Moormann C. Design of axially loaded piles and pile groups in Germany. In: Proceedings of actual practice and recent research results. Design of axially loaded piles European practice, ISSMFE- ERTC3. Brussels; 1997. p. 177–201. [27] Yamashita K, Yamada T, Kakurai M. Simplified method for analyzing piled raft foundations. In: Proceedings of 3rd international geotechnical seminar on deep foundation on bored and auger piles. Ghent; 1998. p. 457–64. [28] Horikoshi K, Randolph MF. Centrifuge modelling of piled raft foundations on clay. Geotechnique 1996;46(4):741–52. [29] Lee JH, Kim YH, Jeong SS. Three-dimensional analysis of bearing behavior of piled raft on soft clay. Comput Geotech 2010;37:103–14.