MÓNG BÈ TRÊN NỀN CỌC

Đây là tải liệu nguyên cứu khoa học được thực hiện bởi một nhóm sinh viên dưới sự hướng dẫn của tiến sĩ, mặc dù đã cố gắng hết sức nhưng không trách khỏi những sai sot, mong các bạn có những góp ý để mình có thể hoàn chỉnh đề tài này một cách tốt nhất, đề tài này nguyên cứu về sự làm việc của móng bè cọc, sự tương tác giữa bè, cọc, và đất nền, các sự phân tích, tính toán và thiết kế,và cuối cùng là ứng dụng của nó, hi vòng với tài liệu này sẽ đem lại cho các bạn cái nhìn tổng quan và tốt nhất về móng bè cọc (pile raft foundation)

PILED RAFT FOUNDATIONS

Be studied by the group of students include: Junior;Thai Binh Duong, Ngoc Phu Nguyen, Thanh Binh Trinh, Quoc Tuan Luu, Van Thao Nguyen

Be supported by PhD Si Hung Nguyen

INDEX

ABSTRACT

1 INTRODUCTION 12

2 SYMBOL TABLE 23

3 DEFINITION

4 ADVANTAGES OF PILED RAFT FOUNDATIONS

5 BACKGROUND OF ANALYSIS

5.1 Interactions in piled raft foundation

5.2 Review of design methods for piled raft foundation

5.2.1 Simplified method – Randolph [6] method 5.2.2 Approximate method – plate on springs approach [1]

5.2.3 More sophisticated computer-based methods 5.2.3.1 Hain and Lee [3] method

5.2.3.2 Reul and Randolph [16] method

6 PROPOSED DESIGN METHOD:

6.1 Modelling of piled raft foundations

6.2 Pile–soil–pile interaction factor

6.3 Pile–soil–raft interaction factor

6.4 Analysis procedure using SAP 2000

7 CENTRIFUGE TESTING PROGRAM

7.1 Tested soil

7.2 Test program and models

7.3 Test procedures

8 RESULTS AND DISCUSSION

8.1 Single pile tests

8.2 Raft tests

8.3 Piled raft tests

8.4 Comparison of piled raft behaviour between centrifuge test, proposed method and Plaxis 3D analysis

8.5 Comparison of bending moment between proposed method and Plaxis 3D analysi

8.6 Comparison of individual piles behaviour between centrifuge test, proposed method and Plaxis 3D analysis

9 APPLICATION OF PILED RAFT FOUNDATIONS

9.1 Ground Conditions and Geotechnical Model

9.2 Foundation Layout

9.3 Overall Stability

9.4 Predicted Performance Under Vertical Loading

9.4.1 Vertical loading 9.4.2 Horizontal loading

10 CONCLUSIONS

11.REFERENCES

ABSTRACT: Piled raft foundations are increasingly being recognised as an economical

and effective foundation system for tall buildings The aim of this essay is to describe a unite element analysis of deep foundations piled and mainly piled raft foundations and sets out some principles of design for such foundations, including design for the geotechnical ultimate limit state, the structural ultimate limit state and the serviceability limit state The advantages of using a piled raft will then be described with respect to two cases: a small pile group subjected to lateral loading Attention will be focussed on the improvement in the foundation performance due to the raft being in contact with, and embedded within, the soil.A basic parametric study is restly presented to determine the incluence of mesh discretisation, of materials - loose or dense sand -, of dilatancy and interface elements Then the behavior of piled raft foundations is analysed in more details using partial axisymmetric models of one pile-raft

1 INTRODUCTION

In traditional foundation design, it is customary to consider first the use of shallow foundation such as a raft (possibly after some ground-improvement methodology performed) If it is not adequate, deep foundation such as a fully piled foundation is used instead In the last few decade, an alternative solution has been designed: piled raft foundation Unlike the conventional piled foundation design in which the piles are designed to carry the majority of the load, the design of a piled raft foundation allows the load to be shared between the raft and piles and it is necessary to take the complex soil-struture interaction effects into account

The concept of piled raft foundation was firstly proposed by Davis and Poulos in

1972 and is now used extensively in Europe, particularly for supporting the load of high buildings or towers The favorable application of piled raft occurs when the raft has adequate loading capacities, but the settlement or differential settlement exceed allowable values In this case, the primary purpose of the pile is to act as settlement reducer

2 SYMBOL TABLE

Numbe

r

1 C resistance property for SLS

8 Ftot,k sum of characteristic values of all actions MN

10 i index for an action

22 Rraft,k characteristic value of the resistance of a MN

23 Rs,k(s) characteristic value of the skin friction resistance of a

pile

MN

3 DEFINITION

The Combined Pile Raft Foundation (CPRF) is a geotechnical composite construction that combines the bearing effect of both foundation elements raft and piles by taking into account interactions between the foundation elements and the subsoil shown in Figure 1.1

The characteristic value of the total resistance Rtot,k (s) of the CPRF depends on the settlement s of the foundation and consists of the sum of the characteristic pile resistances

resistance results from the integration of the settlement dependant contact pressure ( , , )s x y

σ in the ground plan area A of the raft.

, ( ) ( , , )

raft k

R s = ∫∫ σ s x y dxdy

The bearing behaviour of the CPRF is described by the pile craft coeficient αpr

which is defined by the ratio between the sum of the characteristic pile resistanses

m

pile k j j

The pile raft coefficient varies between αpr = 0 (spread foundation) and αpr = 1

(pure pile foundation) Figure 1.2 shows a qualitative example of the dependence between the pile raft coefficient αprand the settlement of a CPRF spr

related to the settlement of a spread foundation Ssf with equal ground plan and equal loading

The pile raft coefficient αprdepends on the stress level and on the settlement of the

CPRF

4 ADVANTAGES OF PILED RAFT FOUNDATIONS

- Piled raft foundations utilize piled support for control of settlements with piles providing most of the stiffness at serviceability loads, and the raft element providing additional capacity at ultimate loading

- Consequently, it is generally possible to reduce the required number of piles when the raft provides this additional capacity In addition, the raft can provide redundancy to the piles, for example, if there are one or more defective or weaker piles, or if some of the piles encounter karstic conditions in the subsoil Under such circumstances, the presence

of the raft allows some measure of re-distribution of the load from the affected piles to those that are not affected, and thus reduces the potential influence of pile “weakness” on the foundation performance

- Another feature of piled rafts, and one that is rarely if ever allowed for, is that the pressure applied from the raft on to the soil can increase the lateral stress between the underlying piles and the soil, and thus can increase the ultimate load capacity of a pile as compared to free-standing piles (Katzenbach et al., 1998)

- A geotechnical assessment for design of such a foundation system therefore needs

to consider not only the capacity of the pile elements and the raft elements, but their combined capacity and interaction under serviceability loading

- The most effective application of piled rafts occurs when the raft can provide adequate load capacity, but the settlement and/or differential settlements of the raft alone exceed the allowable values

- Poulos (2001) has examined a number of idealized soil profiles, and found that the following situations may be favourable:

• Soil profiles consisting of relatively stiff clays

• Soil profiles consisting of relatively dense sands

In both circumstances, the raft can provide a significant proportion of the required load capacity and stiffness, with the piles acting to “boost” the performance of the foundation, rather than providing the major means of support.

Figure 2: Combined Pile Raft Foundations

5 BACKGROUND OF ANALYSIS

5.1 Interactions in piled raft foundation

The behaviour of a piled raft foundation is influenced by the interactions between the piles, raft and soil, and consequently interaction factors have been widely adopted for the prediction of the response of a piled raft In reality, there are two basic interactions, pile–soil–pile interaction and pile–soil–raft interaction, as shown in Figure 3 The pile–soil–pile interaction is defined as the additional settlement of a pile caused by an adjacent loaded pile, and the pile–soil–raft interaction is defined as superposing the displacement fields of a raft caused by a pile supporting the raft The pile–soil–pile interaction is an important consideration in the analysis of pile groups and piled rafts, and the pile–soil–raft interaction is necessary for analysing piled rafts Several approaches for determination of these two interaction factors are tabulated in Table 1

Figure 3 The interactions in a piled raft foundation system.

Table 1 Approaches for determining interaction factors

(α)

w w

α = ∆ – Considering the additional settlement of a pile (ΔW)

caused by an adjacent pile– The contribution of the adjacent pile was not presented clearly in the equation

Poulos [9] Pile–pile

interaction

(α) ∆ wk = ω1∑n j i= Qj kjα – Considering the additional settlement of a pile caused

by adjacent piles in the term

of axial loads of adjacent

piles Q j

Randolph

[11]

ln 1

2 ln

r p rp

m p

r r r r

– Not considering the change

in soil stiffness along the pile and the flexibility of the raft

considering soil stiffness

is ρ which is the degree of

homogeneity of the soil

r p rp

m p

r r r r

– Considering the soil

stiffness along the pile (E sav),

at pile tip (E sb) and pile head

(E sl)– Not considering the flexibility of the raft

Clancy and

Randolph

[2]

Pile–raft interaction

– Can consider the flexibility

of the raft

Nomenclature:

Δw k = additional of pile k caused by other piles

ω1 = displacement due to unit load of pile k and pile j

Q j = the load on pile j; α kj = interaction factor for pile k due to any other pile j within the

group

α rp = interaction factor between a pile and a raft;r r = the diameter of the raft

r p = the diameter of the pile

ρ = the degree of homogeneity of the soil

L = the length of the pile

υ s = Poisson ratio of soil

E sl = soil Young’s modulus at level of pile tip

E sb = soil Young’s modulus of bearing stratum below pile tip

E sav = average soil Young’s modulus along pile shaft

P p = total load carried by pile group in combined foundation

P r = total load carried by raft in combined foundation

k p = overall stiffness of pile group in isolation

k r = overall stiffness of raft in isolation

w pr = settlement of a piled raft foundation

The approach of Poulos and Davis [4] for obtaining the pile–pile interaction factor

considers a pair of vertical piles spaced at (S) and embedded in a horizontally layered soil

The formulation is based on the additional settlement of a pile under the interaction of the other pile Poulos [9] proposed another approach that can be used for calculating the additional settlement of a pile caused by a pile group surrounding it by superposing additional settlement caused by each pile The difference between these two approaches is that in the later method the additional settlement of a pile is a function of the forces of other piles in the pile group

In the approach developed by Clancy and Randolph [2], the interaction factor of a

pile to a raft (α rp) is calculated based on the additional settlement of a circular rigid raft caused by its supporting pile This formulation, however, does not consider the change in soil stiffness along the pile, and therefore Randolph [6]proposed a modified version of his earlier formulation by considering the stiffness of soil at the pile head and the pile tip and

along the pile shaft Nevertheless, neither of Randolph’s approaches considers strength characteristics of soil (e.g., friction angle, cohesion) or the flexibility of the raft.

The approach of Clancy and Randolph [2] is used to calculate α rp when the settlement of the piled raft and the load transmitted to the piles and to the raft are known The advantage of this method is that it can determine the interaction of the pile group to the raft The difficulty of estimating the load transmitted to the pile group and the raft, however, hinders practical use of this formulation

5.2 Review of design methods for piled raft foundation

5.2.1 Simplified method – Randolph [6] method

This method is based on calculation of the total stiffness of the piled raft by means

of the stiffness of the pile group and the stiffness of an unpiled raft in isolation and the interaction between one pile with the region of the raft surrounding the pile Thus, the settlement of the foundation and the ratio of transmitted load to the raft can be calculated

This method can obtain the behaviour of the piled raft in the form of a tri-linear load–settlement curve [ 10] ) Nevertheless, this method only considers the interaction between the piles and the raft and not the interaction between piles in the pile group The application, however, is quiet easy for hand calculation, as the method is fairly straightforward

5.2.2 Approximate method – plate on springs approach [1]

This method is based on the elastic theory and interactions between the components

of the piled raft foundation Poulos [1] modelled a piled raft in the form of a plate supported by springs representing piles This method is implemented via the program GARP (Geotechnical Analysis of Raft with Piles) which allows consideration of the layered soil profile to failure behaviour and the effect of piles reaching their ultimate capacity Four interactions were considered in this program, interaction between elements

of the raft, interaction between piles, influence of the raft on the piles, and influence of the piles on the raft

The remarkable advantage of this method is that it can obtain the distribution of the stress inside the raft and can consider the ultimate capacity of piles Nevertheless, the behaviour of piles under the transmitted load depends on the soil model, with many parameters required when using the GARP program This can cause that the behaviour of piles deviate from the real behaviour if the soil is not modelled reliably Consequently, the obtained settlement of the foundation will inevitably include some errors Moreover, the based on the elastic theory of the analysis is another limitation, and its complexity also prohibits its application for design (it can be only applied by using the GARP program)

5.2.3 More sophisticated computer-based methods

5.2.3.1 Hain and Lee [3] method

Hain and Lee [3] analysed two components, soil and piles, to solve the problem of a piled raft, where the soil elements and the pile elements were arranged compatibly with the raft In the model, the soil surface was meshed into a number of square or rectangular 4-node finite elements The nodes located at the piles are called pile nodes and the remaining nodes are referred to as soil nodes The pile–pile interaction and pile–soil interaction are used to calculate the vertical settlement of each node The total supporting soil–pile group stiffness can then be obtained and the settlement and stress on the raft are estimated This analysis rigorously considers the interaction between soil and piles and solves many problems such as flexibility of the raft, ultimate capacity of piles Nevertheless, this method also has several limitations First, if the raft consists of a series of bending plates, the number of soil nodes will be very high, and the calculation cost is consequently large

Conversely, if the soil nodes are reduced, the number of bending plates is decreased, and the calculation results, especially the internal stress of the raft, will be less accurate In addition, because the effect of the raft in the interactions is not considered and the pile

stiffness is only correlated with Young’s modulus of the pile (E p) and Young’s modulus of

the soil mass (E s ) (K p = E p /E s), the accuracy of the results will be further worsened

5.2.3.2 Reul and Randolph [16] method

This method bases totally on the finite element method The authors used Abaqus program to simulate piled rafts and proposed that modelling the soil and foundation by finite elements can allow the most rigorous treatment of the soil–structure interaction This method has several remarkable advantages

First, the soil can be modelled as a multiphase medium which consists of three components solid phase (grains), liquid phase (pore water) and gaseous phase (pore air), so the geotechnical characteristics of soil can be considered effectively

Second, the nonlinear material behaviour of the soil can be taken in to account with the elastoplastic cap model

Third, the plastic behaviour of soil can be considered by the nonassociated flow

potential (G s ) of the shear surface and the associated flow potential (G c) of the cap

Fourth, the contact between structure and soil and the various types of applied load can be simulated Nevertheless, this method still has some problems In modelling pile–soil interaction, the interface element was not used so the method could not consider the relative motion between the pile elements and soil elements Moreover, the calculating time for obtaining a solution is long and Abaqus program is not easy for practicing engineers to use

In general, the existing methods can be employed to solve the piled raft problem fairly completely However, there exist some limitations as mentioned above, especially with application to engineering work, because they are quite complex (i.e., the approximate methods and more rigorous computer-based methods) This paper hence proposes an analysis method to solve several problems, including:

• Simplification for ease of application for practicing engineers

• Solving piled raft problem without any sophisticated finite element model for soil and helping practicing engineers control well the mechanism of piled rafts

• Using a combination of the single pile and unpiled raft behaviours to estimate the behaviour of the piled raft fairly exactly

• Obtaining nonlinear behaviour of a piled raft foundation by using the nonlinear behaviour of the single pile

• Estimation of the settlement of the foundation and the distribution of the bending moment in the raft with reasonable accuracy

6 PROPOSED DESIGN METHOD

6.1 Modelling of piled raft foundations

In this study, the raft is modelled as a series of bending plates, each pile is modelled

as a pile spring at the pile’s position, and the relative raft–soil stiffness is modelled by means of raft springs with the quantity and the position decided by the designer, as shown

in Figure 2 However, in order to solve the stiffness of the pile springs, it is convenient to assume that vertical forces are only transmitted from the raft to the head of a pile[3] This assumption involves neglecting the lateral pile head force and the lateral pile movement In general, the total vertical loads are considerably greater than the total lateral loads, so the lateral movements of the raft are small In the case of large lateral loads subjected to the raft, the batter piles will be used and can be modelled as lateral pile springs However, this

problem is not considered in the scope of this paper Then, the vertical displacement of a pile is given by:

where w pK is the vertical displacement of the pile K; δ 1J , δ 1K are the displacement due to the

unit load of the piles J and K, respectively, which can be derived from the load–settlement curve of a single pile having the same size; P pJ is the load on pile J; α KJ is the pile–soil–pile

interaction factor of pile J on pile K; P pK is the load on pile K; and n is the number of piles.

Figure 2 Model of piled raft foundation (a) A piled raft foundation (b) Modelling for

proposed design method

The stiffness of pile spring K is given by:

(2) w

where K pK is the stiffness of pile spring K

To solve the stiffness of raft springs, the lateral force and lateral movement are also neglected The vertical displacement of a raft spring is given by:

w rM is the vertical displacement of the raft spring M without pile interactions;

- ρ 1M is the displacement of the raft springM due to the unit load, which can be calculated

from elastic theory or derived from the load–settlement curve of an unpiled raft having the same size as the raft of piled raft

Q M is the load on the raft spring M; and β KM is the pile–soil–raft interaction factor of

pile K for the raft spring M.

The stiffness of the raft spring M is given by:

(4) w

where K rM is the stiffness of the raft spring M

6.2 Pile–soil–pile interaction factor

The pile–soil–pile interaction factor, α, is used to calculate the additional settlement

of a pile caused by adjacent piles In the case of two piles K and J, additional settlement for pile K can be written as follows:

JQJ

α

ω ∆

=

where α KJ is the interaction factor of pile J on pile K

Δw k is the additional settlement of pile K caused by pile J

ω 1J is the settlement due to a unit load of pile J; Q J is the load on pile J

The interaction factor between pile K and pile J can be defined as follows:

additional displacement of pile K caused by unit load on by J

displacement of pile J due to unit load (7)

KJ

α =

In this paper, the finite element method (FEM) via Plaxis 3D Foundation program is employed to obtain this factor The input parameters are presented in Table 2 The soil used is silica sand with two different relative densities, 70% and 40% The parameters of soil are chosen at the level of depth about two-third of the pile length from the pile head The characteristics of the tested soil taken from the drained triaxial tests are presented in detail in the tested soil section In the FEM, the soil is considered as a hardening model of the case of hyperbolic relationship for standard drained triaxial test and the dilatancy of the sand is also considered [15]) The piles are represented by embedded pile elements The embedded pile beam can be placed arbitrarily in a soil volume element, and at the position

of the beam element nodes virtual nodes are created in the soil volume element from the element shape functions Then, the special interface forms a connection between the beam element nodes and these virtual nodes, and thus with all nodes of the soil volume element The interaction with soil at the pile skin and at the pile foot is described by means of embedded interface elements These interface elements are based on 3-node line element with a pairs of nodes instead of single nodes One node of each pair belongs to the beam element, whereas the other (virtual) node is a point in the 15-node wedge element belonging to soil element The skin interaction is taken into account by the development of skin traction and the foot interaction is considered by the development of the foot force

Table 2 Plaxis 3D input parameters

Soil material L/d = 25 and D r = 70%

Dry density (γ d) 15.13 kN/m3

Secant Young’s modulus (E50) 50 MPa

Confinement pressure 150 kPa

settlement was calculated by the difference in the settlements between the case of a single pile and the case of two piles Using Eq (7), the pile–soil–pile interaction for the given

pile spacing can be obtained In this paper, the number of pile spacing (up to S/d = 16) was

selected corresponding with the piled raft models of centrifuge tests Thus, a large value of pile spacing is not necessary for this study The pile–soil–pile interaction curve was constructed as shown in Figure 3

Figure 3 Pile–soil–pile interaction factors for homogeneous soil layer.

(a) Comparison of interaction factors between FEM result obtained for Silica

sand D r = 70%, υ = 0.25 with the result of Poulos and Davis [4]K = 1000, υ = 0.5 (b) Comparison of interaction factors between dense and loose sands in same L/D ratio (c) Comparison of interaction factors between two different L/D ratios in dense sand.

Figure 3a shows a comparison between the FEM results obtained for silica sand

(D r = 70% and υ = 0.25) and the results of Poulos and Davis [4] (overall stiffness K = 1000 and Poisson’s ratio υ = 0.5) in the case of a length–diameter ratio L/d = 25 General

agreement in the trend that the interaction factor decreases with increasing pile spacing between the two results is observed The difference in the values originates from the different Poisson’s ratio, type of soil, and the analysis method, but is still acceptable Poulos and Davis [4]suggested the pile–soil–pile interaction curves for various types of soil and pile lengths based on an elastic continuum analysis These curves can also be used

to obtain the pile–soil–pile interaction factor in an alternative way if the FEM is unavailable

Figure 3b and c shows pile–soil–pile interaction factors, obtained by the finite

element method, as a function of the pile spacing to diameter ratio (S/d) When this ratio increases, the interaction factor decreases This means that when the distance (S) is small, the additional settlement of a pile caused by the other pile is large but when (S) is large, the

additional settlement becomes small and the behaviour of a pile more closely approximates the behaviour of a single pile The interaction factors are also dependent on the density of

soil and the ratio between the pile length and the diameter of the pile (L/d) It simply

explains in prose the form of the interaction equation that the coefficient α depends on the displacement of pile J due to unit load so when the relative density of soil decreases the settlement due to unit load of pile J increases and thus it makes the value of α reduces In the case of increasing pile length, when the length of pile J increases the capacity of this

pile develops making the settlement due to unit load of this pile lessens and thus the value

of α increases Figure 3 presents a comparison of pile–pile interaction curves for two states of silica sand, dense and loose states

6.3 Pile–soil–raft interaction factor

The FEM was employed to construct the pile–soil–raft interaction curve The soil same with the soil used to determine the pile–soil–pile interaction was represented For the

given pile spacing, to derive the pile soil raft interaction factor, β, it was necessary to

prepare two separate models The first model was a piled raft (four piles with the given pile spacing) and the second model was an unpiled raft having raft with the same size as that considered in the piled raft model as shown in Figure 4 The additional settlement

(ΔW) of the raft caused by piles was obtained The applied load for the unpiled raft model

equals the transmitted load to the raft in the piled raft model The additional settlement equals the difference in the settlement values for the raft between the two models The

additional settlement caused by a pile for the raft equals ΔW divided by the number of piles The pile–soil–raft interaction coefficient, β, is then determined as follows:

additional displacement of the raft caused by a pile

(8) displacement of the unpiled raft

β =

Figure 4 Model scheme for obtaining pile–soil–raft interaction

The pile–soil–raft interaction curves were constructed as shown in Figure 5 Figure

5a provides a comparison of pile–soil–raft interaction factors between the results obtained

by the FEM and by the equation from Randolph [6] The curve constructed by Randolph’s

approach was calculated with a Young’s modulus of soil at the pile head E sl = 8.61 MPa,

Young’s modulus at the bearing stratum below the pile tip E sb = 74.75 MPa, the average

Young’s modulus along pile shaft E sav = 46.63 MPa, and Poisson’s ratio υ = 0.25 (these

parameters are derived from silica sand in a dense state as used for the study in this paper)

It can be seen that there is good agreement between the two set of results, both in general trends and in numerical values This indicates that the factor can also be determined by the method of Randolph [6] in an alternative way if the FEM is unavailable

Figure 5 Pile–soil–raft interaction factors for a square raft in homogeneous soil.(a) Comparison of interaction factors between FEM and Randolph [6] in dense sand

(b) Comparison of interaction factors between dense and loose sands in same L/D ratio (c) Comparison of interaction factors between two different L/D ratios in dense sand.

Figure 5b and c shows the pile–raft interaction factor, obtained from finite element

method, as a function of the ratio S/d When the distance (S) increases, the interaction

factors decrease The interaction curves tend to converge to a value of about 10% when the

distance (S) becomes large In comparison, the interaction curve of L/d = 25 is higher than that of L/d = 16.7 This illustrates that as the length of the pile and the soil stiffness

respectively increase, the interaction effect between the pile and one point of the raft

becomes accordingly higher The reason is that the coefficient β depends on the

displacement of the unpiled raft (according to Eq.(8)) When the relative density of soil increases the capacity of the unpiled raft develops so its settlement reduces, and thus the

value of β increases In the case of increasing pile length, the interaction length of piles to

the raft increases raising the pile–soil–raft interaction up

6.4 Analysis procedure using SAP 2000

The proposed method is used to estimate the settlement and bending moment induced in the raft of two piled raft models which are performed in centrifuge tests To conduct this method in a civil engineering analysis package and instruct the practicing engineer reproducing the method, the SAP 2000 structural commercial program, which is being used by many civil design companies at present, is used This program cannot simulate any soil model but with the help of the proposed method, it can solve the piled raft problem well

The analysis requires the following input data: the single pile behaviour, the unpiled raft behaviour, and the pile–soil–pile and pile–soil–raft interaction factors The pile–soil–pile interaction factor plays a role of connecting pile springs working as a pile group while the pile–soil–raft interaction factor helps the plate models operate as a real raft in the piled raft foundation As final outputs, the settlement of the piled raft and the distribution of the bending moment and shearing force of the raft can be obtained Figure 6 shows a flow chart of the analysis procedure When the assumed load transmitted to the piles in the piled raft in the first calculation is larger than the piles’ capacity, the “load cut-off” procedure [3]

is applied, where the piles’ capacity is taken to calculate the settlement of pile springs The remaining load is transmitted to the raft to calculate the settlement of the raft springs

Figure 6 Schematic of flow chart for SAP 2000 analysis

The analysis procedure using SAP 2000 is as follows:

1 Model the piled raft foundation with SAP 2000, where the raft is modelled by a bending plate having the same size as the raft, piles are modelled by pile springs and

relative raft–soil stiffness is modelled by raft springs The plate is meshed into a series of small plates to solve the bending moment and stress of the raft.

2 Determine the pile–soil–pile interaction factors for each pile spring and pile–soil–raft interaction factors for each raft spring based on the interaction curves

3 From the total applied load, assume the load for piles and the load for the raft (about 80% and 20% of the total applied load, respectively), and assume the axial force transmitted for each pile spring and each raft spring (usually at the first calculation, assume that all axial forces of all pile springs are equal and all the axial forces of all raft springs are equal)

4 Calculate the vertical settlement for each pile spring by Eq (1) and each raft spring by Eq (3) The displacements of the pile due to unit load in

Eq (1) (δ1J and δ1K respectively) are derived from the load–settlement curve of a single

pile, and the displacement due to the unit load for the raft spring (ρ1M) is calculated from the load–settlement curve of an unpiled raft or the solution of Boussinesq for shallow foundations [17]

5 Calculate the stiffness of each pile spring by Eq (2) and the stiffness of each raft spring by Eq (4)

6 Assign all the calculated stiffness for all springs of the piled raft model in SAP

2000 This step establishes the boundary conditions for the plate model

7 Solve the system of equations to obtain the preliminary settlement of the piled raft and axial forces transmitted for each spring

8 Calculate the difference in the axial forces of pile springs with a tolerance of about 5–7% If the differential values are larger than 7%, repeat the calculation from step 4

to step 8 to estimate the stiffness of all springs and the settlement of the foundation a second time This iterative process is terminated when the differential axial forces of the pile springs are in a range of 5–7% This tolerance is based on experience so it may be chosen at the designer discretion

7 CENTRIFUGE TESTING PROGRAM

Centrifuge tests were performed using the 240 g ton geotechnical centrifuge equipment at KAIST (Korea Advanced Institute of Science and Technology) in Korea The maximum capacity of the KAIST beam centrifuge, with a 5 m radius, is 2400 kg for up to

100 g of centrifugal acceleration and 1300 kg at 130 g of maximum centrifugal acceleration The detailed specifications of the centrifuge equipment can be found in Kim

et al [14] Figure 7a shows the centrifuge equipment with the testing system developed in this study The tests were carried out at two centrifugal acceleration levels, 50 g and 60 g Two centrifugal accelerations were adopted for making a difference in the pile length between two piled raft models

Figure 7.KOCED geotechnical centrifuge with testing system and test model set-up.

(a) KOCED geotechnical centrifuge with testing system

(b) Test model set-up

7.1 Tested soil

Silica sand, with particle mean diameter D50 = 0.22 mm, a uniformity

coefficient C U = 1.96 and classified as SP type (according to the Unified Soil Classification System), was used for all centrifuge tests Triaxial drained tests were performed to obtain

characteristics of the tested soils, with relative densities, D R ≈ 70% and D R ≈ 40% The test results are presented in Table 3

Table 3 Silica sand parameters

Relative

density

Confinement pressure (kPa)

Depth (m)

E (MPa)ε > 0.2

%

Peak friction

angle (ϕ)

Critical state friction angle

D r = 40% 100 7.6 13.33

(γ d = 1.37 t/m3) 200 15.2 36.84

A homogeneous dry soil model was prepared by means of pluvial deposition to

relative densities D R of 70% and 40% (dense state and loose state, respectively) using a travelling sand spreader, which controls the fall height and travel speed of the deposition curtain The spreader was passed repeatedly over the circular strong model box (900 mm

in a diameter) until the thickness of the sand layer was approximately 400 mm (corresponding with 20 m at 50 g and 24 m at 60 g in the prototype scale)

7.2 Test program and models

In order to verify the applicability of the proposed method, two cases of piled raft model tests were evaluated in the centrifuge tests for comparison; the two piled rafts have different numbers of piles as well as different pile length and pile spacing The first case is sixteen piles (15 m pile length and 0.6 m in diameter in prototype) and 4d pile spacing, and the second case is nine piles (10 m pile length and 0.6 m in diameter in prototype) and 3d pile spacing The piled raft models were loaded by loading equipment fixed to the rigid frame of the box A load cell was installed in the equipment to measure the amount of total applied load The raft settlement was measured by two linear displacement transducers (LVDT) fixed on a frame that was connected to the frame supporting loading equipment The tips of the core of LVDTs rested on the two opposite corners of the raft The average values of data measured by the two LVDTs were taken as the settlement of the foundation The test model set-up is shown in Figure 7b The target of these tests is obtaining the load–settlement curves of the two piled raft models in model scale Then, these curves are converted to prototype scale using the laws of similitude as in Table 4 [18]) to compare with the load–settlement curves of the two piled raft calculated by the proposed method and Plaxis 3D Foundation

Table 4 Scaling factor for centrifuge modelling [18]

Parameter Scaling factor Parameter Scaling factor

Stiffness 1/N Time (diffusion) 1/N2

The material and thickness of the pile model and the raft model are selected in considering the equivalent stiffness between the model scale and the prototype scale In the case of the pile model, the equilibrium of axial strain is considered, and in the case of the raft model the equilibrium of deflection is considered The number of centrifuge tests performed is 10 The test programme are summarised in Table 5 Two tests were performed at 50 g on the single pile model (pile length 220 mm) and a piled raft model having nine piles (pile length 200 mm and three piles were equipped with load cells to measure transmitted axial forces) In the piled raft tests, the rafts need to be completely contacted with the soil surface, whereas in the pile group tests the rafts (or the caps) do not contact with the soil surface In order to make the same penetrated pile length in both piled raft tests and pile group tests, the pile length model of pile group tests is longer than the one of piled raft tests about 20 mm (1.2 m at 60 g in the prototype scale) The models were

made of aluminium alloy (E = 7E+04 MPa) Details of all models are summarised in Table

6, where the prototype and model scale dimensions are reported

Table 5: Test program UR = unpiled raft; SP = isolated single pile; PG = pile group;

Table 6: Dimensions of centrifuge models D m-in = inner diameter of pile; D m-out = outer

diameter of pile; L = length of pile; B r = width of raft;t r = thickness of raft

L m (mm)

B rm (mm)

t rm (mm)

D

m-in (m)

D

m-out (m)

L m (m)

B rm (m)

t rm (m)