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 Symbol Explanation Unit 1 C resistance property for SLS 2 D pile diameter m 3 e pile spacing m 4 E action effect 5 Es stiffness modulus MN/m² 6 F Action MN 7 Fk,i characteristic value of an action i MN 8 Ftot,k sum of characteristic values of all actions MN 9 H sum of horizontal actions MN 10 i index for an action - 11 j index for a pile - 12 k index for characteristic value - 13 n number of actions - 14 m number of piles of a CPRF - 15 qb base pressure of a pile MN/m² 16 qs(z) skin friction of a pile MN/m² 17 R resistance MN 18 Rb,k(s) characteristic value of the base resistance of a pile as a function of settlement MN 19 Rtot,k (s) characteristic value of the total resistance of a CPRF as a function of settlement MN 20 R1,tot,k characteristic value of the total resistance of a CPRF for ULS MN 21 Rpile,k,j characteristic value of the resistance of the pile j of a pile group MN 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 24 s settlement m 25 spr settlement of a CPRF m 26 ssf settlement of shallow foundation m 27 s2 allowable settlement for SLS m 28 Δs2 allowable differential settlement for m 29 V sum of vertical actions MN 30 x,y,z cartesian coordinates m 31 αpr pile raft coefficient - 32 γ partial safety factor - 33 σ(x,y) contact pressure MN/m² 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 R tot ,k (s) of the CPRF depends on the settlement s of the foundation and consists of the sum of the characteristic pile resistances , , ( ) m pile k j j R s ∑ and the characteristic base resistance R raft ,k (s). The characteristic base 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 s x y dxdy σ = ∫∫ The bearing behaviour of the CPRF is described by the pile craft coeficient pr α which is defined by the ratio between the sum of the characteristic pile resistanses , , ( ) m pile k j j R s ∑ and the characteristic value of the total resistance , ( ) : tot k R s , , , ( ) ( ) m pile k j j pr tot k s R s R α = ∑ The pile raft coefficient varies between 0 pr α = (spread foundation) and 1 pr α = (pure pile foundation). Figure 1.2 shows a qualitative example of the dependence between the pile raft coefficient pr α and the settlement of a CPRF pr s related to the settlement of a spread foundation S sf with equal ground plan and equal loading. The pile raft coefficient pr α depends 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. Method Type of interaction Equation Comment Poulos and Davis [4] Pile–pile interaction (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) 1 w n k j kj j i Q ω α = ∆ = ∑ – 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 α ÷ ÷ = − ÷ ÷ r m = 2.5ρL(1 − υ s ) – Considering the additional settlement of a circular rigid raft caused by a pile – Not considering the change in soil stiffness along the pile and the flexibility of the raft. The parameter for considering soil stiffness is ρ which is the degree of homogeneity of the soil Randolph [6] Pile–raft interaction ln 1 ln r p rp m p r r r r α ÷ ÷ = − ÷ ÷ r m = 0.25 + Lζ[2.5ρ(1 − υ) − 0.25] ζ = E sl /E sb ρ = E sav /E sl – Considering the additional settlement of a circular rigid raft caused by a pile – 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 ( ) p r rp pr p r k P w P k α = − – The settlement of piled raft and load transmitted for piles and for raft are needed – Can consider the flexibility of the raft Nomenclature: Δw k = additional of pile k caused by other piles ω 1 = 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. . 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) (δ 1J and δ 1K respectively) are derived from. scope of this paper. Then, the vertical displacement of a pile is given by: ( ) 1 1J 1K 1, K w (1) n pK pJ KJ pK J J P P δ α δ − = ≠ = + ∑ where w pK is the vertical displacement of the pile