EXTENDED ABSTRACT Combined Pile Raft Foundation Rui Diogo Gomes da Silva Supervisor: Prof. Jaime Alberto dos Santos December 2009
1. Introduction The piled raft foundation is an innovative design concept with the purpose of reducing settlements and differential settlements caused by concentrated building loads and load eccentricities. In the last decades, a quick increase in the number of combined pile raft foundations (CPRF) solutions has been observed, particularly in stiff clay soils. Such soils offer reasonably good support for raft foundations, generally providing adequate bearing capacity for the structure. Nevertheless, excessive settlement may occur without the introduction of piles. The main questions that arise in the design of piled rafts concern the relative proportions of load carried by raft and piles, and the effect of the pile support on total and differential settlements. The worldwide largest project for a building founded on a CPRF was established from 1988 until 1990, the 256m high Messeturm in Frankfurt am Main. From the beginning it was clear that for this building a shallow foundation was not possible, because it would have led to settlements in the order of 40-50cm and differential settlements in the order of 15cm. A pure pile foundation represents a large number of long piles and therefore high costs for the foundation. For this reason, a CPRF was designed for this building consisting of 64 piles with a medium length of 30m. About 60% of the total load is supported by piles, with the remaining being transferred directly to the ground. As a result, settlements of about 13cm were reached. The present paper reports the study of Silva (2009), where an investigation was conducted in order to evaluate the applicability of a simple method, proposed by Poulos and Davis (1980) and using the interaction coefficient proposed by Randolph (1983). Else, it was studied the possibilities of using a finite elements analysis, linear and non linear, to analyze the behavior of a CPRF solution. 2. The Concept of Combined Pile Raft Foundation The combined pile raft foundation is a composite construction consisting of the three bearing elements piles, raft and subsoil: (1) where: - total load of the building; - load of the raft; load of the pile group; The combined pile raft foundation allows the reduction of total settlements and differential settlements in a very economic way compared to traditional foundation concepts, because the contribution of both the piles and the raft, in the load distribution process, is considered. 1
One of the main issues concerning the analysis of a combined piled raft foundation is the combination of the bearing effect of both foundation elements, raft and piles, due the interaction between the foundation elements and the subsoil. Figure 1 : Concept of combined pile raft foundation 3. Methods of analysis of CPRF 3.1. Poulos - Davis Randolph (PDR) method In order to estimate the load-settlement behaviour, Poulos and Davis (1980) proposed the following expression, with p for the pile group, and r for the raft: 1 1 (2) where: - settlement; - isolated stiffness; - load; - raft - pile interaction factor. From the reciprocal theorem, the terms of the trailing diagonal of the flexibility matrix must be equal, so that interaction factors are related by: (3) 2
Considering that settlement of piles and raft are identical,, the overall stiffness,, may be expressed as: 1 2 1 (4) It is noted that the above expression differs from that presented by Poulos (2001). However it is consistent with equations (1), (2), (3) and it will be employed in the analyses presented subsequently. For single piles with circular caps of diameter D r, Randolph (1983) has shown that the raft-pile interaction factor,, may be approximated by: ln 1 ln 2 (5) where: (6) and 2,51 (7) Figure 2: Single pile-raft where: - pile diameter - raft diameter - average shear modulus of the soil along the pile; - pile lenght; Poisson s ratio for the soil - shear modulus of the soil at the depth l; - heterogeneity of soil modulus (/ ) It is then possible to define the raft and pile load, and respectively, recurring to: 1 w (8) 1 1 w (9) 3
The PDR method (Poulos, 2001) gives no details regarding the assumed individual elements stiffness. In the analyses reported herein (PDR-RS) the individual elements stiffness are calculated as described below. The raft isolated stiffness is calculated assuming an equivalent circular footing and employing the theory of elasticity, being given by the following equation: where: soil shear modulus 2 41 (10) influence factor Where the influence factor allows to incorporate a variation of soil stiffness with depth. To estimate the pile stiffness Randolph and Wroth (1978) presented an approximated solution based on a separated treatment of the pile shaft and the pile base. The solution allows a linear increase of shear modulus with depth. The pile stiffness is given by: where: - pile radius at base - pile radius at the top - shear modulus of the level of the pile base - pile Young s modulus G l, ρ, ν previously defined 2 4 tanh ln. 2 1 ln 2 ln 2 4 tanh ln 1 1 2 ln (11) This solution may be extended to deal with piles which penetrate on a multi-layer soil by treating each section of the pile shaft independently, retaining compatibility of displacements of the pile shaft between each section. The load settlement ratio for the pile base (the term 4/1 ) in equation (11) is replaced by the load settlement ratio for the section of pile below the one that is currently being considered. 3.2. Strip on Springs Approach (GASP) In this approximate computer method the section of the raft is represented by a strip and the supporting piles by springs. Approximate allowance is made for all four components of interaction (raft-raft elements, pile-pile, raft-pile and pile-raft), and the effects of the parts of the raft outside the strip section being analyzed are taken into account by computing the free-field soil settlements due to these parts. These settlements are then incorporated into the analysis, and strip section is analyzed to obtain the 4
settlements and moments due to the applied loading on that strip section and the soil settlements due to the sections outside the raft. It is possible to consider the nonlinear effects for the strips. The stiffness of the individual piles is computed via the equations of Randolph and Wroth (1978), and simplified expressions are used to obtain the pile-pile interaction factors. This method has been implemented through the computer program GASP (Geotechnical Analysis of Strip with Piles) and presented settlements which are in reasonable agreement with more complete methods of analysis. 3.3. Finite Element Numerical Analysis In this type of analyses the user inputs the elements geometry and elastic properties and the elements stiffness and the interaction coefficients are then a result of the analyses. There are essentially two types of computed numerical analysis: two dimensional and three- dimensional. On the two-dimensional numerical analysis, the foundation is assumed as a two-dimensional (plane strain) problem or an axially symmetric three dimensional problem. In both cases, significant approximations need to be made, particularly in regard to the piles, which must be modeled as a continuous element (out of the plane of analysis) with an equivalent stiffness. Problems may also be found when concentrated loads are used in such analysis. Unless the problem involves a uniform loading on a symmetrical raft, it may be necessary to carry out an analysis for each one of the directions in order to estimate the settlement profile and the raft moments. A complete three-dimensional analysis dispenses the need for the approximate assumptions described above. However, some problems remain, particularly regarding the modeling of the pile-soil interfaces and whether interface elements should be used. 4. Proposed methods 4.1. PDR-RS analysis method The PDR method, as described in section 3.1, is used to study the behavior of CPRF. The method is implemented as an iterative calculation process using FORTRAN language. To introduce the non linearity of the bearing capacity of the soil foundation in this iterative calculation method it is necessary to define the elements stiffness (raft and pile) when bearing capacity is reached. Therefore, when replacing the load defined on the expressions (8) and (9), by the respectively bearing capacity of each element, the new stiffness may be expressed as: (12) '= 1 2 + + +2 + -4 (13) 5
Iterative calculation process is presented in Figure 3. The procedure starts with the introduction of the following constant parameters: raft isolated stiffness (k r ), pile isolated stiffness (k p ) and the raft - pile interaction factor,. k r ; k p ; α rp ; w K pf ; K rf P r ; P p P r P maxr Yes ou P r-p maxr < error P maxr No k r = f(p maxr ; k p ; w) P p P maxp ou No k p =f(p maxp ; k r ; w) w = w + i Yes P p-p maxp < error P maxp Yes w < w max No End Figure 3 : PDR-RS program diagram As can be seen on the PDR-RS program diagram, after the parameter definition the iterative process is initiated. This process goes as follows: Determination of the stiffness contribution of raft and piles to the global stiffness, k rf and k pf, respectively; Determination of the load in each element, P r and P p for the raft and pile, respectively. Verification if the load supported by the raft doesn t exceed the maximum bearing capacity or if the error isn t exceeded. When one of these issues isn t verified, a new stiffness k r is calculated and the process returns to the first step. When both issues are verified the program runs on. Verification if the load supported by piles doesn t exceed the maximum bearing capacity or if the error isn t exceeded. When one of these issues isn t verified, a new stiffness of piles k p is calculated and the process returns to the first step. When both issues are verified the program proceeds to the next step; Verification if the maximum settlement was achieved. If it wasn t, an increment of 1x10-4 to the settlement is introduced, and the iterative process is run again from step one. Otherwise, the maximum settlement was achieved successively and the program is finished. As proposed by Poulos (2001) to taken into account the group effect the raft and pile isolated stiffness s are previously reduced by the group factor n, where n represents the piles number. 6
4.2. Finite element analyses Recurring to the finite element software (PLAXIS 2D) two sets of analysis were carried. In one set both the structural elements and the soil are treated as linear elastic and on the other the soil is treated as a Mohr-Coulomb material instead. Both sets of analyses calculate loads and displacements for a single pile-raft unit, which allows treating the problem as an axissymetric one, as presented in Figure 4. The global behavior of a CPRF system is obtained by multiplying the total load obtained for the single pile-raft analysis by n and apply the group settlement ratio n, where n represents the piles number (Poulos, 2001). 4.2.1. Linear analysis The aim of this set of analyses is to validate the FE analyses procedures. The considered properties for the linear analysis are as follows: Soil: Pile: Raft: E= 30 MPa ; ν = 0.3 E= 3 GPa ; ν= 0.2 D= 0.4 m; L= 10 m E= 3 GPa; ν= 0.2 The results of this set of analyses are compared with the results reported by Clancy and Randolph (1993) in terms of the raft-pile interaction factor, and are shown in Table 1. The pile spacing indicated in the first column is an indicator of the relative raft size, and is similar to the rectangular pile-pile spacing used in larger pile groups. Thus, for a single pile-raft unit with a raft radius r and a pile diameter D, the equivalent rectangular pile spacing in a large piled raft system is given by: S/D= π r/d (14) For regular S/D values, small variations between the models are observed. Differences between the two sets of analyses may be due to the adoption of different parameter values as Clancy and Randolph (1993) just specifies the ratio between E p /E s and not there absolute values. S/D Tests Clancy e Randolph Variation αrp αrp αrp 2 0.64 0.65-2% 3 0.49 0.53-7% 4 0.44 0.45-2% 5 0.39 0.43-9% 6 0.35 0.38-7% 7 0.30 0.35-13% 8 0.28 0.33-13% 9 0.26 0.30-14% Table 1 : Balance between linear analysis and the method proposed by Clancy and Randolph (1993) for L/D=10 and E p /E s =100. 7
4.2.2. Nonlinear analysis Using FE nonlinear analyses various parameters were analyzed, including the influence of the pile length and spacing and on the load percentage supported by each structural element. The results of the complete set of analyses can be found in Silva (2009). In the following section it is shown the results for a particular set of parameters aiming to compare the results with methods of analyses. 5. Application to an hypothetical example The aim of this section is to evaluate the previously described methods, through the comparison with other load-settlement methods for CPRF analysis. Poulos (2001) presents results using several methods for the hypothetical example shown in Figure 5. The analyzed hypothetical example concerns a rectangular 60m 2 surface raft reinforced with 9 piles. This problem will be studied using the PDR-RS method and the FE nonlinear analyses. The results will be compared with those reported by Poulos (2001). The elements properties adopted in the analyses are as follows: Soil: Pile: Raft: E=20MPa; ν=0.3 Φ = 35 ; c = 6.5 kpa δ =34.5 E= 30 GPa; ν= 0.2 δ=34.5º D= 0.5 m; L= 10 m Bearing capacity=0.873mn E= 30 GPa; ν= 0.2 D= 2.9 m Bearing capacity=0.3mpa Figure 4 : PLAXIS axis-symmetric deformed mesh for nonlinear method Figure 5 : Hypothetical example 8
Figure 7 shows the load-settlements curves for an isolated pile raft using the PDR-RS method and FE linear and nonlinear analyses. Figure 6 shows that for this individual analysis of the system, the PDR- RS method (previously reduced), is the more conservative one. 4000 Total Load [kn] 3000 2000 1000 0 0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 Settlement (m) PDR-RS(Previously Reduced) Linear Nonlinear Figure 6 : Individual load settlement analysis by tree different methods. The global behavior of a CPRF system is then obtained by multiplying the total load obtained for the single pile-raft analysis by n and apply the group settlement ratio n, where n represents the piles number (Poulos, 2001). Figure 7 presents the comparison on the load-settlement curves of the CPRF system obtained using the PDR-RS, the FE nonlinear (PLAXIS) analyses and those reported by Poulos (2001): FLAC 2-D; GASP and FLAC 3-D. As can be seen, the PDR-RS (previously reduced) results are quite similar to the ones obtained through the PDR method, which allows concluding that this method describes the load settlement behaviour adequately. Comparing now the nonlinear analysis and the FLAC-3D methods, the results obtained show little difference in the zone of maximum bearing capacity of the pile being the first one more conservative. However, on both the initial elastic zone and the final nonlinear zone the model is quite similar to the FLAC-3D method. 6. Conclusions It s clear that there are several methods for analyzing combined pile raft foundation systems. Some are quite simple and can be implemented with minimal computer requirements, while others are more complex such as the three-dimensional finite elements analysis. The main conclusions of this work may be summarized as follows: 9
Through the comparison between the interaction factor achieved by the PDR-RS method and the one obtained by Clancy and Randolph (1993) it is possible to conclude that the PDR-RS is appropriate to analyze the behavior of an isolated pile-raft element. The linear PLAXIS analysis and the PDR-RS method held to similar results on both the interaction factor and load percentages, which leads to the conclusion that these methods are adequate to study the behavior of CPRF solutions. The nonlinear analysis results, for the hypothetical example, are quite similar to the ones reached through the FLAC-3D analysis. References Figure 7 : Comparison of different analysis methods. Clancy, P. and Randolph, M.F. (1993). Analysis and Design of Piled Raft Foundations. Int. Jnl. NAM Geomechanics, 17: 849 869. Poulos, H.G. (2001). Methods of Analysis of Piled Raft Foundation. A Report on Behalf of Technical Committee TC18 on Piled Foundations, ISSMGE. Poulos, H.G. e Davis, E.H. (1980). Pile Foundation Analysis and Design. Wiley, New York. Randolph, M.F. (1983). Design of piled raft foundations. Proceedings of the International Symposium on Recent Developments in Laboratory and Field Tests and Analysis of Geotechnical Problems, Bangkok: 525 537. Randolph, M.F. e Wroth, C.P. (1978). Analysis of Deformation of Vertically Loaded Piles. Jnl. Geot. Eng. Divn., ASCE, 104(GT12), 1465 1488. Silva, R.D.G. (2009). Combined Pile Raft Foundation, Master degree dissertation, Instituto Superior Técnico. 10