PILE-SUPPORTED RAFT FOUNDATION SYSTEM Emre Biringen, Bechtel Power Corporation, Frederick, Maryland, USA Mohab Sabry, Bechtel Power Corporation, Frederick, Maryland, USA Over the past decades, there has been an increasing recognition of the strategic use of pile-supported rafts in design of heavily-loaded structures to reduce total and differential settlements. However, such a hybrid foundation construction method has not been widely utilized in many countries, including the U.S., due to code limitations. In current practice, the foundation design is based on either (i) the bearing capacity of the raft supported by the subgrade soils, or (ii) solely the pile capacity. This paper addresses the potential use of such hybrid piled-raft systems, where the structural load is shared by both by the piles and the subgrade soils directly beneath the raft, in foundation design of power plant structures. The study assessed some of the characteristics of piled-raft behavior by undertaking three-dimensional finite element analyses of two raft sizes, and various pile layout patterns, including the rafts with piles distributed evenly and only in the central area of the raft. The computer software PLAXIS 3D with the Mohr-Coulomb constitutive soil model was used to facilitate the modeling of such cases. The results presented in this paper indicate how strategically locating the piles could reduce the differential and total settlements. INTRODUCTION Under the high applied loads coming from the superstructure, the addition of piles is primarily required to improve the factor of safety against failure when a raft does not provide adequate bearing capacity. If the bearing capacity of the raft is sufficient to carry the total load with a reasonable safety margin, then the addition of piles is usually intended to reduce the settlements to an acceptable amount. In current practice, the design process for pile-supported raft foundations conservatively concentrates on providing solely the pile capacity to carry the total structural load without taking the contribution of the raft into account. This paper addresses the potential use of hybrid piled-rafts in controlling foundation settlement of power plant structures by considering the support of both the piles and the subgrade soils beneath the raft to carry the load. Several studies (Prakoso and Kulhawy, 2001; Cunha et al., 2001; De Sanctis and Mandolini, 2006) have undertaken to investigate pilesupported rafts, in which the loads coming from the structure are shared by the pile and the raft, have shown that such a hybrid foundation system provides an efficient way of supporting highly-loaded rafts. By sharing the load with the raft, the number of piles needed under the raft foundation is reduced, and the spacing between them is increased. This saves pile costs and reduces the installation schedule. Also, by increasing the spacing between the piles, it provides more accessibility to install conduits and piping below the raft, in addition to more flexibility for construction to add more piles in case of pile replacement. In addition to the primary goal of improved bearing capacity and settlement performance, other positive effects from using pile-supported rafts can be listed as follows: (i) reduction of soil heave inside and outside the excavation, because the piles improve the overall soil conditions by preventing stress relief in the ground; (ii) minimizing construction measures for the control of deformations of structure, facades, and equipment; (iii) better and more economical control of large load differences between heavily-loaded structures adjacent to more lightly-loaded structures, as well as to adjacent properties, thus minimizing risk; (iv) ensuring stability for the entire foundation, when the foundation slab by itself does not provide sufficient stability for the large foundation loads; and (v) creation of an eccentric foundation block for eccentric loading to prevent anticipated tilting (with subsequent centering of the resultant structural load) by an asymmetrical arrangement of the piles. 1
The objectives of this paper are (i) establishing an understanding of the pile-supported raft load sharing mechanism and the behavior of the system in different soil and pile configuration conditions, and (ii) evaluating the settlement performance of pile-supported raft systems for foundation design applications. NUMERICAL MODELING In order to assess some of the characteristics of piled raft behavior, three-dimensional finite element analyses of various piled raft configurations have been undertaken. The computer software PLAXIS 3D with the Mohr- Coulomb elasto-plastic soil constitutive model were utilized. The raft and piles are considered to behave linear elastically. Consideration has been given to design applications where the raft thickness and width easily can be as much as 2 m and 38 m, respectively. In this parametric study, the effect of variations in the pile configurations, length of piles, pile spacing, number of piles, raft width, and raft thickness, under uniform loading were investigated. For simplicity, square shaped rafts, including piled and unpiled (for comparison purposes), were modeled. Table 1. Soil parameters Soil Loose to Medium (LM) Medium (M) Medium to Dense (MD) Dense (D) Classification SP to SW SP to SW SP to SW SP to SW Friction angle, φ (deg) 30 33 36 37 Relative density, RD (%) 35 50 75 88 Elastic modulus, E s (MPa) 21 30 45 53 Total Unit Weight (kn/m 3 ) (10% moist) 19 19 19 19 Void ratio, e 5 3 0 Cohesion, c (kpa) Poisson s ratio, ν s 0.3 0.3 0.3 0.3 Interface strength, R interface 7 7 7 7 Dilatancy angle, ψ ( deg) 0 3 6 8 Soil Parameters The main parameters used in the Mohr-Coulomb constitutive soil model are internal friction angle (φ), cohesion (c), elastic (Young s) modulus (E s ), Poisson s ratio (ν s ), and dilatancy angle (ψ). The stress state at failure is described with effective friction angle and cohesion of soil (PLAXIS 3D Manual, 2007). For this parametric study, four granular soil types (i.e., loose to medium, medium, medium to dense, and dense sand) were selected. The soil parameters adopted are presented in Table 1. In order to avoid any complications during the analyses, a cohesion value of kpa was adopted, as recommended by PLAXIS 3D Manual (2007). Prior to introducing the embedded piles and rafts, and applying the load to the system, the model equilibrium under coefficient of earth pressure at-rest (K o = 1-sinφ) was generated. An interface strength coefficient (R interface ) of 7, as recommended by PLAXIS 3D Manual (2007), was implemented to model the contact area between soil and foundation including the raft and piles. Pile and Raft Parameters In PLAXIS 3D, the raft and piles are considered to behave linear-elastically. For the parametric study, the pile and raft parameters listed in Table 2 were adopted. Table 2. Pile and raft parameters 2
Parameter Raft Pile Elastic modulus (MPa) 34,000 30,000 Poisson s ratio Unit weight (kn/m 3 ) 25 25 B t Note that Reul and Randolph (1994) refer to a study in which concrete samples taken from bored piles as well as in situ integrity testing show that the elastic (Young s) modulus of the piles is generally smaller than the design value obtained from samples under less complex production conditions. Therefore, a smaller value was taken for the elastic modulus of the piles than for the raft. Pile and Raft Configurations L p d p Configuration 1: Configuration 2: s In this parametric study, as shown in Figure 2. six pile configurations and two raft widths were investigated. In configurations 1 through 4, square rafts with a width (B or B r ) of 38 m were used, whereas B was reduced to 20 m in configurations 5 and 6. Configuration 1 had 169 piles evenly distributed under the whole raft area, with a spacing (s) of 3 pile diameter (d p ). In configuration 2, the spacing was increased to 6d p, and the total number of piles used (n) was reduced to 49. In configuration 3, the piles were placed only in the central area of the raft (n = 49, s = 3d p ). In configuration 4, the spacing was increased to 6d p, and n = 16. In configurations 5 and 6, the piles (n = 49 and 16, respectively) were evenly distributed under the whole raft area with s = 3d p and 6d p, respectively. Note that in all configurations, the pile diameter (d p ) was held constant at m. The pile length and raft thickness assigned for each configuration are presented in Table 3. The pile length (L p ) was selected as 19 and 38 m for configurations 1 through 4, and 20 and 40 m for configurations 5 and 6. Thus, L p/b was set equal to either, 1 or 2. Considering the commonly used raft dimensions is 1- and 2-m thick rafts (t or t r ) were selected for the analysis. For comparison purposes, the settlement behavior of the unpiled rafts is taken as the reference for the settlement behavior assessment of piled rafts. n = 169 (13x13), s = 3d p n = 49 (7x7), s = 3d p Configuration 3: Configuration 4: n = 49 (7x7), s = 3d p n = 16 (4x4), s = 6d p Configuration 5: Configuration 6: n = 49 (7x7), s = 3d p n = 16 (4x4), s = 6d p Figure 2. Pile configurations System Configuration Due to two-fold symmetry of the problem, only one quarter of the piled raft was modeled, as shown in Figure 3. The foundation level was set at the ground surface. Only vertical movement was set along the symmetry plane boundaries. In order to avoid any boundary effects on stresses and displacements, the distance to the 3
vertical boundaries in the horizontal direction was set to ten times the width of the raft modeled (i.e., 10B r /2) (Reul-Randolph, 2004), and the total depth (H) to the lower rigid boundary in the vertical direction was set to two times the full width of the raft plus two-thirds of the maximum pile length modeled (i.e., 2B r + 2/3L p ). For comparison purposes, H for a specific piled-raft configuration was kept the same for an unpiled raft. The values of H assigned for each configuration are tabulated in Table 6. Table 3. Loading cases and conditions For Configurations 1 through 4: For Configurations 5 and 6: Case 1 2 3 4 Unpiled 1 Unpiled 2 5 6 7 8 Unpiled 3 Unpiled 4 Raft width, B (m) 38 38 38 38 38 38 20 20 20 20 20 20 Raft length, L (m) B B B B B B B B B B B B Raft thickness, t (m) 2 1 2 1 2 1 2 1 2 1 2 1 Pile diameter, d p (m) 1 1 1 1 none none 1 1 1 1 none none Pile length, L p (m) 19 19 38 38 - - 20 20 40 40 - - Ratio of L p/b 1 1 - - 1 1 2 2 - - Pile spacing, s (m) 3d p and 6d p - - 3d p and 6d p - - Construction Process and Load Type The objective of this parametric study was mainly to investigate the global response of the various piled rafts under uniform loading with increasing intensity up to 250 kpa (5 ksf). The step-by-step construction process in the finite element analyses was as follows: 1. Generate in-situ stress state using K o. 2. Install embedded piles. 3. Re-set all displacements to zero. Apply a vertical pressure of 25 or 50 kpa, equivalent to the weight of the raft concrete (unit weight times thickness). 4. Install raft with actual stiffness. Remove the vertical pressure from Step 3. 5. Apply vertical uniform pressure (q) with increments of 25 kpa until the total applied pressure, including the raft weight, reaches 250 kpa. In all models, following the pile installation, the weight of the raft was applied to the soil. Simulating the real construction process, once the raft concrete was set, the stiffness of the raft was included in the model. By altering the raft thickness from 1 to 2 m, the corresponding variation in raft-soil stiffness ratio was investigated. All results presented in this study are related to the situation after the installation of the piles, so deformations due to the weight of the rafts are considered. The maximum uniform pressure, including the weight of the raft, was 250 kpa. Figure 3. Finite element mesh as defined in PLAXIS 3D 4
RESULTS AND DISCUSSION For a total vertical pressure of 250 kpa, the settlement values were measured at the center, at the mid-point between center and edge, at the mid-point of the edge, and at the corner of the rafts (points A, B, C, and D in Figure 4, respectively). The average settlement (δ avg ) is expressed as a function of settlement at points A, B, C, and D, as follows. δ avg δ A+ 4δ B + 4δ C + 4δ D 13 = Eq. 1 A B C Figure 4. Settlement observation points in PLAXIS 3D Figure 5 shows the performance of piled rafts with varying number of piles from 16 to 169 under a uniform pressure of 250 kpa. For the six pile configurations considered, the color contours show the vertical settlement under six square rafts with a thickness (t or t r ) of 1 m in soil type LM. In Figure 5, the pile length (L p ) is 19 m for configurations 1 through 4 and 20 m for configurations 5 and 6. Due to two-fold symmetry of the problem, only one quarter of the piled raft is presented. The first set of settlement contours consisting of configurations 1 through 4, with B r = 38 m, is presented using a scale from 100 to 320 mm. Due to less impact because of the smaller raft size, the second set of settlement contours consisting of configurations 5 and 6, with B r = 20 m, is presented using a scale from 60 to 120 mm. The results show that the layouts with evenly distributed piles (configurations 1, 2, 5 and 6) show less intensity of settlement as the pile spacing (s) is reduced from 6d p to 3d p, which indicates reduction in settlement regardless of the raft size selected. It is also noticeable that for rafts supported on evenly distributed piles (configurations 1 and 2) the maximum settlement occurs at the center, whereas in the D rafts with a centralized pile group (configurations 3 and 4) the location of the maximum settlement shifts from the raft center towards the edge. Figure 6 shows the settlement performance of piled rafts with varying pile length to raft width ratios (L p /B r ) from to 2. The values presented are the normalized central settlements beneath the rafts supported on evenly distributed piles (configurations 1, 2, 5 and 6). Thus, the ratio of pile group width to raft width (B g /B r ) is equal to. Note that for configurations 1 and 2 the raft width (B r ) is 38 m, whereas B r = 20 m for configurations 5 and 6. The settlement performance is observed for the raft thicknesses of 1 and 2 m, while the pile spacings of 3d p and 6d p are used under a uniform pressure of 250 kpa. The values are normalized by the settlements of unpiled rafts with the respective raft thickness. As would be expected, the normalized central settlement decreases with increasing pile length, as the proportion of load carried by the piles increases. Comparing the settlement behaviors of the evenly piled rafts in four soil types (LM, M, MD and D) indicates that the configurations with L p /B r = 1 are effective in reducing the central settlement by 30 to 50%. Figure 7 shows the settlement performance of piled rafts with varying pile lengths of 19 and 38 m. The values presented are the normalized central settlement and the normalized differential settlement between the center and corner points of the piled rafts supported on evenly distributed piles (configurations 1 and 2) and on a central pile group (configurations 3 and 4). Thus, the ratios of pile group width to raft width (B g /B r ) are equal to and, respectively. Note that a constant raft width (B r ) of 38 m is used in the analysis. The settlement performance is observed for L p /B r ratios (pile length to raft width) of and, while the raft thicknesses (t r ) of 1 and 2 m and the pile spacings of 3d p and 6d p are used, under a uniform pressure of 250 kpa. The values are normalized by the settlements of unpiled rafts with the respective raft thickness. As would be expected, both the normalized central settlement and the differential settlement decrease with increasing pile length, as the proportion of load carried by the piles increases. Comparing the settlement behaviors of the evenly piled rafts with B g /B r = 1 (configurations 1 and 2) and the centrally piled rafts with B g /B r = 5
(configurations 3 and 4) indicates that the configurations with B g /B r = 1 are effective in reducing the central settlement. On the other hand, for a constant raft thickness, the centrally piled rafts with B g /B r = are more effective in reducing the differential settlement, and the layouts with s = 3d p provide the best solution for differential settlement control. The addition of piles to the raft is effective in reducing the central settlement. However, there is an upper limit to the useful number of piles, beyond which little additional benefit is obtained. Between configurations 1 and 2, the improvement achieved in central settlement control by increasing the number of piles from 49 to 169 is only 10%. 100 mm 60 mm Config. 1, Case 2, s = 3d p Config. 2, Case 2, s = 6d p Config. 3, Case 2, s = 3d p Config. 4, Case 2, s = 6d p Scale for Config. 1 through 4 Scale for Config.5 and 6. 320 mm 120 mm Config. 5, Case 5, s = 3d p Config. 6, Case 5, s = 6d p Figure 5. Vertical settlement contours for t r = 1m, q = 250 kpa, L p = 19 (and 20) m, soil type LM Matching some prerequisites at the lowest cost is another factor in determining the optimum layout for settlement control. The cost of the foundation is broadly linked to the total length of the piles, (nl p ). Figure 8 shows the settlement performance of piled rafts versus the total length of the piles. The values presented are the normalized central settlement and the normalized differential settlement between the center and corner points of the piled rafts supported on evenly distributed piles (configurations 1 and 2) and on a central pile 6
group (configurations 3 and 4). Thus, the ratios of pile group width to raft width (B g /B r ) are equal to and, respectively. Note that a constant B r of 38 m is used in the analysis. The settlement performance is observed for L p /B r ratios (pile length to raft width) of and, while the raft thicknesses of 1 and 2 m and the pile spacings of 3d p and 6d p are used, under a uniform pressure of 250 kpa. The values are normalized by the settlements of unpiled rafts with the respective raft thickness. Comparing the settlement behaviors of the uniformly piled rafts with B g /B r = 1 (n = 49 to 169) and the centrally piled rafts with B g /B r = 0.5 (n = 16 to 49), it is clear that increasing the length of the piles is, for this case, a more effective design strategy for improving foundation performance than increasing the number of piles. The results show that at a given total length of the piles (nl p ), the layouts with s = 6d p provide the better solution for differential settlement control compared to the layouts with s = 3d p. If the layouts that have the same total length of piles are considered (i.e., configurations 2 and 3), then the centrally piled rafts with B g /B r = are more effective in reducing the differential settlements. 1 Normalized Central Settlement 0.3 0.1 0 0 1 1.5 2 Soil LM 0.3 0.1 0 1 1.5 2 Soil M 0.3 0.3 0.1 0.1 0 1 1.5 2 Soil MD 0 1 1.5 2 Soil D Pile Length / Raft Width Figure 6. Ratio of pile length to raft width vs. central settlement. 7
1 Soil LM - Soil LM Normalized Central Settlement Soil M Soil MD Normalized Centre- to-corner Differential Settlement - Soil M Soil MD Soil D Pile Length (m) Soil D Conf.1 Bg/Br= tr=1m s=3m n=169 Conf.1 Bg/Br= tr=2m s=3m n=169 Conf.2 Bg/Br= tr=1m s=6m n=49 Conf.2 Bg/Br= tr=2m s=6m n=49 Conf.3 Bg/Br= tr=1m s=3m n=49 Conf.3 Bg/Br= tr=2m s=3m n=49 Conf.4 Bg/Br= tr=1m s=6m n=16 Conf.4 Bg/Br= tr=2m s=6m n=16 0 Figure 7. Pile length vs. central and differential settlements 8
1 Soil LM - Soil LM Normalized Central Settlement Soil M Soil MD Normalized Centre- to-corner Differential Settlement - Soil M Soil MD Soil D Total Pile Length (m) 0 1000 2000 3000 4000 5000 6000 700 Soil D Conf.1 Bg/Br= tr=1m s=3m n=169 Conf.1 Bg/Br= tr=2m s=3m n=169 Conf.2 Bg/Br= tr=1m s=6m n=49 Conf.2 Bg/Br= tr=2m s=6m n=49 Conf.3 Bg/Br= tr=1m s=3m n=49 Conf.3 Bg/Br= tr=2m s=3m n=49 Conf.4 Bg/Br= tr=1m s=6m n=16 Conf.4 Bg/Br= tr=2m s=6m n=16 0 Figure 8. Total pile length vs. central and differential settlements 9
CONCLUSION A close assessment of the results leads to the following conclusions for practical design: 1. The addition of piles to the raft is effective in reducing the central settlement. However, there is an upper limit to the useful number of piles, beyond which little additional benefit is obtained. This limit is usually less than the number of piles conventionally used to support the full load from the structure. 2. The longer the piles, the more effective they are in reducing the central and the differential settlements. 3. For control of differential settlement, if loading is uniformly distributed, the optimum performance is likely to be achieved by concentrating the piles near the centre area,rather than using a large number of evenly distributed piles beneath the raft area, or increasing the raft thickness. 4. For each value of pile length, an optimum value of the quantity nl p exists, corresponding to the maximum reduction of the differential settlement and to values of B g /B r in the range. 5. From the presented analysis and method of design, reduction in number of piles could be achieved by taking into consideration the load sharing capacity of the soil. By applying this method, considerable reduction in the foundation cost could be achieved. Geoenvironmental Engineering, pp. 707-708. 4. Poulos, H.G. (2000). Chapter 16: Practical Design Procedures for Piled Raft Foundations, Design Applications of Raft Foundations, Hemsley, J.A. (Editor), Thomas Telford Ltd., London. 5. Poulos, H.G. (2001). Pile Raft Foundations: Design and Applications, Geotechnique, Vol. 51, No. 2, pp. 95-113. 6. PLAXIS 3D Foundation, Version 2, Finite Element Code for Soil and Rock Analyses. 7. PLAXIS 3D Foundation Material Models Manual (2007). Version 2, EDs, Brinkgreve, R.B.J. and Swolfs, W.M. 8. Reul, O., and Randolph, M.F. (2004). Design Strategies for Piled Rafts Subjected to Nonuniform Vertical Loading, J. Geotechnical and Geoenvironmental Engineering, Vol. 130, No. 1, pp. 1-13. REFERENCES 1. Prakoso, W.A., and Kulhawy, F.H. (2001). Contribution to Piled Raft Foundation Design, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 127, No. 1, pp. 17-24. 2. Cunha, R.P., Poulos, H.G., and Small, J.C. Investigation of Design Alternatives for a Piled Raft Case History, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 127, No. 8, pp. 623-641. 3. De Sanctis, L. and Russo, G. (2002). Discussion of Contributing to piled raft foundation design by Prakoso, W.A. and Kulhawy, F.H., Vol. 127, No. 1, pp. 17-24., Journal of Geotechnical and 10