Numerical Analysis of Piled Raft Foundation in Sandy and Clayey Soils

Transcription

1 Numerical Analsis of Piled aft Foundation in and Clae Soils Author Oh, Erwin, Lin, D., Bui, Quan-Minh, Huang, Min, Surarak, Chanaton, Balasubramaniam, Bala Published 9 Conference Title Proceedings of the 7th International Conference on Soil Mechanics and Geotechnical Engineering Copright Statement IOS Press. This is the author-manuscript version of this paper. eproduced in accordance with the copright polic of the publisher. Please refer to the publisher website for access to the definitive, published version. Downloaded from Link to published version Griffith esearch Online

2 Numerical Analsis of Piled aft Foundation in and Clae Soils Analse Numériue De La Fondation Dans Pile ojet Et sols argileu E.Y. N Oh Griffith School of Engineering, Griffith Universit, Queensland, Australia. D. G. Lin Department of Soil and Water Conservation, National Chung Hsing Universit, Taichung, Taiwan (.O.C) Q. M. Bui, M. Huang, C. Surarak, A. S. Balasurbamaniam Griffith School of Engineering, Griffith Universit, Queensland, Australia. ABSTACT This paper presents 2-D and 3-D numerical analsis of un-piled raft and piled raft foundation on two different soil conditions. The numerical analsis was carried out in two case studies with three tpical load intensities of the serviceabilit load. The first case stud investigates the raft-pile-soil interaction in sand soil. The second case stud eamines the raft-pile-soil interaction in soft cla. Finall, the behaviours of piled raft foundation in two different case studies are assessed and conclusions are made.. Kewords : piled raft, raft thickness, PLAXIS, FLAC. INTODUCTION Piled raft foundation is an economical alternative to the conventional piled foundation. This paper is on numerical analsis of piled raft foundations using PLAXIS (Brinkgreve and Broere, 6.) and FLAC (995). The numerical analsis was carried out in two case studies with tpical load intensities of the serviceabilit load. Etensive parametric studies were carried out with the variables pile spacing, number of piles, pile diameter, raft dimension ratio, and raft thickness. Historicall, the pile raft analsis has its origin to the pile group analsis. Earl work of Meerhof (959) were empirical in nature and relates to the settlements of pile groups. Later, the important work of Fraser and Wardle (976), Poulos and Davis (98), andolph (3) reviewed the relation to the pile group analsis, load transfer mechanism and other pertinent aspects related to the fundamentals of pile group analsis. The contributions from Tomlinson (986), Coduto (), and Poulos (993) also studied in relation to the euivalent raft analsis. The contributions from Poulos (993), and Clanc and andolph (993) reviewed the euivalent pier methods of analsis in piled raft foundations. The more rigorous methods of piled raft analsis began with the contributions of Kuwabara (989), and etended b Poulos (993) with further contributions from Ta and Small (996), and Zhang and Small (). Notabl, Prakoso and Kulhaw () used the PLAXIS software in the 2-D analsis of piled raft foundations. In this paper, the first case stud investigates the raft-pilesoil interaction in sand soil (as shown in Figure ). The stratigraph of the soil laers for the first case stud are: (a) Laer - 5m of loose to medium dense sand; (b) Laer 2 8m of dense sand; (c) Laer 3 - Organic peat and silt clas with average thickness 3m; (d) Laer 4 - Ver dense sand with thickness varing from depth of 6 to 22m; (e) Laer 5 - Stiff cla inter-bedded with sand strips; (f) Laer 6 - Argilliteweathered rock. The second case stud eamines the raft-pilesoil interaction in soft cla (see Figure 2). The subsoil is generalised into three laers: (a) 5m of soft cla; (b) 5m of stiff cla; (c) 2m of sand kn/m Dense d=.8m Peat Ver Dense 8m Stiff Cla ock s=3d-6d Figure. Geotechnical model for case stud. 2 CASE STUDY 2. Soil Profile and Properties B t=.6m L p =3m L-.5 L-9.5 L-2.5 L-8.5 L-26.5 The simplified soil profile for case stud and the summar of the soil properties used in the numerical analsis are shown in Figure and Table. The stratigraph of the soil laers are given below. i. Laer : Loose to medium dense sand 5m thick with SPT in the range of 5 to, with static water table 3.5m below ground surface. ii. Laer 2: Dense sand 8m thick and SPT val-ues over 5. iii. Laer 3: Organic peat and silt clas with av-erage thickness 3m. iv. Laer 4: Ver dense sand with thickness varing from depth of 6 to 22m and SPT values over 5. v. Laer 5: Mainl stiff cla inter-bedded with sand strips, but idealized as homogeneous stiff cla 8m thick with SPT values of about 3

3 vi. Laer 6: Argillite-weathered rock E s,ν E,ν E 2,ν 2 E 3,ν Soft Cla Stiff Cla Figure 2. Geotechnical model for case stud 2. Table. Summar of soil properties adopted fro case stud. Loose to Medium Dense Peat Medium Stiff Cla Thickness (m) Unit Weight, γ (kn/m 3 ) Saturated Unit Weight γ sat, (kn/m 3 ) Undrained Cohesion 25 8 s u (kn/m 2 ) Frcition Angle, φ (deg) Dilatant Angle, ψ (deg) Young s Modulus, E s (MN/m 2 ) Poisson s atio, ν Parametric Stud The main purpose of a parametric stud is to investigate the piled raft performance under the changes of the geometr of the dimensions. Therefore, the numbers of cases for parametric stud are as man as piled raft geometr dimensions. Specificall, the piled raft dimensions include pile spacing, number of piles, pile diameters, pile lengths for pile groups and raft thickness, raft dimension ratio (L/B) (B, L: the width and length of raft). The plane strain models are also simulated for the case of the variation in raft dimension ratio (L/B). Details of piled rafts and pile groups in this parametric stud are described and summarized in Table Settlement of Piled aft Foundation Figure 3 illustrates a plan view of the piled raft in the 3D case. The piles are indicated b circles w to w 4 represents the settlements at the corner points of the raft. w 5 to w 8 correspond to the settlement of the centre of the sides of the raft. w 9 to w 2 are the settlements at the mid points of the lines bisecting the sides of the raft. w 3 is the settlement at the centre of the raft. Thus the settlements are computed at 3 locations in the raft. The average settlement w 3D for the 3D case at the centre is given b w 3D 3 = w /3 () i= i Figure 4 illustrates a diagram similar to Figure 3 for the 2D case. Onl a half of the cross section of the raft is shown with the centre (C), the edge (E) and the mid point of the centre and the edge (F). The settlement values at the centre(c), the edge (E) and the point at midwa between the centre and the edge (F) are denoted as w C, w E and w F respectivel. The positive values of the settlements are indicated in the downward direction. In the 2D case, the average settlement under plane strain is given b w2 D = ( wc + 2wF + 2 we) /5 (2) L P where, w C is the settlement at the center of the raft ( Point C); w F is the settlement at the a uarter of raft width ( Point F); w E is the settlement at the edge point (Point E). Table 2. Details of piled rafts and pile groups in parametric stud Varied aft Dimensions Pile Group Geometr Geometr Width Thickness Pile No. of Pile Diameter Length (m) (m) Spacing Piles (m) Pile Spacing Number of Piles Pile Diameter d d 5d 2 2 6d d d 4 4 4d aft d Dimension atio Δw=ma (w, w 3)-min (w, w 3) w 3 3D = w i i= Figure 3. Plane view of 3-D piled raft and raft settlement. For the 3D as well as for the 2D case, the maimum settlement of the raft (w or w ma ) is alwas found to be at the centre. The maimum settlement will simpl be referred to as the raft settlement. In presenting the results of the settlement, often the raft settlement is normalized with the raft width. In this paper the term normalized settlement thus refers to w/ B, where w is the maimum settlement (at the centre) and B is the width (smaller dimension in plan) of the raft. For 3D analsis, the differential settlement of the raft is taken to be the difference between the maimum and minimum value of the 3 points mentioned above (as in Figure 3). Normall, the value of the differential settlement is the difference in settlement values of the center point and the 4 corner points. For 2D models, the differential settlement is the difference in settlement between the center and the edge. Similar to the maimum settlement, the differential settlement is also normalized with the width of the raft. Thus the normalized differential settlement refers to is taken as ( Δ w/ B). 3 ESULTS AND DISCUSSIONS FO CASE STUDY 3. Effect of Pile Spacing A 33 pile group is analsed with pile spacings of 3d, 4d, 5d and 6d. The pile length is kept constant as 8m. The diameter of the piles is.8m. The intensit of loading is, 4 and 6 kn/m 2. Figure 5 provides the normalized settlement with different pile spacing. The average settlement increased from 3mm to 27mm when the intensit of loading is kn/m 2 and the pile spacing increased from 3d to 6d. Generall, a pile spacing of 2d to 3d is adopted and as such for this spacing a settlement of 3mm is noted when the intensit of loading is /3

4 kn/m 2. The maimum settlements are ver close to the average values. The differential settlements for the above cases are, 3 and 6 mm and are rather small. Δw2D ΔwF Centre Point (C) /4 Point (F) Δw2D = wc-we; w2d = ( wc+2we+2wf)/5 Edge Point (E) Figure 4. Definition of raft settlement for the 2-D Case w/b ( -3 ) we Pile Spacing, s (d) kn/m 2 4kN/m 2 6kN/m 2 Figure 5. Normalized settlement vs. pile spacing. 3.2 Effect of Number of Piles A 44m raft is analsed with 33, 44 and 55 piles. The pile spacing varied from 4 to 7d. The results are presented in Figure 6. The increase in the number of piles had little effect on the normalized settlements. The effects are more pronounced at higher values of and when the number of piles increased from 9 to 6. w/b ( -3 ) Number of Piles, n kn/m 2 4kN/m 2 6kN/m 2 Figure 6. Normalized settlement vs. no. of piles. 3.3 Effect of Pile Diameter The normalized settlement presented in Figure 7 is more or less the same for the three pile diameters studied. It is likel because the value of pile spacing increases when the pile diameters rises. Conseuentl, the effect of pile-pile interaction becomes less and piles in piled raft work likel as single piles. 3.4 Effect of aft Dimension atio In this section, the results of the analsis where the (L/B) ratio of the raft is changed while B is kept constant will be presented and discussed. The (L/B) ratio was changed from to 3, while the number of piles changed from 33 to 39. The normalized settlement is presented in Figure 8. The normalized settlement increased sharpl with the (L/B) ratio when the value is 6 kn/m 2. wf wc Normalized Differential Settlement Δw/B ( -3 ) Pile Diameter, d (m) kn/m 2 4kN/m 2 6kN/m 2 Figure 7. Normalized differential settlement vs. pile diameter w/b ( -3 ) atio L/B kn/m 2 4kN/m 2 6kN/m 2 Figure 8. Normalized settlement vs. raft dimension ratio (Case 4) 4 CASE STUDY 2 In the second case stud, the load capacit of raft as well as pile group is considered for the analsis. The piled raft foundation sstem is approimated to a plane strain case and analsed using two-dimensional finite difference method. The soil is discretized into a rectangular finite difference mesh and is modelled as a linear elastic material. The raft is modelled as a beam structure under plane strain condition. The piles are modelled using pile elements, which allow the shear and normal interaction at the pile-soil interface with appropriate scaled stiffness and strength values. The effect of structural connections between raft and piles is also considered. The suitabilit of piled raft foundation in soft cla is assessed. FLAC program was adapted to analse of the piled raft sstem. The conversion of problem from 3-D to 2-D plane strain condition was carried out through scaling the pile parameters with spacing in the out-of plane direction. The loading was chosen in the working range as encountered in practice. The thickness of the raft was varied to investigate the effect of the relative stiffness of the raft on load transfer, load proportion and settlement. The numerical eperimental variables are summarized in Table 3. The subsoil for case stud 2 is generalized into three laers (see Figure 2) for the simplicit of analsis. The soil parameters obtained from the back analsis are given in Table 4. 5 ESULTS AND DISCUSSIONS FO CASE STUDY 2 The settlement from the analsis of the piled raft sstem were presented with normalized distance ( / B ), as an abscissa and 2 normalized settlement ( I = we i s / B( υs) ) as an ordinate. w i is settlement at point i, E s is the Young s modulus of soft cla, υ s is the Poisson s ratio, is the vertical load intensit at the raft surface and B is the raft width. As shown in Figure 9, the un-piled raft shows a bowl shaped settlement. The differential settlement of thin raft is larger than

5 thick rafts. As shown in Figure, similarl, the piled raft shows a bowl shaped settlement. The settlement at the edge of raft strip deviates downwards from the general bowl shape. Thinner piled rafts shoed a slightl wave shape of settlement, and have larger differential settlement than the thick piled rafts. The values of settlement for various loading cases and raft thickness of un-piled and piled raft are presented in Table 5. Table 3 Loading case and raft dimension Load case Vertical Load, kpa Horizontal Load, kpa Moment, kn-m/m 2 aft thickness, m Table 4. Summar of soil properties adopted for case stud 2. Soil laers Soft cla Stiff cla Depth, m ~5 5~3 3~9 Young s modulus, E, MPa Poisson s ratio, ν Mass densit, ρ i, kn/m wies/b(-νs 2 ) Normalized Distance, /B t=.5m t=m t=2m t=5m - Figure 9. Normalized settlement of un-piled raft with 5m width., ωies/b(- νs 2 ) Normalized Distance, /B E,ν E,ν E 2,ν 2 E 3,ν Case a Case 2 Case 3 -z B -z L /2 E,ν E,ν E 2,ν 2 L B /2 s s z L P As presented in case stud with sand soil condition, the maimum settlement of the piled rafts depends on the pile spacing and the number of piles. The raft thickness does not have a significant effect. From the results given in case stud 2 with clae subsoil, the settlement of un-piled raft was similar for different raft thickness. aft thickness was found to have obvious effect on differential settlement. The settlement of piled raft at the piled areas showed a bowl shape settlement pattern. Further, the edge of the raft strip showed a downward deviation from the settlement bowl. EFEENCES Brinkgreve,. B. J. and Broere, W., 6. PLAXIS Version 8 Manual. Delft Universit of Technolog and Plais b. v., the Netherlands Clanc, P. and andolph, M.F., 993. Analsis and Design of Piled aft Foundations. Int. Jnl. Num. Methods in Geomechs., 7, Coduto, D.P.,. Foundation Design, principles and practices (2nd ed.). New Jerse, USA: Prentice Hall. Fraser,.A., and Wardle, L.J., 976. Numerical analsis of rectangular rafts on laered foundations. Géotechniue. 26(4), Itasca, 995. Fast Lagrangian Analsis of Continua (FLAC) Manual. Kuwabara, F Elastic analsis of piled raft foundations in a homogeneous soil. Soils Found, 29(), Meerhof, G.G., 959. Compaction of sands and bearing capacit of piles. Journal of Soil Mechanics, ASCE, 85(SM6), -29. Poulos, H.G., and Davis, E.H., 98. Pile foundation analsis and design. New York: Wile. Poulos, H. G., 993. An Approimate Numerical Analsis of Pile aft Interaction. Int. Jnl. Num. Anal. Meths. In Geomechs., 8, Prakoso, W.A., and Kulhaw, F.H.,. Contribution to piled raft foundation design. J Geotech Engng Div, ASCE, 27(), -7. andolph, M.F., 3. Science and empiricism in pile foundation design. Geotechniue, 53(), Ta, L.D., and Small, J.C., 996. Analsis of Piled aft Sstems in Laered Soil. International Journal of Numerical and Analsis Methods in Geomechanics,, Tomlinson, M.J., 986 Foundation Design and Construction. 2 nd ed. New York: Pitman Publishing. Zhang, H.H. and Small, J.C.,. Analsis of Capped Piled Groups Subjected to Horizontal and Vertical Loads. Computers and Geotechnics, 26, -2. E 3,ν Figure. Normalized settlement of piled raft. Table 5. Summar of raft and piled raft settlement. Unpiled raft Piled raft Wi (mm) Wi (mm) Edge Centre Edge Centre (t=.5m) (t=.5m) (case 2, t=m) 38.5 (case 2, t=m) 37.8 (t=5m) (t=5m) 38.9 (case 3, t=5m) 4.3 (case 3, t=5m) 6 CONCLUSIONS In this paper, numerical analsis of un-piled raft and piled raft foundation on two different soil conditions are presented. The numerical analsis was carried out in two case studies with three tpical load intensities of the serviceabilit load. The subsoil was modelled as linear elastic materials the raft being modelled as beam element, and the piles were simulated b element with shear and normal coupling springs. In case stud, geotechnical parameters were obtained several in-situ tests. As for case stud 2, the geotechnical and structural parameters were obtained from the back analsis of static pile load test data.