SETTLEMENT PREDICTION OF SOME VERTICALLY ...

Settlement prediction of some vertically loaded pile groups

Wei Dong Guo

SETTLEMENT PREDICTION OF SOME VERTICALLY LOADED PILE GROUPS

Wei Dong GUO1

ABSTRACT: Settlement prediction is a critical issue in design of pile foundations, especially with the increasing use of settlement reduction piles. There are various methods for the prediction. However, the most efficient method is the BEM approach that is based on closed-form solutions for single piles. In this paper, settlements of several practical cases have been predicted using a BEM based program GASGROUP developed by the author, which was published a few years ago. The program was developed from closed-form solution for a single vertically loaded pile and use of pile-pile interaction factor that were also developed by the author and his co-author. Analyses of 12 pile groups are conducted for which measured settlements are available. The predicted settlement is within 7% of measured data for piles installed in normal consolidated soil. With regards to piles in overconsolidated clay, as anticipated, the settlement is overestimated due to negligence of the ground level modulus. The current solutions well capture the predominant impact of depth of underlying rigid layer, profile of shear modulus, etc by utilizing shear modulus profile theoretically deduced from load-settlement curve of a single pile, and/or using reported value directly. They are very efficient both in terms of preparing input data and the computation. Prediction of settlement about a large group (say, 697) piles can be fulfilled within a few minutes. Thereby, the program may be utilized for general design. KEYWORDS: piles, numerical modelling and analysis, settlement, soil-structure interaction, practical projects 1.

INTRODUCTION

Various techniques have been developed to predict the settlement of pile groups. Most numerical approaches are either based upon direct analysis of the entire pile group itself or using the superposition principle in conjunction with interaction factors. With respect to large pile groups, the prediction of settlement becomes almost impossible using finite element and/or finite difference methods [1]; while the superposition technique is generally simple, efficient and achievable [2]. In particular, the interaction factors have been presented in chart form and empirical expressions. Nevertheless, the explicit expression of pile-to-pile interaction factors derived from the closed-form solution for a single vertically loaded pile is more rigorous, attractive and readily to be used [3]. Closed-form solution for a vertically load pile [3], and the interaction factors developed for pile groups [1] are utilized in the program GASGROUP. Their main features are as follows: 1. Shear modulus of the soil varies as a power, n of depth, z: G = Agzn, where Ag = gradient of the distribution; n = non-homogeneity profile, which is selected to follow either a SPT profile (for sand) or a CPT profile (for clay). The effect of modulus at mudline can be catered for using 1

Senior Lecturer, Griffith University, Australia

1 of 6

Settlement prediction of some vertically loaded pile groups

Wei Dong Guo

the new solution by Guo [4], which is remarkable for an overconsolidated clay as demonstrated later on. The parameter Ag may be determined by matching predicted pile-head stiffness with measured pile load-displacement relationship. 2. The shaft displacement, w, is directly related to the local shaft stress, τ0, by w = (τ0r0/G)ζ, where r0 = radius of an equivalent solid pile; and ζ = shaft load transfer factor that is given by  1 −ν s L  + B  ζ = ln A 1+ n r 

o



(1)

Where νs = Poisson’s ratio of the soil; L = pile length. Expressions for A & B were generated by fitting Eq. (1) with those values of ζ obtained using the numerical FLAC analysis [5]. The A & B parameters were found to be affected by H/L (H = depth of an underlying rigid layer), λ (= the ratio of pile Young’s modulus, Ep over soil shear modulus at level just above pile-tip, GL), and L/r0. In case of H/L > 4, the parameters used are A = 2.5, and B = 0[6]; Otherwise, they should be estimated using the expressions developed by Guo & Randolph [5]. 3. The base settlement wb is estimated through the solution for a rigid punch acting on an elastic half-space by wb = Pb(1-νs)ω/[4roGB] It is directly related to the base load, Pb, the shear modulus just below the base of the pile, GB, and the pile base shape and load factor, ω. In case of H/L > 4, ω is assumed as 1.0 [5]; Otherwise, it should be estimated using the expressions incorporating various factors [5]. 4. The closed-form solutions for a single pile were then used to find expressions for pile-pile group interaction factor [1]. This is achieved by superimposing displacement field of a neighboring identical pile into a concerned single pile in light of the interaction factor, α12 α12 = Cv/Cv2√(ζ2/ζ) – 1

(2)

where Cv and Cv2 are functions of modified Bessel functions of fractional order. Cv depends on the values of ζ and ω for a single pile, and Cv2 on ζ2 and ω2 for a pile in a two-pile group. The latter factors were related to the spacing of the piles, s, and the pile radius, r0. 5. Settlement wi, of any pile i in a group is predicted using the superposition principle [1,2] with ng

wi = w1 ∑ Pjα ij

(3)

j =1

where Pj is the individual pile load; w1 is the settlement of a single pile under unit head load; αij is the interaction factor between pile i and j determined using Eq. (2); ng is the number of piles in the group. 2.

GASGROUP

The GASGROUP was written in FORTRAN 90 and it can operate in Microsoft WindowsTM platform. It allows settlement of a large group piles to be computed efficiently. A simple program called ‘GL-Estimate’ has been developed as well to facilitate back-calculation of the soil shear modulus and its distribution against measured pile-head stiffness, Pt/wt of a single pile (Pt, wt = the average load taken by an individual pile in a group, and the settlement of a single pile under the load, respectively). The parameters needed for the back-estimation are as follows: n, L, r0, Pt/wt, Ep, H/L, νs, GL/GB and ζ. With respect to estimation of group settlements, the layout (foundation shape and pile spacing) of piles in a group, and total load PG on the group are required. A settlement ratio Rs is calculated from the program GASGROUP, which renders the group settlement Sg to be estimated as Rswt. 3.

CASE STUDY

Eight new case studies were analyzed using the GASGROUP program. Relevant parameters are provided in Table 1. Due to space limitation, only six cases are elaborated subsequently. 2 of 6

Settlement prediction of some vertically loaded pile groups

Wei Dong Guo

Case 1 Dashwood House Dashwood House [7] is a 15 storey, 61 m high building located close to Liverpool St Station in London. The building has a single storey basement resting on a rectangular piled raft foundation. The pile group consisted of 462 (21×22) bored piles, each having a diameter of 0.485 m and a length of 15 m. They were capped by a rectangular raft of 33.8×32.6 m. The Young’s modulus, Ep was 30 GPa. The piles in the group were arranged in a grid of 1.5 m square spacing. The subsoil profile beneath the building was 1 m placed compacted gravel, followed by approximately 29 m of London clay, and 10 m of Woolwich and Reading beds. The shear modulus G for the London clay was estimated as: G = 30+1.33z (MPa). Poisson’s ratio, νs was taken as 0.5. The overall load on the foundation was 279 MN, under which measured settlement was 33 mm [7]. The equivalent n was found to be 0.2~0.4. This ‘n’ allows a shear modulus to be determined in terms of the constant of Pt/wt. Under an average working load of 604 kN per pile, settlement of a single pile was estimated as 1.17 mm.The results thus obtained are as follows: (i) n = 0.2, Ag = 26.1 MPa/m0.2, GL = 44.92 MPa, PG/(GLwtr0) = 668.8, Rs = 32.68, and Sg is evaluated accordingly as 38.2 mm. Or (ii) n = 0.4, Ag = 18.8 MPa/m0.4, GL = 55.51 MPa, PG/(GLwtr0) = 543.6, and Rs = 32.47, and Sg = 38 mm. The estimated settlement of 38~38.2 mm is within 15% of the measured value. It is quite satisfactory in view of 462 piles in the group. The discrepancy may be attributed to any difference between the calculated single pile settlement of 1.17 mm and the actual one. Table 1 Summary of parameters for group pile analysis Case L (m) r0 (m) Ep(GPa) n νs GL (MPa) GL /GB Spacing (m) H/L wt (mm)

Case 2

1 15 0.2425 30 0.4 0.5 50.0 1-3 1.5 1.9 1.17

2 4.5 0.084 210 0.5 0.5 38. 1-3 0.505 4 0.26

3 13 0.225 30 0.4 0.5 38.72 1-3 1.6 1-4 0.85

4 13.1 0.137 13.44 0.65 0.5 151 1-3 0.82 4 2.85

5a & 5b 20 0.30 23 1.0 0.3 145 ~ 147 1-3 2.14 1.75~2.7 1.3

6 9.15 0.1365 13.4 0.0 0.3 43.43 3.0 0.82 1.5 4.56

7 20. 0.45 26 0.4 0.5 40 1 2.93 3 4.0

8 31 0.34 26 0.8 0.3 68 1 2.5 1.5 3.15

Jacked Piles in London Clay

A series of field tests was conducted on pile groups embedded in London clay [8]. Each tubular steel pile has an external radius of 84 mm and a wall thickness of 6.4 mm. The piles were embedded to a depth of 4.5 m and at a spacing of three pile diameters. The clay extends from the mudline to a depth of about 30 m. Shear modulus was 15.6 MPa at the surface, and linearly increased to 38.0 MPa at the pile base. Poisson’s ratio was assumed to be 0.5. The measured loadsettlement curve for pile A (the middle pile) shows a settlement of 0.23 mm at an average working load of 33.3 kN. Settlement of the 3-pile group loaded with a rigid pile-cap was recorded as 0.38 mm under a total load PG of 100 kN. n was found as 0.5. The measured ratio of Pt/wt = 145 kN/mm allows GL = 43.6 MPa to be backcalculated. The parameters thus deduced and results calculated are as follows: n = 0.5, Ag = 20.53 MPa/m0.5, GL = 43.6 MPa, PG/(GLwtr0) = 100.1, and Rs = 1.79. The latter renders a settlement of 0.41 mm to be estimated for the group, which is close to the measured value of 0.38 mm. Case 3

Stonebridge Park Apartment Building

The Stonebridge Park Apartment building [9] is a 16 storey block of apartments, located in the London borough of Brent. The building is 43.3 m long by 19.2 m wide. The foundation consists of a heavily reinforced concrete raft 0.9 m thick resting on 351 cast in situ bored concrete piles. The piles are 0.45 m in diameter and 13 m in length, formed at a square spacing of 1.6 m. The shear modulus distribution of the subsoil is described by G = 20 + 1.44z (MPa). 3 of 6

Settlement prediction of some vertically loaded pile groups

Wei Dong Guo

The average working load per pile was 565 kN as any load carried by the raft was ignored. At the end of construction the actual settlement of building was measured at about 10.5 mm. Over a period of 4 years, however the settlement increases by 70% to 18 mm. Non-homogeneity factor, n was estimated as 0.4. Incremental loading tests were carried out on the site prior to construction albeit with a limited duration for each load increment. This results in a higher Pt/wt and consequently shear modulus. Due to the constraints, an estimate of the ‘n’ value will be used along with GL of 38.72 MPa. The derived parameters and results are: n = 0.4, Ag = 13.8 MPa/m0.4, GL = 38.72 MPa, PG/(GLwtr0) = 399.3, Rs = 36.7, and Sg = 31.9 mm. The estimated settlement of the pile group is rather large compared to the measured value of 19 mm. However, a lower H/L ratio of 1.5~2.0 will lead to a reduced settlement of 17.7~25.2 mm. Compared to measured data, an underlying rigid layer may exist at a depth of, say, 20 ~ 26 m. Case 4. Driven Piles in Over-consolidated Clay A series of tests on single piles and a pile group were driven into stiff overconsolidated clay at the University of Houston [10]. The full sized pile group was constructed with nine 273 mm diameter closed ended steel pipe piles that have a wall thickness of 9.3 mm. The piles were driven to a penetration of 13.1 m into the clay. The 9-pile group was installed in a 3×3 configuration with a centre-to-centre spacing of 6r0. Two separate piles were installed 3.7 m from the centre of the group and on opposite sides. The 9-pile group was connected to a rigid reinforced concrete block. The two single piles and the 9 pile group were loaded to failure, back analysis showed the clay had a shear modulus at the surface of 47.9 MPa, and it increased linearly to 151 MPa at the base of the pile. Poisson’s ratio of the soil was estimated as 0.5. The load – settlement curve of single pile test indicates that at the average load of 550 kN per pile, the settlement was 2.85 mm, thus the ratio of Pt/wt was estimated to be 260 kN/mm. The group settlement of the 3×3 pile group was measured at 4.55 mm. n was found as 0.65 from the reported shear modulus distribution. Young modulus of an equivalent solid pile was estimated using Ep =Esteel [ro2-(ro-t)2]/ro2, where E of steel = 200 GPa, ro and t = the outside radius, and wall thickness of the pile. GL was back-estimated as 263.57 MPa in terms of the ratio of Pt/wt and n. The outcome for this group is as follows: n = 0.65, Ag = 49.5 MPa/m0.65, GL = 263.57 MPa, PG/(GLwtr0) = 26.28, and Rs = 2.34. The latter allows a settlement of the group to be estimated as 6.68 mm. The computed settlement exceeds the measured value by 2 mm approximately, which may be attributed to the highly overconsolidated clay; to the gradual underestimation of the modulus at greater depths by using the ‘n = 0.65’; and to the existence of any underlying rigid layer. All these factors could reduce the calculated settlement, which is not fully considered herein. Case 5

Napoli Holiday Inn & Office Tower

The structures [11] were developed as part of the new Directional Centre of Napoli. They consist of steel frames with reinforced concrete stiffening cores. The rigid foundation slabs have a thickness varying between 1.2 and 3.5 m. They in turn rest on 314 (Office Tower) and 323 (Holiday Inn) auger piles of the “PressoDrill” type with a diameter of 0.6 m and a length of 20 m. Young’s modulus of the piles was back-calculated as 23 GPa. The total load of each of the structures is approximately 200 MN. The average permanent load per pile is about 670 kN. The subsoil of the site from the surface downwards is as follows: man-made ground; volcanic ashes/organic soils; stratified sands; cohesionless pozzolana; and volcanic tuff. The thickness of the upper soils is about 16 m, at this depth a peat layer is found, where the qc values are very small. The thickness of stratified sands increases from 5 to 20 m from the Office Tower towards the Inn. This follows the deeper pyroclastic formation from 22 to 37 m below the surface. The piles are arranged in 15×20 (Office Tower) and 15×21 (Holiday Inn). The Office Tower site is 1,308 m2, thus, the average single pile area was 4.36 m2, giving a pile spacing of approximately 2.18 m. This average spacing was assumed uniform throughout both sites. 4 of 6

Settlement prediction of some vertically loaded pile groups

Wei Dong Guo

Office Tower The sub-soil of this site has an underlying volcanic tuff layer approximately 35 m below the surface. The ratio of H/L was estimated to be 1.75. The GL was back estimated as 145.2 MPa by using a Pt/wt = 600 kN/mm determined from single pile tests. The shallow embedded depth of the rigid layer allows GL/GB to be estimated as 3.0. As a consequence, the following calculations are obtained: GL = 147.9 MPa, PG/(GLwtr0) = 253.4, and Rs = 16.96. The settlement of the group is thereby evaluated as 22.0 mm. Holiday Inn The rigid layer of volcanic tuff dramatically increases with depth across the site. The depth of the layer is 54 m and increases underneath the Holiday Inn site. Thereby, the H/L ratio was taken as 2.7, with a corresponding GL/GB value of 2.0. The GL of 143.9 MPa was then back-calculated, using the same Pt/wt. These allow PG/(GLwtr0) = 185.8, and Rs = 23.19 to be obtained. Settlement of the group is thus computed to be 30.15 mm. The analysis conducted using a ratio GL/GB varying between 1.0 and 3.0 induces less than 1 mm difference in the computed settlement. The measured settlements at the Office Tower ranged between 9.2 mm at the edge and 29.1 mm at the centre of the foundation, with an average of 20.8 mm. Should depth of the rigid layer be smaller than 35 m below the office tower, the calculated settlement will be smaller. The actual measured settlements at the Holiday Inn range between 26.9 and 32.7 mm with an average of 30.9 mm, almost matching the computed settlement. Overall, the computed settlements closely agree with the measured ones. Table 2 Comparison between predicted and calculated settlement of group piles Case

Description

1 2 3

Dashwood house (OCR > 1) Jacked Piles in London Clay Stonebridge Park Apartment Driven Piles in Houston Clay (OCR > 1) Napoli: (a) Office Tower (b) Holiday Inn San Francisco 5-Pile Frankfurt Building Twin 39-Stoery Building Molasses tank Ghent Terminal Silos 19-storey concrete building 5-storey building

4 5 6 7 8 9 10 11 12

Case 6

G = 18.8z0.4 G = 20.53z0.5 G = 13.8z0.4

Number of piles 462 3 351

Observed so (mm) 33 0.38 18

Predicted sp (mm) 37.98 0.41 17.7

G = 49.5z0.65

9

4.55

6.68

G = 7.195z G = 7.367z G = 43.43 G = 11.94z0.4 G = 4.36z0.8 G = 0.504z G = 28.6 G = 12.19z0.5 G = 10.03z0.8

314 323 5 84 266 55 697 132 20

20.8 30.9 5.75 45 40 29~30 180 64 10~20(14)

22.0 30.15 5.56 47 40.3 28.7~29.2 186.3 63.5 12.6

Modulus (MPa)

Refer

[1] [1] [1] [1]

San Francisco 5-pile Group [12]

Load tests to failure were performed on a single pile and a five-pile group installed in hydraulicfill sand at a site in San Francisco [12]. The closed-end steel pipe piles were 273 mm in diameter and 0.0093 in wall thickness. All piles were driven to a depth of 9.15 m below the ground surface through a 300 mm pre drilled hole to a depth of 1.37 m at a spacing of 6r0. The piles were connected by 1.8 m rigid thick reinforced concrete cap. The subsoil at the site was sandy gravel fill to a depth 1.37 m below the surface, followed by a hydraulic-fill layer of clean sand down to 12.2 m, further down by bedrock located at a depth 14.3 m. Results of CPT indicate the nonhomogeneity factor n may be taken as 0.0, as a uniform distribution of the modulus is noted. The Pt/wt was obtained as 222 kN/mm. This allows shear modulus at the pile toe to be backestimated as 43.43 MPa. At an average load of 311.5 kN per pile, the single pile settlement was measured as 4.56 mm, while the group settlement was measured as 5.75 mm. With the calculated Young’s modulus of the pile, it follows that: n = 0, Ag = 43.43 MPa, GL = 43.43 MPa, PG/(GLwtr0) = 152.8, Rs = 1.22, and Sg = 5.56 (mm). This estimated 5.56 mm well match with measured value of 5.75 mm. 5 of 6

Settlement prediction of some vertically loaded pile groups

Wei Dong Guo

Cases 7 and 8 are provided in Table 2 together with Cases 9~12 analyzed previously [1]. 4.

COMMENTS and CONCLUSIONS

A wide variety of geological conditions were encountered for 12 cases investigated so far. A comparison between the observed and calculated settlements for all cases is provided in the Table 2. For normal clay, the predictions are within 7% to the measured data. Lack of information may be complemented through parametric analysis, such as the affect of the H/L in Case 3. Below are some key findings in this study. • Using average pile center-center spacing has negligible effect on the predicted settlement. • Variation of GL/GB from 1 to 3 has limited effect on the predicted settlement. • A shallow rigid layer of H/L < 2 will have obvious effect on the prediction. • Existing distribution of shear modulus, and also back estimated one should be used in calculating settlement. • Inaccuracies can creep into the back estimation method due to the selection of Pt/wt from a plot, as misinterpretation of the initial gradient may occur. Prediction of settlement of a single pile is necessary. Representing the soil shear modulus distribution can be difficult with overconsolidated clays as observed in Cases 1, and 4. • The program is efficient with all calculations taking under 2 min, even for a 697 pile group that cater for all important factors such as expanded pile bases, varying sub-soil profiles and depths to rigid layers. Dean Purdy and Chad Bunyan are acknowledged for their assistance in conducting the case studies. 5. REFERENCES 1. Guo, W. D. and Randolph, M. F., “An efficient approach for settlement prediction of pile groups”, Geotechnique, Vol. 49, No. 2, 1999, pp. 161-179. 2. Poulos, H. G., “Analysis of the settlement of pile groups”, Geotechnique, Vol. 18, No. 4, 1968, pp. 449-471 3. Guo, W. D. and Randolph, M. F., “Vertically loaded piles in non-homogeneous media”, Int. J. Num. & Analy. Methods in Geomech., Vol. 21, No. 8, 1997, pp. 507-532 4. Guo, W. D., "Vertically loaded single piles in Gibson soil." J. of Geotech. And Geoenvironmental Engrg. Div., ASCE, Vol. 126, No.2, 2000, pp.189-193. 5. Guo, W. D. and Randolph, M. F., "Rationality of load transfer approach for pile analysis." Computer and Geotechnics. Vol. 23, No.1-2, 1998, pp. 85-112. 6. Randolph, M. F. and Wroth, C. P., “Analysis of deformation of vertically loaded piles”, J. of Geotech. Engrg. Div., ASCE, Vol. 104, No. 12, 1978, pp. 1465-1488 7. Green, P. and Hight, D., “The instrumentation of Dashwood House”, Tech. Note, No.78, CIRIA, London, 1976. 8. Cooke, R. W., Price, G. and Tarr, K., “Jacked piles in London clay: interaction and group behavior under working conditions”, Geotechnique, Vol. 30, No. 2, 1980, pp. 97-136 9. Cooke, R. W., Bryden-Smith, D. W., Gooch, M.N & Sillett, D. F., “Some observations of the foundation loading and settlement of a multi-storey building on a pile raft foundation in London Clay”, Proc. Int. Civil Eng. Conf., Pt 1.Vol. 70, 1981, pp. 433-460 10. O’Neill, M.W, Hawkins, R.A and Mahar, L. J., “Load-transfer mechanisms in piles and pile groups”, J. of Geotech. Engrg., Vol. 108, No.12, 1982, pp.1605-1623 11. Mandolini, A. and Viggiani, C., “Settlement of piled foundations”, Geotechnique, Vol. 47 No. 4, 1997, pp. 791-816 12. Briaud, J.L., Tucker, L. M. and NG, E., “Axially loaded 5 pile group and single pile in sand”, Proc. 12th Int. Conf. SMFE, 2, 1989, pp. 1121-1124 13. Purdy, D., “Settlement prediction of pile groups”, Undergraduate thesis, Monash University, 2002. 14. Bunyan, C., “Design of vertically loaded pile groups”, Undergraduate thesis, Griffith University, 2004 6 of 6