P. Kitiyodom, T. Matsumoto & R. Sonoda
Kanazawa University, Kanazawa, Japan
ABSTRACT: In this paper, post-analysis of the deformation of a large piled raft foundation was carried out using a three-dimensional analysis program PRAB. The soil parameters used in the analysis were obtained from the back analysis of the results of the pile load test that was conducted at the construction site. In the defor-mation analysis of the whole foundation, the concept of the equivalent pier was employed. The results of the analysis match well with the measured distribution of the foundation settlements.
1 INTRODUCTION
A commercial building was constructed in Kagoshima City, Japan in 2003 to 2004. The building is 7- storied building with a basement floor, having a building area of 9000 m2, a floor area of 50000 m2 and a maxi-mum height of 45 m (Figure 1). The building has a composite structure consisting of steel reinforced columns and steel beams. Piled raft foundation was employed for this building to reduce the average set-tlement as well as the differential setset-tlements. The raft supported by 160 piles was placed on a sandy ground The building was constructed using reverse construc-tion method, in which construcconstruc-tion of the superstruc-ture (building) and the substrucsuperstruc-ture (foundation) were constructed simultaneously, in order to reduce the construction period.
A static vertical pile load test was carried out at the construction site. Moreover, during the construc-tion stage, settlements of the foundaconstruc-tion and the water pressure beneath the raft were monitored. In this paper, post-analysis of the deformation of the founda-tion was carried out using a computer program PRAB that has been developed by Kitiyodom & Matsumoto (2002, 2003).
The back analysis of the results of the pile load test was carried out first to obtain the soil parameters for the analysis of the piled raft foundation. In the analy-sis of the piled raft foundation, in order to reduce the computation time, the concept of the equivalent pier in which a number of piles are model as an equiva-lent pier was employed. The results of the analysis are compared with the observed settlements of the foun-dation, and the validity of the concept of the equiva-lent pier is discussed.
2 SITE DESCRIPTION
Borehole investigations were carried out at 5 loca-tions (EB-1 to EB-4 and B-1) within the construc-tion site to characterise the soil condiconstruc-tions (Figure 1).
Borehole investigations at EB-1 to EB-4 were carried out in 1993 to explore soil stratification and to obtain
-70 load test of pile
B
Building area above the ground surface
Pile diameter(m) Pile length(m) D = 1.5 20 D = 1.8 20 D = 2.0 25 D = 1.8 25
Figure 1. Elevation view of building, soil profiles, SPT-N- values and arrangement of piles.
distributions of SPT blow count, N, to depths of 50 m to 65 m. Detail borehole investigation was carried out at B-1 in 2002.
In this borehole investigation, PS-logging (elastic wave exploration) was carried out as well to estimate velocities of primary wave, Vp, and secondary wave, Vs, to a depth of 30 m below the ground level, which is nearly equal to levels of tip of piles.
The borehole investigations showed that the strati-fication at the construction site is almost horizontal.
The soil layers to a depth of 60 m are sand or sandy silt or silt. The N-values are 10 to 20 to a depth of 50 m. A gravel layer having N-values larger than 50 exists below a depth of 60 m.
Figure 2 summarised the results of SPT at B-1 and EB-2, and PS-logging at B-1. The shear wave veloci-ties, Vs, of the soils deeper than 30 m were estimated using an empirical equation (Equation 1) proposed by Ohta & Goto (1976):
Vs=68 79. ×N0 171. ×H0 199. ×Yg×St (m/s) (1) where H is the depth from G.L. (m), Yg the geologic time coefficient, and St is parameter depending on soil type.
SPT N-values at point B-1 and EB-2 are very simi-lar to a depth of 30 m, and it is seen that Vs meas-ured by means of PS-logging and estimated using Equation 1 are almost identical to the depth of 30 m.
Based on these results, the variation of the shear mod-ulus at small strain level, G0, to a depth of 63 m was
estimated by means of Equation 2 and indicated in Figure 2.
G0=ρtVs2 (2)
where ρt is wet density of the soil (ρt= 1.6 ton/m3 was assumed for depths greater than 30 m).
3 FIELD OBSERVATIONS & PILE LOAD TEST 3.1 Field observations
The field observations included measurements of settlements of the raft at 45 points and water pressure beneath the raft.
Figure 3 shows the time histories of the total load from the building and measured water pressure beneath the raft. The construction of the building was completed in September 2004. The raft (mat slab of the basement floor) was completed at the end of December 2003. Hence the foundation was regarded as a pile group until the end of December 2003, and was regarded as a piled raft after that.
The raft base was located at 6.5 m below the original ground surface. The original ground water table (3.0 m below the ground level) was lowered to 7.5 m below the ground level until the end of Febru-ary 2004, by means of deep wells. Then, the lowered ground water table was recovered to the original water table. The measured increase in the water pressure of 35 kPa corresponded to this recovery of the ground water table.
3.2 Pile load test
A test pile was constructed additionally at a location indicated by ‘star’ symbol in Figure 1. The test pile was a cast-in-situ concrete pile having a length of 32.0 m and a diameter of 1.0 m.
Shaft friction of the pile to a depth of 7.5 m was cut off by installing a double steel tube to this depth.
Axial forces were measured at 6 levels of the pile (Figure 4) and shaft resistance at sections between the strain gauge levels was derived from the axial forces.
Figure 2. Modelling of foundation and ground.
0 0 10 20 30 40 50
Depth from G.L. (m)
200
0 400 600 800
Total vertical load (MN)
Date(yy.mm.dd)
Figure 3. Time histories of the total load from the building and measured water pressure at the raft base.
4 POST-ANALYSIS 4.1 Analytical method
The post-analysis was carried out using a simplified three-dimensional deformation analytical program PRAB that has been developed by Kitiyodom &
Matsumoto (2002, 2003). This program is capable of estimating the deformation and load distribution of piled raft foundations subjected to vertical, horizontal and moment loads, using a hybrid model in which the flexible raft is modelled as thin plates alone or beams alone or combination of thin plates and beams, the piles as elastic beams and the soil is treated as inter-active springs (see Figure 5). Both the vertical and horizontal resistances of the piles as well as the raft base are incorporated into the model. Pile-soil-pile, pile-soil-raft and raft-soil-raft interactions are taken into account based on Mindlin’s solutions (Mindlin, 1936) for both vertical and horizontal forces. The considered soil profile may be homogeneous semi-infinite, arbitrarily layered and/or underlain by a rigid base stratum. Note that the estimation of non-linear deformation of the foundations can be calculated by employing the bi-linear response of the soil springs.
4.2 Equivalent pier concept
For calculation relating to large structures supported by a number of pile groups, Poulos & Davis (1980) proposed the equivalent pier method. Horikoshi &
Randolph (1999) employed this method to estimate
the overall settlement of piled rafts. In this method, a number of piles are replaced by a single ‘equivalent pier’ as shown in Figure 6.
As suggested by Randolph (1994), the diameter of the equivalent pier, Deq, can be taken as
Deq= 2 Ag/π (3)
where Ag is the plan area of the pile group as a block.
Young’s modulus of the equivalent pier, Eeq, is then calculated as
Eeq=Es+(Ep−E A As) tp/ g (4) where Ep is Young’s modulus of the pile, Es the aver-age Young’s modulus of the soil penetrated by the piles, and Atp is the total cross-sectional area of the piles in the group.
Randolph & Clancy (1993) discussed the applica-bility of the equivalent pier method and proposed an appropriate parameter to categorize as
R= ns L/ p (5)
where n is the number of piles and s is the pile spac-ing. It was shown in their work that the equivalent pier approach was suitable for values of R less than 4 and certainly for values less than 2.
Figure 4. Seating of test pile, and soil profile and SPT-N
values obtained at borehole EB-2.
0 10 20
Depth from G.L. (m)
Pumise
Figure 5. Modelling of piled raft foundation.
y
x b
b
Figure 6. Concept of equivalent pier method.
Deq
Actual piled raft Piles replaced by equivalent pier
4.3 Back-analysis of vertical pile load test In order to determine the soil parameters appropri-ately, back-analysis of the vertical load test of the test pile was carried out prior to the analysis of the whole foundation. The test single pile and the ground were modelled as Figure 4. Young’s modulus of the pile Ep= 2.27 × 107 kPa was employed. The maxi-mum shaft friction, fmax, of each section (see Figure 4) obtained from the static vertical pile load test results was adopted in the back-analysis.
Figure 7 shows comparison of the analysed and measured load-settlement curves of the pile head and the pile base. Good matching was obtained if the shear modulus of the soil obtained from PS-logging was reduced by a factor of 2 for the soils surrounding the pile shaft and by a factor of 5 for the soil beneath the pile base. These reductions in the shear moduli of the soils may be reasonable, considering disturbance of the soils around the pile, and difference of strain levels between the pile load test and PS-logging. Such reduction in the shear moduli of the soils around the pile are considered also in the post analysis of the whole foundation.
4.4 Analyses of the whole foundation system The modelling of the foundation and the ground has been shown in Figure 2. It was judged that modelling of the ground to the depth of 63 m is needed when analysing the whole foundation because the influ-ence of the wide length of the raft of 156 m reaches to deeper depths. Note here that SPT N-values for depths greater than 63 m were very large and the depth of 63 m was assumed to be a bed stratum.
Figure 8 shows the piles and the equivalent piers arrangement. Property of the equivalent piers are summarised in Table 1. It can be seen that the values of R in all types of equivalent piers are less than 2.
The interaction factors and soil springs at the raft nodes were calculated using the shear moduli, G0, at small strain level shown in Figure 2, while reduced shear moduli estimated from the back-analysis of the static load test mentioned in the previous section were used for estimation of the soil springs at the pile nodes. For the estimation of the Young’s modulus of a equivalent pier and soil springs at the equivalent pier nodes, the soil moduli, G0, at small strain level were employed.
Figure 9 shows a side view of the building. In the modelling of the foundation structure, the raft was modelled by combination of thin plates and beams.
The raft base was located at 6.5 m below the original
Unit (m)
Figure 8. Arrangement of piles and equivalent piers.
Table 1. Properties of equivalent piers.
Pier type Deq(m) Lp(m) Eeq(kPa) R
1 11.17 20 2.51 × 106 1.27
2 20.31 20 1.76 × 106 1.90
3 11.17 25 2.52 × 106 1.14
Figure 7. Comparison of load-settlement curves of the test pile.
Load on pile head, or load transmitted to pile base (kN)
Vertical displacement (mm)
Pile head (measured) Pile base (measured) Pile head (calculated) Pile base (calculated)
Figure 9. Construction areas of superstructure in stages of pile group and piled raft.
Vertical Load Super structure area in piled raft
z
Super structure area in pile group G.L.
5.0m35.9m
RF
ground surface. In the analysis, the construction of the superstructure was divided into two stages in which the foundation acted as a pile group and as a piled raft. The hatching indicates the area of the superstruc-ture constructed in the stage of piled raft.
In the deformation analysis of the whole structure, rigidity of the superstructure was neglected and verti-cal loads from the superstructure were directly applied on the raft nodes. The analysis was carried out in two stages. The first stage was the deformation analysis in stage of pile group where the raft resistance was not expected. The deformation analysis in stage of piled raft was carried out after the end of the first stage, considering the existence of the raft resistance. The stress conditions at the end of the first stage were used for the initial conditions in the second stage.
Figure 10 shows the distributions of loads on the raft. In the analysis, the loads acting on the top of the piles, which were modelled as an equivalent pier, were summed up and placed on the top of the equiva-lent pier node. In analysis for the stage of pile group foundation, load increments shown in Figure 10(a) were applied on the raft in 20 steps, in order to allow for the slippage of the pile and the pier shaft, and the
failure of the pile and the pier base. In analysis for the stage of piled raft foundation, load increments of Figure 10(b) were applied on the raft. Note here that the ground water level was recovered at the construc-tion stage of the piled raft as menconstruc-tioned earlier. The buoyancy force due to the water pressure at the raft base was also taken into account in addition to the load increments of Figure 10(b).
Figures 11 and 12 show the distributions of calcu-lated and measured settlements of the raft in the x-direction at y = 40.5 m (see Figure 1, section A-A') in stage of pile group
Vertical displacement (mm)
in stage of piled raft
Vertical displacement (mm)
at the final construction stage
Vertical displacement (mm)
x axis (m) (at y = 40.5 m) (a) Increments of settlements in stage of pile group
(b) Increments of settlements in stage of piled raft
(c) Total settlements at the final construction stage Figure 11. Calculated and measured settlements (at
y = 16.2 m).
Figure 10. Distribution of loads on the raft.
0
Vertical load increments (kN)
x distance (m)
(a) Superstructure load increments in stage of pile group
0
Vertical load increments (kN)
x distance (m)
(b) Superstructure load increments in stage of piled raft
section B-B'), respectively. Increment of settlements in stage of pile group are shown in Figures 11(a) and 12(a), those in stage of piled raft are shown in Figures 11(b) and 12(b), and the total settlements at the final construction stage are shown in Figures 11(c) and 12(c). In the figures, the calculated results of Son-oda et al. (2008) in which all of piles were modelled as piles in the analysis using PRAB are also shown.
It is seen from the figure that although the analyses tends to overestimate the measured settlements in the stage of pile group foundation and underestimate the measured settlements in the stage of piled raft founda-tion, the analyses predicted the measured total
settle-ments fairly well. It can be seen from the both analysis results that the analysis results using equivalent pier concept match very well with the analysis results of Sonoda et al. (2008). This demonstrates the validity to model some piles in the piled raft as the equivalent piers. Note that the calculation time using equivalent pier concept is less than 1/3 of the calculation time used in Sonoda et al. (2008).
Moreover, the distributions of calculated and measured total settlements of the raft are shown in Figure 13(a) for the distributions of settlements in the x-direction at y = 16.2 m, and in Figure 13(b) for distributions of settlements in the y-direction at x = 132.0 m. It is seen again from the figures that there are good agreements between the analysis results and the measured settlements.
5 CONCLUDING REMARKS
Deformation analysis of a piled raft foundation for a building constructed using reverse construction method was presented. The foundation system acted as a pile group in earlier stage and then acted as a piled raft in later construction stage in the reverse construction method. Detailed field measurements including settlements of the raft and the water pres-sure beneath the raft, and a static load test of a test pile were carried out during the construction work.
Post-analysis of the foundation system was carried out using a simplified three-dimensional deformation analysis method. In this paper, some of the piles were Figure 12. Calculated and measured settlements (at
x = 3 4.8 m).
in stage of pile group
Vertical displacement (mm)
y axis (m) (at x = 34.8 m)
(a) Increments of settlements in stage of pile group
0 10 20 30 40 50 60
in stage of piled raft
Vertical displacement (mm)
y axis (m) (at x = 34.8 m)
(b) Increments of settlements in stage of piled raft
0 10 20 30 40 50 60
at the final construction stage
Vertical displacement (mm)
y axis (m) (at x = 34.8 m)
(c) Total settlements at the final construction stage
Figure 13. Calculated and measured total settlements.
0 20 40 60 80 100 120 140 160
at the final construction stage
Vertical displacement (mm)
x axis (m) (at y = 16.2 m)
(a) Calculated and measured total settlements (at y = 16.2 m)
20
at the final construction stage
Vertical displacement (mm)
y axis (m) (at x = 132.0 m)
(b) Calculated and measured total settlements (at x = 132.0 m)
0 10 20 30 40 50 60
modelled as the equivalent piers. The shear moduli of the ground were estimated from PS-logging and back analysis of the static pile load test. It was shown that the calculated settlements were acceptable for practi-cal design purpose.
It was found from this case study that the analysis results using equivalent pier concept in which piles are modelled as equivalent piers match very well with the analysis results of the full model, and the calcula-tion time of the analysis using equivalent pier concept are less than 1/3 of the calculation time of the full model analysis.
The above conclusions encourage the use of the simplified deformation analysis with the equivalent pier concept in the alternative designs of a large piled raft foundation.
ACKNOWLEDGEMENTS
The authors deeply thank to Kyushu Railway Com-pany and Kagoshima Terminal Building Corporation and Yasui Architects & Engineers, Inc. for their per-mission to use the valuable field measurement data.
REFERENCES
Horikoshi, K. & Randolph, M.F. 1999. Estimation of overall settlement of piled rafts. Soils and Foundations 39(2):
59–68.
Kitiyodom, P. & Matsumoto, T. 2002. A simplified analysis method for piled raft and pile group foundations with batter piles. International Journal for Numerical and Analytical Methods in Geomechanics 26: 1349–1369.
Kitiyodom, P. & Matsumoto, T. 2003. A simplified analysis method for piled raft foundations in non-homogeneous soils. International Journal for Numerical and Analytical Methods in Geomechanics 27: 85–109.
Mindlin, R.D. 1936. Force at a point interior of a semi-infinite solid. Physics 7: 245–256.
Ohta, Y. & Goto, N. 1976. Estimation of S-wave velocity in terms of characteristics indices of soil. Butsuri-Tanko Society of Exploration Geophysicists of Japan 29(4):
31–41. (in Japanese).
Poulos, H.G. & Davis, E.H. 1980. Pile foundation analysis and design. New York: Wiley.
Randolph, M.F. 1994. Design methods for pile group and piled rafts. Proc. of 13th Int. Conf. on SMFE, New Delhi 5: 61–82.
Randolph, M.F. & Clancy, P. 1993. Efficient design of piled rafts. Proc. of Deep Foundation on Bored and Auger Piles, Ghent, Belgium: 119–130.
Sonoda, R., Matsumoto, T., Kitiyodom, P., Moritaka, H. &
Ono, T. 2008. A case study of piled raft foundation con-structed using reverse construction method and its post-analysis. Canadian Geotechnical Journal. (accepted)
Deep Foundations on Bored and Auger Piles – Van Impe & Van Impe (eds)
© 2009 Taylor & Francis Group, London, ISBN 978-0-415-47556-3