A Case of 3-D Small Pile Group Modeling in Stiff Clay Under Vertical Loading

The behavior of experimental pile groups is simulated by 3-D finite element modeling in this paper. The modeled results are compared to small-scale tests in a row of three closely spaced piles in the London clay. The tests aimed at investigating soil-pile-cap interaction and pile-group effect. It is shown that 3-D FE modeling can be regarded as an appropriate tool to predict settlements and load-transfer mechanisms in pile groups under working conditions, with a satisfactory match between simulated and measured results.


Introduction
3-D finite element modeling is an effective tool to simulate soil-pile-cap interaction since pile elements with prescribed ultimate values of tip resistances and nearly any type of shaft distribution can be assigned to individual piles, applicable boundary conditions can be easily simulated, efficient constitutive soil models can be selected, and plate elements can be used to simulate the structural response of the pile cap.In this paper the simulations have been performed by the program Plaxis 3-D Foundation version 2.1.
The results of tests on three closely spaced and aligned piles tested by Cooke et al. (1980) in the London Clay are used for comparison with the present 3-D FEM analysis.The piles were tested under equal pile loading, equal pile displacements and also with the piles connected by a rigid concrete cap on the clay surface.The settlements in each pile were measured by loading the piles individually and simultaneously.In each case, predictions of settlements and load transfer are presented and compared to the experimental results.
The tests were performed in 5 m long, 168 mm diameter steel pipe piles with 6.4 mm wall thickness, embedded 4.5 m in the soil.The tests were performed in Hendon, Northern London.The soil parameters for the numerical analyses were obtained from a comprehensive literature review (Freitas, 2010) which also included the instrumentation and the field investigation conceived by Cooke et al. (1980).

Test Lay Out and Soil Parameters
Figure 1 shows a sketch of the test comprising three aligned piles A, B and C installed by jacking in this order.
The distance s between the pile axes was 3 pile diameters.Piles A and B had settlement gauges near the top and load cells at the top and at other three locations in the shaft.Pile C was not instrumented since it was expected to behave similarly to pile B under assumption of symmetry.
The three piles were monitored with horizontal inclinometers whose readings were obtained with aid of the observation trenches shown in Fig. 1.The trenches were installed sufficiently far from the testing piles (Cooke et al., 1980).The main trench was set six months before installation of pile A. The trench was 5.2 m deep, with the working face 2.1 m away from the pile alignment.The secondary trench had the working face 2.7 m away from the axis of pile A, to install the inclinometers.The secondary trench was set after the tests on piles A and B, but before installing pile C. Cooke et al. (1980) reported that although the effects of drilling, instrumentation, and installation of the observational trenches on the pile-soil stiffness are not strictly known, evidence suggests that such effects are small and therefore have been neglected in the numerical analyses.
A concrete pile cap 1.5 m long, 0.5 m wide and 0.3 m thick was cast around the pile heads and rigidly connected to them, in order to produce identical settlements in the three piles.The base of the cap was 0.2 m below ground level with no contact between the vertical sides of the cap and the surrounding soil.
The piles were loaded incrementally with each increment maintained for a period of nearly 3 minutes, up to settlement stabilization.Due to the low loading applied, an elastic behavior has been observed.The test rarely surpassed one hour, Cooke et al. (1980).
The piles were loaded according to the sequence shown in Fig. 2. The tests designation is the same adopted by Cooke et al. (1980).
Test 1: Pile A loaded alone to 57.5 kN (about 60% of the estimated ultimate load of the isolated pile estimated by Cooke et al., 1980)  Test 7: Piles A, B and C loaded simultaneously by the rigid pile cap to 120 kN keeping the bottom cap surface in contact with the clay, preventing however the soil contact with the side faces.Some adjustments on the loading pattern were needed to ensure as much as possible uniform settlement of the cap.Test 7 occurred 8 months after the installation of pile C and 2 weeks after the cap was finished.
Considering the low permeability of the soil and the short time interval between tests 2 and 3 (only 6 weeks), the corresponding results are nearly equivalent and Test 3 has been discarded.Test 3 occurred 10 weeks after installation of pile B and aimed at the investigation of the time effect on piles A and B and also the effect in load settlement curve.Test 6 was also discarded as some adjustments in the measuring equipment reported by Cooke et al. (1980) could bring additional difficulties in the numerical analysis, in addition to the fact that Test 6 was also similar to Test 4, whose analyses are illustrated in the present paper.Test 6 occurred 13 months after installation of pile B and 6 months after the installation of pile C.
The London clay specific weight ranges from 18.1 to 18.8 kN/m 3 (Kovacevic et al., 2001;Davies et al., 2008).The value g = 18 kN/m 3 was assigned to the present analysis.
The high overconsolidation of the London Clay gives rise to K 0 values greater than unity.Skempton (1961) and   Skempton & La Rochelle (1965) reported K 0 values between 2.0 and 2.5 in the upper clay layer (upper 10 m), decreasing to K 0 = 1.5 down to 30 m. Freitas (2010) summarized K 0 profiles proposed by Bishop et al. (1965) and Hight et al. (2003) in Fig. 3, which support the value K 0 = 2 assigned to the present numerical analyses.Cooke et al. (1979) summarized the values of undrained shear strength and undrained elastic modulus reported by Marsland (1971Marsland ( , 1974)).Gasparre et al. (2007) compared the stiffness parameters obtained by benderelement aided triaxial tests and HCA tests (instrumented hollow cylinder apparatus) for depths ranging from 0.8 m to 7.9 m.Accordingly, those authors reported E u values for the London clay in the range 122 ± 3 MN/m 2 for the benderelement tests, and E u values (inferred from G u ) in the range 112 ± 14 MN/m 2 for the static HCA tests, with good agreement to the band indicated in Fig. 4. Finally, Marsland (1974) recommended a linear E u profile ranging from 35 kN/m 2 at the ground surface to 78 kN/m 2 at the depth of 4.6 m, which is very close to the E u profile proposed in this paper.By combining the results of undrained elastic modulus by Marsland (1971) to several other results reported in the literature for the London clay (references above), Freitas ( 2010) assigned E u = 33 MN/m 2 at the ground surface, increasing linearly to 177 MN/m 2 at 4.5 m below the ground, which is very close to the profile recommended by Marsland (1974).The full line in Fig. 4 shows the E u profile selected for calculation.It falls within the shaded area, which is limited according to the references listed in the fig-ure.The selected E u profile was adjusted to fit the results of Test 1 and to satisfy equation 1 below: where W s is the interaction factor, s is the pile spacing and R s is the settlement ratio defined by the ratio of the average group settlement to the settlement of an isolated pile under the average load on the piles of the group.
Table 1 shows a summary of the soil parameters assigned to the FEM modeling.The Young modulus E = 2.1 x 10 8 kN/m 2 and the Poisson's ratio n = 0.2 were assigned to the hollow steel piles and to the steel plate on top of the cap (a composite cap consisting of a 25 mm thick steel plate on top of the 0.3 m high concrete cap was used in the tests).E = 2.1 x 10 7 kN/m 2 and n = 0.2 were assigned to the concrete portion of the cap.According to data obtained from instrumentation, Cooke et al. (1979) obtained maximum skin friction resistances of 66.7 kN/m 2 and 107.1 N/m 2 (at the top and at the tip, respectively) and maximum unit base bearing of 9.2 MPa.These values were selected as ultimate resistances to model the piles in the numerical analyses.Freitas (2010) present further details of the modeling.

Model Definition
The external boundaries on the horizontal (XZ) plane are fully restrained and the discretization of the FE mesh is shown in Fig. 5.The ground level was set at the elevation Y = 0 m, from which a single layer of the London clay was simulated down to Y = -30 m.The simulation extended to the same depth as the investigation carried out in Hendron, North London.The water table was assumed to coincide with the ground level.As the tested pipe piles had closed  conical tips, they were modeled as massive piles with equivalent specific weight.
The numerical modeling was based on undrained analyses.According to Brinkgreve & Swolfs (2007) y = 0 was assigned to the dilatancy angle.The Mohr Coulomb failure criterion was selected for simplicity, considering that the piles were loaded to about 60% of the ultimate loading capacity.For the analyses of the tests without the pile cap the FEM mesh had 15,450 elements and 40,561 nodes, whereas the tests with the pile cap the mesh comprised 17,496 elements and 47,752 nodes.Mandolini (1999) and de Sanctis & Mandolini (2006) pointed out that even when the load-settlement response of a single loaded pile is markedly non-linear, adjacent unloaded piles usually exhibit a linearly increasing settlement.Referring to the tests performed by Cooke et al. (1980) and by Caputo & Viggiani (1984), Mandolini (1999) stated that when the soil surrounding the pile shaft is highly stressed, the rapid decrease of the shear stresses within short distances from the loaded shaft makes elastic conditions prevail.Mandolini (1999) also pointed out that the interaction factor defined by Cooke et al. (1980) is constant and independent on the load level.The findings above support the validity of the linear approach to model the mutual interaction among piles.

Results
In the following the results of the numerical analyses are presented for tests 1, 2, 4, 5 and 7 (Freitas, 2010).As already explained in session 2, considering the low permeability of the soil and the short time interval between tests 2 and 3 (only 6 weeks), the corresponding results are nearly equivalent and Test 3 has been discarded.Test 6 has also been discarded as some adjustments in the measuring equipment reported by Cooke et al. (1980) could bring additional difficulties in the numerical analysis.

Test 1 -Two piles (B and A) in a row and Pile (A) Isolated
The load settlement curve of pile A and B loaded simultaneously is shown in Fig. 6 and compared with the corresponding curve at the end of the test on pile A (loaded alone) before the installation of pile B. Figure 6 presents the corresponding numerical and experimental results and also illustrates that the load applied in each pile is the same when only pile A is loaded and when pile A and B are loaded simultaneously.Poulos (1968) introduced the interaction factor (a) to evaluate the interaction between two piles loaded simultaneously: where (r 12 ) is the additional settlement on pile (1) due to the loading of the adjacent pile (2), whereas (r 11 ) is the settlement of pile (1) due to its own load.For a more convenient data interpretation the interaction factor (Eq. 1) was redefined by Cooke et al. (1980) as:   m/day where (r 12 ) is the induced settlement in pile (1) due to loading of pile ( 2) and (r 22 ) is the settlement of the loaded pile (2).Another useful definition is the settlement ratio (R s ) previously defined as Eq. 1.In the particular case of two equal piles equally loaded the additional settlements due to the interaction are equal.Cooke et al. (1980) observed that for three pile diameters spacing the settlements of the two piles loaded simultaneously were nearly identical for all loading levels and about 25% higher than the settlement of the isolated pile, that is, R s = 1.25.Numerical analysis using Plaxis 3D Foundation showed good agreement with the results shown in Fig. 6.The value of interaction factor obtained from the numerical analysis was W 3 = 0.20, or R s = 1.20.
Figure 7 presents the contours of vertical displacements obtained in a vertical plane passing through the piles axis.It also shows the respective view for both analyses.Cooke et al. (1980) pointed out that the loadsettlement curves were expected to depart from linearity for axial loads higher than 40 kN, and for this reason the loads on each pile in all tests were limited to this value.This limit may not be noticed when using a simple model such as Mohr-Coulomb.However, considering that all tests have been limited to the linear range and the linear approach is well supported in the literature for mutual pile interaction, the Authors considered that the use of more complex constitutive models would not be justifiable for the present application.

Test 2 -Row With Two Piles (B and A)
In test 2 the settlements of pile A loaded separately and the effect on pile A by loading pile B are compared with those obtained with piles A and B loaded simultaneously, as shown in Fig. 8.
Settlement predictions of pile A are close to the experimental value.When the load is applied at the neighbor pile B, the experimental settlements in pile A are slightly higher than the numerical results for loads higher than 30 kN, and converge to the experimental values in the case where both piles are loaded simultaneously.Cooke et al. (1980) present the load transfer for piles A and B. The load transfers are nearly equal in the numerical analysis due to the symmetry of the piling, which makes it unnecessary to represent the load transfer produced by pile B. It is worth noting that the minor differences on the transfer curve are attributed not only to small numerical errors, but also to the fact that the finite element mesh becomes slightly asymmetric in the automatic generation of  the tetrahedral elements.The results obtained for pile A are shown in Fig. 9. Santana (2008) observed that for a pile group a larger proportion of the load is transferred to the pile tips when compared to isolated piles under the same loading, as also confirmed in the present numerical analysis (Fig. 9).According to Cooke et al. (1980) the displacement produced by the source pile generates negative friction on the adjacent piles and therefore a higher load is transferred to the tip, as shown in Fig. 9.
The load transferred by the group to the pile tips is usually less pronounced in clays than in sands.However, Fig. 9 shows that even for clays the higher the loading level, the higher the load transferred by the two-piled group comparably to the isolated pile, as indicated by the higher slopes of the higher load curves.
Figures 10-a (pile A loaded separately) and 10-b (piles A and B loaded simultaneously) show that the displacements at the ground surface are negligible for dis-   tances higher than 12.5 diameters (2.1 m) from the loaded piles, as also confirmed by Cooke et al. (1980).

Tests 4 and 5 -Row With Three Piles (B, A and C)
Tests 4 and 5 are shown in Fig. 11 according to the following scenarios: i-pile A is loaded alone; ii-pile B is loaded and its effect on pile A (or C) is observed: iii-pile C is loaded and its effect on pile A (or B) is observed; iv-piles A, B and C are loaded simultaneously.
According to Fig. 11, the numerical results for the settlements of pile A (6) are slightly higher than those obtained experimentally (1).On the other hand, the modeled influence on pile A when pile B is loaded (or pile C, by symmetry) practically coincided with the experimental results (2, 3, 7 and 8).The results obtained from the sum of the effects of loads on each pile in pile A (4) are lower than the results obtained when the three piles are loaded simultaneously (5).The settlements in A when the piles in the group are loaded simultaneously are nearly identical to those obtained experimentally (5 and 10).
The numerical results for loading pile B provided values of settlement in pile B a little higher than those obtained experimentally.The numerical values for pile B considering the three piles loaded simultaneously were also a little higher than the experimental results, as shown in Fig. 12.
According to Fig. 13, the numerical results for loading pile C, denoted as (8), provided settlement in C slightly higher than those obtained experimentally (3).However, the effect on pile C for loading pile B, denoted as (7), practically coincided with the experimental data (2), whereas the effect on pile C for loading pile A (6) was slightly lower than the experimental results (1).
The experimental results obtained from the sum of the effects of the loadings on each pile on pile C, denoted as (4) in Fig. 13, were lower than those obtained when the three piles were loaded simultaneously (5).The numerical analysis produced similar results in both cases.The settlements obtained by the numerical analysis in C when the pile group was loaded simultaneously (10) were similar to those obtained experimentally (5).Although by symmetry the response of piles B and C should be similar, the experimental settlements on pile B were smaller than those on pile C in the tests with three piles.Clearly such response cannot be reproduced in the numerical results by the simple Mohr-Coulomb model.In fact, pile B has been tested previously in the two-pile array, what most likely caused some overconsolidation in the soil around the pile, in addition to possible soil natural inhomogeneity.
The load transfer obtained experimentally and numerically for pile A is shown in Fig. 14.It is seen that the numerical response is closer to the experimental behavior of the pile A in the group than the same pile loaded alone.
Figure 15 shows the response of pile B, which by symmetry is similar to the response of pile C.
Figure 16 presents the vertical displacements field for the case where the three piles are installed and simultaneously loaded with the same load of 40 kN.
Figure 17, similarly to Fig. 10, also illustrates that for piles B, A and C loaded simultaneously the displacements at the ground surface are negligible for distances larger than 12.5 diameters (2.1 m).

Test 7 -Row with Three Piles (B, A and C) and Pile Cap
Test 7 compares the settlements obtained when piles A, B and C were loaded simultaneously by the rigid pile cap with the settlements obtained by the three piles loaded simultaneously without the pile cap. Figure 18 illustrates the pile arrangement in the numerical model.Cooke et al. (1980) reported that for the group of three piles with the pile cap loaded incrementally up to the   load of 118.7 kN successive adjustments were needed in the loading as an attempt to ensure as much as possible uniform settlements on the pile cap.These adjustments were not entirely successful, as illustrated in Fig. 19.Clearly, these trial adjustments were not possible to be reproduced in the numerical analysis.As a result, a more rigid behavior of the cap was obtained in the simulated results, as shown in Fig. 19.Therefore the difference between the modeled and the experimental results are attributed to the uncertainty in the application of the loads.Nevertheless, a good agreement was obtained on the average settlements, as illustrated in Fig. 20. Figure 21 illustrates the load transfer for test 7.
The load in Fig. 20 is that for the whole group in test 7, while only the central pile is represented in test 4 (considering the three piles loaded simultaneously).
For the case the pile group is loaded through the cap, greater loads were observed experimentally for higher load levels, both for central pile (A) and also for the corner one (B).
For test 7, it is observed on Fig. 22, through both sections A'A (a) and B'B (b), the field of vertical displace-    ments, numerically obtained in 3-D finite element modeling, when all piles were carried out under 39.6 kN.

Conclusions
The paper summarizes some results from Freitas (2010) who extensively examined different arrangements of pile groups through 3-D FEM modeling.The back analysis of Test 1 (isolated pile) enabled the Authors to successfully predict other pile interaction schemes tested by Cooke et al. (1980) and to validate the numerical analyses of the tested piles.
The numerical analyses of test 2 showed that the superposition effect of loading two piles separately was very close to the results obtained when both piles were loaded si-multaneously.The small differences observed in the load transfer in both piles are attributed to minor differences due to the asymmetric pattern of the automatically generated meshes.
In tests 4 and 5 the effect on pile A when loading pile B (or C by symmetry) coincided fairly well with the experimental data.However, in the tests with three piles, the measured settlements of pile B were lower than the settlements of pile C, a trend not observed numerically.This is probably because pile B had been previously loaded in the sequence with only two piles, causing some over-consolidation in the nearby soil.
The difference between experimental and numerical results in test 7 was mainly attributed to the testing defi-    ciencies reported by Cooke et al. (1980) to reproduce the effect of a rigid cap response.The model realistically captured the influence of a nearly rigid cap, with small differential settlements of the three piles, as expected.
It was shown that 3-D FEM analysis is an effective tool to predict pile group settlements and load transfer mechanisms in pile groups.The differences between modeled and experimental results were generally very small in all tests.
to compare to piles A and B loaded simultaneously (to the same value).Test 1 occurred 16 weeks after the test in Pile A and 1 week after the installation of pile B. Test 2: Piles A and B loaded separately to 40 kN (about 40% of the ultimate load) to compare to piles A and B loaded simultaneously.Test 2 occurred 4 weeks after the installation of pile B. Test 4: Piles A, B and C loaded simultaneously up to 40 kN to measure the shaft distribution and the soil displacements in piles A and B. Test 4 occurred 13 months after installation of pile B and 6 months after the installation of pile C. Test 5: Piles A, B and C loaded separately and in increments up to 40 kN to measure the shaft distribution and the soil displacements in piles A and B. Test 5 occurred 13 months after pile B and 6 months after the installation of pile C.

Figure 1 -
Figure 1 -Main features of the test set-up (adapted from Cooke et al., 1980).

Figure 2 -
Figure 2 -Loading sequences for the tests.

Figure 5 -
Figure 5 -System of axes in a horizontal plane X-Z.

Figure 6 -
Figure 6 -Load versus settlement curve for pile A and piles A and B, test 1 (adapted from Freitas, 2010).

Figure 7 -
Figure 7 -Settlements for the pile loaded alone ((a) and (c)), and piles A and B loaded simultaneously ((b) and (d)), for the pile load of 50 kN (Freitas, 2010).

Figure 10 -
Figure 10 -Vertical displacement (u y ) at the ground surface for loads of (a) 40 kN at pile A (central pile) and (b) 40 kN in piles A and B (Freitas, 2010).

Figure 14 -
Figure 14 -Results of the Tests 4 and 5 -Load Transfer for pile A (adapted from Freitas, 2010).

Figure 15 -
Figure 15 -Results of the Tests 4 and 5 -Load transfer for pile B (Similar to pile C) (adapted from Freitas, 2010).

Figure 16 -
Figure 16 -Vertical displacement in perspective (a) and a section through the axis of the piles (b) for the simultaneous loading of 40 kN at the piles B, A and C (Freitas, 2010).

Figure 17 -
Figure 17 -Vertical displacements at the top of the ground for the loading of 40 kN in each of the piles B, A and C (Freitas, 2010).

Freitas
et al.

Figure 22 -
Figure 22 -Vertical displacements of the piles under 39.6 kN for section A'A (a) and vertical displacement for the section B'B (b)(Freitas, 2010).

Figure 21 -
Figure 21 -Results from Test 7 -Load transfer on piles B and A (adapted from Freitas, 2010).