A numerical interpretation of load tests on bored piles

Computers and Geotechnics 37 (2010) 425–430

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Technical Communication

A numerical interpretation of load tests on bored piles Luciano Tosini, Annamaria Cividini *, Giancarlo Gioda Politecnico di Milano, Department of Structural Engineering, Milan, Italy

a r t i c l e

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Article history: Received 6 November 2009 Received in revised form 27 December 2009 Accepted 4 January 2010 Available online 25 January 2010 Keywords: Load–settlement data Piles Granular soil Finite element analyses

a b s t r a c t The finite element interpretation is discussed of two load tests carried out on bentonite slurry piles bored in granular soils. The first case concerns a pile belonging to a 12 pile group. An axisymmetric finite element model that reproduces, with reasonable accuracy, the experimental results is developed. The model is then extended to three-dimensional conditions and applied to the analysis of the entire group. The results suggest some comments on the different assumptions that can be adopted in the calculations and on their effects on the global load–settlement curve of the pile group. The second case concerns a load test in which, in addition to the load–settlement data, also the axial strains along the pile were measured through electrical extensometers. The numerical back analyses highlight an apparent contradiction between the two sets of experimental data. On their bases some conclusions are drawn on the possible causes of the observed inconsistency and on the influence of the construction technology on the interaction between the pile tip and the soil underneath it. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction The prediction of the settlements of deep foundations in granular soils is not always straightforward due to the difficulties met in defining the values of the mechanical parameters influencing them. In most design instances, in fact, the design is based solely on the results of penetrometer tests, which provide only approximated mechanical parameters of the granular soil. In addition, the pile settlements depend on the mechanical characteristics of the pile/soil interface that, in turn, are influenced by the adopted construction technology. The possible limited accuracy of the computed settlements suggests carrying out load tests to quantitatively assess the behaviour of the deep foundation under loading. In some instances, however, the load test does not directly provide the sought results, in particular when the behaviour of a pile group has to be evaluated on the basis of the load test on a single pile. In other instances the results present some apparent inconsistencies that make their interpretation somewhat controversial. Here the back analyses of two load tests on bored piles are presented based on two- and three-dimensional, elastic–plastic finite element calculations. Among the various approaches proposed in the literature for the analysis of piles under vertical loads, see e.g. [1–5], the finite element method was adopted here since it can be easily applied to inhomogeneous deposits accounting for their non-linear stress–strain behaviour. The first examined case aims at evaluating the load–settlement curve of a 12 pile group based on the results of a load test on a sin* Corresponding author. Tel.: +39 02 2399 4331; fax: +39 02 2399 4220. E-mail address: [email protected] (A. Cividini). 0266-352X/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.compgeo.2010.01.001

gle pile. The back analysis of the test led to an acceptable calibration of the numerical model in 2D axisymmetric regime. When extended to 3D conditions, the calculations show the appreciable influence of the different assumptions that can be introduced in the analysis of the entire group. The second case concerns a load test in which, in addition to the load–settlement data, also the axial strains along the pile were measured through electrical extensometers. The numerical back analyses highlight an apparent contradiction between the two sets of experimental data. On their bases some conclusions are drawn on the possible causes of the observed inconsistency and on the influence of the construction technology on the soil–pile interaction. 2. First load test The first load test was carried out on a bentonite slurry bored pile belonging to a 12 pile group. The pile has a length of 17 m and a diameter of 1.2 m. Due to the characteristics of the structure, and to the thickness of the foundation mat connecting the group, the pile heads are located at a level of about 5 m below the ground surface. Before undertaking the axisymmetric interpretation of the test the influence of discretization was investigated through a series of elastic analyses. They were carried out adopting grids with increasing number of quadrilateral, four node isoparametric elements. The corresponding number of nodes ranges between 1250 and 4340. To limit the boundary effects the discretized zone has radius R and height H of 40 m. Fig. 1 shows the variation with the number of nodes of the ratio between numerical settlements wFE

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Fig. 1. Variation of the ratio between numerical settlements wFE and that derived from Poulos and Davis solution [6] wPD with increasing refinement of the mesh.

and that deriving from the elastic solution proposed by Poulos and Davies [6] wPD. These results indicate that, for the problem at hand, acceptable results can be obtained even when using moderately refined meshes. The calculations discussed in the following were then based on a grid consisting of 1870 nodes and of 1782 elements. The soil deposit consists of sand and gravel with a marginal percentage of silt. The pile design was based on the results of standard penetration tests summarized in Fig. 2a. The same figure indicates the nine layers introduced in the finite element calculations. Note that the depth in Fig. 2 is measured from the head of the pile and that the high NSPT values obtained at two locations depend on the presence of boulders. Consequently, they were disregarded in the calculations. Fig. 2b and Fig. 2c report, respectively, the estimated variation with depth of the friction angle u0 and of the elastic modulus ratio E/E* [7]. The value of E* was evaluated on the basis of the load test

Fig. 3. First load test: experimental results (solid line) and numerical simulation based on the calibrated finite element model (dashed line).

results (solid line in Fig. 3) by matching the slope of the initial part of the load–settlement diagram. To allow for an acceptable estimation of the plastic strains in the vicinity of the pile, 5 cm thick interface elements [8] were placed along it and below its base. An elastic behaviour was assumed for the pile with an elastic modulus of 29  103 MPa. An elastic perfectly plastic behaviour, obeying Mohr–Coulomb yield criterion with a non-associated flow rule, was adopted for the soil layers. The non-linear analyses were carried out through the finite element code SoSIA, for soil structure interaction analysis [9], based on the iterative initial stress algorithm [10]. Some details on the implementation of the yield criterion have been presented in [11].

Fig. 2. First load test: (a) results (triangles) of the standard penetration tests, (b) estimated variation with depth of the friction angle u0 and (c) of the non-dimensional elastic modulus ratio E/E*.

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form the difference between measured and calculated displace^ max , ments is divided by the maximum measured displacement u

FðpÞ ¼

2 n ^ X ui  ui ðpÞ 1

Fig. 4. Contour lines of the error function for K0 = 0.5: d is the dilatancy parameter and a is the friction angle reduction factor.

It should be observed that, since E* was calibrated on the basis of the load test results, the evaluated variation of the soil elastic modulus with depth is already influenced by the disturbance due to construction. Consequently it was assumed that the elastic modulus of each interface element coincides with that of the corresponding soil layer. The remaining mechanical parameters entering in the numerical analyses are: the angle of plastic dilation w, governing the flow rule, that depends on the friction angle u0 through a parameter d, i.e. tan w = d tan u0 ; the reduction factor a of the interface friction angle u*, i.e. tan u* = a tan u0 ; the coefficient of horizontal pressure K0 relating the normal horizontal stress between pile and soil to the vertical in situ stress. The above parameters, collected in vector p, were evaluated through a back analysis that consists in minimizing the discrep^ and the correspondancy F between the n measured settlements u ing numerical results u(p). In order to express F in non-dimensional

Fig. 5. Detail of the horizontal section of the 3D finite element mesh.

^ max u

;

8 9 > = : where p ¼ d > ; : > K0

ð1Þ

The back analysis was carried out assigning different values to K0 and working out, for each of them, the values of a and d that minimizes the function F. Some remarks on the minimization algorithms suitable for the back analysis of geotechnical problems can be found in [12]. Fig. 4 reports the contour line of the error function for one of such minimizations. The calibration process led to the following ‘‘optimal” values of the sought parameters: E* = 750 MPa; K0 = 0.5; a = 0.68; d = 0.07. The small value of the coefficient d shows the negligible effect of plastic dilation for the problem at hand. Having calibrated its material parameters, the numerical model was extended to three-dimensional conditions to investigate the behaviour of the 12 pile group. Taking advantage of its double symmetry only 1/4 of the problem was discretized into a mesh of eight node brick elements. A detail of the horizontal section of the mesh, in the vicinity of the pile group, is shown in Fig. 5. The calculated load–settlement diagrams are summarized in Fig. 6. Curve (a) represents the mere superposition of the load–settlement diagram calculated for a single pile (cf. Fig. 3), i.e. the pile interaction is neglected. Curve (b) refers to the actual 3D case in which the pile group is connected to a foundation mat and the interaction between the mat and the underlying soil is accounted for. Finally, curve (c) represents the 3D case in which the mat–soil interaction is neglected. This condition could represent the case of an extremely severe erosion of the soil underneath a bridge pier. The numerical results show the increase of settlements due to the interaction between the piles (curves b and c) with respect to the case in which the interaction is neglected (curve a). In addition, the calculation permits a quantitative assessment of the effects of the interaction between the foundation mat and the underlying soil.

Fig. 6. Calculated load–settlement curves for the 12 pile group: (a) simple superposition of 12 independent piles; (b) pile group and interaction between soil and foundation mat; and (c) pile group without soil–mat interaction (the dashed line represents the overall working load of the foundation).

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Fig. 7. Second load test: experimental results (solid line) and numerical simulation based on the calibrated finite element model (dashed line).

Fig. 8. Second load tests: axial force from the extensometer measurements (solid line) and numerical results based on the calibrated numerical model (dashed line).

In particular, it can be observed that depending on the assumptions adopted in the calculations the expected settlement of the pile group under working loads (dashed line in Fig. 6) varies between 6.5 mm and 10.5 mm.

3. Second load test This test was carried out on an 80 cm diameter bored pile having length of 11.5 m. Since the in situ investigation indicates that the soil profile is reasonably uniform, mechanical properties constant with depth were used in the numerical back analysis of the load test. Adopting a mesh having the same characteristics of that used for the first problem, but for the pile geometry, and applying the already described numerical procedure, the back analysis in axisymmetric regime led to the following parameters relevant to the numerical model: E* = 700 MPa; K0 = 0.6; a = 0.7; d = 0.03. The consequent numerical results are compared in Fig. 7 with the experimental ones. In this case, in addition to the load–settlement data, also the axial strains where measured along the pile through electrical extensometers located at 3.65 m, 7.10 m and 10.15 m from the pile head. Four extensometers were placed at each elevation. Table 1 reports the average strains measured at the various depths during

Fig. 9. Second load test: axial force from the extensometer measurements (solid line) and numerical results considering a soil–pile adhesion of 50 kPa (dashed line).

Table 1 Axial strains measured along the pile during the second load step. Applied load (kN)

400 600 800 1000 1200 1400 1600 1850

z = 3.65 m

z = 7.10 m

z = 10.15 m

Average strain, e  106

Axial load (kN)

Average strain, e  106

Axial load (kN)

Average strain, e  106

Axial load (kN)

10.50 19.00 29.00 39.00 47.25 58.25 69.75 78.25

164.9 298.4 455.5 612.6 742.2 915.0 1095.6 1229.1

5.50 10.25 16.00 21.00 24.25 30.75 36.50 40.50

86.4 161.0 251.3 329.9 380.9 483.0 573.3 642.8

2.00 4.67 7.67 9.67 10.67 14.67 17.67 19.67

31.4 73.3 120.4 151.8 167.5 230.4 277.5 308.9

z = depth from the pile head.

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the second load step and the corresponding axial loads. These were calculated adopting a pile elastic modulus of 31  103 MPa, which accounts for the actual area of the concrete section and of the steel bars present within it. The distribution of the axial load at the end of the second load step, which corresponds to point A of the load–settlement diagram in Fig. 7, is compared with the finite element results in Fig. 8. It can be observed that, while the calibrated numerical model provides an acceptable approximation of the load–settlement data (cf. Fig. 7), a large difference exists between the computed axial force and that deriving from the experimental data (cf. Fig. 8). Note that, according to the experimental data in Fig. 8, a vanishing vertical load reaches the pile tip and, hence, the limit skin friction has not been reached yet. On the contrary, the calibrated numerical model indicates that about half of the applied load is carried by the base and that, consequently, the limit skin friction was reached at least in the upper portion of the pile. In order to overcome the above apparent contradiction various attempts were made, by modifying the soil parameters, which aimed at limiting the axial force at the pile tip. The most successful one consisted in introducing some adhesion at the soil–pile interface that could depend on the silty fraction present in the granular deposit. Fig. 9 shows the load– settlement diagram obtained by a finite element analysis in which an adhesion of 50 kPa was assumed. Beside the fact that this seems a relatively high value for the soil at hand, this provision eliminates any similarity between the experimental and calculated load–settlement curves, as shown by the diagrams in Fig. 10. Note, in particular, the difference existing between the settlements at the end of the second load cycle represented by points B and A in Fig. 10 that correspond, respectively, to the numerical and experimental diagrams in Fig. 9. It does not seem reasonable to assume that the difficulties met in modelling both sets of experimental data could merely depend on errors in the values of the soil parameters. They should rather depend on some aspects of the field problem that were not properly accounted for in the numerical simulation of the load test. A possible cause of the observed discrepancy could be the presence of a soft zone at the pile tip that depends, for instance, on the

partial cleaning of the excavation bottom or on the presence of a zone where the concrete was mixed with the bentonite slurry. The finite element model was then modified adopting a vanishing elastic modulus for the interface elements underneath the pile tip and reducing the soil–pile adhesion to 20 kPa. The corresponding numerical results are shown in Figs. 11 and 12. Apparently the introduction of a soft zone below the base of the pile improves the agreement between experimental and numerical results, even though some discrepancy can still be observed (cf. Fig. 12). This could depend on the assumed homogeneity of the soil deposit or on the limits of the relatively simple constitutive model

Fig. 10. Second load test: comparison between experimental results (solid line) and numerical ones with soil–pile adhesion of 50 kPa (dashed line).

Fig. 12. Second load test: comparison between experimental results (solid line) and numerical ones considering a soft zone at the pile tip (dashed line).

Fig. 11. Second load test: axial force from the extensometer measurements (solid line) and numerical results with a soft zone at the pile tip (dashed line).

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adopted in the calculations. It seems then reasonable to conclude that the presence of the mentioned soft zone could be a possible cause of the measured marginal load transferred to the pile tip.

nique. It could be also mentioned that a more effective interpretation of the second load test could have been reached if the vertical load at the pile tip were directly measured through a load cell or a flat jack.

4. Conclusions

Acknowledgements

The two discussed case histories show that the back analysis of load tests could represent a practical procedure for calibrating the numerical models of deep foundations. The first examined problem show that, when dealing with pile groups, the parameters obtained from the axisymmetric interpretation of the load test on a single pile can be adopted for the three-dimensional analysis of the entire group. In this case, in addition to the interaction between the piles, the finite element model can also account for the elastic–plastic interaction between the foundation mat and the underlying soil. In the second test the numerical analysis highlighted an apparent contradiction of the in situ measurements. In fact, the strains measured along the pile show that a limited load is transferred to its base. On the contrary, the back analysis of the load–settlement diagram indicates that at least half of the applied load reaches the base. This apparent contradiction is likely to depend on some field condition that is not properly accounted for in the numerical model. In the present context it appears that the mentioned discrepancy between experimental and numerical results can be, at least partially, reduced by introducing in the calculations a soft zone underneath the pile tip. This zone could be due, for instance, to a poor cleaning of the excavation bottom or to the formation of a soft mixture of concrete and bentonite in the vicinity of the pile tip. If this explanation can be accepted, the back analysis provided an insight into an apparent weakness of the construction tech-

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