A numerical interpretation of load tests on bored piles

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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

i n f o

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 ele-ment model that reproduces, with reasonable accuracy, the experiele-mental 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 mea-sured 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 interac-tion between the pile tip and the soil underneath it.

1. Introduction

The prediction of the settlements of deep foundations in granu-lar 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 approxi-mated 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 com-puted settlements suggests carrying out load tests to quantita-tively assess the behaviour of the deep foundation under loading. In some instances, however, the load test does not directly pro-vide 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 inconsis-tencies that make their interpretation somewhat controversial.

Here the back analyses of two load tests on bored piles are pre-sented 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-gle pile. The back analysis of the test led to an acceptable calibra-tion 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 ele-ments. The corresponding number of nodes ranges between 1250 and 4340. To limit the boundary effects the discretized zone has ra-dius R and height H of 40 m.Fig. 1shows the variation with the number of nodes of the ratio between numerical settlements wFE

* Corresponding author. Tel.: +39 02 2399 4331; fax: +39 02 2399 4220. E-mail address:[email protected](A. Cividini).

Computers and Geotechnics 37 (2010) 425–430

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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 re-ﬁned 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 per-centage of silt. The pile design was based on the results of standard penetration tests summarized inFig. 2a. The same ﬁgure indicates the nine layers introduced in the ﬁnite element calculations. Note that the depth inFig. 2is measured from the head of the pile and that the high NSPTvalues obtained at two locations depend on the presence of boulders. Consequently, they were disregarded in the calculations.

Fig. 2b andFig. 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

results (solid line inFig. 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 as-sumed 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. 1. Variation of the ratio between numerical settlements wFEand that derived

from Poulos and Davis solution[6]wPDwith increasing reﬁnement of the mesh.

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*.

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

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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 mod-ulus of each interface element coincides with that of the corre-sponding soil layer.

The remaining mechanical parameters entering in the numeri-cal 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} K0relating 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-ancy F between the n measured settlements ^u and the correspond-ing numerical results u(p). In order to express F in non-dimensional

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

FðpÞ ¼X n 1 ^ ui uiðpÞ ^ umax 2 ; where p ¼

a

d K0 8 > < > : 9 > = > ;: ð1Þ

The back analysis was carried out assigning different values to K0and working out, for each of them, the values of

a

and d that minimizes the function F. Some remarks on the minimization algo-rithms suitable for the back analysis of geotechnical problems can be found in[12].Fig. 4reports 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 sym-metry 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 inFig. 5.

The calculated load–settlement diagrams are summarized in

Fig. 6. Curve (a) represents the mere superposition of the load–set-tlement 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 addi-tion, the calculation permits a quantitative assessment of the effects of the interaction between the foundation mat and the underlying soil.

Fig. 4. Contour lines of the error function for K0= 0.5: d is the dilatancy parameter

andais the friction angle reduction factor.

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

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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In particular, it can be observed that depending on the assump-tions adopted in the calculaassump-tions the expected settlement of the pile group under working loads (dashed line inFig. 6) varies be-tween 6.5 mm and 10.5 mm.

3. Second load test

This test was carried out on an 80 cm diameter bored pile hav-ing length of 11.5 m. Since the in situ investigation indicates that the soil proﬁle is reasonably uniform, mechanical properties con-stant 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 axi-symmetric 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 ax-ial 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. 7. Second load test: experimental results (solid line) and numerical simulation based on the calibrated ﬁnite element model (dashed line).

Table 1

Axial strains measured along the pile during the second load step.

Applied load (kN) 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) 400 10.50 164.9 5.50 86.4 2.00 31.4 600 19.00 298.4 10.25 161.0 4.67 73.3 800 29.00 455.5 16.00 251.3 7.67 120.4 1000 39.00 612.6 21.00 329.9 9.67 151.8 1200 47.25 742.2 24.25 380.9 10.67 167.5 1400 58.25 915.0 30.75 483.0 14.67 230.4 1600 69.75 1095.6 36.50 573.3 17.67 277.5 1850 78.25 1229.1 40.50 642.8 19.67 308.9

z = depth from the pile head.

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

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).

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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 inFig. 7, is compared with the ﬁnite element results inFig. 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 inFig. 8, a vanish-ing vertical load reaches the pile tip and, hence, the limit skin fric-tion 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 adhe-sion at the soil–pile interface that could depend on the silty frac-tion 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–set-tlement curves, as shown by the diagrams inFig. 10. Note, in par-ticular, the difference existing between the settlements at the end of the second load cycle represented by points B and A inFig. 10

that correspond, respectively, to the numerical and experimental diagrams inFig. 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 prop-erly accounted for in the numerical simulation of the load test.

A possible cause of the observed discrepancy could be the pres-ence 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 vanish-ing elastic modulus for the interface elements underneath the pile tip and reducing the soil–pile adhesion to 20 kPa. The correspond-ing numerical results are shown inFigs. 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. 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).

Fig. 12. Second load test: comparison between experimental results (solid line) and numerical ones considering 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.

4. Conclusions

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 interpre-tation of the load test on a single pile can be adopted for the three-dimensional analysis of the entire group. In this case, in addi-tion to the interacaddi-tion 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 appar-ent contradiction of the in situ measuremappar-ents. 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–settle-ment 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 mod-el. In the present context it appears that the mentioned discrep-ancy 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-nique. It could be also mentioned that a more effective interpreta-tion 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.

Acknowledgements

The authors wish to thank Michela Chiorboli and Mario De Mir-anda for providing the experimental data and for their technical comments.

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