INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS. VOL. 3,131-143 (1979)

OBSERVED AND PREDICTED TEST PILE BEHAVIOUR

MARIO O’ITAVIANI * University of Rome, Rome, Italy

AND

SILVANO MARCHEITIS University of L’Aquilu, Italy

SUMMARY

The results obtained from a loading test on a bored, cast-in-place pile instrumented with six pairs of load cells at different levels are compared with the results obtained from a non-linear finite element analysis based on the geotechnical parameters of the cohesive soils in which the pile was bored.

Settlements computed using deformability parameters obtained by a standard laboratory test were much larger than the measured settlements. Satisfactory results are instead obtained assuming E, =

lOOOc, and c, = c,. The distribution of the vertical stresses within the pile and of the shear stresses in the soil adjacent to

the pile obtained by the numerical analysis are compared with the measured values. A fair agreement is found at loads below failure but differences between experimental and computed

values are found at loads close to failure.

INTRODUCTION

In the present paper, experimental results obtained from a loading test on an instrumented pile are compared with the results obtained from a non-linear finite element analysis based on the geometry and the geotechnical parameters as determined by standard in situ and laboratory investigations.

It is well known that many aspects of pile foundation behaviour are still not clear and it is hoped that some light on the problem could be thrown by a detailed comparison of the behaviour of single piles or pile groups predicted by the application of numerical techniques and observed behaviour.’.’

Some of the points to be investigated are, for instance, the validity of the assumption of undrained conditions for the whole duration of the loading test, the choice of the deformability parameters to be used in the numerical model, and the distribution of shear stresses near the base of the pile.

In this study, the problem considered in detail is that of the choice of the deformability parameters which could lead to a satisfactory prediction of the behaviour of a foundation pile, particularly in an essentially cohesive soil.

* Associate Professor of Engineering Geology $Associate Professor of Soil Mechanics.

0363-9061/79/0203-0131$01.00 @ 1979 by John Wiley & Sons, Ltd.

Received 14 March 1977 Revised 28 October 1977

132 MARIO OTTAVIANI AND SILVANO MARCHE'ITI

TEST CONDITIONS

The test was carried out on a pile, cast in place in an uncased bore-hole drilled in the presence of water and bentonite. A rather heavy reinforcement cage was installed before placing the concrete in the bore-hole. The diameter of the pile was 0-60 m and the length 23-5 m.

The test was carried out about six weeks after casting the pile and included two loading cycles: the first reached about 2 M N in 10 increments each lasting about 15min; after unloading the pile the second cycle was carried out in the same day up to failure, which was reached by plunging, at a load of 3.4 MN.

The foundation soil at the test site (Rome, Viale Giulio Cesare) consists of nearly normally consolidated clay, silt and sand as shown in Figure l(a). The undrained shear strength of the cohesive soil as measured in situ by a vane shear test and in the laboratory by triaxial tests is shown in Figure l(b).

The results of a static penetrometer test carried out very close to the pile location are shown in Figure l(c). Considerable variations of the geotechnical properties of the soil at the test site are quite evident and certainly the authors, had they had the choice, would have carried out the test in a more homogeneous soil.

OBSERVATIONS

As shown in Table I, six pairs of strain cells were installed at different levels in the pile. At each level, two cells were placed 180" from each other in order to obtain an average value independent of the unknown bending moment inevitably present in the pile.

Table I

Percentage of soil type

Cylindrical Depth Length cu 'P C, element no. (m) (m) sand silt clay MN/mZ MN/m2 MN/mZ a

I 1.80 0-12 0.66

4.00 0.10 0.56 2.80 11 38 51 0.18 2.4 res. res.

I1 3.20 32 31 37 0.16 1.9 0.14 0.87 7.20

I11 5.80 47 30 23 0.11 variable 0.06 0.55 13.00

IV 4.00 13 34 53 0.09 1.9 0.06 0.66 17.00

V 4.50 12 45 43 0.08 1.4 0-07 0.83 21.50

The cells (see Figure 2) are made of a stainless steel vertical rod placed between two circular plates: the rod is instrumented by using four strain gauges each wired in a full bridge arrange- ment. Similar cells are described by Barker and R e e ~ e . ~ In Figure 3, details of the cells placed on the reinforcement cage are shown.

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134 MARIO O'ITAVIANI AND SILVANO MARCHE'ITI

TEST PILE BEHAVIOUR 135

Special protection for the cells against possible damage due to the operation of concrete placing was assured by welding to the cage a sort of steel handle around each cell.

The calibration factor of the cells has been determined as the ratio between the average values of the signals (mV/V) from the cell pair placed at the pile head and the corresponding applied loads (MN).

For each value of the applied load, readings were taken from all the cells. The readings were then converted into loads (MN) using this calibration factor. The load distribution along the pile was obtained by plotting the value of such loads against the depth.

The mobilized shear strength along the pile, ~ ( z ) , at each load was obtained as the ratio of the load difference between two subsequent cell levels and the lateral area of the pile surface included between the two levels. The mobilized shear strength was therefore considered, as a first approximation, constant along each pile segment. This procedure was considered prefer- able to that based on the differentiation of the load curve Q ( z ) , obtained as the best fit to the experimental data, since the measure points were too few to allow this method to be applied.

EXPERIMENTAL RESULTS

Figure 4 shows the curve of load versus settlement obtained for the two loading cycles. Figure 5 shows for both cycles the distribution of the load in the pile at different depths for several values of the load applied at the head of the pile. For the second cycle, the distribution of the

L O A O I M N I

Figure 4. Load-settlement curves for pile head for the two loading cycles

average mobilized shear strength along the pile surface is plotted in Figure 6 for some values of the applied load. The experimental points have been joined by straight lines even though several discontinuities may exist along the real ~ ( z ) curve.

The last two columns of Table I show the experimental values of the shear strength at failure c,, and the ratio a = c,/c, for the soil adjacent to each pile segment. For the first pile segment near the pile head, c, (see Figure 6) has a value smaller than that reached at Q = 3 MN, which can thus be considered as a peak value, while the values of c, and Q at failure can be assumed as residual values. The observed decrease of c, and a at failure has not been considered in the following finite element analysis. A more detailed presentation of the experimental results has been reported el~ewhere.~

136 MARIO O’ITAVIANI AND SILVANO MARCHETTI

3 a a e,

C

- .-

9 .-

TEST PiLE BEHAVIOUR

I MOBlLlSEO SHEAR STRENGTH z (MN/nf l

137

D

Figure 6. Mobilized shear strength at the soil pile interface for several values of the applied load in the second cycle

FINITE ELEMENT ANALYSIS OF OBSERVED BEHAVIOUR

The observed data obtained from the loading test have been analysed in detail using the finite element method.

The computer program used in the present study is that previously employed by Esu and Ottaviani.' This program can be used to analyse axisymmetric structures made of materials having a hyperbolic type stress-strain curve.6 Even though the soil around the test pile includes some thin sandy layers, the silt and clay content is clearly predominant and the soil can be considered on the whole as cohesive. Undrained conditions during the load application have therefore been assumed for the analysis.

In this case the value of the tangent modulus to the hyperbolic stress-strain curve is given by (Duncan and Chang6)

E , = E , 1-R,- ( *1-u3)2 2C"

As shown in Figure 1, the geotechnical properties of the soil are far from being uniform, therefore it was necessary for the analysis to subdivide the soil into several layers of different characteristics (see Figure 7). A total of 396 rectangular elements and 444 nodes has been used for the finite element model.

Other characteristics of the soil introduced in the model were unit weight y = 1.8 gm/cm3, Poisson's ratio v = 0.48 and ratio u ~ / ( T , before applying the load equal to 0.9. To consider the effects of bore-hole drilling and of concrete placing, the strength of the soil c, in a 4 cm thick

138

c, =0.10 ”

c, =009 ”

c, =0.08 ”

c, =0.10 If

MARIO OlTAVIANI AND SILVAN3 MARCHETTI

Figure 7. Finite element model of the soil-pile structure

TEST PILE BEHAVIOUR 139

ring along the pile interface was assumed to be less than that away from the The value of c, has been assumed to be equal to 0 . 5 ~ ~ for all the soil layers in contact with the pile.

As for the deformability parameters of the soil, the results obtained from undrained triaxial tests on undisturbed isotropically reconsolidated and unconsolidated samples were first consi- dered. The values of the initial tangent modulus to the consolidated undrained curves vary between 13 and 33 MN/m2 for reconsolidation pressure cr3 = 0-2 MN/m2 and between 27 and 40 MN/mZ for u3 = 0-4 MN/m2.

The initial tangent moduli to the unconsolidated curves, for cell pressure equal to 0.2 MN/m2, vary between 10 and 20 MN/m2. For all the tests the higher values of Ei were relative to soil samples taken at depths from 0 to 10 m; the lower values were relative to soil samples taken at depths varying between 10 and 25 m. All the values of Rf computed from the same curves were very close to 0.9.

On the basis of the laboratory results reported here, a first computation was carried out assuming for the soil from the surface to a depth of 10 m, E, = 25 MN/m2 and for the soil at greater depths E, = 15 MN/m2.

For the concrete, also considered non-linear, it was assumed that E, = 40,000 MN/m2, v = 0.25 and the compressive strength is 50 MN/m2.

The determination of the load settlement curves and of the stress distribution in the soil and in the pile was carried out by simulating the experimental procedure. The load has therefore been applied by several increments subdividing the failure load of 3-4 MN in 12 intervals of decreasing value.

Figure 8 shows the experimental load settlement curve (curve a) relative to the second cycle and the computed curve (curve b) obtained with the geotechnical parameters just described. It is quite clear that the computed settlements are much higher than those actually measured during the test. These results show that the modulus values of the soil obtained from labora- tory tests are much smaller than those verified in siru. This type of discrepancy is commonly found in the literature2" and depends mainly on the sampling and testing procedures that rarely leave the soil samples undisturbed and, particularly in the present case, on the inhomogeneity of the soil.

A different approach to the problem of the soil deformability parameters was then chosen. A second series of analysis was undertaken neglecting the laboratory results and taking into consideration the empirical relationship which directly relates undrained shear strength to modulus value:'

E, = Pcu

On the basis of the laboratory determined Ei, the average value of p would have been about 150. After a few attempts, good results have instead been obtained with a value of P equal to 1,000. Similar values of p for stiff clays were also found by Desai"" and by Ottaviani and Cappellari" for the same type of analysis. The load settlement curve so obtained is shown in Figure 8 (curve c). There is a rather close approximation to the experimental curve for all the load increments, including the failure area.

= 1,200. Even though such a curve is closer to the experimental curve a, it must be taken into consideration that the observed settlements are actually settlements relative to the fixed points of the measurement frame which were located, as is routinely done, at about 4 m from the pile head; subtracting from the curve c the settlement values computed at 4 m from the pile, one obtains a curve practically coincident with the experimental curve. The value of p = 1,200 appears therefore too high and the results shown hereafter are relative to the choice of P equal to 1,000. Curve e

Curve d of Figure 8 is the load settlement curve computed for

140 MARIO OTTAVIANI AND SILVANO MARCHETTI

of Figure 8 shows the shortening of the pile length under the load. It can be seen that a substantial part of the computed settlement is actually due to the pile shortening and that the non-linearity of the pile concrete is not to be neglected for values of the vertical stress at the pile head of about 10 MN/m2.

Figure 9 shows the values of the vertical stress (avp) within the pile measured by the strain cells and the corresponding values computed for p = 1,000 at loads Q = 1.5 MN and Q =

0

7

2

3

4

Y

L E 5 5 6

7

8

9

70

71 Figure 8. Measured and computed load-settlement curve for pile head (second loading cycle): (a) measured curve; (b) computed curve with deformability parameters obtained by laboratory tests; (c) computed curve with deformability parameters obtained as E, = 1,00Oc,; (d) computed curve with deformability parameters obtained as Ei = 1 , 2 0 0 ~ ~ ; (e)

computed curve of pile shortening

TEST PILE BEHAVIOUR

dVp ( M N / ~

141

0

2

4

6

8

70

Z ( m ) 12

14

76

18

20

22

24

1

I

7--T--.- I

15

i -i ----I

I

-+ I I I

Figure 9. Vertical stress distribution in the pile at Q = 1.5 MN and Q = 3.4 MN: measured values and computed curves

3.4 MN at failure. For Q = 1.5 MN the approximation between observed and computed values is satisfactory, but for Q = 3-4 MN there are some differences in the upper portion of the pile. It can be seen that a small fraction of the load is carried by the pile base even at failure.

Figure 10 shows, for the same value of p, the distribution of the shear stresses in the soil immediately around the pile obtained with the finite element analysis and, with the procedure

142 MARIO OTTAVIANI AND SILVANO MARCHETTI

ZRz ( M N / ~ )

Figure 10. Shear stress distribution in the soil adjacent to the pile at Q = 1.5 MN and Q= 3.4 MN: measured values and computed curves; dashed line shows c, distribution assumed along the pile

described above, from the experimental results. Also, in this case there is a good agreement between experimental and computed values for Q = 1.5 MN, but for Q = 3.4 MN, at failure, there are some differences, especially at depths z = 6 m and z = 20 m. The differences found for crVp and T at failure can be explained by considering that the values of c, obtained from the

TEST PILE BEHAVIOUR 143

experimental results (see Table I) are in some points rather different from the distribution assumed for the finite element analysis which was simply equal to 0 .5~” (see Figure 10). Therefore, at loading conditions below failure there could be a fair agreement between experimental and computed values, but at failure there could be differences since the computed shear stresses distribution cannot but follow closely the assumed distribution of c,.

Furthermore, the constitutive model chosen for the soil may not be valid near failure loads when, for instance, strain-softening phenomena may occur.

In conclusion, the results of the analysis show that in the present case if one had assumed for design purposes a proportion of skin friction equal to half the shear strength of the cohesive soil, i.e. a = 0.5, and furthermore had one assumed an initial tangent modulus distribution for the soil equal to l,OOOc,, i.e., p = 1,000, the experimental findings would have been predicted satisfactorily.

2

ACKNOWLEDGEMENTS

The present study was carried out in connection with the construction of the subway system in Rome.

The Authors wish to thank Dr. Ing. Alfio Chisari, General Manager of Metroroma S.p.A., for the help and the co-operation offered for this study.

The present research was partly financed by C.N.R. contract number 76.01608.07.

REFERENCES

1. C. S . Desai, ‘Numerical design analysis of piles in sands’, J. Geotech. EngngDiu., Proc. Am. SOC. Civ. Engrs (1974). 2. C. S. Desai, ‘Soil-structure interaction and simulation problems’, Znt. Symp. on Numerical Methods in Soil

3. W. R. Barker and L. Reese, ‘Instrumentation for measurement of axial load in drilled shafts’, Research Report

4. S . Marchetti and L. D’Angelo, ‘Misure di sollecitazione nei pali di fondazione in calcestruzzo’, Riu. Ztal. Geotech.

5. F. Esu and M. Ottaviani, ‘Behaviour of bored piles in a non-linearly elastic soil’, Zng. Ciuile, 46, (1973). 6. J. M. Duncan and C. Y. Chang, ‘Nonlinear analysis of stress and strain in soils’, J. Soil Mech. Found. Diu., Proc.

7. F. Esu and M. Ottaviani, Discussion of Proc. Paper 10617 (by C. S . Desai), J. Geotech. Engng Din, Proc. Am. Soc.

8 . G. W. CIough and A. I. Mana, ‘Lessons learned in finite element analysis of temporary excavations in soft clay’,

9. B. B. Broms, ‘Stability of flexible structures’, 5th European Conf. SMFE, 2, Madrid (1972).

Mechanics and Rock Mechanics, University of Karlsruhe, Germany (1975).

89-6, Center for Highway Research University of Texas, Austin (1969).

3, (1976).

A m . SOC. Ciu. Engrs 96, (1970).

Ciu. Engrs (1975).

2nd Znt. Conf. on Numericul Methods in Geomechanics, BIacksburg, Virginia, I (1976).

10. C. S. Desai. Closure and reply to discussion (by Esu and Ottaviani), J. Geotech. Engng Diu., Roc. Am. SOC. Ciu. ~~ _ _ . _

Eng. (1976). 11. M. Ottaviani and G. Cappellari, ‘Time behaviour of axially loaded bored piles in a cohesive soil’, Roc. VZ

European Con$ SMFE, Wien (1976).