INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, VOL 1 1, 645-650 ( 1 987)

INTERACTION BETWEEN TORSIONAL AND AXIAL PILE RESPONSES

MICHAEL GEORGI ADIS'

Depurrmrnt of Civil Engineering Unitiersity of Thessuloniki, Greece

SUMMARY

The effect of axial load on the torsional pile response and the effect of torque on the axial pile response are investigated. To perform this investigation, a computer program was developed which uses the transfer matrix method tg analyse a pile supported by a series of coupled axial and torsional elasto-plastic springs. The study indicated that the ultimate torsional and axial pile capacities, as well as the axial displacements and rotations, are significantly affected by the combined load action.

INTRODUCTION

It is well known that one of the main aspects in pile analysis is the determination of the nonlinear axial pile response. Although most pile foundations loaded laterally are liable to undergo some torsion due to eccentricity of the applied load, the cases in which the torsional pile response is critical are rather limited. However, there are some types of structure such as the offshore monopodes (e.g. very large diameter and small wall thickness single-pile platforms) on which significant torsional loads may be applied (e.g. due to ship impact forces) compared to their axial load. Numerical methods for piles subjected to torsion have been presented by Poulos,' Randolph' and Chow.3

Currently, the axial and torsional pile responses are treated independently, ignoring the effects of tangential stresses around the pile shaft on the axial pile response and the effects of axial shaft stresses on the torsional pile response. However, when a pile is loaded with both torque and axial force, the separate examination adopted in current practice can produce misleading results unless the applied loads are very small and the soil response is linear. Otherwise, the soil behaves nonlinearly, especially close to the ground surface where the combined high axial and tangential stresses exceed the ultimate pile shaft resistance, and consequently the resulting pile head rotation and axial displacement are larger.

This paper describes an analysis for determining the influence of torque on axial pile response and the influence of axial load on torsional pile response. The pile is considered as an elastic beam, while the soil is modelled with two series of elasto-plastic springs, one torsional and one axial. Each pair of springs acts independently until, at some depth, the vectorial sum of the tangential and axial reactions becomes equal to the ultimate unit pile shaft resistance. The numerical analysis is performed with the transfer matrix Finally, an application of this method is presented, which demonstrates the importance of the interaction.

'Lecturer. Formerly Project Enginee , DAppolonia Cons. Engrs.

0363-9061/87/060645-06$05.00 0 1987 by John Wiley & Sons, Ltd. Received 9 October 1986

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FOUNDATION MODEL AND ANALYSIS

The foundation model utilized in this study is illustrated in Figure 1. The pile is treated as an elastic beam which is divided by (n ) nodes into (n - 1) segments. A pair of elasto-plastic springs, comprising an axial spring and a torsional spring, is attached to each node. Another spring is attached to the pile base to represent the end bearing resistance.

The initial stiffness KTi of the torsional spring ( i ) can be related to elastic soil parameters by simplifying the state of stresses at the pile-soil interface,'^^ and can be determined from the following equation (Figure 2a):

(1) l i + l i - 1 KTi=xD2Gsi-

where D is the pile diameter, GSi is the shear modulus of the soil at (i), and li is the length of the ith pile segment. The ultimate resistance of the torsional spring is

2

n)r

Figure 1. Foundation model

Figure 2. Deformation characteristics of torsional and axial springs

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IP

ZTi/D I Figure 3. Combined torsional-axial response

where fui is the unit shaft resistance of the pile at node (i), and can be determined from one of the conventional bearing capacity methods,6 as well as from either axial or torsional pile load tests.’

The initial stiffness K A i of the ith axial spring can be evaluated either theoretically* or from cone penetration or pressure-meter tests as described by Briaud and Meyer,’ or from the following empirical equation which is often utilized in offshore pile design (Figure 2b):

K A i .= P,,i/~,i (3) where zCi is the axial displacement required to mobilize the ultimate shaft resistance at the ith node (on the order of 2.5 mm), and PUi is the ultimate axial resistance of the ith spring determined from the equation

(4) I i + l i - 1 P,i = .Dfui ~

2

If the pile is loaded simultaneously with torsion and axial force (Figure 3), each node is subjected to a combined shaft force Ri which is equal to

( 5 )

where Pi is the axial shaft force at node (i), and Ti is the shaft torque at node (i). Similarly, the total combined (axial and tangential) node displacement ui is

(6) where zi is the axial displacement of node (i), and Si is the rotation of node (i).

Figure 3(b) shows an element of the pile shaft, on which the surrounding soil applies an axial load Pi and a tangential load 2Ti/D. These forces are combined to a total force Ri developed due to the pile element movement ui. When R i reaches the ultimate shaft friction Rui which is independent of the axial load-torque combination, displacements continue to increase at constant Ri( = Rui). To account for this combined behaviour, the axial and torsional springs of each node are modified as soon as Ri becomes equal to Rui. The ultimate axial shaft resistance P,, is set

Ri = J [ P f + (2Ti/D)2]

ui = J [zf + ( SiD/2)2 J

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equal to Pmi and the ultimate torsional shaft resistance TUi is set equal to Tmi (Figure 2). Beyond these values the pile node moves without increase of the axial and torsional resistances. It is noted that when axial only load is applied to the pile, then Pmi = Pui, and when torsional only load is applied, then Tmi = Tui. The ultimate combined shaft resistance Rui can be computed from the following equation which essentially is identical to equation (4):

The pile base spring, can be modelled either theoretically or by the following load displacement relationship proposed by Vijayvergiya," which was also used in the present analysis:

pb = q u b A v ( z b / z c b ) ( 8 )

where Pb is the load at the pile base, qub is the dtimate unit end bearing, A is the area of the pile base, ib is the pile base displacement, and zCb is the displacement required to mobilize the full end bearing (on the order of 005 D).

A torsional base spring is not necessary to be introduced in the analysis because its contribution to the response of ordinary piles is expected to be minor'. For short end bearing piles, in which the torsional resistance of the base may be significant compared to the shaft resistance, an elasto-plastic torsional base spring can be introduced. The initial stiffness of this spring is:3

K , , = fGbD3 (9) where Gb is the shear modulus of the soil at the pile base. The ultimate resistance of the torsional base spring can be computed from the following equation:

Tub = SD(7tCDz + Pb tan 4) (10)

where 4 is the friction angle between pile and soil at the pile base, and c is the pile adhesion at the pile base.

The above foundation model was incorporated into a transfer matrix ~ c h e m e ~ . ~ which provided the variation of axial force, torque and axial and torsional displacements along the pile length. According to this scheme, the state vector of the left-hand side of the first node (consisting of the axial displacement, the rotation, the torque and the axial force) is multiplied by the point transfer matrix of this node, which includes the stiffnesses of the axial and torsional spring, to produce the state vector of the right-hand side of the node. This state vector is multiplied by the field transfer matrix of the first pile segment, which includes the axial and torsional stiffnesses of the segment, to produce the left-hand side state vector of the second node. The same procedure is repeated for all nodes until the right-hand side state vector of the last node is expressed as a product of the left-hand side state vector of the first node and the global transfer matrix (product of all the intermediate point and field transfer matrices) of the pile. Knowing two boundary conditions at the top of the pile (torque and axial force applied to the pile) and two boundary conditions at the bottom of the pile (relationships 8, 9 and 10 between axial force, axial displacement, torque and rotation), the state vector of the first node and consequently the state vectors of the other nodes can be determined. To account for the elasto-plastic spring behaviour, an iterative procedure was adopted.

APPLICATION

The method described above was used to compute the response of a typical offshore steel pipe pile embedded in clay. The pile had a diameter of 152m (60in.), a wall thickness of 37mm

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A X I A L D I S P L A C E M E N T (m.n)

R O T A T I O N ( t a n @ )

Figure 4. Axial load vs. axial displacement (a) and torque vs. pile head rotation (b)

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(It in.) and a length of 50m (164ft.). The undrained shear strength and the shear modulus of the clay were 100 kN/m2 and 5 MN/m2, respectively. The unit shaft resistance, fui, computed for this undrained shear strength," was 50 kN/m2.

To demonstrate the effect of the applied torque on the axial pile response and the effect of the applied axial load on the torsional pile response, several combinations of torque and axial load were studied and the results are presented in Figure 4. The relationships between axial load and axial pile head displacement for different values of the applied torque are shown in Figure 4(a). Similarly, Figure 4(b) presents the relationships between torque and pile head rotation for different values of the applied axial force.

It is evident that both the ultimate pile capacity and the pile rotations and axial displacements are greatly affected by the combined loading. A torque applied at the pile head reduces significantly the ultimate axial pile capacity and increases the axial displacement, while the application of an axial load reduces the ultimate torsional capacity and increases the pile rotation. A pile subjected to large torsional loads exhibits, apart from large rotations, significant axial movements; similarly. a pile loaded with a large axial force produces not only axial movements but also significant rotations. Similar results were obtained for other soil conditions and pile stiffnesses.

CONCLUSIONS

An analysis has been presented which provides the response of piles subjected to combined axial and torsional loads. The piles can be embedded in multilayered soil profiles and their cross-section can vary with depth. The soil is represented by a series of elasto-plastic springs which can support both axial and torsional forces transmitted through the pile.

The analysis illustrated that piles loaded simultaneously with torque and axial force exhibit significantly lower torsional and axial bearing capacities and larger rotations and axial displacements than piles loaded only with torque or axial force. This occurs because the overall pile response depends on the combined (axial plus torsional) stresses applied to the pile shaft, while the ultimate shaft resistance per unit area is independent of the load combination.

I t is recommended to avoid treating the axial and torsional pile responses separately because this could produce dangerously misleading results.

REFERENCES

1. H. G. Poulos, 'Torsional response of piles'. J . Geotech. Enq. Diu. A.S.C.E., 101 (GTIOI. 1019-1035 (1975). 2. M. F. Randolph. 'Piles subjected to torsion', J . Geotech. Enq. Dir. A.S.C.E.. 107 (GT8). 1095-1 I I 1 (19Rll. 3. Y. K . Chow. 'Torsional response of piles in nonhomogeneous soil'. J . Geoteck. Etiy. A.S.C.E., 111 (GT7). 942-947

4. E. C. Pestel and F. A. Leckie, Matrix Merhods in Elmo-mechonics, McGraw-Hill, London, 1963. 5. M. Georgiadis 'Flexible landing mats on clay', Ph.D. thesis, Dept. of Civil Engineering, Univ. of Southampton, U.K.

6. M. J. Tomlinson, Pile Design and Corisfructiori Practice. Viewpoint Publication, Cement and Concrete Association,

7. U. W. Stoll. 'Torque shear test of cylindrical friction piles', Cio. Eng. A.S.C.E.. 42(4). 63-64 (1972). 8. M. F. Randolph and C. P. Wroth,'Analysisofthe deformation of vertically loaded piles', J . Georech. Eny. Diu. A.S.C.E.,

9. J . L. Briaud, and B. Meyer, ' I n siru tests and their application in offshore design. Proc. A.S.C.E. Specialty Conf. on

10. V. N. Vijayvergiya, 'Load-Movement characteristics of piles', PORTS '77 Conf. Long Beach CA, pp. 269-284 (1977). I 1. American Petroleum Institute. 'Recommended practice for planning. designing, and constructing fixed offshore

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