Numerical modelling of tension piles

Transcription

1 Numerical modelling of tension piles S. van Baars Ministry of Public Works, Utrecht, Netherlands W.J. van Niekerk Ballast Nedam Engineering, Amstelveen, Netherlands Keywords: tension piles, shaft friction, installation effect, bearing capacity, case study, CPT ABSTRACT: For determinations of the ultimate tension capacity of a piled foundation, often use is made of empirical relations between soil strength and skin friction. The disadvantage of these (analytical) methods is that they are in general not very accurate for most soil conditions. Therefore a numerical method for determination of the ultimate bearing capacity is presented here. Results were successively compared with actual test results which were measured during pile tests. It was found that the numerical model assessed the actual pile bearing capacity more closely than analytical models based on empirical calculation rules. Therefore lower factors of safety can be accepted. The behaviour of the (virtual) interface between pile and soil significantly influences the behaviour of the pile. 1 INTRODUCTION Foundations of large civil constructions are often loaded in tension. For determination of the ultimate tension capacity of a piled foundation, often use is made of empirical relations between soil strength and skin friction. In these methods the actual circumference of the pile is multiplied by the skin friction that can be generated from the soil as measured in the laboratory or in situ, e.g. through the results of unconsolidated undrained tests or torvane tests, which form the basis for s u (undrained shear strength) based methods. Other methods take the in-situ shear strength and stress into account through in-situ measurement of the soil resistance based on the q c (cone resistance) following from the Dutch CPT tests. It can be shown that from a substantial amount of pile tests, satisfying relations between q c and s u based methods exist for cohesive soils (Van Niekerk et al. 1998). These convenient and simple to use methods are considered as analytical. The disadvantage of the analytical methods is that they are in general not very accurate for most soil conditions. This is for instant caused by changing soil stresses due to installation effects. Other inaccuracies can follow from relaxation of soil stresses due to excavations of normally and over-consolidated soils. Especially granular soils are susceptible to this phenomenon. During loading of a tension pile, the surrounding soil stress is reduced due to uplift of the soil mass surrounding the piles. This yields changes in the ultimate bearing capacity which is often based on empirical values for compression loading. Finally during construction of cast in situ piles, soil stresses are governed by the concrete pressure during curing of the concrete. The soil stresses generated from the cast in situ piles are subject to phenomena related to execution of the piling works, such as the maintained hydraulic head during and after casting of the concrete. The accuracy of analytical methods is reduced by not taking into account all these soil stress related items. Therefore in contrast to the analytical methods a numerical method for determination of the ultimate bearing capacity is presented here. The presented method here was used by Van Niekerk (1996 a, b) and Van Baars (1997) for research purposes to determine the suitability of a finite element model to implement the in-situ stresses after installation of a pile. Results were successively compared with actual test results which were measured during pile tests on the De Gaag 1

2 aqueduct project as a test case for the Second Beneluxtunnel project. Both projects are situated in the Netherlands. 2 THEORY OF PLAXIS MODELLING In this paper pile shaft capacity is assessed by subsequently modelling in-situ soil conditions and soil conditions after driving of the pile. Here it is initially assumed that for the in-situ soil conditions prior to installation, the soil was considered to be normally consolidated. This allows for a simple calculation to generate the horizontal and vertical stresses before installation, according equation 1: σh = K0 σv (1) in which K 0 is determined by Poisson s ratio ν according equation 2: ν K o = (2) 1 ν For overconsolidated soil other value s of K 0 apply. With these equations the soil stress can be determined at every point of the FEM mesh, as well on every boundary of the model. The study of a single, axially loaded pile typically allows for the use of an axi-symmetric mesh. Since internal stress states of the pile and effects of diameter changes due to loading (Poisson effect) are neglected, the pile could be modelled by modelling the skin only. It is proposed here to model the skin by a beam element. This procedure has two advantages compared to modelling of the pile with elastic soil elements. Firstly, the number of elements reduces, which allows for faster calculation in especially versions of PLAXIS prior to release 7.0 and secondly, this allows for applying a random traction load on the boundary where the beam element is put. The possibility to do so, enables one to use any stress distribution measured on the pile, as for instance proposed by Lehane and Jardine (1994). In their proposal the radial effective stress on the shaft is determined by the cone resistance, vertical effective stress and relative penetration depth. Thus, not only the soil resistance but also the effect of on-going penetration of the pile tip, and its effect on in-situ stress is modelled. The in-situ stress acting on the pile can be modelled by applying a traction load on the mesh boundary as presented in Figure 2. In the (simplified) mesh of Figure 1. interface elements are situated along the pile shaft. By applying the following steps the stresses after installation can be generated: 1. Perform an elastic calculation with traction loads on the 'free' boundaries to generate a stress condition with equal K 0 for the entire mesh. The pile is not present yet. Radial displacements are allowed. 2. Apply additional traction loads along the future pile shaft location to model pile installation effects. 3. Activate the beam element and lock its position by prohibiting displacements of the nodes in radial direction (See Figure 4-5.) The radial stress increase caused by installation has now been introduced in the FEM mesh correctly. The interface elements next to the pile are subject to a stress greater or at least different than the original stress and are subject to shear. By applying a pile head displacement the pile can be loaded. 3 GENERAL PLAXIS RESULTS AND SUITABILITY OF THE MODEL Shaft capacity of the basic model was compared with the shaft capacity of a modified model, which differed from the original, by varying the length/diameter ratio, the reference shear modulus, the 2

3 internal friction angle, the interface friction angle, the stress state before and after installation, the presence of a compressible layer, the load direction, the distance of a reaction force on the soil surface and last but certainly not least, the interface thickness. The load displacement curves for all different scenarios have been compared in the study. As was to be expected from field experience, the general load displacement curve is initially virtually linear, after which the load needed for additional displacements decreases. The ultimate shaft capacity is determined as the point were displacements continue without load increase. The results of varying input parameters that particularly involve PLAXIS modelling are highlighted below. It was found that the load direction had little effect on the ultimate shaft capacity; the shaft capacity in tension loading is some 10% lower than it is in compressive loading. It is considered that this (minor) difference is caused by the difference in principal stress rotation. The load displacement behaviour of the pile is mainly determined by the dimensions of the pile and the soil shear modulus. The shaft capacity is mainly determined by the dimensions of the pile, the radial stress on the shaft, the shaft friction angle, the degree of consolidation and the interface thickness. The importance of the interface thickness is caused by the dilatant behaviour of the interface, which can cause additional radial stress increase. Increase of the interface thickness led to a significant higher shaft capacity of the pile. Additional information on dilatancy and the importance of a correct thickness of the dilatant zone can be found in Houlsby (1991). The influence of the interface is also discussed below in the explanatory calculation presented. 4 APPLICATION For economical reasons, in the Netherlands and some surrounding countries, the most common method of calculation of the ultimate bearing resistance of a pile is the q c method. In this method the maximum shear force that can be generated along a pile shaft is determined by the integral of the cone resistance multiplied by a shear factor over the full height of all relevant layers. The shear resistance factor is dependent on the soil type and the pile type. The main merit of this method is its simplicity. Based on a CPT test, only an easy assessment can be made of the total bearing capacity. Its main drawback however is its large inaccuracy because of its highly empirical basis for shaft resistance factors. Also no direct relation between the diameter of the CPT cone and the diameter of a pile is appropriately taking into account the soil displacement and subsequent stressing of the surrounding soil. Furthermore the effect of stress reduction during retrieval of a tube or other equipment during installation of cast in situ piles is not considered. In addition to this, the method does not consider the effect of variation of the concrete level when not at ground level during installation of a pile, see Lings et al (1994). For instance, at The De Gaag aqueduct casting of concrete was terminated at 11.5 m below ground level. In numerical calculations these effects can be considered accurately. 5 CASE VIBROCOM PILE DE GAAG 5.1 Choice of Pile For the tension pile research near De Gaag 3 Vibro piles, 3 Vibrocom piles, 2 HP piles and a single steel tubular pile were test loaded. In this paper, cast in situ piles (i.e. Vibro or Vibrocom piles) are considered, mainly because the in-situ stresses for those piles are better known than for steel piles. Furthermore it was found later that the w/c ratio of the concrete used for the Vibro piles was lower than usual, which yielded less stress increase in the soil than usual. Also air and water intrusions were formed during installation, as appeared after excavation of the pile. It was therefore considered most interesting to model the Vibrocom piles. 3

4 Table 1. Geotechnical model De Gaag - Vibro piling. No. Stratum γ wet [kn/m 3 ] G 50 [kn/m 2 ] c u [kn/m 2 ] φ' [deg] ψ ' [deg] y top [m to NAP] 6 Clay (+peat) Clay (+sand) Sand B 19 10, Peat Clay Sand A 20 25, Geotechnical profile of De Gaag Below the used model of the geotechnical conditions are given. Ground level is situated at NAP -1.6 m. In Sand layer A the ground water table is found at NAP m, whereas in the higher Holocene layers the ground water table is found at NAP m. Measured bearing capacities were compared with manual calculations, the latter based on CPT results (q c method). CPT results were available in sufficient amounts in contrast to the amount of direct soil tests to determine strength and stiffness of various layers. Table 1. therefore contains best estimates that should however be assessed carefully. 5.3 Pile installation Prior to installation of the Vibrocom piles a casing Ø 1.1 m was driven to NAP m, during which the casing was cleared. Subsequently Vibro tubes with lost tip (Ø 557/508 mm) were driven to NAP m. Successively an instrumented prefab core (Ø 320 mm) was installed in the tube and the annular space was filled with concrete mortar. By using the casing, the pile was not installed in the upper two clay layers. It was considered in design that these layers would not contribute to the ultimate bearing capacity before the deeper sand layers has failed (loads in excess of the maximum shear stress in the sand). For Pile B problems with the piling hammer occurred, which have led to interruptions and once a maximum delay of 15 minutes. Although no clear indication is found that this pile has been influenced by these interruptions, the bearing capacity is significantly more than for Piles A and C. 6 NUMERICAL MODELLING OF THE GEOMETRY 6.1 Soil For numerical calculations the entire geometry needs to be modelled. In this case the lower boundary is put at NAP m, whereas the outer boundary of the axi-symmetric mesh is put at 10 m from the centre line of the pile axis. Calculations are made using 15-noded triangular elements in between 6 verticals and 15 horizontal mesh lines. Positions of the mesh nodes are mainly determined by the pile wall (w), pile length (l), boundaries (b), soil layers (s), additional nodes for weak layers (xw) and additional nodes for the thick soil layers (xt). In Table 2 the positions are given for the horizontal mesh lines. For the position of the vertical mesh lines the results of Table 3 apply. Two PLAXIS mesh blocks are used, one supporting the pile tip and the other along the first up to the pile top. In Figures 1-3 the mesh is shown. 4

5 Figure 1. Connectivity plot. Figure 2. Boundary A (soil). Figure 3. Boundary B (mortar). Figure 4. Boundary conditions. Figure 5. Displacement at one node. 5

6 Table 2. Horizontals b xt l xt xt xt s xw s xw s l s s b Table 3. Verticals b w b 6.2 Interface Much of the pile strength depends on its interaction with the subsoil through the interface layer. The roughness of this interface is found to be 0.8 to 1.0 times the in situ shear strength of the soil. In this paper the strength of the interface is taken at 0.9 times the soil strength. At NAP m a change in the effective soil stresses occurs at the boundary of the casing and the pile. Since the interface contains only one integration node at this point, there is only one strain and one stress. Only by applying an additional node this singularity problem can be avoided. Here this is achieved by applying an extra interface perpendicular to the previous interface. The new interface needs not to be extended in the mesh. Since the pore pressure P changes at NAP m, also here an additional interface is required. 6.3 Pile In simple situations the pile can be modelled using one beam element, however here two beams should be used, i.e. one for the pile shaft (NAP to m) and one for the casing (NAP to m). These beam elements can be activated during calculations. In the calculations the casing is put on the same vertical as the tubular pile for convenience, although the radius in nonequivalent. To avoid numerical problems, pile stiffness parameters EA and EI shall not be taken to big in relations to the soil stiffness. However piles should be stiff enough to model actual soil behaviour. 6.4 Boundary condition A (soil) Initially the boundary stresses are kept equivalent to the in-situ horizontal effective stress. To avoid changes in the soil stresses at every change of soil type, it was chosen to apply an equivalent soil pressures coefficient at rest of K 0 = 0.5. Introduction of the stress in the mesh was done numerically by applying first a load step considering gravity [Mweight = 1]. The soil stresses introduced to the mesh were derived from equations 1 and 2. The horizontal effective stresses are calculated using: σ A ' = ( zγ p) K0 (3) wet where z = depth and p = water pressure. At pile tip level (NAP m) we thus find a maximum horizontal effective stress of kn/m 2 and a vertical effective stress of kn/m 2. To model stress increase from driving of the piles, the horizontal effective stress is temporarily increased, which is a simplification of complex matter. It can be assumed that during driving the soil will never react completely passive, which denotes K<K p. If chosen to adopt K = 2 then the effective horizontal stress needs to be increased temporarily by a factor f = K/K o = 2/0.5 = 4 to model pile driving effects. 6

7 6.5 Boundary condition B (mortar) For the final stage of the installation, it is assumed that the effective stress at the pile shaft is dependent on the mortar pressures during curing [Load B]. The weight of the mortar is taken at γ mortar = 22 kn/m 3. Concrete mortar has been installed to level NAP m. Since the ground water table at this level is 1 m lower than at ground level, while this is not the case for the fluid mortar, an additional pressure of 10 kn/m 2 is accounted for in the deeper layers starting at NAP m. Thus we find that the support pressure B is dependent on the depth z: σ B ' = ( z )( 22 10) { + 10 } (4) Near the pile tip (z = NAP m) we find a maximum horizontal and vertical effective stress of kn/m 2. When the pile would be installed to ground level, the pressure would be significantly higher: σ B ' = ( ) ( 22 10) = kn / m 2 (5) Effects of higher support pressure are considered later. 7 NUMERICAL MODEL TENSION PILE IN DETAIL Below is given in detail the procedure for all stages of the numerical test loading of the pile: A. Boundary condition A (soil) is activated, while the inner boundary is resisted to move horizontally. Thus boundary condition A acts only vertically on mesh block no. 1. Also the weight of the soil elements is activated. [load A = 1, boundary_x = fixed, Mweight = 1] B. Casing (Beam II) is activated. [staged construction, beam II = + ] C. Inner boundary is released. The upper three nodes resist the casing (Beam II). Below the casing (place of futur tension pile), boundary condition A satisfies equilibrium. [below casing: boundary_x = loose] D. To model stressing of the soil from pile driving, boundary condition A (soil) is increased by a factor 4. [load A = 4] E. By pulling the Vibro tube the soil is unloaded, but also reload by the fluid mortar. The increased boundary pressure A is replaced at the same time by boundary pressure B (mortar). [load A = 0, load B = 1] F. During curing of the pile, de inner boundary of the mesh is resisted from deforming horizontally. Beam I ( = tension pile) is activated and Beam II ( = casing) is deactivated to prevent the latter from being pulled up. [boundary_x = fixed, staged construction, beam I = +, beam II = -] The tension pile is now ready to be pulled. G. All displacements from previous can now be reset (to zero). By applying a forced displacement to a single node on Beam II (Figure 4 and 5) the pile is pulled out. [reset displacements, Σ_Mdispl = 0.1] By multiplying the vertical force (Force y = normal force in Beam I) by 2π and plotting this force against the total displacements [Sum-Mdisp], a load displacement curve is generated, as given in Figure 6. Failure of the soil appears rather locally, i.e. directly next to the pile shaft (Figure 7). Plastic points are only found next to the shaft and the pile tip. 7

8 Force [kn] Displacement [m] Figure 6. Force versus displacement of the tension pile. B B C D B A D C B C C τ max A = 0.1 B = 0.3 C = 0.5 D = 0.7 E = 0.9 Figure 7. Ratio of shear stress to maximum shear stress. 8 RESULTS PILE LOAD TESTS The measured pile bearing capacities as measured at De Gaag strongly deviated from the empirical calculation results as based on the q c method (pre-calculated), even if q c results are considered 8

9 Table 4. Measured and analytical calculated bearing capacities. Pile Measured [kn] Pre-calculated [kn] Post-calculated [kn] A B C which are taken after installation of the pile (post-calculated), see Table 4. According the numerical simulation the ultimate bearing capacity is 1740 kn, which is only 16% less than the average capacity of the three piles, and only 5% less than the average capacity of Piles A and C. This means that the numerical results are almost equal to the measured results. From additional numerical simulations followed that by increasing the hydraulic mortar head level to ground level, a bearing capacity of 4200 kn could be achieved, which is an increase in bearing capacity of 140 %. 8.1 Dynamic pile driving versus static calculation Computer programs like PLAXIS and most others are based on static equilibrium. However this condition is not to be found during pile driving, from which it can be concluded that the process itself of pile driving, in principle, can not be modelled accurately. It can however be considered that pile driving gives more irregular stress distribution after driving than casting piles in situ. In numerical simulations, only temporarily soil is stresses additionally to model the pile driving. The assumed stressing of the soil is however introduced in the mesh. In the presented simulation here, was found that if the temporary stressing of the soil was abandoned at all, the ultimate resistance was only 6% lower, which yields that in this case less accurate modelling of the soil stressing has no significant effects on the results of cast in situ pile calculations. 8.2 Interface behaviour In the numerical calculation of the tension pile, an interface is modelled. It can be questioned whether or not this is justifiable (does this interface exist in reality?) and furthermore one can wonder how to model an interface. It was found earlier however (Van Niekerk 1996a) that the interface strength can increase the ultimate significantly by either increasing the dilatancy or the virtual thickness, if an Advanced Mohr Coulomb model is used. From research performed by, among others, Tejchman and Wu (1995) follows that a rough steel surface is remarkably well capable of transferring shear stresses from a solid body to the soil. It follows that rough surfaces need hardly or no shear strength reduction at all. 8.3 Time dependent behaviour For geotechnical calculations time is usually a major issue, especially for cohesive soils. In the presented calculation an undrained strength is used rather than a drained strength. For actual constructions however it might be considered using drained parameters to model longer time spans of loading, or continuous loading in one direction. It suggested here to study creep phenomena on the bearing capacity of a tension pile in a similar study as presented in this paper. 8.4 Differences in stiffness In the De Gaag case we find mainly cohesive top layers and at greater depth mainly non-cohesive layers, which is typical for Dutch soils. The deeper layers are stiffer and therefore considered to fail 9

10 prior to the upper layers, from which yields that the upper and lower layers can not resist the tension load at the same time. Therefore the total resistance of the pile should not be equivalent to the sum of the maximum individual contribution of the soil layers. However, simulations of the tension pile with a hydraulic mortar head level up to ground level (with a bearing capacity of 4200 kn) showed that the sum of the individual contribution was only 1% higher than the total resistance. So the philosophy for pile constructions with bearing only in deeper layers, contains two mistakes. Firstly, the contribution of the upper layers hardly need any reduction. Secondly, the higher mortar head creates a much higher mortar pressure [load B]. 9 CONCLUSIONS AND RECOMMENDATIONS In general numerical modelling of test loading of a tension pile proves to be a convenient research tool. Effects of changes in soil stress, soil stiffness and interface behaviour in particular can be studied in detail. In relation to this, determination of correct soil parameters remains an issue of great importance. From the explanatory case was found that the numerical model assessed the actual pile bearing capacity more closely than analytical models based on empirical calculation rules. Therefore lower factors of safety can be accepted, which will reduce the number or size of the tension piles. Installation effects and their modelling in numerical models remains an issue of concern. Dynamics during installation, as well as poor execution of piling works can change soil parameters beyond the conventional models for assessing pile bearing capacities. Time dependent effects are generally neglected in empirical models but can be taken into account in numerical models. The behaviour of the (virtual) interface between pile and soil influences mostly the behaviour of the pile. Its presence and properties should be studied more in detail to determine the actual behaviour of the soil, as should the effects of differences of stiffness of various subsequent layers. Ultimately the best way to compare shaft resistance in numerical models and prototypes is probably comparing load displacement curves. By closely modelling the loading-unloading from prototypes in computers, soil and pile models can be calibrated, yielding more information of actual soil conditions and pile bearing capacities. REFERENCES Baars, S. van Case Study: Numerical Modelling of Tension Piles. Report BSW-R-97.48, Dutch Ministry of Public Works. Houlsby, G.T How the dilatancy of soils affects their behaviour. Proc. 10th European Conference on Soil Mechanics, Balkema Rotterdam, pp Lehane, B.M. and Jardine, R.J., 1994 Shaft Capacity of Driven Piles in Sand: A New Design Approach. Proc. Boss, July 1994, pp Lings, M.L., Ng, C.W.W. and Nash, D.F.T. 1994, The Lateral Pressure of Wet Concrete in Diaphragm Wall Panels Cast under Bentonite, Proc. Institution Civil Engineers; Geotechnical Engineering, July 1994, pp Niekerk, W.J. van. 1996a Modelling of a single tension pile in sand. PLAXIS Bulletin, no. 15. Niekerk, W.J. van. 1996b Calculation of a tension pile, Handout Annual PLAXIS Users Meeting (24 April 1996), Utrecht, The Netherlands. Niekerk, W.J. van, Rösingh, J.W. and Tonnisen, J.Y Performance of bored piles in Lignite, Proc. of 3th International Conference on Bored and Auger Piles, Balkema, Rotterdam. Tejchman and Wu 1995 Int. Journ. Num. and Anal. Meth. In Geomechanics, vol 19, pp Tomlinson, M.J Pile design and foundation analysis. London: Viewpoint Publications. 10