Single Pile Simulation and Analysis Subjected to Lateral Load

Transcription

1 Single Pile Simulation and Analysis Subjected to Lateral Load Jasim M Abbas Ph D Student, Department of Civil and Structural Engineering, Universiti Kebangsaan Malaysia jasimalshamary@yahoo.com Zamri Hj Chik, Ph.D. Associate professor, Department of Civil and Structural Engineering Universiti Kebangsaan Malaysia irzamri@vlsi.eng.ukm.my Mohd Raihan Taha, Ph.D Professor, Department of Civil and Structural Engineering Universiti Kebangsaan Malaysia drmrt@vlsi.eng.ukm.my ABSTRACT The results of the 3D finite element analysis on the behavior of single pile under lateral loadings are presented in this paper. The effect of pile shape for both circular and square cross-section on pile response was investigated. In addition, an effect of slenderness ratio L/B is also be carried out in this analysis. Linear elastic model of pile was used for modelling the piles. Mohr-Coulomb model was used to simulate the surrounded soil. The pile soil interaction composed of 6-node interface elements. A good correlation between the experiments and the analysis was observed in validation example. It was found that the pile response is affected by the amount of loading, the pile cross sectional shape and pile slenderness ratio. The lateral resisting of pile increase in proportioned to the square shape of the pile. In both pile shape, a short pile (L/B = 8.3) gave a small amount of lateral tip deflection than the long piles with a slenderness ratio more than 8.3 for the same amount of loading. Also, the negative base deflection is high for short pile and reduces to zero for long piles. KEYWORDS: single pile, shape effect, lateral load, Mohr-Coulomb

2 Vol. 3, Bund. E INTRODUCTION Pile foundations are used to support the heavy structure and can act in the dual role of carrying the applied load to deeper, strong layers, and also of reinforcing the soil. In the case of foundations of bridges, transmission towers, offshore structures and other type of huge structures, piles are also subjected to lateral loads. This lateral load resistance of pile foundations is critically important in the design of structures under loading from earthquakes, soil movement, waves etc. According to Poulos and Davis (98) the maximum deflection of the pile is the major criterion on the design. The square cross-section piles is one of the most common type of deep foundation to support high rise building especially in southeast Asia (Fellenius et al., 999 and Zhang, 3). These shapes of piles according to Johnson (6) include solid concrete octagonal and square piles. One of the disadvantages of this pile shape is the pile instillation relatively complex in case of large diameter and highly lengths. As reported by Poulos and Davis (98), the first attempts to study the lateral behavior of piles included two-dimensional finite element models in the horizontal plane. Several investigations have attempted to study the behavior of pile under lateral load (Muqtadir et al. 986, Yang et al. 5, and Karthigeyan et al., 6, 7) using 3D finite element analysis. Since the three dimensional finite element analyses are widely used now, the analyses of laterally loaded piles are investigated by this approach in this study. The effects of pile shape for both circle and square cross-section on pile response are investigated in addition to the effect of slenderness ratio to explore the response of laterally loaded piles. NUMERICAL MODEL Finite element analyses were performed using the software PLAXIS 3D FOUNDATION version.. According to the finite element method a continuum was divided into number of (volume) elements. Each element consists of a number of nodes. Each node has a number of degrees of freedom that correspond to discrete values of the unknowns in the boundary value problem to be solved. Mesh Generation In order to perform the finite element calculations, the geometry has to be divided into elements. A composition of finite elements is called a finite element mesh. The basic soil elements of a 3D finite element mesh are represented by the 5-node wedge elements as shown in Figure. These elements are generated from the 6-node triangular elements. The 5-node wedge element is composed of 6-node triangles in horizontal direction and 8-node quadrilaterals in vertical direction. According to Karthigeyan (6 and 7), the soil mass dimension depends on the pile diameter and length. The width of soil mass is taken as 4B, in which, B is the pile diameter or pile width. The soil mass effect on the pile response is diminishing for the width more than 4B. The height of soil mass is L+B, in which, L is the length of pile.

3 Vol. 3, Bund. E 3 y Pil L+ z x 4 (a) 4 L= pile length B= pile wid. (b) Figure : 3D finite element mesh for soil mass and location of pile (a) 3D-FE mesh, and (b) 5-node wedge LINEAR ELASTIC MODEL OF PILE (PERFECT-PLASTICITY) This model represents Hooke's law of isotropic linear elasticity used for modeling the stress-strain relationship of the pile material. The model involves two elastic stiffness parameters, namely Young's modulus, E, and Poisson's ratio, ν, as shown in Figure. It is primarily used for modeling of stiff structural member for example piles in the soil (Brinkgreve and Broere, 4). σ perfectly plastic perfectly elastic E=young s Figure : stress strain curve (Johnson, 6) Hooke's law in 3D can be expressed as in Eq.. Two parameters are used in this model, the effective Young's modulus, E', and the effective Poisson's ratio, ν'. ε

4 Vol. 3, Bund. E 4 zx yz xy zz yy xx zx yz xy zz yy xx E ) )( ( () The relationship between Young's modulus E and other stiffness moduli, such as the shear modulus G, the bulk modulus K, and modulus elasticity E, is given by: ) ( E G () ) ( 3 E K (3) ) )( ( ) ( E E (4) MOHR-COULOMB SOIL MODEL This elasto-plastic model is based on soil parameters that are known in most practical situations. The Mohr-Coulomb model is used to compute realistic bearing capacities and collapse loads of footings, as well as other applications in which the failure behavior of the soil plays a dominant role. The model involves two main parameters, namely the cohesion intercept, c and the friction angle, υ. In addition to three parameters namely Young's modulus, E, Poisson's ratio, ν, and the dilatancy angle, ψ need to calculate the complete σ ε behavior. Mohr Coulomb s failure surface criteria shown in figure 3. According to Johnson (6), the failure envelope only depend on the principal stresses (σ, σ 3 ), and is independent of the intermediate principle stress (σ ). When mapped in three-dimensional stress space, Mohr Coulomb criteria resolved into an irregular hexagonal pyramid. This pyramid forms the failure/yield envelope, which is turn governs how soil will behave. The material behaves elastically if the stress point lies within the failure envelope. However, if the stress reaches the yield surface the material will undergo a degree of the plastic deformation. In the Mohr Coulomb model used herein, it is assumed that the soil has a linear elastic relationship until failure.

5 Cohesion intercept Vol. 3, Bund. E 5 Shear stress (τ) Mohr Coulomb failure envelope υ friction angle c σ 3 σ normal stress (σ) Figure 3: Mohr Coulomb s failure surface (Johnson, 6). The usual definition of the equation of Mohr-Coulomb surface is (Smith & Griffith, 98): 3 3 F sin c cos (5) Which, when rewritten in terms of invariants and Lode angle θ becomes: sin sin F I sin J cos ccos 3 (6) 3 where and J 6 I x y x y y z z z x xy yz zx (7) (8)

6 Vol. 3, Bund. E 6 INTERFACE ELEMENTS Interfaces are modeled with 6-node interface elements. Interface elements consist of eight pairs of nodes, compatible with the 8-noded quadrilateral side of a soil element. Along degenerated soil elements, interface elements are composed of six node pairs, compatible with the triangular side of the degenerated soil element. Each interface has a 'virtual thickness' assigned to it which is an imaginary dimension used to obtain the stiffness properties of the interface. The virtual thickness is defined as the virtual thickness factor times the average element size. The average element size is determined by the global coarseness setting for the D mesh generation. The default value of the virtual thickness factor that is used in this study is.. The stiffness matrix for quadrilateral interface elements is obtained by means of Gaussian integration using 3x3 integration points. The position of these integration points (or stress points) is chosen such that the numerical integration is exact for linear stress distributions. The 8-node quadrilateral elements provide a second-order interpolation of displacements. Quadrilateral elements have two local coordinates (ξ and η). ξ=-. ξ= ξ= η = η =. η=- 5. Figure 4: Local numbering and positioning of nodes ( ) and integration points (x) of an 8-node quadrilateral element The shape functions of 8-node elements can be written as Eq. 9 (below). N = ( ξ) ( η) ( ξ η) / 4 N = (+ξ) ( η) ( +ξ η) / 4 N 3 = (+ξ) (+η) ( +ξ+η) / 4 N 4 = ( ξ) (+η) ( ξ+η) / 4 (9) N 5 = ( ξ) (+ξ) ( η) / N 6 = ( ξ) (+ξ) (+η) / N 7 = ( η) (+η) (+ξ) / N 8 = ( η) (+η) ( ξ) /

7 Vol. 3, Bund. E 7 VALIDATION OF THE NUMERICAL MODEL The finite element model of the whole geotechnical structure that was developed was verified based on the results of full-scale pile load tests. The case study that simulates and meshes development is presented in the next section. Case study I (Jamaludin and Hussein 998) Large diameter bored piles of.m diameter were used for the construction of the new.km road dual carriageway viaduct on an existing road. The road project is situated in Port Klang, and links the West Port to Kuala Lumpur, Malaysia. The length of each bored pile is approximately 75m with steel casing being used for the top 3m. The bored piles were designed to carry loads ranging from 3 to 6 kn. The generalized subsoil properties consist of very soft silty clay with traces of sea shells with depth m. Below this layer is a m of soft silty clay. Medium dense to dense silty sand is about m, and 7m of medium stiff silty clay. The lowest layer consists of very dense fine grained sand. The properties of soil were listed in Table. The same load sequence was apply on the pile after complete the whole geotechnical model. The comparison between the finite element simulation and the reported data is shown in Figure 5. There are good comparison between the experimented results of three piles and the present simulation model. The piles were deflecting not in the same magnitude at the field test due to the variability of soil properties. Parameter Table : Geotechnical properties of the soil layers for case Name Very soft silty clay with traces of sea shells Soft silty clay Medium dense to dense silty sand Medium stiff silty clay Very dense fine grained sand Unsaturated kn/m 3 γ soil weight unsat Saturated γ sat kn/m 3 soil weight Young s E E+9 kpa modulus Poisson s ν constant Cohesion c kpa Friction angle υ Pile Unit

8 Load (tons) Vol. 3, Bund. E present FEM simulation 4. Jamaludin et al. (998) - pile Jamaludin et al. (998) - pile Jamaludin et al. (998) - pile Settlement (mm) Figure 5: Comparison of finite element results with field test data of Jamaludin, 998 RESULTS AND DISCUSSION Pile behavior mainly depends on the interaction between pile material and the soil media when piles are subjected to lateral load. This study includes: () the load intensity. Started from the small loading and increased gradually in equal magnitude during the load stages, () pile shape. This factor include the pile cross-sectional shape, first is a ordinary circular shape and the second is a square (rectangular) shape, and (3) the slenderness ratio (L/B). The influence of these factors are summarized in the following sections. Analysis Layout The analysis consists of a number of models to explore the behavior of piles under lateral load. The number of main models is eight which are divided equally between circle and square cross sections. The load was change from the lowest which started from 5 kn to the highest i.e. 4 kn. The analysis is used to explore the behavior of pile in this range of loading. The pile diameter is fixed as.m during the analysis for circular pile shape and also the width was fixed.m for square pile shape. The slenderness ratio was also changed during the analysis to assess the performance of pile when the slenderness ratio (L/B) is changed from 8.3 for (short pile) to.8 for (long pile). The tested piles were not covered by cap. In this case it takes the assumption of a free head pile.

9 Vol. 3, Bund. E 9 Material Properties and Dimensions In this study, circular and square cast in place test pile was used to simulate the behavior of piles under lateral load. These piles were embedded into sandy soil in one layer. The test piles and soil properties and dimensions are summarized in Table. Table 3: Pile and soil properties Pile details Soil details Circle parameters crosssection Square cross-section Parameters Values Size mm D x mm Friction angle (υ) 3 Length m m Dilation angle (ψ) - Type of pile Concrete Concrete Unit weight (γ) 8kN/m 3 Grade of concrete M5 M5 Young s modulus (E s ) MPa Young s modulus E p 5 MPa 5 MPa Earth pressure (k ).5 Poisson s ratio (ν s ).5.5 Poisson s ratio (ν).3 Study the Influence of pile shape All the analysis was performed in two stages. The first stage is to analyze piles that have traditional shape (circular cross section). Then piles of square shape were evaluated in second stage. The lateral behavior of pile in two cross sectional shape assessed depends on the type of soil mentioned in Table. This section includes also the load effect on the laterally loading piles with two shapes. The pile of circular cross section was firstly tested by applied the load in the tip of pile then made a test for square pile cross - section. The loading consists of small amount of loading which is 5 kn (Karthigeyan 6 and 7) in the beginning of loading stages. The investigation continues to reach a maximum amount of loading that always using in the design of piles when subject to lateral load. The lateral load deflection curve of two pile shape is shown in Figure 7 a & b, that detailed the lateral deflection response increased with increased the amount of loading. Pile deflection change depends on the pile load increment. In the first stage of load, the pile response was uniform that mean, the pile deflection improves linearly. But the square pile is more resistant than a circular shape, due to the high contact surface area between the pile and surrounded soil. The pile deflection increase around 6% when the load increase was load by 5 % in the case of square and circle pile shape. The comparison of circle and square pile shape in the lateral load deflection curve is shown in Figure 8. From this comparison can show the square shape pile has a small tip deflection than the circular shape pile in the same load intensity. The maximum tip deflections of two pile shape are detailed in Table 4. The maximum tip deflection of circle and square pile shapes shows in Figures 7. The lateral deflections of the piles are uniform and increased smoothly in the first half of loading. At higher loads, the piles behaved non-uniformly that result from non-linear response of soil around pile.

10 Load (kn) Load (kn).m Vol. 3, Bund. E Figure 8 shows the lateral tip deflection differences between two pile shapes This is supported by Johnson (6). The loads kn and 5 kn produces a deflections of.4b and.5b, respectively. From these results, it was observed that the pile with square shape is able to resist the load by about 3 % than pile with circular shape. Table 4: Maximum tip deflection Lateral Tip Deflection (mm) L/B = 8.3 L/B =.5 L/B = 6.6 L/B =.8 Load (kn) Circle Square Circle Square Circle Square Circle Square m.m L/D = 8.3. L/D = 8.3 L/D =.5 L/D =.5. L/D = 6.6. L/D = 6.6 L/D =.8 L/D = Lateral deflection (mm) (a) Circular cross section lateral deflection (mm) (b) Square cross section Figure 7: Lateral load deflection curve of single pile: (a) Circular cross section and (b) Square cross section

11 Lateral Load (kn) Vol. 3, Bund. E Circle pile shape, L/B=8.3 Circle pile shape, L/B=.5 Circle pile shape, L/B=6.6 Circle pile shape, L/B=.8 Square pile shape, L/B=8.3 Square pile shape, L/B=.5 Square pile shape, L/B=6.6 Square pile shape, L/B= Lateral Deflection (mm) Figure 8: Comparison of square and circle pile shape in the lateral load deflection curve Influence of the Slenderness Ratio The pile deformation due the lateral load is also influenced by pile slenderness ratio (L/B). In Figures 9 and, the effect of slenderness ratio on the deformation behavior of pile under lateral load show circular and square pile shape: (a) the short pile (L/B = 8.3) give a small amount of lateral tip deflection for the same amount of loading than the piles have the slenderness ratio more than 8.3. (b) the deflection along the pile is always in the direction of load (assumed negative). These values changed to positive and pass through zero depending on the slenderness ratio. For the short pile (L/B = 8.3,.5), the point of inflection is /5 from the base of the pile, while the long pile (L/B = 6.7,.8), the point position is 3/5 from the base. This is due to the slenderness of the pile that carry the load along pile length in the case of short piles but the upper part of pile carry applied load in the case of long piles. In the case of short pile, the pile body tends to rotate around the inflection point and produce a small negative deflection close to the pile base as shown in Figure 9a and Figure a. The negative deflection occurred in the opposite direction of load. The maximum negative deflection occurred exactly in the base of pile. The circular pile shape has a smaller deflection than the square pile shape because of high pile stiffness. These negative deflection reduce to zero when slenderness ratio increased about 5% and the as shown in Figure 9b and Figure b with small negative deflection in the case of square pile shape due to high stiffness. For slenderness ratio of 6.7, the maximum negative deflection occurred in the middle part between the base and the

12 Vol. 3, Bund. E inflection point. In the case of long piles, the base deflection is zero and same time the base make a small positive base deflection as shown in Figure 9c and Figure c. Finally, the negative deflection occurred near to the inflection point. That means, this region is critical closed to inflection point, while the base deflection is zero as shown in Figure 9d and Figure d. Figure 9: Lateral deformation of single pile along the depth of circular cross section: (a) L/D=8.3, (b) L/D=.5, (c) L/D=6.7, (d) L/D=.8

13 Depth (m) Depth (m) Depth (m) Depth (m) Vol. 3, Bund. E Load = 5 kn Load = kn 6 Load = 5 kn Load = kn 4 Load = 6 kn Load = 3 kn Load = 35 kn Load = 4 kn (a) L/D=8.3 Lateral deformation (mm) 4 Load = 5 kn Load = kn 8 Load = 5 kn 6 Load = kn Load = 5 kn 4 Load = 3 kn Load = 35 kn Load = 4 kn (b) L/D=.5 lateral deformation (mm) Load = 5 kn Load = kn Load = 5 kn Load = kn Load = 5 kn Load = 3 kn 5 Load = 35 kn Load = 4 kn (c) L/D=6.7 Lateral deformation (mm) Load = 5 kn 5 Load = kn Load = 5 kn Load = kn Load = 5 kn Load = 3 kn 5 Load = 35 kn Load = 4 kn (d) L/D=.8 Lateral deformation (mm) Figure : Lateral deformation of single pile along the depth of square cross section: (a) L/D=8.3, (b) L/D=.5, (c) L/D=6.7 and (d) L/D=.8 CONCLUSIONS Based on the results of the numerical study of the pile under lateral load, the following conclusions can be drawn: The amount of loading is directly affected on deflection and deformation of pile. In the first stages of load, the lateral pile deflection response along pile length was uniform and small. When the load is increased, the deflection becomes non- uniform. The percentage of pile tip deflection is much more than the percentage of deflection in the pile body.

14 Vol. 3, Bund. E 4 The pile shapes also effect the pile response. The square pile is more resistant the lateral load than a circular shape due to the high contact surface area between the pile and surrounded soil and high bending resistance. The pile deformation that occurs due to lateral load is influenced by pile slenderness ratio (L/B). The short pile (L/B = 8.3) gives a small amount of lateral tip deflection for the same amount of loading than piles having the slenderness ratio more than 8.3. For the short pile (L/B = 8.3,.5), the point of inflection is /5 from the base of pile. In this case the long piles (L/B = 6.7,.8), the point position is 3/5 from the base of pile. In addition the pile body tend to rotate around the inflection point and produce a small negative deflection near to the pile base depend on the magnitude of loads and slenderness ratio. REFERENCES. Brinkgreve, R.B.J. & Broere, W. (4) PLAXIS 3D FOUNDATION - version Netherlands.. Jamaludin, A., and Hussein, A. N. (998) The performance of large diameter bored piles used for road project in Malaysia. Proceedings of the 3rd International Geotechnical Seminar on Deep Foundation on Bored and Auger Piles, Ghent, Belgium pp Johnson, K., Lemcke, P., Karunasena, W., Sivakugan, N. (6) Modelling the load deformation response of deep foundation under oblique load. Environment Modelling & Software, NO., pp Fellenius, B. H., Altaee, A., Kulesza, R., and Hayes, J. (999) O-cell testing and FE analysis of 8-m-deep barrette in Manila, Philippines Journal of Geotechnical and Geoenvironmental Engineering. Vol. 5, No.7, pp Ismael, N. F. (998) Lateral loading tests on bored piles in cemented sands. Proceedings of the 3rd International Geotechnical Seminar on Deep Foundation on Bored and Auger Piles, Ghent, Belgium pp Karthigeyan, S., Ramakrishna, V. V. G. S. T., and Rajagopal K. (6) Influence of vertical load on the lateral response of piles in sand. Computer and Geotechnics, Vol. 33, pp Karthigeyan, S., Ramakrishna, V. V. G. S. T., and Rajagopal K. (7) Numerical Investigation of the Effect of Vertical Load on the Lateral Response of Piles. Journal of Geotechnical and Geoenvironmental Engineering, Vol. 33, No. 5, pp Muqtadir, A., and Desai, C. S. (986) Three-dimensional analysis of a pile-group foundation. International Journal of Numerical and Analytical Methods Geomechanics Vol., pp.4 58.

15 Vol. 3, Bund. E 5 9. Poulos, H.G., Davis, E.H. (98) Pile Foundation Analysis and Design. John Wiley & Sons, Inc, United States.. Smith, I.M., Griffith, D.V. (98) Programming the Finite Element Method, Second Edition. John Wiley & Sons, Chisester, U.K.. Yang, Z. and Jeremiæ, B. 5) Study of Soil Layering Effects on Lateral Loading Behavior of Piles. Journal of Geotechnical and Geoenvironmental Engineering, Vol. 3, No. 6, pp Zhang, L. M. (3) Behavior of Laterally Loaded Large-Section Barrettes. Journal of Geotechnical and Geoenvironmental Engineering, Vol. 9, No. 7, pp ejge