Numerical modeling of skin resistance distribution with depth in piles ...

Numerical Modeling of Skin Resistance Distribution With Depth in Piles Ramli Nazir Associate Professor (Ir.Dr), Department of Geotechnics and Transportation, Faculty of Civil Engineering, Universiti Teknologi Malaysia (Malaysia)

Ehsan Momeni PhD Student in Geotechnical Engineering, Department of Geotechnics and Transportation, Faculty of Civil Engineering, Universiti Teknologi Malaysia (Malaysia); [email protected]

Nurly Gofar Associate Professor, Faculty of Engineering, Universitas Indo Global Mandiri (Indonesia)

Harnedi Maizir PhD Student in Geotechnical Engineering, Department of Geotechnics and Transportation, Faculty of Civil Engineering, Universiti Teknologi Malaysia (Malaysia)

ABSTRACT Proper estimation of axial bearing capacity of driven piles plays an important role in pile design. The amount of ultimate load which can be carried by skin of the pile determines the type of the piles as they are classified according to their load-transfer mechanism. Although there are numerous methods for skin resistance prediction of piles such as analytical methods, empirical methods, and High Strain Dynamic Pile Test (HSDPT) but often in semi-empirical methods, there is an amount of uncertainty more specifically in case of sandy soils for which collecting undisturbed sample is difficult. On the other hand, performing insitu tests such as instrumented pile load test or HSDPT for estimation on distribution of skin resistance with depth is time consuming and expensive. Hence use of numerical method is often of interest. This paper gives an insight into the load-transfer mechanism of a driven pile in sandy soil using finite element code, Plaxis. The end-bearing and skin resistance capacity of the pile were predicted using stress analysis. The outputs of numerical modelling were compared with a well-established empirical method for estimation of ultimate axial bearing capacity of the pile. The results show that numerical prediction on the percentage of the ultimate load which is carried by skin or shaft of the pile is in close agreement with that of empirical method.

KEYWORDS:

Driven Pile, Skin Resistance, Load-Transfer Mechanism, Bearing

Capacity.

INTRODUCTION Pile foundations are very effective in transferring the structural loads through weak soil strata into denser soils or competent rocks. The bearing capacity of a driven pile foundation which plays a significant role in design of pile foundation can be estimated by summation of both end-bearing and skin resistance capacities. In driven piles, distribution of skin resistance with depth depends - 2477 -

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on load-transfer mechanism. Load-transfer mechanism is a function of soil properties, diameter and surface roughness of the pile. However, determining the actual load-transfer mechanism of the pile is complicated due to nature of soil behavior. Although it is possible to obtain the true skin resistance distribution of any pile by providing relevant instrumentation but it is not practical. Apart from using instrumented pile, analytical methods, semi-empirical methods, high strain dynamic testing of the deep foundations and numerical methods may be used for estimation of skin resistance distribution with depth.

BACKGROUND Depending on type of the soil, the analytical formulation for prediction of axial bearing capacity can be found in classical foundation engineering books (Bowles, 2002; Das, 2004). However, the use of analytical methods in estimation of skin resistance distribution with depth in sandy soils is problematic due to the difficulty and uncertainty in collecting undisturbed sample in sandy soil which can affect the laboratory tests results. On the other hand, in-situ test such as Standard Penetration Test (SPT) or Cone Penetration Test (CPT) can provide data for direct use in pile design by employing established semi-empirical correlation. The well-established Meyerhof correlation (1967) for which SPT (N) value is related to skin resistance has been used extensively. The use of CPT data for determination of skin resistance with depth is highlighted in literatures. Lehane et al. (2000; 2012) conducted a comprehensive study on prediction of local skin resistance using CPT data. Different CPT correlations for skin resistance estimation were compared in his study. It is worthy to note that often the bearing capacity of foundations estimated by means of empirical methods is higher than the predicted bearing capacity using other methods. (Das, 2004; Meranda, 2005; Momeni et al., 2013). The distribution of skin resistance with depth can be estimated through High Strain Dynamic Testing of Piles (ASTM D4945-08). The test is provided by means of a Pile Driving Analyzer (PDA). HSDPT is based on one dimensional wave propagation theory. High strain dynamic testing consists of estimation of soil resistance from force and velocity measurements. These data are recorded using pairs of accelerometer and strain transducer installed near the top of a driven pile which is impacted by a hammer (Smith, 1960; Rausche et al., 1972; Rausche et al., 1986; Hannigan, 1990; Momeni et al., 2013). Due to nonlinear behavior of the soil, numerical modeling for prediction of skin resistance variation with depth of piles is popular. Sabri (2001, 2005) conducted a comprehensive study on the skin resistance and insitu stresses of a single driven pile in sand. Distribution of skin resistance with depth using numerical modeling is investigated in recent literatures, for example, Feizee and Fakharian (2008) conducted a numerical analysis for which the soil resistance with depth was predicted using finite difference method. Vehnert and Vermeer (2004) did a finite element study for estimation of pile capacity and its distribution. The variation of skin resistance with depth is also highlighted in a study by Broere and Van Tol (2006).

METHODOLOGY This study is mainly divided into two stages. The first stage deals with estimation of endbearing and skin resistance capacities of a driven pile using a well-established empirical correlation. In the second stage, the finite element analysis for estimation of skin resistance with depth is conducted. The estimated ultimate load from the first stage was considered as initial load in finite element analysis.

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Empirical Prediction of Pile Capacity and its Distribution It is mentioned earlier that often the empirical methods of bearing capacity prediction i.e SPT correlations gives higher bearing capacity than that of other methods. Applying an initial load which is guessed to be equal or higher than axial capacity of the pile is a prerequisite of subsequent finite element analysis. Hence, this section gives an insight into empirical estimation of driven pile capacity and its distribution using SPT (N) value correlations. In-situ test such as SPT test are used extensively in subsurface investigation mainly due to the fact that the test is relatively simple. Apart from that, the relevant data can be obtained readily during the ground investigation. There are many SPT correlations for which both skin and end bearing resistance of piles are related to SPT (N) value. However, Meyerhof (1967) proposed the following correlations for which either end-bearing capacity or skin capacity in homogeneous soil can be estimated. Qu= Ap qp + p L fave qp(kN/m2) = 40 N L/D 400 N fave (kN/m2) = 2 Ñ

(1) (2) (3)

In the above equations, Qu is ultimate axial capacity, Ap is area of the pile, qp is ultimate stress, D, L are diameter and length of the pile respectively, N is average SPT (N) value between 10D above and 4D below tip of the pile, fave is average unit skin resistance, Ñ is average SPT (N) value, and p is the perimeter of the pile. Shioi and Fukui (1982) also confirmed the coefficient of 2 in Meyerhof SPT correlation for skin resistance estimation. Study by Xiano and Yang (2011) shows that in tropical areas like Singapore and Malaysia, the range of 1.5 to 2.5 can be used in the SPT correlation for prediction of skin resistance. Material properties for this study were obtained from site investigation (SI) data of an eight stories building project for which precast pre-stressed concrete driven piles were used as foundation. The SI report covers the whole relevant laboratory tests in addition to SPT tests and CPT tests. Among driven piles, a reference pile with the diameter of 350 mm and length of 10 meter was considered for subsequent analyses. The soil profile obtained using SPT test is shown in Figure. 1.

Figure 1: Soil Profile

Finite Element Analysis The essence of using finite element method is to approximate a complicated solution by a model that consists of piecewise-continuous simple solution. In this study the analyses were carried out using the commercial finite element software, PLAXIS. The version 2010 of this program is capable of modeling static plane strain or two dimensional axisymmetric problems

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using 6 or 15 nodes triangular soil element. The following paragraphs detail the finite element model. The pile in this study was modeled as a rigid nonporous material. Taking advantage of the symmetric feature of the problem about the vertical axis, axisymmetric model of the pile was considered and it was defined as a column of concrete. The behavior of concrete was modeled Linear Elastic (LE). In order to minimize boundary effects, the working area was set as 17 m width by 17 m depth. Due to static type of analysis, standard fixity boundary condition was used. The soil profile (see Figure 1) indicates that the soil consists of almost three sandy layers. Engineering properties of the soil obtained from SI data and relevant correlations are tabulated in Table 1. Standard Hardening Soil (HS) model was considered as constitutive model for defining the soil behavior. Brinkgreve (2005) has discussed the advantages of this model in sandy soil over other well-established constitutive models. In this model, the effect of stress path on soil stiffness and soil behavior is highlighted. Drained behavior of soil was considered because of the type of the material. Young`s modulus were obtained using different correlations based on SPT and CPT tests (Poulus, 1989; Vermeer and Schanz 1997; Bowles, 2002; Brinkgreve, 2005). In HS model, the unloading-reloading poisson`s ratio should be used. Therefore, the value of 0.2 which is recommended in Plaxis Manual (2010) was used. Earth pressure coefficient, Ko, was approximated using Jacky`s formula (Ko = 1-sin). Ground water level was defined to be 1 meter below the soil surface. The global geometry of the axisymmetric model used for this study is shown in Figure 2.

Figure 2: Global geometry of the axisymmetric model

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Table 1: Material Properties Symbol

1st layer Sandy Clay

2nd layer Sand

3rd layer Sand

Pile

Unit

Material Model

-

HS

HS

HS

LE

-

Unit weight



20.19

18

18.17

24

kN/m3

sat

21.2

19.5

19.63

24

kN/m3

E

4000

14392

21552

2.6E7

6031

15990

25860

-

(50)

12060

15990

25860

-

Eref(ur)

36190

47970

77580

-

ur, 

0.2

0.2

0.2

0.15

-

Power (Stress level)

m

1

0.5

0.5

-

-

Earth pressure coefficient

Ko

0.79

0.49

0.51

-

-

Friction angle



12

30.5

29

-

o

Cohesion

C

10.44

0.06

0.08

-

kN/m2

Material

Saturated unit weight

ref

E Module of elasticity

(oed) ref

E

Poisson`s ratio

kN/m2

It is worthy to note that in Table 1, soil stiffness parameters are approximate which is mainly due to lack of direct test such as Pressuremeter test; hence one should rely on empirical correlations. Numerous correlations have been developed in order to relate soil stiffness to SPT (N) value. Most of these correlations are collected in NOVOSPT software (Afkhami, 2009). With the aid of this software, the variation of Young`s modulus of sandy layers with depth were examined for numerous SPT (N) value correlation i.e. sand correlations. However, as it is shown in Figure. 3, the predicted Young`s modulus are quite variable, site specific and consequently unreliable. Apart from that, it is well established that soil stiffness is a function of depth (Brinkgreve, 2005); thus selecting a constant value within a soil layer is another approximation. However, study by Momeni (2012) for a same case study shows that, in case of using load distribution approach in PLAXIS, changing the soil stiffness parameters do not have significant effect on ultimate bearing capacity of driven piles.

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Figure 3: Young`s modulus predicted usingSPT (N) value correlation In order to have a better prediction of skin resistance distribution, 15 noded elements were used in the finite element analysis. This will result in fourth order interpolation for displacements. Consequently, the numerical integration involves twelve Gauss points. A comprehensive meshconvergence study in PLAXIS conducted by Lebeau (2008) shows that in sandy soils, the output curves have same shapes for calculations performed with coarse, medium and very fine mesh; hence in this study, medium grain mesh was adopted. However, in order to have more stress points, the generated mesh was enriched on top of the pile with the aid of refine line option. According to PLAXIS manual (Brinkgreve and Broere, 2010), an interface line needs to be defined along the length of the pile. However, in order to prevent stress oscillation in the stiff corner area as shown in Figure. 2 the interface was extended 0.5 below the pile inside the soil body. This “longer” interface enhances the flexibility of the finite element mesh in these areas and thus prevents non-physical stress results. A sand interface strength factor (Rinter) of 1.0 was considered in this study as it is suitable for representing rough surface-soil interaction. The generated mesh before analysis is shown in Figure 4.

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Figure 4: Generated mesh before analysis Calculation module in PLAXIS was divided into three phases. The first phase dealt with defining the ground water level and consequently generating the hydrostatic pore water pressure. The effective stresses also were introduced using Ko procedure in this phase. Pile material was assigned to the relevant cluster in second phase. Using plastic analysis, the load was applied by means of distributed load approach in the last phase.

RESULTS AND DISCUSSION Having the site investigation data as shown in Figure 1, empirical analyses were performed by substituting the SPT (N) values into the relevant equations mentioned in previous sections. The total bearing capacity obtained with the aid of empirical method using SPT correlations is 1283 kN which is distributed to end bearing of 923 kN and skin resistance of 360 kN, or 28% of the total capacity is derive from skin friction. Before running the calculation module in PLAXIS, an initial load must be applied on driven pile. Hence the ultimate load obtained from empirical method which is guessed to be at least equal or more than failure load was considered for initial load in PLAXIS. Using stage construction approach, Analysis for node located at top right side of the pile was performed. The deformed mesh and the load-displacement curve are shown through Figure 5 to 7 respectively.

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Figure 5: Mesh deformation after analysis

Figure 6: load-displacement curve obtained from the first attempt (stage construction option) As shown schematically in Figure 6, the soil body collapsed under initial load of 1283 kN. In the second attempt, the load obtained from the last analysis was applied and it is found that the pile can carry up to 919 kN. The resistance of the soil under the load is shown schematically in the Figure 7

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Figure 7: Load-displacement curve obtained from the final analysis However, the predicted ultimate obtained load i.e. 919 kN must be validated with the ultimate load assessed by means of summation of skin resistance and end bearing capacity obtained from stress analysis. Distribution of skin resistance with depth usually corresponds to the variation of shear strength with depth at interface (Vehnert and Vermeer, 2004; Broere and Van Tol, 2006). Distribution of shear strength can be determined by making cross section at interface along the length of the pile. However, in order to get skin resistance forces, the corresponding shear strength values must be multiplied by the surrounding area of the pile. Table 2 shows the distribution of shear stress and corresponding skin resistance with depth. From this table it is found that the total skin resistance is 187.60 kN.

Table 2: Skin resistance distribution with depth Segment No 1

Average shear Stress (kN/m2) 17.26

2

13.86

3

Length (m) 0.97

Skin Resistance (kN) 18.40

Cumulative Skin Resistance (kN) 18.40

1.12

17.06

35.46

14.67

1.25

20.15

55.61

4

15.40

1.33

22.51

78.12

5

16.61

1.33

24.28

102.4

6

17.35

1.75

33.38

135.78

7

20.96

2.25

51.82

187.6

For an axisymmetric problem, the base load can be calculated by integrating the stress at 2.5 cm below the pile base with the cross section of the pile. Note that the weight of the pile should be subtracted. Analysis shows that the total stress at the base of pile is equal to 7907 kN/m2 which yields in a net end bearing capacity of 738.1kN after subtracting the weight of the pile. Hence the

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axial capacity of pile from finite element analysis is 925.7 kN. This value is in good agreement with the failure load obtained from load displacement curve which was 919 kN. The small difference shows that estimated ultimate loads are in really good agreement and 6 kN difference might be due to stress oscillation and the average values used in study. The skin resistance distribution with depth is shown in Figure.8. From this figure it can be determined that almost 21% of the ultimate load obtained from stress analysis is carried by the skin of the pile. This percentage is in close agreement with the results of empirical method for which almost 28% of the ultimate load is carried by the skin of the pile.

Figure 8: Skin resistance distribution with depth using numerical modeling

CONCLUSIONS Based on the finite element analysis results, the following conclusion can be drawn. 1. Empirical estimation of end-bearing and skin resistance capacity are slightly higher than that of finite element analysis. 2. The ultimate load estimated from load-displacement curve is in very good agreement with the ultimate load obtained through stress analysis in finite element analysis. 3. Almost 21% of the ultimate axial capacity of driven pile is carried by skin of the pile which is in a good agreement with the results of the empirical method for which almost 28% of the ultimate load is carried by skin of the pile.

ACKNOWLEDGEMENTS The second author would like to thank University Teknology Malaysia for its financial support via allocating International Doctoral Fellowship.

REFERENCES 1. Afkhami, A. (2009) NovoSPT: Version 1. Novo Tech Software Ltd. North

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Vancouver, BC Canada. 2. ASTM D 4945-08. (2008) Standard test method for high-strain dynamic testing of piles. American Society for Testing and Materials. 3. Bowles, J. E. (2002) Foundation Analysis and Design. New York: McGraw Hill 4. Brinkgreve, R. B. J. (2005) Selection of Soil Models and Parameters for Geotechnical Engineering Application. Journal of Geotechnical and Geoenvironmental Engineering, ASCE. 5. Brinkgreve R. B. J., Broere W. (2010) Plaxis Manual, Version 9. 6. Broere, W., Van Tol, A. F. (2006) Modelling the Bearing Capacity of Displacement Piles in Sand. Proceeding of the institution of Civil Engineers. Geotechnical Engineering. 159. Issue GE3. Pages 195-206. 7. Das, B.M. (2004) Principles of Foundation Engineering. (6thed.). USA: Brooks/Cole 8. Davisson, M.T. (1973) High Capacity Piles. Department of Civil Engineering Department, Illinois Institute of Technology, Chicago. 9. Feizee, S.M., and Fakharian, K. (2008) Application of a continuum numerical model for pile driving analysis and comparison with a real case. Computers and Geotechnics, Vol. 35, 406-418. 10. Goble, G. G., Rausche, F., and Moses, F. (1970) Dynamic Studies on the Bearing Capacity of Piles - Phase III. Final Report to the Ohio Department of Highways, Case Western Reserve Univ., Cleveland, Ohio. 11. Hannigan, P.J. (1990) Dynamic Monitoring and Analysis of Pile Foundations Installations, DFI, Sparta, New Jersey. 12. Jaky, J. (1944) the Coefficient of Earth Pressure at Rest. In Hungarian (A nyugalmi nyomas tenyezoje), J. Soc. Hung. Eng. Arch. (Magyarm Mernokes Epitesz-Egylet Kozlonye), 355–358. 13. Lebeau, J. H. (2008) FE-Analysis of piled and piled raft foundations, Graz University of Technology. Project Report. 14. Lehane, B. M., Li, Y., Williams, R. (2012) Shaft Capacity of Displacement Piles in Clay. Journal of Geotechnical and Geoenvironmental Engineering Division. American Society of Civil Engineers, ISSN: 1943-5606. 15. Lehane, B.M., Chow, F.C., McCabe, B.A. and Jardine, R.J. (2000) Relationships between shaft capacity of driven piles and CPT end resistance. Proc. Instn. Civ.Engrs, Geotechnical Engineering, 143, 93-101. 16. Meranda, L, J. (2005) Analysis of Spread Footing Foundation as a Highway Bridge Alternative. Ohio University. Master Thesis. 17. Meyerhof, G. G. (1976) Bearing Capacity and settlement of pile foundation. Journal of the Geotechnical Engineering Division. American Society of Civil Engineers, vol. 102, No.GT3, PP. 197-228. 18. Momeni, E. (2012) Axial Bearing Capacity of Piles and Modelling of Distribution of Skin Resistance with Depth. Universiti Technology Malaysia, Master Thesis. 19. Momeni, E., Maizir, H., Gofar, N., Nazir, R. (2013) Comparative Study on Prediction of Axial Bearing Capacity of Driven Piles in Granular Material. Jurnal Teknologi 61(3). 20. Poulus, H. G. (1989) Pile Behavior-theory and application. Geotechnique, pp.366403

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21. Rausche, F., Moses, F., Goble, G. G. (1972) Soil Resistance Predictions from Pile Dynamics. Journal of the Soil Mechanics and Foundation Division ASCE. 22. Rausche, F., Goble, G. G., Likins, G. (1985) Dynamic Determination of Pile Capacity. J Geotech. Eng; 111(3):367–83. 23. Wehnert, M., and Vermeer, P. A. (2004) Numerical Analyses of Load Tests on Bored Piles. Proceedings of the 9th International Symposium on Numerical Methods in Geomechanics, Ottawa, Canada. Balkema, Leiden, pp. 505–511. 24. Shanz, T., Vermeer, P. A., Bonnier, P. G., and Brinkgreve, R. B. J. (1999) Hardening Soil Model: Formulation and Verification. Beyond 2000 in Computational Geotechnics, Balkema, Rotterdam, pp. 281-290. 25. Sabri, M. (2001) Shaft Resistance of a Single Vertical or Batter Pile in Sand Subjected to Axial Compression or Uplift Loading. Concordia University. Master Thesis. 26. Sabri, M. (2005) Insitu Stresses and Capacity of Driven Piles in Sand. Concordia University. PhD Dissertation. 27. Smith E. A. L. (1960) Pile-driving analysis by the wave equation. Journal of Soil Mechanic and Foundation Division. ASCE, Div;86 (EM 4):35-61. 28. Shioi, Y., and Fukui, J. (1982) Application of N-value to design of foundations in Japan. 2nd European Symposium on Penetration Testing, vol. l, pp.159-164. 29. Xiao, D., and Yang, H. (2011) Back Analysis of Static Pile Load Test for SPT-Based Pile Design: a Singapore Experience. Geotechnical Special Publication, No.120. ASCE.

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