A 3D NUMERICAL EVALUATION OF THE INFLUENCE OF INTERFACE

ADHESION ON THE DEFORMATION PATTERN OF SOILS DURING

PENETRATION OF A RIGID OBJECT

S. Farhangi, Trow Associates Inc., Brampton, Ontario, Canada (formerly University of Southampton) D. J. Richards & C. R. I. Clayton, School of Civil Engineering and the Environment, University of Southampton, UK ABSTRACT Many geotechnical processes are associated with penetration and an understanding of the influence of the penetration parameters on the stress/strain behaviour of soil is essential for interpretation of these processes. A range of 3D numerical analyses were performed and the changes within the soil were determined for adhesive and non-adhesive interfaces. The results indicate that the interface adhesion has a significant influence on soil deformations around the penetrating object. RÉSUMÉ Beaucoup de procédés géotechniques sont liés aux phénomènes de pénétration. La compréhension de la contribution des paramètres de pénétration aux contraintes exercées sur les sols est essentielle à l'interprétation de ces procédés. Des analyses numériques 3D ont été réalisées et les modifications apportées au sol ont été déterminées pour des interfaces adhésives et non-adhésives. Les résultats indiquent que l'adhérence contribue de manière significative à la déformation du sol autour de l'outil de forage. 1. INTRODUCTION Many geotechnical topics are associated with penetration, including foundation elements (e.g. push-in piles, caissons), in-situ devices (e.g. cones, dilatometers and push-in pressure cells), and samplers. The various techniques adopted to evaluate the influence of the penetration process on the stress/strain behaviour of soil are briefly discussed here. Experimental techniques used to evaluate the soil behaviour included visual inspection, triaxial and chamber tests. The soil displacement around a penetrating object was assessed using various visual techniques such as X-ray photos (Gerber, 1929) stereo-photogrammetric methods (Butterfield et al., 1970) and PIV methods (White, 2002). Visual techniques are however, only really applicable to two-dimensional problems as they require an exposed surface (e.g. cross section) to assess the soil deformation patterns during penetration. Changes in soil characteristics adjacent to a penetrating object can be examined by applying a known stress or strain path to a soil specimen in a triaxial test. For example, to assess sampling disturbance effects, a series of triaxial tests with the peak strains set to values typically reached during sampling was undertaken by Siddique (1990). The main drawback of this method is the requirement for a known stress/strain path to be applied in the test. Chamber tests have been used to calibrate in-situ devices such as dilatometers (Baldi et al., 1986) and cones (Houlsby & Hitchman, 1988) as well as to

investigate the influence of various soil parameters on the capacity of scaled foundation models (Lehane & Gavin, 2001; Lee et al., 2003). The main limitation of chamber tests is the influence of the boundaries (Fahey et al., 1989). The influence of boundaries needs to be both assessed and minimised prior to generalising the results of chamber tests. Theoretical analysis of soil penetration is difficult due to the large deformations and non-linearities involved. However, various approximate analytical techniques have been proposed to provide an insight into the complex soil behaviour during penetration. The main analytical techniques used for studying the penetration of an object into a soil mass included bearing capacity, cavity expansion, and strain path methods. One of the first analytical techniques to analyse cone penetration was to treat the penetration process as a bearing capacity problem (Skempton, 1951). The bearing capacity method is however limited to simple geometries, requires an assumed failure mechanism and overlooks the effect of the soil’s stress/strain relationship. The cavity expansion method (CEM) has been extensively used to determine the stresses in soil around symmetrical objects including piles, cones and pressuremeters (Mair & Wood, 1987). The analogy between the penetration and cavity expansion was first noted by Bishop et al. (1945). General solutions for the spherical/cylindrical cavity expansion problems within a soil mass have been derived for various constitutive models such as linear elastic/perfectly plastic (Vesic, 1972) and non-linear elastic/perfectly plastic (Bolton &

1221

Sea to Sky Geotechnique 2006

Whittle, 1999) models. In comparison to the bearing capacity method, CEM has the advantage of considering both the elastic and plastic deformations; it does neglect however, the dependency of deformations on the direction of the penetration. The strain path method (SPM) arguably provides the most realistic solution to modelling penetration by incorporating the kinematics of the penetration process (Baligh, 1975). Soil deformations are estimated in the SPM from particles tracked along streamlines that form around the penetrating object when placed in a uniform fluid flow (Baligh, 1984). A major limitation of this method is that the SPM fails to address the effects of adhesion between the penetrating object and soil, as it was based on fluid flow formulations (Baligh, 1985). Numerical analysis of soil penetration is extremely difficult due to the high rates of change adjacent to the tip of the penetrating object. Various numerical methods (Griffiths, 1982; Teh, 1987; Kiousis et al., 1988; Budhu & Wu, 1992; Van den Berg, 1994; Hu & Randolph, 1998; Yu et al., 2000; Abu-Farsakh et al., 2003) have been employed to simulate the perpetration. A range of simplifications have been adopted in these analyses to reduce the numerical difficulties encountered with such large deformations. The majority of these analyses were limited to two-dimensional geometries. Furthermore, most of these analyses were not capable of simulating the flow of soil around the penetration object (i.e. small strain formulation). In addition, due to modelling constraints, the interface between soil and the penetrating object is modelled either as fully rough or smooth (non-slip or full slip) and the influence of various degrees of adhesion has not been assessed on the behaviour of the soil. A three-dimensional numerical approach was used to simulate the undrained penetration of an idealised three dimensional object and to investigate the influence of interface adhesion on the stress/strain behaviour of the adjacent soil. The modelling methodology and the results of these analyses are presented in this paper. 2. METHODOLOGY A systematic programme of three-dimensional analyses was undertaken using FLAC3D to investigate the influence of interface adhesion on the soil behaviour during the undrained penetration of an idealised three-dimensional geometry. FLAC3D (Fast Lagrangian Analysis of Continua) is an explicit finite difference program used extensively for the analysis and design of various challenging geotechnical problems over the last two decades (Itasca, 2002). FLAC3D is capable of incorporating the influence of interface adhesion in penetration analyses (Cundall & Hart, 1992). Various parameters defined for the interface element in a 3D model are shown in Figure 1. The idealised three-dimensional geometry termed the “chisel” (Figure 2), which can represent a dilatometer (Marchetti, 1980) or a pushed-in pressure cell (Tedd et al., 1989) geometry, had

a half thickness of w=4.2mm and half width of B=50.4mm(12w) in all the analyses. Symmetry allowed a quarter of the penetration problem to be analysed, as shown in Figure 3. Various boundary conditions assigned to various soil grid points are also shown in Figure 3. Boundary conditions for soil grid points on the axes of symmetry (x=y=0) were controlled by an auxiliary L-shaped mirror to prevent the grid-points from moving inside the axes (Farhangi et al., 2006a; Farhangi et al., 2006b). A surface load, equal to the initial isotropic in-situ stress of the soil, was assigned to the upper boundary of the soil.

T

D

Interface node (P)

ksSSs

Target face (area=A)

kn

S slider

Ss shear strength

T tensile strength

D dilation

kn normal stiffness

ks shear stiffness

Figure 1. The schematic view of interface parameters

(b) Cross-section (A-A′)(a) Elevation

A

A′

2B

4w

w

2w

Figure 2. The schematic view of the “chisel” Elastic and Tresca constitutive models were used for the “chisel” (Ec=4.55GPa, µc=0.33) and soil respectively. The incompressible behaviour of the saturated cohesive soil was simulated by using a Poisson’s ratio of µs=0.499 for the soil. The soil had a shear modulus of G=1MPa, a drained bulk modulus of K=2MPa, and an undrained shear strength of Su=100kPa. Penetration was simulated by assigning a constant vertical velocity to the “chisel”. The model was then stepped through the analysis until the intended length of penetration was reached (length=velocity×time).

1222

Sea to Sky Geotechnique 2006

Surface load

xy

A

A

H

H

Rol

ler

boun

darie

s

Roller boundaries

O

L/2

Rol

ler

boun

darie

s

z

initial

final

Figure 3. The schematic view of 3D penetration models One-sided interface elements available in FLAC3D were used to facilitate the penetration of the “chisel”. The sliding of the soil relative to the “chisel” on the axes of symmetry was simulated by defining smooth interfaces (i.e. only had a normal stiffness) on these planes. The soil-chisel interaction was simulated by defining the interfaces on the “chisel”, which in addition to normal stiffness, had shear stiffness and adhesion. A comprehensive description of the methodology used and results obtained from three-dimensional analyses are currently in review (Farhangi et al., 2006b). 3. RESULTS AND DISCUSSION In common with all numerical analyses, it is necessary to assess carefully the influence of the various modelling parameters on the calculated results (Richards et al., 2005). To graphically evaluate the influence of introducing adhesion to the soil-chisel interface, strain paths, displacement patterns and principal stress indicators were compared between models with adhesion factors of 0 and 0.75. In addition, the strain paths were determined for adhesion factors of 0.25 and 0.5. The interface adhesion factor, (α) is defined as α=Cint/Su, where Cint is the interface shear strength. Table 1 lists typical interface adhesion factors (α) measured in a range of tests between saturated clays and various materials. The strain path is a graphical means for highlighting changes in the soil strain levels during the penetration process. A strain path shows the cumulative strain increments (ε=∑εinc) plotted for a particular soil element against its vertical position relative to the position of the “chisel” tip (z) and normalised by the half-width of the “chisel” (z/w). Strain paths were presented for an element located at (x0=10w, y0=2w, z0=0) at the start of penetration.

Table 1. Measured interface adhesion factor (a) for saturated clays Test Structural

material Adhesion factor α (%)

Reference

Steel 44-103

Timber 57-88

Pile loading

Concrete 84-100

(Tomlinson, 1957)

Steel 25-50

Timber 40-50

Shear box test

Concrete 40-60

(Potyondy, 1961)

Steel 34-56 Ring shear

Glass 24-52

(Lemos & Vaughan, 2000)

The strain path for horizontal strain (εxx) was insensitive to the value of interface adhesion factor (α), as shown in Figure 4(a). The strain path for the shear strain (εxz) is shown for models with various adhesion factors (α) in Figure 4(b). Shear strain levels increased for a higher α as the tip of the penetrating “chisel” passed the soil element (z/w>0). The divergence between the shear strain paths as a result of a higher interface adhesion (α) increased from z/w=20 until the end of the strain path (z/w=96).

εxx

-0.01 0 0.01 0.02 0.03 0.04 0.05-100-80

-60

-40

-200

20

40

60

80100

z/w

x0/w=10 & y0/w=2

-+- α = 0.75-○- α = 0.50-□- α = 0.25-∆- α = 0.00

εxz

-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01-100

-80

-60

-40

-200

20

40

60

80100

z/w

x0/w=10 & y0/w=2

-+- α = 0.75-○- α = 0.50-□- α = 0.25-∆- α = 0.00

α increasing

Figure 4. Influence of interface adhesion (α) on strain paths for (a) εxx and (b) εxz strains

1223

Sea to Sky Geotechnique 2006

The displacement pattern for a soil element adjacent to the chisel tip was determined by recording its position during the penetration process. The displacement pattern in adhesive (α=0.75) and non-adhesive (α=0) models in the x-y, x-z and y-z planes are illustrated in Figures 5 and 6.

0 1 2 3-3

-2

-1

0

z (m

m)

0.1

0.2

y (m

m)

0.3

x0/w=10, y0/w=2

x (mm)

▬▬ Adhesive (α=0.75)

▬ ▬ Non-adhesive (α=0)

Figure 5. The displacement pattern of a soil element determined from adhesive/non adhesive analyses in the x-y and x-z planes

x0/w=10, y0/w=2

0.1 0.2 0.3

▬▬ Adhesive (α=0.75)

▬ ▬ Non-adhesive (α=0)

y (mm)

-3

-2

-1

0

z (m

m)

Figure 6. The displacement pattern of a soil element determined from adhesive/non-adhesive analyses in the y-z plane

It is evident from the non-adhesive analyses that the soil element is monotonically pushed away from the “chisel” in the x-y plane during the penetration. However, the soil element returned to its initial vertical position (z) as the penetration continued. This feature has also been observed in the displacement measurements obtained from the three-dimensional penetration tests in artificial soil (Gill & Lehane, 2001). Figures 5 and 6 also show that although horizontal displacements (i.e. in the x and y direction) were relatively similar in the adhesive and non-adhesive penetration models. The vertical displacements (z) were markedly different. The influence of adhesion on the displacement patterns predicted in these soil penetration analyses was similar to the influence of viscosity in the fluid flow analyses obtained by Gill & Lehane (2000). The principal stress indicators (PSI) show the direction and relative magnitude of the principal stresses for soil elements. Examination of PSI is straight forward in two-dimensional (i.e. plane strain) analyses. Figure 7 shows the magnitude and direction of PSI at various stages of penetration for adhesive and non-adhesive interfaces in two-dimensional penetration models.

Penetration depth (D)=

0

¼ L

½ L

¾ L

L

(a) Non-adhesive (α=0)

(b) Adhesive (α=0.75)

H

A

XO

H

Pen

etra

tion

leng

th (L

)

Z

Figure 7. The principal stress indicators in adhesive and non-adhesive 2D penetration models (Farhangi, 2006)

A snap shot of the PSI at the end of penetration are shown in the three-dimensional adhesive and non-adhesive models on the y=5w plane in Figure 8. It can be seen that the PSI adjacent to the “chisel” were severely affected by introducing adhesion to the interface.

1224

Sea to Sky Geotechnique 2006

(a) α=0

(b) α=0.75

Figure 8. The principal stress indicators in adhesive and non-adhesive 3D penetration models

4. CONCLUSION Due to modelling constraints, many of previous numerical penetration analyses have been limited to two-dimensional geometries. Furthermore, the effect of interface adhesion between soil and the penetrating object has not been investigated in the majority of these analyses. In this work, the influence of the interface adhesion was assessed on the behaviour of soil during the undrained penetration of a three-dimensional idealised geometry. It was observed that the strain paths, displacement patterns and principal stress indicators for soil elements adjacent to the penetrating object were severely affected by the introduction of the adhesion on the soil-object interface. Consequently, it was concluded that the influence of adhesion should be incorporated in all analyses aimed to assess the soil behaviour during penetration. 5. ACKNOWLEDGEMENTS This research was undertaken as part of the first author’s PhD studies at the University of Southampton, under the supervision of the co-authors. The author would also like to thank the Trow Associates for their support.

6. REFERENCES Abu-Farsakh, M. Y., Tumay, M. T. & Voyiadjis, G. Z.

(2003). Numerical Parametric Study of Piezocone Penetration Test in Clays. ASCE International Journal of Geomechanics, 3, 2, 170-181.

Baldi, G., Bellotti, R., Ghionna, V. & Jamiolkowski, M. (1986). Flat dilatometer tests in calibration chamber. Proceedings of the Use of in situ tests in geotechnical engineering, Virginia, 431-446.

Baligh, M. M. (1975). Theory of Deep Site Static Penetration Resistance. Dept. of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, Research Report R75-56.

Baligh, M. M. (1984). The strain path method. Dept. of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, Research Report R84-01.

Baligh, M. M. (1985). Strain Path Method. ASCE Journal of Geotechnical Engineering, 111, 9, 1108-1136.

Bishop, R. F., Hill, R. & Mott, N. F. (1945). Theory of Indentation and Hardness Tests. Proceedings of the Physical Society of London, 147-159.

Bolton, M. D. & Whittle, R. W. (1999). A non-linear elastic perfectly plastic analysis for plane strain undrained expansion tests. Geotechnique, 49, 1, 133-141.

Budhu, M. & Wu, C., S. (1992). Numerical analysis of sampling disturbances in clay soils. International Journal for Numerical and Analytical Methods in Geomechanics, 16, 7, 467-492.

Butterfield, R., Harkness, R. M. & Andrawes, K. Z. (1970). A stereo-photogrammetric method for measuring displacement fields. Geotechnique, 20, 3, 308-314.

Cundall, P. A. & Hart, R. D. (1992). Numerical modelling of discontinua. Engineering Computations, 9, 2, 101-113.

Fahey, M., Been, K., Horsfield, D. & Jefferies, M. G. (1989). Discussion: Calibration chamber tests of a cone penetrometer in sand. Geotechnique, 39, 4, 729-731.

Farhangi, S. (2006). A numerical study of spade cell penetration. University of Southampton, Southampton, UK, PhD thesis.

Farhangi, S., Richards, D. J. & Clayton, C. R. I. (2006a). Numerical determination of soil deformations around a penetrating object in 2D and 3D models. Proceedings of the 6th European conference on numerical methods in geotechnical engineering.

Farhangi, S., Richards, D. J. & Clayton, C. R. I. (2006b). Three-dimensional analysis of soil behaviour around penetrating objects. Geotechnique (submitted to).

Gerber, E. (1929). Untersuchungen uber die Druck-verteilung im Oertlick Belasteten Sand. Zurich, Dissertation Technische Hochschule.

Gill, D. R. & Lehane, B. M. (2000). Extending the Strain Path Method analogy for modelling penetrometer installation. International Journal for Numerical and Analytical Methods in Geomechanics, 24, 5, 477-489.

Gill, D. R. & Lehane, B. M. (2001). An Optical Technique for Investigating Soil Displacement Patterns. Geotechnical Testing Journal, 24, 3, 324-329.

Griffiths, D. V. (1982). Elasto-Plastic Analyses of Deep Foundations in Cohesive Soil. International Journal for

1225

Sea to Sky Geotechnique 2006

Numerical and Analytical Methods in Geomechanics, 6, 211-218.

Houlsby, G. T. & Hitchman, R. (1988). Calibration chamber tests of a cone penetrometer in sand. Geotechnique, 38, 1, 39-44.

Hu, Y. & Randolph, M. F. (1998). A practical numerical approach for large deformation problems in soil. International Journal for Numerical and Analytical Methods in Geomechanics, 22, 5, 327-350.

Itasca. (2002). FLAC 3D ver. 2.1, Fast Lagrangian Analysis of Continua in 3 Dimensions User's guide. 1st ed., Minnesota, Itasca Consulting Group Inc.

Kiousis, P. D., Voyiadjis, G. Z. & Tumay, M. T. (1988). A large strain theory and its application in the analysis of the cone penetration mechanism. Journal for Numerical and Analytical Methods in Geomechanics, 12, 1, 45-60.

Lee, J., Salgado, R. & Paik, K. (2003). Estimation of the load capacity of pipe piles in sand based on CPT results. ASCE Journal of Geotechnical and Geoenvironmental Engineering, 129, 5, 391-403.

Lehane, B. M. & Gavin, K. G. (2001). Base resistance of jacked pipe piles in sands. ASCE Journal of Geotechnical and Geoenvironmental Engineering, 127, 6, 473-480.

Lemos, L. J. L. & Vaughan, P. R. (2000). Clay interface shear resistance. Geotechnique, 50, 1, 55-64.

Mair, R. J. & Wood, D. M. (1987). Pressuremeter Testing. Methods and Interpretation. Construction Industry Research and Information Association (CIRIA), London.

Marchetti, S. (1980). In situ tests by flat dilatometer. ASCE Journal of Geotechnical Engineering, 106, 3, 299-321.

Potyondy, J. G. (1961). Skin friction between various soils and construction material. Geotechnique, 11, 339-353.

Richards, D. J., Clayton, C. R. I. & Farhangi, S. (2005). Two-dimensional analysis of soil behaviour around a penetrating object. Canadian Geotechnical Journal (submitted 12/12/2005).

Siddique, A. (1990). A numerical and experimental study of sampling disturbance. University of Surrey, Guildford, UK, PhD thesis.

Skempton, A. W. (1951). The Bearing Capacity of Clays. Building Research Congress, Division 1, 180-189.

Tedd, P., Towell, J. J., Charles, J. A. & Uglow, I. M. (1989). In-situ measurement of earth pressures using push-in spade-shaped cells-10 years' experience. Proceedings of the Geotechnical Instrumentation in Civil Engineering Projects, Nottingham, 701-715.

Teh, C. I. (1987). An analytical study of cone penetration test. University of Oxford, Oxford, PhD thesis.

Tomlinson, M. J. (1957). The adhesion of Clay Piles Driven in

Clay Soils. Proceedings of the 4th International Conference on Soil Mechanics and Foundation Engineering, London, 66-71.

Van den Berg, P. (1994). Analysis of soil penetration. Delft University of Technology, Delft, PhD thesis.

Vesic, A. S. (1972). Expansion of Cavities in Infinite Soil Mass. ASCE Journal of Soil Mechanics and Foundations, 98, 3, 265-290.

White, D. J. (2002). An investigation into the behaviour of pressed-in piles. University of Cambridge, Cambridge, UK, PhD thesis.

Yu, H. S., Herrmann, L. R. & Boulanger, R. W. (2000). Analysis of steady cone penetration in clay. ASCE Journal of Geotechnical and Geoenvironmental Engineering, 126, 7, 594-605.

1226

Sea to Sky Geotechnique 2006