Numerical modelling of CPT in clay to evaluate ...

3rd International Symposium on Cone Penetration Testing, Las Vegas, Nevada, USA - 2014

Numerical modelling of CPT in clay to evaluate bearing capacity for shallow foundations T. Boufrina and A. Bouafia University Saâd Dahleb of Blida, Department of Civil Engineering, Blida, Algeria

ABSTRACT: This paper presents a numerical analysis of the cone penetration test (CPT) in clay using the finite element method (FEM). The procedure simulates the problem of large displacement of the cone into an elastic perfectly plastic soil by the means of the numerical finite element code CRISP using the updated Lagrangian method in order to determine the tip resistance, qc. A parametric study allows to determine the cone factor Nk and then the bearing capacity factor Kc that is useful for the evaluation of the bearing capacity of shallow foundations for either strip footings (problem of plane strain) or square/circular footings (problem of axisymmetry).

1

INTRODUCTION

Cone penetration test is today one of the most widely used and accepted in situ tests methods for soil investigation worldwide. It provides soil profiling, and has a strong theoretical basis for interpretation. A large amount of high-quality in situ digital data can be recorded directly by CPT in a relatively short time in the field. These data can subsequently be post-processed to provide quick delineations of the subsurface conditions, including layering, soil types, and geotechnical engineering parameters, as well as both direct and indirect evaluations of foundation systems, including shallow footings, driven pilings, drilled shafts, and ground modification. It produces also an enormous amount of physical information based on correlations with other tests such as the pressuremeter test (PMT) and the standard penetration tests (SPT). In the context of interpreting the soil response to the process of cone penetration and thus determining geotechnical parameters, a numerical approach is initially carried out through a theoretical assimilation by assuming the penetrometer to a rigid steel surface that penetrates the soil. This allows applying the classical theory of bearing capacity. Many studies have been performed in this field based in general on physical modeling of CPT or using correlations between the penetrometer tip resistance qc and soil parameters (Bouafia 2011). In this study, a finite element modeling of the problem of deep penetration of a conical tip is performed into an ideal elastic-plastic soil. Over more than 50 years, several approaches have been adopted to deal with the problem of deep penetration. Among others, bearing capacity theory (Meyerhof 1961; Durgunoglu & Mitchell 1975), cavity expansion theory (Vesic 1972 and Yu & Houlsby 1991), the Strain Path Method proposed by Baligh (1985), Calibration Chamber Testing and the finite element analysis (Walker & Yu 2006). However, each approach presents some disadvantages and none of these methods leads to a rigorous solution. 517

   

2

NUMERICAL MODELING

The finite element method is one of the methods that can be used to predict the cone factor into clay. The difficulties lie in the complexity of soil deformation around the cone which comes from pushing the penetrometer into the ground, as well as the complex behavior of the interface. At present, there are no rigorous solutions to the problems of penetration (Walker &Yu 2006); the methods used are often based on simplified theories. Other numerical methods have been used to model cone penetration, but these do not provide satisfactory correlations. As cone penetration involves large-scale deformations at the CPT/soil interface so that is difficult to make a rigorous numerical modeling and therefore some approximations are often adopted. The commercial code CRISP V.5.3 is used in this study. The cone is simulated as a rigid axially symmetric surface, which penetrates the soil at a constant rate of 2 cm/s. To allow penetration into the finite element continuum, a frictional contact element with a virtual diameter d = 1mm is simulated (Fig.1) that will allow the penetrometer to slide over the soil mass so that the penetration process could be modeled realistically. During calculation, the cone slides over the interface element such that the contact between soil and cone could be established. An updated Lagrangian approach proposed by CRISP is pursued. Lagrangian formulation allows large deformations to be considered using “Update Lagrangian method” as the cone is advanced into a homogenous elastic perfectly plastic soil obeying the Drucker-Prager yield criterion until steady state is achieved. The radius (r0) of the cone is about 18 mm with a cross sectional area of approximately 10cm2 and an apex angle of 60°. The geometry of the considered system is also shown in Figure 1. CPT

 

Slip element  

 

Prescribed   displacement

 

Refined   zone

    Soil meshing      

 

 

(a) (b) Figure 1. General view of the meshing with interface element –a. cone at 0.5 m, b. cone at 1.5 m

 

Table 1 represents the mechanical and physical characteristics of the clays, these chese characteristics are the undrained elasticity modulus 𝐸! , the undrained cohesion 𝑐! , the internal angle of friction𝜑, the compressibility factor of water 𝐾! , the unit weight of the soil 𝛾, the unit weight of water 𝛾! , Poisson coefficient 𝜈!  and the coefficient of earth at rest 𝑘! . N.B: Clay 1: dense clay, clay 2: medium clay and clay 3: soft clay         518

Table 1. Mechanical and physical characteristics of the different types of clays 𝐸!

3

𝐶!

𝐾!

(MPa)

(kPa)

(GPa)

Clay1

40

300

2.61

Clay2

10

200

0.65

Clay3

2

100

𝛾

𝛾! 3

𝜈!

 𝐾!

𝜑!   (°)

0.499

1

0

3

(kN/m )

(kN/m )

20

10

RESULTS AND DISCUSSION

3.1 Soil deformation around the cone Cone penetration process is, as previously mentioned, a large strain large displacement phenomenon; small strain finite element analysis is unable to generate the required ultimate tip resistance for deep penetration. During the penetration process, the cone pushes the particles downwards and sideways, this means that the particles lying on the axis of symmetry will move horizontally. These points move a distance equal to the radius of the cone while particles of soil around the cone also move vertically.

 

 

 

Figure 2. Vertical displacement around the cone

The whole process of penetration can be seen by viewing the displacement field around the penetrometer, as shown in Figure 2, it can be seen that the vertical displacement increases gradually from the top to the bottom of the cone and reaches its maximum in the axis of symmetry.

3.2 Cone factor The cone factor is defined as follows:       519

𝑁! =

𝑞! − 𝜎!!                                                                                                                    (1) 𝑐!

Figure 3 shows the variation of the cone factor depending on the cone penetration depth. It was found qc exhibits a steady increase in the cone factor until a certain critical depth equal to 5r0.

             

  Figure 3. Variation of the cone factor versus the normalized depth z/r0

               

 

3.3

Effect of rigidity index (𝐼! )  on cone factor

Rigidity index 𝐼!  of soil is defined as the ratio of the shear modulus (G) to its shear strength: 𝐼! = 𝐺 𝜏!"# 𝜏!"# = 𝐶! + 𝜎!! ×𝑡𝑔𝜑  

(2)  

(3)  

In the case of clays (𝜑 = 0)  : 𝐼! = 𝐺 𝐶!

(4)

Figure 4 shows that the cone factor increases with higher values of rigidity index for the three categories of clays, so an approximate linear increase of the cone factor is observed.

      520

  Figure 4. Variation of the cone factor versus the rigidity index Ir

3.4

BEARING CAPACITY FACTOR

3.4.1 Indirect approach The analytical approach presented below allows to derive the bearing capacity of shallow foundations by calculating the bearing capacity factor.  

3.4.1.1 Clayey soil-Strip foundation The bearing capacity expression from cone penetration test can be written as follows: ∗ 𝑞! =   𝐾!! ×𝑞!" + 𝑞!                         (5) From laboratory tests, the expression of the ultimate limit pressure in clayey soils is given by: (6) 𝑞! = 0.5𝛾! 𝐵𝑁! + 𝛾𝐷𝑁! + 𝐶! 𝑁! For clayey soils, where: 𝑁! = 0, 𝑁! = 1  and  𝑁! = 5.14,  the last expression becomes: 𝑞! = 𝛾𝐷 + 𝑁! ×𝐶! (7) As previously mentioned in this work, the undrained cohesion can be calculated from the cone factor as: 𝐶! =   (𝑞! − 𝜎!! ) 𝑁! (8) 𝑞! = 𝛾𝐷 + (𝑁! /𝑁!  )(𝑞! − 𝜎!! )         (9) Analogically, we can determine the bearing capacity factor for a strip footing into a clayey soil by: !

𝑘!! = !! 1 − !

!!! !!

(10)

More simply, as    𝜎!! ≪ 𝑞! , we may write (11) 𝑘!! ≈ 𝑁! 𝑁! By replacing 𝑁! = 5.14  and 𝑁! by the values found in this numerical analysis, 𝑘!! values can be estimated.

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Table 2. Bearing capacity factor values for strip foundations 𝑬𝒖 (MPa)

𝑪𝒖 (kPa)

𝑲𝒘 (GPa)

𝒌𝟎𝒄

Clay1

40

300

2.61

0.42

Clay2

10

200

0.65

0.36

Clay3

2

100

0.13

0.26

 

3.4.1.2

Clayey soil-square/circular foundation

𝑞! = 0.5𝛾! 𝐵𝑁! 𝑓! + 𝛾𝐷𝑁! 𝑓! + 𝐶! 𝑁! 𝑓!

(12)

Where: 𝑁! = 0 for clayey soils 𝑓!, 𝑓!  and  𝑓! are shape factors such as for a square footing : 𝑓! = 0.6, 𝑓! = 1 +   tan 𝜑 , (tan 𝜑 = 0) though 𝑓! = 1,  𝑓! = 1 +

! !!

(𝑁! = 5.14) though  𝑓! = 1.2

∗ + 𝑞! 𝑞! = 𝛾𝐷 + 6.168×𝐶!  and  𝑞! =   𝐾!! ×𝑞!"

𝑘!! = (𝑁! ×𝑓! ) 𝑁!

(13) Table 3. Bearing capacity factor values for square/circular foundations 𝑬𝒖 (MPa)

𝑪𝒖 (kPa)

𝑲𝒘 (GPa)

𝒌𝟏𝒄

Clay 1

40

300

2.61

0.51

Clay2

10

200

0.65

0.43

Clay3

2

100

0.13

0.31

3.5 Direct approach The bearing capacity can be estimated directly from the CPT, based on a bearing capacity factor, 𝐾!  𝑡ℎ𝑎𝑡  can be defined as follows:           𝐾! = (𝑞! − 𝑞! )/𝑞! (14) 𝑞!  : Ultimate pressure of the shallow foundation numerically estimated (Hamidi, 2009) 𝑞! : Initial vertical overburden stress 𝑞! : Cone tip resistance 𝐾!   is function of the shape of the foundation and the soil type; it may be given by: ! 𝐾! = 𝐾!! + 𝐾!! 1 − 𝐵/𝐿         (15) !

Such as Kc0 andKc1can be estimated by interpolation as follows: 𝐵 𝐿 = 1 → 𝐾!! (For square or circular foundation) 𝐵 𝐿 → 𝐾!  (For rectangular foundation) 𝐵 𝐿 = 0 → 𝐾!!  (Strip foundation)       522

   

 

  Figure 5  𝐾!! and 𝐾!! values for different soil categories and different types of foundations from numerical analysis

Figure 5 plots the bearing capacity factors for different soil categories and different type of foundations against normalized depth such as D refers to the diameter of the cone. 4 COMPARISON WITH EXPERIMENTAL RESULTS A comparison study has been undertaken to compare the results found in this work with other published values such as those proposed by the French standard DTU-13.12. Table 4 shows the comparison with DTU-13.12 that indicates a slight difference but, in general, the agreement between the two approaches is good. Table 4. Comparison between Kc values issued from DTU-13.12 and this study 𝑩

𝑩

Strip footing ( = 𝟎)

Square/circular foundation  (   = 𝟏)

𝐾!!

𝐾!!

𝑳

𝑳

D/B

DTU13.12

Clay1 (Soft)

Clay 2 (Medium)

Clay 3 (Stiff)

DTU13.12

Clay1 (Soft)

Clay2 (Medium)

Clay 3 (Stiff)

0.1 0.5 1 1.5

0.25 0.31 0.33 0.34

0.19 0.22 0.27 0.28

0.22 0.27 0.30 0.31

0.24 0.29 0.31 0.34

0.28 0.38 0.43 0.44

0.20 0.28 0.30 0.32

0.22 0.32 0.38 0.40

0.23 0.38 0.43 0.43

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5 CONCLUSIONS Many researches have employed numerical methods to model the process of cone penetration in different soil types. The main problem with some of these methods is the poor correlations they gave that weaken their reliability. Another problem, as pointed out by Teh & Houlsby (1985) is that smallstrain finite element analysis (Griffiths; 1982; De Brost & Vermeer, 1984) does not provide accurate solutions for the problem of large deformation and thus is incapable to generate the necessary residual stress field around the cone and to achieve the correct ultimate cone resistance. A numerical study of CPT by FEM was undertaken in view of the evaluation of the bearing capacity of shallow foundations in clay soils. A cone factor can be determined for each type of soil, this cone factor Nk depends on soil parameters such as: cohesion, initial vertical overburden stress and penetrometer resistance. Pursuing some approaches based on cone factor and soil type, the two bearing capacity factors Kc0 and Kc1 useful for the determination of the bearing capacity of shallow foundations were determined and a good agreement was found with those recommended in the French code of foundation engineering DTU-13.12. that was based on loading shallow foundations on real scale. REFERENCES Ahmadi, M.M., Byrne, P.M. &Campanella, R.G. 2005. Cone tip resistance in sand: modeling, verification and applications. Ahmadi, M.M., Byrne, P.M. &Campanella., R.G. 1999. Simulation of cone Penetration using FLAC. Dept. of Civil Engineering, University of British Columbia, Vancouver, Canada. Bolton, M.D., Gui, M.W., Garnier, J., Corte, J.F., Bagge, G., Laue, J. &Renzi, R. 1999. Centrifuge cone penetration tests in sand. Géotechnique 49, No. 4,543-552 Bouafia, A. 2011. Les essais in situ dans les projets de fondations (in French: In-Situ tests for foundation engineering), edited by : OPU (University Publications Office), Algiers, 3rd edition, ISBN : 978.9961.0.0612.4, 300 p. Durgonuglu, H.T., Mitchell, J.K. 1975. Static penetration resistance of soils. I-II. In: proceedings of the ASCE Spec Conference on In Situ Measurement of Soil properties, vol.1: p.51-89. Hamidi, A. 2009. Étude de quelques aspects d’interaction sol/fondations (in French: Study of some soil/foundation interaction), Dissertation of Post-graduation in civil engineering, Université de Blida, 180 pages. Huang, W., Sheng, D., Sloan, S.W.,Yu, H.S, 2004. Finite element analysis of cone penetration in cohesionless soil, Computers and Geotechnics 31(2004)517-528 Houlsby, G.T. & Wroth, C.P. 1982. Determination of undrained strengths by cone penetration tests. Proceedings of the Second European Symposium on Penetration Testing/ Amsterdam/ 24-27 Levadoux, J.N. &Baligh, M.M. 1985. Consolidation after undrainedpiezocone penetration I: PREDICTION. Lu, Q., Randolph, M.F., Hu. Y., Bugarski. I.C.2004: A numerical study of cone penetration in clay. Géotechnique 54, No. 4, 257-267 Markauskas, D., Kacianauskas, R. &Katzenbach, R. 2003.Numeric analysis of large penetration of the cone in untrained soil using FEM. Journal of civil engineering and management, vol IX, No 2, 122-131. Can Geotech J 42: 977-993 Robertson, P. K., & Cabal K.L. (Robertson) 3rd Edition January 2009: Guide to cone penetration testing for geotechnical engineering. Robertson, P.K. 1990. Soil classification using the cone penetration test. Canadian Geotechnical Journal, 27 (1), 151-8. Frank, R.1999. Fondations superficielles, Techniques de l’Ingénieur C246, 31 pages. Salgado, R., Mitchell, J.K. &Jamiolkowski, M. 1997.Cavity expansion and penetration resistance in sand. Journal of geotechnical and geoenvironmental engineering Teh, C. I. &Houlsby, G.T. 1991. An analytical study of the cone penetration test in clay.Géotechnique 41, No. I, 17-34 Walker, J., Yu, H.S. 2006. Adaptive finite element analysis of cone penetration in clay. ActaGeotechnica (2006) I: 43-57

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