Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

Things Measured by Cone Penetration Tests other than Material Properties
Tadashi KAWAI
Associate professor, Civil and Environmental Engineering, Tohoku University, Sendai, Japan
Email: tadashi.kawai.b2@tohoku.ac.jp

Kotaro KUBOTA
Former Graduate Student, Civil and Environmental Engineering, Tohoku University, Sendai, Japan

Jong-Kwan KIM
Researcher, Geotech. Eng. Research Inst., Korea Inst. of Civil Eng. and Building Tech., Goyang, Korea

Motoki KAZAMA
Professor, Civil and Environmental Engineering, Tohoku University, Sendai, Japan

Toshihiro NODA
Professor, Disaster Mitigation Research Center, Nagoya University, Nagoya, Japan

ABSTRACTThe cone penetration test is a proven method for evaluating soil properties, yet relatively little research has been
conducted to understand penetrometer readings (CPT-data) as a complicated boundary value problem. The interpretationof CPT-data tends to rely on empirical relationships, many of which have been developed over the years for soil
identification and classification. Those studies tend to have an implicit expectation that the relationship between the CPTdata and a single soil parameter is independent, e.g. the friction angle can be estimated directly from CPT-data without
the need to consider any boundary value problems. In this study, a series of numerical analysis by using FEM (GEOASIA)
was conducted to demonstrate the complexity of the penetration mechanism. A description of the calculation proceduresis first provided with some preliminary calculation results with various displacement ratios at the supposed cone apex.
The results highlight the differences in the resistances at the cone tip even when the friction angle is the same and areevidence of the complexity of the penetration problem.
Key words: Cone penetration, Stratigraphic order, FEM, Deformation

1. Introduction
The Cone Penetration Test (CPT) is extensively usedreadings as a complicated boundary value problem.

as an in-situ soil investigation method. The estimation of

CPT data is that readings are influenced not only by thesoil parameters, such as the internal friction angle, aresoil at the location of the cone tip but also by the soil

typically performed using the cone penetration resistancewithin an influence zone which extends some distanceobtained from the CPT. However, since cone penetration

both beneath and above the tip. Ahmadi & Robertson

resistance is not a physical parameter unique to soil

(2005) studied the 'thin-layer effects' on the CPT-data.

material but rather a response value of the ground, it is

They conducted a series of FEM numerical analyses using

reasonable to assume that estimating soil parameters

so-called cavity expansion modeling and concluded that

directly from cone penetration resistance is problematic,

the full tip resistance may not be reached in thin stiff layers

at best. Even though the cone penetration test is a provenbecause of the influence of the upper/lower softer layers.

method for evaluating soil properties, relatively little

Recently, Mo et al. (2017) also conducted the similar

research has been conducted to understand penetrometersystematic analysis and compared their numerical results

One of a complicating factors in the interpretation of- 401 -

Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

with the field data. Further, Ma et al. (2017) conducted an

expansion modeling to realize the soil responses duringextensive parametric study using a large deformationcone penetration after careful consideration of thefinite-element analyses, then, based on their numericalexperimental results. The validity of the modeling method

results, they proposed a procedure for interpreting thewas also carefully confirmed by Ahmadi . (2005) andlayer boundaries and undrained shear strength from

Ahmadi & Dariani (2017). Therefore, the same modelingmeasured CPT-data after taking the thin-layer effect into

method was adopted in this study. A description of theaccount. Meanwhile, an experimental investigation by Mo

calculation procedures is firstly provided with someet al. (2015) obtained the extent of soil deformation

preliminary calculation results achieved by the use ofaround a penetrated cone using centrifuge testing. Theirvarious displacement ratios at the supposed cone apex andresults revealed that the cone penetration is a complicatedthe upper rod.

boundary value problem. As for the field CPT-data,

There has been relatively little research done on the

Thevanayagam et al. (2017) evaluated the relationships

effect of soil dilatancy on CPT measurements related to

between liquefaction resistance and CPT-data andlayered configurations. Neither the detailed soil stress-

considered the combined effect of penetration velocity andstrain and dilatancy-strain histories associated with CPT

the coefficient of consolidation Cv, which is composed ofnor the relationship to the distribution of the load on thepermeability k and compressibility mv. This can beprobe are well understood. Therefore, the results which

considered field evidence that the cone penetration is ashow different cone tip resistances despite the same

complicated boundary value problem. Therefore, in orderfriction angle are then provided to highlight complexity ofto obtain the soil properties of the target location, thethe penetration problem.

response behavior of the soil should be evaluated as aboundary value problems which takes the many factors
shown in Fig. 1 into account at the same time:
consolidation (drainage), shear deformation and thedilatancy of the target soil and its neighbor layers.
As preparation for a future numerical investigation
focused on the details of the combined effects of soil
properties and various boundary conditions, a series ofnumerical analyses was conducted using a FEM code
named GEOASIA® (All Soils All States All Round Geoanalysis Integration) developed by Asaoka et al. (1998a),
Asaoka & Noda (2007) and sophisticated by Noda et al.
(2008), in which the Super/subloading Yield Surface
Cam-clay model, in short, the SYS Cam-clay model(Asaoka . 1998b, 2000, 2002) was used as the constitutive
equation of the soil skeleton. As shown in the results
reported by Tolooiyan & Gavin (2011) from a series ofnumerical simulations using multiple soil modelingFig. 1 Penetration mechanisms; the logic solving it as aboundary value problem

methods and obtained different results, the soil modelingmethods greatly influence the obtained results. As such, inorder to evaluate the complicated boundary value problem,

2. Numerical analysis - Models and settings
The finite element mesh and boundary conditions

it is clearly necessary to adopt a more sophisticated model

used are shown in Fig. 2. The over burden pressure

which represents soil behavior as close to reality as

equivalent to the depth of 9.0 m with the same density as

possible.

Layer 1 is given at the top of the model. The effect of theAmong the various analysis methods of cone

gravity force was taken into account in the calculations.

resistance, Mo . (2017) adopted the so-called cavity

The penetration part is magnified in Fig. 3, where the- 402 -

Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

axisymmetric coordinates were adopted. As shown in Fig.

modulus and strength settings of Layer 2 series were given

3, the nodal points on the left-hand side border of the FEM

for a common dense sand image, but different dilatancy

mesh, which were pushed away toward the right-hand sidecharacteristics were used. One of the strong points ofand downward along the supposed cone path, werenumerical investigation is that the soil behaviors can bedirectly moved to realize the ground movements during

easily changed in order to study the influences from eachcone penetration by following the cavity expansionof soil characteristic separately. Fig. 4 shows the element

modeling described in Armadi & Robertson (2005) inbehaviors (drained triaxial loading) using the SYS Cam-detail. The nodal points were moved from the top one. The

clay model for the material parameter sets of 2-1, 2-2, 2-3.

supposed cone apex angle and diameter were 60 degrees
and 30 mm respectively, then the horizontal displacement

Table 1.

of each nodal point was as much as 15 mm after all fourCam-clay model

calculation stages; each calculation stage involved 2500

Meanings of each material property in SYS

A. Elasto-plastic parameters

time integration steps (time span 0.0005 s) at a cone

A1: Compression index λ ~penetration speed of about 5 mm/s toward the depth. These

A2: Swelling index κ ~size and speed parameters were set as a preliminary study

A3: Critical state constant M

for future experimental validations by using a calibration

A4: Specific volume at q=0 and p'=98.1 (kPa) on NCL N

chamber and a miniature cone.
The required material constants and the meanings of

A5: Poisson's ratio ν
B. Evolution rule parameters
B1: Degradation index of structure a (b =c =1.0)

each parameter are listed in Table 1. The parameter values

B2: Degradation index of overconsolidation m

set for virtual models used in this study are given in Table

B3: Evolution index of rotational hardening b r

2 along with the initial values (Table 3) describing theB4: Limit of rotational hardening m binitial soil state. These values are expected to provide a

C. Permeability k (cm/s)vague image of loose and dense sand for Layer 1 andD. Specific gravity of soil particles G sLayer 2 (2-1, 2-2, 2-3), respectively. All of the shear
Table 2.

Settings of the material parameters for each layer

Layer 1(loose)Fig. 2

A1： λ
A2： κ
A3：M
A4：N
A5： ν
B1：a
B2：m
B3：b r
B4：m b
C：k
D：G saxisymmetric FEM mesh and boundary conditions
φ cone / 2 = 0.015 m

0.046
0.0055
1.40
1.73
0.3
0.73
0.30
0.5
0.5
0.001
2.65

Layer 2
2-2

2-1
0.060
0.0080
1.35
1.90
0.3
5.00
0.09
2.5
0.8
0.010
2.65

2-3

0.080
0.0026
1.35
1.99
0.3
4.00
0.21
1.0
0.7
0.010
2.65

0.100
0.0040
1.08
2.06
0.3
5.00
0.13
5.0
1.0
0.010
2.65

DH =0.0

Table 3.

DV230°

Layer 1(loose)DHc

Degree ofoverconsolidation 1/R
Degree of structure 1/R *Lateral stress ratio
Specific volume v 0

DV1
Horizontal：fix Vertical ：free

Fig. 3

Settings of the initial conditions for each layer

Calculated procedures of cone penetration- 403 -

2-1

Layer 2
2-2

2-3

2

142

152

363

25
1.0
1.80

1.5
0.6
1.82

1.5
0.6
1.84

2
0.6
1.82

Shear stress τ [kPa]

Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

between Layer 1 (loose; contractive) and Layer 2 (dense;

300

Layer 2 Materials

250

expansive), and also Layer 2 and Layer 3 (loose;

σ'm=87kPa, drain

200

contractive). The ranges of all the stress contours were150

unified from -30 kPa to 30 kPa. By the penetration, the

100

2-1

50

2-2

vertical stress mainly increases downward positively,

2-3

which is translated as compression in this figure, and the

0
0.00

0.50

1.00

1.50

horizontal stress tends to increase laterally at first. This

Shear strain γ

lateral compression moves not only the lateral soil

Volumetric strain

0.02
2-1

2-2

2-3

surrounding the CPT-rod but also the soil located below

0.00
0.00

0.50

1.00

1.50

-0.02

the penetration depth, as such the lateral stress directly-0.04

beneath the cone center is slightly reduced as a

-0.06

consequence. If the soil moves outside toward the radius-0.08

direction, the larger r results in a larger volume, and this

-0.10

Shear strain γ

Fig. 4

results in a reduction in the circumferential stress

Examples of the element responses of SYS Cam

component.
The volumetric strain contours are also shown in Fig.

clay model calculated by using the material properties shown in

5. In spite of the high lateral compression along the CPT-

Table 2 and 3.

rod, all the highly sheared elements in the two or three
3. Numerical analysis - Preliminary calculations
Since the functions to define friction are limited atlines from the penetration border showed expansion, eventhe border, i.e. FEM mesh boundary or the contact surface

sand. Then, outside of those elements, a highly contracted

between two different materials, they are not implemented

area suddenly emerged especially in Layer 1. Thisin the FEM code used in this study, and the magnitudes ofcontracted zone was attenuated gradually toward thethe vertical displacements at the cone apex and rod mustoutside. While all these soil behaviors seem rational, they

be prescribed. As the numerically achieved results ofsuggest that penetration is a complex problem of soil

Ahmadi . (2005) and also the experimentally achieved

deformation. Further, because of the existence of the layer

results of Arshad . (2014) show, since the ratio of verticalboundaries, the stress distributions indicates considerable

displacement to horizontal displacement is dependent oncomplexity in the penetration mechanisms.

in Layer 1, which was composed of the contractive loose

the various conditions, e.g. material kinds, penetration
speed, and so on, there is no hint to determine the value ofTable 4.

the ratio without an concrete target image. In abandoning

displacement ratios

any attempt to validate the value adopted in this study, ourfocus was on investigating the dilatancy effect on thepenetration resistances by calculating a virtual soil model:
a series of numerical analyses were conducted to grasp theextent of influence of the displacement ratios on thepenetration resistance, as shown in Table 4.
Before comparing those results, in order to help
develop a realistic image of the soil behavior caused bypenetration, various contours for Case 1, which is thestandard case in this study, were prepared, as seen Fig. 5.
In this figure, the same components of stress are arrangedin the same column and the results at the same penetration
depth are arranged in the same row. In each contour, twodotted lines are drawn to make it easy to see the borders- 404 -#
Case1
Case2-1
Case2-2
Case2-3
Case2-4
Case2-5
Case3-1
Case3-2
Case3-3

Cases for searching the appropriate vertical

R1(DV1/DHc)
0.5
0.9
0.7
0.3
0.1
0
0.5

R2
(DV2/DV1)
0.08

Layer 2

0.08

2-1

0.12
0.05
0.03

2-1

2-1

Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

kPa
⊿σ'r

kPa

⊿ σ'y

Fig. 5

kPa

⊿σ'θ

kPa

⊿ τry

kPa

⊿σ'm kPa⊿ε pvolume⊿(q/p')

Typical penetration influence on the increments of stress components and volumetric strain (Case1).

- 405 -

Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

In order to simulate the deformation of soils aroundat the rod to the one at the cone apex were set 0.12, 0.08,

the cone tip by penetration, it is necessary to apply

0.05, or 0.03. Contrary to the apparent influences of thehorizontal displacement and vertical displacement to thevertical displacement ratio at the cone apex, around thenodal points where the cone tip penetration is realized, andcone shaft the vertical displacement ratio had little effectto apply vertical displacement to the nodal points toon the penetration resistance, as shown in Fig. 8. A ratio

represent the rod after passing through the cone tip.

of 0.08 was therefore adopted: there was no specific

Although the final horizontal displacement obviously

motivation in choosing this value.

becomes equal to that of the cone radius, the extent of the

Tip resistance (MPa)
1.0
2.0

0.0

vertical displacement is unclear, and is dependent on the

h= 9

3.0

φ cone2various conditions cited by Ahmadi . (2005).
9.2

In order to grasp the extent of influence of theof analyses was carried out in which the ratio (R1) of the

9.4

DV1
R1 = Dthe larger DV1

Hc

9.6

vertical displacement to the horizontal displacement at thecone apex was changed to 0, 0.1, 0.3, 0.5, 0.7, 0.9. The tip

9.8

resistances of those analyses are plotted in Fig. 6; the

0.9

0.7

0.5

0.3

0.1

0

10

lateral and vertical axes are tip resistance and depth,
respectively. The cone tip resistance for each value ofpenetration was calculated from the summation of the

DHc
DV1

Depth (m)displacement ratios on the penetration resistance, a series

30°

Fig. 6

Influence of the vertical displacement ratio at thecone apex on the tip resistancecontributions of the related elements which configure thekPacone tip apex. That is, the vertical pressure and the vertical⊿σ'rcomponent of shear stress were multiplied by the side area

DV1
R1=

of each element.

DHc
= 0.9

As reported by Ahmadi . (2005), it was confirmed

= 0.5

= 0.1

that with increasing vertical displacement at the cone apex,
the tip resistance becomes larger, as shown in Fig. 6.
⊿σ'yFurther, with increases in the vertical displacement ratio,
the range of the influenced zone becomes larger, as shownin Fig. 7. As mentioned above, because no value for thevertical displacement ratio was considered correct in thisstudy, a value of 0.5 was adopted in the later analyses forFig. 7

convenience. It is noted that this is smaller than thepenetrated cone.

Stress distributions around and beneath therealistic number confirmed by Ahmadi . (2005) in their
0.0

comparison of the calculated results with experimentalh=

Tip resistance (MPa)
1.0
2.0

9

3.0

φ cone2measurements. This smaller value is expected to result in

DH =0.0

9.2

a shallower zone of influence below the cone tip.
Depth (m)In cone penetration, because the soil around the rod
is continuously dragged vertically downward by sleeve
friction during penetration, vertical displacement occurs.
As yet, however, no detailed investigation has been carried

30°

9.4
R2 =
9.6

DV2
DV1

DV2

0.12
0.08
0.05
0.03

9.8

out to determine how much displacement occurs.
Therefore, by applying the vertical displacement to the10

nodes at the rod after passing through the cone tip, the dragdue to sleeve friction was reproduced and its influence wasFig. 8

Influence of the vertical displacement ratio aroundthe cone shaft on the tip resistanceinvestigated. The ratios (R2) of the vertical displacement- 406 -

Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

4. Numerical analysis - Influence of soil dilatancy
In order to confirm that the cone penetration is indeedof the tip resistance of Case 1 in Layer 2 at the later stage

the complicated problem suggested by Fig. 1, a series of(loose) and the resistance is expected to decrease, suggests

calculations was carried out using soil materials havingthat adopting 0.6 as the value had meaning. This is because

the same shear stress-shear strain relation but different

the stress increasing zone recognized by the contour

dilatancies (Table 5). The complicated nature of thereached the bottom boundary in Case 1 at the point which

problem is thought to be related to the volumetric balancecorresponds to the sudden increase of the tip resistanceof the space, which is an equilibrium of conservation ofshown in Fig. 9. That is, the cone tip sensed the bottom

mass caused by elastic volume change, consolidation,boundary through Layer 3 as it penetrated Layer 2.

of penetration, where the cone tip comes closer to Layer 3

dilatancy and ejections. Because it is implicitly expectedthat there should be a unique relationship in the empirical

Table 5.

Trial cases to grasp dilatancy effects

co-relations between the cone tip resistances and the#friction angles of sandy soils, the results is useful toestimate the in-situ friction angles from the cone tip

Case1
Case4-1
Case4-2

resistance. If it were valid, since the shear stress-shear
strain relation is similar, as confirmed in Fig. 4, whichmeans the internal friction angle is equal, the measured tip

R1(DV1/DHc)
0.5

R2(DV2/DV1)
0.08

0.5

0.08

Layer 2
2-1
2-2
2-3

Tip resistance (MPa)
1.0

0.0

2.0

h= 9

resistances would be also similar. However, despite
having the same strength, there is a large difference in theLayer 1
9.2

tip resistances, as shown in Fig. 9. On the other hand, theDepth (m)tip resistances from Case4-1 (Mat. #2-2) and Case4-2(Mat. #2-3) were almost the same in spite of their different
dilatancy. The stress and volumetric strain distributions

9.4

9.6

Layer 2
Material #2-1(Case1)
2-2(Case4-1)
2-3(Case4-2)

Start sensing
Layer 3

Start sensing
the bottom
boundary

shown in Figs. 10 and 11 were taken into account todevelop a possible reason for this, as explained below.

9.8

Fig. 10 shows the vertical stress distributions at theLayer 310

two stages of penetration: the contour ranges of thesecases was adjusted to be more sensitive than those in Fig.
5. Although the stress increasing range did not extend to

Fig. 9Influence of the dilatancy characteristics of theLayer 2 material and the stratigraphy on the tip resistancethe border between Layer 2 and Layer 3 in Case 1-6kPa(material #2-1) in the earlier stage shown in upper row in

6kPa
⊿σ'y

Fig. 10, those ranges in the other two cases had alreadyreached to the border. Therefore, a comparison of the tip

Case1

Case4-1

Case4-2

resistances in Fig. 9 indicates that until this stage ofMat. #2-1

Mat. #2-2

Mat. #2-3

penetration, the resistance was larger with larger
dilatancies. On the other hand, after this penetration stage,
since the material properties and/or responses of Layer 3⊿σ'ymight be reflected in the tip resistance at Layer 2 only in
Case 4-1 and 4-2, the tip resistances of those two cases
became asymptotically the same value despite thedifferences in dilatancy. It should be acknowledged that

Fig. 10 Vertical stress distributions at the two stages of

the change in the contour range gives different

penetration process; the stress increased zone reached theimpressions depending on the maximum value, and there

boundary between Layer 2 and Layer 3 in Case 4-1 and 4-2

does not appear to be any logical meaning in adopting the(upper), the stress increased zone reached the bottom boundary

value of 6 kPa, as we did. However, the sudden increasein Case 1 (lower)- 407 -

Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

5. Concluding remarks
As preparation for a future numerical investigation

Asaoka A., Noda, T. & Kaneda, K. 1998a. Displace-on the details of the combined effects of soil properties andcon-straint conditions on velocity field of soil. Soils

various boundary conditions on cone penetration

and Foundations, 38 (4), pp. 173-181.

ment/traction boundary conditions represented byresistance, a series of numerical analysis was conducted

Asaoka, A., Nakano, M. & Noda, T. 1998b. Super loading

using a FEM code named GEOASIA. After a preliminary

yield surface concept for the saturated structured

study designed to reveal the vertical displacements aroundsoils. Proc. 4th Eur. Conf. Num. Meth. Geotech.

the cone apex and rod, a value of 0.5 times of the

Engrg, NUMGE98, pp. 232-242.

horizontal displacement was adopted for the vertical

Asaoka, A., Nakano, M. & Noda, T. 2000. Superloading

displacement at the cone apex, which was less than theyield surface concept for highly structured soil

result reported in the literature from experimental studies.

behav-ior, Soils and Foundations, 40 (2), pp. 99-110.

Although the vertical displacement adopted was moderate

Asaoka, A., Noda, T., Yamada, E., Kaneda, K. & Nakano,

and was expected to result in a smaller influence zone thanM. 2002. An elasto-plastic description of two distinct

that in a case with larger vertical displacement like thevol-ume change mechanisms of soils. Soils andexperimental value, the cone tip resistances were sensitive

Foundations, 42 (5), pp. 47-57

to the combined effects between the boundary conditions

Asaoka A. & Noda, T. 2007. All soils all states all roundand the deformation characteristics. This was especiallygeo-analysis integration, International Workshop on

the case with regard to the dilatancy of soils.

Constitutive

The authors freely acknowledge that besides being

Modelling-

Development,

Implementation, Evaluation, and Application, Hongconducted in-situ, this study was employed slightly

Kong, China, pp. 11-27.

exaggerated conditions both with regard to the material

Ma, H., Zhou, M., Hu, Y., & Hossain, S. M. 2017.

properties and the boundary conditions. As such, further

Interpretation of Layer Boundaries and Shearinvestigations are needed to prove the validity of theStrengths for Stiff-Soft-Stiff Clays Using Conemodeling method. A comparison of a series of calibration

Penetrationchamber tests, and then a series of numerical parametric

Geomechanics, 17(9), pp. 06017011-1-11, ASCE.

studies based on proper analytical conditions is required

Mo, P.Q., Marshall, A.M. & Yu, H.S. 2015. Centrifuge

in order to determine the precise nature of those combinedmodelling of cone penetration tests in layered soils.

effects in practice.

Geotechnique, 65 (6), pp. 468-481.

Test:

LDFE

Analyses.

Int.

J.

Mo, P.Q., Marshall, A.M. & Yu, H.S. 2017. Interpretationof Cone Penetration Test Data in Layered Soils Using

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