Report: The use of CPT and Vs for assessment of saturated soil deposits
in the centrifuge
ABSTRACT: The availability of reliable methods for measuring cone penetration resistance and shear wave
velocity in centrifuge models is important in order to fully characterize the soil. It is particularly important for
soil deposits assessed for liquefaction potential. The paper presents the results of two centrifuge experiments
performed at Rensselaer Polytechnic Institute to characterize saturated granular soil deposits using in-flight
cone penetration test (CPT). The two experiments are performed on saturated Ottawa F#55 sand deposits
placed at 40% and 75% relative densities. The cone penetration resistance is measured at 50g. The measured
values of cone penetration resistance and shear wave velocity are analyzed and compared to theoretical
predictions.
1. INTRODUCTION
Cone penetration resistance (CPT) is an important
parameter for estimating geotechnical properties of a
wide range of soils. These properties include relative
density, friction angle, Young’s and shear moduli,
small strain shear modulus, overconsolidation ratio,
compressibility,
undrained
shear
strength,
sensitivity, coefficient of consolidation and
permeability (Robertson & Robertson, 2006).
Shear wave velocity (Vs) is an important
parameter for the design of geotechnical systems,
particularly in seismically active areas. The Vs value
reflects geotechnical properties such as shear
stiffness and density of the soil in addition to being
an important parameter for the design and site
response purposes. The Vs is also used to evaluate
the stiffness of foundation, site response during
earthquakes, liquefaction potential, soil density, site
classification, soil stratigraphy and settlement of
foundations (Richart et al. 1970; Seed and Idriss
1970; Andrus & Stokoe 1997; Dobry et al. 2000;
Seed et al 2003; McGillivray and Mayne 2004).
The availability of a reliable method for
measuring shear wave velocity and cone penetration
resistance in the centrifuge soil models is important
for soil characterization. Modeling using
geotechnical centrifuge is a powerful technique that
can be used to test soil and soil structure interaction
under static or dynamic loading. In many of these
tests, an estimation of shear wave velocity profile
and cone penetration resistance is necessary in order
to fully characterize the soil and link with field case
histories. The paper presents the bender elements
system and the CPT used in the geotechnical
centrifuge lab at Rensselaer Polytechnic Institute
(RPI) to measure the shear wave velocity profile and
tip resistance for sandy soil models.
2. INSTRUMENTATION
2.1.Bender elements
Bender elements are used to measure the shear wave
velocity in centrifuge soil models at Rensselaer
Polytechnic Institute (El-Sekelly, 2011). Bender
elements are piezoelectric transducers that can
generate and detect mechanical waves in soil
models. Primary and secondary wave velocities can
be obtained using this system. The value of the shear
wave velocity is estimated by measuring the time
difference between generating and receiving of the
shear wave. The bender elements used in this
research were built in the centrifuge lab at RPI.
Details of the bender elements system and the
assembly process are discussed in El-Sekelly (2011).
2.2.CPT and Robot
Tip resistance is measured using an in-flight CPT
tool shown in Figure 1. The CPT tool is mounted on
the 4-Degree of freedom robot shown in Figure 2.
The in-flight robot is designed to perform multiple
tasks while the centrifuge is spinning. The robot is
capable of articulating in three linear dimensions
and rotating around one axis. The CPT tool used in
this research is 12mm in diameter and 150mm in
length.
X & Y path
for the robot
Load Cell
Location of
the CPT tool
Figure 2.
(Nees@RPI)
The 4-Degree of freedom robot
friction. The main purpose of using the 2D laminar
container in this research is to have comparable
boundary condition during the dynamic experiments
used in the soil liquefaction assessment.
3. EXPERIMENTAL PROCEDURES
Connection
with robot
Figure 1. The In-flight CPT tool (Nees@RPI)
2.3.laminar container(2D)
The experiments were conducted in the 2D laminar
container shown in Figure 3. The 2D laminar
container is designed specifically for use with RPI’s
2D shaker and is constructed from 45 twelve-sided
lightweight aluminum alloy rings arranged in a
stack. Each ring is 8.9 mm (0.35 inches) in height
with a 594 mm (23.4 inches) mean inside diameter,
and each ring is separated from each other by 60
roller bearings, specially designed to allow motion
in the two horizontal directions with minimal
The data presented in this paper corresponds to two
centrifuge experiments conducted in the 2D laminar
container. The height of the soil model in the two
experiments was 24 cm representing a prototype
depth of 12 m at 50g. The scaling factors for
different test properties were adopted from Whitman
& Arulanandan (1985).
Experiments TW1 and TW2 were conducted on
saturated Ottawa F#55 sand deposits placed at
relative densities of 40% and 75%, representing
relatively loose and dense sand deposits
respectively. Ottawa F#55 sand is a clean uniform
fine sand with a specific gravity of 2.665, grain size
distribution characterized by D10=0.161 mm,
D50=0.25 mm, and a uniformity coefficient of 1.522.
The minimum and maximum void ratios are
emin=0.58 and emax=0.77. The fine content of Ottawa
F#55 sand is less than 0.1%. Properties of the soil
used in experiments TW1 and TW2 are presented in
Table 1.
Centrifuge basket
In-flight robot
Figure 3. 2-D laminar container (dimensions in cm)
The method used for building the model is the dry
pluviation method, where the sand is placed in
layers, typically 0.5 inch thick, using a pluviator.
The container is then placed on the centrifuge
platform as shown in Figure 4. The saturation was
then performed by de-airing the model and then
percolation of de-aired water at a very slow rate to
insure full saturation of the model.
Table 1. Soil properties for Tests TW1 & TW2
Condition (Dry/Satu.)
γ (sat.) (KN/m³)
Dr %
TW1
TW2
Satu.
19.2
50
Satu.
19.8
80
The CPT was conducted at 50g. The CPT tool was
pushed into the soil model, using RPI robot, at a rate
of 0.5mm/sec to a depth of 120mm representing 6m
of sand deposit in the prototype scale. Corte et al.
(1991) revealed that there is no noticeable effect of
the rate of penetration on the tip resistance in the
range from 0.5 to 10 mm/sec. The rate of 0.5
mm/sec used in this research was chosen to avoid
any contribution of pore pressure build-up due to
progression of the cone into the soil.
2D laminar container
Figure 4. The centrifuge basket with the robot and
the 2-D laminar container in place
4. RESULTS AND ANALYSIS
The profiles of tip resistance versus vertical
effective stress for both experiments are shown in
Figures 5&6. For purpose of comparison, the tip
resistance is normalized to its value at 1atm (101.33
kPa). The normalization of tip resistance is
performed according to the method presented by
Boulanger (2003), in which the author used the
following formulas (Eqs. 1-3) to calculate the
normalized tip resistance, 𝑞𝐶1𝑁 .
𝑃𝑎
𝐶𝑁 = (
𝜎′𝑣𝑜
𝑚
)
(1)
m=0.784 - 0.521. 𝐷𝑟
𝑞
𝑞𝐶1𝑁 = 𝐶𝑁 (𝑃𝐶 )
𝑎
(2)
(3)
where
𝜎′𝑣𝑜
=vertical
effective
stress;
𝑃𝑎 =atmospheric
pressure
(101.33
kPa);
𝐶𝑁 =Normalization factor for tip resistance; 𝐷𝑟
=relative density of sand; 𝑞𝐶1𝑁 =normalized tip
resistance; 𝑞𝐶 =tip resistance at 𝜎′𝑣𝑜 ; and m
=overburden normalization exponent
0
0
Dr=40%
20
30
40
50
60
20
30
40
50
0
2
4
6
Dr=75%
10
Vertical Effevtive Stress [Kpa]
10
Vertical Effevtive Stress [Kpa]
Vertical Effevtive Stress [Kpa]
10
0
Dr=40%
20
30
40
50
60
8 0 102 124 146 168 1810 2012
14
16
60
18
0
Tip resistance Q [MPa]
Tip resistance Q [MPa]
Dr=75%
10
Vertical Effevtive Stress [Kpa]
0
20
30
40
50
20
2
4
6
60
8 0 102 124 146 168 1810 20
12
14
16
18
20
Tip resistance Q [MPa]
Tip resistance Q [MPa]
Figure 5. The profile of tip resistance versus
vertical effective stress for TW1
Figure 6. The profile of tip resistance versus vertical
effective stress for TW2
The maximum measured tip resistance was used in
the process of normalization. The reason for using
the maximum measured tip resistance is that the
normalized tip resistance becomes stable after a
penetration depth of about 8-10D (critical depth), as
indicated by the results presented by Bolton & Gui
(1993), where D is the cone diameter. This happens
to be the maximum depth the cone was able to reach
in the experiment. Further penetration might have
caused the water above the soil surface to seep into
the wires of the load cell damaging the tool (Figure
1). A new and longer CPT tool is currently being
developed in the lab to overcome the limitation of
the CPT tool used in this research. The new tool has
a smaller diameter and can penetrate much deeper
into the soil model. Table 2 summarizes all the
corrections and final normalized values of tip
resistance and shear wave velocity.
The shear wave velocity values presented in the
paper are adopted from El-Sekelly (2011.). ElSekelly (2011) measured the shear wave velocities
in centrifuge models for Ottawa F#55 sand deposits
placed at relative densities of 40% and 75% using
bender elements. During the conducted centrifuge
tests, predefined mechanical shear waves were sent
from the sender bender elements to the receiver
bender elements placed at several depths. In all
cases, the sender bender elements were excited with
one cycle of sine wave having a frequency of 7000
Hz. The wave propagates in the soil and is recorded
by the receiver bender elements. The sent wave and
the typical output of the received waves are
presented in El-Sekelly (2011). The first arrival time
of the received wave is identified and the wave
velocity was then calculated using the relation:
𝑑
Table 2: Normalization parameters for TW1 & TW2
m
𝐶𝑁
𝜎′𝑣𝑜 (kPa)
𝑞𝐶 (MPa)
𝑞𝐶1𝑁
𝑉𝑠1 (𝑚/𝑠)
TW1
TW2
0.58
1.44
53.9
5.35
76.81
174
0.39
1.26
55.9
15.2
91.5
194
V= 𝑡
(4)
where, V=velocity of the shear waves, d= distance
between sender and receiver, t= time between
sending and receiving the body waves
For the purpose of comparison, the shear wave
velocities are normalized to their values at 1atm
(101.33 kPa). The normalization of shear wave
velocity is performed using equation (5) (Stokoe et
al., 1985).
𝑃
𝑉𝑠1 = 𝑉𝑠 (𝜎′𝑎 )
0.25
(5)
𝑣𝑜
where 𝑉𝑠1 =Normalized shear wave velocity; 𝑉𝑠
=shear wave velocity at 𝜎′𝑣𝑜 ; 𝜎′𝑣𝑜 =vertical
effective stress; 𝑃𝑎 =atmospheric pressure (101.33
kPa);
A comparison between the actual and the predicted
values of 𝑞𝐶1𝑁 and 𝑉𝑠1 is presented in Figure 8.
Figure 8 indicates that results from this research tend
to fit the formula proposed by Dobry (2010) more
than the one proposed by Andrus et al. (2004). The
sand used in this work is clean Ottawa F#55 sand
with less than 0.1% fines. This is thought to be the
reason why the equation developed by Dobry (2010)
fits better the measured values in this research.
210
220
205
215
Normalized Shear wave velocity, Vs1 [m/s]
Normalized Shear wave velocity, Vs1 [m/s]
Figure 7 shows the change in normalized shear wave
velocity with the change in relative density. The line
is the least square linear regression of the data.
Hardin and Richard (1963) concluded that the
relation between shear wave velocity and void ratio,
and thus relative density, is a linear relation.
where 𝑉𝑠1 =Normalized shear wave velocity; and
𝑞𝐶1𝑁 =normalized tip resistance
200
195
190
185
180
175
170
165
160
155
150
35
This work
Andrus et al. (2004)
Dobry (2010)
210
205
200
195
190
185
180
175
170
165
160
155
40
45
50
55
60
65
70
75
80
Relative Density, Dr (%)
Several researchers have studied the relation
between the tip resistance and the shear wave
velocity and developed empirical formulas relating
the two parameters (Andrus et al. 2004; and Dobry
2010). Andrus et al. (2004) developed his formula
using the results of Holocone sand sites with fine
content, FC≤20%. Dobry (2010) used results from
the same Holocone sand sites but considering only
the sites that involve clean sand with fine content,
FC≤5%.
The formulas developed by Andrus et al. (2004) and
Dobry (2010) are as follows:
Andrus et al. (2004):
(6)
Dobry (2010):
𝑉𝑠1 (𝑚/𝑠) = 51.1(𝑞𝐶1𝑁 )0.272
70
90
110
130
150
170
190
Normalized Tip resistance, q
Figure 7. The relation between normalized shear
wave velocity and relative density
𝑉𝑠1 (𝑚/𝑠) = 62.6(𝑞𝐶1𝑁 )0.231
150
50
(7)
210
230
250
c1N
Figure 8. Comparison between measured and
predicted 𝑞𝐶1𝑁 and 𝑉𝑠1
5. DISCUSSION AND CONCLUSION
Two centrifuge experiments were conducted at
Rensselaer Polytechnic Institute on Ottawa F#55
sand deposits placed at relative densities of 40% and
75%. In the two experiments, the tip resistance was
measured for the soil model at 50g. The shear wave
velocities are adopted from El-Sekelly (2011). The
results indicate a difference of about 150% in the
normalized tip resistance between the two relative
densities. The difference in the normalized shear
wave velocity is much less (about 10%). The results
suggest that the tip resistance is much more sensitive
than the shear wave velocity to the change in
relative density and thus, the liquefaction resistance
of saturated sand deposits. Also, the results compare
very well with the equation developed by Dobry
(2010).
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