1
Technical Report TR-2016-04
Cone Penetration Results for 3mm
Glass Beads and 20-30 Ottawa sand
Kyle Williams1
1University of Wisconsin-Madison, Madison, WI 53706-1572
February 2016
2
1 Introduction
Chrono Granular is a toolkit that is part of Chrono::Engine. Chrono::Granular is used to assist in
the setup and running of DEM Tests. In an effort to provide validity to Chrono::Granular, a
series of traditional and simple Geotechnical Engineering tests were selected. Fall Cone
Penetration tests were selected as one of the methods to evaluate Chrono::Granular.
Fall Cone Penetration tests were selected to provide physical data to evaluate two key areas of
Chrono::Granular. The objectives are listed below:
Perform static cone penetration tests to compare with Chrono simulations for static
loading by using zero drop height
Perform dynamic cone penetration tests to compare with Chrono simulations for dynamic
loading by using different finite drop heights
To facilitate the completion of these objectives, the procedure and equipment in both the British
and Swedish standards, as well as the procedure and methods presented by Likos and Jaafar
(2014) were modified. This paper details the materials, methods, and results used to provide a
point of comparison with Chrono::Granular simulations.
2 Material Properties
Two materials were selected to evaluate the ability of Chrono Granular to simulate the motions
and behavior of granular material. Jaygo Dragonoite® Type M Article 5005 Glass beads,
referred to herein as glass beads, was selected as the first material. 20-30 Ottawa sand, referred
to herein as sand, was selected as the second material. The materials were selected because of
high roundness and uniform particle size. Table 1 lists the properties used for conducting the
tests. The maximum and minimum densities for each material were determined using ASTM
D4253-14 and ASTM D5254 respectively. The specific gravity was determined for each material
using ASTM D854-14. The maximum and minimum void ratios were then determined using
equation 1:
𝑒 =
𝐺𝑠 ∗ 𝜌𝑤𝑎𝑡𝑒𝑟𝜌𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙
(1)
where
e =void ratio
Gs = specific gravity
ρwater = density of water
ρmaterial = maximum or minimum index density for minimum or maximum void ratio
3
Table 1 Test Material Properties
Property Glass Beads Sand
Grain Size 3 mm ± 0.3 mm See Figure 1
Minimum Density (g/cm3) 1.50 1.52
Maximum Density (g/cm3) 1.63 1.78
Specific Gravity 2.50 2.65
Minimum Void Ratio 0.66 0.47
Maximum Void Ratio 0.53 0.74
Figure 1 Grain size distribution for 20-30 Ottawa Sand
3 Methods
3.1 Equipment
4” Proctor compaction mold with collar extension
4” Extrusion plate
6” Proctor compaction mold with collar extension
6” Extrusion plate
Linear variable differential transformer (LVDT)
o Omega Model LD610 ± 100 mm stroke length
40 cm adjustable vertical stand with 0.1 mm fine adjustment
30° apex angle fall cone with brass LVDT connector
60° apex angle fall cone with brass LVDT connector
Funnel
Balance sensitive to 0.01g
Computer with Labview software to record LVDT output
4
3.2 Apparatus Description
The fall cones used were the 30º and 60º, British and Swedish standard fall cones respectively.
The fall cones were removed from the plunger heads (Figure 2). The fall cones were then
connected to brass adapters to facilitate connection to the LVDT rod (Figure 3).
The LVDT was used to measure the displacement of the cones with time during penetration.
First the zero point on the LVDT was determined and marked with a piece of tape, which
prevented the rod from retreating further into the LVDT than the zero point. The LVDT was then
attached to the adjustable vertical stand. The adjustable vertical stand allowed the LVDT to be
raised and lowered based on the fall height of the test being conducted. The vertical stand had a
range of 40 cm and was adjustable by 0.1 mm. The LVDT and stand were placed on an elevated
platform that allowed full motion of the LVDT rod and fall cone to fall into the center of the 4”
and 6” proctor molds.
The 4" and 6" proctor molds were those specified in ASTM D698. The extensions were left on
the proctor molds for several reasons. The extensions facilitated the filling of the proctor molds
and compaction for the high relative density cases, and allowed the material to move vertically
when the cone penetrated without mass spilling out of the molds.
Figure 2 Fall Cones without Plungers
Figure 3 Fall Cones with LVDT connectors
5
Figure 4 View of Assembled Apparatus;
1. LVDT, 2. Zero Mark, 3. Fall cone and Adapter,
4. Adjustable Vertical Stand
Figure 5 Apparatus on elevated platform; sample
prior to final lift of material
Table 2 Fall Cone Properties
Property 30 Degree Fall Cone 60 Degree Fall Cone
Length, L (mm) 34.36 22.10
Width, W (mm) 9.21 19.86
Mass when attached to
LVDT (g) 141.1 135.7
Young’s Modulus (GPa) 193 193
Poisson’s Ratio 0.3-0.31 0.3-0.31
1
2
3
4
6
3.3 Experimental Program
A series of tests was performed in accordance with the testing matrix shown in Table 3 to
determine the penetration rates and final penetration into the two materials. One of the variables
used in the testing matrix was the relative density of the material. Relative density was
determined using equation 2.
𝐷𝑟 =
𝜌𝑚𝑎𝑥 − 𝜌
𝜌𝑚𝑎𝑥 − 𝜌𝑚𝑖𝑛 (2)
where
Dr =relative density
ρmax= maximum density (Table 1)
ρmin = minimum density (Table 1)
ρ = design density
Table 3 Summary of cone penetration testing program
Figure 6 Relationship between cone height and drop height
Cone Height (L)
Drop Height
Width (W)
7
Another variable that was changed in the testing program was the drop height of the cone. The
drop heights were normalized by the height of the cone. For example, the 30º fall cone has a
cone height, Ch, of 34.39mm. The drop heights used are 0.0Ch, 0.5Ch, and 1.0Ch, therefore, the
drop heights for the 30º fall cone are 0.0mm, 17.2mm, and 34.4mm respectively.
3.4 Procedure
The following procedure was used for each series of tests. The procedure was only modified
slightly to achieve the desired change in the testing program, i.e. a change in fall height, relative
density, etc. Prior to testing, bulk samples of the materials were allowed to air dry. These bulk
samples provided the samples used in the testing program.
1. Determine mass of sample needed to fill container at desired relative density.
2. Pour sample into container
a. For the low relative density case, the material is placed in accordance with ASTM
D5254.
b. For the high relative density case, the material is placed in lifts. After each lift, an
extrusion plate is placed onto the material. The center of the extrusion plate is
then hit with a standard proctor hammer ten times. This is repeated for a total of
four lifts.
3. The cone is then lowered to the surface of the material to determine the zero elevation.
a. For a fall height of 0.0 the LVDT stand is lowered to the zero mark on the LVDT
Rod without moving the cone.
b. For a fall height of 0.5 the LVDT stand is lowered to the zero mark on the LVDT
Rod without moving the cone. The LVDT stand is then raised by the fall height.
Then the cone is raised until the LVDT rod is at the zero mark.
c. For a fall height of 1.0 the LVDT stand is lowered to the zero mark on the LVDT
Rod without moving the cone. The LVDT stand is then raised by the fall height.
Then the cone is raised until the LVDT rod is at the zero mark
4. The recording software is activated.
5. The cone and LVDT rod is released allowing the cone to fall into the material until
movement stops.
The following is a detailed description of the procedure above and how it was used when glass
beads were placed in the 4" proctor, compacted to a high relative density, and subjected to
penetration from the 30° fall cone from a drop height of 1.0.
1. Mass of glass beads needed to fill the 4" proctor is calculated using the maximum
density.
2. Approximately 1/4 of the mass is poured into the proctor.
3. Material is covered with an extrusion plate and hit with a standard proctor hammer 10
times.
4. Steps 2 and 3 are repeated 3 times.
5. The cone and LVDT rod are then lowered to just touch the surface of the material.
6. The LVDT stand is lowered until the zero mark on the rod is reached.
8
7. The LVDT stand is raised by the drop height.
8. The cone and LVDT rod are then raised until the zero mark on the rod reaches the LVDT.
9. The recording software is then activated.
10. The cone and LVDT rod are released, allowing the cone to free fall into the material.
11. Steps 1-10 are repeated 2 more times.
4 Glass Bead Results
The cone penetration trend results for the glass beads are presented in the following sections. The
results are separated into the results from the 30° fall cone and the 60° fall cone.
The abbreviations used in each graph are as follows:
Dr = relative density
Dh = drop height
Ch = cone height
Remainder of page intentionally left blank
9
4.1 30 Degree Fall Cone
(a)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
cem
en
t (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
Test 1
Test 2
Bead Surface30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 0%
Dh: 0 Ch
Displacement (cm)
Test 1: 6.38
Test 2: 6.49
Test 3: 6.32
Test 3 Time vs
Displacement
not recorded. Final
Displacement Only
(b)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt
(cm
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
Test 1
Test 2
Test 3
Bead Surface
Displacement (cm)
Test 1: 8.66
Test 2: 8.87
Test 3: 8.75
30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 0%
Dh: 0.5 Ch
(c)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
Test 1
Test 2
Test 3
Bead SurfaceDisplacement (cm)
Test 1: 10.66
Test 2: 10.63
Test 3: 10.94
30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 0%
Dh: 1.0 Ch
Figure 7 Cone penetration trends for low relative density in a 4” proctor: (a) 0.0 Drop height; (b) 0.5 Drop height; (c) 1.0 Drop height
(a)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
cem
en
t (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Test 1
Test 2
Test 3
Bead Surface
Displacement (cm)
Test 1: 3.98
Test 2: 4.60
Test 3: 4.55
30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 100%
Dh: 0 Ch
(b)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt
(cm
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
Test 1
Test 2
Test 3
Bead Surface
Displacement (cm)
Test 1: 6.56
Test 2: 6.25
Test 3: 5.70
30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 100%
Dh: 0.5 Ch
(c)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30D
isp
lace
me
nt (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
Test 1
Test 2
Test 3
Bead SurfaceDisplacement (cm)
Test 1: 8.31
Test 2: 8.09
Test 3: 7.40
30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 100%
Dh: 1.0 Ch
Figure 8 Cone penetration trends for high relative density in a 4” proctor: (a) 0.0 Drop height; (b) 0.5 Drop height; (c) 1.0 Drop height
10
(a)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
cem
en
t (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
Test 1
Test 2
Test 3
Bead Surface 30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 0%
Dh: 0 Ch
Displacement (cm)
Test 1: 6.20
Test 2: 6.28
Test 3: 6.29
(b)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt
(cm
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
Test 1
Test 2
Test 3
Bead Surface
Displacement (cm)
Test 1: 8.39
Test 2: 8.52
Test 3: 8.63
30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 0%
Dh: 0.5 Ch
(c)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
10.5
11.0
Test 1
Test 2
Test 3
Bead Surface
Displacement (cm)
Test 1: 10.62
Test 2: 10.65
Test 3: 10.57
30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 0%
Dh: 1.0 Ch
Figure 9 Cone penetration trends for low relative density in a 6” proctor: (a) 0.0 Drop height; (b) 0.5 Drop height; (c) 1.0 Drop height
(a)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
cem
en
t (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Test 1
Test 2
Test 3
Bead Surface
Displacement (cm)
Test 1: 4.97
Test 2: 5.00
Test 3: 5.08
30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 100%
Dh: 0 Ch
(b)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt
(cm
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
Test 1
Test 2
Test 3
Bead Surface
Displacement (cm)
Test 1: 7.18
Test 2: 7.26
Test 3: 7.18
30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 100%
Dh: 0.5 Ch
(c)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
Test 1
Test 2
Test 3
Bead Surface Displacement (cm)
Test 1: 9.40
Test 2: 9.23
Test 3: 9.26
30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 100%
Dh: 1.0 Ch
Figure 10 Cone penetration trends for high relative density in a 6” proctor: (a) 0.0 Drop height; (b) 0.5 Drop height; (c) 1.0 Drop height
11
4.2 60 Degree Fall Cone
(a)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
cem
en
t (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Test 1
Test 2
Test 3
Bead Surface
Displacement (cm)
Test 1: 3.92
Test 2: 3.89
Test 3: 4.01
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 0%
Dh: 0 Ch
(b)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt
(cm
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
Test 1
Test 2
Test 3
Bead Surface
Displacement (cm)
Test 1: 5.38
Test 2: 5.36
Test 3: 5.70
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 0%
Dh: 0.5 Ch
(c)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
Test 1
Test 2
Test 3
Bead SurfaceDisplacement (cm)
Test 1: 6.37
Test 2: 6.35
Test 3: 6.37
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 0%
Dh: 1.0 Ch
Figure 11 Cone penetration trends for low relative density in a 4” proctor: (a) 0.0 Drop height; (b) 0.5 Drop height; (c) 1.0 Drop height
(a)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
cem
en
t (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
Test 1
Test 2
Test 3
Bead Surface
Displacement (cm)
Test 1: 2.40
Test 2: 2.23
Test 3: 2.63
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 100%
Dh: 0 Ch
(b)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt
(cm
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Test 1
Test 2
Test 3
Bead Surface
Displacement (cm)
Test 1: 3.84
Test 2: 4.34
Test 3: 3.66
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 100%
Dh: 0.5 Ch
(c)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30D
isp
lace
me
nt (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
Test 1
Test 2
Test 3
Bead Surface Displacement (cm)
Test 1: 5.21
Test 2: 4.92
Test 3: 5.72
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 100%
Dh: 1.0 Ch
Figure 12 Cone penetration trends for high relative density in a 4” proctor: (a) 0.0 Drop height; (b) 0.5 Drop height; (c) 1.0 Drop height
12
(a)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
cem
en
t (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Test 1
Test 2
Test 3
Bead Surface
Displacement (cm)
Test 1: 3.80
Test 2: 3.55
Test 3: 3.76
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 0%
Dh: 0 Ch
(b)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt
(cm
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
Test 1
Test 2
Test 3
Bead Surface
Displacement (cm)
Test 1: 5.24
Test 2: 5.20
Test 3: 5.16
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 0%
Dh: 0.5 Ch
(c)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
cem
ent (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
Test 1
Test 2
Test 3
Bead Surface
Displacement (cm)
Test 1: 6.62
Test 2: 6.45
Test 3: 6.03
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 0%
Dh: 1.0 Ch
Figure 13 Cone penetration trends for low relative density in a 6” proctor: (a) 0.0 Drop height; (b) 0.5 Drop height; (c) 1.0 Drop height
(a)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
cem
en
t (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Test 1
Test 2
Bead Surface
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 100%
Dh: 0 Ch
Displacement (cm)
Test 1: 3.31
Test 2: 3.29
Test 3: 3.17
Test 3 Time vs
Displacement
not recorded. Final
Displacement Only
(b)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt
(cm
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Test 1
Test 2
Test 3
Bead Surface
Displacement (cm)
Test 1: 4.68
Test 2: 4.65
Test 3: 4.75
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 100%
Dh: 0.5 Ch
(c)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
Test 1
Test 2
Test 3
Bead Surface Displacement (cm)
Test 1: 5.62
Test 2: 5.67
Test 3: 5.68
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 100%
Dh: 1.0 Ch
Figure 14 Cone penetration trends for high relative density in a 6” proctor: (a) 0.0 Drop height; (b) 0.5 Drop height; (c) 1.0 Drop height
13
5 Sand Results
The cone penetration trend results for the sand are presented in the following sections. The
results are separated into the results from the 30° fall cone and the 60° fall cone.
The abbreviations used in each graph are as follows:
Dr = relative density
Dh = drop height
Ch = cone height
Remainder of page intentionally left blank
14
5.1 30 Degree Fall Cone
(a)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
cem
en
t (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Test 1
Test 2
Test 3
Sand Surface
Displacement (cm)
Test 1: 3.98
Test 2: 3.74
Test 3: 4.37
30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 0%
Dh: 0 Ch
(b)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt
(cm
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
Test 1
Test 2
Test 3
Sand Surface
Displacement (cm)
Test 1: 6.76
Test 2: 6.44
Test 3: 6.94
30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 0%
Dh: 0.5 Ch
(c)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
10.5
Test 1
Test 2
Test 3
Sand SurfaceDisplacement (cm)
Test 1: 9.31
Test 2: 9.46
Test 3: 9.53
30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 0%
Dh: 1.0 Ch
Figure 15 Cone penetration trends for low relative density in a 4” proctor: (a) 0.0 Drop height; (b) 0.5 Drop height; (c) 1.0 Drop height
(a)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
cem
en
t (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Test 1
Test 2
Test 3
Sand Surface30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 100%
Dh: 0 Ch
Displacement (cm)
Test 1: 2.96
Test 2: 2.96
Test 3: 3.19
(b)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt
(cm
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Test 1
Test 2
Test 3
Sand Surface
30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 100%
Dh: 0.5 Ch
Displacement (cm)
Test 1: 4.56
Test 2: 4.59
Test 3: 4.32
(c)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30D
isp
lace
me
nt (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
Test 1
Test 2
Test 3
Sand Surface
30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 100%
Dh: 1.0 Ch
Displacement (cm)
Test 1: 6.72
Test 2: 6.60
Test 3: 6.64
Figure 16 Cone penetration trends for high relative density in a 4” proctor: (a) 0.0 Drop height; (b) 0.5 Drop height; (c) 1.0 Drop height
15
(a)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
cem
en
t (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Test 1
Test 2
Sand Surface30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 0%
Dh: 0 Ch
Displacement (cm)
Test 1: 4.61
Test 2: 4.30
(b)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt
(cm
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
Test 1
Test 2
Test 3
Sand Surface
Displacement (cm)
Test 1: 7.04
Test 2: 7.11
Test 3: 6.95
30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 0%
Dh: 0.5 Ch
(c)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
Test 1
Test 2
Test 3
Sand SurfaceDisplacement (cm)
Test 1: 9.32
Test 2: 9.47
Test 3: 9.53
30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 0%
Dh: 1.0 Ch
Figure 17 Cone penetration trends for low relative density in a 6” proctor: (a) 0.0 Drop height; (b) 0.5 Drop height; (c) 1.0 Drop height
(a)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
cem
en
t (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Test 1
Test 2
Sand Surface
Displacement (cm)
Test 1: 3.41
Test 2: 3.38
Test 3: 3.68
30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 100%
Dh: 0 Ch
Test 3 Time vs Displacement
not recorded. Final
Displacement Only
(b)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt
(cm
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
Test 1
Test 2
Test 3
Sand Surface
30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 100%
Dh: 0.5 Ch
Displacement (cm)
Test 1: 4.89
Test 2: 4.92
Test 3: 5.32
(c)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
Test 1
Test 2
Test 3
Sand Surface
30 Degree ConeMass: 141.4 gCh: 34.39 mm
Dr: 100%
Dh: 1.0 Ch
Displacement (cm)
Test 1: 7.77
Test 2: 8.01
Test 3: 7.82
Figure 18 Cone penetration trends for high relative density in a 6” proctor: (a) 0.0 Drop height; (b) 0.5 Drop height; (c) 1.0 Drop height
16
5.2 60 Degree Fall Cone
(a)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
cem
en
t (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Test 1
Test 2
Test 3
Sand Surface
Displacement (cm)
Test 1: 2.29
Test 2: 2.56
Test 3: 2.30
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 0%
Dh: 0 Ch
(b)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt
(cm
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Test 1
Test 2
Test 3
Sand Surface
Displacement (cm)
Test 1: 3.78
Test 2: 4.18
Test 3: 3.94
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 0%
Dh: 0.5 Ch
(c)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
Test 1
Test 2
Test 3
Sand Surface
Displacement (cm)
Test 1: 6.76
Test 2: 6.93
Test 3: 6.60
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 0%
Dh: 1.0 Ch
Figure 19 Cone penetration trends for low relative density in a 4” proctor: (a) 0.0 Drop height; (b) 0.5 Drop height; (c) 1.0 Drop height
(a)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
cem
en
t (c
m)
0.0
0.5
1.0
1.5
2.0
Test 1
Test 2
Test 3
Sand Surface
Displacement (cm)
Test 1: 1.66
Test 2: 1.55
Test 3: 1.77
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 100%
Dh: 0 Ch
(b)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt
(cm
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Test 1
Test 2
Test 3
Sand Surface
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 100%
Dh: 0.5 Ch
Displacement (cm)
Test 1: 3.17
Test 2: 3.13
Test 3: 3.02
(c)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Test 1
Test 2
Test 3
Sand Surface
Displacement (cm)
Test 1: 4.45
Test 2: 4.57
Test 3: 4.53
30 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 100%
Dh: 1.0 Ch
Figure 20 Cone penetration trends for high relative density in a 4” proctor: (a) 0.0 Drop height; (b) 0.5 Drop height; (c) 1.0 Drop height
17
(a)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
cem
en
t (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Test 1
Test 2
Sand Surface 60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 0%
Dh: 0 Ch
Displacement (cm)
Test 1: 2.45
Test 2: 2.56
Test 3: 2.25
Test 3 Time vs Displacement not recorded. Final Displacement Only
(b)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt
(cm
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Test 1
Test 2
Test 3
Sand Surface
Displacement (cm)
Test 1: 3.63
Test 2: 3.89
Test 3: 3.58
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 0%
Dh: 0.5 Ch
(c)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
Test 1
Test 2
Test 3
Sand Surface Displacement (cm)
Test 1: 5.39
Test 2: 5.52
Test 3: 5.65
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 0%
Dh: 1.0 Ch
Figure 21 Cone penetration trends for low relative density in a 6” proctor: (a) 0.0 Drop height; (b) 0.5 Drop height; (c) 1.0 Drop height
(a)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
cem
en
t (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
Test 1
Test 2
Test 3
Sand Surface
Displacement (cm)
Test 1: 2.02
Test 2: 1.73
Test 3: 1.80
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 100%
Dh: 0 Ch
(b)
Time (s)0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
ce
me
nt
(cm
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Test 1
Test 2
Test 3
Sand Surface
Displacement (cm)
Test 1: 3.41
Test 2: 3.10
Test 3: 3.22
60 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 100%
Dh: 0.5 Ch
(c)
Time (s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Dis
pla
cem
ent (c
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Test 1
Test 2
Test 3
Sand Surface
Displacement (cm)
Test 1: 4.25
Test 2: 4.29
Test 3: 4.66
30 Degree ConeMass: 135.7 gCh: 22.10 mm
Dr: 100%
Dh: 1.0 Ch
Figure 22 Cone penetration trends for high relative density in a 6” proctor: (a) 0.0 Drop height; (b) 0.5 Drop height; (c) 1.0 Drop height
18
6 Discussion
6.1 Impact Velocity
The data was analyzed from point of release to a distance of 0.5 Ch for both the 30º and 60º fall
cones. Trend lines were generated from the lower and upper bounds of the data sets, neglecting
extreme outliers. The trend lines were forced to have a displacement intercept of 0. This
provided more conservative trend lines. The velocity ranges were calculated by solving for the
time required to reach the material surfaces for the 0.5 and 1.0 Dh. This time was then used to
determine the velocity at impact with the material. The accelerations were determined by taking
the 2nd derivative of the trend line equations. The calculated acceleration was then compared
with gravity to determine the friction forces. The data is presented in tables 4-7.
Table 4 30º Falling trends from glass results
Bounds Trend Line
Equation R2
Acceleration
(m/s2)
Friction
(N)
0.5 Dh 1.0 Dh
Time
(s)
Velocity
(m/s)
Time
(s)
Velocity
(m/s)
Upper 3.182𝑡2 − 0.0484𝑡 0.9984 6.36 0.488 0.0815 0.470 0.112 0.664
Lower 4.313𝑡2 + 0.0265𝑡 0.9997 8.63 0.166 0.0602 0.546 0.0863 0.771
Table 5 30º Falling trends from sand results
Bounds Trend Line
Equation R2
Acceleration
(m/s2)
Friction
(N)
0.5 Dh 1.0 Dh
Time
(s)
Velocity
(m/s)
Time
(s)
Velocity
(m/s)
Upper 3.120𝑡2 − 0.0725𝑡 0.9943 6.24 0.505 0.0868 0.469 0.117 0.658
Lower 4.313𝑡2 + 0.0474𝑡 0.9999 8.63 0.166 0.0579 0.547 0.084 0.772
Table 6 60º Falling trends from sand results
Bounds Trend Line
Equation R2
Acceleration
(m/s2)
Friction
(N)
0.5 Dh 1.0 Dh
Time
(s)
Velocity
(m/s)
Time
(s)
Velocity
(m/s)
Upper 3.240𝑡2 − 0.0652𝑡 0.9952 6.48 0.452 0.0695 0.385 0.0933 0.539
Lower 4.427𝑡2 + 0.0975𝑡 0.9998 8.85 0.136 0.0403 0.454 0.0605 0.633
Table 7 60º Falling trends from glass results
Bounds Trend Line
Equation R2
Acceleration
(m/s2)
Friction
(N)
0.5 Dh 1.0 Dh
Time
(s)
Velocity
(m/s)
Time
(s)
Velocity
(m/s)
Upper 3.357𝑡2 − 0.0598𝑡 0.9936 6.71 0.421 0.0671 0.391 0.0905 0.548
Lower 4.605𝑡2 + 0.0622𝑡 0.9999 9.21 0.081 0.0428 0.456 0.0629 0.642
19
6.2 Frictional Forces
In the initial selection and design of the testing apparatus it was assumed that frictional effects
due to the LVDT rod would be negligible. To check this assumption the accelerations
determined.
The trend lines used to determine the impact velocity were also used to calculate the actual
acceleration exhibited by the falling cone. The trend lines indicated a range of accelerations, also
indicating a range of frictional forces exhibited.
This range of frictional variances could be attributed to the manner in which the rod was
restrained. To maintain the zero mark on the rod before releasing, an additional lateral force
could have been applied to the rod. This additional force could have caused the rod to move
away from a vertical alignment. Once the rod was released this would cause additional friction as
the rod moved to realign itself while falling. Several tests produced displacement trends with
several data points indicating a large oscillation in the displacement. Visual observations did not
present any indication of this. These data points were treated as noise and removed from the data
sets; however, these points could be an indication of the additional friction forces generated from
the realignment of the LVDT rod when falling.
However, it is worth noting that several of the tests produced a trend line that had an acceleration
very close to that of gravity. This indicates that with proper setup and release, this testing
apparatus can produce near frictionless results indicative of true free fall.
7 Acknowledgements
This project was sponsored by US Army TARDEC under Rapid Innovation Fund (RIF) grant
W56HZV-14-C-0254. Any opinions, findings, and conclusions or recommendations expressed in
this material are those of the author and do not necessarily reflect the views of US Army
TARDEC.
8 References
British Standards Institution (BSI). (1990). “British standard methods of test for soils for civil
engineering purposes.” BS 1377-2, London
Likos, W., & Jaafar, R. (2014). Laboratory Fall Cone Testing of Unsaturated Sand. Journal of
Geotechnical and Geoenvironmental Engineering, 140(8), 04014043.
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