technical report tr-2016-04 - university of wisconsin ...sbel.wisc.edu/documents/tr-2016-04.pdf ·...

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


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


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


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


Test 1: 8.31

Test 2: 8.09

Test 3: 7.40


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


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


Dr: 0%

Dh: 1.0 Ch


(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


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


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


Dr: 100%

Dh: 1.0 Ch


11


(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


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


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


Test 1: 6.37

Test 2: 6.35

Test 3: 6.37


Dr: 0%

Dh: 1.0 Ch


(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


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


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


Test 1: 5.21

Test 2: 4.92

Test 3: 5.72


Dr: 100%

Dh: 1.0 Ch


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


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


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


Dr: 0%

Dh: 1.0 Ch


(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


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


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


Test 1: 5.62

Test 2: 5.67

Test 3: 5.68


Dr: 100%

Dh: 1.0 Ch


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


(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


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


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


Dr: 0%

Dh: 1.0 Ch


(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


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


Dr: 100%

Dh: 1.0 Ch

Displacement (cm)

Test 1: 6.72

Test 2: 6.60

Test 3: 6.64


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


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


Dr: 0%

Dh: 1.0 Ch


(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


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


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


Dr: 100%

Dh: 1.0 Ch

Displacement (cm)

Test 1: 7.77

Test 2: 8.01

Test 3: 7.82


16


(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


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


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


Dr: 0%

Dh: 1.0 Ch


(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


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


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


Dr: 100%

Dh: 1.0 Ch


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


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


Dr: 0%

Dh: 1.0 Ch


(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


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


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


Dr: 100%

Dh: 1.0 Ch


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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