December 2011 

NASA/CR—2011-217323

Constitutive Soil Properties for Mason Sand and 

Kennedy Space Center 

Michael A. Thomas and Daniel E. Chitty 

Applied Research Associates, Inc., Albuquerque, New Mexico
1$6$67,3URJUDPLQ3URILOH

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December 2011 

NASA/CR—2011-217323

Constitutive Soil Properties for Mason Sand and

Kennedy Space Center 

Michael A. Thomas and Daniel E. Chitty 

Applied Research Associates, Inc., Albuquerque, New Mexico
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 

$FNQRZOHGJPHQWV

Applied Research Associates, Inc (ARA) conducted this soil study under contract to 

NASA Langley Research Center’s (LaRC) prime contractor for engineering support, 

ATK Space. ATK Space is the Technology Engineering and Aerospace Mission Support 

(TEAMS) prime contractor. The study was conducted for LaRC’s Landing Systems ADP 

group, charged with evaluating the new Orion launch abort scenario at Kennedy Space 

Center (KSC). Dr. Edwin Fasanella, LaRC, sponsored the study. ARA developed soil 

models for LaRC use in modeling an Orion impact on KSC sand and a surrogate test 

sand, Mason Sand. This report provides constitutive soil properties for landing 

simulations. The primary author is Michael A. Thomas, with contributions from Daniel 

E. Chitty, Martin L. Gildea, and Stephen R. Quenneville. All are engineers with ARA. 

LS-DYNA is a registered trademark of the Livermore Software Technology Corporation 

(LSTC).

The use of trademarks or names of manufacturers in this report is for accurate reporting and does not 

constitute an official endorsement, either expressed or implied, of such products or manufacturers by the 

National Aeronautics and Space Administration. 
Abstract 

Accurate soil models are required for numerical simulations of land landings for the Orion Crew 

Exploration Vehicle (CEV). This report provides constitutive material models for two soil 

conditions at Kennedy Space Center (KSC) and four conditions of Mason Sand. The Mason 

Sand is the test sand for LaRC’s drop tests and swing tests of the Orion. The soil models are 

based on mechanical and compressive behavior observed during geotechnical laboratory testing 

of remolded soil samples. The test specimens were reconstituted to measured in situ density and 

moisture content. Tests included: triaxial compression, hydrostatic compression, and uniaxial 

strain. A fit to the triaxial test results defines the strength envelope. Hydrostatic and uniaxial 

tests define the compressibility. The constitutive properties are presented in the format of LSDYNA Material Model 5: Soil and Foam. However, the laboratory test data provided can be 

used to construct other material models. 

The soil models are intended to be specific to the soil conditions they were tested at. The two 

KSC models represent two conditions at KSC: low density dry sand and high density in-situ 

moisture sand. The Mason Sand model was tested at four conditions which encompass measured 

conditions at LaRC’s drop test site. 

iii
Table of Contents 

1 Introduction...........................................................................................................................................1

2 LS-DYNA Material Model 5 Description ............................................................................................2

3 Methodology for Obtaining Constitutive Soil Properties .....................................................................4

3.1 Geotechnical Laboratory Tests....................................................................................................4

3.1.1 Grain Density ..........................................................................................................................4

3.1.2 Grain size distribution .............................................................................................................5

3.1.3 Moisture content......................................................................................................................5

3.1.4 Triaxial compression...............................................................................................................6

3.1.4.1. Triaxial test apparatus..................................................................................... 6 

3.1.4.2. Soil specimen preparation............................................................................... 7 

3.1.4.3. Deriving constitutive parameters from triaxial test results............................. 8 

3.1.5 Hydrostatic compression.......................................................................................................13

3.1.5.1. Deriving constitutive parameters from hydrostatic compression ................. 14 

3.1.6 Uniaxial strain .......................................................................................................................14

3.1.6.1. Deriving constitutive parameters from uniaxial strain.................................. 15 

4 KSC Low Density Dry Sand...............................................................................................................22

4.1 Location.....................................................................................................................................22

4.2 General description....................................................................................................................23

4.2.1 Soil classification ..................................................................................................................25

4.3 Laboratory test data ...................................................................................................................25

4.3.1 Grain density and grain size analysis ....................................................................................25

4.3.2 Triaxial compression.............................................................................................................26

4.3.3 Hydrostatic compression.......................................................................................................32

4.3.4 Uniaxial strain .......................................................................................................................34

4.4 LS-DYNA Material Model 5 inputs..........................................................................................41

5 KSC High Density In Situ Moisture Sand ..........................................................................................42

5.1 Location.....................................................................................................................................42

5.2 General description....................................................................................................................42

5.3 Laboratory data..........................................................................................................................43

5.3.1 Triaxial compression.............................................................................................................45

5.3.2 Hydrostatic compression.......................................................................................................51

5.3.3 Uniaxial strain .......................................................................................................................52

5.4 LS-DYNA Material Model 5 inputs..........................................................................................58

6 Mason Sand at 97/4% .........................................................................................................................59

6.1 Laboratory test data ...................................................................................................................59

6.1.1 Correlating Mason Sand to “Clean Sand” from 2008 ...........................................................61

6.1.2 Triaxial compression.............................................................................................................62

6.1.3 Hydrostatic compression.......................................................................................................67

6.1.4 Uniaxial strain .......................................................................................................................68

6.2 LS-DYNA Material Model 5 inputs..........................................................................................74

7 Mason Sand at 96/8% .........................................................................................................................75

7.1 Triaxial compression .................................................................................................................76

7.2 Hydrostatic compression ...........................................................................................................80

7.3 Uniaxial strain ...........................................................................................................................81

7.4 LS-DYNA Material Model 5 inputs..........................................................................................86

8 Properties for Mason Sand at 100 lbs/ft3 dry density and 5% water content ......................................87

iv
8.1 Triaxial compression .................................................................................................................88

8.2 Hydrostatic compression ...........................................................................................................92

8.3 Uniaxial strain ...........................................................................................................................93

8.4 LS-DYNA Material Model 5 inputs..........................................................................................98

9 Mason Sand at 100/15% .....................................................................................................................99

9.1 Triaxial compression ...............................................................................................................100

9.2 Hydrostatic compression .........................................................................................................104

9.3 Uniaxial strain .........................................................................................................................105

9.4 LS-DYNA Material Model 5 inputs........................................................................................110

10 Model to Model Comparisons .....................................................................................................111

11 Closing Remarks..........................................................................................................................117

12 References....................................................................................................................................118

Appendix A: LS-DYNA Theory Manual for Material Model 5 ..............................................................119

v
1 

1 Introduction 

Langley Research Center (LaRC) was tasked with modeling the interaction between the Orion 

spacecraft and soil. The principle site of interest is Kennedy Space Center (KSC). The scenario 

is a launch abort event where the Orion impacts the sands surrounding the launch pad. LaRC is 

approximating the KSC sand with Mason Sand, locally available at LaRC. The drop test site is 

LaRC’s gantry facility. An Orion boilerplate was dropped on Mason Sand, the surrogate 

replacement for KSC sand. LaRC is interested in determining soil factors influence Orion’s 

safety during impact. 

This report quantifies soil conditions and provides constitutive soil properties to support LaRC’s 

numerical modeling of Orion boilerplate tests. For this modeling, LaRC is using LS-DYNA, a 3-

dimensional finite element software program. Applied Research Associates, Inc. (ARA) 

performed soil sampling on field visits to each site. The soil samples were shipped to ARA’s 

geotechnical laboratory for a series of laboratory tests. The tests were designed to yield the 

required constitutive inputs for LS-DYNA’s Material Model 5: Soil and Foam. 

This document is intended as a stand-alone report. It supplements the 1 Feb 2008 report titled 

“Constitutive Soil Properties for Cuddeback Lake, CA and Carson Sink, NV.” The KSC models 

replace those from “Constitutive Soil Properties for Unwashed Sand and Kennedy Space Center” 

dated 13 May 2008. Comparisons between the new and old models are made throughout the 

report. 
2 

2 LS-DYNA Material Model 5 Description 

LS-DYNA Material Model 5 was identified by LaRC for modeling the soils in preliminary 

calculations. The constitutive properties derived in this report are tailored for constructing this 

type of model. This section describes the physical meaning of each of the model inputs. Section 

3 addresses how each of the model inputs were obtained from material testing. 

Because soil strength is pressure dependent, a pressure dependent material model is necessary for 

constitutive modeling. In LS-DYNA, Material Model 5: Soil and Foam is the most basic of the 

pressure dependent strength models available. It is also the oldest LS-DYNA pressure dependent 

model and therefore has accumulated a considerable amount of user experience and feedback. 

As a result, the model is quite robust given its simple inputs. 

Defining the model requires shear and unloading bulk moduli, three coefficients that define the 

quadratic shear failure surface, a pressure cutoff value that defines the maximum tension 

allowed, and 10 points on a pressure-volume strain curve to define compressibility. Table 2-1 

defines these inputs. Based on LaRC preference for their numerical modeling, the material 

model inputs are provided in pounds and inches. 

The elastic shear modulus, G, describes shear deformation when the soil is initially loaded. The 

bulk unloading modulus, BULK, describes the expansion of the soil when the load is reduced. 

These two parameters are necessary because the loading and unloading behavior of soil is not 

equal due to permanent deformations. 

The a0, a1, and a2 inputs define a quadratic fit to a strength curve. The strength curve is defined 

as a yield surface plotted in J2’ versus pressure space. Pressure is the mean stress, the average of 

all the principle stresses on the material. Pressure is positive in compression. J2’ is the second 

invariant of the stress deviator. Material tests define points on the yield surface, and the 

quadratic fit is LS-DYNA’s approximation of material strength. In the LS-DYNA manual, the 

second invariant of the stress deviator is denoted J2. In this report, the more common notation, 

J2’, is used to represent the same quantity. 

Volumetric strain behavior is defined by the natural log of the relative volume and is negative in 

compression. Relative volume is the ratio of the current soil cell volume to the initial volume at 

the start of the calculation. The volumetric strain is represented as a 10 point curve in pressure 

versus volume strain space. Each point on the curve is obtained from material testing at the 

given pressure. 

The LS-DYNA Theory Manual describes Material Model 5 in more detail. Appendix A contains 

excerpts from the manual. 
3 

Table 2-1. LS-DYNA Material Model 5 Inputs. 

Input Obtained from soil test: Description 

MID N/A LS-DYNA’s material identification number. A unique 

number identifying an input set of material properties. A 

number must be assigned. 

RO Nuclear density field test Mass density. Obtained from dividing weight density 

(mass/unit volume) by gravity. 

G Uniaxial strain Elastic shear modulus. The slope of the shear stress vs. shear 

strain curve. Can be computed from constrained modulus and 

Poisson’s ratio from a uniaxial test. 

BULK Hydrostatic compression Unloading bulk modulus. It is the slope of the mean stress vs. 

strain curve when the pressure is reduced (unloaded) from a 

higher pressure load. Can also be obtained from uniaxial 

strain unloading. 

A0 Triaxial compression A quadratic fit coefficient. In a J2’ vs. p (second invariant of 

stress difference vs. pressure) plot, a0 represents the 

intersection of the shear failure envelope’s (or yield surface) 

quadratic fit and the J2’ axis. a0 coefficient is the Y-intercept. 

The J2’ vs. p plot is derived from stress difference vs. normal 

stress. 

A1 Triaxial compression a1 is a quadratic fit coefficient. It is the initial slope 

coefficient of the shear failure envelope’s quadratic fit. 

A2 Triaxial compression a2 is a quadratic fit coefficient. It is the curvature coefficient 

of the shear failure envelope’s quadratic fit. 

PC Triaxial compression “Pressure cut-off.” Maximum tension stress allowed, 

representing tensile fracture. It is the mean stress intercept of 

the shear failure envelope. 

VCR This is a flag variable. 

VCR=0 

VCR=0 turns on volumetric crushing, defined by the 10 points 

on the pressure-volume curve. VCR=1 turns off. The 

pressure-volume curve defines the deformation of the material 

at 10 pressures. 

REF This is a flag variable. 

REF=0 

This option controls the use of reference geometry to initialize 

the pressure. REF=0 is recommended. This option does not 

initialize the deviatoric stress state. 

EPS1, P1 EPS1=0, P1=0 This is the first point on the pressure volume curve; at zero 

loading there is zero volume change. EPS is the natural 

logarithmic volume strain = (ln [ 1 - İvolume ]), where İvolume = 

(initial volume – current volume)/initial volume 

EPS2, P2 Uniaxial strain 2nd pressure-volume point 

EPS3, P3 Uniaxial strain 3rd pressure-volume point 

EPS4, P4 Uniaxial strain 4th pressure-volume point 

EPS5, P5 Uniaxial strain 5th pressure-volume point 

EPS6, P6 Uniaxial strain 6th pressure-volume point 

EPS7, P7 Uniaxial strain 7th pressure-volume point 

EPS8, P8 Uniaxial strain 8th pressure-volume point 

EPS9, P9 Uniaxial strain 9th pressure-volume point 

EPS10, P10 Uniaxial strain 10th pressure-volume point 
4 

3 Methodology for Obtaining Constitutive Soil Properties 

This section describes the methodology for deriving LS-DYNA material model inputs from 

laboratory test data. 

3.1 Geotechnical Laboratory Tests 

ARA operates a specialized geotechnical laboratory in South Royalton, VT where the soil 

samples were shipped for testing. The types of tests conducted for this effort are listed and 

explained below: 

x Grain density 

x Grain size distribution 

x Moisture content 

x Hydrostatic compression 

x Uniaxial strain 

x Triaxial compression 

The Atterberg limits test does not apply here because the soils are sands. 

3.1.1 Grain Density 

A given volume of soil is comprised of solid particles and void space. The grain density (Ug) of a 

soil is the density of the solid particles. Knowing the grain density of a soil allows one to 

perform accurate saturation and void volume calculations. Soils typically have a grain density of 

2.7 +/- 0.1 g/cm3

. Although not specifically used in constitutive modeling, the grain density is a 

basic piece of information useful for characterizing the soil as a whole. 

The grain density is measured according to the procedures defined by ASTM D854-83. This test 

is performed using a pycnometer, a special-purpose glass flask with a drilled ground glass 

stopper that allows it to be filled with the same volume of water with density ȡw. First, the 

weight of a 100-ml pycnometer is determined. Second, the pycnometer is filled with distilled, 

de-aired water to its fill point and re-weighed, (ma). Then, the water is dumped, and an oven 

dried soil sample is placed in the dried pycnometer and weighed to determine the mass of the 

oven-dried sand sample (mo). Distilled, de-aired water is added to the pycnometer again to 

slightly above the soil sample. The air entrapped in the sample soil is removed by vacuum. 

More de-aired, distilled water is added to the pycnometer until reaching the same fill point, and 

the mass of pycnometer, soil, and water (mb) is recorded. Finally, the grain density of the soil is 

computed, including temperature corrections, which are not shown, by the following: 

> @   a b

w

g m m m

m

  

0

U 0 U Equation 3-1
5 

3.1.2 Grain size distribution 

A given soil contains a variety of particle sizes. The relative proportions of all particle sizes is 

captured by defining grain size distribution. The distribution is a good indicator of general soil 

behavior. A soil with mostly fine grains will have poor drainage, retain water for long periods of 

time, exhibit cohesive strength, and have very low shear strengths at high moisture contents. The 

low shear strength in fine grained soils is due to pore pressures building up during loading 

because of the poor drainage. This pore pressure reduces the effective shear stress, carried by 

grain-to-grain contact in the soil. Grain size distribution is also essential in recommending 

surrogate soils to replace a soil of interest. Soils with similar grain size distributions tend to have 

similar behavior. The grain size distribution is not specifically used in LS-DYNA, but it offers 

great insight into what the soil is comprised of, and how it will behave with varying moisture 

levels. 

Wet or dry sieve analysis can be used to obtain grain size distribution, also a basic test. Dry 

grain size distribution tests on soils are performed with the material in the oven-dried condition. 

The sample is broken up and shaken through a stack of sieves that are graduated from coarse at 

the top to fine at the bottom. The material retained on each sieve is then weighed, and the results 

are presented in terms of the percent passing (or percent finer than) each sieve size as a function 

of the logarithm of the grain size. The sieves used for this characterization effort were US 

standard meshes of No. 5, 10, 20, 30, 40, 70, 100, 140, and 200. Wet sieving flushes the soil 

with water, further breaking up cohesive particles that would otherwise not pass through a sieve. 

Once flushed, the retained soil is dried and weighed. Dry sieving is less reliable because 

cohesive blocks of soil grains can distort the distribution. However, wet sieving is much more 

time consuming because the retained soil must be completely dried. 

3.1.3 Moisture content 

The moisture content of a soil is another basic test and key property. It is the gravimetric ratio of 

water to dry soil material. Although not a direct input to LS-DYNA’s Material Model 5, water 

plays an important role in soil strength and knowing the moisture content in conjunction with 

grain density allows one to compute saturation and air void volumes in the soil. Soils have an 

optimum moisture content, at which soil strength is maximized. Any moisture content lower or 

above this optimum value will reduce the soil strength. At lower values, removing water also 

removes some cohesion strength. At higher values, the extra water causes pore pressures to 

build up in the soil, reducing its effective strength. Approximate moisture content (w%) can be 

obtained through field testing with a nuclear density gage, and verified through laboratory 

testing. Laboratory testing to obtain moisture content is performed by first weighing a set of soil 

samples. Then the samples are oven dried and weighed again to measure the difference caused 

by the loss of water. The difference in weight is mw. The oven dried weight is ms. Individual 

moisture content is calculated for each sample, and the results are averaged. The formula for 

calculating water content is: 

s

w

m

m

w% Equation 3-2
6 

 

3.1.4 Triaxial compression 

The results of triaxial compression tests are used to define the strength envelope, or yield surface 

as it’s referred to in LS-DYNA, of the soil. The following paragraphs describe the triaxial 

testing machine, how the sample is tested, and how the coefficients of the shear failure surface, 

a0, a1, and a2 are derived from laboratory test data. 

3.1.4.1. Triaxial test apparatus 

All of the mechanical property tests were performed in a triaxial compression test apparatus, 

which is illustrated schematically in Figure 3-1. For each test, a cylindrical specimen of soil is 

first prepared inside a fluid-tight membrane to prevent infiltration of the confining fluid (air). In 

the triaxial apparatus, it is possible to apply two independently controlled components of load to 

the test specimen, as appropriate to each individual test. Pressurized fluid (air) in the vessel is 

used to impose a hydrostatic stress, simulating the effect of adjacent soil in the field. The other 

component of load is derived from a piston, which extends through a seal in the top of the 

pressure vessel, loading the cylindrical specimen in the axial direction. Electronic 

instrumentation is used to measure both the applied loads and the resulting deformations of the 

soil specimens. The following paragraphs describe in more detail how the test specimens were 

prepared, instrumented, and tested. 
7 

3.1.4.2. Soil specimen preparation 

The first step in the test process is to pack the soil to the measured field density inside the latex 

rubber membrane that separates the specimen material from the confining fluid. The membrane 

lines the inside of a steel cylinder mold, which can be removed by splitting in half. The soil is 

placed in the mold in measured lifts and compacted to the field density. The soil sample 

reconstitution is described in more detail in the individual material chapters. Once the mold is 

filled, the top cap is installed in the same manner as the bottom cap, and final measurements of 

the specimen dimensions and mass are made. The sample is then placed in the triaxial apparatus. 

Figure 3-2 illustrates how the membranes are sealed on each end to hardened steel endcaps 

through which the axial load was applied. The membrane was then sealed to the bottom cap 

using sealant and O-rings. Figure 3-3 is a “ready to test” photograph. 

Pressure

Source

Hydraulic Cylinder

for Axial Loading

Load Frame

Piston

Load Cell

Test Specimen

Pressure Vessel

Pressure

Transducer

Figure 3-1: Schematic and photograph of a triaxial compression test apparatus. 
8 

Electronic instruments were used to monitor the applied loads and 

specimen responses during the tests. Three linear variable differential 

transformer (LVDT) type displacement transducers were installed as 

illustrated in Figure 3-2 to provide measurements of specimen 

deformations under load. A pressure transducer was used to monitor the 

confining pressure, which is equal to the radial stress on the on the 

specimen, and a load cell measured the axial load. The load cell was 

located inside the pressure vessel to eliminate errors that would result 

from seal friction if it were outside the vessel. The necessary corrections 

were made to eliminate the effects of confining pressure on the load cell 

output. All of the instruments were calibrated against standards traceable 

to the National Institute of Standards Technology (NIST) and adjusted to 

provide the necessary measurement resolution over the expected range of 

each test. A microcomputer based digital data acquisition system was used to record the 

transducer output at equally-spaced discrete intervals in time. 

3.1.4.3. Deriving constitutive parameters from triaxial test results 

In the triaxial compression, or strength test, the specimen is loaded hydrostatically to a preselected confining pressure. The confining pressure is then held constant while a compressive 

axial strain is imposed. The imposed axial strain induces an increment of axial stress above the 

confining pressure level, and that stress difference results in shear stresses on all planes except 

the principal directions parallel and perpendicular to the specimen axis. The shear strength of 

Figure 3-3: Specimen 

photo.

Figure 3-2: Schematic of an instrumented soil specimen. 

O-ring 

V= confining 

 pressure 

c

Vҏ= axial pressure 

a

Fluid-Tight Seal

Steel Base Cap

Steel Top Cap 

Membrane

Specimen Preparation and Loading Instrumentation

Specimen Specimen

Axial

Deformation

Gages

Radial

Deformation

Gage
9 

earth materials is strongly dependent on the normal stress level. By performing strength tests at 

a range of confining pressure levels, the strength envelope (yield surface) of the material can be 

defined. The measured specimen deformations provide additional information on the material’s 

volumetric response to shear loading. For this effort, confining pressures of 2, 5, 10, 20, and 

50 psi were selected. Each test corresponds to a point on the strength (yield surface) curve, and 

the maximum shear stresses achieved at these pressures define the strength of the materials over 

the stress range of interest. The lower confining pressures simulate the near surface soil 

conditions. 

Two components of load are measured in the triaxial compression test. The measured confining 

pressure is equal to the radial stress on the specimen. Force is also measured in the axial 

direction, from which the axial stress is determined. The strength data in this report are 

presented in terms of true axial stress, Va. True axial stress is computed at each evenly spaced 

time interval. It is defined as the total axial load divided by the current cross sectional area of the 

specimen as derived from the radial deformation measurement. True stress difference, Vǻ, is the 

difference between the true axial stress and the confining pressure. Because the confining 

pressure is always applied to the current area, it is naturally a measure of true radial stress, Vc. 

For presentation of strength results, the true stress difference is plotted against true mean stress, 

V , which is the average of the stresses in three perpendicular directions. True mean stress is 

equal to pressure p in LS-DYNA, as explained in the following derivation. The triaxial test 

outputs are: 

 Vǻ = Va - Vc = true stress difference 

 V = (Va + 2Vc) / 3 = true mean stress 

where: Va = true axial stress 

 Vc = true radial stress = confining pressure 

 V = p = pressure, as explained in the following derivation 

To relate the triaxial test data to LS-DYNA’s yield surface, one must use Equation 19.5.1 in LSDYNA’s user manual (see Appendix A) to describe the shear failure surface in Material Model 5 

format: 

 

LS-DYNA Equation 2.10 specifies sij as the deviatoric stress tensor defined by: 

 

Where p is the pressure and q is the bulk viscosity. Because viscosity is not used in Material 

Model 5, q = 0. LS-DYNA Equation 2.11 defines p as: 

Equation 3-4 

Equation 3-3 

Equation 3-7 1 1

3 3 ij ij kk p   V G V

( ) Equation 3-6 ij ij ij s pq  V G

Equation 3-5 

2

01 2

1

2 ij ij ss a ap ap  
10 

 where: Vij = the stress tensor 

Gij = the Kronecker delta, which is one if the subscripts are the same and zero 

otherwise 

Equation 3-5 and Equation 3-7 are written using indicial notation, in which summation over the 

repeated subscripts in each term is implied. Thus, p is simply the mean (average) of the three 

diagonal components of the stress tensor, shown in Equation 3-4. 

In the special case of the triaxial compression test, the measured stresses are principal stresses 

and the intermediate principal stress is equal to the minimum principal stress. Specifically, the 

axial stress, Va, is the maximum principal stress and the other two principal stresses are equal to 

the confining pressure, Vc. In triaxial testing, one of the most important data outputs is principal 

stress difference, Vǻ, given in Equation 3-3. Vǻ is also referred to as the stress deviator. 

Because the stresses measured with respect to the axial and radial directions on the test specimen 

are principal stresses, the stress tensor expressed relative to those axes has no off-diagonal 

components, and is given by: 

Returning to Equation 3-6, the expanded version of the stress deviator tensor, s, is given by: 

 

In a triaxial compression test, p is given by: 

 

Equation 3-10 2

3

a c p

V  V 

Equation 3-9 

0 0

0 0

0 0

a

c

c

p

s p

p

V

V

V

a o 

« » 

¬ 1⁄4 

Equation 3-8 

0 0

0 0

0 0

a

c

c

V

V V

V

a o

« » « »

« » ¬ 1⁄4
11 

and: 

 

 

Thus, Equation 3-9, still for the special case of triaxial compression loading, can be re-written: 

 

The left hand side (LHS) of Equation 3-5 is the second invariant of the stress deviator tensor, 

defined as J2’: 

 

When the stress tensor is a diagonal, the indicial notation of Equation 3-14 expands to: 

 

Further, for the triaxial compression deviator stress tensor given by Equation 3-13, we have: 

 

The foregoing development details the methods for computing J2’ (the LHS of Equation 3-5) and 

p from the stresses measured in the triaxial compression tests at the strength limit (or elastic 

limit). Once triaxial data are converted to J2’ and p, one can plot the resulting of values of J2’

against p and perform a quadratic fit to define the required Material Model 5 coefficients, a0, a1, 

and a2. 

Equation 3-16    

2 2

2 2 2

2

1 21 1

23 3

J § · V ' ' V c    ̈  ̧ © 1

    Equation 3-15 

222

2 11 22 33

1

2

J sss c  a o ¬ 1⁄4

Equation 3-14 2

1

2 ij ij J ss c 

Equation 3-13 

2 0 0

3

0 0

3

0 0

3

s

V

V

V

'

'

'

a o

« »

 



¬ 1⁄4

Equation 3-11 3 3 2 2( ) 2

3 33

aa c a

a p

V V V VV V

V   '  

Equation 3-12 

3 2

3 33

ca c ca

c p

V V V VV V

V    '  
12 

An example strength envelope based on triaxial compression tests is presented in terms of mean 

stress and stress difference in Figure 3-4. Also shown is the linear fit to the triaxial compression 

test data that corresponds to reasonable values of cohesion and friction angle. To derive the 

coefficients for input to LS-DYNA, it is necessary to fit the square of the stress difference, as 

defined by Equation 3-16. The strength data is re-plotted in terms of J2’ versus pressure p, and is 

shown in Figure 3-5. Material Model 5 uses a quadratic fit to describe this yield surface, given 

in Equation 3-17. 

 

Therefore, the Material Model 5 strength coefficients are: 

0 0.490

1 1.386

2 0.979

A

A

A

 

 

 

Mean Stress (psi)

Stress Difference (psi)

0 5 10 15 20 25 30 35 40 45 50

0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

Bad Point?

V'=1.213+1.714V m i.e. I = 41.8q, C = 0.633 psi

Figure 3-4: Example strength envelope. Black points represent 

peak strengths from triaxial tests. Blue line is a strength fit. 

Equation 3-17 2

2 J   0.490 1.386 0.979 p p
13 

Pressure - P (psi)

Second Invariant of Deviator - J2 (psi2

)

NASA Cudeback B

0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

J2 = 0.49 + 1.386 P + 0.979 P2

Figure 3-5: Strength envelope in terms of LS-DYNA’s yield surface, J2’ vs. p. Black points from Figure 3-4 

are converted to J2’ and plotted as pink points. 

3.1.5 Hydrostatic compression 

Hydrostatic compression tests are also conducted using the triaxial device. In the hydrostatic 

compression test, the cylindrical soil specimens are loaded only by fluid (air) pressure, without 

any piston loading. The stresses on the specimen are the same in all directions and there is no 

shear stress on any plane. This is referred to as the hydrostatic state of compression. Material 

Model 5’s pressure p is equal to the fluid pressure. The results of these tests are used to define 

the volumetric deformation behavior of the material for modeling. The stress state is completely 

defined by the confining pressure. When confining pressure is reduced, the soil expands at a 

different rate than compression. This expanding rate yields the bulk unload modulus (BULK, 

see Table 2-1). 

In the laboratory, LVDT measurements are used to define axial and radial deformations which, 

in turn, are used to compute the current volume of the specimen at each time step. The 

volumetric strain, Hv, can be computed using the following equation: 
14 

 Where Vd = current (deformed) volume of the specimen 

and Vo = initial specimen volume (including grains and void space) 

3.1.5.1. Deriving constitutive parameters from hydrostatic compression 

The axial and radial specimen strains are recorded as the fluid pressure increases inside the 

vessel. The recorded data forms a pressure versus volumetric strain curve. The test typically 

starts with an initial rate of compression, denoted as I in Figure 3-6. 

Figure 3-6: Theoretical hydrostatic compression curve. Pressure p vs. volumetric strain İv. The slope of 

Segment IV, the unloading portion, corresponds to the bulk unloading modulus. (Figure © Leonard Schwer, 

LSTC class material) 

3.1.6 Uniaxial strain 

The uniaxial strain test also utilizes the triaxial device, albeit differently. In a uniaxial strain test, 

the axial stress and confining pressure are applied in such a way that the specimen undergoes 

compressive axial strain with no strain in the radial direction. The uniaxial strain loading is 

accomplished with an automated loading control system using the radial deformation 

measurement as feedback in the control loop. If the radial strain increases, the confining 

pressure is increased to return the radial strain to zero. Because no radial strain is allowed in a 

uniaxial strain test, the axial strain is equal to the volumetric strain in the specimen. There is a 

difference between axial and radial stress, and hence shear stresses exist in the specimen. 

However, the uniaxial strain constraint typically prevents the stress state from reaching the 

strength envelope, and failure of the specimen does not occur. The Material Model 5 shear 

modulus G and the pressure-volume curve can be derived from uniaxial strain data, as described 

in the following section. 

o

o d

v V

V V

H Equation 3-18
15 

3.1.6.1. Deriving constitutive parameters from uniaxial strain 

The elastic constants to calculate shear modulus G are derived from a uniaxial strain test. First, 

Poisson’s ratio can be obtained from an axial stress versus confining pressure plot, a uniaxial test 

output. There are two independent components of loading applied, confining pressure and axial 

load. Other linear combinations of these two independent components can yield other properties. 

For example, the mean stress and stress difference are invariants of the stress tensor and 

deviatoric stress tensor, respectively. To assure consistency, two different derivations of 

Poisson’s ratio are presented below. As an aid, example plots are provided. 

The first derivation is based on a relationship between axial stress and confining pressure. The 

elastic Poisson’s ratio value can be derived from the initial portion of the axial stress versus 

confining pressure curve. A fitted line is drawn over the initial curve portion. The inverse slope 

of the fitted line is commonly called lateral earth pressure, k0. Poisson’s ratio, Q, is related to k0

by: 

 

Figure 3-7 is an example application of the first method of obtaining Q from uniaxial test results. 

Commonly, there is a very small region at the beginning of the test where the data look 

somewhat incoherent because the loading piston is just making contact with the specimen. 

Usually, uniaxial strain control cannot maintained in this region because of sample “seating,” 

when the loading piston closes the tiny gaps between test hardware contact points. Because it 

occurs at very low stress only, it is ignored for this analysis. The Poisson ratio Q is derived from 

the initial linear portion of the test. In Figure 3-7, the initial linear portion reaches 35 psi axial 

stress. By fitting a line to that region, we find that it has a slope of 4.406. So k0 = 1/4.406. 

From Equation 3-19, k0 = 0.227 and Q = 0.185. 

Equation 3-19 0

0 1

k

k

Q 
16 

Figure 3-7: Example of axial stress vs. confining pressure plot from uniaxial test. 

The second method of deriving Q is to examine the stress path in terms of mean stress and stress 

difference. Uniaxial test data can be used to plot mean stress versus stress difference, as shown 

in Figure 3-8. The definitions of mean stress and stress difference are shown in Equation 3-3 and 

Equation 3-4. The slope of this different curve can also be used to calculate Q. 

In Figure 3-8, the slope does not have a commonly used name or symbol. For convenience, call 

the slope of the line k*. It is seen that k* = 1.598. Poisson’s ratio is related to k* by: 

 

Thus, Q = 0.185, which agrees with the first derivation. 

Confining Pressure (psi)

Axial Stress (psi)

0 25 50 75 100 125

0

25

50

75

100

125

k0 = 1/4.406 =>Q = 0.185

Uniaxial Strain Test Data

Slope = 4.406

Equation 3-20 

*

*

3

6

k

k

Q  
17 

Figure 3-8: Example of stress difference vs. mean stress plot from uniaxial test. 

The preceding paragraphs present two approaches to defining Poisson’s ratio, which is one 

elastic constant. It is necessary to have one more elastic constant for a complete set. Consider 

the stress-strain curves plotted in Figure 3-9. In a uniaxial strain test, the radial strain is 

constrained to be zero, and the axial strain is the same as the volume strain. In Figure 3-9, axial 

strain is plotted against both axial stress and mean stress. As with the definition of Poisson’s 

ratio, for the purpose of defining elastic constants, attention is confined to the initial linear 

regions of the curves. First, consider the axial stress curve in Figure 3-9. The initial slope of the 

axial stress curve is the constrained modulus, M, of the material. It is defined as the ratio of axial 

stress to axial strain under uniaxial strain conditions. From Figure 3-9, it is seen that M = 6950 

psi. 

Similarly, the slope of the mean stress-volume strain curve is defined as the bulk loading

modulus, K. Actually, bulk modulus is defined as the ratio of pressure to volumetric strain under 

hydrostatic loading, but as long as the material behaves elastically, this definition is equivalent. 

From Figure 3-9, K = 3370 psi. It is of interest to know how these values relate to other elastic 

constants. Recall that Young’s modulus, E, is the ratio of axial stress to axial strain under 

unconfined compression (or tensile) loading. The relations between E and the constrained and 

bulk moduli are: 

Equation 3-22 

Equation 3-21 

(1 )

(1 )(1 2 )

3(1 2 )

E M

E K

Q

Q Q

Q

  

 

Mean Pressure (psi)

Stress Difference (psi)

0 25 50 75 100 125

0

25

50

75

100

125

Slope = 1.598 => Q = 0.185

Uniaxial Strain Test Data

Slope = 1.598

Strength Envelope from Triax Tests
18 

From those two equations, it is straightforward to find the relationship between M and K: 

 

If the right hand side (RHS) of Equation 3-23 is computed from the values of M and K

determined above and the left hand side (LHS) is computed from Q, it is found that both are 

equal to 2.06. Thus, we have a consistent set of elastic constants. During Material Model 5 

input derivation, slight fit adjustments for constrained and bulk moduli were made to ensure 

Equation 3-23’s consistency. The final elastic constant of interest is the shear modulus, G, which 

is related to E and Q by: 

Equation 3-23 

3(1 )

(1 )

M

K

Q

Q

 

Axial Strain

Stress (psi)

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

0

25

50

75

100

125

Note: Both curves offset by -0.0002 (strain).

Axial Stress

Mean Stress

K = 3370 psi

M = 6950 psi

Figure 3-9: Example stress vs. strain curves from uniaxial test.

Equation 3-24 2(1 )

E G

Q 
19 

In summary, for the initial linear loading phase, the elastic constants for the example case are: 

Table 3-1: Example summary of elastic constants from uniaxial strain testing 

Young’s Modulus E 6370 psi 

Poisson’s Ratio Q 0.185 

Shear Modulus G 2690 psi 

Bulk Loading Modulus K 3370 psi 

Constrained Modulus M 6950 psi 

The unload bulk modulus is derived from the same uniaxial strain test data as shown in Figure 

3-9. Because bulk modulus is required, attention is restricted to the mean stress vs. volume 

strain curve. Figure 3-10 is an expanded view of the unload region. As the unloading behavior 

is not very linear, geotechnical expertise is used to approximate the curve with a single line. The 

portion shown as a heavy blue line was considered in the linear fit. The resulting value of unload 

modulus is Ku = 17,000 psi. 

Axial Strain

Mean Stress (psi)

0.025 0.03 0.035 0.04 0.045 0.05

0

25

50

75

100

125

Approx. Unload Bulk Modulus

Note: Curve offset by -0.0002 (strain).

Uniaxial Strain Test Data

Slope = 17,000 psi

Figure 3-10: Expanded view of the unload region of the uniaxial strain test. 
20 

According to the LS-DYNA documentation, the compressibility curve used for Material Mode 5 

is defined in terms of logarithmic strain, which is defined as: 

 

where: V = current volume 

 V0 = initial unstressed volume 

Because there is no radial strain in the uniaxial strain test, the cross sectional area remains 

constant and the logarithmic strain can be computed from the initial length and change in length 

of the specimen as: 

where: L0 = initial specimen length 

 'L = change in length (positive in compression) 

The logarithmic strain is negative in compression. The pressure-logarithmic strain curve from 

the uniaxial strain test is presented in Figure 3-11 along with the ten-point idealization for input 

to LS-DYNA. The tabulated points are: 

Table 3-2: Example pressure-volume points from uniaxial strain test. 

Pressure 

(psi)

Logarithmic 

Strain

0 0.0000

16.39 -0.0050

18.24 -0.0056

20.44 -0.0064

22.48 -0.0072

24.31 -0.0080

28.42 -0.0100

36.81 -0.0149

52.42 -0.0250

70.6 -0.0378

The ten points are chosen in such a way to best characterize the shape of the compressibility 

curve. 

log

0

ln V

V

H

§ ·  ̈  ̧ © 1 Equation 3-25 

0

log

0

ln L L

L

H

§ ·  '  ̈  ̧ © 1

Equation 3-26 
21 

Logarithmic Strain

Mean Stress (psi)

-0.05 -0.045 -0.04 -0.035 -0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0

0

20

40

60

80

100

Data from Uniaxial Strain Test

Points to Define Comp. Curve

Figure 3-11: Example of ten points on the pressure-volume compressibility curve in terms of logarithmic 

strain. 
22 

4 KSC Low Density Dry Sand 

The general description, field observations, test data, and Material Model 5 inputs for KSC Low 

Density Dry (LDD) Sand is discussed in this chapter. KSC LDD Sand comprises the soft 

shoreline near the beach dunes. It is above the waterline and almost completely dry. It is a fine 

sand deposited under low density conditions, making it the weakest and most compressible KSC 

sand. 

4.1 Location 

KSC lies on a sand bar deposit from the Eocene era (Ref. 9). Most of the surface sands were 

deposited within the last 7000 years, making all sands closely related in terms of origin. The 

sands near the KSC Pads have common parent material constituents and similar grain size 

distributions. Figure 4-1 is an aerial view of Launch Pads 39A and 39B. 

Figure 4-1: Aerial view of Kennedy Space Center. Pad A is the southernmost. Pad B is the northernmost 

(top of figure) 
23 

KSC LDD Sand lies along the coastal dunes. The KSC LDD Sand can reasonably represent any 

KSC sand deposit that falls under these conditions: fine sand, ~80 lbs/ft3

 surface density and < 

5% moisture content. Figure 4-2 displays a soil map and sands under similar conditions. 

Figure 4-2: KSC soil map, sourced from Dynamac (Ref. 9). “Palm Beach Sand” was the sampling source for 

KSC Low Density Dry Sand. Immokalee and Paola sand also fall under similar conditions. The areas labeled 

urbanland are Pads 39 A and B. 

4.2 General description 

KSC LDD Sand was the softest soil observed at KSC. It is a fine sand deposited by wind and 

ocean movements thousands of years. The sand type was observed to remain consistent to a 

depth of 30 inches. It is highly likely that the sand is uniform with depth across the entire KSC 

coastline. A small portion of the sand attributes its source to organic particle accumulation. The 

surf zone sand, KSC High Density Flooded Sand, contains higher organic particle content, such 
24 

as shell fragments. The natural methods of deposition add very little compaction to the soil. As 

a result, the soil surface deforms several percent strain when loaded with even small pressures. 

This is because LDD sand is cohesionless and very dependent upon confining pressure for 

strength. The sand’s ability to highly compress is due to the granular nature of sand when it is 

very dry. In the lack of moisture, there is no cohesive force to resist shear stress, and without 

significant confining pressure, the low density soil responds by compressing to a stronger density 

to support load. 

Most coastal terrain had less than a 5% slope except for the dunes. LDD sand’s surface is 

essentially barren of vegetation except for the dunes. Table 4-1 shows Dynamac’s field density 

measurements that were typically sampled up to 3 inches depth. A steel ring is driven to a 

shallow depth and the soil mass is recovered from inside the ring. Notice the very low field 

minimum density. This is due to very shallow sampling. The field minimum value of 56.2 

lbs/ft3

 appears to be very low, and may not be a realistic minimum value. It is also extremely 

difficult to handle a specimen below 80 lbs/ft3

, so all KSC LDD Sand tests were conducted at the 

minimum feasible density (Table 4-2). 

Table 4-1: Field density measurements from Dynamac 2000 report (Ref. 9) 

KSC coastal sand Samples N Field Min Field Max Mean

Wet Density (lbs/ft3) 23 56.2 87.4 74.3 

Table 4-2: Absolute density minimum and maximum from ARA laboratory’s 4”x8” specimen cylinder mold 

Absolute Lab 

Min

Absolute Lab 

Max

Min Feasible 

for Testing 

Wet Density (lbs/ft3) 64 99 80 

 Figure 4-3: KSC LDD Sand sampling site (left). Uniformity with depth apparent (right). 
25 

4.2.1 Soil classification 

KSC Low Density Dry Sand is classified as SP in the Unified Soil Classification System, a 

poorly graded fine sand. The poor gradation indicates that most particle sizes are about the 

same. Classification was based on standard sieve analysis. 

Table 4-3: KSC Low Density Dry Sand soil classification. Source – Dynamac 2000. 

Soil Class Mean Grain Size (mm) USCS Class 

Coastal (includes KSC Low Density Dry 

Sand and High Density In Situ w% Sand) 

0.31 SP, fine sand 

4.3 Laboratory test data 

Laboratory tests conducted on KSC LDD Sand are presented in this section. The test log 

summarizes the tests using the triaxial apparatus. 

Table 4-4: Test log for KSC LDD Sand. 

Test ID Sample 

ID 

Type Confining 

Pressure 

(psi) 

Moisture 

content 

Wet 

Density 

(lbs/ft3) 

Dry 

Density 

(lbs/ft3) 

Grain 

Density 

Gs

(g/cm3)

Porosity 

n

M10B08 Pad A Triax 2 3.05% 80.00 77.51 2.67 53.4% 

M10D08 Pad A Triax 5 3.04% 80.00 77.49 2.67 53.4% 

M11E08 Pad A Triax 10 2.78% 80.00 77.83 2.67 53.3% 

M11H08 Pad A Triax 20 2.78% 80.00 77.83 2.67 53.3% 

M12B08 Pad A Triax 50 2.89% 80.00 77.74 2.67 53.4% 

M12I08 Pad A Uniax 50 2.70% 80.00 77.84 2.67 53.3% 

A29C08 Pad A Uniax 50 3.20% 80.00 77.52 2.67 53.5% 

U24D09 Pad A Triax 75 3.28% 80.00 77.46 2.67 53.5% 

U26B09 Pad A Triax 100 3.06% 80.00 77.62 2.67 53.4% 

U29B09 Pad A Triax 75 2.96% 80.00 77.70 2.67 53.4% 

L10A09 Pad A Uniax 100 3.03% 80.00 77.65 2.67 53.4% 

4.3.1 Grain density and grain size analysis 

Figure 4-4 displays the dry sieve results for KSC LDD Sand. Dry sieve analysis was provided 

from the Dynamac report (Reference 9). ARA also performed sieve analysis on samples from 

the dunes near Pad A. These samples were used to construct specimens for KSC LDD testing. 

The Pad A samples have fewer course particles than the averaged coastal class sand. The 

flooded sand samples from the surf zone contain shell fragments, which increase the coarse grain 

count. From the “percent finer by weight”, the coefficient of uniformity (Cu) can be calculated 

by dividing the 60th percentile diameter by the 10th percentile. Sands with similar Cu have a 

similar ratio of large particles to small particles. The Pad A samples are a reasonable 
26 

representation of the averaged coastal area because of the similar distribution of particle sizes in 

the fine region. 

Grain Size in Millimeters

Percent Finer by Weight

Percent Coarser by Weight

Grain Size Distribution

5 4 3 2 1 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.07 0.05

#4 #6 #8 #10 #12 #16 #20 #30 #40 #50 #60 #70 #100 #140 #200 #270

U.S. Standard Sieve Sizes Hyd. Anal.

Silt or Clay Gravel Sand

F Coarse Medium Fine

0 100%

10% 90%

20% 80%

30% 70%

40% 60%

50% 50%

60% 40%

70% 30%

80% 20%

90% 10%

100% 0

Coefficient of Uniformity (Cu) for sands. Lower Cu= more uniform.

Dynamac KSC Coastal Class Sand (Dune and Beach, Averaged) Cu=1.6

ARA sampled KSC Dune sand near Pad A (LDD Model) Cu=1.9

Figure 4-4: KSC LDD Sand grain size distribution and coefficient of uniformity, and comparison with 

Dynamac average for coastal class sand. 

4.3.2 Triaxial compression 

The triaxial compression test results for KSC LDD Sand are shown in Figure 4-5 through Figure 

4-9. The notable difference between the new and old KSC LDD Sand model is the introduction 

of cohesion. The old model assumed no cohesion. The new model assumes a very small amount 

of cohesion, 0.25 psi. This cohesion produces a small intercept coefficient in the linear strength 

fit in Figure 4-7. The slope coefficient has barely changed in the new model, from 1.230 to 

1.222. The failure surface is essentially the same. 
27 

KSC LD Dry Sand - traixial all.grf

 Strain (%)

 True Stress Difference (psi)

KSC Low Density Dry Sand Triaxial Tests

78 lbs/ft3 dry density, 3% water content

Sample Source: Pad A

-15 -12.5 -10 -7.5 -5 -2.5 0 2.5 5 7.5 10 12.5 15 17.5 20

0

30

60

90

120

150

180

210

240

270

300

330

m Radial Axial o Confining Pressure (psi) and test date

 2 (2008)

 5 (2008)

 10 (2008)

 20 (2008)

 50 (2008)

100 (2009)

 75 (2009)

Figure 4-5: KSC LDD Sand triaxial test results. 
28 

KSC LD Dry Sand - Mohr Circle.grf

Normal Stress V (psi)

Shear Stress W (psi)

KSC Low Density Dry Sand Mohr Circles

78 lbs/ft3 dry density, 3% water content

0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500

0

25

50

75

100

125

150

175

200

225

250

Angle of internal friction 

I = 30.5q

Assumed cohesion = 0.25 psi

due to very low moisture

Confining pressures (psi) and test date

2 (2008)

5 (2008)

10 (2008)

20 (2008)

50 (2008)

75 (2009)

100 (2009)

Fit W = 0.25 + 0.589V

Figure 4-6: Mohr circles based on KSC LDD Sand’s triaxial tests 
29 

KSC LD Dry Sand - traixial stress diff vs mean stress.grf

Mean Stress P (psi)

Stress Difference 

V' (psi)

KSC Low Density Dry Sand Triaxial Tests

78 lbs/ft3 dry density, 3% water content

0 25 50 75 100 125 150 175 200 225 250

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

400

Correlation = 0.9988

Confining Pressures (psi) and test date

2 (2008)

5 (2008)

10 (2008)

20 (2008)

50 (2008)

75 (2009)

100 (2009)

Fit V' = 0.519 + 1.222P

Figure 4-7: KSC LDD Sand’s strength envelope from triaxial data. 
30 

Figure 4-8: Old versus new KSC LDD linear strength fit. 

KSC LD Dry Sand - traixial stress diff vs mean stress compare.grf

Mean Stress P (psi)

Stress Difference 

V' (psi)

KSC Low Density Dry Sand Triaxial Tests

78 lbs/ft3 dry density, 3% water content

0 20 40 60 80 100 120 140 160 180 200

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

Correlation = 0.9988

Confining Pressures (psi) and test date

2 (2008)

5 (2008)

10 (2008)

20 (2008)

50 (2008)

2008 Fit V'=1.23*P

75 (2009)

100 (2009)

2009 Fit V' = 0.519 + 1.222P
31 

KSC LD Dry Sand - traixial mean stress vs J2'.grf

Mean Stress P (psi)

Second Invariant J2' (psi2)

KSC Low Density Dry Sand

78 lbs/ft3 dry density, 3% water content

0 25 50 75 100 125 150 175 200 225

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

13000

14000

15000

Correlation = 0.9954

Confining Pressures (psi)

2

5

10

20

50

75

100

J2' = 0.08979 + 0.4228P + 0.4978P2

Figure 4-9: KSC LDD Sand, Material Model 5 yield surface fit from triaxial test data. 
32 

4.3.3 Hydrostatic compression 

A hydrostatic test was conducted prior to each triaxial test. The 100 psi hydrostatic test is shown 

in Figure 4-10. Midway through the hydrostatic test, the specimen was unloaded and reloaded. 

When 50 psi is reached for the first time, the specimen is unloaded to zero, then reloaded again 

until 100 psi is reached. Then the specimen is reloaded to 100 psi again, and the triaxial test is 

performed. 

The flat portions of the curve represent large deformations that occur very quickly. The low 

density sand is collapsing into a denser structure as more pressure is applied. When starting at 

this low density, the sand “jumps” to a higher density in discrete steps. This behavior stops after 

2.9% strain during the hydrostatic test. The uniaxial tests also show this behavior. 

The initial bulk modulus fit is drawn between zero and 1% strain, consistent with the modulus 

fits from the uniaxial tests. The bulk unload fits are drawn to the initial unloading portion of the 

curve, also consistent with the uniaxial fit. These fits reflect the hydrostatic test’s compression 

loading. It is important to note that uniaxial tests have shear and compression, and the peak 

mean stress is greater than the 100 psi confining pressure. The hydrostatic fits are not used to 

define the model, but they do provide additional insight. 
33 

KSC LD Dry Sand - hydrostatic 100 psi.grf

 Volumetric Strain (%)

 Confining Stress (psi)

KSC Low Density Dry Sand Hydrostatic Compression Test

78 lbs/ft3 dry density, 3% water content

100 psi confining pressure

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4

0

10

20

30

40

50

60

70

80

90

100

Hydrostatic compression test

100 psi Bulk Unload Fit Ku = 21180 psi

50 psi Bulk Unload Fit Ku = 15560 psi

Initial Bulk Modulus Fit K = 285 psi

Figure 4-10: 100 psi hydrostatic compression test on KSC LDD Sand. Hydrostatic fits are drawn to initial 

loading and unloading portions of the curve. 
34 

4.3.4 Uniaxial strain 

Three uniaxial strain tests were run on KSC LDD Sand, two at 50 psi and one at 100 psi. The 

100 psi uniaxial strain data for KSC LDD Sand is shown in Figure 4-11. Comparisons to the 50 

psi tests are show in Figure 4-12. Is it important to note the flat portion of all three tests. The 

flat portion physically represents the loading piston pressing into the specimen, but no additional 

load is seen by the load cell at the bottom of the specimen. This means the downward movement 

of the piston is compressing the sand, but the sand is collapsing without taking additional load. 

Void space within the sand is being closed, but without the soil skeleton transmitting additional 

load to the load cell at the bottom. This phenomenon is attributed to testing at such low 

densities. The skeleton collapses by forcing sand grains into void spaces until enough grain 

contacts have formed to carry additional load. 

The flat portion occurs at different strains in each test. Despite all three tests having the same 

target density (80lbs/ft3

), the specimen density can change when placed into the vessel. This is 

because low density cohesionless sands are very sensitive to movement. The sands will compact 

under slight vibration, resulting in slightly higher density. The change in axial length is known 

because the axial LVDT readings can be compared to the original specimen mold height. 

However, the radial change is not fully known due to vacuum and membrane. The sand’s 

density is not high enough to stretch the membrane to make uniform, full contact with the inner 

walls of the mold. Also, the specimen is placed under 0.5 psi vacuum to stabilize the sand for 

movement into the vessel. These factors slightly increase the specimen density before the test 

begins. This problem is only unique to testing KSC LDD Sand, as the other models have 

sufficient density to avoid these sensitivities. 

The stress-strains below 2% in Figure 4-12 show two uniaxial tests (red and blue curves) have 

very similar initial loading. The third (black curve) is higher. Also, once the skeleton collapse 

(flat portion) is complete, the slopes of all three tests appear parallel. The third test is suspected 

to have started at a higher density than the other two. The specimen most likely settled to higher 

density during handling. The higher density created an initial modulus much higher than the 

other two. Yet after the skeleton collapse, the parallel slopes suggest remarkably uniform 

behavior, even for the suspected higher density specimen. The KSC LDD model uses fits drawn 

to the red and blue curves because these specimens were closer to the target density when the test 

began, and the two tests were very similar during initial loading. The Poisson ratio and shear 

modulus G are derived from this initial loading. 

The ten selected pressure-volume points are based on the 100 psi uniaxial test. The comparison 

to the 2008 KSC HDD Sand model is shown in Figure 4-16. The new model experiences 1% 

more strain before stress load increases again, which occurs at 3.8% versus 2.8%. 
35 

KSC LD Dry Sand - uniaxial axial mean K and M.grf

Volumetric Strain (%)

Stress (psi)

KSC Low Density Dry Sand Uniaxial Strain Test

78 lbs/ft3 dry density,3% water content

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8 5.2 5.6 6 6.4 6.8 7.2 7.6 8

0

25

50

75

100

125

150

175

200

225

250

Axial stress

Mean stress

Bulk Modulus K = 169.3 psi

Constrained Modulus M = 267.5 psi

Figure 4-11: KSC LDD Sand 100 psi uniaxial strain test results. Constrained and bulk moduli fits shown. 

-
36 

KSC LD Dry Sand - uniaxial axial vs vol strain M.grf

Volumetric Strain (%)

Axial Stress (psi)

KSC Low Density Dry Sand Uniaxial Strain Test

78 lbs/ft3 dry density,3% water content

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8 5.2 5.6 6 6.4 6.8 7.2 7.6 8

0

20

40

60

80

100

120

140

160

180

200

220

Confining Pressure, Date

100 psi (July 2009)

50 psi (March 2008)

50 psi (April 2008)

Figure 4-12: Comparison of all three KSC LDD Sand uniaxial strain tests. One 100 psi test and two 50 psi 

tests. Axial stress vs. strain shown. 
37 

KSC LD Dry Sand - uniaxial shear mod G.grf

 Volumetric Strain (%)

 Stress Difference (psi)

KSC Low Density Dry Uniaxial Strain Test

78 lbs/ft3 dry density,3% water content

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8 5.2 5.6 6 6.4 6.8 7.2 7.6 8

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

Slope = 147.4 o G = 73.7 psi

Uniaxial strain test

Shear Modulus G = 73.7 psi

Figure 4-13: KSC LDD Sand 100 psi uniaxial strain test results plotted as stress difference vs. strain. Shear 

modulus G fit shown. Shear stress is half of stress difference. Uniaxial strain is equal to shear strain. 
38 

KSC LD Dry Sand - uniaxial bulk unload.grf

 Volumetric Strain (%)

 Mean Stress (psi)

KSC Low Density Dry Sand Uniaxial Strain Test

78 lbs/ft3 dry density, 3% water content

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8 5.2 5.6 6 6.4 6.8 7.2 7.6 8

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

Bulk Unload Modulus

Ku = 37390 psi

Uniaxial strain test

Bulk unload modulus fit

Figure 4-14: KSC LDD Sand 100 psi uniaxial strain unloading portion. Determination of bulk unloading 

modulus Ku (BULK) by linear fit to initial unloading. 
39 

KSC LD Dry Sand - uniaxial poisson.grf

 Confining Stress (psi)

 Axial Stress (psi)

KSC Low Density Dry Sand Uniaxial Strain Test

78 lbs/ft3 dry density,3% water content

0 20 40 60 80 100 120 140 160 180 200

0

15

30

45

60

75

90

105

120

135

150

165

180

195

210

225

240

255

270

285

300

Slope = 2.227 o X = 0.310

Uniaxial strain test

Poisson's ratio fit

Figure 4-15: KSC LDD Sand 100 psi uniaxial strain test. Determination of Poisson’s ratio via uniaxial strain 

test. 
40 

KSC LD Dry Sand - uniaxial pres-vol curve.grf

Logarithmic Volume Strain

True Mean Stress, P (psi)

KSC Low Density Dry Sand

78 lbs/ft3 dry density and 3% water content

50 and 100 psi Uniaxial strain tests

-0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

10-point fit to 50 psi test

50 psi Uniaxial Strain Test (2008)

100 psi Uniaxial strain test (2009)

10-point fit to 100 psi test

Figure 4-16: KSC LDD Sand Material Model 5 pressure-logarithmic volume curve with 10 input points. 

New (100 psi) and old (50 psi) models shown. 
41 

4.4 LS-DYNA Material Model 5 inputs 

The recommended set of inputs for modeling KSC LDD Sand at 78 lbs/ft3

 dry density and 3% 

water content in LS-DYNA Material Model 5: Soil and Foam is shown in the table below. 

Table 4-5: Material Model 5 inputs for KSC LDD Sand

 Input Value Units

Mass density RO 0.000120 lb s2

/in4

Shear modulus G 73.7 psi 

Bulk unloading modulus K 37390 psi 

Yield surface coefficient A0 0.08979 psi2

Yield surface coefficient A1 0.4228 psi 

Yield surface coefficient A2 0.4978 - 

Pressure cutoff PC -0.5 psi 

 

 Input Value Input Value Units

Pressure-volume point EPS1 0.0000 P1 0 psi 

Pressure-volume point EPS2 -0.01586 P2 2.685 psi 

Pressure-volume point EPS3 -0.03794 P3 2.85 psi 

Pressure-volume point EPS4 -0.04539 P4 18.14 psi 

Pressure-volume point EPS5 -0.04783 P5 18.66 psi 

Pressure-volume point EPS6 -0.05250 P6 33.2 psi 

Pressure-volume point EPS7 -0.05748 P7 48.9 psi 

Pressure-volume point EPS8 -0.06560 P8 88.05 psi 

Pressure-volume point EPS9 -0.06940 P9 111.24 psi 

Pressure-volume point EPS10 -0.07320 P10 134.8 psi 

Table 4-6: Summary of elastic constants 

Young's Modulus E 193 psi

Poisson's Ratio Q 0.310 

Shear Modulus G 73.7 psi

Initial Bulk Modulus K 169.3 psi

Constrained Modulus M 267.5 psi
42 

5 KSC High Density In Situ Moisture Sand 

This chapter describes the KSC High Density In situ moisture (HDI) Sand model. High density 

means the tested density reflects the more compacted areas around KSC. These include launch 

pads, road embankments, and other man-made areas. In situ moisture means that the sand was 

tested as sampled from the site. No changes in moisture content were made. The KSC HDI 

Sand model’s purpose is to simulate the denser, stiffer areas around Pads 39 A and B. These 

areas are denser than any naturally deposited sand. 

5.1 Location 

The KSC HDI Sand was sampled from man-made areas. Most notable was within the ring road 

of Pad 39 B. It represents the “Urbanland” zones marked in Figure 4-2. According to local 

KSC experts, the fill material was taken from nearby sources. The sands from man made areas 

are very similar to sands from other areas. It is not uncommon for coastal areas to have uniform 

sand deposits. 

5.2 General description 

Nearly all man-made areas are topped with grass-like vegetation. A sandy topsoil layer 1-2 

inches thick covers the surface. The topsoil can be described as a sandy organic mix. This thin 

layer was ignored for modeling purposes in favor of the underlying sand. The underlying sand 

was the sample source for the KSC HDI Sand model. 

The sands underlying man-made areas were also consistent with depth. The sand remained 

uniform to a depth of at least 30 inches. This is indicative of the geologically uniform sand 

deposits that created Merritt Island. The sand was also damp due to moisture being trapped 

underneath the topsoil. Topsoil prevents the sand from drying out. No bodies of water were 

nearby, and the pads are elevated above the waterline. Because no recent rains occurred, the 

moisture content obtained from samples is believed to be representative of most man-made areas. 

Figure 5-1 illustrates the topsoil layer. 

The unrealistic minimum density shown in Table 5-1 suggests the surface density measurements 

performed by Dynamac are not suitable for use in Orion impact modeling. The mean of 69.3 

lbs/ft3

 is extremely low and may represent the first inch of depth, but certainly not the range of 

interest for impact modeling. ARA ran exploratory tests at 90 lbs/ft3 wet density, but these were 

almost as soft as the KSC LDD sand model. Because the urban areas are mechanically flattened 

and compacted, ARA assumed a wet density of 100.3 lbs/ft3

 to represent a higher than natural 

relative density. 
43 

Table 5-1: Density measurements of surface sands from Dynamac 2000 report 

KSC disturbed sand (man-made areas) Samples N Field Min Field Max Mean

Wet Density (lbs/ft3) 22 37.4 87.4 69.3 

Table 5-2: KSC HDI Sand soil classification. Source – Dynamac 2000. 

Soil Class Mean Grain Size (mm) USCS Class 

Disturbed (man-made areas) 0.18 SP, fine sand 

Figure 5-1: Excavation at Pad 39 B, inside ring road. Topsoil is brown. Underlying sand is tan. 

5.3 Laboratory data 

The KSC HDI Sand is classified as poorly graded fine sand (USCS - SP). The Dynamac grain 

size distribution indicates that it is 75% fine sand, 10% medium sand, 5% coarse sand, and 10% 

organic fines. The organic fines come from the topsoil, and are not present at depth. The test log 

is shown in Table 5-3. ARA performed grain size distribution on samples extracted from within 

Pad B. The samples purposely do not contain topsoil because the sand itself is the focus of the 

model. These results are shown in Figure 5-2, and the fines are absent in ARA’s grain size 

distribution. This leads to the difference in the coefficient of uniformity. 
44 

Grain Size in Millimeters

Percent Finer by Weight

Percent Coarser by Weight

Grain Size Distribution

5 4 3 2 1 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.07 0.05

#4 #6 #8 #10 #12 #16 #20 #30 #40 #50 #60 #70 #100 #140 #200 #270

U.S. Standard Sieve Sizes Hyd. Anal.

Silt or Clay Gravel Sand

F Coarse Medium Fine

0 100%

10% 90%

20% 80%

30% 70%

40% 60%

50% 50%

60% 40%

70% 30%

80% 20%

90% 10%

100% 0

Coefficient of Uniformity (Cu) for sands. Lower Cu= more uniform.

Dynamac Urbanland Class Sand (Pad areas with topsoil, Averaged) Cu=2.5

ARA sampled KSC Interior Pad B beneath topsoil (HDI Model) Cu=1.4

Figure 5-2: Grain size distribution for KSC HDI Sand, compared to Dynamac average. 

 

Table 5-3: Test log for KSC HDI Sand. * The italicized tests were not used to create the KSC HDI model. 

Test ID Sample ID Type Confining 

Pressure 

(psi) 

Moisture 

content 

Wet 

Density 

(lbs/ft3

) 

Dry 

Density 

(lbs/ft3

) 

Grain 

Density Gs

(g/cm3

)

Porosity 

n

M28A08* Pad B Uniax 50 15.32% 90 78.04 2.67 53.2% 

M31C08* Pad B Triax 2 16.96% 90 76.95 2.67 53.9% 

M31E08* Pad B Triax 5 16.60% 90 77.19 2.67 53.8% 

A1C08* Pad B Triax 10 17.25% 90 76.76 2.67 54.0% 

A2A08 Pad B Triax 2 15.75% 100.3 86.62 2.67 48.0% 

A8B08 Pad B Triax 2 15.69% 100.3 86.42 2.67 48.0% 

A7E08 Pad B Triax 5 18.37% 100.3 84.43 2.67 49.2% 

A7C08 Pad B Triax 10 17.65% 100.3 84.93 2.67 48.9% 

A3A08 Pad B Triax 20 16.31% 100.3 85.94 2.67 48.3% 

A4A08 Pad B Triax 50 16.27% 100.3 85.98 2.67 48.3% 

A10B08 Pad B Uniax 50 15.76% 100.3 86.41 2.67 48.0% 

Y12B09 Pad B Triax 75 N/A 100.3 N/A 2.67 N/A 

Y13D09 Pad B Triax 75 13.71% 100.3 88.18 2.67 47.1% 

Y14B09 Pad B Triax 100 14.81% 100.3 87.34 2.67 47.6% 

L9A09 Pad B Uniax 100 16.52% 100.3 86.05 2.67 48.3% 

G13B09 Pad B Triax 50 16.10% 100.3 86.36 2.67 48.0% 
45 

5.3.1 Triaxial compression 

The KSC HDI model was extended to higher pressures via three additional triaxial tests. The 50 

psi triaxial was repeated, and an additional 75 and 100 psi tests were performed. In total, the 

triaxial strength envelope is based on 8 triaxial tests at 2, 5, 10, 20, 50, 75, and 100 psi confining 

pressures (50 psi ran twice). The 50 psi test was repeated because it was truncated at 10% strain 

in 2008. Although truncated, it was already well past the peak strength and did not affect the 

model. In 2009, testing resumed at 50 psi to confirm the same peak strength. After testing, the 

peak strength differed only by 1 psi. The 2008 test peaked at 108.7 psi, and the 2009 test peaked 

at 109.7 psi. The results are shown Figure 5-3. Strength envelope analysis and LS-DYNA yield 

surface fits are shown in Figure 5-5 and Figure 5-7. 

The new model’s strength parameters are similar to the old, but weaker. The linear fit 

coefficients in Figure 5-5 have a reduced slope coefficient. The new 75 and 100 psi data points 

fall short of a linear extension of the old model, but do not stray far. The 50 psi test was ignored 

in the old model; it is included in the new model due to the new focus on higher stress behavior. 

The slope coefficient was reduced to fit the 50, 75, and 100 psi points. Overall, the model’s 

strength did not change significantly. 
46 

KSC HD in situ w% Sand - triaxial all.grf

 Strain (%)

 True Stress Difference (psi)

KSC High Density In Situ Moisture Sand Triaxial Tests

87 lbs/ft3 dry density, 16% water content

Sample Source: Pad B

-15 -12.5 -10 -7.5 -5 -2.5 0 2.5 5 7.5 10 12.5 15 17.5 20

0

30

60

90

120

150

180

210

240

270

300

330

m Radial Axial o

Confining Pressures (psi) and test date

 2 (2008)

 5 (2008)

 10 (2008)

 20 (2008)

 50 (2008)

 75 (2009)

100 (2009)

 50 (2009)

Figure 5-3: KSC HDI Sand model’s triaxial compression test results. Performed 50 psi test twice. 
47 

KSC HD in situ w% Sand - Mohr Circle.grf

Normal Stress V (psi)

Shear Stress W (psi)

KSC High Density In-situ Moisture Sand Mohr Circles

87 lbs/ft3 dry density, 16% water content

0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500

0

25

50

75

100

125

150

175

200

225

250

Internal angle of friction 

I = 31.5q

Assumed 1 psi cohesion

due to water

Confining Pressures (psi) and Date

2 (2008)

5 (2008)

10 (2008)

20 (2008)

50 (2008)

75 (2009)

100 (2009)

Fit W = 1 + 0.6116*V

50 (2009)

Figure 5-4: Mohr circles for KSC HDI Sand. Mohr circles for 50 psi tests plot essentially on top of each 

other. 
48 

KSC HD in situ w% Sand - strength envelope.grf

Mean Stress P (psi)

Stress Difference 

V' (psi)

KSC High Density in situ moisture Sand

87 lbs/ft3 dry density, 16% water content

0 25 50 75 100 125 150 175 200 225 250

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

400

Correlation = 0.9992

Confining Pressures (psi) and test date

2 (2008)

5 (2008)

10 (2008)

20 (2008)

50 (2008)

75 (2009)

100 (2009)

Fit V' = 2.065 + 1.260*P

Figure 5-5: KSC HDI Sand model’s strength envelope. The two 50 psi peak strengths were combined into 

one value. 
49 

KSC HD in situ w% Sand - strength envelope compare.grf

Mean Stress P (psi)

Stress Difference 

V' (psi)

KSC High Density in situ moisture Sand

87 lbs/ft3 dry density, 16% water content

0 20 40 60 80 100 120 140 160 180 200

0

15

30

45

60

75

90

105

120

135

150

165

180

195

210

225

240

Correlation = 0.9992

Confining Pressures (psi) and test date

2 (2008)

5 (2008)

10 (2008)

20 (2008)

50 (2008)

2008 Fit V' = 2.028 + 1.382*P

75 (2009)

100 (2009)

2009 Fit V' = 2.065 + 1.260*P

Figure 5-6: Old versus new KSC HDI linear strength fit. 
50 

KSC HD in situ w% Sand - J2' v P.grf

Mean Stress P (psi)

Second Invariant J2' (psi2)

KSC High Density in-situ moisture Sand

87 lbs/ft3 dry density, 16% water content

0 25 50 75 100 125 150 175 200 225

0

3000

6000

9000

12000

15000

18000

21000

24000

27000

30000

Correlation = 0.9989

Confining Pressures (psi)

2

5

10

20

50

75

100

Fit J2' = 1.421 + 1.734P + 0.529*P2

Figure 5-7: KSC HDI Sand Material Model 5 yield surface fit from triaxial data. The two 50 psi peak 

strengths were combined into one value. 
51 

5.3.2 Hydrostatic compression 

The hydrostatic test loads the specimen to 50 psi, then unloads, then reloads to 100 psi. These 

two cycles are shown in Figure 5-8, plotted on the same scale as KSC LDD Sand in Figure 4-10 

to illustrate the relative stiffness between the two. The fits shown below are not used in the KSC 

HDI model, but shown for comparison to the uniaxial data in the next section. 

KSC HD in situ w% Sand - hydrostat 100 psi.grf

 Volumetric Strain (%)

 Confining Stress (psi)

KSC HDI Sand Hydrostatic Compression Test

87 lbs/ft3 dry density, 16% water content

100 psi confining pressure

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4

0

10

20

30

40

50

60

70

80

90

100

Hydrostatic compression test

Initial bulk modulus fit K = 1107 psi

50 psi bulk unload fit Ku 13940 psi

100 psi bulk unload fit Ku = 20440 psi

Figure 5-8: 100 psi hydrostatic compression test for KSC HDI Sand. 
52 

5.3.3 Uniaxial strain 

KSC HDI Sand model’s uniaxial strain test results are shown in Figure 5-9 through Figure 5-13. 

The 100 psi uniaxial strain test compares very favorably with the previous 50 psi test. The 100 

psi test essentially extends where the 50 psi test terminated. The new model is a higher pressure 

extension of the old model with very similar properties. 

KSC HD in situ w% Sand -uniaxial axial stress vs conf stress.grf

 Confining Stress (psi)

 Axial Stress (psi)

KSC High Density In-situ Moisture Sand Uniaxial Strain Test

87 lbs/ft3 dry density, 16% water content

0 25 50 75 100 125 150 175 200 225 250

0

25

50

75

100

125

150

175

200

225

250

275

300

325

350

375

400

425

450

475

500

Slope = 2.611 o Q = 0.277

Uniaxial strain test

Poisson's ratio fit

Figure 5-9: KSC HDI Sand model’s uniaxial strain test. Axial stress vs. confining stress plotted to calculate 

Poisson’s ratio from slopes. 
53 

KSC HD in situ w% Sand -uniaxial stress vs strain.grf

 Axial Strain (%)

Stress (psi)

KSC High Density In-situ Moisture Sand

87 lbs/ft3 dry density, 16% water content

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

400

Bulk Modulus K = 2537 psi

Constrained

Modulus

M = 4562 psi

Axial stress

Mean stress

Fits

Figure 5-10: KSC HDI Sand model’s uniaxial strain test. Stress vs. axial strain plotted to obtain constrained 

modulus from axial stress and Initial Bulk Modulus from mean stress. 
54 

KSC HD in situ w% Sand -uniaxial stress diff vs strain.grf

 Volumetric Strain (%)

 Stress Difference (psi)

KSC High Density In-situ Moisture Sand Uniaxial Strain Test

87 lbs/ft3 dry density, 16% water content

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

Slope = 2814 psi

Shear Modulus G = 1407 psi

Uniaxial strain test

Fit

Figure 5-11: KSC HDI Sand model’s uniaxial strain test. Stress difference vs. strain difference plotted to 

obtain shear modulus G. 
55 

KSC HD in situ w% Sand - mean stress vs strain.grf

 Axial Strain (%)

Mean Stress (psi)

KSC High Density In-situ Moisture Sand

87 lbs/ft3 dry density, 16% water content

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

Bulk Unload Modulus

Ku = 43428 psi

Uniaxial strain test

Bulk Unload Modulus

Figure 5-12: KSC HDI Sand model’s uniaxial strain test. Mean stress vs. volumetric strain plotted to obtain 

bulk unloading modulus Ku (BULK). Fit drawn to initial unloading. 
56 

KSC HD in situ w% Sand -uniaxial pres-vol curve.grf

Logarithmic volume strain

True Mean Stress, P (psi)

KSC High Density in situ moisture sand

87 lbs/ft3 dry density and 16% water content

50 and 100 psi uniaxial strain tests

-0.015 -0.0135 -0.012 -0.0105 -0.009 -0.0075 -0.006 -0.0045 -0.003 -0.0015 0

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

100 psi Uniaxial Strain Test (2009)

10-point fit to 100 psi test

50 psi Uniaxial Strain Test (2008)

10-point fit to 50 psi test

Figure 5-13: KSC HDI Sand model’s uniaxial strain tests. Mean stress vs. logarithmic volume strain plotted 

to obtain 10 pressure-volume points for Material Model 5 compressibility curve. 
57 

Logarithmic volume strain

True Mean Stress, P (psi)

Uniaxial compression test

Alternate 90 lbs/ft3 wet density test on Pad B Sand

-0.04 -0.036 -0.032 -0.028 -0.024 -0.02 -0.016 -0.012 -0.008 -0.004 0

0

4

8

12

16

20

24

28

32

36

40

44

48

52

56

60

64

68

72

76

80

78 lbs/ft3 dry density and 16% water

Figure 5-14: Alternate test run on Pad B sample material at 90 lbs/ft3 wet density (see Table 5-3). This 

condition was not used to construct the KSC HDI Sand model. 
58 

5.4 LS-DYNA Material Model 5 inputs 

The recommended set of inputs for modeling KSC HDI Sand at 87 lbs/ft3

 dry density and 16% 

water content in LS-DYNA Material Model 5: Soil and Foam is shown in the table below. The 

pressure-volume points are based on the 100 psi uniaxial test. 

Table 5-4: Material Model 5 inputs for KSC HDI Sand 

 Input Value Units

Mass density RO 0.000150 lb s2

/in4

Shear modulus G 1407 psi 

Bulk unloading modulus K 43428 psi 

Yield surface coefficient A0 1.421 psi2

Yield surface coefficient A1 1.734 psi 

Yield surface coefficient A2 0.529 - 

Pressure cutoff PC -1.0 psi 

 

 Input Value Input Value Units

Pressure-volume point EPS1 0 P1 0 psi 

Pressure-volume point EPS2 -0.001 P2 2.537 psi 

Pressure-volume point EPS3 -0.002 P3 7.191 psi 

Pressure-volume point EPS4 -0.003 P4 13.00 psi 

Pressure-volume point EPS5 -0.004 P5 20.12 psi 

Pressure-volume point EPS6 -0.006 P6 37.68 psi 

Pressure-volume point EPS7 -0.008 P7 60.14 psi 

Pressure-volume point EPS8 -0.010 P8 85.07 psi 

Pressure-volume point EPS9 -0.012 P9 113.2 psi 

Pressure-volume point EPS10 -0.01394 P10 141.9 psi 

Table 5-5: Summary of elastic constants 

Young's Modulus E 3594 psi

Poisson's Ratio Q 0.277 

Shear Modulus G 1407 psi

Initial Bulk Modulus K 2537 psi

Constrained Modulus M 4562 psi
59 

6 Mason Sand at 97/4% 

Mason Sand is the surrogate KSC sand used at the Orion boilerplate drop test site at LaRC. 

ARA produced four Mason Sand models at four distinct conditions. This chapter describes the 

Mason Sand model at 97 lbs/ft3

 dry density and 4% water content. 

6.1 Laboratory test data 

LaRC identified three locally available sands for purchase and requested ARA perform grain size 

analysis to identify the closest one to KSC sands. The results are shown in Figure 6-2. The 

Yorktown Mason Sand was the closest match to KSC Pad A sand. The coefficient of uniformity 

was the closest, and both were sub-angular to sub-rounded particle shape. After the Mason Sand 

was selected for use in the Orion boilerplate drop tests, ARA performed minimum and maximum 

density analysis. ARA dried the Mason Sand and carefully placed it into a 4 inch diameter by 8 

inch tall cylinder to achieve the lowest density in that volume. ARA also compacted the dried 

sand in one inch lifts to achieve the maximum density. The results are shown in Table 6-1. 

Although similar in grain size distribution, Mason Sand’s density values vary considerably from 

KSC LDD sand because the shell fragments in KSC LDD reduce the density. These fragments 

are much larger than the sand grains and are lower than the grain density (see Figure 6-1). 

Table 6-1: Minimum and maximum density of Mason Sand 

Based on 4”x8” cylinder mold Minimum Maximum

Dry Density (lbs/ft3) 92.5 107.8 

Figure 6-1: KSC LDD (left) and Mason Sand (right) visual comparison. Note the shell fragments in the KSC 

LDD sand. 

ARA conducted five triaxial tests and two uniaxial tests for this Mason Sand model. The triaxial 

confining pressures were 10, 20, 50, 75, and 100 psi. The second uniaxial test was run at 96 

lbs/ft3

, which was an early exploratory test to investigate the effects of lower density. There was 
60 

also a 100 psi hydrostatic compression test which unloaded and reloaded at 50 and 100 psi. The 

test log for Mason Sand at 97 lbs/ft3

 dry density and 4% water content is shown in Table 6-2. 

Table 6-2: Test log for Mason Sand at 97/4% 

Test ID Sample ID Type Confining 

Pressure 

(psi) 

Moisture 

content 

Wet 

Density 

(lbs/ft3

) 

Dry 

Density 

(lbs/ft3

) 

L28B09 Mason Sand Triax 10 4.16% 100.88 96.85 

L29B09 Mason Sand Triax 20 4.08% 100.88 96.92 

L31E09 Mason Sand Triax 50 4.04% 100.88 96.96 

G3B09 Mason Sand Triax 75 3.97% 100.88 97.02 

G4G09 Mason Sand Triax 100 4.01% 100.88 96.99 

G25A09 Mason Sand Uniax 100 4.05% 100.88 96.95 

L14C09 Mason Sand Uniax 100 4.07% 99.84 95.94

Grain Size in Millimeters

Percent Finer by Weight

Percent Coarser by Weight

KSC Sands vs. Surrogate Sand Candidates

Grain Size Distribution

5 4 3 2 1 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.07 0.05

#4 #6 #8 #10 #12 #16 #20 #30 #40 #50 #60 #70 #100 #140 #200 #270

U.S. Standard Sieve Sizes Hyd. Anal.

Silt or Clay Gravel Sand

F Coarse Medium Fine

0 100%

10% 90%

20% 80%

30% 70%

40% 60%

50% 50%

60% 40%

70% 30%

80% 20%

90% 10%

100% 0

Coefficient of Uniformity (Cu) for sands. Lower Cu= more uniform.

ARA sampled KSC Dune sand near Pad A (LDD Model) Cu=1.9

ARA sampled KSC Interior Pad B beneath topsoil (HDI Model) Cu=1.4

Branscome - Charles City Class A Sand Cu=2.9 (vendor data)

Yorktown Mason Sand (acutal) Cu = 2.1

Yorktown Materials Concrete Sand Cu=2.7

Figure 6-2: Grain size distribution for KSC surrogate sand candidates 
61 

6.1.1 Correlating Mason Sand to “Clean Sand” from 2008 

LaRC also asked ARA to compare some sand that was already on-site at the gantry facility to the 

Mason Sand. This sand was tested and referred to as “clean sand” in the 2008 report. LaRC 

wished to ascertain the source of this sand by comparing the grain size distributions. The sand’s 

vendor source was unknown. A new 2009 sample was taken and compared to the actual Mason 

Sand sample, as well as the older 2008 clean sand sample. The results of the analysis are shown 

in Figure 6-3. The clean sand is most likely the same as Mason Sand because it displays 

remarkably similar distributions. 

Sieve Size

Percent Finer by Weight

Percent Coarser by Weight

Gantry's Clean Sand Correlated to Mason Sand

Grain Size Distribution

5 4 3 2 1 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.07 0.05

#4 #6 #8 #10 #12 #16 #20 #30 #40 #50 #60 #70 #100 #140 #200 #270

U.S. Standard Sieve Sizes Hyd. Anal.

Silt or Clay Gravel Sand

F Coarse Medium Fine

0 100%

10% 90%

20% 80%

30% 70%

40% 60%

50% 50%

60% 40%

70% 30%

80% 20%

90% 10%

100% 0

Sand type with Coefficient of Uniformity Cu. Lower Cu = more uniform

Old "Gantry Clean Sand" (sampled Feb 2008) Cu = 2.6

Yorktown Mason Sand (acutal) Cu = 2.1

New LaRC Gantry Sand (sampled May 2009) Cu=2.7

Figure 6-3: Correlation of Mason Sand and Gantry “Clean Sand”. 
62 

6.1.2 Triaxial compression 

ARA performed five triaxial tests for each condition of Mason Sand. Results are shown in 

Figure 6-3 through Figure 6-14. In Figure 6-14, the slightly denser 97 lbs/ft3

 was less stiff at 

mean stresses above ~30 psi than the 96 lbs/ft3

 sand. We believe this is due to natural variations 

of the material and experimental accuracies. 

Figure 6-4 illustrates the physical deformation of the Mason Sand specimen after the triaxial test 

is complete. The zoom boxes show the radial strain gage before and after the test. 

Figure 6-4: Photographs of Mason Sand triaxial test 

BEFORE AFTER 
63 

Mason Sand - 97 pcf 4% Triax.grf

 Strain (%)

 True Stress Difference (psi)

Mason Sand Triaxial Compression Tests

97 lbs/ft3 dry density, 4% water content

-12 -10.5 -9 -7.5 -6 -4.5 -3 -1.5 0 1.5 3 4.5 6 7.5 9

0

30

60

90

120

150

180

210

240

270

300

330

m Radial Axial o

Confining Pressures (psi)

 10

 20

 50

 75

100

Figure 6-5: Mason Sand triaxial test results for 10, 20, 50, 75, and 100 psi confining pressures. 
64 

Mason Sand - 97 pcf 4% Mohr Circle.grf

Normal Stress V (psi)

Shear Stress W (psi)

Mason Sand Mohr Circles

97 lbs/ft3 dry density, 4% water content

0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500

0

25

50

75

100

125

150

175

200

225

250

Internal angle of friction M = 35.3q

Assumed 1 psi cohesion

due to moisture

Triaxial Confining Pressures (psi)

10

20

50

75

100

Linear fit W = 1 + 0.7074V

Figure 6-6: Mohr circles based on Mason Sand’s triaxial tests 
65 

Mason Sand - 97pcf 4% Triax strength linear.grf

Mean Stress P (psi)

Stress Difference 

V' (psi)

Mason Sand Triaxial Tests

Udry = 97 lbs/ft3 and w=4%

Peak stress differences plotted

0 25 50 75 100 125 150 175 200 225 250

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

400

V' = k + aP

k = (6*c*cos M)/(3-sin M)

c = 1 psi cohesion

Correlation = 0.9990

10

20

50

75

100

Fit V' = 2.0217 + 1.418P

Figure 6-7: Mason Sand strength envelope results. 
66 

Mason Sand - 97 pcf 4% Triax J2' vs P.grf

Mean Stress P (psi)

Second Invariant J2' (psi2)

Mason Sand Triaxial Tests

Udry = 97 lbs/ft3 and w=4%

0 25 50 75 100 125 150 175 200 225

0

5000

10000

15000

20000

25000

30000

35000

Correlation = 0.9989

Confining pressures (psi)

10

20

50

75

100

Fit J2' = 1.362+1.911P+0.670P2

Figure 6-8: Mason Sand Material Model 5 yield surface fit from triaxial test data. 

 
67 

6.1.3 Hydrostatic compression 

Following the loading prescription for KSC sands, the Mason Sands were hydrostatically 

compressed to 50 psi and unloaded to zero pressure. Then, they were loaded to 100 psi and 

unloaded again. Finally, they were returned to 100 psi for a second time. The hydrostatic 

loading preceded each of the triaxial tests. Figure 6-9 is the hydrostatic compression test 

preceding the 100 psi triaxial strength test. 

Mason Sand - 97 pcf 4%w hydrostat.grf1

 Volumetric Strain (%)

 Confining Stress (psi)

Mason Sand Hydrostatic Compression Test

97 lbs/ft3 dry density, 4% water content

100 psi confining pressure

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

0

10

20

30

40

50

60

70

80

90

100

Hydrostatic compression test

Initial bulk modulus K = 2997 psi

50 psi bulk unload modulus Ku = 16550 psi

100 psi bulk unload modulus Ku = 25520 psi

Figure 6-9: 100 psi hydrostatic compression test of Mason Sand at 97/4% condition. Hydrostatic fits drawn. 
68 

6.1.4 Uniaxial strain 

Mason Sand - 97 pcf 4%w uniax modulus K, M.grf

 Axial Strain (%)

Stress (psi)

Mason Sand Uniaxial Strain Test

97 lbs/ft3 dry density and 4% water content

100 psi confining pressure

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

0

25

50

75

100

125

150

175

200

225

250

275

300

325

350

375

400

425

450

475

500

Axial stress

Mean stress

Bulk Modulus K = 2760 psi

Constrained Modulus M = 5096 psi

Figure 6-10: Mason Sand uniaxial strain test results. Constrained and bulk moduli fits shown. 
69 

Mason Sand - 97 pcf 4%w uniax shear mod G.grf

 Volumetric Strain (%)

 Stress Difference (psi)

Mason Sand Uniaxial Strain Test

97 lbs/ft3 dry density and 4% water content

100 psi confining pressure

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

Uniaxial strain test

Shear Modulus G = 1752 psi

Figure 6-11: Mason Sand uniaxial strain test results plotted as stress difference vs. strain. Shear modulus G 

fit shown. Shear stress is half of stress difference. Uniaxial strain is equal to shear strain. 
70 

Mason Sand - 97 pcf 4%w uniax bulk unload.grf

 Volume Strain (%)

Mean Stress (psi)

Mason Sand Uniaxial Strain Test

97 lbs/ft3 dry density and 4% water content

100 psi confining pressure

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

Uniaxial strain test

Bulk Unload Modulus fit Ku = 56470 psi

Figure 6-12: Mason Sand uniaxial strain unloading portion. Determination of bulk unloading modulus Ku

(BULK) by linear fit. 
71 

Mason Sand - 97 pcf 4%w uniax poisson.grf

 Confining Stress (psi)

 Axial Stress (psi)

Mason Sand Uniaxial Strain Test

97 lbs/ft3 dry density, 4% water content

100 psi confining pressure

0 25 50 75 100 125 150 175 200 225 250

0

25

50

75

100

125

150

175

200

225

250

275

300

325

350

375

400

425

450

475

500

Slope = 3.195 o Q = 0.238

Uniaxial strain test

Poisson ratio fit Q = 0.238

Figure 6-13: Determination of Poisson’s ratio via uniaxial strain test. 
72 

Mason Sand - 97 pcf 4%w uniax pres-vol.grf

Logarithmic Volume Strain

 Mean Stress (psi)

Mason Sand Uniaxial Strain Test

97 lbs/ft3 dry density and 4% water content

100 psi confining pressure

-0.012 -0.011 -0.01 -0.009 -0.008 -0.007 -0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

Uniaxial strain test

Material Model 5 Pressure-Volume input points

Figure 6-14: Mason Sand Material Model 5 pressure-logarithmic volume curve with 10 input points. 

Obtained from uniaxial strain test. 
73 

Mason Sand - 97 pcf 4%w uniax pres-vol compare.grf

Logarithmic Volume Strain

 Mean Stress (psi)

Mason Sand Uniaxial Strain Test

97 lbs/ft3 vs 96 lbs/ft3 dry density and both 4% water content

100 psi confining pressure

-0.012 -0.011 -0.01 -0.009 -0.008 -0.007 -0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

Dry density comparison

97 lbs/ft3

96 lbs/ft3

Figure 6-15: Comparison of 96 vs. 97 lbs/ft3 dry densities at the same 4% water content. 
74 

6.2 LS-DYNA Material Model 5 inputs 

The recommended set of inputs for modeling Mason Sand at 97 lbs/ft3

 dry density and 4% water 

content in LS-DYNA Material Model 5: Soil and Foam is shown in the table below. 

Table 6-3: Material Model 5 inputs for Mason Sand 

 Input Value Units

Mass density RO 0.000151 lb s2

/in4

Shear modulus G 1752 psi 

Bulk unloading modulus K 56470 psi 

Yield surface coefficient A0 1.362 psi2

Yield surface coefficient A1 1.911 psi 

Yield surface coefficient A2 0.670 - 

Pressure cutoff PC -0.5 psi 

 

 Input Value Input Value Units

Pressure-volume point EPS1 0 P1 0.00 psi 

Pressure-volume point EPS2 -0.001 P2 2.76 psi 

Pressure-volume point EPS3 -0.002 P3 8.43 psi 

Pressure-volume point EPS4 -0.003 P4 17.26 psi 

Pressure-volume point EPS5 -0.004 P5 28.49 psi 

Pressure-volume point EPS6 -0.005 P6 42.96 psi 

Pressure-volume point EPS7 -0.006 P7 59.90 psi 

Pressure-volume point EPS8 -0.007 P8 79.15 psi 

Pressure-volume point EPS9 -0.009 P9 125.63 psi 

Pressure-volume point EPS10 -0.01031 P10 160.80 psi 

Table 6-4: Summary of elastic constants 

Young's Modulus E 4339 psi

Poisson's Ratio Q 0.238 

Shear Modulus G 1752 psi

Initial Bulk Modulus K 2760 psi

Constrained Modulus M 5096 psi
75 

7 Mason Sand at 96/8% 

This chapter describes properties for the Mason Sand model at 96 lbs/ft3

 dry density and 8% 

water content. The test log is shown in Table 7-1. 

Table 7-1: Test log for Mason Sand at 96/8% 

Test ID Sample ID Type Confining 

Pressure 

(psi) 

Moisture 

content 

Wet 

Density 

(lbs/ft3) 

Dry 

Density 

(lbs/ft3) 

G18B09 Mason Sand Triax 10 8.04% 103.68 95.97 

G19C09 Mason Sand Triax 20 8.08% 103.68 95.93 

G19E09 Mason Sand Triax 50 7.86% 103.68 96.13 

G19G09 Mason Sand Triax 75 7.83% 103.68 96.16 

G20A09 Mason Sand Hydro 100 8.08% 103.68 95.93 

G20B09 Mason Sand Triax 100 8.08% 103.68 95.93 

G21A09 Mason Sand Uniax 100 8.09% 103.68 95.92 
76 

7.1 Triaxial compression 

Mason Sand - 96 pcf 8% triaxial all.grf

 Strain (%)

 True Stress Difference (psi)

Mason Sand Triaxial Compression Tests

96 lbs/ft3 dry density and 8% water content

-12 -10.5 -9 -7.5 -6 -4.5 -3 -1.5 0 1.5 3 4.5 6 7.5 9

0

30

60

90

120

150

180

210

240

270

300

330

m Radial Axial o

Confining pressure (psi)

 10

 20

 50

 75

 100

Figure 7-1: Mason Sand triaxial test results for 10, 20, 50, 75, and 100 psi confining pressures. 
77 

Mason Sand - 96 pcf 8% Mohr Circle.grf

Normal Stress V (psi)

Shear Stress W (psi)

Mason Sand Mohr Circles

96 lbs/ft3 dry density, 8% water content

0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500

0

25

50

75

100

125

150

175

200

225

250

Internal angle of friction M = 35.0q

Assumed 1 psi cohesion

due to moisture

Triaxial Confining Pressures (psi)

10

20

50

75

100

Linear fit W = 1 + 0.70V

Figure 7-2: Mohr circles based on Mason Sand’s triaxial tests 
78 

Mason Sand - 96 pcf 8% Triax strength linear.grf

Mean Stress P (psi)

Stress Difference 

V' (psi)

Mason Sand Triaxial Tests

Udry = 96 lbs/ft3 and w=8%

Peak stress differences plotted

0 25 50 75 100 125 150 175 200 225 250

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

400

V' = k + aP

k = (6*c*cos M)/(3-sin M)

c = 1 psi cohesion

Correlation = 0.9957

10

20

50

75

100

Fit V' = 2.026 + 1.418P

Figure 7-3: Mason Sand strength envelope results. 
79 

Mason Sand - 96 pcf 8% Triax J2' vs P.grf

Mean Stress P (psi)

Second Invariant J2' (psi2)

Mason Sand Triaxial Tests

Udry = 96 lbs/ft3 and w=8%

0 25 50 75 100 125 150 175 200 225

0

5000

10000

15000

20000

25000

30000

35000

Correlation = 0.9886

Confining pressures (psi)

10

20

50

75

100

Fit J2' = 1.368+1.915P+0.670P2

Figure 7-4: Mason Sand Material Model 5 yield surface fit from triaxial test data. 

 
80 

7.2 Hydrostatic compression 

Mason Sand - 96 pcf 8% hydrostat.grf

 Volumetric Strain (%)

 Confining Stress (psi)

Mason Sand Hydrostatic Compression Test

96 lbs/ft3 dry density, 8% water content

100 psi confining pressure

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

0

10

20

30

40

50

60

70

80

90

100

Hydrostatic compression test

Initial Bulk Modulus K = 1176 psi

50 psi bulk unload modulus Ku = 13100 psi

100 psi bulk unload modulus Ku = 20690 psi

Figure 7-5: 100 psi hydrostatic compression test for Mason Sand at 96/8% condition. 
81 

7.3 Uniaxial strain 

Mason Sand - 96 pcf 8% uniax bulk mod K, M.grf

 Axial Strain (%)

Stress (psi)

Mason Sand Uniaxial Strain Test

96 lb/ft3 and 8% water content

100 psi confining pressure

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

0

25

50

75

100

125

150

175

200

225

250

275

300

325

350

375

400

425

450

475

500

M = 6975 psi

K = 3810 psi

Axial Stress

Mean Stress

Bulk Modulus K = 3810 psi

Constrained Modulus M = 6975 psi

Figure 7-6: Mason Sand uniaxial strain test results. Constrained and bulk moduli fits shown. 
82 

Mason Sand - 96 pcf 8% uniax shear mod G.grf

 Volumetric Strain (%)

 Stress Difference (psi)

Mason Sand Uniaxial Strain Test

96 lbs/ft3 dry density and 8% water content

100 psi confining pressure

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

Slope = 4748 o G = 2374 psi

Uniaxial strain test

Shear Modulus fit G = 2374 psi

Figure 7-7: Mason Sand uniaxial strain test results plotted as stress difference vs. strain. Shear modulus G 

fit shown. Shear stress is half of stress difference. Uniaxial strain is equal to shear strain. 
83 

Mason Sand - 96 pcf 8% uniax bulk unload.grf

 Volumetric Strain (%)

 Mean Stress (psi)

Mason Sand Uniaxial Strain Test

96 lbs/ft3 dry density and 8% water content

100 psi confining pressure

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

Uniaxial strain test

Bulk Unload Modulus Fit Ku = 50446 psi

Figure 7-8: Mason Sand uniaxial strain unloading portion. Determination of bulk unloading modulus Ku

(BULK) by linear fit to initial unloading portion. 
84 

Mason Sand - 96 pcf 8% uniax poisson.grf

 Confining Stress (psi)

 Axial Stress (psi)

Mason Sand Uniaxial Strain Test

96 lbs/ft3 and 8% water content

100 psi confining pressure

0 25 50 75 100 125 150 175 200 225 250

0

25

50

75

100

125

150

175

200

225

250

275

300

325

350

375

400

425

450

475

500

Slope = 3.131 o Q = 0.242

Uniaxial strain test

Poisson's ratio fit

Figure 7-9: Determination of Poisson’s ratio via uniaxial strain test. 
85 

Mason Sand - 96 pcf 8% uniax pres-vol.grf

Logarithmic Volumetric Strain

 Mean Stress (psi)

Mason Sand Uniaxial Strain Test

96 lbs/ft3 and 8% water content

100 psi confining pressure

-0.012 -0.011 -0.01 -0.009 -0.008 -0.007 -0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

Uniaxial strain test

Material Model 5 Pressure-Volume input points

Figure 7-10: Mason Sand Material Model 5 pressure-logarithmic volume curve with 10 input points. 

Obtained from uniaxial strain test. 
86 

7.4 LS-DYNA Material Model 5 inputs 

The recommended set of inputs for modeling Mason Sand at 96 lbs/ft3

 dry density and 8% water 

content in LS-DYNA Material Model 5: Soil and Foam is shown in the table below. 

Table 7-2: Material Model 5 inputs for Mason Sand 

 Input Value Units

Mass density RO 0.000155 lb s2

/in4

Shear modulus G 2374 psi 

Bulk unloading modulus K 50446 psi 

Yield surface coefficient A0 1.368 psi2

Yield surface coefficient A1 1.915 psi 

Yield surface coefficient A2 0.670 - 

Pressure cutoff PC -0.5 psi 

 

 Input Value Input Value Units

Pressure-volume point EPS1 0 P1 0 psi 

Pressure-volume point EPS2 -0.001 P2 3.81 psi 

Pressure-volume point EPS3 -0.002 P3 9.47 psi 

Pressure-volume point EPS4 -0.003 P4 17.68 psi 

Pressure-volume point EPS5 -0.004 P5 28.43 psi 

Pressure-volume point EPS6 -0.005 P6 42.28 psi 

Pressure-volume point EPS7 -0.006 P7 58.24 psi 

Pressure-volume point EPS8 -0.007 P8 76.99 psi 

Pressure-volume point EPS9 -0.009 P9 123.43 psi 

Pressure-volume point EPS10 -0.01044 P10 161.93 psi 

Table 7-3: Summary of elastic constants 

Young's Modulus E 5898 psi

Poisson's Ratio Q 0.242 

Shear Modulus G 2374 psi

Initial Bulk Modulus K 3810 psi

Constrained Modulus M 6975 psi

 
87 

8 Properties for Mason Sand at 100 lbs/ft3 dry density and 5% water content 

This chapter describes properties for Mason Sand at 100 lbs/ft3

 dry density and 5% water 

content. The test log is shown in Table 8-1. 

Table 8-1: Test log for Mason Sand at 100/5% 

Test ID Sample ID Type Confining 

Pressure 

(psi) 

Moisture 

content 

Wet 

Density 

(lbs/ft3) 

Dry 

Density 

(lbs/ft3) 

L1B09 Mason Sand Triax 10 5.03% 105 99.97 

L2B09 Mason Sand Triax 20 4.56% 105 100.43 

L6B09 Mason Sand Triax 50 3.74% 105 101.22 

L6D09 Mason Sand Triax 75 4.71% 105 100.28 

L7A09 Mason Sand Hydro 100 5.02% 105 99.99 

L7B09 Mason Sand Triax 100 5.02% 105 99.99 

L8A09 Mason Sand Uniax 100 5.34% 105 99.68 
88 

8.1 Triaxial compression 

Mason Sand - 100pcf 5% Triax.grf

 Strain (%)

 True Stress Difference (psi)

Mason Sand Triaxial Compression Tests

100 lbs/ft3 dry density, 5% water content

-12 -10.5 -9 -7.5 -6 -4.5 -3 -1.5 0 1.5 3 4.5 6 7.5 9

0

30

60

90

120

150

180

210

240

270

300

330

m Radial Axial o

Confining Pressures (psi)

 10

 20

 50

 75

100

Figure 8-1: Mason Sand triaxial test results for 10, 20, 50, 75, and 100 psi confining pressures. 
89 

Mason Sand - 100pcf 5% Mohr circle.grf

Normal Stress V (psi)

Shear Stress W (psi)

Mason Sand Mohr Circles

100 lbs/ft3 dry density, 5% water content

0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500

0

25

50

75

100

125

150

175

200

225

250

Internal angle of friction M = 37.9q

Assumed 1 psi cohesion

due to moisture

Triaxial Confining Pressures (psi)

10

20

50

75

100

Linear fit W = 1 + 0.7782V

Figure 8-2: Mohr circles based on Mason Sand’s triaxial tests 
90 

Mason Sand - 100pcf 5% Triax strength linear.grf

Mean Stress P (psi)

Stress Difference 

V' (psi)

Mason Sand Triaxial Tests

Udry = 100 lbs/ft3 and w=5%

Peak stress differences plotted

0 25 50 75 100 125 150 175 200 225 250

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

400

V' = k + aP

k = (6*c*cos M)/(3-sin M)

c = 1 psi cohesion

Correlation = 0.9985

Confining Pressures (psi)

10

20

50

75

100

Fit V' = 1.985 + 1.565P

Figure 8-3: Mason Sand strength envelope results. 
91 

Mason Sand - 100pcf 5% Triax J2' vs P.grf

Mean Stress P (psi)

Second Invariant J2' (psi2)

Mason Sand Triaxial Tests

Udry = 100 lbs/ft3 and w=5%

0 25 50 75 100 125 150 175 200 225

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

Correlation = 0.9980

Confining pressures (psi)

10

20

50

75

100

Fit J2' = 1.313+2.071P+0.8164P2

Figure 8-4: Mason Sand Material Model 5 yield surface fit from triaxial test data. 

 
92 

8.2 Hydrostatic compression 

The hydrostatic test on the 100/5% Mason Sand was more extensive than the previous Mason 

Sand models. The 100/5% Mason Sand was loaded and unloaded a total of five times; one for 

each triaxial test pressure. In Figure 8-5, the Mason Sand is loaded and unloaded from 10, 20, 

50, 75, and 100 psi pressures. Again, the Mason Sand is returned to 100 psi for the triaxial 

strength test. 

Mason Sand - 100pcf 5% hydrostat.grf

 Volumetric Strain (%)

 Confining Stress (psi)

Mason Sand Hydrostatic Compression Test

100 lbs/ft3 dry density and 5% water content

100 psi confining pressure

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

0

10

20

30

40

50

60

70

80

90

100

Hydrostatic compression test

Initial bulk modulus K = 2100 psi

50 psi bulk unload modulus = 15900 psi

100 psi bulk unload modulus = 26820 psi

Figure 8-5: 100 psi hydrostatic compression test on Mason Sand at 100/5% condition. 
93 

8.3 Uniaxial strain 

The 100/5% Mason Sand uniaxial test is shown in Figure 8-6 through Figure 8-9. The loading 

portions of the uniaxial strain test are emphasized in bold on the data curves. These loading 

portions illustrate the corresponding fit. 

Mason Sand - 100 pcf 5% Uniax stress vs vol strain.grf

 Axial Strain (%)

Stress (psi)

Mason Sand Uniaxial Strain Test

Udry = 100 lbs/ft3 and w=5%

100 psi confining pressure

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

0

25

50

75

100

125

150

175

200

225

250

275

300

325

350

375

400

425

450

475

500

Constrained Modulus

M = 10101 psi

Bulk Modulus

K = 5356 psi

Axial stress

Axial loading portion for determining M

Mean stress

Mean loading portion for determining K

Fits to initial loading

Figure 8-6: Mason Sand uniaxial strain test results. Constrained and bulk moduli fits shown. 
94 

Mason Sand - 100 pcf 5% Uniax stress diff vs vol strain.grf

 Volumetric Strain (%)

 Stress Difference (psi)

Mason Sand Uniaxial Strain Test

Udry = 100 lbs/ft3 and w=5%

100 psi confining pressure

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

0

25

50

75

100

125

150

175

200

225

250

Slope = 7118

Shear modulus G = 3559 psi

Uniaxial strain test

Loading portion of test

Fit to initial loading

Figure 8-7: Mason Sand uniaxial strain test results plotted as stress difference vs. strain. Shear modulus G 

fit shown. Shear stress is half of stress difference. Uniaxial strain is equal to shear strain. 
95 

Mason Sand - 100 pcf 5% Uniax mean stress vs vol strain.grf

 Volumetric Strain (%)

 Mean Stress, P (psi)

Mason Sand Uniaxial Strain Test

Udry = 100 lbs/ft3 and w=5%

100 psi confining pressure

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

Bulk Unload Modulus

Ku = 71580 psi

Uniaxial strain test

Unloading portion of test

Bulk Unload Modulus

Figure 8-8: Mason Sand uniaxial strain unloading portion. Determination of bulk unloading modulus Ku

(BULK) by linear fit. 
96 

Mason Sand - 100 pcf 5% Uniax axial stress vs conf stress.grf

 Confining Stress (psi)

 Axial Stress (psi)

Mason Sand Uniaxial Strain Test

Udry = 100 lbs/ft3 and w=5%

100 psi confining pressure

0 25 50 75 100 125 150 175 200 225 250

0

25

50

75

100

125

150

175

200

225

250

275

300

325

350

375

400

425

450

475

500

Slope = 3.395 o Q = 0.228

Uniaxial strain test

Loading portion of test

Linear fit to loading portion

Figure 8-9: Determination of Poisson’s ratio via uniaxial strain test. 
97 

Mason Sand - 100 pcf 5% Uniax pres-vol points.grf

Logarithmic Volume Strain

Mean Stress P (psi)

Mason Sand Uniaxial Strain Test

Udry = 100 lbs/ft3 and w=5%

100 psi confining pressure

-0.01 -0.009 -0.008 -0.007 -0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

Uniaxial strain test

Material Model 5 Pressure-Volume input points

Figure 8-10: Mason Sand Material Model 5 pressure-logarithmic volume curve with 10 input points. 

Obtained from uniaxial strain test. 
98 

8.4 LS-DYNA Material Model 5 inputs 

The recommended set of inputs for modeling Mason Sand at 100 lbs/ft3

 dry density and 5% 

water content in LS-DYNA Material Model 5: Soil and Foam is shown in the table below. 

Table 8-2: Material Model 5 inputs for Mason Sand

 Input Value Units

Mass density RO 0.000157 lb s2

/in4

Shear modulus G 3559 psi 

Bulk unloading modulus K 71580 psi 

Yield surface coefficient A0 1.313 psi2

Yield surface coefficient A1 2.071 psi 

Yield surface coefficient A2 0.8164 - 

Pressure cutoff PC -0.5 psi 

 

 Input Value Input Value Units

Pressure-volume point EPS1 0.0000 P1 0 psi 

Pressure-volume point EPS2 -0.001 P2 5.356 psi 

Pressure-volume point EPS3 -0.002 P3 14.41 psi 

Pressure-volume point EPS4 -0.003 P4 27.22 psi 

Pressure-volume point EPS5 -0.004 P5 44.71 psi 

Pressure-volume point EPS6 -0.005 P6 66.03 psi 

Pressure-volume point EPS7 -0.006 P7 92.15 psi 

Pressure-volume point EPS8 -0.007 P8 122.6 psi 

Pressure-volume point EPS9 -0.008 P9 157.1 psi 

Pressure-volume point EPS10 -0.00861 P10 179.3 psi 

Table 8-3: Summary of elastic constants 

Young's Modulus E 8741 psi

Poisson's Ratio Q 0.228 

Shear Modulus G 3559 psi

Initial Bulk Modulus K 5356 psi

Constrained Modulus M 10101 psi

 
99 

9 Mason Sand at 100/15% 

This chapter describes properties for Mason Sand at 100 lbs/ft3

 dry density and 15% water 

content. The test log is shown in Table 9-1. 

Table 9-1: Test log for Mason Sand at 100/15%. *Moisture content not available in test log. 

Test ID Sample ID Type Confining 

Pressure 

(psi) 

Post-test 

Moisture 

content 

Wet 

Density 

(lbs/ft3

) 

Dry 

Density 

(lbs/ft3) 

L15C09 Mason Sand Uniax 100 15%* 115 N/A 

L17D09 Mason Sand Triax 10 14.42% 115 100.50 

L20B09 Mason Sand Triax 20 14.37% 115 100.54 

L21C09 Mason Sand Triax 50 14.11% 115 100.78 

L22C09 Mason Sand Triax 75 14.53% 115 100.40 

L22D09 Mason Sand Hydro 100 13.63% 115 101.20 

L22E09 Mason Sand Triax 100 13.63% 115 101.20 
100 

9.1 Triaxial compression 

Mason Sand - 100 pcf 15% Triax.grf

 Strain (%)

 True Stress Difference (psi)

Mason Sand Triaxial Compression Tests

100 lbs/ft3 dry density, 15% water content

-12 -10.5 -9 -7.5 -6 -4.5 -3 -1.5 0 1.5 3 4.5 6 7.5 9

0

30

60

90

120

150

180

210

240

270

300

330

m Radial Axial o

Confining Pressures (psi)

 10

 20

 50

 75

100

Figure 9-1: Mason Sand triaxial test results for 10, 20, 50, 75, and 100 psi confining pressures. 
101 

Mason Sand 100pcf 15% Mohr circle.grf

Normal Stress V (psi)

Shear Stress W (psi)

Mason Sand Mohr Circles

100 lbs/ft3 dry density, 15% water content

0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500

0

25

50

75

100

125

150

175

200

225

250

Internal angle of friction M = 37.4q

Assumed 1 psi cohesion

due to moisture

Triaxial Confining Pressures (psi)

10

20

50

75

100

W = 1 + 0.767V

Figure 9-2: Mohr circles based on Mason Sand’s triaxial tests 
102 

Mason Sand - 100pcf 15% Triax strength linear.grf

Mean Stress P (psi)

Stress Difference 

V

' (psi)

Mason Sand Triaxial Tests

Udry = 100 lbs/ft3 and w=15%

Peak stress differences plotted

0 25 50 75 100 125 150 175 200 225 250

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

400

V' = k + aP

k = (6*c*cos M)/(3-sin M)

c = 1 psi cohesion

Correlation = 0.9986

Confining Pressures (psi)

10

20

50

75

100

Fit V' = 1.992 + 1.525P

Figure 9-3: Mason Sand strength envelope results. 
103 

Mason Sand - 100pcf 15% Triax J2' vs P.grf

Mean Stress P (psi)

Second Invariant J2' (psi2)

Mason Sand Triaxial Tests

Udry = 100 lbs/ft3 and w=15%

0 25 50 75 100 125 150 175 200 225

0

5000

10000

15000

20000

25000

30000

35000

40000

Correlation = 0.9983

Confining pressures (psi)

10

20

50

75

100

Fit J2' = 1.323+2.0252P+0.7752P2

Figure 9-4: Mason Sand Material Model 5 yield surface fit from triaxial test data. 

 
104 

9.2 Hydrostatic compression 

Mason Sand - 100pcf 15% hydrostat.grf

 Volumetric Strain (%)

 Confining Stress (psi)

Mason Sand Hydrostatic Compression Test

100 lbs/ft3 dry density and 15% water content

100 psi confining pressure

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

0

10

20

30

40

50

60

70

80

90

100

Hydrostatic compression test

Initial bulk modulus = 1392 psi

50 psi bulk unload modulus = 15000 psi

100 psi bulk unload modulus = 22500 psi

Figure 9-5: 100 psi hydrostatic compression test for Mason Sand at 100/15% condition. 
105 

9.3 Uniaxial strain 

Mason Sand - 100 pcf 15% Uniax stress vs vol strain.grf

Volumetric Strain (%)

Stress (psi)

Mason Sand Uniaxial Strain Test

Udry = 100 lbs/ft3 and w=15%

100 psi confining pressure

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

0

25

50

75

100

125

150

175

200

225

250

275

300

325

350

375

400

425

450

475

500

Bulk Modulus K = 3071 psi

Constrained Modulus M = 5731 psi

Axial Stress

Mean Stress

Fits

Figure 9-6: Mason Sand uniaxial strain test results. Constrained and bulk moduli fits shown. 
106 

Mason Sand - 100 pcf 15% Uniax stress diff vs vol strain.grf

 Volumetric Strain (%)

 Stress Difference (psi)

Mason Sand Uniaxial Strain Test

Udry = 100 lbs/ft3 and w=15%

100 psi confining pressure

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

0

25

50

75

100

125

150

175

200

225

250

Slope 3990 psi

Shear Modulus G = 1995 psi

Uniaxial strain test

Fit

Figure 9-7: Mason Sand uniaxial strain test results plotted as stress difference vs. strain. Shear modulus G 

fit shown. Shear stress is half of stress difference. Uniaxial strain is equal to shear strain. 
107 

Mason Sand - 100 pcf 15% Uniax mean stress vs vol strain.grf

 Volumetric Strain (%)

 Mean Stress (psi)

Mason Sand Uniaxial Strain Test

Udry = 100 lbs/ft3 and w=15%

100 psi confining pressure

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

Bulk Unload Modulus

Ku = 62580 psi

Uniaxial strain test

Bulk unload modulus

Figure 9-8: Mason Sand uniaxial strain unloading portion. Determination of bulk unloading modulus Ku

(BULK) by linear fit. 
108 

Mason Sand - 100 pcf 15% Uniax axial stress vs conf stress.grf

 Confining Stress (psi)

 Axial Stress (psi)

 Uniaxial Strain Test (L15C09) to 100 psi

Udry = 100 lbs/ft3 and w=15%

100 psi confining pressure

0 25 50 75 100 125 150 175 200 225 250

0

25

50

75

100

125

150

175

200

225

250

275

300

325

350

375

400

425

450

475

500

Slope = 3.3 o X = 0.233

Uniaxial strain test

Poisson's ratio fit

Figure 9-9: Determination of Poisson’s ratio via uniaxial strain test. 
109 

Mason Sand - 100 pcf 15% Uniax pres-vol points.grf

Logarithmic Volume Strain

Mean Stress P (psi)

Mason Sand Uniaxial Strain Test

Udry = 100 lbs/ft3 and w=15%

100 psi confining pressure

-0.01 -0.009 -0.008 -0.007 -0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

Material Model 5 Pressure-Volume input points

Uniaxial strain test

Figure 9-10: Mason Sand Material Model 5 pressure-logarithmic volume curve with 10 input points. 

Obtained from uniaxial strain test. 
110 

9.4 LS-DYNA Material Model 5 inputs 

The recommended set of inputs for modeling Mason Sand at 100 lbs/ft3

 dry density and 15% 

water content in LS-DYNA Material Model 5: Soil and Foam is shown in the table below. 

Table 9-2: Material Model 5 inputs for Mason Sand

 Input Value Units

Mass density RO 0.000172 lb s2

/in4

Shear modulus G 1995 psi 

Bulk unloading modulus K 62580 psi 

Yield surface coefficient A0 1.323 psi2

Yield surface coefficient A1 2.025 psi 

Yield surface coefficient A2 0.7752 - 

Pressure cutoff PC -1.0 psi 

 

 Input Value Input Value Units

Pressure-volume point EPS1 0.0000 P1 0 psi 

Pressure-volume point EPS2 -0.001 P2 3.071 psi 

Pressure-volume point EPS3 -0.002 P3 9.715 psi 

Pressure-volume point EPS4 -0.003 P4 19.86 psi 

Pressure-volume point EPS5 -0.004 P5 33.54 psi 

Pressure-volume point EPS6 -0.005 P6 51.55 psi 

Pressure-volume point EPS7 -0.006 P7 73.46 psi 

Pressure-volume point EPS8 -0.007 P8 99.78 psi 

Pressure-volume point EPS9 -0.008 P9 129.9 psi 

Pressure-volume point EPS10 -0.00920 P10 171.3 psi 

Table 9-3: Summary of elastic constants 

Young's Modulus E 4920 psi

Poisson's Ratio Q 0.233 

Shear Modulus G 1995 psi

Initial Bulk Modulus K 3071 psi

Constrained Modulus M 5731 psi

 
111 

10 Model to Model Comparisons 

Plots of model to model comparisons for all Mason Sand conditions and KSC sands are included 

as Figure 10-1 and Figure 10-2. These figures demonstrate the relative strength and 

compressibility of each soil model. The strengths are compared using the linear fits of stress 

difference versus mean stress. The compressibility is compared by the 10 point pressure-volume 

fit for each model. Ranked from strongest to weakest in terms of strength, the order is: Mason 

Sand 100 / 5%, Mason Sand 100 / 15%, Mason Sand 97 /4%, Mason Sand 96 / 8%, KSC HDI, 

KSC LDD. 

Ranked in terms of stiffest to softest compressibility, the order is the same, with the exception 

that the Mason Sand 97 / 4% and 96 / 8% are almost tied. Figure 10-2 shows an anomaly for 

Mason Sand. The extra uniaxial test on Mason Sand at 96 / 4% produced an overall stiffer 

model than the 97 / 4%. Generally speaking, as density increases, the stiffness will also increase. 

In this case, the slightly less dense specimen produced less strain at the end of the test. However, 

when the curves are examined closely, the 97 / 4% model was stiffer until 0.03 strain. The two 

models crossed, and the 96 / 4% model experienced 0.0006 less strain at the same peak mean 

stress of 161 psi. This anomaly is probably due to variations in the material samples. 

Comparisons to older constitutive models, such as Carson Sink and Cuddeback Lake, are shown 

in Figure 10-4 and Figure 10-5. 
112 

Figure 10-1: Comparison of sand strengths between models. 

Mean Stress P (psi)

Stress Difference V' (psi)

Mason Sand Triaxial Tests

Comparisons of Strength

0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

320

340

Conditions (lbs/ft3) and % moisture

96 / 8%

97 / 4%

100 / 5%

100 / 15%

KSC HDI 87 / 16%

KSC LDD 78 / 3%
113 

Figure 10-2: KSC and Mason Sand comparison of stiffness. Plot enlarged between 0 and -0.015 strain to 

display Mason Sands more clearly. KSC LDD Sand extends beyond the plot range. 

Logarithmic Volume Strain

 Mean Stress (psi)

Mason Sand Uniaxial Strain Tests

Comparisons of Pressure-Volume Curves

-0.015 -0.0135 -0.012 -0.0105 -0.009 -0.0075 -0.006 -0.0045 -0.003 -0.0015 0

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

Conditions (lbs/ft3) and % moisture

96 / 4%

96 / 8%

97 / 4%

100 / 5%

100 / 15%

KSC LDD 78 / 3%

KSC HDI 87 / 16%
114 

pressure-volume comparision.grf

Logarithmic Volume Strain

 Mean Stress (psi)

Mason Sand Uniaxial Strain Tests

Comparisons of Pressure-Volume Curves

-0.075 -0.07 -0.065 -0.06 -0.055 -0.05 -0.045 -0.04 -0.035 -0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

Conditions (lbs/ft3) and % moisture

96 / 4%

96 / 8%

97 / 4%

100 / 5%

100 / 15%

KSC LDD 78 / 3%

KSC HDI 87 / 16%

Figure 10-3: KSC and Mason Sand comparison over entire strain range. Note how significantly more 

compressible the KSC LDD Sand model is compared to the other sands. 
115 

all soils.grf

Mean Stress P (psi)

Stress Difference 

V' (psi)

All Soils

Comparisons of Strength

0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

320

340

Conditions (lbs/ft3) and % moisture

96 / 8%

97 / 4%

100 / 5%

100 / 15%

KSC HDI 87 / 16%

KSC LDD 78 / 3%

Cuddeback Soil A (clay)

Cuddeback Soil B (silt)

Carson Sink Dry (clay)

Carson Sink Wet (clay)

Gantry's "Unwashed sand"

KSC High Denstiy Flooded Sand

Gantry's "Clean Sand"

Figure 10-4: Strength comparison of all soils. 
116 

pressure-volume comparision3.grf

Logarithmic Volume Strain

 Mean Stress (psi)

All soils

Comparisons of Pressure-Volume Curves

-0.26 -0.24 -0.22 -0.2 -0.18 -0.16 -0.14 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

Conditions (lbs/ft3) and % moisture

96 / 4%

96 / 8%

97 / 4%

100 / 5%

100 / 15%

KSC LDD 78 / 3%

KSC HDI 87 / 16%

Cuddeback Soil A (clay)

Cuddeback Soil B (silt)

Carson Sink Dry (clay)

Carson Sink Wet (clay)

Gantry's "Unwashed sand"

KSC High Density Flooded Sand

Gantry's "Clean Sand"

Figure 10-5: Compressibility comparison of all soils. 
117 

11 Closing Remarks 

The tests on Mason Sand reveal a significantly stronger and stiffer material than the KSC sands. 

The differences in both strength and compressibility create a harsher impact material. From the 

new testing on KSC sands, there minimal changes to the KSC models. The varying amounts of 

strain in the KSC LDD model is sensitive to the low density testing. For Mason Sands, multiple 

uniaxial test excursions helped quantify compressibility sensitivity to density and moisture. 

The soil models presented here are based on static strength and compressibility tests. No attempt 

was made at impact loading the soil, nor accounting for strain rate effects. All test specimens 

were reconstituted from field acquired samples. Mason Sand was purchased from a local 

construction vendor, Yorktown Materials, and shipped to ARA. ARA constructed the Mason 

Sand specimens to LaRC specifications. 

LS-DYNA Material Model 5: Soil and Foam is a basic model well suited for preliminary design 

purposes. However, this is not the only soil model available. There have been many pressuredependent material strength models developed for LS-DYNA, one of which is Material 

Model 25, the Geological Cap model. It is more complex than Material Model 5 because it uses 

kinematic hardening parameters. It uses two surfaces, an initial yield surface and a failure 

surface. The kinematic hardening parameters alter the behavior of the soil when moving from 

the initial yield to failure. This feature makes Material Model 25 a higher fidelity soil model 

because it accounts for more dynamic effects. The laboratory tests required to construct Material 

Model 25 are the same as Material Model 5. Using the test data presented here, it is possible to 

construct a Geological Cap model. It is also possible to construct other models with the 

hydrostatic compression unload/reload test data. 
118 

12 References 

1. “LS-DYNA Theory Manual,” 2006, Livermore Software Technology Corporation, 

Livermore, California. 

2. ASTM D2850-03a(2007) Standard Test Method for Unconsolidated-Undrained Triaxial 

Compression Test on Cohesive Soils. 

3. ASTM D6938-08 Standard Test Method for In-Place Density and Water Content of Soil 

and Soil-Aggregate by Nuclear Methods (Shallow Depth). 

4. ASTM D6913-04e1 Standard Test Methods for Particle-Size Distribution (Gradation) of 

Soils Using Sieve Analysis. 

5. ASTM D2216-05 Standard Test Methods for Laboratory Determination of Water 

(Moisture) Content of Soil and Rock by Mass. 

6. ASTM D854-06 Standard Test Methods for Specific Gravity of Soil Solids by Water 

Pycnometer. 

7. ASTM D6951-03 Standard Test Method for Use of the Dynamic Cone Penetrometer in 

Shallow Pavement Applications. 

8. ASTM D4318-05 Standard Test Methods for Liquid Limit, Plastic Limit, and Plasticity 

Index of Soils (Atterberg Limits). 

9. “Soil, Groundwater, Surface Water, and Sediments of Kennedy Space Center, Florida: 

Background Chemical and Physical Characteristics,” 2000, Dynamac Corporation, 

NASA Environmental Program Office, KSC, FL. 

10. “Constitutive Soil Properties for Cuddeback Lake, CA and Carson Sink, NV,” 2008, 

Applied Research Associates, NASA Langley Research Center, Hampton, VA. 

11. “Geology, Geohydrology And Soils Of Kennedy Space Center: A Review”, 1990, 

Bionetics Corporation, Kennedy Space Center, FL. 

12. Leonard Schwer, LS-DYNA Instructor at Livermore Software Technology Corporation. 

Class materials used in Figure 3-6. 
119 

Appendix A: LS-DYNA Theory Manual for Material Model 5 

Appendix A is taken from the “LS-DYNA Theory Manual,” 2006, Livermore Software 

Technology Corporation, Livermore, California. The excerpts shown below are from the 

Material Model 5 description starting on Page 19.21 of the LS-DYNA Theory Manual. 

LS-DYNA is a registered trademark of the Livermore Software Technology Corporation. 

The following boxed figures are copied from the LS-DYNA Theory Manual. The copied pages 

refer to the equations used in deriving constitutive parameters in Chapter 3. 
120 

Krieg, R. D., “A Simple Constitutive Description for Cellular Concrete,” Sandia National 

Laboratories, Albuquerque, NM, Rept. SC-DR-72-0883 (1972). 
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Contractor Report

 4. TITLE AND SUBTITLE

Constituitive Soil Properties for Mason Sand and Kennedy Space Center

5a. CONTRACT NUMBER

NNL07AA00B

 6. AUTHOR(S)

Thomas, Michael A., Chitty, Daniel E.

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

 NASA Langley Research Center

Hampton, Virginia 23681-2199 

 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

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 REPORT NUMBER

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NASA

13. SUPPLEMENTARY NOTES

This report was prepared by Applied Research Associates, Inc., under NASA contract NNL07AA00B with ATK Space 

Systems, Inc.

Langley Technical Monitor: Ralph D. Buerhle

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified - Unlimited

Subject Category 31

Availability: NASA CASI (443) 757-5802

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email: help@sti.nasa.gov)

14. ABSTRACT

Accurate soil models are required for numerical simulations of land landings for the Orion Crew Exploration Vehicle (CEV). This report provides constitutive 

material models for two soil conditions at Kennedy Space Center (KSC) and four conditions of Mason Sand. The Mason Sand is the test sand for LaRC’s drop 

tests and swing tests of the Orion. The soil models are based on mechanical and compressive behavior observed during geotechnical laboratory testing of 

remolded soil samples. The test specimens were reconstituted to measured in situ density and moisture content. Tests included: triaxial compression, 

hydrostatic compression, and uniaxial strain. A fit to the triaxial test results defines the strength envelope. Hydrostatic and uniaxial tests define the 

compressibility. The constitutive properties are presented in the format of LSDYNA Material Model 5: Soil and Foam. However, the laboratory test data 

provided can be used to construct other material models. The soil models are intended to be specific to the soil conditions they were tested at. The two KSC 

models represent two conditions at KSC: low density dry sand and high density in-situ moisture sand. The Mason Sand model was tested at four conditions 

which encompass measured conditions at LaRC’s drop test site. 

15. SUBJECT TERMS

Crew Exploration Vehicle; Landing; Orion; Soil

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128

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747797.06.13.06.31.04.40

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NASA/CR-2011-217323

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01- 12 - 2011