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TECHNICAL REPORT NO. 6-763
SHOCK-ABSORBING MATERIALSReport 2
CELLULAR CONCRETE AS A BACKPACKING MATERIAL
by
G. C. Hoffm
Civil Engineering DepartmertB106 C. E . Building
University of IllinoisUrbana, Illinois 61801
0l 00 0 ID
,~ ~?sii#AiI r flit
June 1971
Sponsored by Defense Atomic Support Agency
Conducted by U. S. Army Engineer Waterways Experiment Station, Vicksburg, Mississippi
metadc303920
APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED
Destroy this report when no longer needed. Do not returnit to the originator.
The findings in this report are not to be construed as an officialDepartment of the Army position unless so designated
by other authorized documents.
TECHNICAL REPORT NO. 6-763
SHOCK-ABSORBING MATERIALSReport 2
CELLULAR CONCRETE AS A BACKPACKING MATERIAL
by
G. C. Hoff
June 1971
Sponsored by Defense Atomic Support Agency
Nuclear Weapons Effects Research SC 210
Conducted by U. S. Army Engineer Waterways Experiment Station, Vicksburg, Mississippi
ARMY-MRC VICKSBURG, MISS.
APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED
THE CONTENTS OF THIS REPORT ARE NOT TO BE
USED FOR ADVERTISING, PUBLICATION, OR
PROMOTIONAL PURPOSES. CITATION OF TRADE
NAMES DOES NOT CONSTITUTE AN OFFICIAL EN-
DORSEMENT OR APPROVAL OF THE USE OF SUCH
COMMERCIAL PRODUCTS.
3
ABSTRACT
The use of low-density cellular concrete, having an oven-dry unit
weight of 50 pcf or less, as a backpacking material for deeply buried pro-
tective structures was studied. Cellular concrete was found to be suitable
for this type of application. A number of physical properties of cellular
concrete were determined to provide input to design codes. Constrained
compressive crushing stress levels from 20 to 1,000 psi for slow rates of
loading were observed. Rapid-loading tests and equation of state measure-
ments were also made to determine the rate sensitivity of the concrete.
Compressional wave velocities from 2,000 to 6,000 ft/sec were also measured.
Modulus of elasticity values from 20,000 to 220,000 psi were measured for
concretes in the as-cast condition with respect to moisture. Flexural
strength to compressive strength ratios from 0.16 to 0.33 were observed.
Early age stiffening characteristics of cellular concrete were also studied.
Some design procedures based on the data analysis are suggested.
Some possible areas of difficulty during prototype use of cellular
concrete as a backpacking, such as lift heights, cold joints, temperature
problems, and water-saturation problems, are also explored. Lift heights
should not exceed those that cause an increase in density over the desired
density by more than a stipulated amount in the lower portion of the lift.
The effects of joint roughness and curing on the joint performance are min-
imal. Temperatures over about 120 F tend to cause collapse of the struc-
ture of unhardened low-density cellular concrete. In a free-water environ-
ment, saturation of the cellular concrete is inevitable unless steps are
taken to prevent the water from reaching the concrete. Suggestions for
doing this are offered.
PREFACE
This study was conducted in the Concrete Division of the U. S. Army
Engineer Waterways Experiment Station (WES) under the sponsorship of the
Defense Atomic Support Agency (DASA) as part of Nuclear Weapons Effects Re-
search (NWER) Subtask SC 210, "Response of Buried Structures to Ground
Shock." The work was accomplished under the general supervision of
Mr. T. B. Kennedy, former Chief of the Concrete Division, Mr. Bryant
Mather, present Chief of the Concrete Division, and Mr. J. M. Polatty,
Chief of the Engineering Mechanics Branch. Other staff members actively
participating in the investigation were Messrs. J. L. Hawley, Donato Bres-
cia, and G. C. Hoff. Mr. B. R. Sullivan, Chief of the Engineering Physics
Section, prepared Appendix C. Mr. Hoff was project leader and prepared
this report.
Directors of the WES during the investigation and the preparation and
publication of this report were COL Alex G. Sutton, Jr., CE, COL John R.
Oswalt, Jr., CE, COL Levi A. Brown, CE, and COL Ernest D. Peixotto, CE.
Technical Directors were Messrs. J. B. Tiffany and F. R. Brown.
5
CONTENTS
ABSTRACT------------------------------------------------------------- 4
PREFACE-------------------------------------------------------------- 5
NOTATION------------------------------------------------------------- 11
CONVERSION FACTORS, BRITISH TO METRIC UNITS OF MEASUREMENT----------- 12
CHAPTER 1 INTRODUCTION---------------------------------------------- 13
1.1 Design and Construction Considerations------------------------ 131.2 Objective----------------------------------------------------- 161.3 Scope--------------------------------------------------------- 16
1.3.1 Physical Properties--------------------------------------- 161.3.2 Construction Problem Areas-------------------------------- 17
CHAPTER 2 MATERIALS AND FABRICATION, AND PLACING EQUIPMENT ANDPROCEDURES-------------------------------------------------18
2.1 Materials------------------------------------------------------ 182.1.1 Portland Cement--------------------------------------------182.1.2 Foaming Agent-----------------------------------------------19
2.2 Mixture Procedures and Proportions---------------------------- 192.3 Specimen Preparation and Curing------------------------------- 262.4 Placing Equipment and Procedures------------------------------ 262.5 Surface Sealers----------------------------------------------- 27
CHAPTER 3 TEST EQUIPMENT AND PROCEDURES----------------------------- 28
3.1 Constrained Compression Tests--------------------------------- 283.1.1 Slow-Loading Tests---------------------------------------- 283.1.2 Rapid-Loading Tests--------------------------------------- 283.1.3 Multiple-Shot Loading Tests------------------------------- 29
3.2 Flexural Strength Tests--------------------------------------- 303.2.1 Modulus of Rupture Determinations------------------------- 303.2.2 Horizontal Joint Tests------------------------------------ 30
3.3 Ultrasonic Pulse Velocity Tests------------------------------- 323.4 Rate-of-Hardening Tests--------------------------------------- 323.5 Modulus of Elasticity and Poisson's Ratio Tests--------------- 323.6 Temperature Studies------------------------------------------- 33
3.6.1 Adiabatic Temperature Rise-------------------------------- 333.6.2 Mixture Water Temperature Study--------------------------- 333.6.3 Lift Heat Effects----------------------------------------- 333.6.4 Ambient Air Temperature Effects--------------------------- 334
3.7 Lift Height Study--------------------------------------------- 343.8 Moisture Studies---------------------------------------------- 35
3.8.1 Saturation Study------------------------------------------ 353.8.2 Flow and Erosion Tests------------------------------------ 363.8.3 Surface Sealer Tests-------------------------------------- 37
CHAPTER 4 TEST DATA AND ANALYSIS PLAN------------------------------- 51
4.1 Constrained Strength Determinations--------------------------- 514.2 Modulus of Rupture Determinations----------------------------- 524.3 Ultrasonic Pulse Velocity Determinations---------------------- 52
6
4.4 Modulus of Elasticity and Poisson's Ratio Determinations----- 534.5 Regression Analysis------------------------------------------ 534.6 Data Dispersion---------------------------------------------- 54
CHAPTER 5 TEST RESULTS--------------------------------------------- 55
5.1 CONSTRAINED COMPRESSION TEST RESULTS------------------------- 555.1.1 Slow-Loading Test Results-------------------------------- 555.1.2 Rapid-Loading Test Results------------------------------- 555.1.3 Multiple-Shot Loading Test Results----------------------- 55
5.2 Flexural Strength Test Results------------------------------- 555.2.1 Modulus of Rupture Test Results-------------------------- 555.2.2 Horizontal Joint Test Results---------------------------- 56
5.3 Ultrasonic Pulse Velocity Test Results----------------------- 565.4 Rate-of-Hardening Test Results------------------------------- 565.5 Modulus of Elasticity and Poisson's Ratio Test Results------- 575.6 Temperature Study Results------------------------------------ 57
5.6.1 Adiabatic Temperature-Rise Results----------------------- 575.6.2 Mixture Water-Temperature Results------------------------ 575.6.3 Lift Heat Effects Results-------------------------------- 585.6.4 Ambient Air Temperature Effects-------------------------- 58
5.7 Lift Height Results------------------------------------------ 585.8 Moisture Study Results--------------------------------------- 58
5.8.1 Saturation Results--------------------------------------- 585.8.2 Flow and Erosion Test Results---------------------------- 595.8.3 Surface Sealer Test Results------------------------------ 59
CHAPTER 6 DISCUSSION OF TEST RESULTS------------------------------- 86
6.1 Constrained Strength-Deformation Characteristics------------- 866.1.1 Slow-Loading Results------------------------------------- 866.1.2 Rapid Loading-------------------------------------------- 936.1.3 Multiple-Shot Loading Capability------------------------- 94
6.2 Flexural Strength-------------------------------------------- 956.2.1 Modulus of Rupture--------------------------------------- 956.2.2 Horizontal Joint Tests----------------------------------- 96
6.3 Ultrasonic Pulse Velocities---------------------------------- 986.4 Rate of Hardening-------------------------------------------- 996.5 Modulus of Elasticity and Poisson's Ratio-------------------- 1006.6 Temperature Problems----------------------------------------- 1016.7 Lift Height Results------------------------------------------ 1056.8 Saturation Problems------------------------------------------ 106
CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS-------------------------- 117
7.1 Conclusions-------------------------------------------------- 117
7.2 Recommendations---------------------------------------------- 120
APPENDIX A DEVELOPMENT OF A LABORATORY TEST METHOD FOR LOW-DENSITY CONCRETE BACKPACKING---------------------------- 121
A.1 Constrainment-------------------------------------------------121A.2 Specimen and Test Preparations------------------------------- 124A.3 Piston Size-------------------------------------------------- 125A.4 Deformation Rates-------------------------------------------- 126
7
APPENDIX B TEST DATA----------------------------------------------
APPENDIX C OBSERVATIONS ON THE EQUATION OF STATE OF CELLULARCONCRETE-------------------------------------------------169
C.1 Theoretical Considerations------------------------------------169C.2 Experimental Method------------------------------------------ 170C.3 Experimental Results----------------------------------------- 171
REFERENCES----------------------------------------------------------177
TABLES
5.1 Summary of Constrained Stress Versus Freshly Mixed Density,Correlation Regression Coefficients, a = a(d)b +2 Sest,y----- 60
5.2 Summary of Modulus of Rupture Versus Freshly Mixed Density,Correlation Regression Coefficients, R = a(d)b +2 Sest,ypsi---------------------------------------------------------- 61
5.3 Summary of Horizontal Joint Test Results--------------------- 625.4 Summary of Ultrasonic Pulse Velocity Versus Freshly Mixed
Density, Correlation Regression Coefficients, V = (a + bd)+2 Sest---------------------------------------------------- 63
5.5 Summary o Modulus of Elasticity and Poisson's Ratio Data---- 645.6 Secant Modulus of Elasticity Versus Hardened Density Rela-
tion, Es = a(d)b +2 5est,y -------------------------------- 655.7 Summary of Temperature-Rise Study Batching Data-------------- 656.1 Summary of Ultrasonic Pulse Velocity (V) Versus Cement Con-
tent (C) Relations, V = aCb +2 Sest,y , ft/sec--------------- 112
FIGURES
3.1 Typical test record for a slow-loading test----------------- 393.2 Slow-loading constrained compression test configuration----- 403.3 Impact air hammer apparatus (IAHA)---------------------------- 413.4 Typical test record for a rapid-loading test---------------- 433.5 Joint scriber and scribe pattern---------------------------- 443.6 Horizontal joint study sampling schedule-------------------- 453.7 Lift height study, 30-foot column--------------------------- 463.8 Lift height study, 16-foot column--------------------------- 463.9 Pressure pycnometer----------------------------------------- 473.10 Low-head, unlimited reservoir permeability test equipment--- 483.11 Specimen container------------------------------------------ 493.12 Sealer study falling head permeameter----------------------- 505.1 Typical stress-deformation curves--------------------------- 665.2 Summary of stress versus freshly mixed density relations,
slow-loading tests, 28-day strength------------------------- 675.3 Summary of stress versus freshly mixed density relations
for rapid-loading tests, 28-day strength-------------------- 685.4 Stress-deformation relations for multiple-shot loading------ 695.5 Summary of the modulus of rupture versus freshly mixed
density relations------------------------------------------- 695.6 Summary of ultrasonic pulse velocity versus freshly mixed
density relations for water-cement ratios 0.66 and 0.76----- 70
8
133
5.7
5.8
5.9
5.10
5.11
5.125.135.14
5.155.165.175.185.195.205.215.225.236.1
6.2
6.3
6.4
6.5
6.6
6.7
A.1A.2A.3A.4
A.5A.6A.7A.8B.1-B.27B.28-B.31B.32-B.35
Summary of ultrasonic pulse velocity versus freshlymixed density relations for water-cement ratios 0.86and 0.96---------------------------------------------Summary of ultrasonic pulse velocity versus freshlymixed density relations showing effect of water-cementratio, 28 days age-----------------------------------Penetration resistance versus time relations for 23-and 32-pcf nominal density concretes------------------Penetration resistance versus time relation for 39-and )3-pcf nominal density concretes------------------Summary of secant modulus of elasticity versus freshlymixed density relations-------------------------------Adiabatic temperature development curve---------------Effect of mixture water temperature on early-age heat--Effect of hydration heat on adjoining lifts ofconcrete----------------------------------------------Effect of 100 F air-curing temperature----------------Effect of 120 F air-curing temperature----------------Effect of lift height on concrete density-------------Saturation curve for a cellular concrete--------------Flow data for 23-pcf concrete-------------------------Flow data for 32-pcf concrete-------------------------Erosion data for 23-pcf concrete----------------------Erosion data for 32-pcf concrete----------------------Sealer effectiveness test results---------------------Yield stress versus theoretical porosity relation fora neat cellular concrete------------------------------Relation between yield stress and the design parameter,dc/(l + k)-------------------------------------------Relations between design parameter, dc/(l + k) , andfreshly mixed density for various water-cement ratios--Proposed relation between stress ratio and design pa-rameter, dc/(l + k) , for cellular concrete-----------Rapid loading versus slow loading relation for the av-erage stress to 40 percent deformation characteriza-tion, ' 0 .40- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Ultrasonic pulse velocity versus cement content rela-tions for neat cellular concrete----------------------Secant modulus of elasticity versus modulus parameterrelation----------------------------------------------Rock-backpacking-structure configuration---------------Thick-walled cylinder stresses------------------------Split-wall confining pipe-----------------------------Loading pistons--------------------------------------Typical constrained stress versus deformation relation-Effect of piston diameter on stress-------------------
Effect of piston size on bottoming point--------------Rate of deformation effects---------------------------Test data, stress versus density relations------------Test data, modulus of rupture versus density relations-Test data, modulus of elasticity versus densityrelations---------------------------------------------
9
71
72
73
74
757576
77787980808182838485
113
113
114
114
115
115
116128129130130131131132132
134-160161-164
165-168
C.1 Schematic of experimental setup------------------------------ 173C.2 Particle velocity versus time histories---------------------- 174
C.3 Particle velocity versus time histories when impacted withaluminum driver plate---------------------------------------- 175
C.-- Pressure versus time histories------------------------------- 176
10
NOTATION
The principal symbols used in this report are listed below. Special-
purpose subscripts and symbols are not listed but are explained in the text.
a,b = equation coefficients
B = beam width
C = cement content, or elastic wave velocity
d = density
D = beam depth
E = modulus of elasticity
f' = yield strengthck = water-cement ratio
L = length
n = porosity
p = pressure
P = load
r = radius
R = modulus of rupture
S = strength
T = time
u = particle velocity
U = energy, or shock wave velocity
V = compressional wave velocity; also, volume (with appropriatesubscripts)
W = weight
X,Y = rectilinear coordinates
E = strain or deformation
y = unit weight
p = specific gravity
a = stress
11
CONVERSION FACTORS, BRITISH TO METRIC UNITS OF MEASUREMENT
British units of measurement used in this report can be converted to metric
units as follows.
Multiply By To Obtain
inches
feet
cubic feet
cubic yard
pounds
pounds per square inch
pounds per cubic foot
Fahrenheit degrees
foot -pounds
feet per second
2.54
0.3048
0.02832
0.764555
453.5924
0.070307
16.02
5/90.138255
0.3048
centimeters
meters
cubic meters
cubic meters
grams
kilograms per square centimeter
kilograms per cubic meter
Celsius or Kelvin degreesa
meter-kilograms
meters per second
12
a To obtain Celsius (C) temperature readings from Fahrenheit (F)readings, use the following formula: C = (5/9)(F - 32). Toobtain Kelvin (K) readings, use: K = (5/9)(F - 32) + 273.15.
CHAPTER 1
INTRODUCTION
1.1 DESIGN AND CONSTRUCTION CONSIDERATIONS
The use of low-density1 cellular concrete as a backpacking for deeply
buried structures requires an understanding of the properties and character-
istics of these concretes when they are placed as large volume sections in
underground environments. The protective structure designer requires num-
bers that represent the physical properties of the in-place concrete; and
because of the special use of cellular concrete in this situation, these
numbers are generally not available in the literature. The construction
engineer is faced with the problem of using a material as backpacking that
normally is used for roof and floor fills (Reference 1). Some of the con-
struction problems associated with making this transition are unique.
The first area of concern is the in-place physical properties of the
cellular concrete. The effective use of a backpacking requires that its
compressive strength and deformation capabilities be known (Reference 2).
A number of external factors will influence the resistance to loading of-
fered by a cellular concrete of predetermined design. The first of these
will be the degree of constrainment of the concrete when loaded. This con-
straint is a result of the deeply buried configuration (Appendix A). The
values used to describe the strength of the backpacking should reflect
this constrainment. Unfortunately, the actual amount of constrainment and
manner of loading of the concrete are variables that may never be exactly
known and, therefore, must be approximated.
Cellular concrete is a load- and strain-rate sensitive material (Ref-
erence 3). The time rate and history of loading of the backpacking are
variables that will depend on a number of external factors over which a
designer may have no control; yet these factors can influence the
1 Low-density means the concrete has an oven-dried density of less than
50 pcf. (A table of factors for converting British units of measurement
to metric units is presented on page 12.)
13
resistance offered by the backpacking when it is loaded. The backpacking
may also be subjected to repeated shock loadings, the frequency and inten-
sity of which may not be known.
Other physical properties such as flexural strength, compressional
wave velocity, modulus of elasticity, and Poisson's ratio are also essen-
tial for design purposes. These properties and the compressive strength
of the cellular concrete should be obtained in such a manner that the con-
dition of the concrete when evaluated approaches that of the in-place con-
crete. An important consideration in this respect is the moisture condi-
tion of the concrete when tested. The in-place concrete will remain at
essentially the same moisture content as when cast, because it will be
sealed on the outer periphery by competent rock and on the ends and inner
periphery by the liner it is protecting. The characterizing parameters for
each type of test should represent concrete in the as-cast moisture
condition.
The cellular concrete, having been designed properly, must then be
fabricated and put in place in such a manner that the finished product
actually represents the designed concrete. Some of the construction prob-
lems associated with the actual use of cellular concrete as backpacking
have been examined (Reference 4), but some others require additional study.
Assuming the concrete can be satisfactorily made and brought to the point
of placement, the depth or lift height to which the concrete can be placed
at one time must be known.
In a deep lift, the very high air content of the cellular concrete
allows the lower regions of the lift to compress or consolidate in the un-
hardened state due to the increasing superincumbent loads resulting from
the unhardened concrete in the upper region. As will be mentioned later,
the consolidation problem may be further compounded by increasing tempera-
tures of and moisture migration in the concrete. In consolidating, the
density of the concrete is increased. As the cellular concrete strength
is a function of the density (Reference 3), the strength will also increase.
When a particular backpacking design strength is to be uniform throughout
the concrete mass, this increase, and hence strength gradient, is not de-
sirable. It is also not desirable from an economy standpoint because it
l4
will take more cement to fill a given volume than was initially planned.
Once a satisfactory lift height is determined, where a controlled amount of
density change occurs for a given cellular concrete design, construction
schedules can be established.
By having to place the cellular concrete in lifts for large sections,
the problem of joint preparation arises. Because of the planned mode of
resistance of the buried structure to loading, it is desirable that large
sections of the backpacking do not slide across joints and thus produce a
more serious loading condition than anticipated. Properly designed cold
joints should enable the cellular concrete backpacking to act as a single
mass.
Associated with both the lift height and cold joint problems is the
problem of heat both in and around the cellular concrete. Because of the
high air content of the concrete and, hence, its insulating characteristics,
and the possibility of the confining rock medium behaving as an infinite
heat sink, large amounts of the heat caused by the hydration of the cement
will remain in the concrete for long periods of time. Unhardened cellular
concrete placed in hot environments will experience a reduction of the sur-
face tension of the air bubbles in the void system and a subsequent expan-
sion of the heated air in the bubble. This causes the bubbles to burst
with resulting consolidation of the concrete. This hot environment can
exist in the upper regions of large placements where the bottom of the
placement has begun to stiffen and is developing very hot temperatures. It
can also exist at the interface between a lift of older hot concrete and a
lift of new unhardened concrete, or it can exist in the hot air environment
provided by heat loss from hydrating adjacent sections of concrete. Again,
this is not desirable from the standpoints of both design and economy. Ap-
propriate steps must be taken to reduce, eliminate, or work around these
temperature problems.
Once the cellular concrete is in place it probably will not be seri-
ously affected by any external factors other than loading (Reference 3),
with the exception of water. For the strengths and densities of cellular
concrete being considered for backpacking in this study, cellular concrete
should be considered as being susceptible to water infiltration even at
15
very low water pressures (Reference 3). The presence of additional water
in the concrete reduces the amount of void space and greatly affects the
performance of the concrete. To adequately design against the infiltration
of water into the cellular concrete, an understanding of the saturation
characteristics of this concrete is essential.
The problems described above will vary in complexity and severity for
each set of field conditions. Obtaining solutions to these problems for
all possible situations would be a formidable task. The studies described
herein were done, for the most part, in preparation for an actual field job
involving buried structures backpacked with cellular concrete (References
4 and 5). In most cases, the studies were not designed to provide in-depth
answers to the specific problem area studied, but were meant instead to
produce qualitative results that would provide guidance to the individuals
undertaking the actual work.
1.2 OBJECTIVE
The objective of the study was to investigate low-density cellular
concrete for use as a backpacking material for deeply buried structures.
Specifically, the investigation was to determine some physical properties
of the concrete that were indicative of its desired in-place performance
and to examine some problems associated with placing large mass sections
of cellular concrete in underground environment.
1.3 SCOPE
1.3.1 Physical Properties. A constrained compression test was de-
veloped (Appendix A) and used to evaluate numerous mixture designs of cel-
lular concrete for both slow and rapid rates of loading. A limited number
of test specimens were evaluated for multiple-shot loading capabilities.
Other physical properties such as flexural strength, compressional
wave velocity, modulus of elasticity, and Poisson's ratio were also deter-
mined for a number of different mixture proportions. All physical proper-
ties were determined while the concrete was in a moisture condition approx-
imating that of the as-cast condition. Some measurements of the response
of concrete to high-pressure shock loading were also attempted (Appendix C).
16
1.3.2 Construction Problem Areas. Selected mixtures were studied for
hydration temperature development, techniques for reducing this temperature,
and the effects of this temperature on additional placements of fresh con-
crete. The effect of lift height on density of the concrete and the prep-
aration of cold joints related to lift construction were also studied.
The effect of free water on in-place cellular concrete was studied and
an examination of some surface sealers for moisture exclusion was conducted.
17
CHAPTER 2
MATERIALS AND FABRICATION, AND PLACING EQUIPMENT AND PROCEDURES
2.1 MATERIALS
2.1.1 Portland Cement. Type III cement was used for all the concrete
in the program with the exception of some Type I cement that was used in
portions of the temperature studies. The portland cements representing
both the Type I (RC-551) and Type III (RC-560) met the requirements for
Types I and III, respectively, and had the following chemical and physical
characteristics:
Chemical Analysis Physical Properties
Constituents Percent Type I Type IIIRC-554 RC-560
Type I Type IIIRC-554 RC-560
S i02
A1203
Fe2023CaO
MgO
SO3s3
Ignition loss
Total
Insolubleresidue
Na20
K20
Total alkaliesas Na 0
2C3A
CiS
20.7
4+.8
4.1
61.7
1.8
2.3
1.4
0.99
0.10
0.18
0.26
0.35
6
60
21.1
4.8
4.0
64.6
1.8
2.14
1.4
100.1
0.01
0.13
0.23
0.28
6
58
Normal consistency,pct
Setting time, Gill-more, hours:minutes
Initial
Final
Autoclave expan-
sion, pct
Air content ofmortar, pct
Compressive strengthof mortar, psi
1 day
3 days
7 days
28 days
(Continued)
18
25.0
3:x +5:30
0.01
8.3
2,850
3,765
5,145
27.2
3:20
6:50
0.01
7.2
2,390
3,810
5,165
Chemical Analysis Physical Properties
Constituents Percent Type I Type IIIRC-554 RC-560
Type I Type III
RC-554 RC-560
C2S 14 17 Surface area, air
C A? - - 12 permeability fine-I4i ness (Blaine),
cm2/g 3,845 4,790
Specific gravity 3.14 3.13
Heat of hydration,cal/g
7 days 77.7 80.8
28 days 89.7 91.4
2.1.2 Foaming Agent. A foaming agent, AD-186, was used to provide
the stable air-bubble system necessary for the fabrication of cellular con-
crete. A spectroscopic analysis of the foaming agent indicated the presence
of decomposition products of proteins reacted with aliphatic fatty acids or
salts of fatty acids. The manufacturer refers to his product as a hydro-
lyzed stabilized protein foaming agent.
For use, a premixed solution of a predetermined concentration of
foaming agent and water was prepared. The solution was then placed in a
pressure container and subjected to a controlled air pressure. The air
pressure forced the solution through a discharge line into a blending noz-
zle that agitated the solution and combined it with compressed air. The
resulting product that issued from the blending nozzle was a stable, pre-
formed foam having the consistency of shaving cream obtained from aerosol
cans. This preformed foam provides the stable air-bubble system in the
cellular concrete.
2.2 MIXTURE PROCEDURES AND PROPORTIONS
All the cellular concrete was batched in a 5.5-ft3 horizontal-drum
mortar mixer. The rubber-edged blades of the mixer were modified to obtain
19
better mixing action by adding heavy-duty 1-inch screening between the
struts of each individual blade. The batching sequence was water followed
by cement, which was mixed until a well-blended slurry was obtained. The
preformed foam was then added and blended into the slurry until a uniform
consistency of cellular concrete was obtained.
The following procedure was used to design all of the neat cellular
concretes used during the program.
The total size of a batch of neat cellular concrete can be expressed
in terms of the volumes of all the constituents in the batch:
Vb = V + V (2.1)
where
Vb = volume of batch, ft 3
b3V = volume of neat slurry, ft3
5
V = volume of preformed foam, ft 3
The volume of slurry is composed of cement, water, and entrained air:
V5 =Vc +Vsw +Vsa (2.2)
where
Vc = volume of cement, ft 3
Vs= volume of slurry water, ft 3
V = volume of entrained slurry air, ft 3
The preformed foam volume is composed of the volume of foam air and the
volume of premixed solution:
V =V +V (2-3)
20
where
Vfa = volume of foam air, ft3
V = volume of foam water, ft 3
Substituting in Equation 2.1:
V = V + V + V + V + V (2.4)b c sw sa fa 'w (
The proportioning of the cellular concrete begins with the selection
of the desired freshly mixed density and water-cement ratio for the con-
crete. The water-cement ratio by weight of the ingredients of the concrete
can be expressed as
k W(2.5)
wc
where
k = water-cement ratio of the slurry, dimensionless
W = weight of total water in concrete, pounds
We = weight of cement in concrete, pounds
The weight of the total water is composed of the weight of the slurry water
plus the foam water:
Wtw =sw + W f(2.6)
where
W = weight of slurry water, pounds
W = weight of foam water, pounds
The amount of air needed to form the cellular structure of the concrete
is determined by the density of concrete desired once the water-cement and
properties of the cement are known. The density is expressed as:
21
Wb
d Wb - (2.7)c Vb
where
do = freshly mixed concrete density, pcf
Wb = total weight of mixture ingredients, poundsb3
V = total batch volume, ft3b
The total batch weight is:
w = w + w(.)b c tw (2.8)
=W +W +Wc sw fw
From Equations 2.5, 2.7, and 2.8, the batch volume can be written as:
W + W-c tw
b dc
W + kwc cdc
WVb = (k + 1) (2.9)
c
or
Wc k+ 1c(2.10)
The concrete volume requirement and/or batching equipment capacity will
then determine the amount of cement in the batch. Having determined the
amount of cement, the total amount of water needed can be found from Equa-
tion 2.5. The volumes of cement and water can then be found as:
22
W
V = pc(2.11)Cew
and
V = ---- (2.12)tw 7w
where
pc = specific gravity of the cement, dimensionless
w unit weight of water, pcf
The volume of air in the slurry Vsa is usually small with respect to the
air volume provided by the foam. For simplicity in design, the required
batch air, Va , can be written as:
Va = Vsa + V fa Vfa (2.13)
and assumed to be provided entirely by the foam. From Equation 2.1,, then
V = V - V - V (2.1)a b c tw (.4
where Vb, C , and Vtw have already been determined.
The foam-producing generator nozzle operates at a constant discharge
rate and produces a foam of constant density. Assuming all of the solids
of the foam to be water, the foam density, df , is expressed as:
W
fwd -(2.15)f Vf
From Equations 2.3 and 2.15
V ~ V = V - vfa a f fw
d V= V -f~
f 7
1 - d
Va = V w(2.16)a f 7
23
and7
Vf= = W d V (2.17)S 7- d aw f
From Equation 2.17, the exact amount of foam to be put in the batch is
determined.
The amount of slurry water that must be initially added to the cement
can be found from Equations 2.6 and 2.15, where:
W = dV (2.18)fw f f
and
Wsw = W -W (2.19)swtw fw
The water-cement ratio in the slurry before the foam is added is then:
Wk sw
1 Wc
where k = water-cement ratio of ingredients initially added to mixer,dimensionless
As an example, assume that a 4.0-ft 3 batch of 32-pcf concrete with a final
water-cement ratio of 0.86 is needed. The specific gravity of the cement
is 3.15; the foam density is 2.3 pcf; and the unit weight of water is
62.3 pcf from Equations 2.5, 2.10, 2.11, and 2.12.
bdc (4.0)(32) = 68.8 poundsc k+1 1.8
Wtw = kWc = 0.86(68.8) = 59.2 pounds
Wc 68.83VC,= W = 688 = 0.350 ft3c pcyw (3.15)62.3
Wt 5Vt = = 59.2 0.950 ft3
tw 7Y 62.3w
The volume of air and foam required can then be found from Equations 2.14
and 2.17.
va =Vb --c vtw = (.o - 0.350 - 0.950) ft3
V = 2.700 ft3
V = 7 wd V = 62.3 2.700 ft3f 7w - df a 62.3 -2.3
Vf = 2.925 ft 3
The foam and slurry waters can then be found from Equations 2.18 and 2.19.
W = d V = 2.3(2.925) pounds
= 6.7 pounds
W 5 = WW -W = 59.2 - 6.7
= 52.5 pounds
Hence, if 68.8 pounds of cement and 52.5 pounds of water are blended in the
mixer to form a slurry and the 2.925 ft3 of foam is added, the desired con-
crete with respect to density and water-cement ratio should be obtained.
Small adjustments may have to be made to compensate for air content changes
during mixing.
For comparison purposes throughout the studies reported herein, it was
attempted to use five specific water-cement ratios by weight, i.e. 0.66,
0.76; 0.86, 0.96, and 1.06, and four specific freshly mixed densities of
23, 32, 39, and 43 pcf at each water-cement ratio. Exceptions were not
uncommon and are noted where they occurred. The number of batches pro-
viding test specimens for the slow-loading tests were 13, 31, 31, 21, and
36 for the 0.66, 0.76, 0.86, 0.96, and 1.06 water-cement ratios, respec-
tively. The number of batches providing specimens for the rapid-loading
test were 16, 22, 16, and 30 for the 0.76, 0.86, 0.96, and 1.06 water-cement
ratios, respectively.
25
2.3 SPECIMEN PREPARATION AND CURING
Except where stated otherwise, all specimens were cured in their
casting molds for 24 hours and upon removal from these molds were immedi-
ately placed and sealed in polyethylene plastic bags and stored at 73 F
until tested.
The test specimens for all of the constrained compression tests were
cast as 6- by 12-inch cylinders. Forty-eight hours before being tested,
each specimen was removed from its bag and the top and bottom 3 inches were
sawed off. The remaining 6- by 6-inch cylinder was then resealed in its
plastic bag until tested. At testing time, the time lapse from removal of
the specimen from the bag to the start of test was only a few minutes.
When a 6- by 12-inch cylinder was used for a specific type of test, the
unformed end of the cylinder was trimmed with a saw to eliminate surface
irregularities.
Each 6- by 12-inch cylinder used for the Poisson's ratio and modulus
of elasticity determinations was instrumented with two A-9-6 electrical
strain gages placed vertically and diametrically opposite and two similar
gages placed circumferentially and diametrically opposite. The gages were
bonded to the specimens by means of a very low modulus, flexible epoxy
binder (CRD-EP-1). The binder also was used to cover the gage for water-
proofing purposes. To avoid moisture loss from the specimens during gage
mounting, a special polyethylene tent was built and the mounting was done
within the tent at a relative humidity of 98 percent. The surface of the
specimen was not dried in any way before, during, or after the gages were
mounted. The gages were mounted after 24 days of continuous bag curing.
2.4 PLACING EQUIPMENT AND PROCEDURES
The placing of the cellular concrete in all molds and formwork with
the exception of the lift height study was done by pouring the very fluid
concrete from the mixer into a bucket and from the bucket into the desired
container. No vibration or consolidation of the concrete was attempted.
The concrete for the columns cast during the lift height study was pumped
from the mixer to the point of placing using an open-throat positive
displacement pump and continuous plastic hose.
26
2.5 SURFACE SEALERS
The
studies.
following materials were used as surface sealers in the moisture
WES Designation Description
CRD CM-9 Styrene -butadiene product
CRD CM-lO Two-component epoxy thinnedwith a volatile solvent
CRD CM-ll Paraffin-resin mixture
CRD CM-12 Liquid latex
CRD CM-8 Vinyl-based liquid-type solvent
CRD CM-13 Asphalt
CRD CM-1+ Latex wall paint
RC-560 Neat Type III cement slurry
- - Hydraulic cement slurry
27
CHAPTER 3
TEST EQUIPMENT AND PROCEDURES
3.1 CONSTRAINED COMPRESSION TESTS
The details of the design of the constrained compression test are con-
tained in Appendix A.
A split-wall confining pipe was used to provide lateral constraint to
the concrete tested in compression. The steel pipe (Figure A.3) had a
6-inch-inside diameter with 1/4-inch-thick walls and accommodated a 6-inch-
high specimen. The 1/4-inch wall thickness resulted in negligible lateral
strains for the largest vertical loads experienced during the program.
After placing the specimen in the pipe, both closure bolts were torqued to
a final closure of 5 ft-lb. Loads were applied through a 4-inch-diameter
loading piston centered on the 6-inch-diameter specimen. The constraining
pipe, loading piston, closure torque, and specimen size (6- by 6-inch cyl-
inder) were the same for both the slow- and rapid-loading tests.
3.1.1 Slow-Loading Tests. Load was applied to the specimens using a
30,000-pound Universal testing machine operating at a constant rate of
loading piston movement of 0.18 in/min (3 percent deformation per minute).
Deformations were measured by a linear slide-wire potentiometer affixed to
the base platform and the moving loading head of the testing machine.
Loads were converted to applied stress by dividing the magnitude of the
applied load by the area of the 4-inch-diameter loading piston. The re-
sulting stress-deformation data from each test were recorded in a graphical
form (Figure 3.1) using an X-Y recorder. Figure 3.2 shows the slow-loading
test arrangement.
3.1.2 Rapid-Loading Tests. Rapid-loading tests were conducted using
the Impact Air Hammer Apparatus (IAHA). A cross section of the IAHA is
shown in Figure 3.3. Load was applied to the specimen through the 4-inch-
diameter piston on the end of the driving shaft. The driving shaft had a
maximum travel distance of 4 inches.
Before beginning a test, a small amount of gas pressure is placed in
the trigger actuator chamber to lock the triggering mechanism in place on
the driving shaft. The specimen is then placed and centered under the
28
loading piston. The upper surface of the specimen is brought in full con-
tact with the bottom surface of the loading piston by means of an adjustable
turnscrew on the bottom of the base bearing plate of the apparatus. The
desired amount of gas pressure is then placed in the accumulator tank, and
the specimen is ready for testing. By electrically releasing the gas pres-
sure through an orifice in the actuator chamber, the triggering mechanism
rotates and releases the driving shaft that, due to the accumulator tank
pressure, drives the loading piston into the specimen.
Compressed nitrogen gas was used as the load gas for all tests. The
amount of gas pressure required for each individual test depended on the
energy absorbing capacity of the sample being evaluated. Experience with
the IAHA and the cellular concrete allowed the IAHA operators to vary the
gas pressure from test to test, depending on the material being evaluated,
such that the total time of test for a full 14 inches of deformation of each
sample never varied from 15 3 msec. Rise times to the start of the crush-
ing plateau varied between 2 and 4 msec.
Loads were measured by a recording load cell placed between the driv-
ing shaft and the loading piston. Deformations were measured using a lin-
ear slide-wire potentiometer fastened to the IAHA frame and the driving
shaft. The output from both the load cell and the slide-wire potentiometer
was recorded on a dual-trace oscilloscope photograph record such as that
shown in Figure 3.4. The electrical impulse that released the gas in the
trigger actuator chamber also operated the shutter on the oscilloscope cam-
era, thus opening the shutter at the instant the test began. Both traces
on the photograph record are on a common time basis. The upper trace in-
dicates total deformation in inches at any point in time; the lower trace
indicates the load on the sample at any point in time. By combining the
load and deformation on a common time basis and converting the load to
stress over the area of the loading piston and deformation to percent of
total sample height, a stress-deformation record such as shown in Figure
3.1 was obtained.
3.1.3 Multiple-Shot Loading Tests. The multiple-shot loading tests
were conducted exactly like the rapid-loading tests (Section 3.1.2) with
the exception that only enough pressure was used in the accumulator tank
29
to partially deform the specimen on the first loading. After the first
loading shot, the driving shaft and piston were reset for firing, the load-
ing surface of the specimen was brought in contact with the piston face by
means of the baseplate turnscrew, the accumulator tank was recharged, and
the air hammer was fired again. This behavior would duplicate a rock frag-
ment driven into the backpacking by an initial shock wave and then driven
in even farther by a second shock wave.
Two oscilloscope records were obtained for each test, one for each of
the two shots. The records were combined so that the point where the first
record ended was the point where the second record began. Deformation for
both shots, expressed in percent, was referenced to the initial height of
the specimen before the testing began.
3.2 FLEXURAL STRENGTH TESTS
Flexural strength tests were made to determine the modulus of rupture
of the cellular concrete at various densities and water-cement ratios and
also to evaluate the effects of cold joints in the concrete for a selected
mixture. In both cases, the equipment and testing were in accordance with
CRD-C 16-66, "Flexural Strength of Concrete (Using Simple Beam with Third-
Point Loading)."
3.2.1 Modulus of Rupture Determinations. Six-inch-square by 20-inch-
long beams were evaluated. The distance between each support and its
closest loading point and between both loading points was 6 inches. All
beams were placed in plastic bags immediately after removal from the cast-
ing forms and were bag-cured at 73 F until tested at 28 days age. Each
beam remained in the bag until testing time when it was removed, immediately
placed in the load apparatus, and tested.
3.2.2 Horizontal Joint Tests. Cellular concrete with a freshly placed
density of 32.7 pcf at a water-cement ratio of 0.86 by weight was used to
fabricate sixteen 2-foot cubes. Each cube was placed in two lifts. The
first lift was placed to a depth of 1 foot and allowed to harden. Before
placing the second lift, the top surface of the first lift was prepared
four different ways. Eight cubes had the top surface exposed to air for
3 days before the next lift was placed. Four of these eight had the
30
surface scribed in a waffle pattern to provide some roughness for the next
lift to bond to. The remaining four air-dried cubes were left in the as-
cast condition. The last cubes were treated in the same manner as the
first eight with the exception that the exposed surface was sealed in plas-
tic to prevent drying. The seal was removed at the time the fresh concrete
was placed.
The scribing was done using a simple apparatus resembling an ordinary
leaf and grass rake. Eight 5/32-inch-diameter by 3/4-inch-long prongs ta-
pered to a point were used as shown in Figure 3.5a. The scribing was done
at right angles to the cube mold, with the first indentation occurring at a
distance of 3/4 inch from the mold. The resulting pattern is shown in Fig-
ure 3.5b. The depth of scribing was approximately 1/2 inch. All loose
material resulting from scribing was removed with a vacuum cleaner.
The second lift was placed to the top of the mold. The top surfaces
of the first eight blocks were again exposed to air drying while the sur-
faces of the second eight were sealed in plastic. After the second lift
had cured 28 days, the forms were removed and the blocks sampled. The
sampling originally was to involve drilling some 6-inch-diameter cores
from each block and also to saw some 6- by 6- by 24-inch beams from each
cube. The sampling arrangement is shown in Figure 3.6. Half of the beams
shown in the top view were to have been drilled cores. The drilling op-
eration was extremely difficult; and because of the weak, brittle nature
of the concrete, very few intact cores were obtained. None of the cores
were tested because no useful comparison data could be obtained from
the small number of cores available. Only 11 of the 16 blocks were cored.
A no-joint control beam was obtained from each lift. The other beams
from each block included the joint at their center. Immediately after saw-
ing, each beam was placed in a plastic bag and stored until the concrete in
the second lift was 60 days old, at which time each beam was tested in
third-point flexure. This method placed the cold joint in the region of
maximum moment and presented a severe loading situation for the joint. The
plane of failure was noted for each beam along with the maximum failure
load.
31
A 4-inch cube was sawed from each half of each broken flexure beam and
oven-dried to a constant weight. The densities of the cubes were then de-
termined in order to establish if density variations between the two lifts
of concrete were influencing the failures of the beams. Compressive
strengths of each cube were also determined in accordance with ASTM C513.
3.3 ULTRASONIC PULSE VELOCITY TESTS
Ultrasonic pulse velocity equipment and tests were in accordance with
CRD-C 51-68, "Tentative Method of Test for Pulse Velocity Through Concrete."
All samples were 6-inch-diameter by 12-inch-(normal) high cylinders that
were continuously bag-cured with interruptions in curing occurring only for
the few minutes required to obtain a pulse velocity reading at a given age.
Velocities were determined for all pulse velocity samples at ages of 3, 7,
14, 28, and 60 days and also at 90 and 180 days for concrete samples made
with water-cement ratios of 0.86 and 0.96.
3.4 RATE-OF-HARDENING TESTS
Rate of hardening of the cellular concrete was determined in accord-
ance with CRD-C 68-69, "Time of Setting of Concrete Mixtures by Penetration
Resistance," with the exceptions that none of the specimens were consoli-
dated by mechanical means and that the minimum spacing between penetration
points was 2 inches. Specimens of concrete made at water-cement ratios of
0.76, 0.86, 0.96, and 1.06 with nominal densities of 23, 32, 39, and 43 pcf
at each water-cement ratio were evaluated at varying time intervals to
90 hours total elapsed time after batching.
3.5 MODULUS OF ELASTICITY AND POISSON'S RATIO TESTS
The modulus of elasticity and Poisson's ratio were determined in ac-
cordance with CRD-C 19-66, "Static Young's Modulus of Elasticity and Pois-
son's Ratio in Compression of Cylindrical Concrete Specimens."
The test specimens were 6- by 12-inch cylinders with sawed ends so
capping was not necessary. All specimens were bag-cured from the time of
removal from the mold until tested. The curing of each specimen was in-
terrupted for a few hours at 24 days of age for the instrumenting of the
32
specimen with electrical-resistance strain gages. Care was taken during
instrumentation to prevent moisture loss from the specimens. Two 6-inch
gages were mounted diametrically opposed in a vertical direction with two
similar gages mounted circumferentially opposed at the midpoint of the
specimen. After the gage installation, each specimen was returned to its
curing bag where it remained until testing at 28 days age. With the excep-
tion of the ends of each cylinder that were in contact with the testing
machine, the curing bag remained around the specimen during test to prevent
surface drying of the cylinder. When tested, each cylinder had a moisture
content approximating that of the as-cast condition. Data were obtained in
the form of stress-strain records for both sets of gages by using an X-Y
recorder.
3.6 TEMPERATURE STUDIES
3.6.1 Adiabatic Temperature Rise. The adiabatic temperature rise of
cellular concrete made with Type III cement (RC-560) with a water-cement
ratio of 0.86 and a freshly mixed density of 43.9 pcf was determined in ac-
cordance with CRD-C 38-66, "Method of Test for Temperature Rise in Con-
crete," with the exception that the concrete was not vibrated when placed.
3.6.2 Mixture Water Temperature Study. Because of the expense in-
volved in conducting the quantitative adiabatic tests, a simpler but quan-
titatively less accurate test was used to obtain qualitative heat develop-
ment results that would reflect the general effects of varying the mixing
water temperature.
Eight thick-walled polystyrene picnic coolers were used as both the
container and insulator for the concrete. Each cooler was filled with one
batch of concrete. Each batch of concrete was a different combination of
the cement type and mixing water temperature variables. Using thermometers,
two concurrent temperature measurements were made in each cooler at points
near the center of the concrete mass. The measurements were made at vari-
ous time intervals through 15 hours total elapsed time.
3.6.3 Lift Heat Effects. This test was designed to produce qualita-
tive results relating to the effects of the heat generated in a hardened
lift of concrete on the temperatures developed in fresh cellular concrete
33
placed on the surface of the hardened concrete.
Two 2-foot cubes of concrete were cast, each cube being composed of
two 1-foot lifts. Three thermocouples were placed in each lift. In each
cube, the first thermocouple was placed 1-1/2 inches below the top surface
of the lift and at the center of the horizontal area of the lift. The
second and third thermocouples were placed directly below the first but at
depths of 6 and 10-1/2 inches below the lift surface, respectively. The
concrete placed in each lift was not vibrated. After placing the concrete
in the first lift, the thermocouples in that lift were monitored to deter-
mine the heat development in the lift. After initial stiffening of the
first lift had occurred, the second lift was placed and its thermocouples
were monitored along with the first lift thermocouple nearest the joint be-
tween the two lifts. The heat development as indicated by these thermo-
couples was measured until it appeared to reach peak values and began to
decline.
3.6.4 Ambient Air Temperature Effects. Three 6- by 12-inch cylinders
were made from each of four different densities of cellular concrete. Im-
mediately after casting, one cylinder from each density was placed in air
temperatures of 80, 100, and 120 F and allowed to harden. After 24 hours
curing, one-half of the cylinder mold was removed and the amount of damage
to each cylinder noted.
3.7 LIFT HEIGHT STUDY
Two columns of cellular concrete were placed and sampled to determine
the variation in density of the concrete with increasing lift height. The
first column was cast in a 6-inch-inside-diameter by 30-foot-long plastic
pipe (Figure 3.7). The pipe was plugged on the lower end and placed in a
9-inch-inside-diameter cased hole in the ground. Concrete with a unit
weight of 32.4 pcf and a water-cement ratio of 0.86 was pumped into the
pipe through a 50-foot-long, 2-inch-inside-diameter plastic hose. Pumping
was done with an open-throat, positive displacement pump. The end of the
discharge hose was kept at a distance of approximately 1 foot from the
freshly placed concrete surface with the hose being continually withdrawn
from the pipe during placing.
34
The concrete was allowed to harden and cure for 3 days at which time
the annulus between the hole casing and the pipe was gradually filled with
water. The water caused the pipe to be displaced and float out of the
casing. As the pipe moved out of the casing, sections of the pipe approxi-
mately 12 inches long were cut off and immediately measured and weighed.
Twenty-nine sections were obtained. At a later date, the concrete in each
section was removed and the weight of the plastic pipe determined. By sub-
tracting this weight from the original weight measurement that included the
pipe, the density of the concrete in each section was calculated.
The second column was cast in a 48-inch-diameter by 16-foot-long cor-
rugated culvert pipe (Figure 3.8). The cellular concrete mixture had a
unit weight of 31.8 pcf. The pumping equipment and procedures were the
same as for the 30-foot column. After hardening and curing for 3 days,
3-foot sections of the corrugated pipe were removed from top to bottom of
the pipe and 1-foot-thick slices were cut from the exposed concrete by
means of a chain saw. Each slice was immediately quartered with an 8-inch
cube being cut from the center of each quarter by a diamond saw. The weight
and measurements of each cube were determined immediately after cutting.
Cutting was done without the use of water or oil so as not to change the
density of the concrete through the addition of some fluid which might have
been absorbed. The average density of the four cubes from each slice was
reported as the as-cast density of the concrete at that point. The cubes
were then oven-dried, and the oven-dry density of the concrete was obtained
so as to get an indication of moisture variations in the column.
3.8 MOISTURE STUDIES
3.8.1 Saturation Study. Five 6- by 12-inch cylinders were used to
determine the amount of available voids in a selected design of concrete
that could be filled with free water. The 28-day bag-cured and oven-dried
densities of the concrete were 51 and 33 pcf, respectively.
Each cylinder, in the bag-cured condition, was placed in a pressure
pycnometer (Figure 3.9). The pycnometer was filled with measured amounts
of water until it contained a specified volume of material (specimen plus
water). The water completely covered the specimen. Pressure was then
35
applied gradually to the surface of the water, thus forcing the water into
the specimen. Additional measured amounts of water were continually added
to the pycnometer to maintain a constant filled volume as the water in the
pycnometer was forced into one specimen. When a pressure of 1,200 psi was
reached, no additional water could be added to the system, thus indicating
saturation of the specimen. The amount of voids available for filling by
water was determined from the volume of water forced into the specimen plus
the volume of water initially in the specimen (bag-cured weight minus oven-
dry weight divided by 62.3). During the buildup to 1,200-psi water pres-
sure, the amounts of water forced into the specimen at pressures of 50, 150,
300, and 600 psi were also noted.
3.8.2 Flow and Erosion Tests. A low-head, unlimited reservoir perme-
ability unit (Figure 3.10) was used to determine the water flow character-
istics and erosion possibilities of the cellular concrete. The unit, as
used, tested six 6- by 6-inch test cylinders simultaneously at pressure
heads that were determined by the head losses through the system.
Each specimen was bag-cured 28 days before being placed in a specimen
container (Figure 3.11). The specimen container was constructed from a
standard 6- by 12-inch concrete cylinder mold that was held between two
8- by 8- by 1/4-inch-thick steel plates by means of four bolts. Rubber
gaskets were used as seals between the container and end plates. A 1-inch
nipple was welded in the center of the top plate for connection to the
water reservoir. A deflection flange was placed directly under the nipple
opening to prevent surface erosion of the specimen by water coming into the
container. The bottom plate had a 1-inch-diameter hole in its center to
allow water passing through the concrete to discharge from the container.
Immediately after removal from the curing bag, the peripheral area of
the cylinder was given an initial coating of vinyl-based sealer and the
specimen was replaced in the curing bag. Approximately 4 hours later, a
second coat of sealer was applied over the first; and before it could
harden, the specimen was placed in the bottom half of the split-walled
specimen container that was then tightly closed about the specimen to pre-
vent leakage. Molding clay was used to seal the top edge of the specimen.
The water reservoir consisted of an elevated barrel of a constant
36
volume. The barrel was continually filled with water, with an overflow
outlet at the top of the barrel providing a constant water level in the
barrel. Outlets at the bottom of the barrel provided the source of water
for the test specimens.
The bottom of each specimen container was immersed in water contained
in a metal trough (Figure 3.11). An overflow was provided in the trough to
maintain the water level in the trough at a constant level. The overflow
was constructed so it would allow the collection of overflow water.
After the specimen was in place in the container and the hoses from
the reservoir to the container were connected, water was allowed to flow
through the system with any air in the system being bled off through a
bleeder tube. The head on each specimen was determined from piezometer
tubes. After 15 minutes of flow time, the initial flow determination was
made by collecting the overflow water in a known volume container and meas-
uring the time it took to collect it. The water sample was also used to
determine total solids of the water passing through the specimen. Addi-
tional measurements of the same type were made over the duration of the
test. The total elapsed flow time did not exceed 80 hours for any test.
3.8.3 Surface Sealer Tests. A falling head permeameter was used to
determine the effectiveness of various types of surface sealers. By plac-
ing a known head of water on a sealed concrete surface and then measuring
the loss of head with time as the water passes through the sealed surface,
an indication of the sealers' effectiveness can be obtained.
The permeameter was constructed by placing a 6-inch-inside-diameter by
6-foot-long Plexiglas pipe on the sealed surface of an 18-inch cellular
concrete cube (Figure 3.12). The concrete had a freshly mixed density of
31 pcf and water-cement ratio of 1.06 by weight. Ten cubes were cast and
cured 7 days in the wooden forms in which they were cast. The exposed top
surface of the concrete was covered with a polyethylene sheet during curing
to prevent drying. On the seventh day, the polyethylene sheet was removed
and surface irregularities of the concrete were scraped off. The coating
was then applied over the entire surface and allowed to dry for 3 days.
The coating thickness varied from material to material because of the
widely different consistencies of the various material sealers.
37
Manufacturers' guidelines for coating application were followed when pro-
vided. In all cases only one coat was applied. The average thickness of
the paraffin and cement slurry coatings was approximately 1/16 inch.
After the coating had dried for 3 days, the bottom of the wooden form
was removed and the cube with the side forms still on was placed on wooden
supports in a large tank as shown in Figure 3.12. The tank was filled with
water to the level of the top surface, of the concrete, with an outlet pro-
vided in the tank to maintain that level. The vertical Plexiglas pipe was
centered on the block and sealed around the outer edge with modeling clay
to prevent water leakage. The pipe was then filled to its top with water
and the test observations were immediately begun. The filling of the pipe
took approximately 2 minutes. Care was taken not to erode or damage the
sealed surface during filling.
Water-level determinations were made visually using a tape measure
affixed to the pipe. The total elapsed time at which any given water level
was observed was measured with a stopwatch and referenced to the time at.
which the pipe was completely filled.
The same procedure was used for all nine sealers. The control block
(no sealer) was evaluated at 10 days age using the same procedures.
38
1600
-1200
concon
U)w Ua
IdDUn , ,
800
400
0
2 OrO
[ _ _I _I _ _ I __ I _ _ J I _ _
I0 20 30 40 50 60DEFORMATION, PCT
Figure 3.1 Typical test record for a slow-loading test.
70 800
.. ms M s +30,o60 LB UNI1VERSAL ITEST ING MACHINE
Figure 3.2 Slow-loading constrained
compression test configuration.
4o
- 8.6" -EXHAUST
2 WAY SOLENOID
4-::
l
O" RINGS
jli
I I
i
I
I I -
w - I
II
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I III
Q IIIU Iz iw
F-U Q
cc Ixw
U
F-
LOAD
I
II I ICI I. ,
i '
o.
w
I
a.
ICE'
w
z
J
Milli
CLAMP 'I
CELL r
ACCELEROMETER
4" I
4.5"
2 WAY SOLENOID
GAS LINE TO TRIGGER
CROSS SECTION
SCALE IN INCHES0 1 2 3
GAS SOURCE
Figure 3.3 Impact air hammer apparatus (IAHA).
0
U1
Z
0
w
0
F-
lu
Cf)
C9
O
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W
J
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3
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Figure 3.4 Typical test record for arapid-loading test.
43
T
7 AT/2-/N.
FRONT VIEW
a. JOINT SCRIBER
44
SIDE VIEW
A-TOP V/EWOF FIRSTL IF T
b. JOINT SCRIBE PATTERN
Figure 3.5 Joint scriber and scribe pattern.
6.14 /Z' 0-
-
o-5ii_
HH
TOP VIEW
U
U
2-FT CUBE
-6" X6" E 24"JO/NT BEAMS (6)
CONTROL BEAMS (2)
SIDE VIEW
HORIZONTALALJO/N T
Figure 3.6 Horizontal joint study sampling schedule.
Figure 3.7 Lift height study, 30-foot column.
Figure 3.8 Lift height study,16-foot column.
4A?
*1
46
All,
«
K
y.
'r
L
.tip rK. A
M
C.
i
sy
aa
rr #5
Figure 3.9 Pressure pycnometer.
N
1I
4 "t ' t
i
r
s
' 4 ?
p
..
z 717'Wt
S
s, .
-11
ar
Figure 3.10 Low-head, unlimited reservoirpermeability test equipment.
48
I /e
x
titer. -s 3
S
. P', M
TO WATER RESERVOIR
SHUTOFF VALVE
BLEEDER TUBE
TOPIEZOMETER
TUBES
1/4-INCH REDRUBBER GASKET ---
DEFLECTION FLANGE
TROUGH
TEST
WATER LEVEL SPECIMEN
1/4-INCH RED RUBBER GASKET
Figure 3.11 Specimen container.
49
-/NT/AL WATER LEVEL
_T1
I -
_jul
65
CONTI NUALLY CHANGINGWATER LEVEL
CLAY SEAL
- -. CELLULAR- -: CONCRETE
- - - 4 - - -
Figure 3.12 Sealer study
OUTLET
_WOODENFORMS
falling head permeameter.
50
h
ho = 6 FT
SEALED SURFACE-
LH
vr
IZ .411 1 z .411lif I
_-
CHAPTER 4
TEST DATA AND ANALYSIS PLAN
4.1 CONSTRAINED STRENGTH DETERMINATIONS
All measured loads were converted to stress in pounds per square inch
of area of contact of the loading piston. The stress to yield strain is
predominantly a compressional stress and from yield strain to 40 percent
deformation is a combination of compressive and shear stresses. The defor-
mation of each sample was expressed as the amount of deformation per unit
length of sample times 100 to equal percent deformation. Typical stress-
deformation curves for the cellular concrete are shown in Figure 5.1.
In order to describe the stress-deformation characteristics of each
sample tested in constrained compression, three values of stress are deter-
mined. These values in pounds per square inch are: (a) yield stress a ,
(b) average stress to 40 percent deformation 0.40 , and (c) stress at
40 percent deformation 00.4 0 . The percent of deformation at which the
average stress x0.40 occurs is midway between yield strain and 40 per-
cent deformation. Yield strain can be assumed to be approximately 2 per-
cent when not specifically given.
The values of yield strain Ey , yield stress cy , and stress at
40 percent deformation a0.40 are obtained directly from the output records
from each test. The average compressive stress between yield strain and
40 percent deformation for curves such as those shown in Figure 5.1 can be
calculated by first determining the amount of plastic energy (nonrecover-
able) U absorbed per unit volume of material. The general case for de-p
termining the absorbed plastic energy is:
UE0.40- d (4.1)Ey
where U is equal to the area under the stress-deformation curve betweenp
the yield strain Ey and 40 percent deformation E0.40 . The average
stress T0.40 to 40 percent deformation can then be expressed as:
51
U
0.40 E0.40 - y
Various techniques can be used to determine U . The stress-p
deformation records obtained from the constrained loading tests of this
program were integrated by mechanical means.
4.2 MODULUS OF RUPTURE DETERMINATIONS
The flexural strength of concrete as determined from the third-point
loading of simple beams (Test Method CRD-C 16) is characterized by a param-
eter, R , called the modulus of rupture. When the fracture occurred within
the middle third of the span length as it did for all the flexural strength
test beams and horizontal joint beams in the study, the modulus of rupture
was calculated as
R ~ 2 (4-3)BD
where
R = modulus of rupture, psi
P = maximum applied load, pounds
L = span length, inches
B = average width of beam specimen, inches
D = average depth of beam specimen, inches
4.3 ULTRASONIC PULSE VELOCITY DETERMINATIONS
The compressional wave velocity of concrete as determined from the
ultrasonic pulse velocity test (Test Method CRD-C 51) is characterized by a
parameter, V , called the pulse velocity. It is determined simply as
V = (4.4)
52
where
V = pulse velocity, ft/sec
L = path length, feet
T = effective time it takes the pulse to pass through the specimen,seconds
4.4 MODULUS OF ELASTICITY AND POISSON'S RATIO DETERMINATIONS
The electrical resistance strain gages provided output for both ver-
tical and circumferential strains. X-Y recorders were used to put the
output in the form of stress-strain curves. By using each test record
separately and the secant technique at 40 percent of the yield strength of
the concrete as shown on the record being used, the modulus of elasticity,
E , was determined. Poisson's ratio was determined at the same point.
4.5 REGRESSION ANALYSIS
Where a sufficient range of freshly mixed densities and characteriza-
tion parameters associated with these densities existed for a particular
cellular concrete water-cement ratio, a relation between the density and
the test parameter was developed. This was done for the characterization
values representing stress, modulus of rupture, ultrasonic pulse velocity,
and secant modulus of elasticity. Inspection and analysis of the data in-
dicated that the line-of-best-fit as determined by least-squares techniques
for the relations developed could be expressed in most cases in the form of
a curvilinear regression of the equation
Y = aXb (4.5)
where
Y = characterization value (a, R, V, or E)
X = freshly mixed density, pcf
a,b = equation coefficients
The graphical presentations of these relations include statistical
53
tolerance limits for the data. These limits were established from the
standard error of the estimate, Sesty , where:
n 2(y. - y)2
Se = > (4.6)est,y n - 2
i=land
y. = observed dependent variable
y = predicted dependent variable
n = number of observations
An expression of +2 S established statistical tolerance limits that- est,y
enclosed the range within which approximately 95 percent of all future ob-
servations can be expected to fall.
4.6 DATA DISPERSION
When a number of observations were made of particular test measure-
ments involving specified test variables, the measure of dispersion used
for those observations was the standard deviation of a single observation.
It was calculated as
2 -EX - xxs(x) = n - 1 (-7)
where
s(x) = standard deviation of a single observation
x = observed dependent variable
54
CHAPTER 5
TEST RESULTS
5.1 CONSTRAINED COMPRESSION TEST RESULTS
5.1.1 Slow-Loading Test Results. Each test produced a stress-
deformation record similar to those shown in Figure 5.1. The curves in
Figure 5.1 are typical of those obtained over the range of densities at
each water-cement ratio. Using the stress characterization values, a rela-
tion between density and stress for each water-cement ratio was obtained.
These relations are summarized in Table 5.1 and are shown graphically in
Figures B.1 through B.15. Summaries of the curvilinear regressions for
each characterization stress are shown in Figure 5.2.
5.1.2 Rapid-Loading Test Results. The stress-deformation curves were
obtained by combining, on a common time basis, the two traces from each
oscilloscope photograph. In each case, the resulting stress-deformation
curve had the same general shape as the curve obtained from the slow-loading
test of a companion specimen (see Figure 5.1). The characterizing stress
values were different, however, and were used to develop the stress-density
relations shown in Figures B.16 to B.27. These relations are summarized in
Table 5.1 and in Figure 5.3.
5.1.3 Multiple-Shot Loading Test Results. Four cylinders each at
densities of 21 and 45 pcf, and five cylinders each at densities of 29.5
and 40 pcf were evaluated. All the concrete had a water-cement ratio of
0.86. The stress-deformation curves were derived from oscilloscope records
and were combined for each density so as to obtain an average stress-
deformation curve for that density. The average curves for all four den-
sities are shown in Figure 5.4.
5.2 FLEXURAL STRENGTH TEST RESULTS
5.2.1 Modulus of Rupture Test Results. A total of 180 flexure beams
were tested. Concretes with water-cement ratios of 0.76, 0.86, 0.96, and
1.06 were evaluated with the number of beams for each water-cement ratio
being 51, 44, 51, and 34, respectively. The beams for each water-cement
ratio represented 11 batches of concrete with the exception of the
55
1.06 water-cement ratio where only 8 batches were made.
The results of the modulus of rupture determinations were related to
the freshly mixed density and are shown in Figures B.28 to B.31. A summary
of the regression analyses for this data is shown in Figure 5.5 and
Table 5.2.
5.2.2 Horizontal Joint Test Results. A summary of the horizontal
joint test results is shown in Table 5.3. In the few instances where data
omissions occur, the samples from those blocks were not suitable for test-
ing. One entire block (for the moist-cured, unprepared surface variables)
did not have any satisfactory samples.
None of the joint beams experienced a failure across the joint. Only
one of the fifty beams tested did not fail in the concrete from the lower
lift.
5.3 ULTRASONIC PULSE VELOCITY TEST RESULTS
A total of 172, 6- by 12-inch cylinders were tested. Concretes with
water-cement ratios of 0.66, 0.76, 0.86, and 0.96 were evaluated with the
number of cylinders for each water-cement ratio being 36, 36, 48, and 52,
respectively. The cylinders for each water-cement ratio represented 12
batches of concrete. In most instances, the ultrasonic pulse velocity was
determined for each cylinder at ages of the concrete of 3, 7, 14, 28, and
60 days. The 0.86 and 0.96 water-cement ratio concrete cylinders were also
evaluated at 90 and 180 days age.
Ultrasonic pulse velocity versus freshly mixed density relations were
developed for each water-cement ratio and concrete age and are summarized
in Figures 5.6 and 5.7. The line-of-best-fit in each case can be repre-
sented by the relation X = aXb . A summary of the regression coefficients
and related statistical information is given in Table 5.4. The effect of
water-cement ratio on the pulse velocity for the range of densities evalu-
ated at 28 days age is shown in Figure 5.8.
5.4 RATE-OF-HARDENING TEST RESULTS
One sample each from concretes with water-cement ratios of 0.76, 0.86,
0.96, and 1.06 and nominal densities of 23, 32, 39, and 43 pcf at each
56
water-cement ratio was evaluated. The resulting penetration resistance
versus elapsed time curves (from the time the water in the mixture first
came in contact with the cement) for each sample are shown in Figures 5.9
and 5.10. The median value of the freshly mixed density for the four
batches representing each nominal density is also indicated along with the
variation in density that occurred.
5.5 MODULUS OF ELASTICITY AND POISSON'S RATIO TEST RESULTS
Modulus of elasticity and Poisson's ratio determinations were made for
concrete with nominal densities of 23, 32, 39, and 43 pcf each at water-
cement ratios of 0.66, 0.76, 0.86, and 0.96. One batch of concrete at each
density and water-cement ratio provided the specimens for those variables.
A summary of the data is shown in Table 5.5. The modulus was determined
using the secant technique at 40 percent of the yield strength of the con-
crete cylinder being tested. Poisson's ratio was determined at the same
point.
Relations between the freshly mixed density at 28 days age and the
secant modulus at the same age are shown for each water-cement ratio in
Figures B.32 to B.35 and are summarized in Figure 5.11 and Table 5.6. The
line-of-best-fit for the limited amount of data available was in the form
Y = aXb in each case.
5.6 TEMPERATURE STUDY RESULTS
5.6.1 Adiabatic Temperature-Rise Results. Three batches of concrete
were used to fill the adiabatic container. The concrete had an average
freshly mixed density of 43.9 pcf and a cement content of 6.78 bags/cu yd.
The temperatures of the mixture ingredients and resulting concrete at time
of placement are shown in Table 5.7.
The adiabatic temperature development curve for the concrete is shown
in Figure 5.12. Testing was terminated at 213 F because of the possibility
of equipment damage due to the increasing water vapor pressure in the
concrete.
5.6.2 Mixture Water-Temperature Results. The initial temperatures of
the mixture ingredients and the temperature of the concrete when placed are
57
shown in Table 5.7. The temperature development curves for concretes made
with mixing water temperatures of 40, 60, 80, and 100 F for both Type I
(RC-554) and Type III (RC-560) cement are shown in Figure 5.13.
5.6.3 Lift Heat Effects Results. The concrete, made with both Type I
(RC-554) and Type III (RC-560) cement, had a water-cement ratio of 0.86
with average (for both lifts) freshly mixed densities of 36.8 and 35.2 pcf,
respectively, and cement contents of 4.75 and 4.95 bags/cu yd, respectively.
The heat development curves for both lifts of both mixtures are shown in
Figure 5.14 in the form of a temperature increase from the initial placing
temperature versus elapsed time from initial placing of each lift. Peak
temperatures of 170 and 182 F occurred in the bottom of the second lifts
for the Type I and Type III mixtures, respectively.
5.6.4 Ambient Air Temperature Effects. The concrete was made at nom-
inal densities of 23, 32, 39, and 43 pcf, all with a water-cement ratio of
0.86 by weight. The measure of damage due to the increased curing tempera-
ture was by visual inspection and resulted in only qualitative comparisons.
These comparisons can be made from the photographs in Figures 5.15 and 5.16.
5.7 LIFT HEIGHT RESULTS
Figure 5.17 shows the hardened densities for both lift heights as func-
tions of the depth of concrete in the lift. In the as-cast condition, the
density appeared to vary approximately 7 pcf in a 16 -foot lift and approxi-
mately 20 pcf in a 30-foot lift. The first 16 feet of the 30-foot lift
showed a density change of approximately 12 pcf. The amount of evaporable
water in the 16-foot lift appeared to be a fairly uniform amount over the
entire lift height, varying from approximately 11 pcf near the top of the
lift to 13 pcf at the bottom.
5.8 MOISTURE STUDY RESULTS
5.8.1 Saturation Results. The saturation data for the five cylinders
evaluated were averaged and are presented in Figure 5.18 as the relation
between available void space filled and water pressure. No measurable
amounts of water, as dictated by the degree of sophistication of the
58
pycnometer, could be forced into the specimens after a water pressure of
1,200 psi was reached.
5.8.2 Flow and Erosion Test Results. Two specimens each of concrete
with water-cement ratios of 0.76, 0.86, and 0.96 and nominal freshly mixed
densities of 23, 32, and 43 pcf, respectively, were tested. All specimens
were bag-cured 28 days before testing.
The waterhead was determined at any given time by the varying losses
in the system. The densities of 23, 32, and 43 pcf had average heads of
5.10, 6.09, and 6.61 feet, respectively, over the test time period and
range of water-cement ratios used.
The results of the flow portion of the tests are shown in Figures 5.19
and 5.20 for the 23- and 32-pcf concrete, respectively. The total flow
time was approximately 50 hours for the 23-pcf concrete and 80 hours for
the 32-pcf concrete. No flow was observed for the 43-pcf concrete.
The results of the erosion portion of the test are shown in Figures
5.21 and 5.22 for the 23- and 32-pcf concrete, respectively. The average
total solids in the tap water prior to its passing through each specimen
was 333 ppm. This determination and the other total solids measurements
were made by evaporating the water samples at 194 F and drying the residue
at 210 F.
5.8.3 Surface Sealer Test Results. The results of the sealer study
are shown in Figure 5.23 in the form of a waterhead-time relation. The
sealers showing little reduction in head with time can be considered as
being more effective than those that show a rapid head loss with time.
The reference numbers in Figure 5.23 correspond to the following sealer
types: (1) no sealer, (2) styrene-butadiene product, (3) two-component
epoxy thinned with a volatile solvent, (4) paraffin-resin mixture,
(5)' liquid latex, (6) vinyl based liquid-type solvent, (7) asphalt, (8) la-
tex wall paint, (9) neat Type III cement slurry, and (10) hydraulic cement
slurry.
59
TABLE 5.1 SUMMARY OF CONSTRAINED STRESS VERSUS FRESIfLY MIXED DENSITY, CORRELATION REGRESSION COEFFICIENTS. o = a(d)b +2 St,y
Water- Freshly No. of Yield Stress, o Average Stress to 40% Deformation, Stress at 40% Deformation,Cement Mixed Samples y_00.400.40
Ratio Density a b S Correla-Range est,y tion a b S Correla- a b S Correla-
Coeffi- est,y ion est,y tioncient Coeffi- Coeffi-
cient cient
pcf
Slow-Loading Tests:
0.66
0.76
0.86
0.960
1.06
20 to 47
22 to 43
23 to 46
18 to 44
23 to 45
143
98
109
64
111
23.25 x 10-5
32.76 x 10-5
22.32 x 10-4
30.79 x 10-4
13.75 X 104
3.875
3.713
3.095
2.960
2.625
50.2
39.3
25.5
20.5
21.0
0.952
0.963
0.944
0.949
0.943
10.82 x 105
22.16 x 10-
14.06 x 10-4
38.12 x 10~4
64.61 x 10_
4.141
3.873
3.268
2.927
2.756
53.7
37.0
18.0
18.3
19.6
0.964
0.978
0.972
0.980
0.975
49.33 x 10-6
11.81 x l0-5
48.55 x 10~5
22.99 x 10-4
23.18 x 10-
4.407
4.086
3.605
3.110
3.080
69.6
h5.8
28.9
27.9
28.3
0.964
0.974
0.970
0.969
0.961
Rapid-Loading Tests:
0.76
0.86
0.96
1.06
23 to 43
23 to 46
18 to 43
23 to 46
47
68
46
83
17.99 x 10-4
20.56 x l0o-3
28.73 x 10- 3
31.28 x 10-3
3.391
2.643
2.550
2.467
48.0
52.4
24.3
42.3
0.975
0.963
0.988
0.935
13.41 x 10-4
15.62 x 10-3
25.81 x 10-3
24.71 x 10-3
3.478
2.715
2.558
2.528
47.6
55.1
18.8
33.0
0.981
0.964
0.994
0.965
37.97 x 10-5
53.46 x 10-4
14.73 x 10-3
16.65 x 10-3
3.851
3.039
2.726
2.657
59.4
63.8
27.9
52.9
0.980
0.973
0.987
0.951
TABLE 5.2 SUMMARYRELATION
OF MODULUS OF RUPTURE VERSUS FRESHLY MIXED DENSITY,REGRESSION COEFFICIENTS, R = a(d)b +2 S , psi
- est,y
Water- Freshly No. of Regression Standard CorrelationCement Mixed Samples Coefficients Error of CoefficientRatio Density a b the Estimate
Range Sesty
pcf
0.76 23 to 42.8
0.86 23 to 43
0.96 22 to 43
1.06 23 to 42
51 2.740 x 10 -3 2.665
44 6.983 x 10-4 2.970
51 6.569 x 10-4 2.962
34 7.022 X 10 4 2.930
COR-
5.2
4.7
2.9
0.953
0.971
0.969
0.979
TABLE 5.3 SUMMARY OF HORIZONTAL JOINT TEST RESULTS
Block Surface Joint Lift Cube Test Results Beam Test ResultsNo. Curing Surface Location
No. of Oven-Dry Cube Control Beams Joint Beams Failure LocationsCubes Density Strength
Modulus of No. of Modulus of s(x Bottom Across Top
Mean s(x' :Mean s(x) Rupture Beams Rupture Lift Joint Lift
pcf pcf psi psi psi psi psi
7 Air Unprepared BottomTop
8 BottomTop
9 BottomTop
14 BottomTop
2 Air Prepared BottomTop
4 BottomTop
5 BottomTop
8 BottomTop
11 Moist Unprepared BottomTop
17 BottomTop
19 BottomTop
1 Moist Prepared BottomTop
3 BottomTop
6 BottomTop
15 BottomTop
21.721.4
21.220.9
21.722.4
20.721.4
20.221.1
20.821.2
21.021.9
20.721.5
21.221.9
21.621.6
21.621.5
20.521.0
21.221.1
21.522.9
21.321.6
0.6
0.34C.260.29C. 54
0.27
0.53
0.570.22
0.540.h2
0.130.49
0.390.80
0.110.111.20
0.35
0.55
0.39
0.200.17
0.370.33
0.270.62
0.370.70
62.170.9
64.463.9
57.471.0
51.067.7
49.577.6
58.687.8
54.268.6
46.873.8
60.074.2
57.067.2
65.865.4
50.492.6
7.973.594.90h.1O
7.8710.43
5.2710.91
2.7013.22
3.9521.80
3.226.27
6.2014.53
4.5913.81
15.804.31
7.01
5.964.936.38
55.0 6.4470.4 4.87
58.679.8
51.565.3
3.5012.55
3.756.93
16.121.2
20.6
18.220.5
16.016.7
18.821.2
16.8
18.221.2
16.416.1
21.9
20.9
18.318.5
22.322.9
17.019.4
18.518.5
17.20.615.718.9
2 10.8 1.48 2 0 0
2 9.6 2.19 2 1 0
2 13.8 3.32 1. 0 1
6 13.2 1.36 6 0
3 13.6 2.37 3 0
0
3 13.3 1.62 3 0 0
2 10.0 0.92 2 0 0
6 11.5 2.20 6 0 0
1 12.0 -- 0 0
6 13.5 4.13 6 0 0
4 16.6 1.74 6 0 0
3 12.8 0.46 3 0 0
2 15.3 3.54 2 0 0
2 20.0 6.01 2 0 0
6 13.1 1.07 6 0 0
R)
TABLE 5.4 SUMMARY OF ULTRASONIC PULSE VELOCITY VERSUS FRESHLY MIXED DENSITY, CORRELATION REGRESSION COEFFICIENTS, V = ad +2 Sest- s,y
Age w/c = 0.66 w/c = 0.76 w/c = 0.86 w/c = 0.96
No. of a b Standard Corre- No. of a b Standard Corre- No. of a b Standard Corre- No. of a b Standard Corre-Obser- Error of lation Obser- Error of lation Obser- Error of lation Obser- Error of lation
vations Estimate Coef- vations Estimate Coef- vations Estimate Coef- vations Estimate Coef-
Sest,y ficient Sest,y ficient Sest,y ficient Sest,y ficient
days ft/sec ft/sec ft/sec ft/sec
3 36 154.45 0.897 146
7 36 189.22 0.875 203
14 36 187.73 0.896 193
28 36 215.16 0.870 194
60 36 22
90 --
180 --
0.985 36 368.75 0.621 129
0.977 36 344.37 0.680 118
0.982 36 332.18 0.716 144
0.982 36 374.23 0.696 119
0.972 48 274.71 0.647 191
0.983 48 297.17 0.660 232
0.984 48 258.41 0.744 181
o.988 48 308.36 0.722 235
5.59 0.863 211 0.979 36 428.81 0.668 133 0.986 48 334.10 0.724 249
-- -- -- -- -- -- -- -- -- 48 312.58 0.747 281
-- -- -- -- -- -- -- -- -- 34 356.82 0.714 244
0.915 36 685.45 0.345 64
0.909 36 562.92 0.476 82
0.962 52 506.26 0.543 75
0.948 52 495.49 0.575 86
0.951 52 499.98 0.586 85
0.944 52 542.45 0.564 114
0.959 52 570.58 0.549 105
uJ\
0.934
0.973
0.984
0.985
0.986
0.973
0.977
TABLE 5.5 SUMMARY OF MODULUS OF ELASTICITY AND POISSON'S RATIO DATA
Water- Freshly No. of Yield Yield Strain, E Poisson's Secant Modulus
Cement Mixed Tests Stress, cry_ Ratiob of Elasticity
Ratio Density yea
Mean s(x)a s(x) Mean s(x) Mean s(x)
pcf
o.66
0.76
4-z
0.86
0.96
22.832.238.443.2
23.631.839.043.8
23.632.0
39.443.0
23.231.639.243.0
4555
4553
5555
5545
psi psi
19
78213257
3474
166213
22
57106160
2129
5655
1.07.4
25.454.7
1.59.1
13.925.8
0.76.5
18.117.0
1.52.9
11.42.7
in/in
1,322
1,3341,8261,508
1,3551,4281,5481,46o
1,0601,0001,1821,404
1,032544650562
in/in
88207282362
11525682
227
4241
246235
334313323
psi
0.1980.2190.2050.195
0.2270.2500.2050.193
0.2520.2010.2270.226
0.2340.1920.2370.214
0.0230.0140.0250.018
0.0150.0130.0290.009
0.0390.0250.0230.017
0.0120.0410.034o.o16
psi
17,37069,770140,930188,190
33,70063,930
121,950167,680
26,85072,620
110,030145,980
22,720
59,85092,440
105,370
2, 3203,65020,4909,890
7201,000
13,9605,070
8606,7405,6402,780
8608,7709,6002,000
a s(x) = standard deviation of a single observation.
b Calculated at 0.4 o .
TABLE 5.6 SECANT MODULUS OF ELASTICITY VERSUS HARDENED DENSITY RELATION,E = a(d)b +2 S
s - est,y
All concrete made with Foaming Agent M and evaluatedmoisture condition.
at the as-cast
Water- No. of Density a b S CorrelationCement Specimens Range esty CoefficientRatio
pcf
0.66 19 22.8 to 43.2 0.00023 3.637 14.15 0.9930.76 17 23.6 to 43.8 0.00797 2.623 9.90 0.9900.86 20 23.6 to 43.0 0.00449 2.765 6.70 0.9920.96 19 23.2 to 43.0 0.00914 2.507 6.10 0.983
TABLE 5.7 SUMMARY OF TEMPERATURE-RISE STUDY BAT CHING DATA
Cement Round Water- Freshly Initial Temperature, FNo. Cement Mixed
Ratio Density Water Cement Slurry Concrete
pcf
Type I 1 0.86 35.6 40 65 50 58(RC-566) 2 o.86 35.2 60 65 64 67
3 0.86 35.0 80 65 82 804 0.86 33.6 100 65 94 92
Type III 1 0.86 37.6 40 65 45 58(RC-567) 2 0.86 36.8 60 65 65 69
3 0.86 35.6 80 65 81 824 0.86 36.4 100 65 95 92
Adiabatic Test:
Type III Avg of 0.86 43.9 42 60 50 52(RC-567) three
batches
65
DENSITY=23.0 PCFW/C=0.88
DENSITY=38.5 PCFW/C=0.86
20 40 60 0
DEFORMATION, PCT
DENSITY=3I.9 PCFW/C=0.86
DENSITY=43.0 PCFW/C=0.86
20 40
Figure 5.1 Typical stress-deformation curves.
66
400
200
0
U)a-
,U)
400
200
00 60
I I I I
800
600
'GAO
400(ORP06
0"2 00
16 22 26 30 34 38 42 46
c. YIELD STRESS
800
600 ,
400 10-
0g
200
18 22 26 30 34 38 42 46
b. AVERAGE STRESS800 __________
a-
zO 600
ac
0w* 400f-)
200
U
08 22 26 30 34 38 42 46
FRESHLY MIXED DENSITY, PCF
c. 40PCT DEFORMATION
Figure 5.2 Summary of stress versus freshlymixed density relations, slow-loading tests,28-day strength.
67
/
P 0"
SIo
0 "
6.6bog6
a
_ q
i
5
U)
CL
U)
J
U)0.
z0
4
0LL.
0
F-)
a.
0
U)0.
NWQ-
4
0
U)
a.
U)
600
400
200
OL18
033'
22 26 30 34 38 42 46FRESHLY MIXED DENSITY, PCF
c. 40 PCT DEFORMATION
Figure 5.3 Summary of stress versus freshly mixed den-sity relations for rapid-loading tests, 28-day strength.
68
800
600 ----
200 -
6l 22 26 30 34 38 42 46
ca. YIELD STRESS00 ____
600
4 00
00
2006
8 22 26 30 34 38 42 46
b. AVERAGE STRESS800r
-7
1b _
i i i
i
5
0" 6 .,
0.0
I
750_
SHOT I SHOT 2
6000 h/
WATER-CEMENT RATIO= 0.86 (BY WEIGHT)
300 -- - ' ...
I0 20
III' II
c
\ +
30 40
DEFORMATION, PCT
50 60
Figure 5.4 Stress-deformation relations for multiple-shot loading.
22 26 30 34
FRESHLY MIXED DENSITY, PCF
38 42
o.--
0
Figure 5.5 Summary of the modulus of rupture versus
freshly mixed density relations.
69
U)0.
U)wI-,)
, ~II .
150
00 70 80
80
jtj 60CL
I-
00U.
J
00 _
28-DAY STRENGTH
+ E
06.
~- 6- -6
-K--
18 46
I -r -- -
i i i i P -+
1 21
6000 28DAY
600060DAY
I4DAY
5000
47DAY
4000 3A
3000
200022 26 30 34 38 42
a. WATER-CEMENT RATIO 0.667000
0
0
22_0 1_ _ _ _ _ _
28 30 34 38
FRESHLY MIXED DENSITY, PCF
b. WATER-CEMENT RATIO 0.76
42
46
46
Figure 5.6 Summary of ultrasonic pulse velocity versus freshlymixed density relations for water-cement ratios 0.66 and 0.76.
70
7000
uw
U-
F-)
0LJ
w
J
u
z0U)
__ +_ i i i +--------
uw 600'
LA-
I-uo 500'w
wN,J
a 400
z0
S300'
20
2SDAY60O >
0t/4DAY
SDAY
0)
j DAY
i E + I
r
6U00
uw
F-
F-
0Jw
J
B.
0U
J
26 30134 326 30 34 38
FRESHLY MIXED DENSITY, PCF
b. WATER-CEMENT RATIO 0.96
42 46
Figure 5.7 Summary of ultrasonic pulse velocity versus freshlymixed density relations for water-cement ratios 0.86 and 0.96.
71
90 DAY/IODAY
5000
4000
3000
2000
1000
6000
5000
4000
3000
2000
uw
Fi-
0Jw
J
z0U
I-J
60 DA Y
3 AY
22 26 30 34 38 42 46
a. WATER-CEMENT RATIO 0.86
60,90, AND 80 D AY
28 DAY
3 DA Y
-
I00022
J
6000
sooo -0
4000
3000
18 22 28 30 34FRESHLY MIXED DENSITY, PCF
38 42
Figure 5.8 Summary of ultrasonic pulse velocity versus freshly mixeddensity relations showing effect of water-cement ratio, 28 days age.
72
UwNF-L
0Jw
w
U
z0N'
F-J
46
60
Figure 5.9 Penetration resistance versus time relations for
23- and 32-pcf nominal density concretes.
73
80
WATER -CEMENT
RA T/0
-- /.06
10 20 30 40 50 80 70 80 90
a. FRESHLY MIXED DENSITY = 22.5 0.5 PCF
0.6
0 10 20 30 40 50 60 70 80 9ELAPSED TIME, HOURS
b. FRESHLY MIXED DENSITY = 32.4 0.4 PCF
U)
40
201
200
150
U,a~
U,U,
I-U)
00l
50
0
0
0
2 00
150 "Ti O -
Soc
0 10 20 30 40 50 60 70 809
Q. FRESHLY MIXED DENSITY = 39.3 0.3 PCF00
300
200-
0
C
__________
0 10 20 30 40 50ELAPSED TIME, HOURS
b. FRESHLY MIXED DENSITY = 43 PCF
Figure 5.10 Penetration resistance versus time relation for39- and 43-pcf nominal density concretes.
74
60 70 80 90
0
?U0 r
DATA USED FOR EACH WATER CONTENTRATIO REPRESENT THE SECANT MODULUSFROM THE ORIGIN TO 0.4fc 0 \ /
60.
/
022 26 38 42 46
Figure 5.11 Summary of secant modulus of elasticityversus freshly mixed density relations.
2O
f10..
170
130TYPE I CEMENT
CEMENT CONTENT = 6.65 BAGS/CU YDWATER-CEMENT RATIO= 0.86 (BY WEIGHT)
FRESHLY MIXED DENSITY = 43 PCF
90
5o0_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
10 20 30 40ELAPSED TIME, HR
50 60 70
Figure 5.12 Adiabatic temperature development curve.
75
0
x< 150
I-U
100JW
0N,
D
0
18 30 34FRESHLY MIXED DENSITY, PCF
k
TEST TERM/NA TED-,
213 F
LL.0
w
wa-
0
P -
i'
i
,in
w
170
/00 F 80F130
60 F40 F M/X WATERTEMPERA TURE
90
50
a. TYPE I CEMENT
170
13 0 ~/0 0F..--
130
80 F
40 F MIX WATERTEMPERA TURE
90
5000 2 4 6 8 10 12 14 I
ELAPSED TIME, HOURS
b. TYPE MI CEMENT
Figure 5.13 Effect of mixture water temperature onearly-age heat.
76
w
w
w
6
I
0 E3 12ELAPSED TIME, HR
b. TYPE IE CEMENT
Figure 5.14 Effect of hydration heat on adjoininglifts of concrete .
77
BOT TOM- L /FT / BOTTOM- L /FT 2
80 MIDDLE - MIDDLE- L /F-_ 2LIFT /
/
STOP - L/FT / TOP -L/FT 2
40
0Co 4 8 12 16 2(
a. TYPE I CEMENT
20
BOTTOM-LFr2MIDDLE-L/FT /
80 rO FMIDDLE- LIFr2BOrroM-L/FT i
OP-L/T/ TOP - L/F2
4 0-
02
w
Ix
uzW
4rFe-l0W
a2-
1 yn
I
0
to8 0V4
a. Top view.
Figure 5.15
y:
b. Side view.
Effect of 100 F air-curing temperature.
78
6
a. Top view.
b. Side view.
Figure 5.16 Effect of 120 F air-curing temperature
79
.A
F
1
'
> VF
yy
F
r ;
AS-CAST,30-FT LIFT
42
"
AS-CAST, /6-Fr LIFT34
28
OVEN DRY-16-Fr LIFT
18
10noc
DEPTH FROM16
TO P24
OF LIFT, FT
Figure 5.17 Effect of lift height on concrete density.
120
Ua Ioo
-J-J
w 10 - -- - - - - a
9/000 80
w WATER-CEMENT RATIO= 0.86
-J BAG-CURED DENSITY = 51 PCF
>60I4
600 800WATER PRESSURE, PSI
Figure 5.18 Saturation curve for a cellular concrete.
80
U.
CL}
H
zw
w
LuJzw0
32
0 200 400 1000 1200 1400
n13
An' i I I I i
0, .:
0
WATER-CEMENT RATIO=0.76
0O00- o-
20
10 -
WATER - CEMENT RATIO= 0.86
20
WATER - CEMENT RATIO =0.96
J80 ----
Z80
00
4I 0 - - -- - - ---- --- - --- - - -
O
41 11-
Figure 5.19
10 100 1000TOTAL FLOW TIME, HOURS
Flow data for 23-pcf concrete.
81
0
WATER-CEMENT RATIO =0.76
-- [11----O 000 01~ CD
80
WATER -CEMENT RATIO= 0.86
4C - Q0__
0
20 - -- -
800
WATER -CEMENT RATIO = 0.96
4 10 100 100TOTAL FLOW TIME, HOURS
Figure 5.20 Flow data for 32-pcf concrete.
82
0J
J
Q
F-
U
0w
0
10 20 30 40 50
TOTAL FLOW TIME, HOURS
Figure 5.21 Erosion data for 23-pcf concrete.
83
600
500
400
C')
0U)
-J
I-0
WATER-CEMENTRATIO
o 0.760 0.86A 0.96
00 -
'TAPWATER BASE =333 PPM
300-
2000 60
1800
1600
1400
1200
WATER- CEMENTRAT/O = 0.86
a
rn O000
J
H
WA TER - CE ME NT
RAT/O =0.76
800
WATER- CEMENTRAT/0 =0.96 A
400
TAPWATER = 333 PPM
2000 20 40 60
TOTAL FLOW TIME, HOURS80
Figure 5.22 Erosion data for 32-pcf concrete.
84
1200 1600
ELAPSED TIME, SECONDS
2000
Figure 5.23 Sealer effectiveness test results.
7
31wd
w
coD
I
2I
400 800 2400
Do .5
0 " 0
-- "
O "7
O " 0
9
2,3,4
0
O
l',.
CHAPTER 6
DISCUSSION OF TEST RESULTS
6.1 CONSTRAINED STRENGTH-DEFORMATION CHARACTERISTICS
6.1.1 Slow-Loading Results. As shown in the typical constrained
stress versus deformation curves in Figure 5.1, the cellular concretes
studied have a curve shape approximating that considered to be better for
an efficient backpacking material (Reference 2). In most cases, the slopes
of the initial (elastic) portion and the crushing (plastic) portion of the
curves increase with increasing densities. Locking of the curves generally
did not begin to occur until after 40 percent deformation was reached; but
in a few instances involving the higher density, higher strength concretes,
the locking regime may have begun between 35 and 40 percent deformation.
The start of the locking, in these cases, was not as distinct as that ob-
served for lower densities.
Cellular concrete is limited as far as strength is concerned by the
inherent strength of its constituents and by the formulations necessary to
produce the desirable characteristics of a backpacking. Neat cellular con-
crete is basically a hardened cement paste with a large void content. For
the purposes of this study, porosity, n , will be defined as the volume of
these voids divided by the total volume of the concrete where the voids
consist of the pores in the cement paste (both gel pores and capillary
pores) plus the entrained and entrapped air voids.
Numerous investigators have related the strength of hardened cement
paste to porosity either directly or indirectly. As shown in Reference 6
it was found that:
VS = 120,000 m - 3,600 (6.1)
0
where S is strength of the hardened paste and Vm is the constant in the
BET surface area equation. Vm is proportional to the surface area of the
cement gel, which in turn is proportional to the amount of cement gel.
W0 is the original water content after bleeding. It was later suggested
in References 7 and 8 that the strength of the hardened paste could be
86
empirically related to a volume of gel/space ratio by a power function
where:
S = S (x)b (6.2)
where X = gel/space ratio and could include the effects of entrained and
entrapped air (Reference 8) and b varied somewhat but was approximately
equal to three.
As shown in Reference 9, it was found from experimental evidence that:
s = so(1 - Vp)2 .7 (6.3)
where Vp is the porosity. Based on a simple geometric model, it was sug-
gested in Reference 10 that:
S = s 1 - 1.2V2) (6.4)
It was suggested in Reference 11 that the data for strength as given
in Reference 6 be plotted against (W - W ) = W , i.e., the original watero n e
content less the nonevaporable water content, where W is more closely
related to porosity than Vm/Wo . As shown in Reference 11, it was then
found that:
s3= (1 - We)6 (6.5)
and it was further speculated that the strength of hardened cement paste
could be approximated as:
S = s(1 - vP) 6 (6.6)
In all of the above cases, it is readily obvious that a decrease in
porosity will reflect an increase in the strength of the paste.
For backpacking design purposes, a suggested approach is to relate
the desired strength to the porosity of the cellular concrete which, in
87
turn, is a function of the water-cement ratio, concrete density, and spe-
cific gravity of the cement. This provides some latitude in the selection
of a cellular concrete design for a particular requirement.
Using the notation of Section 2.2, the volume of water in the concrete
will be considered as being composed of both evaporable and nonevaporable
water (Reference 12), that is:
Vw =Vew +Vnw (6.7)
where
VeW = volume of evaporable water
Vnw = volume of nonevaporable water
The space left in the concrete after the evaporable water leaves is con-
sidered as void space. The theoretical porosity, n , for a neat cellular
concrete, as defined above, is then:
Vn = Vt (6.8a)
V +Va ew (.b=V +V +V (6.8b)
c w a
V
V +V +V (6.8c)c nw v
The density expression:
w W +Wd_=t _= c w 69
c t V + V + V (.
t c w a
can be rewritten in terms of water-cement ratio and specific gravities to
be:
(1 + k)W
c Vc +V +Vv(6.10a)c nw v
88
(1 + k)V p 7
V +V +VC nw v
where
pc = specific gravity of the cement
w unit weight of water
The volume of voids is then expressed as:
Vv = ac[1 + k)VCpC7W - d(VC + Vnw)
(6. lob)
(6.11)
Using an average value of 0.20 for the ratio of hydration water to cement
by weight (Reference 12)
nw = 0.20
c
(7 )V
pcyw cor
V =0.20 pcVc
nw c c
Equation 6.11 can then be written as
V =dv -de C
VcdC
(6.12)
(6.13)
(1 + k)VcpcyW - dc(Vc + 0.20 pcVc)]
(1 + k)pcYw - dc(1 + 0.20p )] (6.14)
Substituting in Equation 6.8a,
[(1 + k)pcyw - dc(l + 0.20p)]
(wt/d)
(1 + k)pC7w - dc(1 + 0.20p)]
(1 + k)Wc
+(1+k)pcyw - dc(1 + 0.20pc
V(l + k)pc7
89
Vcn = -
c
c
c
d (1 +0.20pc
n= 1 - dc( + O2p) (6.15)(1 +kp7
c w
Equation 6.15 is the expression for the theoretical porosity of the cellu-
lar concrete in terms of density, water-cement ratio of the freshly mixed
concrete, specific gravity of the cement, and the unit weight of water. It
has been assumed in this development that the specific gravity of water is
unity.
Using the values of specific gravity for the Type III cement of this
study and a unit weight of water of 62.3 pcf, Equation 6.15 can be ex-
pressed as
0.00834d(1-n) = 1+kc (6.16)
In relating the constrained strength of the cellular concrete, as
measured in this study, to porosity, only the yield stress should be con-
sidered as it is basically a compressive stress whereas past the yield
point the stresses are more complex, being functions of both compressive
action and punching shear. These complex stresses may not relate directly
to porosity. Backpackings are usually designed for an average crushing
stress, that is, the average stress value of the crushing plateau of the
stress-deformation curve. To relate porosity to this design value, the re-
lation between y and ~0.40 must be known. The stress-density rela-
tions of Table 5.1 suggest that for a common density, the two stress values
are related in a power function form of
a(.40 (y)B (6.17)
where B = bo.40/by . In analyzing the relation between ay and Q0.40in the form 0040 = a(ay)b for each water-cement ratio, correlation co-
efficients between 0.96 and 0.99 were obtained. Comparing the regressions
obtained in each instance, it was found that statistically they were not
significantly different, thus indicating an independence from the influ-
ence of water-cement ratio. By being independent, all the data were then
90
combined and analyzed with the resulting relation of
-1.008 +7 sa0.4 0 = 1.109(ay) + 76 psi (6.18)
at the 95 percent statistical tolerance limits. The correlation coeffi-
cient was 0.971. For the sake of simplicity, Equation 6.18 can be approxi-
mated as
0.4 0 =1 y175a (6.19)
The data for the 525 constrained slow-loading tests are shown in Fig-
ure 6.1 in the form of a yield stress versus theoretical porosity plot. A
separate least-squares regression analysis of the data for each of the water-
cement ratios indicated that the line-of-best-fit in each instance was in
the form
a = a (1 - n)b (6.20)y
where the coefficients a and b varied somewhat between each water-
cement ratio. Statistically, however, the lines-of-best-fit were not sig-
nificantly different from each other. Correlation coefficients varied be-
tween 0.94 and 0.98. The relation for all the data together can be approx-
imated by the expression
y = 42,000(1 - n) 3 (6.21)
where the 95 percent statistical tolerance limits are at +81 psi and the
correlation coefficient is 0.94.
Combining Equations 6.15 and 6.17, the yield stress can be expressed
as a function of the two principal variables, i.e., water-cement ratio and
freshly mixed density, plus the specific gravity of the cement, where
d (1 + 0.20p c) b
a =a d +0p) (6.22)y [ (1 + k)P7Jw
91
1+020 bdo 1 + O.20pcb
a = (6.23)y r o 1+ k pc(623
From Equations 6.16 and 6.18
a = 0.02436(l+ck) (6.24)
Equation 6.24 is shown graphically in Figure 6.2. The relations between
do/(l + k) and the freshly mixed density, d , are shown in Figure 6.3.
Using these two figures together, along with Equation 6.19, a starting
point in the design of a neat cellular concrete for particular backpacking
requirements of density and strength can be obtained.
The curve in Figure 6.1 represents the results from a particular ce-
ment. Other cements may produce slightly different results. A possible
approach to a more universal design curve for all cements is to put Equa-
tion 6.23 in the form
Q d b1 + 0.20pc
(6.25)a 1+ kp7
Reasonable limits of specific gravity for portland cements are from 3.1 to
3.2. The last term in Equation 6.25 varies then between (0.008388)b and
(0.008226)b , respectively. Assuming the value of b to be of the same
order and magnitude as indicated in Equation 6.24, the specific gravity
term can be assumed to be fairly constant for the practical range of spe-
cific gravities, and hence
a d b
-c~(1>~ (6.26)Q + k
The value of the coefficient b for a wide range of cement brands and
types should be determined by test. The data from the Type III cement of
this study indicate that the value is approximately three. As a third
power function for a range of specific gravities, Equation 6.25 is shown
92
in Figure 6.4. This curve, together with Figure 6.3, may provide a design
technique applicable to most portland cements.
The range of densities and water-cement ratios used in this study is
not necessarily the limits of design that can be used to satisfy backpack-
ing requirements. From practical considerations, however, the lower limit
of density is approximately 18 pcf. It is also doubtful that water-cement
ratios below 0.55 could be used without creating fabrication problems. The
upper limits of density with respect to backpacking use are not so well de-
fined. Densities of 60 pcf have been used (Reference 3) with very good
success. Water-cement ratios above 1.0 (by weight) begin to create fabri-
cation problems because of the excess of free water, which tends to destroy
the stability of the preformed foam.
6.1.2 Rapid Loading. The results of a rapid-loading test often pro-
vide only qualitative results. Different loading systems, techniques, and
rates will provide different test results for the same material. The
rapid-loading test does provide twofold information, however. First, it
does show if the material is strain and/or load rate sensitive; second, it
gives some indication of the magnitude of load resistance that might be ex-
pected. This is evident from the results shown in Figure A.8, Table 5.1,
and Appendix C. The rapid-loading tests, as described in Section 3.1.2,
might produce the response of cellular concrete at some reasonable distance
from the origin of the shock wave producing the loading, while the results
of Appendix C may pertain to very close-in loadings.
By comparing the two equation forms for slow and rapid loading (Table
5.1) at a common water-cement ratio and density, a relation between the two
in the form of
( br/bsa = ar _s (6.27)
is produced where a and b are the equation coefficients of Table 5.1,
a is any of the characterization stresses, and subscripts r and s in-
dicate the rapid- and slow-loading cases, respectively. Comparing the
average stress value, Q0.40 , for the four water-cement ratios for which
both slow- and rapid-loading tests were conducted, it was found that for
93
all practical purposes, the relation between ar and as was independent
of the water-cement ratio. By combining all of the data an expression in
the form
ar= 2.620-9 (6.28)
resulted for the average stress characterization, a0.40 . Equation 6.28
is shown in Figure 6.5 and provides results that are within 10 percent of
what might be determined for each water-cement ratio individually. It is
shown in Equation 6.28 and Figure 6.5 that cellular concrete as tested by
the IAHA is rate-sensitive and, as such, should be treated accordingly in
the analysis of the response of backpacked structures.
6.1.3 Multiple-Shot Loading Capability. If a backpacked structure
survives the effects of its first shock loading and the deformations of the
cavity walls are within the elastic strain region of the medium, the back-
packing should retain almost all of its original potential. If the defor-
mations of the cavity wall were such that partial closure of the cavity
resulted, there would be a corresponding crushing of the backpacking. As-
suming the backpacking does not lock under the initial loading and partial
closure of the cavity, some of the potential of the backpacking theoreti-
cally should be available for additional loading. This is evident in Fig-
ure 5.8. For the range of densities studied at a typical water-cement ra-
tio, the cellular concrete appears to have some multiple-shot resistance
capacity provided the initial loading does not completely crush the mate-
rial. The test configuration approximates the situation where a piece of
rock that has broken from the cavity wall is driven into the backpacking
by the initial shock loading. The majority of the backpacking crushing
takes place in a region adjacent to the area of rock-packing contact. With
additional loading (second shot), the rock is driven further into the back-
packing with additional crushing occurring. The backpacking can then ab-
sorb many thrusts of the rock as determined by its remaining crushing capa-
bility after each loading. The effects of the crushing of the backpacking
due to liner movement should also be considered but is beyond the scope of
this work.
94
It is doubtful that the cellular concrete will be able to rebound and
regain any appreciable amount of its original volume as the forces in the
cellular concrete would not be great enough to force and compact the walls
of the cavity into some semblance of its original form.
The curves in Figure 5.8 show that the cellular concrete achieves the
same crushing stress plateau for both shots. The second shot, however, be-
gins from a zero load point. After the initial loading, assuming partial
closure of the cavity has occurred, it is unlikely that the backpacking
would achieve its original state of stress before loading because of the
dead load of rock mass it would now have to support. Given sufficient
time, the backpacking would probably attempt to creep out from under any
stress concentrations, thus resulting in a somewhat uniform stress through-
out the material. The time it would take to accomplish this, if at all,
would depend on the properties of the material in question. With an ini-
tial stress simulating dead load in the cellular concrete, it is possible
that the second shot crushing stress plateaus as shown in Figure 5.8 would
have been somewhat higher. The manner in which the IA[A operates, however,
did not permit this aspect of the multiple-shot loading to be evaluated.
6.2 FLEXURAL STRENGTH
6.2.1 Modulus of Rupture. Statistically, the modulus of rupture ver-
sus density relations shown in Figure 5.9 for the 0.86, 0.96, and 1.06
water-cement ratio concretes are not significantly different from each
other. A trend toward higher moduli with decreased water contents for a
given density is evident, however. A substantial increase in moduli is
experienced when the water-cement ratio is reduced further from 0.86 to
0.76.
Previous information (Reference 13) has concluded that a reasonable
range of ratios for flexural strength to compressive strength of cellular
concretes is 0.2 to 0.33. Comparing the regression equations of Tables
5.1 and 5.2, a ratio of
a b-bR= -- (d) r y (6.29)Q ay y
95
is obtained where the subscripts r and y denote the modulus of rupture
and yield stress values, respectively. From Equation 6.29, the following
ratios were obtained for a freshly mixed density range of 22 to 43 pcf.
Water-Cement R Flexural StrengthRatio y Yield Strength
0.76 0.16 to 0.330.86 0.19 to 0.210.96 0.211.06 0.19 to 0.24
These values, in general, appear to fall within the range of ratios usually
associated with cellular concretes.
6.2.2 Horizontal Joint Tests. One of the more significant results
of the horizontal joint tests was the fact that none of the flexural joint
beams failed across the joint. All of the beams except one fractured in
the concrete of the lower (or first) lift. In general, the concrete den-
sities, cube strengths, and flexural control beam strengths for the bottom
lifts were less than the values obtained for similar specimens from the
top (or second) lifts. In most instances, the corresponding values from
both lifts statistically were not significantly different. Because the
strength of the cellular concrete (Sections 6.1.1 and 6.2.1) is influenced
by density, among other things, the lower values of compressive and flex-
ural strength corresponding to the lower densities of the bottom lifts are
not unusual.
In all but one instance, the flexural strength of the joint beams is
less than the flexural strength of the control beams from either lift. Be-
cause the joint beams failed in the lower lift concrete, their strengths
might be expected to be the same as the strengths of the lower lift con-
trol beams. This is not the case, however. Observation of the bleeding
characteristics of cellular concrete leads to the speculation that the
difference in flexural strength for the same concrete is due, in large
part, to the increased moisture content of the concrete near the surface
of the lower lift. The excess mixture water in neat cellular concretes
bleeds downward into the concrete. Because of the permeable nature of the
concrete (Section 6.8), the bleed water from the top lift can pass
96
completely through the concrete, carrying with it some finer particles of
-cement. This "erosion" is not of the same magnitude as that discussed in
Section 6.8. It occurs during the setting period of the concrete. Upon
encountering the hardened joint, some of the cement particles are deposited,
thus reinforcing the joint. The bleed water passes into the more mature
concrete of the lower lift and is retained in the upper regions of that
lift. This increases the moisture content of the top regions of the lower
lift and reduces the tensile stresses that develop there as the concrete
attempts to reach a moisture equilibrium while bag-curing. This condition
lowers the flexural strength in the vicinity of the joint.
The average flexural strengths of the joint beams having an air-cured
joint were 12.1 and 12.3 psi for the unprepared and prepared conditions,
respectively. The average flexural strengths of the joint beams having
moist-cured joints were 14.5 and l4.4 psi for the unprepared and prepared
conditions, respectively. For both the moist-cured and air-cured joints,
the effects of joint roughness appear to be minimal with either roughness
condition being adequate. The moist-curing of the lower surface of the
joint seems to provide some benefits by increasing the flexural strength
of the concrete in the top of the lower lift. The increase is not sig-
nificant however. The presence of the joint, in general, reduced the flex-
ural strength of a beam by approximately 6 psi. While this is approxi-
mately 30 percent of the strength of the control beams, the magnitude is
such that the reduction in strength should not affect the overall perform-
ance of a mass of cellular-concrete backpacking that contains horizontal
cold joints.
In summary, for cellular concretes that will be used as backpacking,
the presence of horizontal cold joints does not appear to be a problem
area. The benefits of surface roughness are minimal and the as-cast sur-
face should suffice. The joint appears to be stronger than the concrete
in the immediate vicinity of the joint with most flexural failures occur-
ring in the weaker concrete. Curing of the joint surface by covering with
plastic shortly after casting as opposed to no special curing will improve
the strength of the weaker concrete but not significantly. Addition of
free moisture for curing is not desirable as it fills the voids needed
97
for the deformation capability of the concrete. Curing compounds have not
been studied.
6.3 ULTRASONIC PULSE VELOCITIES
The curves in Figures 5.6 and 5.7 indicate that the compressional wave
velocity of cellular concrete is continuing to increase with age of the
concrete. The curing conditions of the specimens (Section 2.3) were such
that no additional moisture was added to the concrete; hence the principal
phenomenon occurring in the concrete was the formation of additional cement
gel with subsequent decreases in free moisture and porosity. Increases in
the freshly mixed density of the concrete as shown in Figures 5.6 to 5.8
(at any given age or water-cement ratio) also produce increases in the com-
pressional wave velocity. Again the changing phenomenon is an increase in
cement gel content.
As the cement gel content appears to be influencing the magnitude of
the compressional wave velocity, a definite relation between the two can
probably be established. Equation 6.15 can be rewritten to represent the
amount of cement gel present in a given cellular concrete. In the assump-
tions made to arrive at the form of Equation 6.15, however, the degree of
hydration of the cement at a given age with respect to complete hydration
is not considered. Because a number of factors such as cement composition,
fineness, and particle size will affect the amount of hydration products
at a given age, for design purposes it is simpler to relate the wave ve-
locities to something more definite such as the initial cement content of
the concrete. The relations between compressional wave velocity and
cement content for bag-cured neat cellular concrete at various ages are
shown in Figure 6.6. A summary of the equation coefficients can be found
in Table 6.1. The correlation between cement content and compressional
wave velocity appears to improve with age. No reasonable correlation
could be made for data obtained at 3 days age. This is probably due to
the smaller amounts of cement gel and the larger quantities of free mois-
ture present in the concrete at early ages. The higher water-cement ratio
concretes provided the most dispersion to the data at 3 days age.
The effect of path length for the compressional waves was not studied.
98
The void size and distribution may result in longer path lengths as the
wave travels around the voids. This may result in other values of wave
velocity. The difference may not be significant, however. The effect of
moisture content of the concrete also was not studied. The compressional
wave velocity of pure water is approximately 4,800 ft/sec. At high mois-
ture contents (after some saturation) and low cement contents, the velocity
results may be affected.
6.4 RATE OF HARDENING
Rate-of-hardening information is necessary to determine the accessi-
bility of the top surface of the cellular concrete and also for form re-
moval purposes. It has been suggested (Reference 14) that the concrete
possesses a certain "walkability" before it sustains nominal construction
foot traffic. Acceptable walkability occurs at such time as the average
of five tests by a Proctor penetrometer on the periphery of a 30-inch-
diameter circle produces a bearing value in excess of 10 pounds with a
1/4-inch penetration of a 1/20-in2 needle. Walkability, as such, was not
measured for the concretes of this study but may have great utility in the
preparation of job specifications with regard to surface accessibility.
The rate-of-hardening curves in Figures 5.9 and 5.10 provide some in-
sight as to the early age strength development of cellular concrete. In
general, the concretes with the lowest water-cement ratio, and hence the
highest cement content for a given density, begin to stiffen earliest as
might be expected. The data indicate that there are exceptions to this
observation but these must be weighed against the fact that only small
populations are being studied. In no instance was any penetration resist-
ance encountered before 7 hours had elapsed. With one exception, the
range of elapsed time for a resistance value of 1 psi at a particular den-
sity was less than 4 hours. All of the tests were conducted at 73 F. In
a prototype situation, the early stiffening may be accelerated by higher
curing temperatures (Section 6.6), thus permitting earlier construction
traffic and form removal. At densities greater than 30 pcf, forms have
been removed as early as 5 hours after completion of placing when the
cellular concrete sections were very thick and the ambient curing
99
temperatures between 95 and 100 F (Reference 5). The effects of these con-
ditions should be determined by test for each particular job, however.
6.5 MODULUS OF ELASTICITY AND POISSON'S RATIO
Elasticity data on moist-cured low-density cellular concretes appear
to be meager. The elastic moduli generally have design significance when
the concrete is of a semistructural or structural grade and, hence, are
usually not measured for the very low-density concretes. In understanding
the performance of and designing backpacked protective structures, however,
the elastic modulus of the backpacking is an important parameter.
The data represented by the curves in Figure 5.11 indicate that the
elastic modulus increases in a power function form for increasing values
of freshly mixed density. The results of other studies (Reference 14) in-
volving freshly mixed density ranges, which begin at approximately the den-
sities at which this study ends, tend to substantiate the curvilinear re-
lation. At densities greater than 50 pcf, the moduli density relations
have been represented by parabolic curves of approximately the fourth de-
gree (Reference 15).
It has been shown (Reference 15) that the modulus of elasticity of
concrete is a function of unit weight and compressive strength. The
formula
Ec =W1.533/ft (6.30)
presented in the ACI Code (Reference 16) defines this relation for values
of W between 90 and 155 pcf. For a given compressive strength, the mod-
ulus of elasticity of lightweight concrete is usually lower than that of
normal weight concrete (Reference 17); however, in some instances, it has
been shown to be greater (Reference 18). Using Equation 6.30 with the
data obtained from the 75 moduli tests of this study, the relation in Fig-
ure 6.7 was developed. The line-of-best-fit for the data points involved
a decision to use either a straight-line or a simple-power function. For
the range of values on the abscissa, the statistical differences between
the two curves are marginal. For a zero value of density or strength,
100
however, the modulus would also be zero; hence, the selection of the power
function was made. Its use may not be warranted beyond the range of these
data, however.
The line-of-best-fit in Figure 6.7 is expressed as
Ec = (0.o875W1.3 6 5(f,)O.455 + 25) x 103 psi (6.31)
at the 95 percent statistical tolerance limits. The scatter in the data
is such that Equation 6.30 could possibly be considered as a lower bound
in lieu of a tolerance limit as shown in Figure 6.7. Additional tests are
needed to firmly establish this, however. Depending on the importance of
E in the structure-backpacking design, the designer should decide whether
values determined by Equations 6.30 or 6.31 are adequate or whether addi-
tional tests on specific concrete are warranted.
Values for Poisson's ratio of the moist-cured cellular concrete varied
between 0.192 and 0.252. These values are not unreasonable or unusual and
are similar to those reported by other investigators (Reference 13).
6.6 TEMPERATURE PROBLEMS
Heat buildup and temperature rise associated with the hydration of the
cement in the cellular concrete can create serious problems during construc-
tion if proper precautions are not taken. The cement contents of the con-
cretes of this study varied from 3 bags/cu yd for the very low-density,
high water-cement ratio concrete to approximately 8 bags/cu yd for the
high-density, low water-cement ratio concrete. Although at the lower limit
of cement content excessive temperatures might not be expected, the heat
buildup is aided by the insulating characteristics of the concrete (high
air content), which inhibits the dissipation of the heat with time. The
problem is further compounded by the fact that, when used as a backpacking,
the material is placed in very thick sections in a containing media such
as rock which behaves as a very effective heat sink. Cellular concrete
thicknesses of 11 to 12 feet around cylindrical tunnels of substantial
lengths have been placed (Reference 5).
The problems associated with the concrete temperatures are primarily
101
related to fresh concrete in its unhardened state. As shown in Figure 5.12,
in an adiabatic condition, which is approximated by the conditions at the
center of a large mass of cellular concrete, temperatures can become quite
excessive and actually create steam pressure in the concrete. Steam has
been observed coming from thermal cracks in sections of concrete with
thicknesses as small as 2 feet (Reference 19). Once the concrete has
hardened, the elevated temperatures are no problem except that the curing
conditions of the interior mass will produce concrete strengths which may
be different from those obtained from the quality control cylinders repre-
senting that mass of concrete. Thermal cracking generally has little ef-
fect in the overall performance of a backpacking mass. Problems occur when
unhardened concrete is placed in close proximity to the hot, hardened con-
crete. When this occurs, the elevated temperatures cause the air in the
air-bubble system of the concrete to heat up and expand. This is accom-
panied by a reduction in the surface tension of the liquid film forming
the bubble skin. Upon reaching a critical point, the bubble bursts. Many
bubbles may join together to form large voids that then collapse. These
collapses result in either localized "potholing" or a general subsidence
of the surface of the concrete. Subsidence of 4 feet in 12-foot lifts has
been observed (Reference 5). This phenomenon can be seen in Figures 5.16
and 5.17. The unhardened concrete was placed in and allowed to cure at
elevated air temperatures of 100 and 120 F with 80 F being the control
(results not shown). These air temperatures are not uncommon behind bulk-
heads on tunnels that already have some cellular concrete placed behind the
bulkhead. Air temperatures as high as 155 F have been observed. No col-
lapse was observed at 80 F. At 120 F (Figure 5.16), the results are obvi-
ous. The only concrete not collapsed is the 43-pcf concrete, which had the
lowest air content and highest cement content. The air bubbles in the
43-pcf concrete have expanded, thus producing the cracked dome of material
on its top surface. At 140 F (results not shown), even the 43-pcf concrete
experienced complete collapse.
The potential collapse problem associated with the elevated tempera-
tures can be experienced at any stage of a cellular concrete placing opera-
tion. The problem can exist in situations where a new lift is placed on
102
an existing hardened lift that is very hot and has not had its surface
cooled to a sufficient depth before placing of the next lift. The heat
given off by the hardened lift is contained by the fresh concrete; and if
it can build up to a harmful temperature before the fresh concrete has set,
collapse in the lower regions of the new lift may occur. This is shown in
Figure 5.15 for both Type I and Type III cements. The temperatures recorded
for the upper region of the first lift in each case are lower than the
temperatures at the interior and bottom of the lift, due to the dissipa-
tion of the heat through the top of the lift into the air. This transfer
of heat causes the air above existing lifts and behind bulkheads to become
very hot and this hot air in turn can cause the problems mentioned earlier.
After the placement of the second lift in each case, the temperatures in
the bottom of the second lift become greater by as much as 30 F than at
other locations in the lift (Figure 5.15). This is the effect of the heat
of the first lift. If the initial temperature of the fresh concrete of the
second lift is sufficiently high, the fresh concrete can become too hot
after a very short time with resulting bubble collapse. The problem can
also exist in very large volume lifts, such as those experienced when the
total time of placement of the lift exceeded the time required for some of
the concrete placed during the earlier stages of the same lift to reach its
maximum temperature buildup. The concrete between the region that has be-
gun to harden near the bottom of the lift and the concrete that was most
recently placed is then affected in the same manner as fresh concrete
placed on an existing hot lift. An overall subsidence of the surface of
the lift may then be observed, perhaps even while placing is still going
on. While placing a large section of cellular concrete (which experienced
some subsidence) made with a water-cement ratio of 0.85 and a cement con-
tent of 6 bags/cu yd at an ambient air temperature of 95 F, thermocouples
in the bottom of a large lift indicated temperatures of 160 F while placing
was still in progress (Reference 5). Internal temperatures in this section
peaked at 185 F.
To avoid these problems, the initial temperature of the fresh con-
crete should be kept as low as practical. Figures 5.13 and 5.14 show the
effect of mixture water temperature on the early age heat in cellular
103
concrete for Type I and Type III cements, respectively. As has been shown
many times for structural and mass concrete, the cooler the water, the
cooler the concrete. The reduced initial temperatures allow the concrete
to harden before higher damaging temperatures are reached. The effect of
cement fineness is also a factor as the more surface area of cement that is
hydrating initially, the more heat that is generating. The Type III cement
is more finely ground than the Type I and thus contributes more surface
area for early hydration and, hence, more heat. The requirement for fine-
ness of the cement must be balanced with the water requirement for the
backpacking design to prevent excessive water in the concrete. The data
from the cement analysis (Section 2.1.1) show the fineness for the Type I
and Type II cements to be 3,845 and 4,790 cm2/gm, respectively. This dif-
ference is reflected in the temperature curves of Figures 5.13 and 5.14 with
the finer cement, i.e. the Type III, producing higher temperatures than the
Type I cement at comparable periods of early hydration. The total heat
produced by each cement over an extended time period will be approximately
the same, however, as the compositions are not significantly different.
The use of coarser cements, or depressed concrete temperatures, or both,
will produce cement pastes that stiffen at slow rates. The time needed for
stiffening to occur must be balanced against the time that the preformed
foam will retain its bubble structure. If the paste does not harden suffi-
ciently before the bubbles begin to break down, the cellular concrete will
collapse in the same manner as the high temperature collapse.
In summary, elevated temperatures can cause collapse of the air-
bubble system of the cellular concrete while it is in the unhardened state.
This collapse results in localized "potholing" or general subsidence of the
unhardened cellular concrete, which produces density increases and hence
changes in physical properties. These elevated temperatures can be present
in the air behind sealed bulkheads used as the formwork during placing of
the concrete. They can also exist in the lower regions of a lift of un-
hardened concrete that is either influenced by the heat of a hardened lift
of concrete adjacent to it or by the temperatures developed in the new lift
itself because of excessive placement times. The problems can be avoided
by (1) using cooled mixing water and, if possible, cement, (2) using
104
minimum handling and placing times, (3) using low-heat, coarser ground
cements, (4) restricting total placement times to periods that do not allow
internal temperatures to become excessive, and (5) adequately cooling (by
air blowing) the surface of adjacent sections of hardened concrete and the
ambient air in which the fresh cellular concrete is to be placed.
6.7 LIFT HEIGHT RESULTS
The results of both the 16- and 30-foot lifts indicate that density
increases do occur with increasing depth of concrete. The increases may
indicate an increase in the amount of water in the concrete because the
excess water in the mixture (bleed water) has a tendency to flow down into
the concrete. The lower sections might then contain the excess water in
the air void system. The comparison between the as-cast and the oven-dried
cubes from the 16-foot lift tends to discount this as the amount of evapo-
rable water in the concrete appeared to be the same from top to bottom.
The density changes then are only a function of the amount of cement paste
in a given volume. For a density increase, either the number of air voids
per unit volume is decreased, or the existing air voids are compressed, due
to the superincumbent load, while the concrete is still in the unhardened
state. Upon hardening, the number of air cells would then still be the
same but their size would be smaller with the difference in the original
and final volumes being replaced by additional paste.
Figure 5.2 shows that changes in density result in changes in strength.
The change in density of 7 pcf in the 16-foot lift can produce a change in
the crushing level stress (Q0.40) from approximately 100 to 190 psi (Fig-
ure 5.2a) for the concrete design used in that section. Changes of this
magnitude are not desirable because if the stress transmitted through the
backpacking to a structural liner is not fairly uniform, ovaling or dis-
tortion of the liner may result and thus destroy the effectiveness of the
liner's original design.
It is desirable to restrict the lift height of the cellular concrete
to some value that is consistent with the allowable stress differences the
liner in question can stand and the quality control that can be achieved
for the cellular concrete placement. For example, if variation in density
105
due to lift height of +3 pcf from a design density, d , is acceptable from
a strength standpoint, but the quality control during placement can be ex-
pected to be no better than +2 pcf, then the actual lift height that can be
placed should be restricted to that height which yields d +1 pcf.
6.8 SATURATION PROBLEMS
After placement of backpacking around tunnel liners or silos is com-
plete, the problem of groundwater infiltration into the backpacking arises.
All of the materials currently under investigation for use as back-
packing are very porous, with void contents to 80 percent being commonplace.
Cellular concrete is no exception. This high void content is necessary to
meet the structural behavior requirements of the material, i.e., to deform
in excess of 40 percent of the initial thickness of the material with no
appreciable increase in the stress level necessary for yielding to occur.
This deformation is essential in absorbing the movements of the surrounding
medium and in changing the input loading pulse accompanying a nuclear ex-
plosion into an input pulse less detrimental to the buried structure and
its contents. Once the desired stress-strain relation for the materials is
developed, the question then asked about the backpacking is what will hap-
pen if water, from a ground source or introduced by other means, infil-
trates the backpacking material to such a degree that all the available
permeable void space in the material becomes filled with water. Will the
material still be able to absorb the ground movements and change the dy-
namic loading pulse into a less detrimental form?
Cellular concrete possesses both interconnecting voids and noninter-
connecting voids. For the purposes of water saturation, the first of these
void conditions is the less desirable. In this condition, water can
quickly fill all the voids in a given specimen with little difficulty. The
second void condition is perhaps the more desirable condition as each void
would be a separate cell filled with a gas. A rupturing of each cell wall
would be necessary for water to migrate into the cells.
The void space in any given specimen is composed of the space filled
with gas (air and others), both entrained and entrapped, plus the space
filled with free water. This void space is composed of permeable pores
106
available for saturation, permeable pores unavailable for saturation, and
impermeable pores. The short-term saturation tests run on all the con-
cretes fill only the permeable pores available for saturation and those are
not filled completely because of the gas in the pores being compressed and
having no place to go. When referring to a material being completely satu-
rated in this study, what in effect is meant is that no more fluid can be
forced into the available permeable pore spaces without further large in-
creases in water pressure being applied.
The degree to which saturation of the material will occur will depend
not only on the type of void structure but on the strength of the matrix,
and the method by which the water is introduced or applied to the material.
The crushing stresses of the cellular concretes vary from 20 to 900 psi, de-
pending on their particular design. In a closed cell situation, the walls
of the cell will rupture, when subjected to increasing pressures, at pres-
sure levels governed by the strength of the matrix. A low-strength matrix
will fracture and allow the closed cells to fill at much lower water pres-
sures than a high-strength matrix. When we say the cell walls rupture or
fracture, it is not in the catastrophic sense of the word but in the forma-
tion of microcracks, perhaps only one or so per cell, that would allow the
water to migrate into the cell and equalize the pressure in that cell to
that of the cells or other areas supplying the pressurized water. The sta-
bility of the material in mass is not destroyed by this type of saturation,
but the strength is somewhat reduced due to the moisture and the cracking.
Assuming that the above situation is occurring, the question now
arises as to what happens to the gas that originally filled the cells.
This problem relates itself to the manner in which the water is introduced
or applied to the material. Under almost all field conditions, the ground-
water will be transient with respect to location of the material. The gas
in the voids will become compressed as the water pressure increases and
with the migration of the water into the material, the gas will be forced
ahead under pressure with a portion of it probably being moved out with the
transient water. Some of the gas will undoubtedly remain behind in a com-
pressed state in the material. If the material were subjected to a station-
ary hydrostatic pressure, which is highly improbable but could happen, all
107
the gas would remain in the compressed state and it would be virtually im-
possible to fill every void space.
The data shown in Figure 5.18 indicate that water pressures in excess
of 300 psi for a short-time test are necessary to saturate most of the
available permeable void spaces in a very dense (with respect to cellular
concrete backpacking densities) concrete made at an average water-cement
ratio. Under long-term conditions this same degree of saturation could
possibly result at lower water pressures. This saturation results from a
stationary constant pressure situation where the gas remains compressed in
the material. Specimens statically loaded in this condition show a negli-
gible amount of deformation if the volume of water in and around the speci-
men is not allowed to change as loading progresses. If free water is al-
lowed to escape from the system as the static loading progresses, the usual
stress-strain relation for an unsaturated material will result but at a
higher crushing strength level due to the increased water pressure neces-
sary to keep the water in the voids. However, under the dynamic loading
that would result from the shock wave accompanying an explosion, the free
water in the system would not have time to migrate; the shock wave would
then pass through the originally porous material as if it were rigid. Very
little, if any, deformation would result; and in all probability, severe
damage would result to the structure being protected.
The curve in Figure 5.18 indicates that very low water pressures are
all that is required to fill at least half of available voids in cellular
concrete. The results of the low-head permeability testing are shown in
Figures 5.19 and 5.20 and tend to indirectly substantiate this. At average
water heads of approximately 6 feet, water readily passes through the lower
density concretes and tends to fill some of the voids with water. Regard-
less of the water-cement ratio, all of the 23-pcf concretes exhibited the
same general pattern. Initially, the concrete appeared to be experiencing
a flow-rate reduction with time of test run; however, the amount of reduc-
tion reached a maximum within the first 24 hours. A flow-rate increase
then began with most of the maximum reduction in flow rate being regained
within the next 24 to 30 hours. The amount of total solids measured in the
discharge water (Figure 5.21) after the initial total solids was established
108
leveled off at approximately 30 ppm more than the total solids of the tap
water before it passed through the concrete. This leveling off occurred
about the same time as the maximum flow reduction occurred. All the test
specimens were badly eroded and damaged after testing.
Regardless of the water-cement ratio of the 32-pcf concrete, all spec-
imens exhibited the same general behavior pattern (Figure 5.20). The flow
rate through the specimens appeared to decrease with time of the test run.
Within the 80-hour test period, the total solids of the discharge water de-
creased (Figure 5.21) to approximately 30 ppm more than that of the origi-
nal tap water before it passed through the specimens. These specimens did
not appear to be eroded at the top surface as were the 23-pcf specimens.
No appreciable flow could be determined through the 43-pcf concrete
with a water-cement ratio of 0.76; however, some small flows were noted for
the 0.86- and 0.96-water-cement ratio material. These flows were not
enough to accurately measure. The specimens did not appear to be physi-
cally altered by the flow.
The most obvious conclusion drawn from these tests is that the cellu-
lar concrete is very permeable at low densities and low hydrostatic pres-
sure. In being very permeable, the concrete allows the water to reach most
areas of the concrete mass and fill some of the available voids in those
areas. The higher density concretes seem to indicate that, with sufficient
strength development and subsequent reduction in void content, the permea-
bility at low heads is greatly reduced for short-term flow conditions.
Whether or not the concrete will maintain its reduced permeability for ex-
tended periods of time under low heads or for shorter periods of time under
greater heads is not known. Tests of specimens fabricated by two major man-
ufacturers of foaming agents for cellular concrete were conducted by an in-
dependent testing laboratory. The results of those tests showed that at
water pressures of 80 psi, maintained for 24 hours, no water could be
l Private communications; letter dated 26 Jan 1965 from Chemical Concen-
trates, Redondo Beach, Calif.; and letter dated 3 Feb 1965 from Mearl
Corporation, Roselle Park, N. J.
109
forced through cellular concrete, provided the density of the concrete was
greater than approximately 70 pcf. At lower densities, the water flowed
through the specimens at rates that were related to the concrete density.
The total solids measurements made from the discharge water indicate
that the water is picking up some additional total solids as it passes
through the specimen, thus eroding the specimen. The very high values of
total solids that occurred early during the test indicated the severest
period of erosion. Some of the particles eroded evidently plugged the
channels through which flow was occurring and gave the appearance that the
rate of flow through the concrete was decreasing (Figures 5.19 and 5.30).
For the 23-pcf concrete, these plugs were also eroded with time, and the
flow rate picked up. The flow channels then became fairly uniform with a
somewhat constant rate of erosion occurring as is indicated in Figures 5.21
and 5.22. Evidence of the flow channel plugging was also observed for other
backpacking materials tested in a similar manner (Reference 3).
If the material is very permeable, it will probably not be very prac-
tical as a backpacking material if it is used by itself with no other sys-
tems that could divert or resist the intrusion of groundwater. Even if the
cellular concrete can be designed to be almost impermeable by itself, there
is no guarantee that under sustained associations with groundwater on the
surface of the backpacking that either complete or partial saturation of
the concrete will be eliminated. If the material does become saturated,
either partially or completely, the pore-water pressures that may develop
in the concrete may, under certain conditions, apply destructive pressures
to the walls of the pores in the concrete, thus reducing the effectiveness
of the material as backpacking.
The obvious solution to the problem is to build the structures requir-
ing protection in media where there is no water. This is, of course, an
almost impossible task but areas where the groundwater or other water would
present a problem can be treated and maintained in ways that would prevent
water from reaching the cellular concrete backpacking. Grout curtains in
rock, wellpoint systems in soil, drains around the structures, sandwich-
type structures, and many other methods could be applied to eliminate this
threat of saturation.
110
The possibility of waterproofing the surface of the cellular concrete
also exists. However, complete waterproofing would not be the answer for
elevated pressures. An ideal backpacking can have a crushing stress level
that is very low (25-150 psi) and will deform at that crushing stress for
strains in excess of 40 percent. If the possibility of invasion by free
water from an outside source into this material is eliminated for elevated
pressures, what then would happen to the material when the outside water
pressure goes above the crushing stress level of the material? The gas
that fills the voids in the material would begin to compress, the material
would begin to yield, and as the outside pressure increases the material
would deform more and more, thus failing the material and destroying its
usefulness before it could be loaded by a shock-wave input. Waterproofing
is not the complete answer but would improve the effectiveness of the mate-
rials at lower water pressures.
As shown in Figure 5.23, there are considerable differences in the ef-
fectiveness of the sealers studied. The two most promising appeared to be
liquid latex and neat cement slurry. The neat cement slurry, upon harden-
ing, allowed no water into the sample. The liquid latex allowed just small
quantities but is probably more effective than the results indicate. The
same material has been used on laboratory specimens of many different mate-
rials to prevent moisture from entering the material and has been 100 per-
cent effective. Both the neat cement slurry and the latex can be easily
applied to the surface of the walls of a tunnel in rock in order to seal it
before the backpacking is placed against it.
There are many commercially available products that can be used as
surface sealers. Those evaluated in this study were used only because they
were readily available in the area in which the investigation was conducted.
A proper evaluation should be made of each sealer considered for use in
backpacking operations.
111
SUMMARY OF ULTRASONIC PULSE VELOCITY (V) VERSUS CEMENTCONTENT (C) RELATIONS, V = aCb +2 Sesty , ft/sec
Age No. of Equation Correlation StardardObser- Coefficients Coefficient Error ofvations Estimate
a b Sesty
ft/sec
156
172
172
172
593 0.778
671 0.770
772 0.741
844 0.724
0.879
0.929
0.953
0.960
390
315
256
234
112
TABLE 6.1
days
7
14
28
60
800 *I. .Y.
\ CFo- 42,000 (/ - n/ 3 f ./ PS/
600
&4o ~ 0__ _ _ _ _ _ _ _ __ _ __ _ _ __ _ _ _
80 85 90THEORETICAL POROSITY, n
95 100
Figure 6.1 Yield stressneat cellular concrete.
e 00
a-400
w
U
-J 200w
0-
6 10
versus theoretical porosity relation for a
14 18
(+c( I+C )
22 26 30
Figure 6.2 Relation between yield stress and the design parameter,
dc/(1 + k) .
113
(n0.
U)W
W:
200
'100- - - ---- -------------
9,6
75
0~y=0.02436
U
800
0 1
24 1 4
22 26 30 34FRESHLY MIXED DENSITY, PCF
Figure 6.3 Relations between design parameter, dc/(1 + k) , and freshlymixed density for various water-cement ratios.
(I+0.20pc 3
G0 \ 6 2 .
3Pc
/
SPEC/F/C GRAVTY 3./--
'r t
GRAV/T Y= 3.2
I0 14 18
(I+k)
SPEC/F/C
22
x
26 30
Figure 6.4 Proposed relation between stress ratio anddesign parameter, dc/(1 + k) , for cellular concrete.
11i
FJ1 LIMITS OF ACTUAL TEST DATAIi II
12
14 18 38 42 46
16,000
CAl 12,1000wJ2
0
8 4000
06
8
201 ' '
r I - T- - I I I
I E I I I 1/
10
0"
44A
A
Figure 6.5 Rapid loadingversus slow loading rela-tion for the average stressto 40 percent deformationcharacterization, 0.40 *
u
I
LL
H
U0J
JDa-
UZ0
-J
0
W
Id
O
lb J
inac,)
mH-W10
QD
iooo
RAP/D SO2W62 O~ -800
600
400
200
00 200 400 600
AVERAGE STRESS, 60.40 DETERMINED
BY SLOW LOADING TEST, PSI
60000
500C
4000
3000
2000A fl I AI4I
CEMENT CONTENT, PCT
800
Figure 6.6 Ultrasonic pulse velocity versus cement content
relations for neat cellular concrete .
115
1440 v Iv 3
200
175
150
/I
/0.1 0.2 0.3
W 3/2 J[7x o- 4
0.4 0.5
Figure 6.7 Secant modulus of elasticity versus modulusparameter relation.
116
0
WATER- CEMENT /RATIO 0
O 0.660 +A 0.76
o 0.86
E _ (0 .0 8 75 W '.3 65(fr )0.455 t25) X 103 A
0
q00
00
o0
/ D /
0
0-
-u
~IW
25
1 00
75
50
25
00 0.6
CHAPTER 7
CONCLUSIONS AND RECOMMENDATIONS
7.1 CONCLUSIONS
Based on the results of the testing of this investigation and the in-
formation obtained from published reports and papers reviewed during the
investigation, the following specific conclusions appear warranted:
1. The strength of moist-cured neat cellular concrete is principally
a function of the concrete density and water-cement ratio, and the specific
gravity of the cement. From the data of this study, the yield stress was
determined to be
d 3
ay= 0.2436 (1 d k)(7.1)
A more universal design approach was suggested such that
do ba d k(7.2)
Q C l+ k
for all cements.
Neat cellular concretes made at densities from approximately 18 to
50 pcf and water-cement ratios from approximately 0.6 to 1.1 (by weight)
possess the strength-deformation characteristics required for a suitable
backpacking material regardless of the loading rate applied to the con-
crete. Average crushing stress levels from 20 to 1,000 psi at 28 days for
slow-loading rates can be readily obtained depending on the mixture pro-
portions. Strengths in excess of 1,000 psi, with deformations to 40 per-
cent before locking, also appear to be feasible.
2. Cellular concrete is load and/or strain rate sensitive. For the
rapid-loading system and techniques used in this study, crushing stress
level increases from 95 to 30 percent were observed for the low-strength
(20 psi) and high-strength (1,000 psi) concretes, respectively. The shape
of the stress-deformation curve for cellular concrete does not appear to
change with increased rates of loading.
117
3. Cellular concrete appears to possess a multiple-shot load-
resistance capability provided the initial loadings do not completely crush
the material. Each concrete design has a certain deformation capability.
The portion of that capability not used to accommodate medium movements as-
sociated with earlier shock loadings is available to accommodate additional
loadings.
4. The modulus of rupture of cellular concrete is dependent on the
mixture proportions with higher cement contents and lower water contents
producing higher flexural strengths. The ratio of flexural strength to
compressive yield strength varied from 0.16 to 0.33, which is not unrea-
sonable for low-density cellular concretes.
5. The compressional wave velocity (as measured by ultrasonic pulse
techniques) of neat cellular concrete appears to be directly influenced by
the cement gel content of the concrete. Increased gel contents due to the
continuing hydration of the cement result in increased velocities. In-
creased gel contents, due to increased density (obtained by adding more ce-
ment per unit volume and decreasing the air content) also produce increased
velocities. Free moisture in the concrete also appears to influence the
wave velocity, but only at early ages of the concrete. At later ages
(z 28 days) the moisture effects are not readily apparent. Twenty-eight-
day age concrete produced wave velocities from approximately 3,000 to
6,000 ft/sec depending on the concrete proportions.
6. The modulus of elasticity of moist-cured cellular concrete can be
approximated by the relation E = W1.533 ft in lieu of actual test meas-
urements. This function appears to be a lower bound for the data of this
study. Moduli from 20,000 to 220,000 psi were measured for the concretes
studied. Poisson's ratio for the moist-cured cellular concretes varied
between 0.19 and 0.25.
7. Cellular concretes with higher cement contents than other cellular
concretes at comparable densities begin to stiffen earlier. Based on
Proctor penetration tests, no measurable resistance to load was encountered
before 7 hours age of the concrete regardless of its proportions. This
stiffening may be accelerated in prototype situations due to higher ambient
temperature curing. A measure of "walkability," as defined herein, may be
118
useful in the preparation of specifications for concrete surface accessi-
bility and form removal.
8. The presence of horizontal cold joints in cellular concrete used
as backpacking does not appear to be a problem. The benefits of surface
roughness and special curing during joint preparation are minimal. The
as-cast roughness with air curing should be adequate. Additional free
moisture for curing a joint is not recommended.
9. Density increases, which result in strength increases, do occur
with increasing lift height. This is due primarily to the change in air
content brought about by the compressive action of the superincumbent loads
while the concrete is still in the unhardened state. Lift heights should'
be restricted to some value that is consistent with the allowable stress
differences (brought on by the density changes) that the backpacked liner
in question can accommodate and the quality control that can be achieved
for the cellular concrete placement.
10. Elevated temperatures can cause collapse of the air-bubble system
of the cellular concrete while it is in the unhardened state. This col-
lapse results in localized "potholing" or general subsidence of the un-
hardened cellular concrete, which produces density increases and hence
changes in physical properties. These elevated temperatures can be present
in the air behind sealed bulkheads used as the formwork during placing of
the concrete. They can also exist in the lower regions of a lift of un-
hardened concrete that is either influenced by the heat of a hardened lift
of concrete adjacent to it or by the temperatures developed in the new lift
itself because of excessive placement times. The problems can be avoided
by using (a) cooled mixing water and, if possible, cement, (b) minimum
handling and placing times, (c) low heat, coarser ground cements, (d) re-
stricted total placement times to periods that do not allow internal tem-
peratures to become excessive, and (e) adequately cooled (by air blowing)
surface of adjacent sections of hardened concrete and the ambient air in
which the fresh cellular concrete is to be placed. Care must be exercised
when using approaches (a) and (c) so that the stiffening behavior of the
cement paste is not delayed beyond the time when the bubble structure of
the preformed foam begins its normal breakdown.
119
11. Cellular concretes at densities less than 35 pcf are extremely
vulnerable to water infiltration at very low pressures. At densities from
35 to 70 pcf, the concretes are still quite permeable, the permeability de-
creasing with increasing density. Saturated backpacking loses its deforma-
tion capability. The flow of water into cellular concrete also tends to
erode the same, thus damaging its structural integrity. Waterproofing the
concrete improves its effectiveness at lower water pressures, but by itself
is not a solution to the saturation problem. Structures backpacked with
cellular concrete should be built in media where there is no water avail-
able for saturation of the concrete. In a water-bearing medium, water can
be prevented from reaching the cellular concrete by using conventional con-
struction techniques.
7.2 RECOMMENDATIONS
Additional information on the physical properties of cellular con-
cretes made with different cements should be developed. Emphasis should be
placed on cements that are coarsely ground and whose constituents will
produce low-early heat.
The effects of concrete and curing temperature on all aspects of con-
struction to include rate-of-hardening and physical characteristics should
be studied in depth. Criteria for cellular concrete backpacking specifi-
cations should be developed.
The effects of rate sensitivity on the performance of cellular con-
crete should be explored for the entire range of rise times, amplitudes,
and durations that might be expected in a prototype situation.
120
APPENDIX A
DEVELOPMENT OF A LABORATORY TEST METHODFOR LOW-DENSITY CONCRETE BACKPACKING
The following observations, reasoning, and experimental results are
presented as an insight to the development of the test method and proce-
dures used in the study of cellular concrete when used as a backpacking.
These results and suggestions can be readily extended to the testing of
other types of backpacking materials.
A.1 CONSTRAINMENT
The behavior of backpacking when subjected to shock-wave loading is
complicated and has not yet been precisely defined. The following observa-
tions as to expected backpacking behavior are somewhat simplified but can
be considered adequate as a first approximation.
Consider the backpacking as completely filling the void between a
buried structure and a rock opening (Figure A.l). The backpacking will be
constrained at the outer surface by the rigid rock mass and at the inner
surface by a structure that may vary in stiffness from flexible to very
rigid. The traveling compressive shock wave in the rock, impinging on the
rock-backpacking interface, is partially reflected, thus establishing ten-
sile stresses in the rock that will cause the rock to fracture. The frac-
tured rock is imparted some kinetic energy by the shock wave. It then
leaves the interface and moves into the backpacking until its energy is
dissipated. Some translation of the structure may also occur. In both
cases, crushing of the backpacking will occur at the interface of the mov-
ing element and the backpacking. More severe rock fracturing and back-
packing crushing would be expected at the interface of first contact by the
shock wave than at the opposite side of the section.
Because of the speed of the shock wave, the entire backpacked opening
will become loaded in compression in a very short time interval. The uni-
formity of the loading across the opening is dependent on the decay history
of the loading wave. A reasonable assumption is that the entire section
will be loaded in somewhat uniform compression shortly after initial
121
loading and at a time when the fractured rock elements will still be driv-
ing into the backpacking mass.
Neglecting translatory motions of the structure and the fracturing of
the rock for the moment, consider the backpacking to be a thick-walled
cylinder of semi-infinite length behaving elastically under both internal
and external compressive loading. From Lame's equations for thick-walled
cylinder stresses (Figure A.2), the general case for tangential stresses
can be expressed as:
2 2 2a iri porn (i oroi 1 (A.1)t = 2 2 + 2 2 (
r - r. r - r. r
where
p. = internal pressure
p0 = external pressure
r. = internal radius
r = external radius (r > r.)
r = radius to point of interest (r > r > r.)
Rewriting, where pi = p+ 4
2 2tpr. r
at -po + 2 2 1 + (A.2)ro - r.i ro- 2
= -p + K(Ap)0 -
where 2 2r. r
K= 2 1 +2(A.3)ro - r.
o i r
K = a positive constant depending on cylinder geometry and pointof interest
The sign convention is that a positive sign indicates tension while a neg-
ative sign indicates compression.
122
When p. < p0 , at is always a compressive stress. When p. > p ,
Ap is a positive value and at may represent either a tensile or com-
pressive stress, depending on the relative values of p and p. for a
given geometry. It is expected that the resistance offered by the proto-
type structure (and represented by p.) will be something less than the
shock-wave overpressure (represented by p0), hence the first case will
prevail. An element of backpacking at any distance r will then be sub-
jected to compressive tangential stresses.
The use of Lame's equations infers that the internal and external
pressures are statically applied and of known constant magnitudes, where,
in fact, the inferred situation exists only when any instant of time is
isolated and the pressures existing at that time are determined. For a
finite time interval, both p and p. will be continually changing and,
hence, so will at . The sense of the tangential stress will remain com-
pressive, however, regardless of its magnitude.
The compressive tangential stresses have the effect of providing some
lateral constraint to a backpacking element that is being additionally
loaded by the driving pieces of fractured rock. To reproduce realistic
compressive constraining stresses or forces in a backpacking evaluation
test would be difficult in view of the many variables and unknowns asso-
ciated with each prototype. A simple solution, and the one pursued for
this study, is to use cylindrical backpacking samples and enclose the
sample in a steel pipe. The steel pipe, being much more rigid than the
backpacking, resists the lateral expansion of the cylinder once loading has
begun and thus provides some degree of constraint to the material while it
is being tested.
The actual relation between the prototype compressive constraining
forces and the constrainment provided by the steel pipe cannot be defined
due to the lack of information on prototype behavior. However, it is be-
lieved that the overall effects of constrainment by the pipe contribute to
the performance of the backpacking in such a manner that the results ob-
tained from this type of evaluation test more closely approach that of the
actual behavior of the prototype backpacking than if no constrainment were
provided at all.
123
A.2 SPECIMEN AND TEST PREPARATIONS
The cylindrical specimen of backpacking that is placed in the con-
straining pipe should be of a size that is conveniently available to almost
anyone. For low-density concretes, the 6- by 12-inch cylinder is an ideal
size. Standard cylinder casting procedures can be followed for these con-
cretes with the exception that the concrete should not be vibrated or ex-
cessively consolidated.
The curing of the low-density concrete cylinders should not be done in
an environment where free moisture can come in contact with the concrete.
This includes moist-curing rooms. Because of the porous and absorptive
nature of these concretes, free moisture readily penetrates into the con-
crete and fills the voids necessary for satisfactory performance as a back-
packing. The concrete should, instead, be cured in sealed plastic bags.
Shortly after sealing, the humidity in the bag approaches 100 percent and
the specimen still cures adequately with no additional free moisture being
added to the system.
In preparing the cylinder for testing, the top and bottom 3 inches of
each cylinder should be sawed off and discarded, thus avoiding surface ir-
regularities due to casting, bleeding, and handling. In most instances,
the sawing can be done with a handsaw. Care must be taken to ensure that
the ends of the cylinder remain perpendicular to the sides.
The confining pipe should be of split-wall construction (Figure A.3)
so that the specimen can be easily enclosed in or removed from the pipe.
The pipe requires a nominal 6-inch inside diameter and should have walls no
thinner than 1/4 inch. Closure of the pipe around the specimen can be ef-
fected by two closure bolts set 180 degrees apart at the midpoint of the
pipe height. Other arrangements are also possible. Reproducibility in
testing can be achieved by torquing each of the closure bolts on the pipe
to the same value just prior to testing. For two-bolt closure (Figure A.3),
experimentation has indicated that a closure torque of 5 ft-lb was adequate
to obtain reproducible results with a minimum of additional triaxial com-
pressive forces due to the torquing. If desired, the constraining pipe can
also be bolted to a fixed baseplate.
124
After closure of the pipe is complete, the specimen is ready to be
tested. This is done by forcing an appropriate piston into the concrete at
a desired rate of specimen deformation.
A.3 PISTON SIZE
To represent the rock fragments that will be driven into the back-
packing, a loading piston with a flat, circular end area was determined,
from practical considerations, to be most desirable. Three different
size pistons were studied: 3-, 4-, and a nominal 6-inch diameter (Fig-
ure A.4). The 3-inch-diameter piston was also studied for two-side taper
configurations.
By forcing any of the pistons into a low-density concrete sample at a
constant rate, a stress-deformation test record similar to that shown in
Figure A.5 will be obtained. Stress is determined as the load acting on
the area of the piston face; and deformations are determined as the dis-
placement of the contact face of the loading piston into the specimen with
respect to the original height of the specimen and are usually expressed as
percentages. This constrained stress-deformation curve (Figure A.5) is
characterized by four values of the curve: (1) yield stress, a ; (2) de-
formation at yield, e , percent; (3) average stress Q0.40 between E
and 40 percent deformation E0.40 ; and (4) stress a0.4 0 at 40 percent
deformation. The values of items (1), (2), and (4) can be read directly
from the test record. Item (3), the average stress, is determined as:
(area under curve between Ey and E0.400.40 1O 0 .4 0 - Ey)
One mixture design of cellular concrete was selected for the piston
study. Three rounds of concrete were cast with samples from each round
being evaluated for each of the piston configurations. The results are
shown in Figure A.6. The deformation rate was 0.3 in/min.
The results indicate that higher stress values are achieved with
smaller sized pistons. The test records also reveal that the 6-inch pis-
ton tests "bottom" at smaller deformations than the other piston tests.
Figure A.7 shows a typical set of test records for the three sizes of
125
pistons. The taper effect on the 3-inch piston did not significantly af-
fect the test results.
If the mode of resistance of a test specimen is only normal compres-
sion, the magnitude of the observed stresses should be the same regardless
of the area of the sample loaded. In the case of the 6-inch piston on the
constrained 6-inch cylinder, normal compression was the predominant resist-
ance mode. When the smaller diameter pistons were used, the test became a
punching test and the resistance mode became a combination of normal com-
pression and shear accompanied by horizontal compressive components due to
the constrainment. It is this combination of compression and shear that
resulted in the higher observed stress values for smaller sized pistons. A
penetrating rock projectile will be resisted by both shear and compressive
forces and, hence, would be best represented by a punch-type test.
The bottoming of the stress-deformation record occurs when the slope
of the crushing plateau begins to increase rapidly. Ideally, this should
begin to occur when most of the voids under the loaded area have been
crushed and the remaining solid material begins to resist compression with
little additional deformation. Some increase in the shear resistance may
also develop and, in the case of the 6-inch piston, may be the predominant
mode of resistance. The frictional sidewall resistance that develops when
the 6-inch piston is used becomes so great that the lower portion of the
specimen is never deformed. This does not produce a desirable test result.
The sidewall friction effect will probably persist even when the piston
edge is moved slightly away from the constraining pipe. For this reason,
5-inch pistons were not considered.
Based on the above observations, it was believed that a piston that
loaded the most area so as to obtain the greatest compressive resistance
and yet minimized the sidewall friction effects so that a more realistic
bottoming point could be discerned should be used for the test method. As
the 4-inch piston as shown in Figure A.4 appeared to satisfy these require-
ments, its use was adopted.
A.4 DEFORMATION RATES
The rate-of-deformation studies were conducted using a 30,000-pound
126
universal testing machine operated at controlled rates of loading head
travel. A 4-inch piston was affixed to the loading head through a ball and
socket arrangement that allowed easy alignment of the piston. The same
cellular concrete mixture used in the piston size study was used in this
evaluation. Three rounds of 12 cylinders each were tested. From each
round, three 6- by 6-inch cylinders were tested at a base rate of piston
travel of 0.18 in/min and in accordance with procedures discussed above.
The remaining nine cylinders were tested in groups of three at three dif-
ferent but faster rates of piston movement. Figure A.8 shows the test re-
sults. The strength ratio is the value of tha average stress to 40 per-
cent deformation, Q0.40 , for the faster rate of deformation for a given
round divided by the corresponding value for the base rate of that round.
Only at rates of 10 in/min or greater did the mean strength values at
faster rates of deformation become significantly different from the cor-
responding base rate values. The data in Figure A.8 indicate that a
strength increase with increasing deformation trend is developing as was
expected. For testing purposes, it is suggested that deformation rates be
kept to less than 1 in/min to minimize the deformation rate sensitivity
effects in the concrete.
127
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ,~ G R O U N D S U R F A C E
ROCK - .-
- -BACKPACKING
STRUCTURAL *"L INER **
- - * - 0 e " ,,' **L /NER
0 o 1 / , OPEN/NG
0
Figure A. 1 Rock-b ackpacking -struicture configurati on.
Ur +dCGr
FOR A NONROTATING CYL INDER
_ irt Got+(P-Ptrzr
N+
rir ri-r2 r2
- Pi r-Pro (Pi-P )r2 r?c0r- r r - r2 r
Figure A.2 Thick-walled cylinder stresses.
. c r A t '2.wri1 ~l1 "Y.iE
- xc ~ -I- ~%
Figure A.3 Split-wall confining pipe.
wii
I
----tl'rI"'rr-rtrnfrWtStStfhfMSuittarar4~LL~fl~IUIUSPSISr
Figure A.4 Loading pistons.
130
IK /44
wi
0. 4
ui o.4
z
Er 1 0(40E - Ey& E0.40
0 10 20 30 40 50 80 70DEFORMATION, PCT
Figure A.5 Typical constrained stress versus deformation relation.
3 0 0 ,
I-ZUbJa -
0z
I-
()Wi
w4a
OA
La i
zoo
100
0 8 16 24 32 40
LOADED AREA OF PISTON, IN 2
Figure A.6 Effect of piston diameter on stress.
131
500
EACH CURVE WAS OBTAINED /USING A DIFFERENT DIAMETERLEADING PISTON
400
//
300
BOTTOMING PO/NT3-/N PISTON
200/
4-/N PSTON
6-IN P/STON
100
010
Figure A.7
20 30 40 50 60DEFORMATION, PCT
Effect of piston size on bottoming point.
I I I I ' ' I I I II. I I 'I 'I ' I ' 'II I ' I 'I
0.5 1.0 5 10
DEFORMATION RATE, IN /MIN
Figure A.8 Rate of deformation effects.
132
,)
0
0V
70
1.2
<i.Lx J
z
Z L .
-0 0.
0.8 L0.
_ _ ---- - - - -- --- ----ii ____IT- T --- + + - +
50
0>
,i
APPENDIX B
TEST DATA
133
1000
800
0600
004
200
0118
- T4
- 4 -
i.ti. T
S + f + - - -.-- t ,+-.-' - .- - -- 1- -t - - _ h- - . . _--- -+ - . - - - 4 - , - - - - t -} - - - -a- r t . 4-t f4f-
-- -a- - - - - - -- 1-4. +
- j a + -- a -- - t t .- - - - - - -l . -- a-. - -- r . - - - - - - - -- _ _ - - -- - -r - - - "-- - -. . -' r r - Y . ,- t r +. + - t . - - - - - 4 + -
. }. --- + i - - r-- r ... . + ----.---- 1-----. t . . - ---..---- }--1- . - 1 r . ... , Y--. .- 1 - ---- { -r- -
i4t.. r t - -* - ' - - - --- * - - { - - . - ' - - --- F r-r 1 . *--- - -_ ' -. . . . _ ' _ -- ' t+- . +- -++ -- . -- 1- a- T -- t --
-- - 'tI 41 "rh+t 4 4+.f +
- ; , .. F . .. r_-L+--.1 -+ -- -- . .-.-- r - -. - -- 6 t r -. , . -:--1- - r
t }+--
.- J- }:1 -: . . .. .. . .
4':44*1
t$'Kr ittLI4'
r r-r r 4 t+ +. S Y +.1 -? Y
22 26 30 34 38Freshly Mixed Density, pcf
46
Figure B.l Yield stress versus freshly mixed density relation forcellular concrete with an 0.66 water-cement ratio.
50
1000
22 26 30 34 38 42Freshly Mixed Density, pcf
Figure B.2 Average stress versus freshly mixed density relation forcellular concrete with an 0.66 water-cement ratio.
-T -F .. ... . ... -.----------
..91
... - ..... :.... ...-...--. - .+- .- .- ..-.- . -j-.- - -- - .- - - . --. -- - -. - -- - -- ".- --- I+- -- ---
I --
-= -_. . . - -. _ _- - - - - - - - - - - - - - - - - - - - - - - --- - - - - - - 1i
I -- - --- -- - - - ---- - --- -- - -- -
t -~ 'it t
...---
- 7 -: - -'..j..' - ---- --- ---- -- t > ----- -- -I
- - -- - - - o -- - - - -- - - - -- - --- - - -- - - -- - --- - -
-T - -- ---- ---" ---- ---* --* - t -L .I- . -- -- -- -- - -I-- ' -T 1 .---* + T * t
0800
0
a" 600
4
0
00
4"
al)
bO0
w 200
j1
018 50
3
~- - - S- - - - - - - --4;
1000
800
. i
.. :__. .. S
. .
,
. , .d. .
.. . . ."
:1 . : . ' :
: . ;__.
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22 26 30 34 38 42 46Freshly Mixed Density, pef
Figure B.3 Stress at 40 percent deformation versus freshly mixed density relationfor cellular concrete with an 0.66 water-cement ratio.
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22 26 30 34 38Freshly Mixed Density, pcf
42
Figure B.4 Yield stress versus freshly mixed density relation forcellular concrete with an 0.76 water-cement ratio.
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46 50Freshly Mixed Density, pcf
Figure B.5 Average stress versus freshly mixed density relation
for cellular concrete with an 0.76 water-cement ratio.
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it. - . I . - I - . I . I . . . . . - .. - , . - I I I - . . - . I . obawAsumbloftLI ; i
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ttt
1000
800
26 30 34 38 42 46Freshly Mixed Density, pcf
Figure B.6 Stress at 40 percent deformation versus freshly mixedfor cellular concrete with an 0.76 water-cement ratio.
density relation
4-- -- ----- -f ---1---- I
. -- - - - -- - - - - - - -- -- -- - - -- - - - -- --. -- -- - -- -e - .- - -* ------ - -- -4 { - - _
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18 42
Figure B.7 Yield stress versus freshly mixed density relation for
cellular concrete with an 0.86 water-cement ratio.
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Freshly Mixed Density, pc f
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22 26 4630 34 38Freshly Mixed Density, pcf
Figure B.8 Average stress versus freshly mixed density relation forcellular concrete with an 0.86 water-cement ratio.
-. .-.- f.. ..4.. ... .--. .
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22 26 30 34 38Freshly Mixed Density, pcf
Figure B.9 Stress at 40 percent deformation versus freshly mixed density relationfor cellular concrete with an 0.86 water-cement ratio.
503
500
400
26 30 34 38Freshly Mixed Density, pcf
42 46
Figure B.10 Yield stress versus freshly mixed density relation forcellular concrete with an 0.96 water-cement ratio.
. :i.-F -r -r ---~ -.T-t-rr+r- -
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t --
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22 26 30 34 38 42Freshly Mixed Density, pcf
Figure B.11 Average stress versus freshly mixed density relation forcellular concrete with an 0.96 water-cement ratio.
46 50
-f-:-
- -
-H
- -
500
400
22 26 30 34 38Freshly Mixed Density, pcf
Figure B.12 Stress at 40 percent deformation versus freshly mixed density relationfor cellular concrete with an 0.96 water-cement ratio.
4- L. . . . r . - " = .-.. -t ..-.- t .. - :.L-. '- - . i -- +. - . - i t 1 t r 4- - - '-1' - - - - --. S --- +- -- -
F r , !' '.m-
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.. . -.. . . .. - . p '- . . ..- _ _- + _.--... T+-- - - -_-. t-e. .r ' F -- ' . -+ L- - - +"4.. . -..- .. t -F --- * --
r _+- F-- -- t -- it - - - T- ' ' i / * -+t-4---# .- i -' r .' _ }+r-i r- + --. $-r-- +- - -f t- --- - - -- r +- -- - - - --
S . - .+ . . - --r- + + ----- - -t--4- 1 -t----- , -- - --- -
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y - -4-*-tL'+- ' YT- -1}-' r1 y' 4' * ---+ T-'t --r1T _-r .-- --+-ri-- -*- r --t --
V i -i4_-_,.. . . . - -_ - ---- L - -- -
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7 7 ~ -F
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142
L + F-+---t. . . . . . .. l. t .-... .. r-r J - .1- }-
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4 !-w-_ - -- 'T -ti--i-4 *- - +- L -- x _- -' ++# }t- 4 . L . t +... L '- . r-
L,6
L -} - . -- - . . -- - -. - . . - -- - -T + -- -- - - -b - -- - -+ - - - - --T r - -
t t _ - : .. . L 1 - - -t - 1 - -. i.- - - L-- .- L - F 1 - - - - - - --- - - - _ -.-- -
Lt+.- T1 + +- 1- -+-+-t - - .------ 1 - ---
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30 -- 3 - --
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830004I+0
4200
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08 42 46 50
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- 4 4 - -- --L - .-1 - + -L- --a 4 - - -.4 - -
4001
22 26 30 34 38Freshly Mired Density, pcf
42 46
Figure B.13 Yield stress versus freshly mixed density relation forcellular concrete with a 1.06 water-cement ratio.
500
+44,
--{ _- t -a-- L . " r ! , " ' : : ' ,- + -: ------,-.- - -_-- -.- -}- + . -, -+ 4 A I +. -t -- - -- - -+ -+-+ + .J i i . - - - - -+ : - - - - - - . +-- . r -.'- - ++-r-. - -+ . . - + e+ + + - - - -+ t
- . ---- 4J - - - - ! ,4l } . - - ,--'- -1 _ j + -1 - I- - .+ - -_+ - - - . 1- 4I - - - . . - - L - . . 1. - - 4 a i Y+ L e + -+ e t+ + + r ---? T
. . .i.a-..... -..--... 1-2 .-. . - ..-- . ...-. . . . . ,---------------t---.----------
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rttt- .JJ .. "r L. + .1..... . -..........-... ,...s...a....... +- 1. .)- .e+ I .. . r+ -t --
_. L L . .. . .. ,.. ."+. ..- ar .- .. , .. L . ... .... ...- ..-. --- r ...- "- " , t+e. -- 4 -ty t.. - !.-+.-4 -- fth - -. .J4 --- -1 V-. 1 +- T ! - - - + r o e 4 - A i e -' - - - - y - - - - 9 - - - - -* - - -"- 1 -r- " - , - --- tt t j - i 6- t-- -+
f -1+ t- J J - F - j - - . +- -+ 1 . + -- +-+: -} ! - -- +-}I t ' * ' * * - - . - - - . * ' - - * ' ' - . ' - - i e - + . 4 e - - 0 e t 4 . 4 4 4-- - _} 1 .F .1.i +.} . - " } .- : r f.I + + . .. j - .I . - - - -------i .--- .-J = + ---T +-.--"- e --J e : .1 +-t"-"- --T-" g- + -, --
- J- 4 - 4 - f -- -J -} - 1 l -. - . -J1 1 1+ - - - a 1 + 2 . - 5 - . - - - i - - - - - -. : ---+ ---7*+ -1 }-+.4A --4 -j7yI ..L.L+ .it
- -- } .+ 4. - . + } , .+ - . .1 +. ... ! -_ - - J. -" . .. .1 -J - .. - .1 . ., -, - -, - -. ,-+ - - " -r t -r -J--4- -". -r -4 t
-.- f--} r+- -. t- --J- -- - - - , : y 1 ' .I , , . . .l . . . . . ..J , ..- . .. -. .. - ., ! . a . . l ..- .I4 .-- 4 - - 4 -+ y
-+-- - -+-t---+ -4-r+-t -
1. r1t 1
-t tt .. f. {-. . . -_.. . .. ; - + - - - - - - +.-- --...-- -_-- - -IU - - *- i * t*-
-- iIr - - - - - -t -- H e - -H+
-4 i -i -4+ - ++ ------ -- -'i * ** * ' -- --' --- '' -.-1 --'.1 1 >- '-+++
. i . t . .. . .4 ....' .-........-..............-..-QI '- .K. .-; t ..+ i
.. . ... 4 * t ---* * -' ' -t ---*- -' -s --' ---' -' -' -------1 -----1- --- }- -t -t4e..i. .. -4.. .... ... .. ., ...: .... -. ... .... .- .-- -- ; .-+ I- t -T --*--t -f-* -t + F
.i .; g .. .+ . i t . . . . . . . .... ... .. .s .... ..-. ... . ., 4 .... .. i -i . ----.-' -' 1- -i- t* -I * -
300
14
200
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100
0
118 50
'~~~~~~~~~~~~~~~~~~ 11 lit ''''' e ''+t''-* '+ -
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i.
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. .
- .. +I 1 -h 11 _ - - -
: . : ..- - . .
. IL
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4-1
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II
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j 1
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.
1 j'
22 26 30 34 38 42Freshly Mixed Density, pcf
Figure B.14 Average stress versus freshly mixed density relation forcellular concrete with a 1.06 water-cement ratio.
500
46
. .. l .
................. =
1 .
i4
H4:-
1 I_ h 1 ___l ___i * h l l 1 l i 1 101
18 50
, r
iT I ! I I I I I I ! I I I I I I. . I ,
4-.-.
MCI' = !q,1 i
1
i.:..i._::I:.
-J
.. 1 "- _ ' '._;__.,1 . = . -1 + - . _}_ r _ l m -r - -_1 - - - ;,-r,_,--_ _'t _ -- T __ . __
-
-F-+-- .- 1-
mbommoodolmom1i 6
L
{I
-..- -. ..I-2. > -.
- L -- -
-1 --
L..
04
-r -- .-- - . --
-.-7
- ..2
500
400
22 26 30 34 38 42 46Freshly Mixed Density, pef
Figure B.15 Stress at 40 percent deformation versus freshly mixed density relationfor cellular concrete with a 1.06 water-cement ratio.
L ..- - --
7 -
S--- -- - 1 - --- - - - - --- -
S-it
- r --- -t $j --- --- --' -- ----- -"- --- ---- - ------- --- ---
-- tt-- ------- - -- - - -S
----- -7-- -- - - - - - ..-. --
H
Go
i
300.4
0
ca
200
004
0B 50
1000
800
200
18
..I. _ ., ._ II::
:1:::
- - F-
-1~ EL2_I j:.-1-:1-
-- - -- - -- - - -- -- - - - ------- --- -- -------- --- -fT--
_ _- --- -- -- - - -- - --- ----- - --
-- 1- ----- - -
t i . . . . . . - -- - - -- - - - - . - . -. .- -. -.-.
j - j J- - [ j ---_-_*-H
22 26 4630 34 38Freshly Mixed Density, pct
50
Figure B.16 Yield stress versus freshly mixed density relation forrapidly loaded cellular concrete with an 0.76 water-cement ratio.
~ 600
Co
P4
>+ *00H
L 1 1 I 1 1 I - -- --- - -+- { I 1 E I 1f }
- - -
" _ '
_ [
t
I f T
-- - -
.__-{:
---- ;-
1000
22 26 30 34 38Freshly Mixed Density, pcf
46
Figure B.17 Average stress versus freshly mixed density relation forrapidly loaded cellular concrete with an 0.76 water-cement ratio.
-.....-.- T I.--T- -
- -..t ..}. .. .--- - - - - - -- ----- ----- ---- - -- - -- - - - - - -.. -- -.
-.--. - --.-- . v
--.- - -- -- .. .--.-- - -.-.. -------- - - - - - - - - - - -e . - - - -.- -.- - .-- -- ------------------ -----
1 . .. . .- ; . . . . . . . . . . -...- -
--- - -.-----.--.-.--.-.. -.---- ------ ------- ----. -. ..---.---.-- ------. - --------
- - -_ - - - -
---- ---- - -i---
r _ _ _ I A,_. :._ tIr " 1 -'
--II
800
sa
4J
$1
0
00
aO
4J
4'
200
H
0
0H8 5042
1000
800
0.
V. 600
4 00
- -LP4 -
-.
I.
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,.. ..
Yijt-
.1 .
:I..
.1.I ..- 1:---
- --.-
-
Kb4
- 1 -
..:- -
1::
-m i m - -II I I -
42 46
Figure B.18 Stress at 40 percent deformation versus freshly mixed density relationfor rapidly loaded cellular concrete with an 0.76 water-cement ratio.
-A - & 1--
- -
- Tt:I:t::~ I;:I: 1 II L1Jf~~I14L5LL
L.. IiiiiII..L.'LLI- .. .--.... I. .. . . .
r---- --- - - - - ;-----I- + Ire: -I +" -- --- - -- " }
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.+{
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t .
T 'f
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+ f {
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1
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a L 1
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+:k:
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+
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0&18 26 30 34 38
Freshly Mixed Density, pef50
--- " -
. :...
. ; .
:. j
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.. ...
,
:. ..
. .. .
' 1 i
t
.
-. 1
-
-r
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V.- -------
-1 T - " 1 -T- _ F -- -- F. - -- - - --- - - - _
i i . i m i A 1 m m . ...T r T f 1.r & 4-- 1+. T . 1 4.-- --I
-0-r--- -t- -t -t
i ,_.1 L
1-L-Li!I'"II. ':I i.I1:iIII
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.;
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t,
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I
1-
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-+.
* --1
1000
goo
22 26 30 34 38Freshly Mired Density, pef
Figure B.19 Yield stress versus freshly mixed density relation for rapidlyloaded cellular concrete with an 0.86 water-cement ratio.
- - - - ------ - - - -- - - - -- - - --------- - - -
- -L----- ~- - - - - - - - -- - - . . .-.. . . . . . . .- - - - - --- -
... .. _.. .
....
......................- : :::: T: j7 {
- - --- - -.- -- -. --- - ----- -- -- -- - -- -- -- -- -_ _ .- _ . ..«1 .
.... :r j....I
-- --
-t" Ft -t[ _ -- - * - -- --- - -------- -- ----- - -- ' - - t
. -t 1I . + - -. . 1- -:-j---:--;.--- - ----i.---- - --- --- - -
. 1 1.-+--- -------+--------------.- --.---- -I-
-- -- ,..--- -- It-- - - --- ----. - -- - - - - - - .
600
w
40
p* 600Hk-lNo
200
113 50
E
1000
22 26 30 34 38Freshly Mixed Density, pcf
*2
Figure B.20 Average stress versus freshly mixed density relation forrapidly loaded cellular concrete with an 0.86 water-cement ratio.
800
'600
0
41500
20
- - - +. -t- -{ - -«-r .4 -+- _ _ . r t i t- - _ - 2 - " + - - - - - - - _ - - -- . .- - - - _ - - . . _ _-- - _. _ - - 1 - _ - - --- -+ ---- --- T., ..2 ..3 .+-af t 4 t i - , t - T + ' * - - * ' - - - - -- - - .-- -...- - - - -- - - -- I-- + -r -
111S . . -. -- t ' - - - - -- - t 4 -+.t , -. . -.+ +.- - _ ._- - - -- - - - + - - - _-- - - _ -- -_ - ---. _.- - -- - -- -- _ -_-, -
-$-.y -. --.- $ T- } ;.? I .. - : : : : -- * -- t -- -a ' - - - - - - - - - - - - - -:-: - - - - - --.-- -. - - - - - . . - --. 4-. ---. -
7 1a I I 1 - {+ - i - V 4- + + - + 1 - . - + - - " -l + . ' { - - - - - - - -- _ - - - - - - - - - --------f -+ ----.
-'- -- -- - - - - - - - - - - -
ft S ~ t~ It17t71!-. --- . - . . .-- -----------
........................ ...... ......-.....-...-....... ....-...---- --- - -- '- - - - - - ---- ---- - - - - -
r r
r t
-. ...--- t.t- + + --- + 1- - -- - -. , -- ?. - - 1 - - .. -. . - - . . - - - - - - - - - . . - - - - - - - - - . . . . - . - . . - -. . ...'.-1 1 }. {+...-.
-t +,- -- 4 -4 - .! - + +4 -- -- 1{-+ -+ ,-+ -- 1 -- "----- -- ; -- _..- . -- -- . - i - I...t-. 1--} . .- 1 4 -r...
-t - 1 + - - t - -r -t o - i 3 - 4 , '- - --.t i - - - -- t -- -1- - - -1- - -.- --. ---. . +.-._+ + t . +l r } f 4 l r +. . - .-. . .... ..
-f-} +- -4 {t" , ii.t e 2- -- e- : -- 4 - -7--_ -1.+.. ...... .:..1... ..- . .r-..1.. .. t .. .
t-4 + -- . - 4- i + - l ? . 1 - ' - ' -i t -}4.} 1 . .'-- - - - - -- '4-. * * $-.-a _
H\J1
018 so
1000
800
600.4
OO
0
,~200
22 26 30 34 38Freshly Mixed Density, pef
Figure B.21 Stress at 40 percent deformation versus freshly mixed density relationfor rapidly loaded cellular concrete with an 0.86 water-cement ratio.
+= "I" 111 "
_... .. _. . - *: 1 i{...t J . , . ."}.i. . ... . _ . - L. + ; 1+ . , 1_ ~+ tt
- - t t+.- t 4 {It - 4
7 r- -t
----
-4 i 1:" rat- - -- 4- - -- L} -i-
- - - - -:- -" a '+ -F-}
t - -'I
1
t-- :-1- -: { -1- t"-r -;-i_ 1 .4- - - i It
4 -
-. -T - .. }jl ... ... a ... -i ' 1 - i j1/ Fjin... -1« -- -+-- --- - --- - - - + 1 ._, al --.-- . -- +-;
-r .- -7 7 . -: .. {.t. , -.- J 1-- --- - .-Ii - - - r - -'-t-- * - + -i i ' I
- _ 1 - - . : L . l #. , *-i i it4 ; -i . J- - .: - - - - .. ? - -. - l- - - 4 ' I *}-
- , t4 - t - t - _ - }. t 1 ,. . r P -i --..- :t. * + ' I r r Y----- +} . +, t .
-- r- 1 1f r
: i:7 1+ tlji 4r '44{
-- 4 4 - -- +
-_ _- _- _- _-_-1-_-_-_- _--_-_ ... . .. ..t.l ' i 1 L i..K IJ. t L. -**--- - - -- - - - - - - - -* -- - -- --l-ls
H,J,
-
018 503
* a [U u * P 1
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- :4:,'+. . .4- J s . - ~ i .. .-- ,. - t - .- - 1-. -+I . , ~- * * J . : ,- J 1---- - - -}-.--_ t-i-_- -, - - -
. ..- I- t - -- - - - t- .{_r1t $111-
.+ 1 ]4 . .. C & .}.;. +.} .rI '-, - + +----- t +-i- -t- -+ -- + - +4 I+ t > - 9 j-4- + - -_ , +
-- 7 j, I t 41--+. - -+}- t-- -4w-,+ t--S - 4 4 --- 4 -t j-- 4 4 .
.- ^ -r am-- -41 - ,-2 K- Ji} 1 .t--- r - . - - 4-
_4--
- -1- - - 4- -t 4 -- t - +---ft -- 1- --
- + +ii} -9--+{ r -tL- - . Y. ti t a --T Y t - -
4t T - -- ' *-. - * - -- -- -- - ' - * t4
L- - . - - --- i - <- --- - - -- - - ; - --- +- -;:+>--
4-. ;- i' -t l-1 1- -4._ + - -1 -} i - t - - + -} -
I f r- -- -- -
-2 t-r yt- -i it - I 4t- 4 4+ +44i- L jj-
44-4--j-t tJ
4 - K t - -
.- + 4: + 1+ . 4 4 t t * - 0 1 - + -- + + --- ++4 t - t-
-- 1-t -. ,i. +l}-,-,"-"- -t-,- f-{ 4{ L++-.j--r +4 K4 - -+----.+t - { -J-
.' - - -- +-
- -l i -1 L, . }. .... .J.} .. - -l $. + -. . 4 .4-- , .r . .. } . - - 1 "- +-
- i 4t - +- + ;. +- t - Ir-- - - -- I
4r-1 .J1.--{+ +I -+ + I+ i I 1 + 1 - - i
-{ -r+ .i . } . . y t1 J-_ - +} -- I-
. r .t-- .. + - I . . - - - 4 -
.. .t.ai .. + . -. I 1t - -- er-1 .1. t, 4 - i ? - - 4 j:+ra144,+1:1I . .Jy.r "+ - -- , } a + - - 1 . - + y ..
- + - - '4.4-t-.+++ +- K -1 t "+ - -I . - - 1 -4 - 1+
- - -1 + t - + F u r T+ -4 + . t $ 4 l t -- - - - t J + + - -14 1
22 26 30 34 38Freshly Mixed Density, p f
Figure B.22 Yield stress versus freshly mixed density relation for rapidlyloaded cellular concrete with an 0.96 water-cement ratio.
800
La
44J
00H\ii\J1
200
18 46 so
I Ann
1000
Freshly Mixed Density, pcf
Figure B.23 Average stress versus freshly mixed density relation forrapidly loaded cellular concrete with an 0.96 water-cement ratio.
22 26 30 34 38 42
t + + 1 4
"-
-" r --
';4-r4
.. +4 .. a- ...... 4., y .. i J . -t .+--{+ 1t .' ,- _- - - +.:: -j t. 1 .-- t+ 1:- . + - +_ -t-i-4- - G -i-- --
+ T--._ . + . -" . 4 a 4 , . . . t.-4t - -- t -. -a- _. - _ , +. I T - - 4 - d -
.. I - . ..'- . . . .l. -+ yI.. . . + - - 4 - -- -- ,--. -- 4 . 4-. ,- -- - 4 4- - +- - . . 4 - -- 4-- - --- 4-, - -p 4 - 4- - -
T4-1
4 4 ~ -+ 441:
1.4 i4rm f S
.. - Y J .. } . . . . i1 . y . .+ . }. . . .. a } - .. ; . . :.. i .--- - - - 4 - 4 -..-----. t._., _- _-- ,---. a - 1 -y--+ .". + *1 .44+ .Y+ f -
11
-. 4-f . .,.. -. . 1 .. ... i .. -. 41 , {- .- t-1---r ,- -i++ - -4 +a ' 4a:: . y . . .+.a... .. . . f. ; . . , . .} ' .. .{ j . .. { . .. : ... ;. t. .... 1.+ 1 ,f.-a { - +}r-.t ?- - - 4
- .t r. i .. .. A 4 .i. -+ - ... i ; : , ,{ t i#..- . . . . . .. . . . . ".--: - - ---- t - + - - a - - -- - 1
t. - 1.i , i ... .. . .. .+ . .r ., . ~. . . - 1 . . a . . . . .. _, . . . . 1 . -. $ Y . . . . _i..s. . j. t ' .. i I - - , . . .. 4 . } _. . - _
F-. {..-4-4iit- X+ + -: +. j -1 - . -+ ;-t - -- 1-:7-. - ; --- '-- -. I -i - ; i - *}--. y Y--T 4 - 4
-t X' .' I {-? +11- .- -t--r ----- --- - ----a +44 - + s---4- - --
-- T.-4. -. r. -- X ,-- + -. +-- }- i- I- -1, ;--- + '-- -- 1-' -.- t - --
-~ } }.,.1 aH -- - 2-- - --- i ', . {} , I+ } ++4 7 t
-l - - : ,-- - -- 4 1- ++ -{ +.- + 1 y t- -t r* --- - - - 1-. - . - +-- 1-4
- 1 . t .-! 144 4 - - 4+ --- 4--4- . -- . - --- ,
._+ ... _. .4 4 - } T} . . .. ' . .4 .. 1 {+.4. t. 4 . . .y +11 . . l -. ,. L# { - "--. ~~~~~~.i .r .t.-- , . . . . . , 4 4 .
--. { { +.g-a tt-_1 *} .-{-+--+- }+-J- 1 1 -t- -. , t +- . e + '- -{ -t- . + }- ---
- ++ . It i + - - - r- 4 1 - . . - 44 . J- -- -+ - .- . , -l -1.+ - -
-L iei- --- 2- -- +4--- 444+-- -T--', -- -{-}.+ + { --- } 41 + - 4 - 4 - - - - -_- -A
-r - I . - - f --l 4 -t - a t ? 7 1.1 j} 4 - 41 . t + . 4 j - , . , j j - i . ?.+. i.4
a800
oe
d~ 6000
0
0
a
b00
S 2 0
H
ON
018 so
1000
800
9 600
40
w
-~ ~ 400
0
0
18
4
i 1T
Q~F T2S71 , N T J
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22 26 30 34 38 42 46Freshly Mixed Density, pcf
Figure B.24 Stress at 40 percent deformation versus freshly mixed density relationfor rapidly loaded cellular concrete with an 0.96 water-cement ratio.
50
.I
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' f
r - ;- 1 +---- - -
. ,...
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:: :.
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1000
800
22 26 4630 34 38Freshly Mixed Density, pcf
Figure B.25 Yield stress versus freshly mixed density relation for rapidlyloaded cellular concrete with a 1.06 water-cement ratio.
- I} I o
{-I
2AL --- -K~.V ~-K- -
S600
41
a)e
4 400
H
CC)
200
018503
1000
22 26 30 34 38 42Freshly Mixed Density, pcf
Figure B.26 Average stress versus freshly mixed density relation forrapidly loaded cellular concrete with a 1.06 water-cement ratio.
a800
w0
'~600
4.5
0
0
4. 400
b0
200
H
018 50
- - --- --I- ---
- - -- .-- ---
-I _ 1+
77 17 ? _ _. . . .1... -- * *t-
. . -. . . . .."". . . . .
...1 . ...
T -- 1 - -
1000
800
.
-- - - -
. * +-
' J. 1 1 r a
i . +
l - C - a T .
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.
f f
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ie.
a
w'.
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- ..- - -
. . . . . . .
r 1 1
mu ma mm m. mimi mu m' mi mini ini m mi m - m mm. mu m
26 42 50
Figure B.27 Stress at 40 percent deformation versus freshly mixed density relationfor rapidly loaded cellular concrete with a 1.06 water-cement ratio.
4...:.
----H --
H
0
..
Ii.
.4''
600
400
200
t.i:}}
ajjiiii4a
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r a.
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0f18
t .. .. . . . .... . . . . . . . . . .
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i7 1 i22 30 34 38
Freshly Mixed Density, pef
r
. . I I . I . I . I - - - . I I I . I I - I . I . - - I I . I I I ' . - - T T .
II
11
..
- r
-- I- ----- -.- --
.- .-.--. ...-. ..- -..-. -..------.- .- .
i t - -t- -- t - -{-
i i i i i , , i : ; 1 1 1 1 1 m 1 1 ; .1 i R A -
i i v i i I i , i i . i a 0 . i - v . i . . i . - i -4 - i - - i I --+ - -
-- r----__Z;Tm
.,.,
.
--... ;
...
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.
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-=..4-0-..L-c--
i
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i
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.
.
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.;
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li
.
t
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t - ... .
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i
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---- --
.
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.
. i
018
V t i- T . r. . ! . .t r- a. _- 4 i.i .}-" - + - - .- .- .f . , - --- r - + - , - - - - r- - - --- r - 1 . . + --- t -- -- 1 +--} . 4 1 -
- .---- -,tr y.. - 4--- --- 1t-t I r .t-.1 . .- 2- -4 J ~].t14
.a a n-m. . . -a I ' n n m .- " t.. ... ~ *-r-'-_ . -*a *-.': .''+ +- . - ,- -:- - - -+-- - - -, - . -- 4-4-4t+t-
22 26 30 34 38Freshly Mixed Density, pcf
42 46
Figure B.28 Modulus of rupture versus freshly mixed density relationfor cellular concrete with an 0.76 water-cement ratio.
0~
0.
H
H
I50
fi i i , : I I I : A . : 1 : 1 i i i i I "
AA
- :. -- 2,i :t:a ', ,- ,*.. . . , . .. .. , - .-4-.. ..,-- 4 ,.-
+++- t 1.I..T.4 - ;. - . ~ - 1 Y . t--- t . ry .++ . . : .- 1 . a -1 -}+ - a -r---1 1 }. F'- 1--" .!.+_ - + -Y - ---- L i4-i --- 4-- -- -' 4
-} -- r -{a+4 4- r 1-- * - a - -. - 1 a " - . + _ i+ . - - - . - - - - - - - . . . f . -t o w . -- i . -- - 4 - - a _ L -. 4 4- --{ -
-- 0 - -- +-e-i a-+ 1 , -+ -- + ,-1 + 1 +l - -. _ .f :-- - 1 -- +-+y -+ -*- - 'i1--- r r- +- i + . L - i. -+- k -l+--
94- J- +-t-' -~4 + ++4? TAIi 1 ,+ , -. . - -.- +- 4 4 -. + - - . i +. - «- - t - , * * '.r. .- . t . ._- - a *r : - ' ' --- - - + f - } f * - -+ - J T 4 -- --- 4 '---.-+ - , -. +. .-++ -+ -
L {a -a _-- 1'- -.. 1 t + .: -i t- +- - t- -4f--I+ - I a+ - --- J r--: -- ++e .. 4---+4+y -g. . t--'- f-.+ }-g -- ii +-
++ .- -. -J - + + .. a+ a . -+-. f -i -4 4 - -+ -e - - -- + '- - ' --- 1- - y am .-- * -' " -i---a .-. -- +- r* +.+ - ' 4 . a i 4- +- - --
. - --' - -- - 4 -- - -- - +-+- -- - -- '+ : - -- - ' . + +
T " . -42S i i ti. I i -80+ i .. *.1 . 2 + It - .. " } a I -+ T.
. 1 .. L .L44| r 4 ----e ' '-4 -j+ 4- +: t V-'-- -' -- -- * '- ' - + ,- ,,',+ -' -4'. -44-' - 1 -- 4- t 9 Y4+- - 4- - - -- - -+ + - - - .-- - +- --. ' + - . - 44- -- -.{-4-4
.- 14., . . -. . 4 +..1- .- -...... ,a..ia.--+ -. 4- . 1 + ti J _t ti _4 -F-.- - + - J-a ..- 1 --.4--.- .-44.4-
-4----- -'-- --+t f--i.44-...4 . . ..4 -... .4 .'tpt+.5S + + .It. i44-+ i-- .4.y -. 4- .. 4.4 ' - - { y- -+" - - a 4--{ + + ' - ---4-- . * -- -- - :. +1 - *+ { ' "*+ } i ce *- - -1 -- t- -- r . 4 4 -4+
4 --- + - - '... - - + 4 - - - , - - - -+ - e e e t a
- .1 + ..".. .s..i . .-+.~ l +1 . - - .:- -. . - - - -- - --. - - .: + 1 -! . .--4 - '--
4+-- t -*4 -++ -- -4 -++- 4' +-- -1i-+, -- t-- --- }f-. -- }}-} -- - -- -- t-- r-} as-2 r +r }}-+ -I + 0 - +- 4A f- }-
6a .;.7 1. .+i . - . y .4- . . . - . - - . . - - - . ... : . . -I .L -. 1 . } + - "- -i .+. +y - - - - - - 4 - - - t - - - '4 -l } -a + --+'
+ ---+----4 4j- ---,'-----4--- - - -+4 t-' + +: tlt- e1- ''- - ---- ' - ' *4'--r '-i - 4!e+ , i-+ -'-'-4, + - 4 f-44 ~- t' --
--- t-4 - - -
+- 114-+ -2. - -- 0- -- - - - ' -- - ' - - -* --
.J 11 ..'.i.'.. .V.,-i --- -.. -. --- --. ----v-iii. .---- A4 -4 4-- .-
1 -- t-- -+
L
22
Freshly Mixed Density, pcf42 46 50
Figure B.29 Modulus of rupture versus freshly mixed density relationfor cellular concrete with an 0.86 water-cement ratio.
0
4'
H0)-
inn
- - -- j 4 - 1- - + + -*. - - - + - -Y - - - 'mi-- - + -- + - - . - -. Y-
... "+} . }... . la4 .p -} }-+1 i+: --- -:-1 -++---}- t } 4 -. - 4-. -aed* -. + _ :+ .---. -. --- l -- * }1-- -- 1 .- -. _t- i -4--.L--- --+- -+- -
-... - - - L- . I -+ i+ . f }, }- } - - + . - l -t . {'+. - ' ' - ' r -. . - - +. '- - r -# * - 1 , ta+ -- --- f -
t 44 44' 4ft1 -- t- 4- --- i . L jt:;s . :.: - 4 4 4-- - - 4 -- -- -. -. -- ,, -- - .- -- t-.44
-+ -+1" --- '. -4t-t- --4' -ht-- ---- +-
- .4-4 -. +. .- . - - + - + - - . - - 4 + - - -. .
. - -- . -. '- --y.4' -- -- . - - . I 14-- . -- +
8 0 ' + 4
J + ,tt +
1 - . +4 +4 -W '- 4- 1 - - . ._-... -+. . . f -4- +.- 1;J4 t 4 --- - - F 1.,
wa J i -- ... 4 :. 1 . .. ., . ... . . . ... . .... ,.... . .. . ... ..+.. + . 4 .- + . - -}} a-- « 1 . -. -r _-- - _ . . -. -- _ + - " ,-*- -- 1 _. i l l.-- -. . -+ - * + + Y .ti lt-' } - ----1. * i I *-. .4 -t 4 -- -* 14 ----- -
, - -- - - - - + t-+ + 4 -t1 3 - .- +- '1 . ,-a-. : - - . - - , - -4-1- - - - 1 - . - . - ' -r "+ r. , . + -, . ++ -r - -- t 4 I -- e- - -+ t ----i+ 4 j, 7s 1 7l7
<- . i -! - . - . - - .-- . - - -. .4. - + t.- - 1 i +-- L A fl + - - f - -
- V - t- - i- . {- - { - 4 - { . . - - . .. - - . . . . . . . . .. . . . .. . . . . - - a . ... . : . . . + , r _-- . t +- i t + i t i -t i t b -
-f+. ..2. 44 -. --+ ---
{ -- -t; .PtTla: t i--+- - +4+- 44-- -.4-- -.. --
- -+ 1 1 . 4 -+.1 . . . . . . . . .. . . . . . . . . . . . .. .. . . . t .1 , . r. . l i i -- . . - 1 - T- - 1 . - - -
40 + t { 1:_+ , t
+ 1+ liLl 1 .1t + ---
L+ . .il + . : . . . . . . . . . .{. . .*. . . . . . . .,. . . . . . . . ,.-. ... . - L... :. r« l i . . + .. .i - r.
+ + }- .-i . } l.. i t, , . . .l . , . . . . .1 1 . ,{ .. . . . . . . .. . .. .. . . , . . t i ; , . . - --lt -- 4a- -
14 -r l a. . . .. .. . .: . . . . . . . . . i , ; . , s . . . - . .! - - I.- YI 4 - t - + + 1- '--- r +- , 1 1 +- . .- + -
....-.. . .
20 tr'
1tF } t .1-i- ++. .+. U+ 4 l 4j I
18 26 30 34 38
.t 4 - - -- r-j-4-F H } 11 -t-t +- - - *-,-+4 - --. t } - - 1 t-r - - +"-t-- 'i- -t.. + . ' . ... . -- . - .1--- + -- i .- 1-{ - + +r 4 - - +f - . -- -'-t t t -
- - -4 -j- 4., -,- i - i -1 -- i - -1 -1 4- -.i - 4 i a -4 - - 4 4 - -+ -e - -4 +
100
80
J4 t
4.- , .1 J l. . . .. . 2. - - . - - - 1-' - - - {. - : - t - i . + i + -t + ,t , - .+ 1 a } - - + ! r - - -+-.}' .-
+ + - - - - - - - . - '-' ''.- - - - '' t+--
:- a._ .-_- e-- I-h--
- -. - -- -A 4a ... .- a- -- -+ -
. .J. . . . . . . . . . - - .-- - - - - - --: :- + , * - . - - - - t - ' +- ' - 1 t 4 - + - - 4
- 4 . s . a . - - . - - - - - . --- ----. -- -- -- -* - --- -' ' ' -- ' 4 i i -t - * e- z-4t --T
30 34 38Freshly Mixed Density, pcf
Figure B.30 Modulus of rupture versus freshly mixed density relationfor cellular concrete with an 0.96 water-cement ratio.
4-4 4t1 '~
, -,-,-1 { r i . . , } ,-,- , L . - : :I - - - - - -. t -t- t 1 .}-t i i i i i i
. .P . 4 + -r - + - + +- -
.-.-.. '-+.j. .-----+ - , 1 +. -+-- -t1 , + .-4-- --W 4 t
.- - - -- 4-+4t 1+ - ++ . -1 ' .- L- . -_'- --- 'i I - + - t - + . -L - J . +" -
11 - - .- t t - 1 --t ' ' ' --- *} --' --' ' 3 4 t -i t -i + . ---,r--. --+ + --4-.a. .+ ... : ?
. - ; . . - ' 1-- - - - - ' 4 ' T - *i-s - i-y y a i- + -$ - - + Y +- - - - -9- -+ --+- -- T ----i-'----4 -'-9-1 4-- -- +
4 t .. -4 . , . - . . .E ; a - - - . , 4 4 - . . + - . - . -t - -i 4 -4. t t ' + t ' + + - - + - -- -
sd
4 40.
x"
HJON
18
44-41,111. 11 .111111 lH
I I I I I I Irl
H.+ + f4 4 -4-++--+r+ +-e-t-4 - +++. -- ++-+-+- r- -I 1 1 4-H-t _ .r_ r1I .- 1 + - f1 i.. L .}.._ t t-+-t . - } tr - .- rte Y }- 1 -" .t. r +-* i-a .*. I Y. . f' r" 1
44 { -i't " T t F r t t } t f +
- + 1 r. i. y .a i r-} Y t i" t +. + {r t' Y i t -
:. f i {- i 1; . f r f 1 " 1.. I "Y +-"i L r { t L 1 1 'f-Y t } a+ f y
t-t
42 46 5022 26
I
-t f+ f11--;. 1, 1 f 1--i-H
100
80
22 26 30 34 38Freshly Mixed Density, pcf
Figure B.31 Modulus of rupture versus freshly mixed density relationfor cellular concrete with a 1.06 water-cement ratio.
+-'- - 4 - : +- 4+4 - 1
.--t+4- -- 4 -
t1't-- -,-$-{t. .4 - +. +- .1. --- --.tJ I -f - - . - .---.' ... rt - 4-4+ } i . . i - r . . .l--..I } .L ..... . }. . ,. , } y - _. .- :- - t - « -- t . +--}.Y - -
-+l- 4 - - -- - .I --+ -I. .}}+--' - .. l -'- , - -i - *+ -+t - I +- . -' + - i-- - - - 5 4 - ' T - 4 -*
4 . -. I4Y+4 .. ' . r- -4. ly - .. *-+ --.- Fi L- - . . . :.-. 1 i . - , .. t . .y f- - + - . - . -
4-1- -++-a- -- +- +--. ---- 1- - r - .-.-- r a- + +- - -1 J-..+ll- -+ +++
- 4 -f
+y-+ii -it .i + }
1L %
A}
-+-.r - - .. r .. r r+ . . :, . .} .,-. .t - -+ -. - 4 - + -i--- -- -- -- - --- - .-- -- ,- . - -. - + - +- t-el - - - + - f" ---
.--.
.
+
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.;
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.
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t-i-
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- ,+ t- r! + -
. - -- . - -- - - - - . - - - 1 -- - --t -+-+ - - -+ 1 - - t - + - 1 0
- T - -1
- 1+ - f--. + L a - - + - a t-: - -. +i- --- - I, t . L . I,- . . . . . .1 . i J. - 4 } -- . I. - (+ { . " " - -- -
,
'60-
0.
00
0
H
20
0.18 46 50
25U
-
t - 1-ti
it]t[4 -Th i-I
1T :1.1.4- 11 141414 jj7it f
It htt f* ttttt
1 4 -U4II L 4 t-
-I--
000
k
V
U4
0
U)
0t i-t +1HF F-H+H
t44~ko1Th TE i-44~V
(] -
1 . ti 17-i
tit 4- I-HI1' ti1UtL~~~'t~
*24. 44 144. 2444
26
j 17I
} !t t4
ILL-1-1
30 34 38 42 46Freshly Mixed Density, pcf
Figure B.32 Modulus of elasticity versus freshly mixed density relationfor cellular concrete with an 0.66 water-cement ratio.
1nn
15
t ttt
n[+n410U
*1i41-. "L
h4-
U
18 22 50
,-"4
- r - -
PF
Y LA 1 1 I 1 1 I I 1 1 1 I 1 1 1 1 1 1 1 1 I I I I I I I I l l 1 1 1 I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 . l 1 L L I
1 -t1i qll ILI L
1 a + - TIT i t ,JkT,_f a1t 1 ,1+ + + +f f
4 4' 4
-J- 444 4 4a4
. . . . . . . . . .i--f--f --
t
1 1 1 1 1 1 1 i 1 i 1 m 1 1 1 1 1 1 0 ! i . i i ! 1 1 1 1 1 ! 1 1 1 i 1 m ! M 1 i I I i 1 A I ! 1 1 l 1 1 1 .
.1... . t .+t .
e Jl{J {{{ Jilf{viii+ il a 1 r ii i ii r
t --i i i i i i i i t- i m - i I i 0 1 1 1 1 1 m 1 1 1 1 1 i 0 1 1 0 1 i 0 ! i i i i i 2 i 4 i i m i ! :bo l h I i i i ,
-4 444f}"_
tfiR.
.t
}
+ +
.
+ +
i'-'1J
I-tq
Vl
^iI
. t t-
r t t t t-t i- 44+
ljt4 t ti I 4 t4- i i. I} It r. 1 -!-7-
,. mot. i t +-+ t 1 t -! .: .* } 1
+41
.7 1wlHi -7;
Cr.
4 114tU i i .i [Li+t-'It
44
.i
titI I-r4jjj- I 44 1 -4t -44 j IZ .44
tiMml
I i i i!i i 1111111! I -.. .. I . -].R 14 1i i'1;111111I1 ,;i v ! i.i li; Ai ;4411;71111111' -4 iT ;l4 ii:1i .; i;T;:1i- i 4m
H-f ; '.rl fl .i
tLfYi 't~ s
26
i
{U2fifLN4IL
30
i
~t~t -
00
0
U,
0x,
34 38Freshly Mixed Density, pef
42
[T4
46
Figure B.33 Modulus of elasticity versus freshly mixed density relationfor cellular concrete with an 0.76 water-cement ratio.
-f--i--I --tlff25
20
l-ttt-4
IlIt-II
WIi--lt~t Ptl 1
.. 44f-
- ! 1 1 -{- -- t - -l t - - 4 +
-- I +- +j- I - "--4 -- -4 t - - - - -
-- 4fil4
+5 . 4 4 t-
144 -L-
- 4 - - - t- - -1 - --o . +- - . , -- -- - - --,
'1. .. . . .' . . . _-.. - Y t - ---4. 4 ..... l
HO~N
IN'
22 50
TT -+Hi-jX1.1 ${ :-
+ -1 44 1 1 -- f ' H ' l . l l m i--1- - ++ +-+i f -f +-{- H } -I
{ -- ,4 4
-4,+...r ! +,4t
444 .. -
4I
-i
(
L y
-a
_+
I
i
I 1 1
-4 4 1 4-1 1-- 41' '--1Jl 4 41 1" ! 4 1r;.. 1
I I
i
.n
1Sr
18
250 }
-- -- -l - - - - --- A - ----tA
-- - ------ -t --1- --} ----{
-t -- -- . . t J t -- - -. + -1-, - ---- ------
- - - - - -} - -tt "} } - T-.l!t +_I,- -{. -. . ---- -1. . -- -. a i - -"- - - - J-1-# t.- -.- -
: - - - - - - - -1 ---I- -+ ---1 --+-
- -1- - ---I-{-+ -
151
-+ -T -i {_. t- M-jt I
1t01--$-1-- - -I -t-f--} }--I. 1.i l - 1 -- y - + y -t TL -
1- - - 1 t - I ; } -t . " .- . + } .. ' t t -- +
t. t- F---! --------- f -f T f 1 to---rr- + - a+ 1t } - 1 -t- -1 - I --
- - . _ - + + } } r t :; } r t - - +- 1 +- -- } - r-1 T
-. - - - -,- .- t- --- }i-Y- , " 1aY. .,- - 1
T14
18 22 26 30 34 38 42 46 50Freshly Mixed Density, ocf
Figure B.3)4 Modulus of elasticity versus freshly mixed density relationfor cellular concrete with an 0.86 water-cement ratio.
000
.4
U)
0
-4-p-- I i ik
::: :: : :T::::
- - 1 -- -- --- - +--- - -- - -- f - --- .t- -- - -1*- ---
- " i - ::22 -i~
i2n .
T J _- L 4 1 -- --
I T t
00
0
0
30 34 38Freshly Mixed Density, pef
Figure B.35 Modulus of elasticity versus freshly mixed density relationfor cellular concrete with an 0.96 water-cement ratio.
2 50xFt 2F
I
.__.. _- -
50
..- .- . .- .--... ---
18 22 26 42 46 50
...........-- }---------i -- 1--------i --
-
" I i " I ~~~I 4 I "i , .I .} _.+_.
'---- t-- - "- +---
.- - -- t. __ -- -- t - -_
L L1 V _ L _.
---- +T---- ------------- -- ,--------_ -- .-. -- 1 ----- 1 L
- -- r - - -
--
-
7.:7
I sn
APPENDIX C
OBSERVATIONS ON THE EQUATIONOF STATE OF CELLULAR CONCRETE
The mechanism of attenuation of pressure waves in cellular concrete
has been studied previously from the rigid mechanical point of view that
is applicable for the lower rates of loading as contained in this report.
For loading rates sufficiently rapid that wave mechanics influence the
behavior of the material, the mechanism of attenuation may be appreciably
altered. Wave propagation experiments with cellular concrete have indi-
cated the shock structure of cellular concrete to consist of an elastic
precursor followed by a slower crushing wave (Reference 20). The pressure
associated with the elastic precursor is a function of the input pressure
of the incident wave and is observed to exceed the static yield strength
of the cellular concrete for higher impact velocities. This indicates that
this material, prior to locking, may transmit stresses to a structure in
excess of the elastic yield stress. From a few tests conducted on cellular
concrete, data were produced relating to wave propagation velocities,
width of the transition zone for a step pressure input, and rate of decay
of stress waves in cellular concrete.
C.1 THEORETICAL CONSIDERATIONS
The description of elastic-plastic wave propagation in a material is
predicated on a constitutive relation of the material behavior and the
equations of motion. In the simplest cases, a strain rate independent
behavior leads to many important simplifications that allow computation of
stress and strain relations in a fairly straightforward manner. In this
instance, the Hugoniot jump conditions for one dimension involving stress
(a) and strain (e) are given as
a = pUu (C.l)
E U= U (C.2)U
where
p = density ahead of the wave
169
U = velocity of propagation of the wave
u = particle velocity behind the wave front
This description of materials behavior is essentially hydrodynamic; and for
very soft materials where shear stresses and strain rate dependence are
negligible, these equations should be a fair approximation.
In the elastic range, the relations are essentially the same but are
derived from considerations of elastic behavior, where U = C , the ve-
locity of propagation of elastic waves.
In the case of an elastic-plastic wave reflecting from a liner, the
stresses delivered to the liner can be derived by making the assumption of
purely elastic behavior of the liner. Under these simplifying conditions,
reflected stresses at the liner can be determined from the behavior of the
shock-absorbing concrete under shock loading.
C.2 EXPERIMENTAL METHOD
The shock behavior of cellular concrete was studied from the wave
propagation point of view using impact experiments conforming to one-
dimensional strain conditions. Continuous measurements of propagation and
particle velocities were made using an induction wire transducer. Plane
impacts were produced using a gas-operated gun to launch a flat plate onto
the specimen. The gas gun has a 2-inch bore, 10-foot launch tube, and a
pressure chamber designed for 12,000 psi (Reference 21). Both the weight
of the projectile and breech pressure can be varied to attain different im-
pact velocities.
Test specimens were prepared with induction wires placed at varying
depths from the impact surface along the centerline of the axis of loading
as shown in Figure C.l. The specimen was then placed in a dc magnetic
field such that any axial motion caused the effective length of the wire
to cut lines of magnetic flux thus producing an emf or voltage propor-
tional to the velocity of motion. The output voltage from each wire,
therefore, was recorded as a function of time. The amplitude of the signal
was calibrated in units of particle velocity and the time displacement
between each wire was a measure of the propagation velocity.
170
C.3 EPERIMENTAL RESULTS
The observed particle velocity records for three signal wires are
shown in Figure C.2. The test configuration for shots 1 and 2 was such
that the cellular concrete was impacted directly. The first two shots in-
dicate the existence of an elastic forerunner wave preceding a plastic-
wave. However, this forerunner cannot be distinguished from an air shock
effect since the range facility was not evacuated in this case. An effort
was made to vent the gun barrel at the sample interface; however, it was
difficult to determine if this was sufficient to eliminate all effects of
an air cushion. Therefore, a 1/8-inch-thick aluminum plate was affixed to
the impact surface of the specimen to permit the range facility or barrel
to be evacuated to approximately 10 microns. The records produced using
this test configuration are shown in Figure C.3. Signals for two wires
that were spaced at 12.7-mm intervals from the impact surface at a faster
sweep rate, which was selected to show the elastic portion of the wave
structure, are shown. These same signals were displayed at slower sweep
rates for observing any plastic wave structure. No plastic wave structure
was observed on any of these four tests for a period of observation cover-
ing 200 psec. Propagation velocities correlate closely with the sonic ve-
locity or the velocity predicted from the slope of the elastic portion of
a static stress-strain relation for the samples tested.
The observed pressure-time histories shown in Figure C.4 as computed
from the measured velocity histories show a decay in pressure of approxi-
mately 50 percent over a propagation distance of 12.7 mm. This rate of
decay is not expected to be constant with distance from the impact surface.
Additional data points as a function of distance from impact surface would
be required to determine this. It is possible that this apparent decay is
a function of the test conditions; however, a correlation between this and
wave reflections for this test geometry has not yet been achieved. One
point in question is the velocity of release waves emanating from the outer
edges of the projectile input surface that could diminish the region of
one-dimensional strain. More experiments are required to establish the
contribution due to test geometry.
171
Under certain conditions, an interposed layer of foamed or distended
material may substantially reduce peak pressures transmitted to a struc-
tural wall. The initial shock front does not seem to occupy the rela-
tively narrow zone usually imagined to exist in solids. Therefore, it may
be more accurate to say the pressure attenuation effect is related to a
broadening of the condensing front. Beneficial effects can also be derived
from the existence of forerunners similar to elastic precursors in solid
materials since these carry off momentum from the crushing wave and deliver
it to the structure at a lower pressure.
172
PCMAGNETIC
INDUCTION WIRES AXIAL
PROJECTILE
S
I M
)LE
SPECIMEN
MAGNETIC POLE
Figure C.1 Schematic of experimental setup.
173
1
I
o A AxUW
U,
B-30 30
F-A- 0acc
a-
0 0
250 4-EC 250 SEC -TIME, $SEC
SHOT I -IMPACT VELOCITY = 50 FPS SHOT 2- IMPACT VELOCITY = 75FPS
NOTE: LOCATION OF ZERO POINTS IS ARBITRARY.THE STACKING OF CURVES A, B, AND CIS DONE ONLY TO SHOW THE CHANGEIN WAVE PROFILES.
Figure C.2 Particle velocity versus time histories.
174
"
rA8
0
SHOT 3 - IMPACT VELOCITY = 75 FPS
16
8B-
0
24 4E
-IS A
o BJ
0
SHOT 5-IMPACT VELOCITY =150FPSCL
24
16
8
0 8 16 24 32TIME, ).SEC
SHOT 6-IMPACT VELOCITY = 200 FPS
40
NOTE: ZERO OF CURVE A IS ARBITRARY BUTCURVE B IS IN THE PROPER TIMELOCATION WITH RESPECT TO A.
Figure C.3 Particle velocity versus time histories whenimpacted with aluminum driver plate.
175
A
B
. InI
oo--
I
0.
0.
0.
0.
0.
c.0J
S0.
Y o
U)U)W
F-
0.1
I
6
A4 -
B
2
0
8
6
A
4 -B
2
00
NOTE:
8 16 24 32TIME, ).ASEC
ZERO OF CURVE A IS ARBITRARYBUT CURVE B IS IN THE PROPERLOCATION WITH RESPECT TO A.
Figure C.4 Pressure versus time histories.
176
AB
- -I
4
2
0
6
4
2
0
B
600
300
0
.uu
600
300
0
A
0.
0.
o.;
CA)
wW:
900
800
300
0
1200
900
600
300
004C
REFERENCES
1. ACI Committee 523; "Guide for Cast-In-Place Low Density Con-crete"; Journal, American Concrete Institute, September 1967, Vol. 64,No. 9, Pages 529-535; Detroit, Mich.; Unclassified.
2. G. C. Hoff; "Shock-Absorbing Materials; Backpacking Materialsfor Deeply Buried Protective Structures"; Technical Report No. 6-763,Report 1, March 1967; U. S. Army Engineer Waterways Experiment Station, CE,Vicksburg, Miss.; Unclassified.
3. G. C. Hoff, W. F. McCleese, and J. M. Holzer; "Shock-AbsorbingMaterials; Aging of Backpacking Materials"; Technical Report No. 6-763,Report 4, November 1968; U. S. Army Engineer Waterways Experiment Station,CE, Vicksburg, Miss.; Unclassified.
4. G. C. Hoff; "Shock-Absorbing Materials; Selection of a SuitableLow-Density Concrete for Backpacking for a Proposed Field Test"; TechnicalReport No. 6-763, Report 3, April 1968; U. S. Army Engineer Waterways Ex-periment Station, CE, Vicksburg, Miss.; Unclassified.
5. G. C. Hoff; "Operation Flint Lock, Shot Pile Driver; Grouting andMaterials Control"; Miscellaneous Paper C-69-7, March 1969; U. S. Army En-gineer Waterways Experiment Station, CE, Vicksburg, Miss.; Unclassified.
6. T. C. Powers and T. L. Brownyard; "Studies of the Physical Prop-erties of Hardened Portland Cement Paste"; Journal, American Concrete In-stitute, 1947, Vol. 43, Pages 101-132, 249-336, 469-504, 549-602, 669-712,815-880, 933-992; Detroit, Mich.; Unclassified.
7. T. C. Powers; "The Physical Structure and Engineering Propertiesof Concrete"; Research Department Bulletin 90, July 1958; Research and De-velopment Laboratories of the Portland Cement Association, Chicago, Ill.;Unclassified.
8. T. C. Powers; "The Nonevaporable Water Content of HardenedPortland-Cement Paste--Its Significance for Concrete Research and ItsMethod of Determination"; ASTM Bulletin No. 158, May 1949, Pages 68-76;American Society for Testing Materials, Philadelphia, Pa.; Unclassified.
9. G. Wischers; "Einfluss einer Temperaturanderung auf dieFestigkeit von Zemetstein und Zementmortel mit Zuschlag-StoffenVerschiedener Warmedehnung"; Schriftenreihe der Zementindustrie VereinDeutscher Zementwerke E. V., Dusseldorf, March 1961, Page 50.
10. T. C. Hansen; "Cracking and Fracture of Concrete and CementPaste"; ACI Publication SP-20, 1968, Pages 43-66; American Concrete In-stitute, Detroit, Mich.; Unclassified.
11. A. Auskern; "A Model for the Strength of Cement-Polymer andConcrete-Polymer Systems"; BNL 13493R-2, March 1969; Brookhaven NationalLaboratory, Upton, N. Y.; Unclassified.
177
12. M. Polivka, J. W. Kelly, and C. H. Best; "A Physical Method forDetermining the Composition of Hardened Concrete"; ASTM Special TechnicalPublication No. 205, 1958, Pages 135-152; American Society for TestingMaterials, Philadelphia, Pa.; Unclassified.
13. R. C. Valore, Jr.; "Cellular Concretes; Part 2, PhysicalProperties"; Journal, American Concrete Institute, Vol. 50, No. 10,June 1954, Pages 817-836; Detroit, Mich.; Unclassified.
14. F. C. McCormick; "A Rational Procedure for Proportioning Pre-formed Foam Cellular Concrete Mixes"; Ph. D. Dissertation, 1964; Universityof Michigan, Ann Arbor, Mich.; Unclassified.
15. A. Pauw; "Static Modulus of Elasticity of Concrete as Affectedby Density"; Journal, American Concrete Institute, Vol. 57, No. 12,1960-1961, Pages 679-688; Detroit, Mich.; Unclassified.
16. ACI Committee 318; "Proposed Revision of ACI 318-63, BuildingCode Requirements for Reinforced Concrete"; Journal, American ConcreteInstitute, Vol. 67, No. 2, February 1970, Pages 77-186; Detroit, Mich.;Unclassified.
17. ACI Committee 213; "Guide for Structural Lightweight AggregateConcrete"; Journal, American Concrete Institute, Vol. 64, No. 8, August1967, Pages 433-469; Unclassified.
18. T. W. Reichard; "Creep and Drying Shrinkage of Lightweight andNormal-Weight Concretes"; NBS Monograph 74, March 1964; U. S. Departmentof Commerce, National Bureau of Standards, Washington, D. C.; Unclassified.
19. G. C. Hoff, W. F. McCleese, and A. A. Bombich; "Project BigPapa - Phase III, Cellular Concrete Fragmentation Acceptors"; MiscellaneousPaper No. 6-973, February 1968; U. S. Army Engineer Waterways ExperimentStation, CE, Vicksburg, Miss.; Unclassified.
20. B. R. Sullivan; "Dynamic Compaction of Porous Concrete";Miscellaneous Paper C-68-9, November 1968; U. S. Army Engineer WaterwaysExperiment Station, CE, Vicksburg, Miss.; Unclassified.
21. D. L. Ainsworth and B. R. Sullivan; "Shock Response of Rock atPressures Below 30 Kilobars"; Technical Report No. 6-802, November 1967;U. S. Army Engineer Waterways Experiment Station, CE, Vicksburg, Miss.;Unclassified.
178
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184
UnclassifiedSecurity Classification
DOCUMENT CONTROL DATA - R & D(Security classification of title, body of abstract and indexing annotation must be entered when the overall report is claailied)
1. ORIGINATING ACTIVITY (Corporate author) 12a. REPORT SECURITY CLASSIFICATION
UnclassifiedU. S. Army Engineer Waterways Experiment Station 2. GROUP
Vicksburg, Mississippi
3. REPORT TITLE
SHOCK-ABSORBING MATERIALS; Report 2, CELLULAR CONCRETE AS A BACKPACKING MATERIAL
4. DESCRIPTIVE NOTES (Type of report and inclusive dates)
Report 2 of a series9. AUTHOR(S) (First name, middle initial, laat name)
George C. Hoff
6. REPORT DATE 7a. TOTAL NO. OF PAGES 7b. NO. OF REFS
June 1971 184 21Sa. CONTRACT OR GRANT NO. 9a. ORIGINATOR'S REPORT NUMBER(S)
b. PROJECT NO. Technical Report No. 6-763, Report 2
c- Nuclear Weapons Effects Research 9b. OTHER REPORT NO(S) (Any other numbers that may be assignedSubtask SC 210
d.
10. DISTRIBUTION STATEMENT
Approved for public release; distribution unlimited..
11. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY
Defense Atomic Support AgencyWashington, D. C.
13. ABSTRACT
The use of low-density cellular concrete, having an oven-dry unit weight of 50 pcf orless, as a backpacking material for deeply buried protective structures was studied.Cellular concrete was found to be suitable for this type of application. A number ofphysical properties of cellular concrete were determined to provide input to designcodes. Constrained compressive crushing stress levels from 20 to 1,000 psi for slowrates of loading were observed. Rapid-loading tests and equation of state measure-ments were also made to determine the rate sensitivity of the concrete. Compressionalwave velocities from 2,000 to 6,000 ft/sec were also measured. Modulus of elasticityvalues from 20,000 to 220,000 psi were measured for concretes in the as-cast conditionwith respect to moisture. Flexural strength to compressive strength ratios from 0.16to 0.33 were observed. Early age stiffening characteristics of cellular concrete werealso studied. Some design procedures based on the data analysis are suggested. Somepossible areas of difficulty during prototype use of cellular concrete as a backpack-ing, such as lift heights, cold joints, temperature problems, and water-saturationproblems, are also explored. Lift heights should not exceed those that cause an in-crease in density over the desired density by more than a stipulated amount in thelower portion of the lift. The effects of joint roughness and curing on the jointperformance are minimal. Temperatures over about 120 F tend to cause collapse of thestructure of unhardened low-density cellular concrete. In a free-water environment,saturation of the cellular concrete is inevitable unless steps are taken to preventthe water from reaching the concrete. Suggestions for doing this are offered.
DD po 473 NEPLACKS P FORM 17. 1 JAN 4. WHICH IsI.Nov es 'OS'OLK "FOR ARMY USE. 185 UnclassifiedSecurity Clessification
UnclassifiedSecurity Classification
114. LINK A LINK [ LINK C
ROLE WT ROLE WT ROLE WT
Backpacking
Cellular concretes
Shock absorption
186
- I I I - I -
UnclassifiedSecurity Classification
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