U.S. patent application number 11/858689 was filed with the patent office on 2008-03-20 for optimized concrete compositions.
This patent application is currently assigned to iCrete, LLC. Invention is credited to Per Just Andersen, Simon K. Hodson.
Application Number | 20080066653 11/858689 |
Document ID | / |
Family ID | 37574464 |
Filed Date | 2008-03-20 |
United States Patent
Application |
20080066653 |
Kind Code |
A1 |
Andersen; Per Just ; et
al. |
March 20, 2008 |
OPTIMIZED CONCRETE COMPOSITIONS
Abstract
Design optimization methods can be used to design concrete
mixtures having optimized properties, including desired strength
and slump at minimal cost. The design optimization methods use a
computer-implemented process that is able to design and virtually
"test" millions of hypothetical concrete compositions using
mathematical algorithms that interrelate a number of variables that
affect strength, slump, cost and other desired features. The design
optimization procedure utilizes a constant K (or K factor) within
Feret's strength equation that varies (e.g., logarithmically) with
concrete strength for any given set of raw material inputs and
processing equipment. That means that the binding efficiency or
effectiveness of hydraulic cement increases with increasing
concentration so long as the concrete remains optimized. The
knowledge of how the K factor varies with binding efficiency and
strength is a powerful tool that can be applied in multiple
circumstances. A concrete manufacturing process may include
accurately measuring the raw materials to minimize variation
between predicted and actual strength, as well as carefully
controlling water content throughout the manufacturing and delivery
process.
Inventors: |
Andersen; Per Just; (Santa
Barbara, CA) ; Hodson; Simon K.; (Santa Barbara,
CA) |
Correspondence
Address: |
WORKMAN NYDEGGER
60 EAST SOUTH TEMPLE
1000 EAGLE GATE TOWER
SALT LAKE CITY
UT
84111
US
|
Assignee: |
iCrete, LLC
Beverly Hills
CA
|
Family ID: |
37574464 |
Appl. No.: |
11/858689 |
Filed: |
September 20, 2007 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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11471293 |
Jun 19, 2006 |
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11858689 |
Sep 20, 2007 |
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60691916 |
Jun 17, 2005 |
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Current U.S.
Class: |
106/709 ;
106/713 |
Current CPC
Class: |
G06F 30/13 20200101;
G06F 2111/02 20200101; Y02W 30/94 20150501; Y02W 30/92 20150501;
G06F 30/20 20200101; Y02W 30/91 20150501; G06F 2111/06 20200101;
C04B 28/02 20130101; C04B 28/02 20130101; C04B 14/06 20130101; C04B
18/08 20130101; C04B 18/146 20130101; C04B 24/12 20130101; C04B
40/0096 20130101; C04B 2103/302 20130101; C04B 2103/304
20130101 |
Class at
Publication: |
106/709 ;
106/713 |
International
Class: |
C04B 7/02 20060101
C04B007/02 |
Foreign Application Data
Date |
Code |
Application Number |
Jun 19, 2006 |
US |
PCT/US06/23863 |
Claims
1. In a concrete manufacturing plant that manufactures concrete
from a given set of raw materials and/or processing variables, a
composition of matter comprising an optimized concrete composition
manufactured by the manufacturing plant, the optimized concrete
composition having a minimum slump and strength that are achieved
by mixing together an optimized combination of hydraulic cement,
aggregates, water, and one or more optional components, which
optimized combination is determined using an optimization process
in which a pre-existing mix design previously used by the
manufacturing plant is redesigned and optimized utilizing a design
K factor for use within Feret's strength equation that corresponds
to a design strength of the optimized concrete composition and that
is selected from a plurality of K factors that vary based on
strength for the given set of raw materials and/or processing
variables, the design K factor of the optimized concrete
composition being a signature that differentiates the optimized
concrete composition from a less optimized concrete composition
manufactured using the pre-existing mix design.
2. A composition of matter as defined in claim 1, the optimized
concrete composition being unique as compared to concrete
compositions manufactured by any other manufacturing plant having
its own unique set of raw materials and/or processing
variables.
3. A composition of matter as defined in claim 1, further
comprising at least one of an amine strengthener, water reducing
agent, or air entraining agent.
4. A composition of matter as defined in claim 1, further
comprising at least one of fly ash or silica fume.
5. In a concrete manufacturing plant that manufactures concrete
from a unique set of raw materials and/or processing variables, a
composition of matter comprising an optimized concrete composition
manufactured by the manufacturing plant, the optimized concrete
composition having a minimum slump and strength that are achieved
by mixing together an optimized combination of hydraulic cement,
aggregates, water, and one or more optional components, which
optimized combination is determined using an optimization process
in which an optimized mix design is designed utilizing a design K
factor for use within Feret's strength equation that corresponds to
a design strength of the optimized concrete composition and that is
selected from a plurality of K factors that vary based on strength
and correspond to the unique set of raw materials and/or processing
variables, the design K factor of the optimized concrete
composition being a signature that differentiates the optimized
concrete composition from any other concrete composition
manufactured using raw materials and/or processing variables that
differ from the unique set of raw materials and/or processing
variables employed by the manufacturing plant.
6. A composition of matter as defined in claim 1, further
comprising at least one of an amine strengthener, water reducing
agent, or air entraining agent.
7. A composition of matter as defined in claim 1, further
comprising at least one of fly ash or silica fume.
8. In a concrete manufacturing plant that manufactures concrete
from a given set of raw materials, a concrete building system
comprising a plurality of optimized concrete compositions
manufactured by the manufacturing plant, at least two of the
optimized concrete compositions having different design strengths,
each of the plurality of optimized concrete compositions having a
guaranteed minimum slump and strength that is achieved by mixing
together an optimized combination of hydraulic cement, aggregates,
water, and one or more optional components, which optimized
combination is determined using an optimization process for
designing optimized mix designs used by the manufacturing plant to
manufacture the optimized concrete compositions, each optimized mix
design being designed using a design K factor for use within
Feret's strength equation that corresponds to a design strength of
the optimized mix design and that is selected from a plurality of K
factors that vary based on strength, each optimized concrete
composition having a signature design K factor that differentiates
it from at least one other of the optimized concrete compositions
having a different design strength.
9. A concrete building system as defined in claim 8, the signature
design K factor differentiating each optimized concrete composition
from less optimized concrete compositions manufactured from the
given set of raw materials.
10. A concrete building, system as defined in claim 8, the
signature K factors differentiating the optimized concrete
compositions from concrete compositions manufactured from raw
materials that differ from the given set of raw materials used by
the manufacturing plant.
11. In a concrete manufacturing plant having a given set of raw
material components, a building system comprising a plurality of
design optimized concrete compositions having actual strengths that
more closely reflect their predicted or design strengths compared
to less optimized concrete compositions made from the given set of
raw material components, wherein the optimized concrete
compositions are manufactured according to a method comprising:
providing a plurality of optimized concrete mix designs having
different design strengths that were designed using different
design K factors, wherein each different design K factor was
selected at least in part based on its respective design strength;
and manufacturing the plurality of design optimized concrete
compositions based on the optimized concrete mix designs, each
optimized concrete composition having an optimized ratio of
components so as to have an actual strength that more closely
reflecThat Anitta lects its predicted or design strength compared
to a less optimized concrete composition made from the given set of
raw material components.
12. A building system according to claim 11, the method of
manufacturing the optimized concrete compositions further
comprising making slump adjustments to one or more of the optimized
concrete compositions by adding or altering an amount of an
admixture within the one or more concrete compositions.
13. A building system according to claim 11, the method of
manufacturing the optimized concrete compositions further
comprising weighing or otherwise measuring the components of each
concrete composition with an accuracy of about .+-.2.0%.
14. A building system according to claim 11, the method of
manufacturing the optimized concrete compositions further
comprising monitoring moisture content of solid components and
altering a measured amount of solid components and added batch
water used to manufacture a concrete composition based on detected
changes in the moisture content of the solid components.
15. A building system according to claim 11, the method of
manufacturing the optimized concrete compositions further
comprising mixing one or more of the optimized concrete
compositions using a concrete mixing truck that includes a vessel
containing an admixture for adjusting slump and metering a selected
amount of the admixture into a mixing drum carrying the concrete
composition in order to alter slump in a desired manner.
16. A building system as defined in claim 11, the method of
manufacturing the optimized concrete compositions further
comprising: inputting into a computing system data relating to raw
materials cost; and the computing system designing or identifying
the optimized concrete mix designs at least on part on the basis of
having lower cost.
17. A building system as defined in claim 11, wherein at least one
of the design K factors accounts for an effect on concrete strength
of including an amine strengthener, at least one of the concrete
compositions further comprising an amine strengthener.
18. A building system as defined in claim 11, wherein at least one
of the design K factors accounts for an effect on concrete strength
of including at least one of fly ash or silica fume, at least one
of the concrete compositions further comprising at least one of fly
ash or silica fume.
19. A building system as defined in claim 11, wherein at least one
of the design K factors accounts for an effect on concrete strength
of using a specific mixing apparatus, at least one of the concrete
compositions being mixed using the specific mixing apparatus.
20. A building system as defined in claim 11, the method for
manufacturing the design optimized concrete compositions further
comprising: upgrading and/or recalibrating equipment used by the
concrete manufacturing plant in so that concrete compositions
manufactured by the manufacturing plant using the upgraded and/or
recalibrated equipment has an actual strength that more closely
correlates to design strength compared to previous equipment prior
to upgrading and/or recalibrating.
21. A building system as defined in claim 11, the method for
manufacturing the design optimized concrete compositions further
comprising: a computing system designing or identifying a modified
mix design that yields a concrete composition having a modified
slump but substantially similar strength by altering a ratio of
cement paste to aggregate relative to at least one or the optimized
concrete mix designs; and in the manufacturing a modified concrete
composition according to the modified mix design.
22. A building system as defined in claim 11, wherein each design
optimized concrete composition has a signature design K factor that
is unique as compared to an apparent design K factor for a less
optimized concrete composition made using the given set of raw
materials.
23. A building system as defined in claim 11, wherein each design
optimized concrete composition has a signature K factor that is
unique to the given set of raw materials as compared to a K factor
for concrete having similar strength but manufactured from a
different set of raw materials.
24. A revised design optimized concrete composition made from a
given set of components in order to adjust slump without
significantly altering strength, wherein the revised design
optimized concrete composition is manufactured according to a
method comprising: identifying an existing design optimized
concrete composition that is manufactured according to an optimized
mix design that specifies a specific ratio of components, including
a ratio of cement paste to aggregates, so as to achieve a desired
strength and slump; inputting into a computing system data relating
to particle size and particle packing density of one or more types
of aggregates; the computing system designing a revised design
optimized concrete mix design having a revised ratio of cement
paste to aggregates that yields a revised design optimized concrete
composition having a desired slump without substantially altering
the strength of the revised design optimized concrete composition
compared to the existing design optimized concrete composition; and
manufacturing the revised design optimized concrete
composition.
25. A revised design optimized concrete composition as defined in
claim 24, the method for manufacturing the revised design optimized
concrete composition further comprising the computing system
further determining a revised quantity of each of the components
used to manufacture the revised concrete composition in order to
produce a desired quantity of the revised concrete composition; and
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This application is a division of U.S. application Ser. No.
11/471,293, filed Jun. 19, 2006, which claims the benefit under 35
U.S.C. .sctn. 119(e) of U.S. Provisional Application Ser. No.
60/691,916, filed Jun. 17, 2005. This application also claims the
benefit of earlier filed and co-pending International Application
No. PCT/US06/23863, filed Jun. 19, 2006. The disclosures of the
foregoing applications are incorporated herein in their
entirety.
BACKGROUND OF THE INVENTION
[0002] 1. The Field of the Invention
[0003] The invention is in the field of concrete compositions, more
particularly in the design-optimization of concrete compositions
based on factors such as performance and cost. The invention more
particularly relates to the design and manufacture of concrete
using improved methods that more efficiently utilize all the
components from a performance and cost standpoint and minimize
strength variability, as well as unique methods for redesigning an
existing concrete mix design and upgrading the batching, mixing
and/or delivery system of an existing concrete manufacturing
plant.
[0004] 2. The Relevant Technology
[0005] Concrete is a ubiquitous building material. Finished
concrete results from the hardening of an initial cementitious
mixture that typically comprises hydraulic cement, aggregate,
water, and optional admixtures. The terms "concrete", "concrete
composition" and "concrete mixture" shall mean either the finished,
hardened product or the initial unhardened cementitious mixture
depending on the context. It may also refer to the "mix design",
which is the formula or recipe used to manufacture a concrete
composition. In a typical process for manufacturing transit mixed
concrete, the concrete components are added to and mixed in the
drum of a standard concrete delivery truck, typically while the
truck is in transit to the delivery site. Hydraulic cement reacts
with water to form a binder that hardens over time to hold the
other components together.
[0006] Concrete can be designed to have varying strength, slump,
and other materials characteristics, which gives it broad
application for a wide variety of different uses. The raw materials
used to manufacture hydraulic cement and concrete are relatively
inexpensive and can be found virtually everywhere although the
characteristics of the materials can vary significantly. This
allows concrete to be manufactured throughout the world close to
where it is needed. The same attributes that make concrete
ubiquitous (i.e., low cost, ease of use, and wide availability of
raw materials) have also kept it from being fully controlled and
its fall potential developed and exploited.
[0007] Concrete manufacturing plants typically offer and sell a
number of different standard concrete compositions that vary in
terms of their slump and strength. Each concrete composition is
typically manufactured by following a standard mix design, or
recipe, to yield a composition that has the desired slump and that
will harden into concrete having the desired strength.
Unfortunately, there is often high variability between the
predicted (or design) strength of a given mix design and the actual
strength between different batches, even in the absence of
substantial variability in the quality or characteristics of the
raw material inputs. Part of this problem results from a
fundamental disconnect between the requirements, controls and
limitations of "field" operations in the concrete batch plant and
the expertise from research under laboratory conditions. Whereas
experts may be able to design a concrete mixture having a predicted
strength that closely reflects actual strength when mixed, cured
and tested, experts do not typically prepare concrete compositions
at concrete plants for delivery to customers. Concrete personnel
who batch, mix and deliver concrete to job sites inherently lack
the ability to control the typically large variation in raw
material inputs that is available when conducting laboratory
research. The superior knowledge of concrete by laboratory experts
is therefore not readily applicable or transferable to the concrete
industry in general.
[0008] In general, concrete mixtures are designed based on such
factors as (1) type and quality of hydraulic cement, (2) type and
quality of aggregates, (3) quality of water, and (4) climate (e.g.,
temperature, humidity, wind, and amount of sun, all of which can
cause variability in slump, workability, and strength of concrete).
To guarantee a specific minimum strength and slump as required by
the customer (and avoid liability in the case of failure), concrete
manufacturers typically follow a process referred to as
"overdesign" of the concrete they sell. For example, if the 28 day
field strength of a particular concrete mix design is known to vary
between 2500 psi and 4000 psi when manufactured and delivered, a
manufacturer must typically provide the customer with a concrete
composition based on a mix design that achieves a strength of 4000
psi under controlled laboratory conditions to guarantee the
customer a minimum strength of 2500 psi through the commercial
process. Failure to deliver concrete having the minimum required
strength can lead to structural problems, even failure, which, in
turn, can leave a concrete plant legally responsible for such
problems or failure. Thus, overdesigning self insurance against
delivering concrete that is too weak, with a cost to the
manufacturer equal to the increased cost of overdesigned concrete.
This cost must be absorbed by the owner, does not benefit the
customer, and, in a competitive supply market, cannot easily be
passed on to the customer.
[0009] Overdesigning typically involves adding excess hydraulic
cement in an attempt to ensure a minimum acceptable strength of the
final concrete product at the desired slump. Because hydraulic
cement is typically the most expensive component of concrete
(besides special admixtures used in relatively low amounts), the
practice of overdesigning concrete can significantly increase cost.
However, adding more cement does not guarantee better concrete, as
the cement paste binder is often a lower compressive strength
structural component compared to aggregates and the component
subject to the greatest dynamic variability. Overcementing can
result in short term microshrinkage and long term creep.
Notwithstanding the cost and potentially deleterious effects, it is
current practice for concrete manufacturers to simply overdesign by
adding excess cement to each concrete composition it sells than to
try and redesign each standard mix design. That is because there is
currently no reliable or systematic way to optimize a
manufacturer's pre-existing mix designs other than through
time-consuming and expensive trial and error testing to make more
efficient use of the hydraulic cement binder and/or account for
variations in raw material inputs.
[0010] The cause of observed strength variability is not always
well understood, nor can it be reliably controlled using existing
equipment and following standard protocols by at typical ready-mix
manufacturing plants. Understanding the interrelationship and
dynamic effects of the different components within concrete is
typically outside the capability of concrete manufacturing plant
employees and concrete truck drivers using existing equipment and
procedures. Moreover, what experts in the field of concrete might
know, or believe they know, about concrete manufacture, cannot
readily be transferred into the minds and habits of those who
actually work in the field (i.e., those who place concrete mixtures
into concrete delivery trucks, those who deliver the concrete to a
job site, and those who place and finish the concrete at job sites)
because of the tremendous difference in controls and scope of
materials variation. The disconnect between what occurs in a
laboratory and what actually happens during concrete manufacture
can produce flawed mix designs that, while apparently optimized
when observed in the laboratory, may not be optimized in reality
when the mix design is scaled up to mass produce concrete over
time.
[0011] Besides variability resulting from poor initial mix designs,
another reason why concrete plants deliberately overdesign concrete
is the inability to maintain consistency of manufacture. There are
four major systemic causes or practices that have historically lead
to substantial concrete strength variability: (1) the use of
materials that vary in quality and/or characteristics; (2) the use
of inconsistent batching procedures; (3) overcementing; and (4)
adding insufficient batch water initially and later making slump
adjustments at the job site, typically by the concrete truck driver
adding an uncontrolled amount of water to the mixing drum. The
total variation in materials and practices can be measured by
standard deviation statistics.
[0012] The first cause of variability between theoretical and
actual concrete strengths for a given mix design is variability in
the supply of raw materials. For example, the particle size, size
distribution, morphology, and particle packing density of the
hydraulic cement and aggregates (e.g., course, medium, and fine)
may vary from batch to batch. Even slight differences can greatly
affect how much water must be added to yield a composition having
the required slump. Because concrete strength is highly dependent
on the water-to-cement ratio, varying the water content to account
for variations in the solid particle characteristics to maintain
the required slump causes substantial variability in concrete
strength. Unless a manufacturer can eliminate variations in raw
material quality, overdesigning is generally the only available way
to ensure that a concrete composition having the required slump
also meets the minimum strength requirements.
[0013] Even if a concrete manufacturer accounts for variations in
raw materials quality, overdesigning is still necessary using
standard mix design tables. Standardized tables are based on actual
mix designs using one type and morphology of aggregates that have
been prepared and tested. They provide slump and strength values
based on a wide variety of variables, such as concentration of
cement, aggregates, water, and any admixtures, as well as the size
of the aggregates. The use of standardized tables is fast and
simple but can only approximate actual slump and strength even when
variations in raw materials are measured. That is because the
number of standardized mix designs is finite though the variability
in the type, quality and concentration (i.e., ratio) of raw
materials is virtually infinite. Because standardized tables can
only approximate real world raw material inputs, there can be
significant variability between predicted and actual strength when
using mix designs from standardized tables. Because of this
variability, the only two options are (1) time consuming and
expensive trial and error testing to find an optimal mix design for
every new batch of raw materials or (2) overdesigning.
Manufacturers typically opt for overdesigning, especially in light
of factors other than mix design that cause variations between
design and actual strength.
[0014] The second cause of strength variability is the inability to
accurately deliver the components required to properly prepare each
batch of concrete. Whereas modern scales can theoretically provide
very accurate readings, sometimes to within 0.05% of the true or
actual weight, typical hoppers and other dispensing equipment used
to dispense the components into the mixing vessel (e.g., the drum
of a concrete mixer truck) are often unable to consistently open
and shut at the precise time in order to ensure that the desired
quantity of a given component is actually dispensed into the mixing
vessel. To many concrete manufacturers, the perceived cost of
upgrading or properly calibrating their metering and dispensing
equipment is higher than simply overdesigning the concrete,
particularly since most manufacturers have no idea how much the
practice of overdesigning concrete actually costs and because it is
thought to be a variable cost rather than a capital cost.
[0015] Overdesigning often leads to the third cause of strength
variability, which is overcementing. Overcementing involves
increasing the amount of hydraulic cement in an attempt to achieve
or guarantee a minimum strength by overcoming the effect on
strength by randomly adding water after batching to adjust slump.
This, however, can lead to increases in strength variability, as
hardened cement paste is typically weaker as a structural element
compared to the aggregate components. While adding more cement may
increase the binding strength provided by the cement paste that
holds the aggregates together, more cement can also weaken concrete
by displacing stronger aggregate materials with the weaker cement
paste as a structural component of the hardened concrete. Strength
variability occurs as a result of the foregoing effects working in
opposite directions, but in differing amounts between different
batches of concrete (e.g., due to differences in the
water-to-cement ratio, quality and characteristics of the hydraulic
cement, aggregates and water, and how the concrete is handled when
delivered to a job site).
[0016] Overcementing can also cause microshrnkage, particularly on
or near the surface due to water evaporation, which reduces the
strength and durability of the concrete surface. Microshrinkage
caused by overcementing and poor component distribution can cause
cracks and crazing within 1-2 years of manufacture. Overcementing
can also cause creep, which is the dynamic (and usually
undesirable) growth of concrete masses due to continued long term
hydration and growth of hydration products of the cement
grains,
[0017] The fourth cause of concrete strength variability is the
practice by concrete truck drivers of adding water to concrete
after batching in an attempt to improve or modify the concrete to
make it easier to pour, pump, work, and/or finish. In many cases,
concrete is uniformly designed and manufactured to have a standard
slump (e.g., 3 inch) when the concrete truck leaves the lot, with
the expectation that the final slump requested by the customer will
be achieved on site through the addition of water. This procedure
is imprecise because concrete drivers rarely, if ever, use a
standard slump cone to actually measure the slump but simply go on
"look and feel". Since adding water significantly decreases final
concrete strength, the concrete plant must build in a corresponding
amount of increased initial strength to offset the possible or
expected decrease in strength resulting from subsequent water
addition. Because strength can be decreased by varying amounts
depending on the actual amount of water added by the driver, the
manufacturer must assume a worst-case scenario of maximum strength
loss when designing the concrete in order to ensure that the
concrete meets or exceeds the required strength.
[0018] Given the foregoing, variables, which can differ in degree
and scope from day to day, a concrete manufacturer may believe it
to be more practical to overdesign its concrete compositions rather
than account and control for the variables that can affect concrete
strength, slump and other properties. Overdesigning, however, is
not only wasteful as an inefficient use of raw materials, sometimes
providing concrete that is substantially stronger than what is
required can also be dangerous. For example, because stronger
concrete is often more brittle than weaker concrete, it can fail
before the weaker concrete when subjected to the forces of an
earthquake.
[0019] In an effort to more efficiently design concrete
compositions and take into account variations in the particle size,
particle size distribution, morphology, and packing densities of
the various solid components between different batches of cement
and aggregates, the inventors previously developed a design
optimization process that greatly improved upon traditional methods
for designing concrete mixtures. This process is described in U.S.
Pat. No. 5,527,387 to Andersen et al., entitled "Design Optimized
Compositions and Computer Implemented Processes for
Microstructurally Engineering Cementitious Mixtures" (hereinafter
"Andersen patent"). For brevity, the design optimization process
disclosed in the Andersen patent will be referred to as the "DOC
program" (the term "DOC" being an acronym for "design optimized
concrete").
[0020] The DOC program mathematically relates the properties of
strength, slump and other aspects, such as cost, cohesiveness and
durability, based on the concentrations and qualities of the
various raw material inputs. The DOC program is able to design and
virtually "test" millions of different hypothetical mix designs in
seconds using a computer. This greatly reduces the amount of time
required to carry out trial-and-error testing that would otherwise
be necessary to identify a concrete mixture that is optimized for
strength, slump, cost and/or other desired features. The goal of
the DOC program is to identify an optimal mix design, from among a
large number of hypothetical mix designs, based on such desired
features as slump, strength, and cost. The DOC program fills in
gaps inherent in standardized tables, which include a relatively
small number of mix designs given the variability of raw material
inputs. The DOC program can design and virtually "test" millions of
different mix designs, including those falling between the gaps of
standardized tables, in much less time than it takes to design and
test one mix design using conventional trial-and-error methods.
[0021] First, the raw materials are carefully tested to determine
characteristics that affect the slump, strength, cost, and/or other
desired features of cementitious compositions made therefrom. These
include, for example, the particle size and packing density of the
various aggregate components (e.g., large, medium and small
aggregates) and hydraulic cement particles, and the effect of one
or more optional admixtures (e.g., fly ash, water reducers,
fillers, etc.). Once the raw materials have been characterized with
the required degree of accuracy, their characteristics are input
into a computer used to carry out the optimization process of the
DOC program.
[0022] Thereafter, the DOC program designs a large number of
hypothetical concrete mixtures, each having a theoretical slump and
strength, by varying the concentrations of cement, aggregate,
water, and optional admixtures. The predicted slump and strength of
each hypothetical concrete mixture is determined by inputting the
variables (e.g., the concentration and characteristics of the raw
materials) into a system of interrelated mathematical equations.
One of the equations utilized in the DOC program is a variation of
Feret's strength equation, which states that the compressive
strength of the final hardened concrete composition is proportional
to the square of the volumetric ratio of hydraulic cement to cement
paste, which consists of cement, water and air: .sigma. = K ( V C V
C + V W + V A ) 2 ##EQU1##
[0023] The constant "K" within this equation provides proper
strength units and magnitude. The strength equation can be modified
as follows to predict the strength of concrete that additionally
includes other binders, such as class F fly ash, as part of the
cement paste: .sigma. = K ( V C + 0.3 .times. .times. V FA V C +
0.3 .times. .times. V FA + V W + V A ) 2 ##EQU2##
[0024] The DOC program can be carried out in an iterative manner in
which each iteration yields a hypothetical concrete mixture having
a predicted slump and strength that is closer to the desired slump
and strength than each previous iteration. In addition to slump and
strength, the DOC program can optimize concrete for other desired
features, such as cost, workability, or cohesion. Thus, in the case
where a number of different concrete mixtures may have the desired
slump and strength, the DOC program can identify which of the
mixtures is "optimal" according to one or more other criteria
(e.g., cost, workability and/or cohesion).
[0025] Notwithstanding the foregoing, the DOC program, when
initially invented, was based on the assumption, well-accepted in
the art, that the constant K (or "K factor") within Feret's
strength equation is a true constant and does not vary as long as
the same type of mixing apparatus and source of raw materials are
used each time. It has been well-accepted in the art that if such
variables are kept constant, the K factor remains constant
regardless of variations in hydraulic cement concentration and
concrete strength. As a result of this well-accepted assumption,
the DOC program required significant post-design corrections, even
significant testing and redesign of concrete compositions made
using one or more of the "optimal" mix designs generated by the
program. Thus, the inability of the DOC program to account for
dynamic variability of the K factor limited the practical
application of an otherwise powerful design optimization tool.
SUMMARY OF THE INVENTION
[0026] It has now been discovered that the constant K (or "K
factor") within Feret's strength equation is not a constant but
varies depending on the efficiency with which hydraulic cement is
able to bind or glue the aggregate particles together. That is true
even if the mixing apparatus, aggregate strength, and other factors
that affect strength are kept constant. The K factor, which
dynamically varies with the binding efficiency of the hydraulic
cement binder, can be empirically determined based on concrete
strength. Knowing the dynamic variability of the K factor allows
for more accurate predictions of concrete strength when performing
a design optimizing procedure compared to an optimization procedure
that assumes the K factor remains constant so long as the mixing
apparatus and raw materials also remain constant. The inventive
optimization procedure (hereinafter "improved DOC process")
efficiently identifies one or more optimized mix designs with less
trial and error testing since using the correct K factor in the
first instance naturally reduces the need to correct for errors
that would otherwise arise by using an incorrect K factor to
predict concrete strength.
[0027] Although the binding efficiency of hydraulic cement, and
therefore the K factor, cannot be readily measured directly, the K
factor for a given concrete composition can be determined
indirectly. By rearranging Feret's equation, one can solve for K by
knowing the compressive strength, hydraulic cement volume and
cement paste volume. By testing a range of standard concrete
compositions sold by various manufacturers and then solving for K,
the inventors surprisingly found that the K factor varied with
actual concrete strength, more particularly, that the K factor of
properly prepared concrete increased with increasing compressive
strength and follows a logarithmic curve. The logarithmic curve has
a theoretical limit corresponding to a concrete composition having
perfect component distribution and binding efficiency of the paste
system, which only occurs at very high strength (e.g., containing
the most optimal paste to aggregate ratio and a water-to-cement
ratio of about 0.17 and having perfect distribution of paste and
aggregates throughout the concrete composition). At lower strengths
representative of typical manufacturing needs and specifications,
the K factor lies below the theoretical limit. This indicates that
hydraulic cement is not able to realize its highest theoretical
binding efficiency at lower strengths, but only approaches it at
higher strengths.
[0028] Knowing how the K factor, and therefore the binding
efficiency of hydraulic cement, varies with strength greatly
increases the accuracy by which an optimization procedure that
utilizes an appropriate strength equation can predict concrete
strength for a large number of hypothetical mix designs. On the
other hand, the K factor is independent of changes in slump caused
by changing water concentration and/or variations in the size
and/or morphology of aggregates. Using the foregoing principles
regarding K factor, the improved DOC process can more accurately
identify one or more optimized mix designs from among many
hypothetical mix designs. The improved DOC process efficiently
yields optimized concrete compositions that guarantee a specific
minimum slump and strength at the lowest cost and with minimum
variability due to poor design. The improved DOC process is more
efficient than the original DOC program because knowing in advance
how the K factor varies with strength minimizes the amount of post
design corrections (e.g., through trial-and-error testing) that
might otherwise be required.
[0029] One goal of the improved DOC process is to yield optimized
mix designs that substantially reduce concrete overdesign compared
to conventional mix designs used by concrete manufacturers. In one
aspect of the invention, the improved DOC process can be used to
create one or more optimized mix designs that guarantee concrete
having a specific minimum slump and strength while also reducing
the wasted cost caused by overdesign. Another aspect involves
dynamically optimizing concrete mix designs based on feedback
regarding variations in different batches of raw materials. In yet
another aspect, the improved DOC process can be used to re-design
one or more existing mix designs of a concrete manufacturer.
Identifying variations between the actual (or apparent) design K
factor of an existing mix design and the optimal or theoretical K
factor corresponding to the design strength can be used to
determine the existence and degree of concrete overdesign.
Improving the mix design to better utilize the hydraulic cement and
optimize binding efficiency of the cement paste can by itself
reduce strength variability and the need to overdesign to account
for such variability.
[0030] In addition to providing optimized mix designs, improving
the correlation between predicted strength and actual strength can
be further enhanced by upgrading and/or recalibrating plant
equipment to better ensure that a manufacturer is able to
accurately measure and dispense the raw materials used to
manufacture concrete. Such upgrades may not be economically
practical in the case where a plant uses poor mix designs.
Perfectly calibrated equipment cannot manufacture concrete that is
any better than a poor mix design will allow. The use of optimized
mix designs therefore allows the manufacturer to obtain the full
benefit of any capital equipment upgrades. Because improving plant
equipment alone may not yield much benefit, and because optimized
mix designs cannot by themselves overcome variability imparted by
faulty equipment, improving plant equipment and optimizing mix
designs allows both improvements to realize their full potential,
thus indicating a synergistic relationship.
[0031] In one embodiment, the present invention provides improved
methods for designing and manufacturing optimized concrete mix
designs utilizing a strength equation that employs a unique K
factor value, which varies and is selected depending on the
inherent efficiency of component use of the resulting concrete
composition (e.g., as empirically predicted by the desired minimum,
or "design strength"), all other things being equal. Knowing how
the K factor varies with concrete strength greatly improves the
ability to accurately and efficiently design an optimized concrete
composition because it reduces or minimizes variability between
design and actual strength. Minimizing variability between the
design strength and actual strength reduces the amount of
trial-and-error testing that might otherwise be required to
identify a concrete mix design that is truly optimized for slump
and strength at minimum cost.
[0032] As compared to conventional methods for designing concrete
using standardized tables, the improved DOC process more precisely
considers the actual characteristics of raw materials utilized by a
concrete manufacturer. Standardized tables only roughly approximate
actual slump and strength because the characteristics of raw
materials presumed in the tables rarely, if ever, reflect the true
characteristics of raw materials actually used by a concrete
manufacturer. Each concrete manufacturing plant utilizes raw
materials that are unique to that plant, and it is unreasonable to
expect standardized tables to accurately account for materials
variability among different plants. The improved DOC process is
able to virtually "test" mix designs that more accurately reflect
the raw materials actually utilized by the plant at a given time.
By accounting for variations in the quality of raw materials, the
improved DOC process is able to substantially reduce the degree of
overdesigning of concrete compositions that might otherwise occur
using standardized mix design tables and methods.
[0033] Another aspect of the invention involves the redesigning of
one or more pre-existing mix designs used by a manufacturing plant
to manufacture its commercial concrete compositions. In one
embodiment, the method first involves, as a threshold matter,
determining whether and by how much an existing concrete
composition is overdesigned. Every concrete composition has a
design strength, which is typically determined by the minimum
strength that must be guaranteed for that composition, and an
actual strength that can be measured by properly preparing concrete
under absolute controls based on the mix design and testing its
strength. Because of the tendency of manufacturers to overdesign to
account for expected strength variabilities from batch to batch,
there can be a substantial difference between the apparent design K
factor based on the guaranteed minimum strength of a concrete mix
design and the actual or "true" K factor based on the actual
strength of the concrete when properly manufactured according to
the mix design.
[0034] The extent to which an existing concrete mix design is
overdesigned can be ascertained by: (1) properly preparing a
concrete test sample according to the existing mix design; (2)
allowing the concrete composition to harden; (3) measuring the
actual strength of the hardened concrete composition; and (4)
comparing the actual strength of the concrete composition with the
design strength of the existing mix design. The amount by which the
actual strength deviates from the design strength corresponds to
the degree by which the existing mix design is overdesigned. The
foregoing process requires an amount of time that is necessary for
the concrete composition to cure sufficiently in order to
accurately measure actual strength.
[0035] The degree of overdesign can alternatively be determined in
a more expedited fashion by: (1) determining an apparent design K
factor of the existing concrete mix design based on the design
strength and ratio of components within a concrete composition made
according to the existing mix design; (2) identifying an optimal
theoretical K factor corresponding to the design strength; and (3)
comparing the apparent design K factor of the existing concrete mix
design with the optimal K factor that corresponds to the design
strength. The amount by which the apparent design K factor deviates
from the optimal K factor corresponds to the degree by which the
existing mix design is overdesigned. Knowledge of how the optimal K
factor varies with concrete strength can therefore be used as a
diagnostic tool to determine whether and by how much a pre-existing
mix design is overdesigned without waiting for a concrete test
sample to harden.
[0036] After determining that a pre-existing mix design is
overdesigned, an optimized concrete mix design can be designed
using the improved DOC process. After selecting a design strength
representing the guaranteed specified minimum strength, a revised
or corrected K factor corresponding to the design (or desired)
strength is selected and used in the improved DOC process. An
iterative optimization process utilizing one or more algorithms,
including Feret's equation employing the revised design K factor,
designs and virtually tests a number of hypothetical concrete
compositions in order to identify one or minimum designs optimized
for a specified minimum strength and slump having the lowest cost
or other desired factors. An optimized mix design reduces
variability between design strength and actual strength compared to
the pre-existing concrete mix design, thereby reducing overdesign
and cost of the resulting concrete composition. By correctly
readjusting the relative concentrations of the various components,
the improved DOC process improves the binding efficiency of the
hydraulic cement binder and reduces how much cement is required to
ensure the specified strength requirement. Overcementing can be
greatly reduced or eliminated.
[0037] In summary, by utilizing correct K factors selected based on
design strength, the improved DOC program can accurately and
efficiently redesign each standard pre-existing concrete mix design
utilized by the manufacturing plant in order to improve the binding
efficiency of the cement binder. This reduces or eliminates
overdesigning and reduces cost. An existing concrete manufacturing
plant can be upgraded simply by providing optimized concrete mix
designs even without upgrading and/or recalibrating the
manufacturing plant equipment.
[0038] Variations between actual strength and design strength can
be further minimized by properly controlling the preparation and
handling of the concrete compositions. Some retooling may be
necessary to ensure that the batching and weighing equipment meets
standard ASTM-94 requirements. Thus, according to another aspect of
the invention, affirmative steps can be taken to better control the
measuring and dispensing of the components used to manufacture
concrete. According to one embodiment, the components are
preferably weighed or measured with an accuracy of about .+-.2.0%,
more preferably with an accuracy of about .+-.1.0%, and most
preferably with an accuracy of about .+-.0.5%. The amount of water
included in the concrete composition is carefully controlled so
that it does not significantly change from the time the composition
is first made within the concrete truck and when it is used at the
job site. In order to prevent decreases in actual strength due to
human error, on-site slump adjustments can be made to wet concrete
compositions through the use of special admixtures instead of by
increasing the water content.
[0039] In order to account for all water inputs, the moisture
content of the solid components (e.g., hydraulic cement and
aggregates) can be continuously monitored using moisture sensors
(e.g., microwave sensors that measure absorption of microwave
energy by any moisture present). Through an information feed-back
mechanism, which can be advantageously controlled by a computer,
the amount of batch water that is added to the mixing vessel can be
varied to account for variations in the moisture content of the
solid components. In this way, the total water content within a
batch of concrete can be more accurately controlled, thereby
reducing variations in strength and/or slump that might otherwise
occur.
[0040] In some cases it may be desirable to quickly redesign an
already optimized mix design in order to adjust the slump without
significantly changing the strength. This can be done without
creating a whole new mix design from scratch. To maintain the same
strength, while varying the slump, the same water-to-cement ratio
of the paste is maintained, and only the volume of paste is altered
to adjust slump. Adding more paste to a design optimized concrete
composition increases slump, while adding less paste decreases
slump. Thus, the overall ratio of paste to aggregate is adjusted to
change the slump. Because the water-to-cement ratio of the paste
remains the same, the strength remains essentially the same
according to Feret's equation. In some cases, the ratio of fine to
coarse aggregates may remain the same. In other cases, this ratio
can be altered somewhat depending on the desired effect on other
properties of altering the ratio of paste to aggregate (e.g.,
cohesiveness, durability, etc.). Once the concentrations of the
various components have been adjusted to provide the correct slump,
the overall yield can be corrected by adjusting the quantities of
the aggregates to provide a desired volume of concrete.
[0041] Each of the foregoing embodiments, individually and
collectively, contribute to a reduction in concrete strength
variability, including differences between design and actual
strength and also differences in strength between different batches
made using the same mix design. By reducing or eliminating large
differences between design and actual strength, and/or strength
variability between different batches of concrete, the inventive
methods and systems greatly reduce the overdesign of concrete.
[0042] Like the DOC program disclosed in the Andersen patent, the
improved DOC process can be implemented, at least in part, using a
computing system (i.e., a computer) in order to design and
virtually test a large number (e.g., thousands or millions) of
hypothetical mix designs in a relatively short time period in order
to identify one or more mix designs that are optimized based on
desired criteria (e.g., strength, slump and cost). Briefly stated,
the improved DOC process is able to design and virtually "test"
different mix designs by altering the relative concentrations of
all the raw materials and then calculating, using one or more
algorithms (e.g., those set forth in the Andersen patent), the
slump and strength of each virtual concrete composition made
according to each hypothetical mix design. The improved DOC process
then identifies one or more optimized mix designs having the
desired slump and strength. Afterwards, test samples are made to
determine actual slump and strength. If the slump differs, changes
in slump can be made by increasing or decreasing the concentration
of cement paste. The strength can be kept the same by maintaining
the same water to cement ratio in the cement paste. The strength
can be altered by changing the water-to-cement ratio.
[0043] As with the original DOC program, the improved DOC process
can be embodied by a computer program product comprising a
computer-readable medium (e.g., a physical storage device, such as
a hard drive, memory device, magnetic tape or disk, optical storage
media, or other known digital storage device) that contains
executable instructions for carrying out the computer-implemented
aspects of the inventive method.
[0044] Because each manufacturing plant has its own unique set of
raw materials and/or processing inputs and/or blend efficiencies
(i.e., no two plants use exactly the same combination of raw
materials and possess the exact same equipment calibrated and/or
operated in the exact same manner), it will be appreciated that
each manufacturing plant produces concrete compositions having
unique aspects that are specific to a given manufacturing plant. In
other words, even if two manufacturing plants use the same
standardized mix designs (i.e., recipes), the concrete delivered by
each plant will, in same way, be unique to each plant. That means
that pre-existing concrete mix designs that have been modified and
optimized utilizing the improved DOC program will yield new
concrete compositions that are themselves unique in that they will
have never been manufactured at any time anywhere in the world.
Thus, improved concrete compositions manufactured using optimized
mix designs resulting from the implementation of the improved DOC
process are themselves unique and therefore novel as between all
previously manufactured concrete.
[0045] It turns out that every concrete composition that is made
has its own unique signature design K factor and also an actual K
factor that can be determined by testing the actual strength of the
composition. That is true both before and after implementation of
the improved DOC process. However, after implementation of the
improved DOC process, the signature K factors, both design and
actual, for an optimized concrete composition of a manufacturing
plant will exceed the signature K factors, both design and actual,
of a pre-existing non-optimized concrete composition that was
redesigned or replaced using the improved DOC process. By knowing
and comparing the design and/or signature K factors of both a
pre-existing and an optimized concrete composition of a given
manufacturing plant, one can readily ascertain whether a particular
concrete composition produced by the manufacturing plant was
manufactured using the pre-existing mix design or an optimized mix
design designed using the improved DOC process. Thus, the signature
K factor can be used as a diagnostic tool to distinguish whether a
non-optimized or overdesigned concrete composition or an optimized
concrete composition was used in a building project (i.e., to
determine whether or not the improved DOC process has been
implemented by a concrete manufacturer in designing its concrete
compositions).
[0046] These and other advantages and features of the present
invention will become more fully apparent from the following
description and appended claims, or may be learned by the practice
of the invention as set forth hereinafter.
BRIEF DESCRIPTION OF THE DRAWINGS
[0047] To further clarify the above and other advantages and
features of the present invention, a more particular description of
the invention will be rendered by reference to specific embodiments
thereof which are illustrated in the appended drawings. It is
appreciated that these drawings depict only typical embodiments of
the invention and are therefore not to be considered limiting of
its scope. The invention will be described and explained with
additional specificity and detail through the use of the
accompanying drawings, in which:
[0048] FIG. 1 is a chart that includes K factor curves that
illustrate how the K Factor changes as a function of the
compressive strength of concrete;
[0049] FIG. 2 is a chart that demonstrates how the actual K Factors
of known concrete compositions deviate from K factors along an
optimal K Factor curve, which illustrates the degree by which such
compositions are overdesigned;
[0050] FIG. 3 is another chart showing how the actual K Factors of
known concrete compositions deviate from K factors along an optimal
K Factor curve, which illustrates the degree by which such
compositions are overdesigned;
[0051] FIG. 4 is a schematic diagram that illustrates a computing
system by which design optimization, re-designing, and other
aspects of the invention may be carried out;
[0052] FIG. 5 is a flow chart that illustrates an exemplary
optimization process according to the invention for designing an
optimized concrete mixture;
[0053] FIG. 6A is a packing density chart for the ternary mixture
of cement, quartz sand (0-2 mm), and crushed granite (8-16 mm);
[0054] FIG. 6B is the packing density chart of FIG. 6A with lines
designating how to read a composition corresponding to a density
within the chart;
[0055] FIG. 6C is a graph of a packing density chart showing pseudo
particle lines;
[0056] FIG. 7 illustrates an exemplary slump correction chart used
to correct slump when approximating the particle packing densities
of the solid components.
[0057] FIGS. 8A-8B comprise a logic flow diagram of the
optimization system.
[0058] FIG. 8C is a tree of the logic flow diagram shown in FIG.
8B.
[0059] FIG. 9 is a flow chart that illustrates an exemplary
computer implemented iterative optimization process according to
the invention;
[0060] FIG. 10 is flow chart that illustrates an exemplary
optimization process according to the invention for designing an
optimized concrete mixture which accounts for changes in the K
Factor as compressive strength varies;
[0061] FIG. 11 is a flow chart that illustrates an exemplary
process for manufacturing a concrete composition from an optimized
concrete mix design in order to ensure that the actual strength
closely correlates to the desired or predicted strength;
[0062] FIG. 12 is a flow chart that illustrates an exemplary
abbreviated re-design process for changing the slump of an
optimized concrete mix design without substantially changing the
strength;
[0063] FIG. 13 is a flow chart that illustrates an exemplary
process for redesigning a pre-existing concrete mix design by
employing a correct understanding of the K Factor and how it varies
as a function of concrete compressive strength; and
[0064] FIG. 14 is a flow chart that illustrates an exemplary
process for upgrading an existing concrete manufacturing plant by
employing a correct understanding of the K Factor and how it varies
as a function of concrete compressive strength.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
I. Introduction
[0065] The present invention utilizes a design optimization
process, which is at least in part computer-implemented, that
identifies one or more optimized concrete mix designs that are
optimized relative to, e.g., strength, slump and cost. The design
optimization process is able to account for variability in raw
material inputs and design an optimized concrete compositions based
on variations in raw material qualities. It does this by
effectively designing and testing large numbers (e.g., thousands or
millions) of hypothetical concrete mixtures at least in part by
means of a computer-implemented process in order to identify one or
more mix designs having optimal properties. This process greatly
reduces or eliminates the need for extensive trial-and-error
testing, which is both expensive and time consuming. Moreover,
unlike Shilstone optimization, the improved DOC program is able to
account for particle size variations among different batches of raw
materials and also cost optimize.
[0066] The terms "yard" and "cubic yard" are used interchangeably
throughout this application and shall refer to the typical
volumetric unit of concrete sold in the United States. This
quantity can readily be converted into metric units by known
conversion factors that convert yard into meters, centimeters, or
other desired metric units. By way of example, one cubic yard is
equal to 0.76455486 cubic meters.
II. Relationship of K Factor to Concrete Strength
[0067] An important feature of the invention is the understanding
that Feret's constant K (or "K" factor) is not actually a constant
but is related logarithmically to concrete strength. That means
that increasing the amount of hydraulic cement within an optimized
composition not only increases concrete strength by virtue of the
increased amount of binder, which would be expected, but also
improves the binding effectiveness or efficiency of the paste.
Thus, the increase in strength of concrete as more hydraulic cement
is added to an optimized concrete composition exceeds the strength
that would be predicted by Feret's equation if the K factor were
actually a constant for all strengths. Whereas it was known that
the K factor changed depending on mixing apparatus and aggregate
type and strength, it was heretofore believed that the K factor
remained constant for all strengths as long as the same raw
materials and mixing apparatus were used.
[0068] The term "Feret's equation" refers to the following
equation, which predicts concrete strength based solely on the
volume of hydraulic cement, water and air in the concrete mixture:
.sigma. = K ( V C V C + V W + V A ) 2 ##EQU3##
[0069] For purposes of disclosure and the appended claims, the term
"Feret's equation" shall also refer to the following modified
Feret's equation, which predicts concrete strength based on the
volume of hydraulic cement, class F fly ash, water, and air in the
concrete mixture: .sigma. = K ( V C + 0.3 .times. .times. V FA V C
+ 0.3 .times. .times. V FA + V W + V A ) 2 ##EQU4##
[0070] As can be seen from this version of Feret's equation,
certain types of fly ash contribute to concrete strength but not to
the same degree as hydraulic cement. Moreover, although the volume
of fly ash is shown multiplied by a fly ash constant 0.3, it may
sometimes be appropriate to use a different fly ash constant (e.g.,
ranging from 0.3-0.6) depending on the type of fly ash used. This
substitution can be carried out by those of skill in the art when
appropriate, and such modification shall also constitute "Feret's
equation".
[0071] In general, the term "Feret's equation" shall refer to other
similar variations that may be constructed so long as they at least
relate the predicted compressive strength of the concrete
composition to the ratio of hydraulic cement volume to cement paste
volume (i.e., hydraulic cement, other binders, water and air) in
the concrete mixture (e.g., the use of silica fume, which can
contribute to strength).
[0072] The term "K factor" includes modifications of the exemplary
K factors disclosed herein required to convert the calculated
strength from English units (i.e., pounds per square inch or "psi")
to metric units (e.g., MPa). As is well-known to those of skill in
the art, 1 MPa=145 psi. The term "K factor" shall include other
modifications necessary when altering Feret's equation, as
discussed above.
[0073] It should be appreciated that the K factor is not an
absolute number and is not always the same for all different types
of concrete compositions and/or apparatus used by manufacturing
plants to manufacture concrete. In fact, each manufacturing plant
will have its own unique K factor curve depending on the type and
quality of aggregates, the type and quality of hydraulic cement
used, and the type and quality of mixing apparatus. The K factor
curve will typically move up or increase with increasing mixing
efficiency, aggregate strength, hydraulic cement strength, and
other factors that systematically contribute to concrete
strength.
[0074] So long as system inputs remain essentially the same, the K
factor curve for a particular manufacturing plant can, at least in
theory, be determined by identifying a single K factor point along
the K factor curve and then constructing a logarithmic curve that
passes through that point. Once an inappropriate K factor curve has
been constructed for a particular manufacturing plant, the curve
can be used to design and predict concrete strengths for a wide
variety of different concretes produced by that manufacturing
plant.
[0075] It should also be understood that there are different K
factors depending on the context in which that term is used. The
term "design K factor" refers to the K factor that is utilized
within the improved DOC process of the present invention in order
to design and virtually "test" a large number (e.g., millions) of
different hypothetical mix designs in order to identify one or more
of such mix designs that are "optimal" with respect to strength,
slump, cost and other desired factors. The design K factor will, of
course, vary depending on the design strength, or guaranteed
minimum strength, of a particular concrete composition. For a given
set of raw materials inputs and processing equipment, there will
typically be a single design K factor curve.
[0076] The terms "optimal K factor" and "true K factor" refer to K
factors found along an optimal K factor curve that represents
perfectly designed and mixed concrete by a manufacturing plant
utilizing a given set of raw materials available. Thus, the
"optimal" or "true" K factor can vary between different
manufacturing plants and is therefore not an absolute number.
Nevertheless, for a given set of raw material inputs, there exists
perfectly designed and manufactured concrete for which the optimal
or true K factor can theoretically be used to predict strength.
Because manufacturing plants and personnel cannot produce perfect
concrete every time, there will typically be some degree of
overdesign, however slight, to account for such variability. Thus,
the design K factor will typically differ from (e.g., be lower
than) the optimal true K factor for that given set of raw
materials. Notwithstanding such variation, the design K factor used
to make a well optimized concrete composition will much more
closely correlate to the optimal or true K factor than compared to
apparent design K factors corresponding to less optimized or
non-optimized concrete compositions.
[0077] The term "apparent design K factor" refers to the K factor
that can be ascertained for a preexisting concrete composition that
may not have itself been designed using a K factor. Even if a K
factor is not used to design a concrete composition, it
nevertheless can be assigned an apparent design K factor based on
what K factor would have been used to design such concrete using
the disclosed optimization procedures. In the case of a poorly
optimized or overdesigned concrete composition, the apparent design
K factor will deviate significantly from the optimal or true K
factor. The apparent design K factors of such compositions will
deviate much more than the design K factors of well optimized
concrete made using the same inputs. The apparent design K factor
is determined based on the design strength (i.e., minimum
guaranteed strength) and mix design of the preexisting concrete
composition.
[0078] The term "actual K factor" shall refer to the K factor that
is determined by mixing up a concrete composition according to a
given mix design, allowing the concrete to cure, measuring the
compressive strength of the concrete, and then calculating the
actual K factor based on actual strength and quantity of components
within the concrete composition. For a properly prepared concrete
composition, the actual K factor will exceed the design K factor
since the design K factor typically accounts for variations in
concrete strength.
[0079] A graphic representation of how the K factor varies with the
compressive strength of concrete is depicted in FIG. 1. FIG. 1
actually includes two curved lines following a logarithmic curve
corresponding to two different K factors that have been determined
by the inventors. The lower K factor curve corresponds to concrete
compositions made utilizing hydraulic cement, water, aggregate and
other standard admixtures used in the art. The upper K factor line
corresponds to hydraulic cement compositions that additionally
include an amine strengthener. The K factors used to generate the
lines shown in FIG. 1 were determined by analyzing a wide variety
of standard mix designs utilized in manufacturing plants in various
parts of the United States or variations thereof (e.g., that use a
strengthening amine). In general, the K factor can be calculated
according to the following rearrangement of Feret's equation for
compositions that include hydraulic cement, water, and aggregate: K
= .sigma. ( V C V C + V W + V A ) 2 ##EQU5##
[0080] The strength variable 6T corresponds to the actual strength
that was determined for various concrete compositions ranging in
strength from 500 psi to 8,000 psi. For concrete compositions that
also include fly ash, the K factor can be determined according to
the following rearrangement of a modified Feret's equation: K =
.sigma. ( V C + 0.3 .times. .times. V FA V C + 0.3 .times. .times.
V FA + V W + V A ) 2 ##EQU6##
[0081] The increased K factor corresponding to increased strength
according to the upper line shown in FIG. 1 can be obtained by
utilizing an amine known as "THEED" (i.e.,
tetrahydroxydiethylenediamine, also known as ethanol,
2,2',2'',2'''-(1,2-ethanediyldnitrolo)tetrakis-). In order to
obtain increased strength, and therefore a higher K factor, it is
preferable to utilize up to about 0.5% of THEED, more preferably up
to about 0.25%, and most preferably up to about 0.1%. Once it has
been understood that the K factor varies logarithmically with
concrete compressive strength, one of skill in the art, using
techniques described or readily ascertained from the current
disclosure, can modify the exemplary K factor shown in FIG. 1 to
account for variations based on different concentrations of
THEED.
[0082] FIG. 1 further demonstrates that the "optimal" or
"theoretical" K factors are not absolute or lie along an absolute
fixed curve that is the same regardless of the inputs and mixing
apparatus of the concrete composition. Adding an amine strengthener
raises the K factor (and K factor curve representing all K factors
for that system) based on the increased strength of the resulting
concrete even though the ratio of hydraulic cement to paste remains
the same. The same would be true for other admixtures or
alterations in composition such that there could be a unique or
representative K factor curve for every unique set of raw materials
inputs. The same would be true for different types of mixing
apparatus which might cause the cement paste to behave in unique
ways specific to that mixing apparatus or methodology. In general,
the effect of mixing efficiency on K factor is more dramatic with
increasing cement content and strength (i.e., mixing becomes more
crucial when the potential binding efficiency of hydraulic cement
is maximized). What the graph at FIG. 1 shows is that for any fixed
set of compositional and/or processing variables, the K factor
follows a logarithmic curve relative to compressive strength. That
means the effectiveness of the hydraulic cement, more precisely the
cement paste, as a binder that holds or glues the aggregates
together decreases with decreasing strengths. It also increases
with increasing strength towards a theoretical limit beyond which
no further increase in binding effectiveness is possible (i.e.,
where the binding efficiency is as high as theoretically possible,
with the limit of cement paste strength being at stoichiometric
levels of water and cement and wherein the components are perfectly
mixed. This does not mean, however, that the K factor necessarily
increases with increasing hydraulic cement concentration. Many
manufacturers engage in the practice of overcementing in an attempt
to increase or maximize strength, sometimes with disastrous results
as the concrete composition, if not properly optimized to
accommodate a huge cement increase (e.g., doubling), might undergo
severe microshrinkage cracking and crazing in the short run and
also excessive creep or expansion in the long run.
[0083] What the K factor curves illustrated in FIG. 1 essentially
depict are the optimal K factors for a given set of raw materials
inputs. The design K factor used in an optimization procedure may
be the same or may deviate from the optimal K factor to guarantee a
specific minimum strength and slump. Because some variability
between design strength and actual strength is possible, even in
the case of highly optimized concrete compositions, some amount of
deviation between the design K factor used and the optimal K factor
can be tolerated to account for some expected variation. What
should be understood is that there is less variation between the
design strength and the actual strength of a well optimized mix
design compared to a poor mix design. In other words, the actual
strength of concrete compositions made using optimized mix designs
will more closely corresponding to design strength than concrete
compositions made from a poor mix designs. As a result of this, an
optimized mix design made according to the inventive design
optimization process will have a signature design K factor that
exceeds the design K factor of a poor mix design. Similarly,
because the binding efficiency of cement paste in a well-designed
concrete composition typically exceeds the binding efficiency of
cement paste in a poorly designed concrete composition, the actual
K factor of a well-designed concrete composition would also be
expected to exceed the actual K factor of a poorly-designed
concrete composition. This concept becomes more understandable with
reference to FIGS. 2 and 3.
[0084] The apparent design K factor for each specific mix design
shown in FIGS. 2 and 3 can be determined by inputting values for
cement, water, air and design strength into Feret's equation and
then solving for K. The actual K factors that lie along the K
factor curve can be derived by properly preparing a number of
concrete compositions using standard optimized mix designs used by
a plurality of manufacturers according to ASTM C-94 or other
rigorous standards known in the art, measuring the actual strength
of the concrete test sample, and then solving for K. An optimal K
factor curve can be prepared by plotting measured K factors based
on optimally prepared concrete compositions against the
corresponding compressive strengths.
[0085] In many cases, the actual strength of a concrete test sample
made from a pre-existing concrete mix design may substantially
exceed the design strength, thereby indicating that the
pre-existing concrete mix design is overdesigned. However, this
alone does not provide a precise way to redesign the pre-existing
concrete mix design to reduce or eliminate such overdesigning.
Using a revised design K factor that more closely corresponds to
the optimal K factor within an optimization procedure that utilizes
Feret's equation facilitates the ability to redesign the
pre-existing mix design in order for actual strength to more
closely correspond to design or predicted strength.
[0086] In order to demonstrate the degree by which standard
concrete mix designs used in the industry are overdesigned in
several existing concrete manufacturing plants (and therefore have
an excessively low design K factor), reference is now made to FIGS.
2 and 3. FIG. 2 shows a variety of data points corresponding to
apparent design K factors that were determined for each of a
plurality of standard mix designs utilized by TXI, Tarmac, TTM, VM,
Elmhurst, and Kaneville. The amount by which the data points
deviate from the optimal K factor line shown in FIG. 2 indicates
the degree to which such standard mix designs are or were
overdesigned relative to their design strengths.
[0087] The design K factors shown in the data points below the
optimal K factor line in FIG. 2 were determined utilizing a
rearranged Feret's equation and solving for K, wherein the strength
.sigma. corresponds to the design or predicted strength rather than
the actual strength of the concrete compositions manufactured
according to such mix designs. In every case, the predicted or
design strength was far less than the actual strength when the
compositions were properly manufactured. The amount by which the
tested compositions were found to be overdesigned represents a
potential cost savings if such mix designs could be redesigned
according to the inventive methods disclosed herein. For example,
it is currently estimated that redesigning so as to better optimize
existing concrete mix designs can save between $4 and $10 per yard
of concrete manufactured. Considering that concrete manufacturers
typically enjoy a profit of only about $1 to $2 per yard, the
estimated cost savings are tremendous and represent a substantial
improvement in the art of concrete manufacture.
[0088] FIG. 3 compares the apparent design K factors for a number
of pre-existing concrete mix designs of various manufacturing
plants using in manufacturing concrete compositions that either
include substantial entrained air or are substantially free of
entrained air. Again, the deviation between the data points
representing the apparent design K factors and the optimal K factor
curve shown in FIG. 3 graphically illustrates the potential cost
savings if the pre-existing mix designs were redesigned and
optimized according to the inventive methods disclosed herein.
[0089] As will be readily appreciated, by comparing the apparent
design K factor of an existing concrete mix design with the optimal
K factor for a given compressive strength lying on the curve shown
in FIGS. 1-3, one may readily ascertain the degree by which an
existing concrete mix design and corresponding concrete composition
are overdesigned. Thus, knowing the optimal K factor and how it
varies with compressive strength can be employed as a diagnostic
tool to test whether the mix designs and concrete compositions of a
concrete manufacturing plant are optimized or whether they are
significantly overdesigned. Once it has been determined that an
existing mix design is overdesigned, the mix design can be
redesigned using the improved DOC process in order to identify one
or more optimized mix designs having the desired slump and strength
at lower cost. Because the improved DOC process takes into account
the actual raw material inputs available to the manufacturer, it is
better able to optimize the concrete mixtures compared to
standardized tables, which typically cannot account for variations
in raw materials inputs among different manufacturing plants or
between batches. The improved DOC program understands the dynamic
relationship between optimal K factor and concrete strength, which
allows it to more efficiently identify one or more optimized mix
designs compared to the original DOC program described in the
Andersen patent.
III. Computer-Based Operating Environment
[0090] The operating environment for performing embodiments of the
improved DOC program may comprise a special purpose or
general-purpose computer, including various types of computer
hardware, as discussed in greater detail below. FIG. 4 is a
schematic diagram illustrating an exemplary computing system 100
that may be used to implement features of the present invention.
The described computing system is only one example of such a
suitable computing system and is not intended to suggest any
limitation as to the scope of use or functionality of the
invention. Neither should the invention be interpreted as having
any dependency or requirement relating to any one or combination of
components illustrated in FIG. 4.
[0091] Computing systems are now increasingly taking a wide variety
of forms. Computing systems may, for example, be handheld devices,
appliances, laptop computers, desktop computers, mainframes,
distributed computing systems, or even devices that have not
conventionally considered a computing system. In this description
and in the claims, the term "computing system" is defined broadly
as including any device or system (or combination thereof) that
includes at least one processor, and a memory capable of having
thereon computer-executable instructions that may be executed by
the processor. The memory may take any form and may depend on the
nature and form of the computing system. A computing system may be
distributed over a network environment and may include multiple
constituent computing systems.
[0092] Referring to FIG. 4, in its most basic configuration, a
computing system 100 typically includes at least one processing
unit 102 and memory 104. The memory 104 may be system memory, which
may be volatile, non-volatile, or some combination of the two. An
example of volatile memory includes Random Access Memory (RAM).
Examples of non-volatile memory include Read Only Memory (ROM),
flash memory, or the like. The term "memory" may also be used
herein to refer to non-volatile mass storage such as physical
storage media. Such storage may be removable or non-removable, and
may include, but is not limited to, PCMCIA cards, magnetic and
optical disks, magnetic tape, and the like.
[0093] As used herein, the term "module" or "component" can refer
to software objects or routines that execute on the computing
system. The different components, modules, engines, and services
described herein may be implemented as objects or processes that
execute on the computing system (e.g., as separate threads). While
the system and methods described herein may be implemented in
software, implementations in hardware, and in combinations of
software and hardware are also possible and contemplated.
[0094] In the description that follows, embodiments of the
invention are described with reference to acts that are performed
by one or more computing systems. If such acts are implemented in
software, one or more processors of the associated computing system
that performs the act direct the operation of the computing system
in response to having executed computer-executable instructions. An
example of such an operation involves the manipulation of data. The
computer-executable instructions (and the manipulated data) may be
stored or instantiated in the memory 104 of the computing system
100.
[0095] Computing system 100 may also contain communication channels
108 that allow the computing system 100 to communicate with other
computing systems over, for example, network 110. Communication
channels 108 are examples of communications media. Communications
media typically embody computer-readable instructions, data
structures, program modules, or other data in a modulated data
signal such as a carrier wave or other transport mechanism and
include any information-delivery media. By way of example, and not
limitation, communications media include wired media, such as wired
networks and direct-wired connections, and wireless media such as
acoustic, radio, infrared, and other wireless media. The term
computer-readable media as used herein includes both storage media
and tangible communications media (i.e., sending and receiving
devices which can temporarily store executable instructions, but
not the electronic signals themselves).
[0096] Embodiments within the scope of the present invention also
include computer-readable media for carrying or having
computer-executable instructions or data structures stored thereon.
Such computer-readable media can be any available media that can be
accessed by a general purpose or special purpose computer. By way
of example, and not limitation, such computer-readable media can
comprise physical storage and/or memory media such as RAM, ROM,
EEPROM, CD-ROM or other optical disk storage, magnetic disk storage
or other magnetic storage devices, or any other medium which can be
used to carry or store desired program code means in the form of
computer-executable instructions or data structures and which can
be accessed by a general purpose or special purpose computer. When
information is transferred or provided over a network or another
communications connection (either hardwired, wireless, or a
combination of hardwired or wireless) to a computer, the computer
properly views the connection as a computer-readable medium. Thus,
any such connection is properly termed a computer-readable medium.
Combinations of the above should also be included within the scope
of computer-readable media.
[0097] Computer-executable instructions comprise, for example,
instructions and data which cause a general purpose computer,
special purpose computer, or special purpose processing device to
perform a certain function or group of functions. Although the
subject matter has been described in language specific to
structural features and/or methodological acts, it is to be
understood that the subject matter defined in the appended claims
is not necessarily limited to the specific features or acts
described herein. Rather, the specific features and acts described
herein are disclosed as example forms of implementing the
claims.
IV. Overview of Exemplary Design Optimization Process
[0098] According to a currently preferred embodiment,
computer-implemented design optimized processes according to the
invention can utilize at least some of the features disclosed in
U.S. Pat. No. 5,527,387 to Andersen et al. ("Andersen patent"), the
disclosure of which is incorporated by reference. An important
difference is that the D present invention accounts for the fact
that the K Factor utilized in Feret's equation is not a true
constant but varies logarithmically with the compressive strength
of concrete. In other words, it has now been discovered that
increasing the concentration of hydraulic cement in an optimized
mixture (as opposed to overcementing) increases its effectiveness
or binding efficiency. The concept that the K Factor varies with
concrete strength was not previously known and was therefore not
appreciated in the Andersen patent or incorporated in the original
DOC program (though the original DOC program worked as designed and
intended).
[0099] When implementing the improved DOC process, the design K
Factor utilized in Feret's equation to determine design strength is
selected based on the specific minimum slump and strength of
concrete that must be guaranteed by the manufacturer. In many other
respects, the improved DOC process can be implemented in a manner
similar that the original DOC program disclosed in the Andersen
patent. It should be understood, however, that it is within the
scope of the invention to utilize any set or series of known
algorithms for designing one or more concrete mix designs so long
as the design K factor that is used when calculating strength
according to Feret's equation varies with changes in the desired or
target strength (e.g., increases logarithmically with concrete
strength).
[0100] FIG. 5 is a flow chart that schematically illustrates or
outlines various steps that may be performed according to an
embodiment of the invention. These steps are similar to those
disclosed in the Andersen patent, except that the procedure
illustrated in FIG. 5 selects and then utilizes a design K factor
based on the specific minimum strength and slump requirement when
calculating the design strength of each hypothetical concrete mix
design generated by the improved DOC process. Thus, notwithstanding
the similarity that may exist between the process steps illustrated
in FIG. 5 and those disclosed in the Andersen patent, the process
of FIG. 5 was not known in the prior art as embodied herein. The
twelve steps are summarized as follows: [0101] Step 1: Ascertaining
the maximum packing density and corresponding composition of a dry
concrete mixture having cement and one or more types of aggregate;
[0102] Step 2: Utilizing a K factor corresponding to the desired or
design strength, determining the initial optimal concrete mixture
that is closest to the maximum packing density and has a desired
strength, slump, and cohesion at a specific
fine-to-coarse-aggregate ratio; [0103] Step 3: Utilizing a K factor
corresponding to the design strength, designing various optimal
mixtures and comparing the unit cost for each optimal mixture at
defined fine-to-coarse-aggregate ratios so as to determine the
overall optimal mixture with respect to cost; [0104] Steps 4-7:
Calculating the effects of individually combining different
admixtures including fly ash, silica fume, water reducers, or
fillers, respectively, to identify one or more optimal concrete
mixtures; [0105] Step 8: Determining the best optimal mixture
having desired properties and minimal cost for mixtures that
include fine aggregate, cement, coarse aggregate, mixing water, and
two or more admixtures selected from fly ash, silica fume, and
water reducers; [0106] Step 9: Modifying the resulting mixture to
insure that it reflects the proper concentration of air-entraining
agent so as to have the proper air content; [0107] Step 10:
Utilizing a correction factor to further optimize the results of
the preceding steps and ensure proper slump; [0108] Step 11:
Adjusting porosity if necessary to insure that the selected mixture
has sufficient durability for its intended use; and [0109] Step 12:
Accurately determining the volume or weight of the various
components of a mixture needed to produce a desired concrete
yield.
[0110] The foregoing steps outlined above and depicted in FIG. 5
will now be described with more particularity.
[0111] A. Step 1: Ascertaining Maximum Packing Density
[0112] Step 1 includes ascertaining the maximum packing density of
a dry concrete mixture for a given set of raw materials (i.e.,
cement and one or more types of aggregate). A detailed description
of an exemplary embodiment for determining a ratio of hydraulic
cement and one or more types of aggregates that maximizes particle
packing density is set forth in the Andersen patent at col. 18,
line 1-col. 25, line 5. Various methods, including measuring
techniques and mathematical algorithms, for determining particle
size and packing density for each of the raw materials inputs are
described in this section of the Andersen patent. The discussion at
col. 18, line 1-col. 25, line 5 of the Andersen patent describes
exemplary acts that may be used to carry out step 1.
[0113] Initially, each of the aggregate and cement components are
defined by their respective average diameter size (d') and natural
packing density (.phi.). These values may be experimentally
determined and can be used to calculate the theoretical packing
density of a theoretical concrete composition. The average diameter
size is determined using known methods, such as by plotting the
particle size distribution of each material according to the
Rosin-Rammler-Sperling-Bennett distribution described by the
equation: R(D)=exp{-(d/d')''}
[0114] Where, d is the particle diameter, R(D) is the cumulative
probability that the diameter is less than d, d' is the diameter
for which R(d')=0.368 corresponding to 36.8% residue on that sieve
size, and n is the slope of the line defined by plotting the
percent of particles retained on a sieve versus the sieve size.
[0115] The packing density of each type of material, .phi., is
determined by filling the material into a cylinder having a
diameter of at least 10 times the largest particle diameter of the
material. The cylinder is then tapped against a hard surface until
the material is fully compacted. By reading the height of compacted
material in the cylinder and the weight of material, the packing
density is calculated according to the formula: .phi. = W M SG M V
M ##EQU7##
[0116] Where, W.sub.M=weight of the material,
[0117] SG.sub.M=specific gravity of the material, and
[0118] V.sub.M=volume of the material.
[0119] In this way, not only is the volume of particles quantified
but it is done as a function of particle morphology, specific
surface area and other specific surface characteristics.
[0120] The maximum packing density of a conventional,
three-component mixture including cement, one type of fine
aggregate, and one type of coarse aggregate is determined by
incrementally varying the volume of each component in the mixture
and calculating the corresponding packing density. The various
packing densities are then plotted on a triangular-shaped packing
density chart so as to determine what composition has the maximum
packing density. By way of example, FIG. 6A is a packing density
chart for a ternary mixture of cement, quartz sand (0-2 mm), and
crushed granite (8-16 mm). Side (A) of the chart defines the volume
percent of fine aggregate (sand); side (B) defines the volume
percent of cement; and the bottom or side (C) defines the volume
percent of coarse aggregate (crushed granite). The values inside
the triangle represent the packing density at various percent
volume mixtures of the components. The chart may be read in the
following manner:
[0121] Sub-step 1(a): Select a desired packing density from within
the triangle. By way of example, point "Z" is selected on FIG. 6B
which represents the maximum packing density for the defined
mixture.
[0122] Sub-step 1(b): Determine the percent volume of cement used
in the concrete mixture needed to obtain the packing density at
point "Z" by drawing a horizontal line 20 from point "Z" to side
(B) of the triangle. The value defined by where line 20 and side
(B) of the triangle intersect is the percent volume of cement
needed to obtain the desired packing density. In the example on
FIG. 6B, the percent volume cement is approximately 10%.
[0123] Sub-step 1(c): Determine the percent volume of fine
aggregate in the mixture by drawing a line 22 parallel to side (B)
of the triangle, the line starting from point "Z" and intersecting
side (A) of the triangle. The value defined at where line 22 and
side (A) intersect is the percent volume of fine aggregate needed
to obtain the desired packing density. In the example, the percent
volume of fine aggregate is approximately
[0124] Sub-step 1(d): Since the percent volume of the mixture must
sum to 100%, it logically follows that if the mixture is 10% cement
and 30% fine aggregate, the percent volume of coarse aggregate must
be 60%. This value, however, can also be determined from the
packing density chart by drawing a line 24 parallel with side (A),
the line starting at point "Z" and intersecting side (C). The value
at the intersection of line 24 and side (C) corresponds to the
percent volume of coarse aggregate. As shown in FIG. 6B, the value
turns out to be approximately 60%. Using this method, the
composition can be ascertained for any packing density on the chart
or, using the reverse operation, the packing density can be
ascertained for any desired composition.
[0125] The packing density values within the chart are evaluated
from the Toufar, Klose, and Born model (hereinafter "Toufar model")
used in connection with a correction factor. The Toufar model is a
formula for calculating the packing densities of binary mixtures:
.PHI. = 1 r 1 .PHI. 1 + r 2 .PHI. 2 - r 2 ( 1 .PHI. 2 - 1 ) d 2 - d
1 d 1 + d 2 { 1 - 1 + 4 r 1 r 2 .PHI. 2 .PHI. 1 ( 1 - .PHI. 2 ) [ 1
+ r 1 r 2 .PHI. 2 .PHI. 1 ( 1 - .PHI. 2 ) ] } ##EQU8##
[0126] Where, [0127] r.sub.1=volume of smaller particles, [0128]
r.sub.2=volume of larger particles, [0129] d.sub.1=diameter of
smaller particles, [0130] d.sub.2=diameter of larger particles,
[0131] .phi..sub.1=packing density of the smaller particles, and
[0132] .phi..sub.2=packing density of the larger particles.
[0133] Other models may also be used for calculating the packing
densities of binary mixtures. Examples of applicable models are the
Aim model and the Larrard model discussed in the article Johansen,
V. and Andersen, P. J., "Particle Packing and Concrete Properties"
118-122, Materials Science of Concrete II (The American Ceramic
Society, Inc., 1991), the teachings of which are incorporated by
reference. Additional discussion regarding packing density,
including the use of pseudo-particles to determine packing
densities using the Toufar model for ternary mixtures, is set forth
in the Andersen patent.
[0134] In an alternative embodiment, the average particle size d'
is determined for each component using known methods, but instead
of actually measuring the packing density .phi., the packing
density .phi. for each component is assumed to be either 0.5, 0.55
or 0.6, since solid particles typically have a particle packing
density ranging from 0.5 to 0.6. The optimization program may then
be carried out using the exemplary steps discussed below, with the
proviso that the actual slump is likely to vary from the
theoretical or predicted slump due to variations between true
packing density and the assumed packing density. As a result, a
final correction step for slump is performed at or near the end of
the process (e.g., as part of Step 10 discussed below). Because
slump can be measured the moment a concrete mixture is prepared,
unlike strength, slump corrections are not time consuming. A slump
correction curve, as exemplified by FIG. 7, can be prepared by
preparing two concrete mixtures having higher and lower slumps,
plotting the high and low slumps (e.g., 5 cm and 15 cm) against the
corresponding concentration of water in volume % for the two
concrete mixtures, and then drawing a straight line between the two
points. The water volume correlating to any desired slump is shown
on the curve (e.g., the correlation indicated by the dotted line).
A final mix design having a desired slump can be prepared by
utilizing an amount of water shown on the slump curve corresponding
to the desired slump.
[0135] As part of the improved DOC program, the average particle
size d' measured for each solid component and the particle packing
density for each solid component, whether measured or estimated,
are input into a computing system. These values affect the
properties that are later determined for each of the plurality of
mix designs that are created. The particle size and particle
packing densities permit the computer system, by virtue of one or
more interrelated algorithms, to hypothetically "test" the
resulting properties of each virtual concrete composition based on
the mix designs that are created as part of the design optimization
process.
[0136] B. Step 2: Property Optimization
[0137] Step 2 involves determining an initial concrete mixture that
is closest to the maximum packing density determined in Step 1 and
that has the desired strength, slump, and optionally cohesion at a
specific fine-to-coarse aggregate ratio. A detailed description of
an exemplary embodiment of a process for identifying a concrete
mixture that is optimized with respect to strength, slump and
optionally cohesion is set forth in the Andersen patent at col. 25,
line 8-col. 29, line 10. The term "cohesion" refers to the tendency
of the concrete composition to resist segregation and bleeding.
Various methods including mathematical algorithms for optimizing a
concrete mixture with respect to strength, slump and optionally
cohesion are described in this section of the Andersen patent. The
discussion at col. 25, line 8-col. 29, line 10 of the Andersen
patent describes exemplary acts that may be used to carry out step
2.
[0138] In sub-step 2(a), an initial mixture that is sufficiently
close to the maximum packing density to optimize concrete
properties without segregating or bleeding is selected by first, as
discussed in Step 1, locating the maximum packing density on the
packing density chart and the corresponding volume composition. The
volume of the corresponding cement, fine aggregate, and coarse
aggregate at the point of maximum packing are respectively defined
by the variables V.sub.C(MP), V.sub.F(MP), and V.sub.CA(MP), which
add up to 1.0. Next, the volume of cement is held constant while
the volume of fine aggregate is increased by a quantity defined as
the cohesion safety factor, and the volume of coarse aggregate is
decreased by the same quantity. The mixture is thus moved
horizontally left on the packing density chart. The corresponding
mixture is defined as the initial mixture.
[0139] The volume (V) of the components in the initial mixture are
defined by the equations: V.sub.C=V.sub.C(MP)
V.sub.F=VF.sub.(MP)+CF V.sub.CA=V.sub.CA(MP)-CF
[0140] Wherein, the variable CF represents the cohesion safety
factor and is typically about 0.05. The cohesion safety factor
insures that the mixture has sufficient fine aggregate to make a
cohesive mixture that will not segregate or bleed. Mixtures to the
right of the initial mixture on the packing density chart will
typically segregate or bleed. The cohesion safety factor can vary
in a range between about 0 to about 0.15 depending on the type of
concrete. A lower strength concrete typically requires a higher
cohesion factor up to about 0.15, while a higher strength concrete
requires a lower cohesion factor of less than about 0.05.
[0141] The fine-to-coarse-aggregate ratio of the initial mixture is
defined by a pseudo-particle line extending from the apex of the
packing density chart, through the position of the initial mixture,
and to the coarse aggregate line (FIG. 6C; compare FIGS. 6A-6B).
The following sub-steps are presented as an example of how to
ascertain the optimal concrete mixture along this defined
pseudo-particle line.
[0142] In sub-step 2(b), the packing density of the composition of
the initial concrete mixture is determined as described in Step
1.
[0143] In sub-step 2(c), the amount of mixing water required to
provide the initial concrete mixture with a predetermined desired
slump is ascertained. Determining this amount of water is a
two-step process. First, the amount of water needed to provide the
mixture with a 1 cm slump is determined using the following
formula: W 1 = 1 .PHI. - 1 ##EQU9##
[0144] Where, .phi.=the packing density of the mixture, as defined
in sub-step 2(b), and
[0145] W.sub.1=the volume of water required to give the mixture a 1
cm slump. The value for W.sub.1 is a fraction of the volume of the
solids in the mixture.
[0146] Once W.sub.1 is calculated for a 1 cm slump, the amount of
water needed for the desired slump is calculated using Popovic's
formula as follows: W 2 = W 1 ( S 1 S 2 ) 0.1 ##EQU10##
[0147] Where, W.sub.1=the volume of water needed for a 1.0 cm slump
as previously defined,
[0148] W.sub.2=the volume of water needed to give the mixture a
desired slump,
[0149] S.sub.1=1.0, representing 1.0 cm slump (correct exponent
actually found to be 0.085 by the inventors), and
[0150] S.sub.2=the desired slump in centimeters.
[0151] In sub-step 2(d), using the results from sub-steps
2(a)-2(c), calculating the 28 day compressive strength of the
resulting mixture using Feret's equation: .sigma. = K ( V C V C + V
W + V A ) 2 ##EQU11##
[0152] Where, .sigma.=theoretical 28-day compressive strength of
the concrete mixture in MPa,
[0153] V.sub.C=volume of cement in the mixture,
[0154] W.sub.2=volume of water, defined in Step 2(c), needed to
give the mixture the desired slump,
[0155] K=Feret's constant, which is now discovered to vary with
compressive strength .sigma. as illustrated in FIGS. 1-3, and
[0156] V.sub.A=the volume of air in the mixture and is defined by
the following equation: V .times. A = ( 1 .times. + .times. W
.times. 2 .times. 1 .times. - .times. % .times. .times. AIR 100 ) -
1 - W .times. 2 ##EQU12##
[0157] Where AIR is the estimated percent volume of air in the
mixture. The volume of air in a mixture varies based on the type of
mixer used, the volume of fine aggregate in the mixture, and the
types of admixtures combined with the mixture. The percent volume
of air can be estimated by those skilled in the art and is
generally between about 1% to 2% for a slump greater than 10 cm and
between about 2% to 4% for slump less than 10 cm.
[0158] In sub-step 2(e), the resulting compressive theoretical
strength, G, is compared with the desired strength. If the
theoretical strength of the mixture is less than the desired
strength, sub-steps 2(b)-2(e) are repeated by replacing the initial
mixture with a new mixture and corresponding new packing density.
The composition of the new mixture is obtained by increasing or
decreasing the volume of cement in order to obtain the desired
strength. An estimate of the volume of cement needed to obtain the
desired strength is determined by inputting the desired strength
into Feret's equation and solving for the corresponding volume of
cement according to the following equation: V .times. C .function.
( N ) = ( 1 + W .times. 2 1 .times. - .times. % .times. .times. AIR
100 - 1 ) ( .sigma. D K ) 0.5 ( 1 - .sigma. D K ) 0.5 ( 16 )
##EQU13##
[0159] Where, V.sub.C(N)=volume of cement in the new mixture,
[0160] W.sub.2=volume of water needed to obtain the desired slump
in the initial or previous mixture,
[0161] % AIR=estimated percent volume of air in the mixture,
[0162] K=Feret's constant, which varies with concrete strength,
and
[0163] .sigma.=the desired strength in MPa.
[0164] As the volume of cement changes for the new mixture, the
volume of fine aggregate and coarse aggregate must be normalized so
that the volume of fine aggregate, coarse aggregate, and cement sum
up to 1.0. However, the ratio of fine-to-coarse-aggregate remains
constant. Accordingly, the volume of fine aggregate and coarse
aggregate in the new mixture are defined by the equations:
V.sub.F(N)=r.sub.F(1-V.sub.C(N))
V.sub.CA(N)=r.sub.CA(1-V.sub.C(N))
[0165] Where, r.sub.F and r.sub.CA are the ratios of fine aggregate
and coarse aggregate, respectively, and are constants for each
pseudo-particle line. The ratios are defined by the equations:
r.sub.F=V.sub.F/(V.sub.F+V.sub.CA)
r.sub.CA=V.sub.CA/(V.sub.F+V.sub.CA)
[0166] This new mixture corresponds to the position on the packing
density chart defined by the intersection of the pseudo-particle
line described in sub-step 2(a) and a horizontal line extending
from new volume of cement determined by equation (16) above. As the
volume of cement changes, one moves up or down on the
pseudo-particle line. Sub-steps 2(b)-2(d) are continually repeated
until the theoretical strength of the mixture equals the desired
strength and the resulting mixture for the defined
fine-to-coarse-aggregate ratio has the desired slump and strength
using a minimal amount of cement and water. Typically, the desired
mixture is found within ten iterations.
[0167] C. Step 3: Cost Optimization
[0168] Step 3 involves comparing the unit cost of various optimal
mixtures at defined fine-to-coarse-aggregate ratios so as to
determine one or more overall optimized mixture(s) that are also
optimized in terms of low cost. A detailed description of an
exemplary embodiment for identifying a concrete mixture that is
optimized with respect to cost, while also having the desired
strength and slump, is set forth in the Andersen patent at col. 29,
line 13-col. 30, line 42, which constitute exemplary acts for
carrying out step 3.
[0169] According to one embodiment, this may be accomplished by
first calculating the unit cost of the initial optimal mixture
determined in Step 2. An optimal composition and resulting unit
price is then determined for a second optimal mixture defined by a
new fine-to-coarse-aggregate ratio. The new
fine-to-coarse-aggregate ratio is obtained by decreasing the
percent volume of coarse aggregate by 1% and increasing the percent
volume of fine aggregate, respectively. The unit price of the
second optimal mixture is then compared with the unit price of the
initial mixture. If the price of the initial mixture is less than
the price of the second mixture, the composition of the initial
mixture is the most economical and the process is over. If the
second mixture is less than the price of the initial mixture, the
fine-to-coarse-aggregate ratio is again varied so as to obtain a
third optimal mixture. The cost comparison is then repeated until
the least expensive mixture is obtained.
[0170] The combination of Steps 1-3 provides exemplary methods for
designing a mixture of cement, water, and aggregate having a
desired strength and slump. The amount of water added to the
mixture can be minimized to maximize strength. The proportions of
fine aggregate, coarse aggregate, and cement can be optimized to
minimize the cost of the mixture. Furthermore, using the above
process, mixtures having desired properties can be consistently and
accurately produced independent of the variations in the feedstock.
Steps 1-3 can also be used to determine the mixture of highest
durability. As will be discussed later in Step 11, the mixture with
highest durability is defined as the mixture with the lowest
possible total porosity. This is because, in general, as the
porosity increases the durability of the mixture decreases. Studies
have determined that the porosity of a mixture decreases as the
packing density increases. Thus, mixtures closest to the maximum
packing density would be predicted to generally have the highest
durability.
[0171] Steps 4-7 provide additional optimization possibilities by
optionally calculating the individual effects of combining
different admixtures, such as fly ash, silica fume, water reducers,
or fillers, within a concrete mixture.
[0172] D. Step 4: Determining Effect of Fly Ash
[0173] A detailed description of an exemplary embodiment for
identifying an optimal concrete mixture that includes fly ash is
set forth in the Andersen patent at col. 30, line 44-col. 33, line
63. This section of the Andersen patent includes exemplary
mathematical algorithms relating to the use of fly ash and
exemplary acts corresponding Step 4.
[0174] In general, the process includes first repeating Steps 1 and
2 so as to determine the optimal mixture (without an admixture)
having desired strength and slump properties for a defined
fine-to-coarse-aggregate ratio. Based on the composition of the
resulting optimal mixture, a percent volume of cement is
incrementally replaced with fly ash. As the percent volume of fly
ash is increased, the unit price of each mixture is calculated and
compared to the previous mixture to determine the least expensive
mixture for the defined fine-to-coarse-aggregate ratio.
[0175] The fine-to-coarse-aggregate ratio is then varied by moving
1% to the left on the packing density chart. The above process is
then repeated to determine the least expensive mixture using fly
ash with the new fine-to-coarse-aggregate ratio. The unit price for
the optimal mixtures at the different fine-to-coarse-aggregate
ratios are then compared to determine the least expensive mixture.
The process continues to move to the left on the packing density
chart until the overall optimal mixture having fly ash and the
desired properties is obtained. An exemplary algorithm that
accounts for the effect of fly ash on slump involves the following
modified Popovic's equation: W .times. 2 = W 1 ( S 1 S 2 ) 0.1 - W
FA ##EQU14##
[0176] Where, W.sub.FA is a reduction, as a result of the fly ash,
in the volume of water needed to produce a mixture with a desired
slump and is determined by the equation: W FA = W 1 % .times.
.times. FA 6 100 - 37 ##EQU15##
[0177] Where, W.sub.1=the volume of mixing water required for a 1.0
cm slump in a standard mixture as previously defined, and
[0178] % FA=the percent volume of fly ash in the combination of fly
ash and cement.
[0179] The value for W.sub.2 can then be used to calculate the 28
day strength using a modified version of Feret's equation that
accounts for the fly ash, such as: .sigma. = K .function. ( V C + K
2 .times. V FA V C + K 2 .times. V FA + W .times. 2 + V A ) 2
##EQU16##
[0180] Where K.sub.2 is a constant for fly ash, and typically
ranges between 0.3 and 0.6.
[0181] E. Step 5: Determining Effect of Silica Fume
[0182] A detailed description of an exemplary embodiment for
identifying an optimal concrete mixture that includes silica fume
(aka, fumed silica) is set forth in the Andersen patent at col. 33,
line 65-col. 35, line 40. This section of the Andersen patent
includes exemplary mathematical algorithms relating to the use of
silica fume and exemplary acts corresponding to Step 5.
[0183] The optimal mixture using silica fume can be ascertained in
the same manner used in determining the proper amount of fly ash in
Step 4. However, the formulas for the required amount of water and
resulting strength are different. In contrast to fly ash, silica
fume requires more water for a given slump, but silica fume imparts
a greater strength to the cement mixture. With regard to the
packing density chart, the volume of silica fume is also considered
as part of the volume of cement in the mixture. If desired, a
pseudo particle can be used to represent the combination of the
cement and silica fume. An exemplary algorithm that accounts for
the effect of fumed silica on slump involves the following modified
Popovic's equation: W .times. 2 = W 1 ( S 1 S 2 ) 0.1 + W SF
##EQU17##
[0184] Where, W.sub.SF is an increase, as a result of the silica
fume, in the volume of water needed to produce a mixture with a
desired slump and is determined by the equation: W SF = W 1 %
.times. .times. SF 20 100 20 ##EQU18##
[0185] Where, % SF=the percent volume of silica fume in the
combination of silica fume and cement.
[0186] The value for W.sub.2 can then be used to calculate the 28
day strength using a modified version of Feret's equation that
accounts for the fumed silica, such as: .sigma. = K .function. ( V
C + K 3 .times. V SF V C + K 3 .times. V SF + W .times. 2 + V A ) 2
##EQU19##
[0187] Where, K.sub.3=a reactivity constant describing the strength
development per volume of silica fume comparable to the same volume
of cement. Typically, this value is between 1.5 and 4, with 2 being
the preferred value. The actual value can be empirically determined
for a given silica fume.
[0188] F. Step 6: Determining Effect of Water Reducers
[0189] A detailed description of an exemplary embodiment for
identifying an optimal concrete mixture that includes water
reducers is set forth in Andersen et al. at col. 35, line 45-col.
37, line 55. This section of the Andersen patent includes exemplary
mathematical algorithms relating to the use of water reducers and
exemplary acts corresponding to Step 6.
[0190] Assuming that only water reducers are added to a standard
concrete mixture, the process for obtaining the optimal mixture is
the same as that used for Step 4 to obtain an optimal mixture using
fly ash. The only difference is that the formulas for determining
the required amount of mixing water and the resulting strength are
modified. The process includes determining the optimal mixture for
the first fine-to-coarse-aggregate ratio. Incremental amounts of
water reducers are then added to the mixture. The unit cost of
these mixtures are calculated and compared so as to determine the
optimal mixture having water reducers at the initial
fine-to-coarse-aggregate ratio. The fine-to-coarse-aggregate ratio
is then varied and the process is repeated. By comparing the unit
cost for the optimal mixtures at each fine-to-coarse-aggregate
ratio, the overall optimal mixture using water reducers can be
determined.
[0191] Based on the parameters of the standard water reducer, the
percent volume of water needed to produce a mixture including a
water reducer with a desired slump is determined by the following
equation: W 2 = W 1 ( S 1 S 2 ) 0.1 - W WR ##EQU20##
[0192] Where, W.sub.WR is a reduction, as a result of the water
reducer, in the volume of water needed to produce a mixture with a
desired slump and is determined by the equation: W WR = W 1 %
.times. .times. WR 30 100 .times. .times. ( 2 ) ##EQU21##
[0193] Where, W.sub.1=the volume of mixing water required for a 1.0
cm slump as previously defined, and
[0194] % WR=the percent quantity of water reducer in the mixture by
weight of the cement.
[0195] The value for W.sub.2 can then be used to calculate the
28-day strength using Feret's equation. As water reducers do not
independently contribute to the strength of concrete, the same
formulas used in Step 2 can be used for calculating 28-day strength
and for estimating the volume of cement needed to obtain the
desired strength. Since the amount of water required for the
desired slump is decreased by using a water reducing agent, the
water-cement ratio in the mixture is decreased, thereby, increasing
the strength of the resulting mixture. Accordingly, the amount of
cement can be reduced until a mixture is defined possessing the
desired strength and slump and having the initial 0.1% water
reducing agent. A cost comparison is then performed and if the
mixture with the water reducer is cheaper, an additional 0.1% water
reducer is added to the mixture. The above process is then again
repeated according to the format described in Step 4 for fly ash
until the optimal mixture including a water reducer is
determined.
[0196] G. Step 7: Determining Effect of Fillers
[0197] A detailed description of an exemplary embodiment for
identifying an optimal concrete mixture that includes fillers
(e.g., finely ground rock) is set forth in Andersen et al. at col.
37, line 57-col. 38, line 59. This section of the Andersen patent
includes exemplary mathematical algorithms relating to the use of
fillers and exemplary acts corresponding to Step 7.
[0198] Fillers generally do not possess cementitious properties
and, thus, do not directly contribute to the strength of the
resulting concrete. Similar to fly ash, however, fillers do
decrease the amount of mixing water required to obtain a desired
slump as compared to cement and, accordingly, can indirectly affect
the slump and strength of the resulting concrete. By way of example
and not by limitation, fillers can include calcium carbonate,
dolomite, granite, basalt, and ore that are crushed to have a
particle size similar to fly ash--diameters less than 100 .mu.m.
The reduction in the amount of water need to obtain a desired slump
is a result of the approximately spherical shape of certain fillers
and the lack of hydraulic activity. An exemplary algorithm that
accounts for the effect of fillers on slump involves the following
modified Popovic's equation: W 2 = W 1 ( S 1 S 2 ) 0.1 - W F
##EQU22##
[0199] Where, W.sub.F is a reduction, as a result of the filler, in
the volume of water needed to produce a mixture with a desired
slump and is determined by the equation: W F = W 1 % .times.
.times. FIL 6 100 .times. ( 37 ) ##EQU23##
[0200] Where, % FIL=the percent volume of filler in the combination
of filler and cement.
[0201] The value for W.sub.2 can then be used to calculate the 28
day strength. As fillers do not independently contribute to the
strength of the concrete, the same formulas used in Step 2 can be
used for calculating 28 day strength and for estimating the volume
of cement needed to obtain the desired strength.
[0202] H. Step 8: Combined Design Optimization System
[0203] A detailed description of an exemplary embodiment for
determining the combined effect of adding two or more admixtures to
a concrete mix design (e.g., two or more of fly ash, silica fume,
and water reducer) is set forth in the Andersen patent at col. 38,
line 61-col. 43, line 13. This section of Andersen et al. includes
exemplary mathematical algorithms relative to identifying an
optimal concrete mixture that utilizes multiple admixtures, as well
as acts corresponding to step 8.
[0204] Once the process is understood of how to optimize a concrete
mixture using a single admixture in conjunction with cement, fine
aggregate, coarse aggregate and water, the various processes can be
combined into a system using an embedded "do loop" that allows one
to determine the optimal mixture having selective combinations of
admixtures, the admixtures including fly ash, silica fume and water
reducers. This process essentially accounts for the effects on
slump, strength, cost and other desired factors when utilizing two
or more admixtures. In one aspect, the following exemplary modified
Feret's equation can be utilized that accounts for two or more
admixtures (e.g., fly ash and silica fume) within the cement paste
and their affect on strength: .sigma. = K .function. ( V C + K 2
.times. V FA + K 3 .times. V SF V C + K 2 .times. V FA + K 3
.times. V SF + W 2 + V A ) 2 ##EQU24##
[0205] Where, V.sub.SF=% SF(V.sub.T/100) V.sub.FA=%,FA(V.sub.T/100)
V.sub.C=V.sub.T-V.sub.SF-V.sub.FA
[0206] Where, V.sub.T=the total volume of cement, silica fume, and
fly ash in the mixture. The other variables are as previously and
defined in Step 4 and 5.
[0207] The following equation defines the amount of water required
to give a mixture including fly ash and silica fume a desired
slump: W 2 = W 1 ( S 1 S 2 ) 0.1 - W FA + W SF ##EQU25##
[0208] Where, W.sub.SF and W.sub.FA are as defined in Steps 4 and
5.
[0209] The logic of the optimization procedure may be employed in
Step 8 as depicted in the logic flow diagram shown in FIGS. 8A and
8B and the logic tree shown in FIG. 8C. FIGS. 8A-8C schematically
illustrate exemplary acts corresponding to Step 8. In many ways,
the process is similar to previous steps, except that fly ash and
silica fume only displace a portion of the hydraulic cement. As a
result, the fine-to-coarse aggregate ratio does not need to be
varied in this step. What are varied as the various ratios of
cement, aggregates, fly ash and silica fume to determine an mix
design that is optimized to cost and that includes two or more of
fly ash, silica fume and a water reducer.
[0210] Should the desired strength not equal the calculated
strength, the estimated values for the new volumes of cement, fly
ash, and silica fume can be calculated from the following
equations, respectively: V C .function. ( N ) = ( .sigma. D K ) 0.5
.times. W 2 + V A 1 - ( .sigma. D K ) 0.5 1 + K 2 % .times. .times.
FA 100 - % .times. .times. FA + K 3 % .times. SF 100 - % .times.
.times. SF ##EQU26## V FA .function. ( N ) = % .times. .times. FA V
C .function. ( N ) 100 - % .times. .times. FA ##EQU26.2## V SF
.function. ( N ) = % .times. .times. SF V C .function. ( N ) 100 -
% .times. SF ##EQU26.3##
[0211] Where all variables are as previously defined in Steps 4 and
5.
[0212] Finally, as discussed in relation to step 6, the addition of
water reducers is only taken into consideration in determining the
amount of water required to give a mixture a desired slump.
Accordingly, independent of whether the water reducer is to be
added to the combination of cement and fly ash, cement and silica
fume, or the composition of cement, fly ash and silica fume, the
above defined equations are only varied by subtracting the
reduction in the amount of water required for a desired slump as a
result of the addition of the water reducer.
[0213] For example, the required amount of water for a desired
slump in a mixture containing cement, fly ash, silica fume, water
reducer, fine aggregate, and coarse aggregate is determined by the
following equation: W 2 = W 1 ( S 1 S 2 ) 0.1 - W FA + W SF - W WR
##EQU27##
[0214] Where, the values for W.sub.FA, W.sub.SF, and W.sub.WR are
as defined in Steps 4, 5, and 6, respectively.
[0215] It should also be noted that the affects of other pozzolans
or admixtures can also be added to the optimization process by
simply adding another loop to the iterative process. Similarly,
fillers could have been added to the above system, but since
fillers are seldom (if ever) added to a mixture including other
admixtures, the result would have been the same.
[0216] I. Step 9: Modifications Using Air Entraining Agent
[0217] Step 9 involves optionally modifying the concrete mixture
using an air-entraining agent, if necessary, to ensure that the
concrete composition has a proper air content. A detailed
description of an exemplary embodiment for employing air-entraining
agents, if necessary or desired, is set forth in the Andersen
patent at col. 43, line 15-col. 44, line 13. This section of the
Andersen patent includes exemplary acts corresponding to Step
9.
[0218] Unlike the admixtures discussed above, air-entraining agents
are not modeled into the optimization process and thus must be
corrected after the fact. Air-entraining agents are admixtures that
stabilize bubbles formed during the mixing process by lowering the
surface tension of the water. The air-entraining agent forms a
water repelling film that is sufficiently strong to contain and
stabilize air bubbles. Unlike naturally occurring air bubbles, air
bubbles formed through the use of an air-entraining agent are
extremely small and have a diameter size ranging from about 10 to
about 1000 .mu.m. Benefits to increasing the percent volume of
entrained air voids in concrete are the improved resistance to
freezing and thawing of hardened concrete in moist conditions and
the increased workability of the unhardened concrete mixture.
[0219] Once the optimal mixture is actually produced, the actual
air content in the mixture can be determined. If the air content
for a given slump after completion of the optimization process is
too low or too high compared to the assumed air content used in
sub-step 2(c), the optimization process can be recalculated using
the corrected value for the content of air or the mixture can be
reformed with the appropriate amount of air-entraining agent. The
air content can also modeled according to the discussion in Step 10
below. As with water reducers, the percent volume of an air
entraining agent in a mixture is typically so small that the agent
itself is not taken into account as affecting the volume of the
mixture. However, the resulting amount of air incorporated into the
mixture is taken into consideration in determining the strength of
the mixture.
[0220] J. Step 10: System Correction Factor
[0221] Step 10 identifies and implements a system correction factor
to ensure that the final concrete composition has the desired
slump. A detailed description of an exemplary embodiment for
correcting slump if necessary is set forth in the Andersen patent
at col. 44, line 17-col. 45, line 32. This section of Andersen et
al. includes exemplary mathematical algorithms relative to
correcting slump and exemplary acts corresponding to Step 10.
[0222] Once the iterative process of Step 8 is completed, a linear
regression analysis can be used to improve the accuracy of the
system results. This may be accomplished by plotting the
theoretically determined amount of mixing water required to obtain
a desired slump versus the actual amount mixing water required to
obtain a desired slump. The relationship between the plotted values
is then defined and incorporated into Popovic's formula so as to
increase the accuracy of the theoretical amount of water required
to obtain a desired slump. In practice, the above process includes
the following sub-steps:
[0223] Sub-step 10(a): Determining the theoretical amount of water
required to obtain a desired slump in the optimal mixture defined
in Step 8. This amount corresponds to the value for W.sub.2 solved
from Popovic's formula and is the amount used in determining the
resulting 28-day strength of the optimal mixture.
[0224] Sub-step 10(b): Physically combine the theoretical amount of
water with the optimal concrete mixture of Step 8. Next,
experimentally determine the actual slump and air content of the
mixture. As a result of approximations incorporated into the
optimization process, there will often be a discrepancy between the
actual values for slump and air and the theoretical values for
slump and air.
[0225] Sub-step 10(c): Using Popovic's formula, solve for the
amount of water, W.sub.2, needed to give the defined mixture the
actual slump determined in sub-step 10(b). Sub-steps 10(b) and
10(c) now give the actual and theoretical amounts of water,
respectively, required to give a specific mixture a specific
slump.
[0226] Sub-step 10(d): Repeat Steps 10(a)-10(c) for different
desired slumps. The steps should be repeated at least three times
with the accuracy of the final results improving the more the steps
are repeated. This provides two sets of values corresponding to the
actual and theoretical amounts of water required to obtain a
defined slump.
[0227] Sub-step 10(e): Plot the values of Step 10(d) with the
actual amount of water required for a specific slump on the y-axis
and the theoretical amount of water required for a specific slump
on the x-axis. Studies have shown that such a plot will reveal a
linear relationship.
[0228] Sub-step 10(f): Define the linear relationship of Step 10(e)
in the following form: W.sub.2c=(W.sub.2m)+b
[0229] Where, W.sub.2c=actual amount of water for a defined slump
(in use, the value represents the corrected theoretical amount of
water for a defined slump),
[0230] W.sub.2=theoretical amount of water for a defined slump,
[0231] m=slope of the plot in Step 10(e), and
[0232] b=the y intercept.
[0233] Sub-step 10(g): Plot the experimentally determined air
content values for each the mixtures versus the experimentally
determined slump values for the corresponding mixtures. Define the
correlation in the following form: AIR.sub.ACT=(SLUMPm)+b
[0234] Where, AIR.sub.ACT=the volume of air in a mixture based on
the corresponding slump,
[0235] SLUMP=the slump for a given mixture,
[0236] m=slope of the plot of actual slump versus correspond air
content, and
[0237] b=the y intercept of the slope.
[0238] Sub-step 10(h): The formula of sub-step 10(f) is then
incorporated into the design optimization process such that after
the theoretical amount of mixing water required for a desired slump
is solved for from Popovic's formula, the resulting value for
W.sub.2 is input into equation described for sub-step 10(f) above.
W.sub.2c is then solved for providing an improved or corrected
value for the amount of water required to obtain a desired slump.
The desired slump is then incorporated into the equation described
in sub-step 10(g) to obtain the volume of air in the mixture. The
resulting volume of air and corrected water volume are then used in
Feret's equation to solve for the strength of the mixture. The
optimization process then continues as previously discussed. In
this way the slump can be estimated to within .+-.2 cm.
[0239] K. Step 11: Ensuring Sufficient Durability
[0240] Step 11 ensures the concrete composition has sufficient
durability for its intended use. A detailed description of one
currently preferred embodiment for ensuring sufficient durability,
if necessary or desired, is set forth in that Andersen patent at
col. 45, lines 34-60. This section of Andersen et al. includes an
exemplary mathematical algorithm relating to porosity, which
affects durability, and describes acts corresponding to Step
11.
[0241] The above optimization process can also be used to insure
that the selected concrete composition has sufficient durability
for its intended use. Durability is the ability of a concrete
structure to maintain its integrity over an extended period of time
and is measured in this patent in terms of porosity. Mixtures with
a high porosity typically have an excessively high concentration of
water or fine aggregate and as such have low durability. Total
porosity of a mixture can be determined by the following equation,
where it is assumed 80% of the hydration of the cement has already
occurred: TOTAL .times. .times. POROSITY = ( W W - 0.208 .times. (
W C ) 10 ) + % .times. .times. AIR ##EQU28##
[0242] Where, W.sub.W=weight of water per cubic meter of
concrete,
[0243] W.sub.C=weight of cement per cubic meter of concrete,
and
[0244] % Air=percent volume of air in mixture based on volume of
solids in mixture.
[0245] The above equation can thus be used with the slump and
strength to insure that a mixture has desired properties. That is,
once a mixture has been found to have sufficient strength and
slump, the total porosity can be calculated to determine if it
satisfies the desired porosity level. If porosity is too high, the
percent volume of cement can be increased, thereby decreasing the
porosity of the structure and ensuring that it has sufficient
durability.
[0246] L. Step 12: Optimizing Yield
[0247] Finally, step 12 involves determining the quantities of the
various components of the optimal concrete mixture that are needed
to produce a desired yield of a concrete composition. A detailed
description of one currently preferred embodiment for accurately
producing a desired quantity of concrete from the optimal concrete
mixture is set forth in the Andersen patent at col. 45, line
63-col. 46, line 52. This section of Andersen et al. includes an
exemplary mathematical algorithm relative to determining raw
materials quantities to ensure a desired yield and also acts
corresponding to step 12.
[0248] The volume of a proposed mixture is typically calculated by
dividing the weight of each component by its respective density to
obtain the volume of each component. The volume of each of the
components are then added together to obtain the sum volume of the
resulting mixture. This process, however, does not take into
account that the packing density of the particles is less than 1.0
and, thus, does not consider the interstitial spaces remaining
between the mixed particles. As a result, the actual volume of the
mixture is greater than the calculated volume.
[0249] The process for optimizing yield entails dividing the volume
of each component (as determined by the previously discussed
optimization process) by the total volume of the mixture and then
multiplying the corresponding fractions by the desired volume of
the mixture. These calculations determine the actual volume of each
component that should be added to produce a mixture of a desired
volume. In turn, the volume of the components can be multiplied by
their respective specific gravities to determine the weight of each
component that should be added to a mixture to obtain a desired
yield of concrete.
[0250] By way of example, the volume of cement needed to produce
100 cubic meters of a defined concrete mixture can be determined by
the following equation: Vol. Cement=(V.sub.C/V.sub.T)100
[0251] Where, V.sub.C=the volume of cement in the mixture
determined in Step 10 of the optimization process and is
represented as a fraction of the solids in the mixture, the solids
(i.e., cement, fine aggregate, coarse aggregate and, when relevant,
fly ash and silica fume) summing to 1.0,
[0252] V.sub.T=the total volume of the optimized mixture defined in
Step 8, and is obtained by adding the volume of water, W, in the
mixture to the volume of solids (which sum to 1.0) and dividing the
sum by the volume of air in the mixture.
[0253] Hence, the total volume is represented by the following
equation: V T = W + 1 1 - % .times. .times. AIR 100 ##EQU29##
[0254] Where, the percent air, % Air, in the mixture can be
empirically determined by a trial mix. Using the above equation for
each of the components in the mixture, the volume of each of the
components needed to produce a mixture with a desired yield can be
accurately determined.
V. Computer-Implemented Iterative Design Optimization Sub-Routine
or Process
[0255] According to another aspect or embodiment of the present
invention, there is provided a computer-implemented iterative
optimization process according to the flow chart illustrated in
FIG. 9, which may be utilized alone or in combination with any part
of the generalized process exemplified by Steps 1-12 described in
Section IV. This process includes the following steps: [0256] 1.
providing batches of hydraulic cement and aggregate having specific
characteristics; [0257] 2. selecting a target slump and strength
for the final concrete composition; [0258] 3. measuring the average
particle size and measuring or estimating the packing density for
the solid components comprising hydraulic cement and each type of
aggregate (e.g., fine, medium, and coarse aggregate); [0259] 4.
designing a dry concrete mixture having a concentration ratio of
solid components; [0260] 5. calculating the particle packing
density of the designed dry concrete mixture; [0261] 6. calculating
an amount of water that yields a designed cementitious mixture
having the target slump; [0262] 7. calculating the strength of the
designed cementitious mixture using Feret's equation, or a variant
thereof, utilizing a specific design K factor, from among different
K factors that lie along a K factor curve representative of system
inputs, that is selected based on the target strength (e.g., a
specific minimum desired or design compressive strength of the
final designed concrete mixture); [0263] 8. calculating the
difference between the calculated strength of the designed cement
mixture and the target strength; and [0264] 9. altering the
concentration ratio of the solid components to yield one or more
additional designed dry concrete mixtures and then repeating steps
5 through 8 until the calculated strength of one or more designed
hydrated mixtures equals or is within an acceptable range of
deviation from the target strength.
[0265] The design K factor utilized in this process is ideally the
same as the theoretical or "true" K factor that corresponds to an
ideal target strength. Nevertheless, the design K factor may
deviate from the theoretical K factor in order to guarantee a
specific minimum concrete strength. The amount of deviation
provides a margin of safety to account for variations between
design strength and actual strength that may occur as a result of
variations in raw materials characteristics and/or variations in
processing. Providing a better optimized mix design according to
the invention significantly reduces the standard deviation between
design strength and actual strength as compared to a poor,
unoptimized mix design. Improvements and/or adjustments to
processing equipment, as discussed elsewhere in this disclosure,
can further reduce the deviation between design and actual
strengths. Minimizing and/or monitoring and accounting for changes
in the raw materials can further reduce the deviation between
design and actual strengths.
VI. Identifying Best Optimized Mix Design from Among Several Design
Optimized Hypothetical Mix Designs
[0266] FIG. 10 is a flow chat that illustrates an exemplary process
according to the invention for designing several/hypothetical
optimized mix designs and then identifying the best optimized mix
design. The process illustrated in FIG. 10 demonstrates the use of
a correct design K factor selected based on the desired or target
strength. This process can be utilized using any desired
computer-implemented design optimization procedure that utilizes
Feret's equation or a variation thereof, including any processes
disclosed herein. The design optimization illustrated by FIG. 10
includes the following steps: [0267] 1. selecting the specific
minimum desired or target strength for a concrete composition;
[0268] 2. selecting a design K factor based on the desired or
target strength, which may equal or deviate from theoretical K
factor that corresponds to that strength; [0269] 3. designing,
using the design K factor, a plurality of theoretically optimized
concrete mix designs having a design strength that is theoretically
equal to the desired or target strength; [0270] 4. preparing
concrete test samples based on the theoretically optimized concrete
mix designs; [0271] 5. measuring the actual strengths of the
concrete test samples; [0272] 6. comparing the difference between
the actual strength for each theoretically optimized mix design and
the desired or target strength; and [0273] 7. if the actual
strength is not within an acceptable range of deviation relative to
the desired strength, designing one or more additional concrete mix
designs until the desired strength of one or more additional
concrete mix designs is within an acceptable range of deviation
from the desired strength.
[0274] The acceptable range of deviation between the actual
strength and the desired strength can be selected depending on the
level of certainty desired by the concrete manufacturer. An actual
strength that is outside the acceptable range of deviation
typically indicates a concrete mixture that is overdesigned.
Conversely, an actual strength that falls within the acceptable
range of deviation is indicative of a better optimized mix
design.
VII. Manufacturing an Optimized Concrete Composition
[0275] FIG. 11 is a flow chart that illustrates an exemplary
process for manufacturing an optimal concrete composition design
using an inventive design optimization procedure set forth herein.
The manufacturing process includes the following steps: [0276] 1.
providing an optimal concrete mix design that was determined using
a design K factor that corresponds to a specific minimum desired
strength of the concrete to be manufactured; [0277] 2. determining
a proper quantity for each solid component of the concrete
composition in order to provide an optimized yield that guarantees
a minimum required quantity while minimizing overproduction and
waste; [0278] 3. measuring the moisture content of the solid
components used to manufacture the concrete composition; [0279] 4.
taking into account any moisture within the solid components,
weighing each solid component added to the concrete composition to
an accuracy of about .+-.2.0%, more preferably to an accuracy of
about .+-.1.0%, and most preferably to an accuracy of about 0.5%;
[0280] 5. taking into account any moisture within the solid
components, determining an amount of batch water that, when blended
with the solid components, will yield a concrete composition having
a desired slump (e.g., according to the mix design); and [0281] 6.
blending the components to yield a concrete composition in which
the actual strength and slump closely correlate to the desired
strength and slump.
[0282] According to one embodiment, it may be advantageous to
control the concentration of water from the time the concrete
composition is manufactured until the time it is delivered and used
at the job site to prevent degradation of concrete strength.
Additional information for optimizing the mixing process and
controlling water concentration will now be given.
[0283] A. Controlling the Quantities of Components Added to
Concrete
[0284] In order to obtain a concrete composition in which the
actual strength closely corresponds to the desired or theoretical
strength of the optimized concrete mix design, it is preferable to
carefully weight or otherwise measure the quantity of each
component added to the concrete composition. According to one
embodiment, each component is preferably weighed to an accuracy of
about .+-.2.0%, more preferably to an accuracy of about .+-.1.0%,
and most preferably to an accuracy of about .+-.0.5%. An example of
apparatus that can be used to accurately weigh the various
components added to a concrete delivery/mixer truck within the
foregoing parameters is an Alkon Command Batch Weigh-up &
Batching System. It will be appreciated, however, that it is within
Cu the scope of the invention to utilize any other apparatus known
in the art or that may be developed that is capable of accurately
weighing or otherwise measuring the amounts of the components added
to the concrete mixer truck within the desired level of
accuracy.
[0285] B. Accounting for Variations in Moisture Content of Solid
Components
[0286] According to one embodiment, it is advantageous to account
for variations in the moisture content of the solid components
(i.e., aggregates), which can significantly affect the strength and
slump of the resulting concrete composition. Because moisture adds
weight to the aggregates, failure to account and correct for this
moisture can result in using a lower quantity of one or more
aggregates than what may be required according to an optimized mix
design. Providing a lesser quantity of one or more aggregates than
what was determined by the design K factor to be optional can
indirectly affect the strength of the resulting concrete
composition (e.g., by increasing the amount of water, which
increases the water-to-content ratio). In addition, reducing the
amount of aggregates may increase the relative amount of hydraulic
cement to beyond what was determined to be optimal. In addition to
reducing strength, the unaccounted for excess water will also
increase the overall batch water content, which may increase slump
to beyond what was determined to be optimal.
[0287] To account for moisture, sensors may be used to sense the
moisture content of the solid components. Any moisture sensors
known in the art or that may be developed can be used to monitor
content. An example of a moisture sensor is a microwave sensor,
which beams microwave radiation into a given volume of material
(e.g., fine, medium or coarse aggregate) and then measures the
absorption of microwave energy by any water that may be present.
Because water strongly absorbs microwave energy, the amount of
microwave energy absorbed by a given volume of aggregates
correlates with an amount of moisture within the aggregates. The
information regarding moisture content can be utilized to determine
(e.g., by a computer) how much additional must be weighed out to
provide the correct amount of aggregate and/or how much added water
should be added to the mixture to maintain the correct slump and/or
water-to-cement ratio. In general, smaller aggregates are more
sensitive to changes in moisture due to their generally higher
surface area and ability to absorb moisture into pores.
[0288] C. Use of Admixtures Instead of Water to Increase Slump
[0289] Equally or more important than controlling the initial
quantities of components added to the concrete mixer/delivery truck
is carefully controlling the concentration of batch water in the
concrete composition from between the time the components are added
to the cement mixer drum to when the composition is delivered and
utilized at the job site. In order to maintain a strength that
meets or exceeds the specific minimum strength, little or no
additional water should ever be added to the concrete composition
once the components have been properly batched and mixed
together.
[0290] In the event that it may be desired to alter the slump of
the concrete composition at a job site, only suitable chemical
admixtures for increasing or decreasing slump should be utilized.
For example, where it is desired to increase the slump, one of the
various plasticizers, super-plasticizers or high range water
reducers known in the art can be utilized. Where it is desired to
decrease slump, any of the known rheology modifying agents or water
binding agents known in the art can be utilized. The quantity of
such admixtures added to the concrete composition should be
carefully controlled in order to deliver a concrete composition
having the desired properties of slump and strength.
[0291] D. Specially Designed Concrete Mixing Trucks
[0292] In current practice, slump modifications in concrete are
typically performed at the job site by the concrete truck driver
adding additional water. This is the worst way to ensure desired
strength since concrete truck drivers are typically the least
knowledgeable regarding the deleterious effect of adding water to
concrete. In most cases, drivers go on look and feel rather than
using a slump cone. This practice is so common that concrete
manufacturers are forced by necessity to overdesign their concrete
mix designs by a significant margin.
[0293] In order to prevent a concrete truck driver from
deliberately or inadvertently adding water to the concrete
composition once it leaves the concrete manufacturing site, it is
within the scope of the invention to utilize specially designed
concrete mixing trucks that include a tank or vessel containing one
or more admixtures used to make slump adjustments as needed at the
job site. For example, plasticizers, super-plasticizers or
long-range water reducers known in the art can be contained within
one or more vessels. In addition, the concrete mixing truck may
include a device that accurately measures the slump of the concrete
mixture within the drum. If it is necessary or desired to increase
the slump of the concrete mixture, a pre-determined quantity of the
slump increasing admixture can be injected from the special tank or
vessel into the drum in order to raise the slump to the desired
value.
[0294] A separate vessel or tank may also include admixtures that
are capable of altering the concrete composition in other ways
(e.g., increasing cohesion, decreasing slump, increasing set time,
or retarding set time). Because such admixtures do not typically
affect strength, the desired minimum strength can more easily be
maintained, thereby further decreasing the deviation between actual
and design strength (and actual and design K factor).
[0295] Concrete delivery trucks are typically equipped with water
tanks to add water on site. Some are also equipped with admixture
tanks to meter admixtures. One of skill in the art, knowing how
admixtures affect slump, can readily design a concrete truck that
is able to meter a specific quantity of slump altering admixture as
may be needed to desired to alter slump in the appropriate manner.
Thus, only minor modifications of existing concrete trucks may be
required. Such apparatus comprising means for metering a desired
quantity of admixture to a concrete composition on site.
[0296] E. Abbreviated Re-Design Process to Adjust Slump of an
Optimized Mix Design Without Substantially Altering Compressive
Strength
[0297] In some cases it may be desirable to quickly re-design a mix
design that is already optimized in order to adjust the slump
without significantly changing the compressive strength. This can
be done without creating a whole new optimized mix design using,
e.g., the detailed 12-step design optimization procedure described
above. To maintain the same essential strength, while varying the
slump, the same water-to-cement ratio of the paste is maintained.
Only the volume of paste is altered in order to adjust the slump of
the wet cementitious mixture. In general, adding more paste will
increase slump, while adding less paste will decrease the slump.
Thus, the overall ratio of cement paste to aggregate is adjusted to
change the slump. Because the water-to-cement ratio of the paste
remains the same, the strength will theoretically remain
essentially the same. In some cases, the ratio of fine to coarse
aggregates may remain the same. In other cases, the ratio can be
altered somewhat depending on the effect on the other properties
caused by changing the overall ratio of cement paste to aggregate
(e.g., cohesiveness, durability, and the like).
[0298] A flow chart illustrating an exemplary method for the
abbreviated re-design of a current optimized mix design in order to
adjust slump is shown in FIG. 12. The effect of changing the
overall concentration of cement paste on slump can be determined
using any of the slump equations set forth above and accounting for
the increased or decreased water content depending on whether the
amount of cement paste is increased or decreased compared to the
initial mix design. Adding more cement paste increases slump
because it increases the overall concentration of water-to-solid
components. Conversely, decreasing the quantity of cement paste
decreases slump because it decreases the overall ration of
water-to-solid components.
[0299] According to one embodiment, the process is controlled by a
computer and involves monitoring changes in slump between batches,
which might be caused by variations in aggregate size and/or
moisture. When a change in slump is detected, a
computer-implemented design process involves adjusting the quantity
of water in order to revise the slump, changing the amount of
cement to maintain the same water to cement ratio (and therefore
strength), and altering the relative concentration of aggregates if
needed to maintain a proper amount of cohesiveness. In general,
increasing the ratio of fine aggregate to coarse aggregate
increases cohesiveness but can decrease slump. A decrease in cement
paste may require an increase in fine aggregate to maintain
cohesiveness. Conversely, an increase in cement paste may require a
decrease in fine aggregate to increase slump while avoiding the
deleterious effect of overcementing and in order to better optimize
cost.
[0300] In some cases, it may be possible to select a ratio of fine
to coarse aggregate that is not necessarily perfectly optimized but
that is adequate (e.g., typically within a range of 40:60 to 60:40
parts fine to coarse aggregate). Within this ratio there is often
not a lot of variability in cohesion and segregation, which can
greatly affect concrete performance when placed at a job site. To
ensure a minimum guaranteed strength, a cement paste is designed
having a water to cement ratio that yield the desired strength
(e.g., in the case where the cement paste is the weakest
component). The ratio of cement paste to aggregate is adjusted to
yield the desired slump. While this approach does not optimize
concrete to the same degree of accuracy, it can be employed in many
cases (e.g., smaller jobs where the relatively small cost of
overdesigning may not justify a full-blown optimization procedure
as described herein).
VIII. Redesigning a Pre-Existing Concrete Mix Design
[0301] FIG. 13 is a flow chart that illustrates an exemplary method
for redesigning a pre-existing concrete mix design utilizing the
recently discovered knowledge that and how the K factor used in
Feret's equation varies with changes in concrete strength (i.e.,
logarithmically with increasing strength). The exemplary redesign
process shown in FIG. 13 includes the following steps: [0302] 1.
identifying a pre-existing concrete mix design having a predicted
(or design) strength; [0303] 2. preparing a concrete test sample
from the pre-existing concrete mix design; [0304] 3. measuring the
actual strength of the concrete test sample and determining how
much the actual strength deviates from the design strength
(optional); [0305] 4. determining an apparent design K factor for
the pre-existing concrete mix design based on the design strength
and the ratio of components within the concrete test sample made
from the pre-existing concrete mix [0306] 5. comparing the apparent
design K factor of the pre-existing concrete mix design with the
"true" or optimal K factor corresponding to the design or predicted
strength of the pre-existing concrete mix design; [0307] 6.
identifying a revised design K factor based on the predicted (or
design) strength (e.g., selected based on one of the K factor lines
shown in FIGS. 1-3 or that is appropriate for the given set of raw
material inputs) that is closer to the optimal K factor for the
design strength than the apparent design K factor of the
pre-existing mix design; a K factor curve for the concrete plant
can be optionally constructed by testing the actual strength of one
or more properly prepared concrete compositions of the manufacturer
and plotting the actual K factor(s) versus actual strength; and
[0308] 7. designing, using the revised design K factor, a new
concrete mix design that yields a concrete composition having an
actual strength that more consistently corresponds to the predicted
(or design) strength compared to the pre-existing mix design.
[0309] In the case of an unoptimized, poorly pre-existing mix
design, the difference between the apparent design K factor based
on the design or predicted strength of the pre-existing mix design
and the optimal or theoretical K factor based on the design
strength will be significantly greater than in an optimized mix
design. By rebalancing the relative concentrations of the various
components in order to yield a more optimized mix design (i.e., so
as to more efficiently utilize the hydraulic cement and other
components), the deviation between actual strength and design
strength will be significantly decreased. As a result, the revised
design K factor that is required to guarantee a specific minimum
strength will more closely correspond to the optimal or theoretical
K factor compared to the pre-existing, unoptimized mix design.
Moreover, comparing the difference between the apparent design K
factor and the optimal K factor is a diagnostic tool that enables
one desiring to implement the design optimization procedure of the
present invention to diagnose if, and to what extent, a
pre-existing mix design may be overdesigned. As discussed
elsewhere, the deviation between the design and optimal K factors
can be achieved by carefully accounting for variations in the size
and moisture content of the solid components and/or upgrading
and/or adjusting the manufacturing process and equipment.
IX. Upgrading an Existing Concrete Plant
[0310] FIG. 14 is a flow chart that illustrates an exemplary
embodiment according to the invention for upgrading an existing
concrete manufacturing plant. The process illustrated in FIG. 14
utilizes the discovery that and how the K factor various
logarithmically with changes in concrete strength. The process for
upgrading an existing concrete manufacturing plant includes the
following steps: [0311] 1. manufacturing one or more concrete
compositions using one or more pre-existing mix designs having
predicted strengths; [0312] 2. determining an apparent design K
factor for each of the one or more concrete compositions based on
the design strength and ratio of components of each concrete
composition; [0313] 3. identifying a revised design K factor, based
on the predicted or desired strength of each pre-existing mix
design, which more closely corresponding to the optimal or true K
factor for the design strength compared to the pre-existing mix
design; and [0314] 4. designing, using the revised design K factor
for each pre-existing mix design, one or more revised concrete mix
designs that yield concrete compositions having actual strengths
that more consistently correspond to the predicted or design
strengths compared to the one or more pre-existing mix designs,
respectively.
[0315] Because each manufacturing plant has its own unique set of
raw materials and/or processing inputs (i.e., no two plants use
exactly the same raw materials and possess the exact same equipment
calibrated and/or operated in the exact same manner), it will be
appreciated that each manufacturing plant produces concrete
compositions having unique aspects that are specific to a given
manufacturing plant. In other words, even if two manufacturing
plants use the same standardized mix designs (i.e., recipes), the
concrete delivered by each plant will, in same way, be unique to
each plant. That means that pre-existing concrete mix designs that
have been modified and optimized utilizing the improved DOC program
will yield new concrete compositions that are themselves unique in
that they will have never been manufactured at any time anywhere in
the world. Thus, improved concrete compositions manufactured using
optimized mix designs resulting from the implementation of the
improved DOC process are themselves unique and therefore novel as
between all previously manufactured concrete.
[0316] It turns out that every concrete composition that is made
has its own unique signature design K factor and also an actual K
factor that can be determined by testing the actual strength of the
composition. That is true both before and after implementation of
the improved DOC process. However, after implementation of the
improved DOC process, the signature K factors, both design and
actual, for an optimized concrete composition of a manufacturing
plant will exceed the signature K factors, both design and actual,
of the pre-existing concrete composition that was redesigned using
the improved DOC process. By knowing and comparing the design
and/or signature K factors of both a pre-existing and an optimized
concrete composition of a given manufacturing plant, one can
readily ascertain whether a particular concrete composition
produced by the manufacturing plant was manufactured using the
pre-existing mix design or an optimized mix design designed using
the improved DOC process. Thus, the signature K factor can be used
as a diagnostic tool to distinguish whether an overdesigned or an
optimized concrete composition was used in a building project
(i.e., to determine whether or not the improved DOC process has
been implemented by a concrete manufacturer in designing its
concrete compositions).
[0317] One of the practical affects of upgrading an existing
concrete manufacturing plant is providing mix designs that are
specifically optimized based on the raw materials that are actually
used by the concrete manufacturing plant. It is often the case that
manufacturing plants use standardized mix designs that were made
using raw materials not available to a particular manufacturing
plant. Indeed, manufacturing plants are often owned by a single
entity that provides standardized mix designs for use with every
manufacturing plant regardless of variations in raw material
inputs. As a result, there is large systematic error built into the
standardized mix designs that cannot be accounted for or corrected
by simply providing improved batching equipment. In other words,
even if the components could be measured and batched perfectly each
time, the mix designs would have to account for variations in raw
materials inputs among and between the various manufacturing
plants. The only way to eliminate such systematic error is to
provide an optimized mix design that is specifically tailored to
account for the specific raw materials that are used by a
particular manufacturing plant to make concrete at a given
time.
[0318] The knowledge of how the K factor varies with concrete
strength can be used as a diagnostic tool to identify those aspects
of a manufacturer's batching process that may be in need of
modification. As discussed herein, the improved DOC process can be
used to identify how much paste is needed to achieve a desired
slump, with the K factor specifying the water-to-cement ratio
needed to obtain a specific strength. If particle packing is
optimized for a particular plant, there is little benefit in
spending capital resources to optimize the metering equipment.
Increasing the ability to accurately weigh and batch solid
components will not yield much benefit if particle packing is
already optimized or nearly optimized. If variations in weighing
the aggregates does not appreciatively affect slump, then it will
also not appreciatively affect strength even if the aggregates are
not weighed to a high degree of accuracy.
[0319] On the other hand, where much more cement paste is required
to achieve a desired slump compared to an optimized particle
packing system, that indicates that much more accurately weighing
the aggregates to achieve optimized particle packing will yield
significant benefits. In other words, if more accurately measuring
the fine and coarse aggregates minimizes or eliminates changes in
slump and also reduces or eliminates overcementing required to
achieve desired slump, investment in more accurate weighing
apparatus would be highly beneficial and worth the cost.
[0320] In addition to accurately weighing the various components
added to a batch of concrete, accounting for variations in moisture
content of the aggregates will also yield large benefits in the
case where moisture variation is a problem. Variations in moisture
not only affect how much aggregate is needed but also greatly
affect how much water is contained in the concrete composition,
thereby affecting water-to-cement ratio and slump to a high degree.
Accounting for all water inputs greatly increases the ability to
consistently provide concrete having the desired slump and strength
such that a capital investment in moisture sensing material may be
justified.
X. Examples of Design Optimization Process to Re-Design or Replace
Pre-Existing Mix Designs
[0321] The following examples demonstrate the ability of the
improved DOC process disclosed herein to modify, redesign and/or
replace pre-existing mix designs currently used in the industry in
order to yield improved concrete mixtures that are better optimized
with respect to cost, while also maintaining the desired properties
(e.g., slump and strength). The same procedures can also be carried
out relative to virtually any known mix designed currently known
and used in the concrete industry in order to optimize such
compositions with respect to strength and cost, while also
maintaining other desired properties.
[0322] The inventive design optimization methods were used to
improve mix designs at various concrete manufacturing plants
throughout the United States, demonstrating the universal
applicability of the inventive methods. Examples 1-4 relate to four
optimized concrete mix designs that were made according to the
improved DOC process to improve upon and replace 12 standard mix
designs presently or previously used by a first manufacturing plant
using standardized mix designs. The standard mix designs in the
remaining comparative examples are the same as in Examples 1-4, but
were used by other plants owned by the same manufacturer. For this
reason, the cost of manufacturing concrete at the different plants
differs due to differences in the raw materials cost due to
location and source. Because the quality of aggregates differ from
plant to plant, the design optimization procedure yields different
optimized mix designs for each manufacturing plant in order to
account for such differences in raw material inputs. In this way,
the optimized mix designs are better tailored to the specific raw
materials used by each plant.
[0323] The standard pre-existing mix designs are "comparative
examples" and shall be numbered according to the corresponding
optimized mix design created to take their place (e.g., the
optimized mix design of Example 1 corresponds to, and is designed
to replace, the mix designs of Comparative Examples 1a-1c).
EXAMPLES 1-4
[0324] Examples 1-4 illustrate four optimized concrete mix designs
that were prepared using the improved DOC process described herein.
The four mix designs of Examples 1-4 can replace twelve
pre-existing standard concrete mix designs utilized by an existing
concrete manufacturing plant. Each mix design of Examples 1-4
corresponds to a group of three pre-existing mix designs of similar
type that guarantee a minimum compressive strength, at a specified
slump, and percentage of entrained air when delivered to the
customer. The pre-existing mix designs of the concrete
manufacturing plant, their components, cost (revised Apr. 7, 2006),
and apparent design K factors, will be presented in four groups of
three concrete mix designs, each group having similar properties or
characteristics.
COMPARATIVE EXAMPLES 1a-1c
[0325] The three mix designs of Comparative Examples 1a-1c have a
design strength of 3000 psi, a slump of 4 inches, and minimal
entrained air (1.5%). TABLE-US-00001 Comparative Example 1a 1b 1c
Cost (US$) Compressive Strength 3000 3000 3000 -- (psi) Slump
(inch) 4 4 4 -- Type 1 Cement 370 470 423 $101.08/Ton
(lbs/yd.sup.3) Type C Fly Ash 100 0 0 $51.00/Ton (lbs/yd.sup.3)
Sand (lbs/yd.sup.3) 1570 1470 1660 $9.10/Ton State Rock
(lbs/yd.sup.3) 1700 1700 1714 $11.65/Ton Potable Water
(lbs/yd.sup.3) 280 280 265 negligible Daravair 1400 (air 0 0 0
$3.75/Gal entrain.) (fl. oz./cwt) Daracem 65 (water 0 0 14.8
$5.65/Gal red.) (fl. oz./cwt) % Air 1.5 1.5 1.5 -- Apparent Design
K 234 191 207 -- Factor Cost ($/yd.sup.3) $38.59 $40.62 $41.99 --
Sales Distribution (%) 19.57 80.43 0 -- Within Group Weighted
Average $40.23 -- Cost ($/yd.sup.3) Total Sales (%) of 1.08 --
Concrete Plant
COMPARATIVE EXAMPLES 2a-2c
[0326] The three mix designs of Comparative Examples 2a-2c have a
design strength of 3000 psi, a slump of 4 inches, and substantial
entrained air (5%). TABLE-US-00002 Comparative Example 2a 2b 2c
Cost (US$) Compressive Strength 3000 3000 3000 -- (psi) Slump
(inch) 4 4 4 -- Type 1 Cement 350 470 423 $101.08/Ton
(lbs/yd.sup.3) Type C Fly Ash 100 0 0 $51.00/Ton (lbs/yd.sup.3)
Sand (lbs/yd.sup.3) 1510 1420 1560 $9.10/Ton State Rock
(lbs/yd.sup.3) 1750 1750 1740 $11.65/Ton Potable Water
(lbs/yd.sup.3) 250 260 240 negligible Daravair 1400 (air 4 5 4
$3.75/Gal entrain.) (fl. oz./cwt) Daracem 65 (water 0 0 14.8
$5.65/Gal red.) (fl. oz./cwt) % Air 5 5 5 -- Apparent Design K 237
189 199 -- Factor Cost ($/yd.sup.3) $38.00 $41.37 $42.37 -- Sales
Distribution (%) 74.23 25.77 0 -- Within Group Weighted Average
$38.87 -- Cost ($/yd.sup.3) Total Sales (%) of 17.53 -- Concrete
Plant
COMPARATIVE EXAMPLES 3a-3c
[0327] The three mix designs of Comparative Examples 3a-3c have a
design strength of 4000 psi, a slump of 4 inches, and minimal
entrained air (1.5%). TABLE-US-00003 Comparative Example 3a 3b 3c
Cost (US$) Compressive Strength 4000 4000 4000 -- (psi) Slump
(inch) 4 4 4 -- Type 1 Cement 470 564 517 $101.08/Ton
(lbs/yd.sup.3) Type C Fly Ash 100 0 0 $51.00/Ton (lbs/yd.sup.3)
Sand (lbs/yd.sup.3) 1530 1440 1530 $9.10/Ton State Rock
(lbs/yd.sup.3) 1746 1750 1750 $11.65/Ton Potable Water
(lbs/yd.sup.3) 280 285 280 negligible Daravair 1400 (air 0 0 0
$3.75/Gal entrain.) (fl. oz./cwt) Daracem 65 (water 0 0 18.1
$5.65/Gal red.) (fl. oz./cwt) % Air 1.5 1.5 1.5 -- Apparent Design
K 232 206 226 -- Factor Cost ($/yd.sup.3) $43.73 $45.53 $47.71 --
Sales Distribution (%) 6.81 44.35 48.84 -- Within Group Weighted
Average $46.47 -- Cost ($/yd.sup.3) Total Sales (%) of 12.81 --
Concrete Plant
COMPARATIVE EXAMPLES 4a-4c
[0328] The three mix designs of Comparative Examples 4a-4c have a
design strength of 4000 psi, a slump of 4 inches, and substantial
entrained air (5%). TABLE-US-00004 Comparative Example 4a 4b 4c
Cost (US$) Compressive Strength 4000 4000 4000 -- (psi) Slump
(inch) 4 4 4 -- Type 1 Cement 470 564 517 $101.08/Ton
(lbs/yd.sup.3) Type C Fly Ash 100 0 0 $51.00/Ton (lbs/yd.sup.3)
Sand (lbs/yd.sup.3) 1390 1340 1430 $9.10/Ton State Rock
(lbs/yd.sup.3) 1710 1750 1750 $11.65/Ton Potable Water
(lbs/yd.sup.3) 255 275 255 negligible Daravair 1400 (air 4 5 4
$3.75/Gal entrain.) (fl. oz./cwt) Daracem 65 (water 0 0 18.1
$5.65/Gal red.) (fl. oz./cwt) % Air 5 5 5 -- Apparent Design K 224
212 218 -- Factor Cost ($/yd.sup.3) $43.41 $45.88 $47.99 -- Sales
Distribution (%) 77.31 22.69 0 -- Within Group Weighted Average
$43.97 -- Cost ($/yd.sup.3) Total Sales (%) of 68.58 -- Concrete
Plant
[0329] The following optimized concrete mix designs according to
Examples 1-4 were made according to the improved DOC process and
are intended to replace the 12 mix designs of Comparative Examples
1a-4c. Each optimized mix design takes the place of three mix
designs of similar attributes (e.g., the optimized mix design of
Example 1 takes the place of the pre-existing mix designs of
Comparative Examples 1a-1c). The optimization procedure assumed a
percent absorption for the sand and rock of 1.5% and 2.5%,
respectively, and a percent moisture of 4.57% and 3.18%,
respectively. TABLE-US-00005 Example 1 2 3 4 Cost (US$) Compressive
3000 3000 4000 4000 -- Strength (psi) Slump (inch) 5 5 5 5 -- Type
1 Cement 340 299 375 366 $101.08/Ton (lbs/yd.sup.3) Type C Fly Ash
102 90 113 110 $51.00/Ton (lbs/yd.sup.3) Sand (lbs/yd.sup.3) 1757
1697 1735 1654 $9.10/Ton State Rock (lbs/yd.sup.3) 1452 1403 1434
1367 $11.65/Ton Potable Water 294 269 294 269 negligible
(lbs/yd.sup.3) Daravair 1400 (air 0 1.4 0 1.4 $3.75/Gal entrain.)
(fl. oz./cwt) % Air 2 5.5 2 5.5 $5.65/Gal Cost ($/yd.sup.3) $36.55
$33.72 $38.39 $37.23 -- Weighted Avg. Cost $36.76 -- ($/yd.sup.3)
Cost Savings ($/yd.sup.3) $3.68 $5.15 $8.08 $6.74 -- Per Mix Design
Weighted Avg. $6.60 -- Plant Cost Savings ($/yd.sup.3)
[0330] Many concrete manufacturing plants have an excessive number
of mix designs of similar type in an attempt to satisfy customer
need. Each improved mix design of Examples 1-4 is able to take the
place of three pre-existing standard mix designs of similar type
because it satisfies the criteria of all three mix designs while
also having reduced cost. Reducing the number of mix designs
required to satisfy customer need represents an additional cost
savings to a concrete manufacturing plant because it simplifies the
overall manufacturing process.
[0331] The absolute cost savings ranged from a low of $2.04 per
yard (Example 1 relative to Comparative Example 1a) to a high of
$10.76 per yard (Example 4 relative to Comparative Example 4c). The
weighted average cost of the pre-existing mix designs of
Comparative Examples 1a-4c, based on the percentage of each mix
design sold by the manufacturing plant, is $43.36 per yard (as of
Apr. 7, 2006). The weighted average cost to manufacture concrete
using the four optimized mix designs based on existing sales
percentages for the 12 pre-existing mix designs of the manufacturer
would be $36.76 per yard at the same materials cost per component.
The average overall cost savings for the manufacturing plant would
therefore be $6.60 per yard, assuming the manufacturer were to
replace the 12 pre-existing mix designs of Comparative Examples
1a-4c with the optimized mix designs of Examples 1-4 and continue
to manufacture the same distribution of concrete as before.
[0332] The amount of $6.60 is several times greater than the
typical profit of $1-2 per yard earned by typical concrete
manufacturers after all fixed and variable costs of operating the
manufacturing plant are factored in and accounted for. The improved
design optimization procedures are therefore able to dramatically
improve upon pre-existing mix designs used by manufacturers, which
were thought to be optimal based on decades of testing and use, and
increase profits by several times. This is a surprising and
unexpected result that attests to the contribution to the art of
concrete manufacture provided by the improved DOC process of the
present invention. Whereas the original DOC program of the Andersen
patent had much to commend itself, it could not be readily
implemented in the real world to diagnose and improve upon
pre-existing concrete mix designs in a concrete and verifiable
manner in order to yield demonstrably improved results at reduced
cost. The improvements described herein were necessary to provide
an optimization procedure that could be readily implemented as
illustrated in Examples 1-4.
EXAMPLES 5-8
[0333] Examples 5-8 illustrate four optimized concrete mix designs
that were prepared using the improved DOC process described herein.
The four mix designs of Examples 5-8 can replace twelve
pre-existing standard concrete mix designs of an existing concrete
manufacturing plant, which used the same 12 mix designs as in
Comparative Examples 1a-4c but manufactured concrete using a
different set of raw materials. Each mix design of Examples 5-8
corresponds to a group of three pre-existing mix designs of similar
type that guarantee a minimum compressive strength, at a specified
slump, and percentage of entrained air when delivered to the
customer. The pre-existing mix designs of the concrete
manufacturing plant, their components, cost (revised Oct. 27,
2005), and apparent design K factors, will be presented in four
groups of three concrete mix designs, each group having similar
properties or characteristics.
COMPARATIVE EXAMPLES 5a-5c
[0334] The three mix designs of Comparative Examples 5a-5c have a
design strength of 3000 psi, a slump of 4 inches, and minimal
entrained air (1.5%). TABLE-US-00006 Comparative Example 5a 5b 5c
Cost (US$) Compressive Strength 3000 3000 3000 -- (psi) Slump
(inch) 4 4 4 -- Type 1 Cement 370 470 423 $104/Ton (lbs/yd.sup.3)
Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd.sup.3) Sand
(lbs/yd.sup.3) 1570 1470 1660 $4.46/Ton 3/4 inch Rock
(lbs/yd.sup.3) 1700 1700 1714 $4.46/Ton Potable Water
(lbs/yd.sup.3) 280 280 265 Negligible Daravair (air entrain.) 0 0 0
$3.75/Gal (fl. oz./cwt) Daracem (water red.) 0 0 14.8 $5.65/Gal
(fl. oz./cwt) % Air 1.5 1.5 1.5 -- Apparent Design K 234 191 207 --
Factor Cost ($/yd.sup.3) $29.01 $31.63 $32.42 -- Sales Distribution
(%) 19.57 80.43 0 -- Within Group Weighted Average $31.12 -- Cost
($/yd.sup.3) Total Sales (%) of 1.08 -- Concrete Plant
COMPARATIVE EXAMPLES 6a-6c
[0335] The three mix designs of Comparative Examples 6a-6c have a
design strength of 3000 psi, a slump of 4 inches, and substantial
entrained air (5%). TABLE-US-00007 Comparative Example 6a 6b 6c
Cost (US$) Compressive Strength 3000 3000 3000 -- (psi) Slump
(inch) 4 4 4 -- Type 1 Cement 350 470 423 $104/Ton (lbs/yd.sup.3)
Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd.sup.3) Sand
(lbs/yd.sup.3) 1510 1420 1560 $4.46/Ton 3/4 inch Rock
(lbs/yd.sup.3) 1750 1750 1740 $4.46/Ton Potable Water
(lbs/yd.sup.3) 250 260 240 negligible Daravair (air entrain.) 4 5 4
$3.75/Gal (fl. oz./cwt) Daracem (water red.) 0 0 14.8 $5.65/Gal
(fl. oz./cwt) % Air 5 5 5 -- Apparent Design K 237 189 199 --
Factor Cost ($/yd.sup.3) $28.36 $32.32 $32.74 -- Sales Distribution
(%) 74.23 25.77 0 -- Within Group Weighted Average $29.38 -- Cost
($/yd.sup.3) Total Sales (%) of 17.53 -- Concrete Plant
COMPARATIVE EXAMPLES 7a-7c
[0336] The three mix designs of Comparative Examples 7a-7c have a
design strength of 4000 psi, a slump of 4 inches, and minimal
entrained air (1.5%). TABLE-US-00008 Comparative Example 7a 7b 7c
Cost (US$) Compressive Strength 4000 4000 4000 -- (psi) Slump
(inch) 4 4 4 -- Type 1 Cement 470 564 517 $104/Ton (lbs/yd.sup.3)
Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd.sup.3) Sand
(lbs/yd.sup.3) 1530 1440 1530 $4.46/Ton 3/4 inch Rock
(lbs/yd.sup.3) 1746 1750 1750 $4.46/Ton Potable Water
(lbs/yd.sup.3) 280 285 280 negligible Daravair (air entrain.) 0 0 0
$3.75/Gal (fl. oz./cwt) Daracem (water red.) 0 0 18.1 $5.65/Gal
(fl. oz./cwt) % Air 1.5 1.5 1.5 -- Apparent Design K 232 206 226 --
Factor Cost ($/yd.sup.3) $34.22 $36.56 $38.46 -- Sales Distribution
(%) 6.81 44.35 48.84 -- Within Group Weighted Average $37.33 --
Cost ($/yd.sup.3) Total Sales (%) of 12.81 -- Concrete Plant
COMPARATIVE EXAMPLES 8a-8c
[0337] The three mix designs of Comparative Examples 8a-8c have a
design strength of 4000 psi, a slump of 4 inches, and substantial
entrained air (5%). TABLE-US-00009 Comparative Example 8a 8b 8c
Cost (US$) Compressive Strength 4000 4000 4000 -- (psi) Slump
(inch) 4 4 4 -- Type 1 Cement 470 564 517 $104/Ton (lbs/yd.sup.3)
Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd.sup.3) Sand
(lbs/yd.sup.3) 1390 1340 1430 $4.46/Ton 3/4 inch Rock
(lbs/yd.sup.3) 1710 1750 1750 $4.46/Ton Potable Water
(lbs/yd.sup.3) 255 275 255 negligible Daravair (air entrain.) 4 5 4
$3.75/Gal (fl. oz./cwt) Daracem (water red.) 0 0 18.1 $5.65/Gal
(fl. oz./cwt) % Air 5 5 5 -- Apparent Design K 224 212 218 --
Factor Cost ($/yd.sup.3) $34.37 $37.16 $38.99 -- Sales Distribution
(%) 77.31 22.69 0 -- Within Group Weighted Average $35.01 -- Cost
($/yd.sup.3) Total Sales (%) of 68.58 -- Concrete Plant
[0338] The following optimized concrete mix designs according to
Examples 5-8 were made according to the improved DOC process and
are intended to replace the 12 mix designs of Comparative Examples
5a-8c. Each optimized mix design takes the place of three mix
designs of similar attributes (e.g., the optimized mix design of
Example 5 takes the place of the pre-existing mix designs of
Comparative Examples 5a-5c). The optimization procedure assumed a
percent absorption for the sand and rock of 1.9% and 2.3%,
respectively, and a percent moisture of 4.57% and 3.18%,
respectively. TABLE-US-00010 Example 5 6 7 8 Cost (US$) Compressive
3000 3000 4000 4000 -- Strength (psi) Slump (inch) 5 5 5 5 -- Type
1 Cement 332 302 375 366 $104/Ton (lbs/yd.sup.3) Type C Fly Ash 100
91 112 110 $47.00/Ton (lbs/yd.sup.3) Sand (lbs/yd.sup.3) 1769 1693
1737 1657 $4.46/Ton 3/4 inch Rock 1470 1407 1450 1377 $4.46/Ton
(lbs/yd.sup.3) Potable Water 294 274 295 270 negligible
(lbs/yd.sup.3) Daravair 0 1.4 0 1.4 $3.75/Gal (fl. oz./cwt) % Air
1.8 5.5 1.9 5.4 $5.65/Gal Cost ($/yd.sup.3) $26.97 $25.01 $29.37
$28.66 -- Weighted Avg. Cost $28.09 -- ($/yd.sup.3) Cost Savings
($/yd.sup.3) $4.15 $4.37 $7.96 $6.34 -- Per Mix Design Weighted
Avg. $6.18 -- Plant Cost Savings ($/yd.sup.3)
[0339] Each improved mix design of Examples 5-8 is able to take the
place of three pre-existing standard mix designs of similar type
because it satisfies the criteria of all three mix designs while
also having reduced cost. The reduced number of mix designs is an
additional cost savings as it simplifies the overall manufacturing
process.
[0340] The absolute cost savings ranged from a low of $2.04 per
yard (Example 5 relative to Comparative Example 5a) to a high of
$10.32 per yard (Example 8 relative to Comparative Example 8c). The
weighted average cost of the pre-existing mix designs of
Comparative Examples 5a-8c, based on the percentage of each mix
design sold by the manufacturing plant, is $34.27 per yard (as of
Oct. 27, 2005). The weighted average cost to manufacture concrete
using the four optimized mix designs based on existing sales
percentages for the 12 pre-existing mix designs of the manufacturer
would be $28.09 per yard at the same materials cost per component.
The average overall cost savings for the manufacturing plant would
therefore be $6.18 per yard, assuming the manufacturer were to
replace the 12 pre-existing mix designs of Comparative Examples
5a-8c with the optimized mix designs of Examples 5-8 and continue
to manufacture the same distribution of concrete as before.
EXAMPLES 9-12
[0341] Examples 9-12 illustrate four optimized concrete mix designs
that were prepared using the improved DOC process described herein.
The four mix designs of Examples 9-12 can replace twelve
pre-existing standard concrete mix designs of an existing concrete
manufacturing plant, which used the same 12 mix designs as in
Comparative Example 1a-4c but manufactured concrete using a
different set of raw materials. Each mix design of Examples 9-12
corresponds to a group of three pre-existing mix designs of similar
type that guarantee a minimum compressive strength, at a specified
slump, and percentage of entrained air when delivered to the
customer. The pre-existing mix designs of the concrete
manufacturing plant, their components, cost (revised Oct. 27,
2005), and apparent design K factors, will be presented in four
groups of three concrete mix designs, each group having similar
properties or characteristics.
COMPARATIVE EXAMPLES 9a-9c
[0342] The three mix designs of Comparative Examples 9a-9c have a
design strength of 3000 psi, a slump of 4 inches, and minimal
entrained air (1.5%). TABLE-US-00011 Comparative Example 9a 9b 9c
Cost (US$) Compressive Strength 3000 3000 3000 -- (psi) Slump
(inch) 4 4 4 -- Type 1 Cement 370 470 423 $104/Ton (lbs/yd.sup.3)
Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd.sup.3) Sand
(lbs/yd.sup.3) 1570 1470 1660 $8.12/Ton 1 inch Rock (lbs/yd.sup.3)
1700 1700 1714 $9.36/Ton Potable Water (lbs/yd.sup.3) 280 280 265
Negligible Daravair (air entrain.) 0 0 0 $3.75/Gal (fl. oz./cwt)
Daracem (water red.) 0 0 14.8 $5.65/Gal (fl. oz./cwt) % Air 1.5 1.5
1.5 -- Apparent Design K 234 191 207 -- Factor Cost ($/yd.sup.3)
$36.21 $38.64 $39.82 -- Sales Distribution (%) 19.57 80.43 0 --
Within Group Weighted Average $38.16 -- Cost ($/yd.sup.3) Total
Sales (%) of 1.08 -- Concrete Plant
COMPARATIVE EXAMPLES 10a-10c
[0343] The three mix designs of Comparative Examples 10a-10c have a
design strength of 3000 psi, a slump of 4 inches, and substantial
entrained air (5%). TABLE-US-00012 Comparative Example 10a 10b 10c
Cost (US$) Compressive Strength 3000 3000 3000 -- (psi) Slump
(inch) 4 4 4 -- Type 1 Cement 350 470 423 $104/Ton (lbs/yd.sup.3)
Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd.sup.3) Sand
(lbs/yd.sup.3) 1510 1420 1560 $8.12/Ton 1 inch Rock (lbs/yd.sup.3)
1750 1750 1740 $9.36/Ton Potable Water (lbs/yd.sup.3) 250 260 240
negligible Daravair (air entrain.) 4 5 4 $3.75/Gal (fl. oz./cwt)
Daracem (water red.) 0 0 14.8 $5.65/Gal (fl. oz./cwt) % Air 5 5 5
-- Apparent Design K 237 189 199 -- Factor Cost ($/yd.sup.3) $35.56
$39.36 $40.02 -- Sales Distribution (%) 74.23 25.77 0 -- Within
Group Weighted Average $36.54 -- Cost ($/yd.sup.3) Total Sales (%)
of 17.53 -- Concrete Plant
COMPARATIVE EXAMPLES 11a-11c
[0344] The three mix designs of Comparative Examples 11a-11c have a
design strength of 4000 psi, a slump of 4 inches, and minimal
entrained air (1.5%). TABLE-US-00013 Comparative Example 11a 11b
11c Cost (US$) Compressive Strength 4000 4000 4000 -- (psi) Slump
(inch) 4 4 4 -- Type 1 Cement 470 564 517 $104/Ton (lbs/yd.sup.3)
Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd.sup.3) Sand
(lbs/yd.sup.3) 1530 1440 1530 $8.12/Ton 1 inch Rock (lbs/yd.sup.3)
1746 1750 1750 $9.36/Ton Potable Water (lbs/yd.sup.3) 280 285 280
negligible Daravair (air entrain.) 0 0 0 $3.75/Gal (fl. oz./cwt)
Daracem (water red.) 0 0 18.1 $5.65/Gal (fl. oz./cwt) % Air 1.5 1.5
1.5 -- Apparent Design K 232 206 226 -- Factor Cost ($/yd.sup.3)
$41.46 $43.64 $45.70 -- Sales Distribution (%) 6.81 44.35 48.84 --
Within Group Weighted Average $44.50 -- Cost ($/yd.sup.3) Total
Sales (%) of 12.81 -- Concrete Plant
COMPARATIVE EXAMPLES 12a-12c
[0345] The three mix designs of Comparative Examples 12a-12c have a
design strength of 4000 psi, a slump of 4 inches, and substantial
entrained air (5%). TABLE-US-00014 Comparative Example 12a 12b 12c
Cost (US$) Compressive Strength 4000 4000 4000 -- (psi) Slump
(inch) 4 4 4 -- Type 1 Cement 470 564 517 $104/Ton (lbs/yd.sup.3)
Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd.sup.3) Sand
(lbs/yd.sup.3) 1390 1340 1430 $8.12/Ton 1 inch Rock (lbs/yd.sup.3)
1710 1750 1750 $9.36/Ton Potable Water (lbs/yd.sup.3) 255 275 255
negligible Daravair (air entrain.) 4 5 4 $3.75/Gal (fl. oz./cwt)
Daracem (water red.) 0 0 18.1 $5.65/Gal (fl. oz./cwt) % Air 5 5 5
-- Apparent Design K 224 212 218 -- Factor Cost ($/yd.sup.3) $41.25
$44.05 $46.04 -- Sales Distribution (%) 77.31 22.69 0 -- Within
Group Weighted Average $41.89 -- Cost ($/yd.sup.3) Total Sales (%)
of 68.58 -- Concrete Plant
[0346] The following optimized concrete mix designs according to
Examples 9-12 were made according to the improved DOC process and
are intended to replace the 12 mix designs of Comparative Examples
9a-12c. Each optimized mix design takes the place of three mix
designs of similar attributes (e.g., the optimized mix design of
Example 9 takes the place of the pre-existing mix designs of
Comparative Examples 9a-9c). The optimization procedure assumed a
percent absorption for the sand and rock of 1.9% and 1.8%,
respectively, and a percent moisture of 4.57% and 3.18%,
respectively. TABLE-US-00015 Example 9 10 11 12 Cost (US$)
Compressive 3000 3000 4000 4000 -- Strength (psi) Slump (inch) 5 5
5 5 -- Type 1 Cement 336 293 376 362 $104/Ton (lbs/yd.sup.3) Type C
Fly Ash 101 88 113 109 $47.00/Ton (lbs/yd.sup.3) Sand
(lbs/yd.sup.3) 1768 1721 1742 1671 $8.12/Ton 1 inch Rock 1466 1429
1446 1387 $9.36/Ton (lbs/yd.sup.3) Potable Water 288 263 288 266
negligible (lbs/yd.sup.3) Daravair 0 1.4 0 1.4 $3.75/Gal (fl.
oz./cwt) % Air 2.5 5.6 2.5 5.2 $5.65/Gal Cost ($/yd.sup.3) $34.18
$31.38 $36.34 $35.09 -- Weighted Avg. Cost $34.59 -- ($/yd.sup.3)
Cost Savings ($/yd.sup.3) $3.99 $5.16 $8.16 $6.80 -- Per Mix Design
Weighted Avg. $6.66 -- Plant Cost Savings ($/yd.sup.3)
[0347] Each improved mix design of Examples 9-12 is able to take
the place of three pre-existing standard mix designs of similar
type because it satisfies the criteria of all three mix designs
while also having reduced cost. The reduced number of mix designs
is an additional cost savings as it simplifies the overall
manufacturing process.
[0348] The absolute cost savings ranged from a low of $2.04 per
yard (Example 9 relative to Comparative Example 9a) to a high of
$10.96 per yard (Example 12 relative to Comparative Example 12c).
The weighted average cost of the pre-existing mix designs of
Comparative Examples 9a-12c, based on the percentage of each mix
design sold by the manufacturing plant, is $41.24 per yard (as of
Oct. 27, 2005). The weighted average cost to manufacture concrete
using the four optimized mix designs based on existing sales
percentages for the 12 pre-existing mix designs of the manufacturer
would be $34.59 per yard at the same materials cost per component.
The average overall cost savings for the manufacturing plant would
therefore be $6.66 per yard, assuming the manufacturer were to
replace the 12 pre-existing mix designs of Comparative Examples
9a-12c with the optimized mix designs of Examples 9-12 and continue
to manufacture the same distribution of concrete as before.
EXAMPLES 13-16
[0349] Examples 13-16 illustrate four optimized concrete mix
designs that were prepared using the improved DOC process described
herein. The four mix designs of Examples 13-16 can replace twelve
pre-existing standard concrete mix designs of an existing concrete
manufacturing plant, which utilized the same 12 mix designs as in
Comparative Examples 1a-4c but manufactured concrete using a
different set of raw materials. Each mix design of Examples 13-16
corresponds to a group of three pre-existing mix designs of similar
type that guarantee a minimum compressive strength, at a specified
slump, and percentage of entrained air when delivered to the
customer. The pre-existing mix designs of the concrete
manufacturing plant, their components, cost (revised Oct. 27,
2005), and apparent design K factors, will be presented in four
groups of three concrete mix designs, each group having similar
properties or characteristics.
COMPARATIVE EXAMPLES 13a-13c
[0350] The three mix designs of Comparative Examples 13a-13c have a
design strength of 3000 psi, a slump of 4 inches, and minimal
entrained air (1.5%). TABLE-US-00016 Comparative Example 13a 13b
13c Cost (US$) Compressive Strength 3000 3000 3000 -- (psi) Slump
(inch) 4 4 4 -- Type 1 Cement 370 470 423 $104/Ton (lbs/yd.sup.3)
Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd.sup.3) Sand
(lbs/yd.sup.3) 1570 1470 1660 $8.12/Ton Pea Gravel (lbs/yd.sup.3)
1700 1700 1714 $9.36/Ton Potable Water (lbs/yd.sup.3) 280 280 265
Negligible Daravair (air entrain.) 0 0 0 $3.75/Gal (fl. oz./cwt)
Daracem (water red.) 0 0 14.8 $5.65/Gal (fl. oz./cwt) % Air 1.5 1.5
1.5 -- Apparent Design K 234 191 207 -- Factor Cost ($/yd.sup.3)
$36.14 $38.57 $39.75 -- Sales Distribution (%) 19.57 80.43 0 --
Within Group Weighted Average $38.10 -- Cost ($/yd.sup.3) Total
Sales (%) of 1.08 -- Concrete Plant
COMPARATIVE EXAMPLES 14a-14c
[0351] The three mix designs of Comparative Examples 14a-14c have a
design strength of 3000 psi, a slump of 4 inches, and substantial
entrained air (5%). TABLE-US-00017 Comparative Example 14a 14b 14c
Cost (US$) Compressive Strength 3000 3000 3000 -- (psi) Slump
(inch) 4 4 4 -- Type 1 Cement 350 470 423 $104/Ton (lbs/yd.sup.3)
Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd.sup.3) Sand
(lbs/yd.sup.3) 1510 1420 1560 $8.12/Ton Pea Gravel (lbs/yd.sup.3)
1750 1750 1740 $9.36/Ton Potable Water (lbs/yd.sup.3) 250 260 240
Negligible Daravair (air entrain.) 4 5 4 $3.75/Gal (fl. oz./cwt)
Daracem (water red.) 0 0 14.8 $5.65/Gal (fl. oz./cwt) % Air 5 5 5
-- Apparent Design K 237 189 199 -- Factor Cost ($/yd.sup.3) $35.50
$39.29 $39.95 -- Sales Distribution (%) 74.23 25.77 0 -- Within
Group Weighted Average $36.47 -- Cost ($/yd.sup.3) Total Sales (%)
of 17.53 -- Concrete Plant
COMPARATIVE EXAMPLES 15a-15c
[0352] The three mix designs of Comparative Examples 15a-15c have a
design strength of 4000 psi, a slump of 4 inches, and minimal
entrained air (1.5%). TABLE-US-00018 Comparative Example 15a 15b
15c Cost (US$) Compressive Strength 4000 4000 4000 -- (psi) Slump
(inch) 4 4 4 -- Type 1 Cement 470 564 517 $104/Ton (lbs/yd.sup.3)
Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd.sup.3) Sand
(lbs/yd.sup.3) 1530 1440 1530 $8.12/Ton Pea Gravel (lbs/yd.sup.3)
1746 1750 1750 $9.36/Ton Potable Water (lbs/yd.sup.3) 280 285 280
Negligible Daravair (air entrain.) 0 0 0 $3.75/Gal (fl. oz./cwt)
Daracem (water red.) 0 0 18.1 $5.65/Gal (fl. oz./cwt) % Air 1.5 1.5
1.5 -- Apparent Design K 232 206 226 -- Factor Cost ($/yd.sup.3)
$41.39 $43.57 $45.63 -- Sales Distribution (%) 6.81 44.35 48.84 --
Within Group Weighted Average $44.43 -- Cost ($/yd.sup.3) Total
Sales (%) of 12.81 -- Concrete Plant
COMPARATIVE EXAMPLES 16a-16c
[0353] The three mix designs of Comparative Examples 16a-16c have a
design strength of 4000 psi, a slump of 4 inches, and substantial
entrained air (5%). TABLE-US-00019 Comparative Example 16a 16b 16c
Cost (US$) Compressive Strength 4000 4000 4000 -- (psi) Slump
(inch) 4 4 4 -- Type 1 Cement 470 564 517 $104/Ton (lbs/yd.sup.3)
Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd.sup.3) Sand
(lbs/yd.sup.3) 1390 1340 1430 $8.12/Ton Pea Gravel (lbs/yd.sup.3)
1710 1750 1750 $9.36/Ton Potable Water (lbs/yd.sup.3) 255 275 255
negligible Daravair (air entrain.) 4 5 4 $3.75/Gal (fl. oz./cwt)
Daracem (water red.) 0 0 18.1 $5.65/Gal (fl. oz./cwt) % Air 5 5 5
-- Apparent Design K 224 212 218 -- Factor Cost ($/yd.sup.3) $41.19
$43.98 $45.97 -- Sales Distribution (%) 77.31 22.69 0 -- Within
Group Weighted Average $41.82 -- Cost ($/yd.sup.3) Total Sales (%)
of 68.58 -- Concrete Plant
[0354] The following optimized concrete mix designs according to
Examples 13-16 were made according to the improved DOC process and
are intended to replace the 12 mix designs of Comparative Examples
13a-16c. Each optimized mix design takes the place of three mix
designs of similar attributes (e.g., the optimized mix design of
Example 13 takes the place of the pre-existing mix designs of
Comparative Examples 13a-13c). The optimization procedure assumed a
percent absorption for the sand and pea gravel of 1.9% and 2.6%,
respectively, and a percent moisture of 4.57% and 3.18%,
respectively. TABLE-US-00020 Example 13 14 15 16 Cost (US$)
Compressive 3000 3000 4000 4000 -- Strength (psi) Slump (inch) 5 5
5 5 -- Type 1 Cement 352 305 403 373 $104/Ton (lbs/yd.sup.3) Type C
Fly Ash 106 91 121 112 $47.00/Ton (lbs/yd.sup.3) Sand
(lbs/yd.sup.3) 1734 1692 1690 1648 $8.12/Ton Pea Gravel
(lbs/yd.sup.3) 1429 1394 1392 1358 $9.36/Ton Potable Water 288 277
310 277 negligible (lbs/yd.sup.3) Daravair 0 1.4 0 1.4 $3.75/Gal
(fl. oz./cwt) % Air 2.4 5.8 2.6 5.8 $5.65/Gal Cost ($/yd.sup.3)
$34.75 $31.74 $37.40 $35.45 -- Weighted Avg. Cost $35.04 --
($/yd.sup.3) Cost Savings $3.34 $4.73 $7.03 $6.37 -- ($/yd.sup.3)
Per Mix Design Weighted Avg. $6.14 -- Plant Cost Savings
($/yd.sup.3)
[0355] Each improved mix design of Examples 13-16 is able to take
the place of three pre-existing standard mix designs of similar
type because it satisfies the criteria of all three mix designs
while also having reduced cost. The reduced number of mix designs
is an additional cost savings as it simplifies the overall
manufacturing process.
[0356] The absolute cost savings ranged from a low of $1.39 per
yard (Example 13 relative to Comparative Example 13a) to a high of
$10.53 per yard (Example 16 relative to Comparative Example 16c).
The weighted average cost of the pre-existing mix designs of
Comparative Examples 13a-16c, based on the percentage of each mix
design sold by the manufacturing plant, is $41.18 per yard (as of
Oct. 27, 2005). The weighted average cost to manufacture concrete
using the four optimized mix designs based on existing sales
percentages for the 12 pre-existing mix designs of the manufacturer
would be $35.04 per yard at the same materials cost per component.
The average overall cost savings for the manufacturing plant would
therefore be $6.14 per yard, assuming the manufacturer were to
replace the 12 preexisting mix designs of Comparative Examples
13a-16c with the optimized mix designs of Examples 13-16 and
continue to manufacture the same distribution of concrete as
before.
EXAMPLES 17-20
[0357] Examples 17-20 illustrate four optimized concrete mix
designs that were prepared using the improved DOC process described
herein. The four mix designs of Examples 17-20 can replace twelve
pre-existing standard concrete mix designs of an existing concrete
manufacturing plant that utilized the same 12 mix designs as in
Comparative Examples 1a-4c but manufactured concrete using a
different set of raw materials. Each mix design of Examples 17-20
corresponds to a group of three pre-existing mix designs of similar
type that guarantee a minimum compressive strength, at a specified
slump, and percentage of entrained air when delivered to the
customer. The pre-existing mix designs of the concrete
manufacturing plant, their components, cost (revised Oct. 27,
2005), and apparent design K factors, will be presented in four
groups of three concrete mix designs, each group having similar
properties or characteristics.
COMPARATIVE EXAMPLES 17a-17c
[0358] The three mix designs of Comparative Examples 17a-17c have a
design strength of 3000 psi, a slump of 4 inches, and minimal
entrained air (1.5%). TABLE-US-00021 Comparative Example 17a 17b
17c Cost (US$) Compressive Strength 3000 3000 3000 -- (psi) Slump
(inch) 4 4 4 -- Type 1 Cement 370 470 423 $104/Ton (lbs/yd.sup.3)
Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd.sup.3) Sand
(lbs/yd.sup.3) 1570 1470 1660 $10.80/Ton 1 inch Rock (lbs/yd.sup.3)
1700 1700 1714 $6.25/Ton Potable Water (lbs/yd.sup.3) 280 280 265
Negligible Daravair (air entrain.) 0 0 0 $3.75/Gal (fl. oz./cwt)
Daracem (water red.) 0 0 14.8 $5.65/Gal (fl. oz./cwt) % Air 1.5 1.5
1.5 -- Apparent Design K 234 191 207 -- Factor Cost ($/yd.sup.3)
$35.61 $37.91 $39.35 -- Sales Distribution (%) 19.57 80.43 0 --
Within Group Weighted Average $37.46 -- Cost ($/yd.sup.3) Total
Sales (%) of 1.08 -- Concrete Plant
COMPARATIVE EXAMPLES 18a-18c
[0359] The three mix designs of Comparative Examples 18a-18c have a
design strength of 3000 psi, a slump of 4 inches, and substantial
entrained air (5%). TABLE-US-00022 Comparative Example 18a 18b 18c
Cost (US$) Compressive Strength 3000 3000 3000 -- (psi) Slump
(inch) 4 4 4 -- Type 1 Cement 350 470 423 $104/Ton (lbs/yd.sup.3)
Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd.sup.3) Sand
(lbs/yd.sup.3) 1510 1420 1560 $10.80/Ton 1 inch Rock (lbs/yd.sup.3)
1750 1750 1740 $6.25/Ton Potable Water (lbs/yd.sup.3) 250 260 240
Negligible Daravair (air entrain.) 4 5 4 $3.75/Gal (fl. oz./cwt)
Daracem (water red.) 0 0 14.8 $5.65/Gal (fl. oz./cwt) % Air 5 5 5
-- Apparent Design K 237 189 199 -- Factor Cost ($/yd.sup.3) $34.81
$38.47 $39.35 -- Sales Distribution (%) 74.23 25.77 0 -- Within
Group Weighted Average $35.75 -- Cost ($/yd.sup.3) Total Sales (%)
of 17.53 -- Concrete Plant
COMPARATIVE EXAMPLES 19a-19c
[0360] The three mix designs of Comparative Examples 19a-19c have a
design strength of 4000 psi, a slump of 4 inches, and minimal
entrained air (1.5%). TABLE-US-00023 Comparative Example 19a 19b
19c Cost (US$) Compressive Strength 4000 4000 4000 -- (psi) Slump
(inch) 4 4 4 -- Type 1 Cement 470 564 517 $104/Ton (lbs/yd.sup.3)
Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd.sup.3) Sand
(lbs/yd.sup.3) 1530 1440 1530 $10.80/Ton 1 inch Rock (lbs/yd.sup.3)
1746 1750 1750 $6.25/Ton Potable Water (lbs/yd.sup.3) 280 285 280
Negligible Daravair (air entrain.) 0 0 0 $3.75/Gal (fl. oz./cwt)
Daracem (water red.) 0 0 18.1 $5.65/Gal (fl. oz./cwt) % Air 1.5 1.5
1.5 -- Apparent Design K 232 206 226 -- Factor Cost ($/yd.sup.3)
$40.73 $42.78 $44.97 -- Sales Distribution (%) 6.81 44.35 48.84 --
Within Group Weighted Average $43.71 -- Cost ($/yd.sup.3) Total
Sales (%) of 12.81 -- Concrete Plant
COMPARATIVE EXAMPLES 20a-20c
[0361] The three mix designs of Comparative Examples 20a-20c have a
design strength of 4000 psi, a slump of 4 inches, and substantial
entrained air (5%). TABLE-US-00024 Comparative Example 20a 20b 20c
Cost (US$) Compressive Strength 4000 4000 4000 -- (psi) Slump
(inch) 4 4 4 -- Type 1 Cement 470 564 517 $104/Ton (lbs/yd.sup.3)
Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd.sup.3) Sand
(lbs/yd.sup.3) 1390 1340 1430 $10.80/Ton 1 inch Rock (lbs/yd.sup.3)
1710 1750 1750 $6.25/Ton Potable Water (lbs/yd.sup.3) 255 275 255
negligible Daravair (air entrain.) 4 5 4 $3.75/Gal (fl. oz./cwt)
Daracem (water red.) 0 0 18.1 $5.65/Gal (fl. oz./cwt) % Air 5 5 5
-- Apparent Design K 224 212 218 -- Factor Cost ($/yd.sup.3) $40.40
$43.06 $45.17 -- Sales Distribution (%) 77.31 22.69 0 -- Within
Group Weighted Average $41.00 -- Cost ($/yd.sup.3) Total Sales (%)
of 68.58 -- Concrete Plant
[0362] The following optimized concrete mix designs according to
Examples 17-20 were made according to the improved DOC process and
are intended to replace the 12 mix designs of Comparative Examples
17a-20c. Each optimized mix design takes the place of three mix
designs of similar attributes (e.g., the optimized mix design of
Example 17 takes the place of the pre-existing mix designs of
Comparative Examples 17a-17c). The optimization procedure assumed a
percent absorption for the sand and rock of 1.9% and 3.2%,
respectively, and a percent moisture of 4.57% and 3.18%,
respectively. TABLE-US-00025 Example 17 18 19 20 Cost (US$)
Compressive 3000 3000 4000 4000 -- Strength (psi) Slump (inch) 5 5
5 5 -- Type 1 Cement 335 302 374 366 $104/Ton (lbs/yd.sup.3) Type C
Fly Ash 101 91 112 110 $47.00/Ton (lbs/yd.sup.3) Sand
(lbs/yd.sup.3) 1762 1693 1740 1658 $10.80/Ton 1 inch Rock 1422 1366
1404 1337 $6.25/Ton (lbs/yd.sup.3) Potable Water 295 274 295 270
negligible (lbs/yd.sup.3) Daravair 0 1.4 0 1.4 $3.75/Gal (fl.
oz./cwt) % Air 2.4 5.5 2.2 5.5 $5.65/Gal Cost ($/yd.sup.3) $34.01
$31.63 $36.12 $35.14 -- Weighted Avg. Cost $34.64 -- ($/yd.sup.3)
Cost Savings ($/yd.sup.3) $3.45 $4.12 $7.59 $5.86 -- Per Mix Design
Weighted Avg. $5.75 -- Plant Cost Savings ($/yd.sup.3)
[0363] Each improved mix design of Examples 17-20 is able to take
the place of three pre-existing standard mix designs of similar
type because it satisfies the criteria of all three mix designs
while also having reduced cost. The reduced number of mix designs
is an additional cost savings as it simplifies the overall
manufacturing process.
[0364] The absolute cost savings ranged from a low of $1.60 per
yard (Example 17 relative to Comparative Example 17a) to a high of
$10.03 per yard (Example 20 relative to Comparative Example 20c).
The weighted average cost of the pre-existing mix designs of
Comparative Examples 17a-20c, based on the percentage of each mix
design sold by the manufacturing plant, is $40.39 per yard (as of
Oct. 27, 2005). The weighted average cost to manufacture concrete
using the four optimized mix designs based on existing sales
percentages for the 12 pre-existing mix designs of the manufacturer
would be $34.64 per yard at the same materials cost per component.
The average overall cost savings for the manufacturing plant would
therefore be $5.75 per yard, assuming the manufacturer were to
replace the 12 pre-existing mix designs of Comparative Examples
17a-20c with the optimized mix designs of Examples 17-20 and
continue to manufacture the same distribution of concrete as
before.
[0365] The next two examples are newly optimized mix designs for
self-leveling concrete. Self-leveling concrete manufactured
according to the mix designs of Examples 21 and 22 is characterized
as having sufficiently high slump such that it can level out due to
gravity alone without working and also having sufficient
cohesiveness such that it does not significantly segregate (i.e.,
separate into heavier and lighter components due to gravity).
EXAMPLE 21
[0366] The follow mix design for a self leveling concrete
composition was designed using the improved DOC process disclosed
herein. Such compositions are characterized as being air entrained
and having greater than an 8-inch slump when in a wet condition
prior to curing and a minimum compressive strength of 4000 psi
after 7 days of curing. All weights are SSD. TABLE-US-00026
Component Amount Cement 366 lbs/yd.sup.3 Fly Ash 110 lbs/yd.sup.3
Sand 1801 lbs/yd.sup.3 Rock 1219 lbs/yd.sup.3 Water 261
lbs/yd.sup.3 Daravair 1.3 fl.oz/cwt* Rheomac VMA450 4.0 fl.oz/cwt
Glenium 3030 2.0 fl.oz/cwt* Note: Rheomac added at plant with batch
water; Daravair adjusted at plant for min. 5% air; on-site
adjustment of slump with Glenium 3030
EXAMPLE 22
[0367] The follow mix design for a self leveling concrete
composition was designed using the improved DOC process disclosed
herein. Such compositions are characterized as being air entrained
and having greater than an 8-inch slump when in a wet condition
prior to curing and a minimum compressive strength of 4000 psi
after 7 days of curing. All weights are SSD. TABLE-US-00027
Component Amount Cement 519 lbs/yd.sup.3 Fly Ash 130 lbs/yd.sup.3
Sand 1857 lbs/yd.sup.3 Rock 1245 lbs/yd.sup.3 Water 261
lbs/yd.sup.3 Daravair 1.3 fl.oz/cwt* P. NC534 11.6 fl.oz/cwt
Glenium 3030 5.0 fl.oz/cwt* Note: Glenium added at plant for 4''
slump; Daravair adjusted at plant for min. 5% air; accelerator
added on-site followed immediately by adjustment of slump on-site
with additional Glenium 3030 if necessary.
[0368] The present invention may be embodied in other specific
forms without departing from its spirit or essential
characteristics. The described embodiments are to be considered in
all respects only as illustrative and not restrictive. The scope of
the invention is, therefore, indicated by the appended claims
rather than by the foregoing description. All changes which come
within the meaning and range of equivalency of the claims are to be
embraced within their scope.
* * * * *