AHP in foam concrete

Department of Civil Engineering
Dr.Mahalingam College of Engineering and
Technology, Pollachi-642 003
APPLICATION OF TWO PHASE AHP-TOPSIS METHOD IN
SELECTION OF FOAM CONCRETE MIXES
Project Guide:
Dr. T. Sakthivel, Ph.D.,
Asst. Professor
Dr. Mahalingam college of engineering and technology
Project Co- guide:
Mrs. S. Suthaviji, M.E.,
Asst. Professor
Dr. Mahalingam college of engineering and technology
Project by
Nivitha A (19MST002)
II year M.E. Structural Engineering
Dr. Mahalingam college of engineering
and technology
1

• Abstract
• Introduction
• Objectives
• Literature reviews
• Methodology
• Flowchart of the integrated two phase AHP & TOPSIS
• Steps involved in AHP & TOPSIS method
• Results & discussion
• Conclusions
PRESENTATION OUTLINE
2

Nowadays, decision making plays a major role in deciding the execution of any task. Two phase includes AHP
as well as TOPSIS, both falls under multi criteria decision making (MCDM) tools. These techniques are now
also brought in the field of civil engineering. MCDM techniques are used in various applications of civil
engineering. Concrete mix design is the science to obtain concrete proportions of cement, water, and aggregate,
based on the particular concrete design method and their mix design parameters. However, the suitability of
concrete proportion for foam concrete depends on water, cement, fine aggregate, foaming agent and super
plasticiser ratios. This paper implements the multicriteria decision-making techniques (MCDM) for ranking
foam concrete mix factors and uses the AHP and TOPSIS tools for deciding the final outcomes. The comparison
of AHP and TOPSIS is made on the tests of mechanical properties of foam concrete mixes with compressive
strength, split tensile strength and flexural strength test results obtained at 7, 14 and 28 days respectively.
Results of the experiment are used to cross verify the results obtained from AHP and TOPSIS. Optimum foam
concrete mixes for mechanical properties is M3 (10% GGBS) at 28 days and the least suitable foam concrete
mix is M5 (20% GGBS).
ABSTRACT
3

Multiple-criteria decision making (MCDM)
• Humans make decisions all the time. Decision-making is a very complex and difficult task. During the past decades,
operations research (OR) has come a long way as a field that supports scientific management. OR mainly deals with model
building and algorithmic optimization procedures that facilitate the analysis of complex real-world problems.
• Multiple-criteria decision making (MCDM) has been one of the fastest growing problem areas in many disciplines. The
central problem is how to evaluate a set of alternatives in terms of a number of criteria.
• It is considered as a complex decision making (DM) tool involving both quantitative and qualitative factors. In recent
years, several MCDM techniques and approaches have been suggested to choosing the optimal probable options.
• Each problem has multiple, usually conflicting objectives/criteria and has a different unit of measurement.
• The focus of MCDM lies in fact on decision support, rather than on a theoretical explanation of rational choice.
• It reduces the chance of biased decision making for available choices, as results obtained are cross-verified with
practical experiments.
• These techniques deal with real life problems and provide best solution from all the alternatives available.
INTRODUCTION
4

• The analytic hierarchy process (AHP), is a structured technique for organizing and analysing complex decisions, based
on mathematics and psychology.
• It was developed by Thomas L. Saaty in the 1970s. It represents an accurate approach to quantifying the weights of decision criteria.
Individual experts’ experiences are utilized to estimate the relative magnitudes of factors through pair-wise comparisons.
• Rather than prescribing a "correct" decision, it helps decision makers find one that best suits their goal and their understanding of the
problem.
ANALYTIC HIERARCHY PROCESS
5
Suitable
concrete mix
Compressive
strength
Flexural
strength
% of different materials
used and the different
ages of concrete
Split tensile
strength
GOAL
CRITERIA
ALTERNATIVES
Schematic diagram of AHP analysis in selecting a suitable concrete mix

• TOPSIS, known as Technique for Order of Preference by Similarity to Ideal Solution, is a multi-criteria decision analysis
method which was originally developed by Ching-Lai Hwang and Yoon in 1981 with further developments by Yoon in
1987, and Hwang, Lai and Liu in 1993.
• In this method, the decision is made with the positive ideal solution and the negative ideal solution calculated.
• It selects the alternatives which is closest to the ideal solution and farthest from the negative ideal solution.
• Then it is used in finding the relative closeness coefficient which helps in ranking the alternatives.
TECHNIQUE FOR ORDER OF PREFERENCE
BY SIMILARITY TO IDEAL SOLUTION
6

• The most widely used tools of MCDM includes AHP and TOPSIS. The study presents a framework to identify suitable
concrete mix factors found from the concrete mix design using the two-phase AHP and TOPSIS approach.
• AHP approach uses hierarchy to give solution as per the assigned criteria of objective whereas TOPSIS approach compares
the available ideal solution obtained through calculation.
• The AHP method is used to calculate the weights of the elements (dimensions, criteria and indicators), however, TOPSIS
aims to obtain the final ranking of the alternative closest to the ideal solution.
TWO-PHASE AHP-TOPSIS
7
Criteria AHP TOPSIS Two-phase AHP-TOPSIS (proposed)
Use of hierarchical structure -
To provide objective criteria’s weight -
Comparison of ideal solutions -
Ranking method
Easy to understand

• Foam concrete, also known as Lightweight Cellular Concrete (LCC), Low Density Cellular Concrete (LDCC), and other
terms is defined as a cement-based slurry, with a minimum of 20% (per volume) foam entrained into the plastic mortar.
• It is also called aircrete, foamed concrete, foamcrete or reduced density concrete.
• As mostly no coarse aggregate is used for production of foam concrete the correct term would be called mortar instead of
concrete; it may be called "foamed cement" as well.
• The density of foam concrete usually varies from 400 kg/m3 to 1800 kg/m3. The density is normally controlled by
substituting fully or part of the fine aggregate with foam.
• The foam is created using a foaming agent, mixed with water and air from a generator. The foaming agent must be able to
produce air bubbles with a high level of stability, resistant to the physical and chemical processes of mixing, placing and
hardening.
• Foam concrete is fire resistant, and its thermal and acoustical insulation properties make it ideal for a wide range of
purposes, from insulating floors and roofs, to void filling.
• A few of the applications of foam concrete are: Embankments, precast blocks / wall elements / panel, cast-in-situ / cast-in-
place walls, etc.,
FOAM CONCRETE
8

• To study and select the most suitable concrete mixes under several alternatives having number of sub-criteria is done by
multi criteria decision making (MCDM) tools i.e., two phase AHP and TOPSIS approach.
• An integrated AHP & TOPSIS method are used in order to obtain more probabilistic model analysis in the selection of
foam concrete mixes.
OBJECTIVES
9

LITERATURE REVIEWS
TITLE AUTHOR(s) CONTENT
Optimum selection of concrete batch plant
location model using analytic hierarchy
process (AHP)
Ibrahim. M. Mahdi, et al Final results for (The Selection of Optimum CBP Location) model by selecting
the most optimum site location according to the importance of each factor. The
results have appeared as follows: (CBP location inside region) is preferred by
56.4% (CBP location outside region) is preferred by 43.6% which Normalized
values are obtained from them by summing and dividing each by the sum.
A review of application of multi-criteria
decision making methods in construction
Daniel Jato-Espinoa, et al Applications of multi-criteria decision analysis to construction through a one to
one review of a total of 88 scientific publications presented throughout the last
two decades. Moreover, the review demonstrates how their use is gradually
spreading all over the world, although Asia and Europe clearly excel in this
respect, with almost 80% of the total of papers. Decision makers tend to use the
most widely applied so far, which generally also results in time savings, due to
the fact that there is a deeper knowledge about it in literature.
Multi-criteria decision making for cement
mortar mixture selection by fuzzy TOPSIS
Eyyup Gulbandilara, et al In this paper, TOPSIS method was used as a decision tool to solve the cement
mortar selection problem. The ranking is based on the criteria weighed by the
decision maker. The reason for choosing the fuzzy TOPSIS method is when
selecting the best alternative to evaluate both the most suitable and the most
unsuitable alternative together. As a result, it aims to find the best alternative
among the alternatives according to the weight determined by the decision
makers.
10

LITERATURE REVIEWS
Multiple Criteria Decision Making Theory,
Methods, and Applications in Engineering
Ching-Ter Chang, et al Investigators contribute original research articles as well as review articles on all
aspects of MCDM approaches and fuzzy multi objective programming methods.
Development of advanced MCDM methods for direct or indirect use in
engineering, decision science, and manufacturing operations settings.
Contributions containing computational issues, search strategies, and modelling
and solution techniques to practical problems are also encouraged.
Decision support model for design of
high-performance concrete mixtures using
two-phase AHP-TOPSIS approach
Mohahmed, et al Concrete mix design depends on various mix factors related to ingredients of
concrete and their combinations. An integrated AHP-TOPSIS based MCDM
model to rank the concrete mix guidelines for performance of concrete under
water, sulphate, and chloride attack and performance of concrete for
underground conditions and for evolving the performance based concrete mix
design techniques based on the required mix factors.
State of art surveys of overviews on
MCDM/MADM methods
Edmundas Kazimieras
Zavadskasa , et al
The paper presents synopsis of numerous publications, which describe the use of
traditional MCDM methods and some of the relatively recently developed
methods. Recently, development of hybrid and modular methods is becoming
increasingly important. They are based on previously developed well-known
methods. In order to help researchers and practitioners interested in hybrid
MCDM techniques and applications of hybrid MCDM methods, it is necessary
to publish reviews on these issues in future.
11

LITERATURE REVIEWS
An Approach for Ready Mixed Concrete
Selection For Construction Companies
through Technique for Order Preference by
Similarity to Ideal Solution (TOPSIS)
Technique
Ashish H. Makwana, et al TOPSIS is a simple and understandable method for selecting a suitable bricks.
For various bricks selection, determined attribute set, determined weight of each
criteria, selected criteria ranking method – TOPSIS method and presented a case
study on brick selection. The problem’s solution results show that the proposed
model can be successfully applied for various bricks ranking. The problem
solution result shows that Fly ash (FAL – G) bricks > Sugarcane bassage ash
bricks > Human hair bricks > Clay bricks, it means, that Fly ash (FAL – G)
bricks is the best and Clay bricks is the worst. TOPSIS technique further research
work can be carried out on Ready Mixed Concrete selection as per case study.
An Analysis of Multi-Criteria Decision
Making Methods
Mark Velasquez, et al In recent years, because of ease of use due to advancing technologies, combining
different methods has become common place in MCDA. This paper assessed the
more common methods of MCDM in order to benefit practitioners to choose a
method for solving a specific problem. Identification of common MCDM
methods and identification of strengths and weaknesses is a major step in
establishing the foundation of research in this area, but it is only the first step.
This research could lead to a survey of users to assess which advantages and
disadvantages are more prevalent for each method. The industry could then begin
to research new methods which utilize and incorporate advantages, while
accounting for or altogether eliminating disadvantages.
12

LITERATURE REVIEWS
Technique for order preference by
similarity to ideal solution (TOPSIS) for
spatial decision problems
D. Ozturk a, et al The paper presents an application of GIS-based TOPSIS by applying the
ArcGIS-TOPSIS tool to a real-world problem that involved selection of
settlement site in AtakumSamsun, Turkey. Because the methods performed by
ArcGIS-TOPSIS are generic, the tool can be used for many other decision
applications, including natural resource management, land-use planning and
suitability evaluation.
The TOPSIS of Different Ideal Solution
and Distance Formula of Fuzzy Soft Set in
Multi-Criteria Decision Making
Erin Nabilah Rejab, et al In summary, the comparative study of FPIS and FNIS, as well as the distance
formula in fuzzy soft set on TOPSIS, is important because it can aid future
researchers in solving problems and making decisions. It is possible to suggest
that three distance formulas, as well as various types of FPIS and FNIS, could be
utilised in conjunction with the MCDM technique.
Decision Making Using the Analytic
Hierarchy Process (AHP); A Step by Step
Approach
Hamed taherdoost Analytical Hierarchy Process is one of the most inclusive system which is
considered to make decisions with multiple criteria because this method gives to
formulate the problem as a hierarchical and believe a mixture of quantitative and
qualitative criteria as well. This paper summarizes the process of conducting
Analytical Hierarchy Process (AHP).
13

LITERATURE REVIEWS
Using the analytic hierarchy process for
decision making in engineering
applications: some challenges
Evangelos Triantaphyllou,
et al
This paper examines some of the practical and computational issues involved
when the AHP method is used in engineering applications. The AHP provides a
convenient approach for solving complex MCDM problems in engineering. A
summary of the results of a number of studies on the AHP and pairwise
comparisons by the authors can be found. The above observations suggest that
MCDM methods should be used as decision support tools.
Selection of Method in Construction
Industry by using Analytical Hierarchy
Process (AHP)
P Z Razi, et al This paper aiming in identifying the criteria and suitability for selecting different
kind of construction delivery method in construction by using the multi-criteria
decision making (MCDM) namely the Analytical Hierarchy Process (AHP)
method. Results provide some empirical finding which contractor is suitable
employing the industrial building system(IBS) method and traditional method.
Review of application of analytic
hierarchy process (AHP) in construction
Amos Darko, et al The analytic hierarchy process (AHP) has gained increasing attention in
construction management (CM) domain as a technique to analyse complex
situations and make sound decisions. This paper provides a useful reference for
researchers and practitioners interested in the application of AHP in CM. Future
research is needed to compare and contrast between AHP and other multicriteria
decision-making methods; such work could reveal which techniques provide
optimized solutions under various decision-making scenarios.
14

LITERATURE REVIEWS
An experimental investigation on fibre
reinforced foam concrete
Shalini P., et al., Variables used are Fly ash (70%, 80%, 90%, 100%), MSP (10%, 20%, 30%),
recron-3s fibre 0.25% and 0.5% in this paper. Fly Ash reduces the dry density of
concrete. MSP increases the density of concrete and in certain condition it
exceeds the lightweight concrete limit. When compared to the conventional
concrete strength and density is lower for foamed concrete. Compressive
strength w/o fibre (80% fly ash & 20% MSP) is 7.26 N/mm2 and with fibre (80%
fly ash, 20% MSP & 0.5% fibre) is 12.34 N/mm2
Effect of different types of light weight
aggregate on strength and modulus of
elasticity of cellular concrete
Suhad Mohammed Abd,
et al., In this paper, water-cement: 0.28%, 8% superplasticizer, 10% Silica Fume and
0.4% steel fiber for all mixtures are used. Percentage of replacement fly ash
(50%) show increase compressive strength- approximate of (39%).
Experimental Investigation on Foam
Concrete with Partial Replacement of
Cement By GGBS
Arya Krishnan, et al., w/c ratio 0.5, foaming agent (1%, 2%, 3%, 4%), GGBS (0%,5%,10%,15%,20%).
Compressive strength for 2% foaming agent & 10% GGBS is 19.11 MPa at 28
days. Effect of GGBS increase compressive strength & tensile strength of foam
concrete.
15

LITERATURE REVIEWS
Experimental Investigation on Sand
Replaced Foam Concrete
Hemalatha M, et al., Cement: Fine aggregate (M sand: Eco sand: Foundry sand) ratio is 1:0.5:0.5,
foaming agent (4%, 8%, 12%, 16%), w/c ratio 0.3 & 0.35. Highest compressive
strength of 4% foaming agent is 8.75N/mm2
Experimental Study on the Effect of Water
on the Properties of Cast In Situ Foamed
Concrete
Wenhui Zhao, et al., Foam concrete densities (300 to 800 kg/m3) are taken into consideration. For the
water-level changed condition, after 100 cycles of immersion, the compressive
strength is about 51.5%–84.5% of that in the standard curing state and the elastic
modulus is about 63.5%–82.2% of that in the standard curing state. Moreover, the
strength ratio and the elastic modulus ratio increase with the increase of dry
density.
Engineering Properties of Lightweight
Foamed Concrete Incorporated with Palm
Oil Fuel Ash (POFA)
Yong Chun Yip Targeted density of 1300 kg/m3, w/c ratio 0.52 to 0.62, POFA (25%, 50%),
Compressive strength is gained the highest in the later stage with 6.89MPa,
7.34MPa and 8.34MPa for 28, 56 and 90 days respectively. LFC-PF25 possesses
highest splitting tensile strength as 0.652MPa, 0.927MPa, 0.995MPa and
1.127MPa for 7, 28, 56, and 90 days respectively. LFC-PF25 possesses highest
flexural strength as 2.011MPa, 2.167MPa and 2.451MPa for 28, 56 and 90 days
respectively.
16

LITERATURE REVIEWS
Performance properties of structural fibred-
foamed concrete
Y.H. Mugahed Amran,
et al.,
Densities of foamed concrete (1000, 1300, 1600, and 1900 kg/m3), foam
(0.2%,0.3%, 0.4%, 0.5%). FC specimens without SF and with density of 1900
kg/m3, 58, 42, and 31 MPa of compressive strength was observed in the
specimens with foam volumes of 20%, 30%, and 40%, respectively.
Effect of Adding Waste Plastic Fibers on
Properties of Modified Foamed Concrete at
Various Densities
Nebras M. Mhedi, et al., Concrete densities (1300, 1500, and 1700 kg/m3), w/b ratio 0.35, w/c ratio 0.3,
WPF (0%, 1%). Highest tensile strength is for Fc7aw as 3.035 MPa. The addition
of foam, fly ash and silica fume resulted in a slightly smaller consistency in
contrast to the unmodified mix. The addition of WPF resulted in higher
consistency, where the measured spread diameter is smaller than the diameter of
the modified mix.
Strength Parameters of Foamed Geopolymer
Reinforced with GFRP Mesh
Rafał Krzywo, et al., Three types of coal fly ash (Jaworzno power plant - anthracite coal, Belchatow
and Turow power plants - lignite coal), foaming agent (1%, 2%, and 3%).
average cube compressive strength was 73% higher and flexural strength 29%
higher for the fly ash from Jaworzno than for those from the other two power
plants.
17

LITERATURE REVIEWS
An experimental investigation on light
weight foam cement blocks with quarry dust
replacement for fine aggregate
Madhusudana Reddy B,
et al.,
Densities (800 kg/m3, 1000 kg/m3, 1200 kg/m3, 1400 kg/m3, 1600 kg/m3, 1800
kg/m3), foam (for 30 litres of water 1 litre of foam). Compressive strength for
1200 kg/m3 density is 12.36 Mpa. Compressive strength and water absorption
results show 1200 kg/m3 is the optimum density.
Evaluation of performance of foam produced
with different methodologies for use in foam
concrete production
S S Sahu, et al.,
SLS concentration (1% to 10%), CMC concentration (0.1 % to 0.3%).
Comparative studies on foam production methods indicated that foam produced
based on compressed air method (foam generator) is of better quality with lesser
liquid fraction and drainage compared to that of foam produced with stirrer.
Strength Parameters of Foamed Geopolymer
Reinforced with GFRP Mesh
Osman Gencel, et al., expanded perlite was replaced with 0, 30, 50, 70, and 100% of glass sand, w/b
ratio 0.5, foaming agent with densities of 50 kg/m3, 100 kg/m3. Highest
Compressive strength for G100F50 is 5.32 MPa & G100F100 is 1.34 MPa. Best
overall performing foam concrete mix was the mix containing 50 kg/m3 foaming
agent, 70% glass sand and 30% expanded perlite aggregate.
18

METHODOLOGY
19
Topic selection
Objectives
Literature survey
Data collection
Steps involved in
AHP & TOPSIS

FLOWCHART OF INTEGRATED TWO PHASE AHP & TOPSIS
20
Tabulate the alternatives
considered
Calculate the Pairwise comparison
matrix for each alternative
Determine weighted decision matrix
Calculate normalized priority
vector matrix
Identify positive & negative ideal
solutions
Measure the relative closeness
coefficient of each alternative
Ranking
AHP
TOPSIS

• Step 1: Tabulate the alternatives considered
The alternatives considered in this project are compressive strength, flexural strength & split tensile strength
test results at different ages of foam concrete.
• Step 2: Calculate the Pairwise comparison matrix for each alternative
Pairwise comparison matrix for each alternative is m x m real matrix, where m is the evaluation criteria. Each
entry 𝑎𝑗𝑘 of the matrix A represents the importance of the 𝑗𝑡ℎ criterion relative to the 𝑘𝑡ℎ criterion. If
a. 𝑎𝑗𝑘 > 1, then the 𝑗𝑡ℎ criterion is more important than the 𝑘𝑡ℎ criterion
b. 𝑎𝑗𝑘 < 1, then the 𝑗𝑡ℎ criterion is less important than the 𝑘𝑡ℎ criterion
c. 𝑎𝑗𝑘 = 1, if two criteria have the same importance
Hence the pair-wise comparison matrix is generated as follows:
A =
21
STEPS INVOLVED IN AHP & TOPSIS
a11 …. a1k
…. …. ….
aj1 …. 𝑎𝑗𝑘

• Step 3: Determine weighted decision matrix
First the sum of each column of the pairwise comparison matrix is added and then dividing each matrix values
𝑎𝑗𝑘 by its sum of each column gives another matrix. Later average is taken for each row of the pairwise
comparison matrix to obtain the weights.
A =
Sum n1 …. nn
weights (X)
A = =
22
a11 …. a1k
…. …. ….
a11/ n1 …. a1k/ nn
…. …. ….
aj1/ n1 …. 𝑎𝑗𝑘/ nn
x1j
….
xij

• Step 4: Calculate normalized priority vector matrix
Eigen values are calculated for each alternatives by multiplying matrix A & matrix X, later dividing AX matrix
by matrix X.
AX =
=
eigen value = λ (average)
Then to calculate the normalized priority vector values of each alternatives are calculated by
23
a11 …. a1k
…. …. ….
x1j
….
xij
λ1
….
λn
Vij = xij
(∑(xjk)2)1/2

• Step 5: Identify positive & negative ideal solutions
From the normalized values obtained the highest is considered as the positive ideal solutions (vj
+) & lowest is
considered as the negative ideal solutions (vj
-).
Separation from positive ideal solutions:
H+ = [ ∑ (vj
+– vij)2]1/2
Separation from Negative ideal solutions:
H- = [ ∑ (vj
-– vij)2]1/2
• Step 6: Measure the relative closeness coefficient of each alternative
The relative closeness coefficients are determined by using the below formula
24
Ci
* = H-
(H+ + H-)

• Step 7: Ranking
Ranking the preference order is done based on the values of the relative closeness coefficients (Ci
*) found. The
highest Ci
* is considered as the most preferable mix and the lowest Ci
* is the least preferred.
Highest Ci
* Lowest Ci
* (descending order)
Further, with the above mentioned steps that are involved in AHP & TOPSIS calculations are to be used in foam concrete
mixes test results.
25

FOAM CONCRETE WITH PARTIAL REPLACEMENT OF CEMENT BY GGBS
STEP 1: Mechanical Properties of foam concrete with partial replacement of cement by GGBS
Mechanical properties of foam concrete with partial replacement of cement by GGBS is shown in
the tabulate below. Compression & split tensile strength test results obtained at 7 days & 28 days
are taken into consideration.
26
RESULTS & DISCUSSION
Mix %
GGBS CS at 7 days CS at 14 days CS at 28 days TS at 7 days TS at 14 days TS at 28 days
M1
0 12.59 16.4 18.22 1.48 1.69 1.83
M2
5 12.88 16.6 18.44 1.55 1.55 1.69
M3
10 13.33 16.8 19.11 1.62 1.65 1.9
M4
15 12.22 15.5 17.11 1.41 1.43 1.5
M5
20 8.88 11.3 12.22 1.27 1.34 1.48

STEP 2: Pair-wise comparison for all alternatives
Pair-wise comparison is done for all alternatives with respect to criteria for compressive strength
27
CS
(N/mm2) Mix
7 days 14 days 28 days
M1 M2 M3 M4 M5 M1 M2 M3 M4 M5 M1 M2 M3 M4 M5
7 days
M1 1.000 0.977 0.944 1.030 1.418 0.768 0.758 0.749 0.812 1.114 0.691 0.683 0.659 0.736 1.030
M2 1.023 1.000 0.966 1.054 1.450 0.785 0.776 0.767 0.831 1.140 0.707 0.698 0.674 0.753 1.054
M3 1.059 1.035 1.000 1.091 1.501 0.813 0.803 0.793 0.860 1.180 0.732 0.723 0.698 0.779 1.091
M4 0.971 0.949 0.917 1.000 1.376 0.745 0.736 0.727 0.788 1.081 0.671 0.663 0.639 0.714 1.000
M5 0.705 0.689 0.666 0.727 1.000 0.541 0.535 0.529 0.573 0.786 0.487 0.482 0.465 0.519 0.727
14 days
M1 1.303 1.273 1.230 1.342 1.847 1.000 0.988 0.976 1.058 1.451 0.900 0.889 0.858 0.959 1.342
M2 1.319 1.289 1.245 1.358 1.869 1.012 1.000 0.988 1.071 1.469 0.911 0.900 0.869 0.970 1.358
M3 1.334 1.304 1.260 1.375 1.892 1.024 1.012 1.000 1.084 1.487 0.922 0.911 0.879 0.982 1.375
M4 1.231 1.203 1.163 1.268 1.745 0.945 0.934 0.923 1.000 1.372 0.851 0.841 0.811 0.906 1.268
M5 0.898 0.877 0.848 0.925 1.273 0.689 0.681 0.673 0.729 1.000 0.620 0.613 0.591 0.660 0.925
28 days
M1 1.447 1.415 1.367 1.491 2.052 1.111 1.098 1.085 1.175 1.612 1.000 0.988 0.953 1.065 1.491
M2 1.465 1.432 1.383 1.509 2.077 1.124 1.111 1.098 1.190 1.632 1.012 1.000 0.965 1.078 1.509
M3 1.518 1.484 1.434 1.564 2.152 1.165 1.151 1.138 1.233 1.691 1.049 1.036 1.000 1.117 1.564
M4 1.359 1.328 1.284 1.400 1.927 1.043 1.031 1.018 1.104 1.514 0.939 0.928 0.895 1.000 1.400
M5 0.971 0.949 0.917 1.000 1.376 0.745 0.736 0.727 0.788 1.081 0.671 0.663 0.639 0.714 1.000
SUM 17.601 17.205 16.624 18.134 24.955 13.512 13.349 13.190 14.297 19.611 12.162 12.017 11.596 12.951 18.134

Pair-wise comparison is done for all alternatives with respect to criteria for split tensile strength
28
TS
(N/mm2) Mix
7 days 14 days 28 days
7 days
M1 1.000 0.955 0.914 1.050 1.165 0.876 0.955 0.897 1.035 1.104 0.809 0.876 0.779 0.987 1.000
M2 1.047 1.000 0.957 1.099 1.220 0.917 1.000 0.939 1.084 1.157 0.847 0.917 0.816 1.033 1.047
M3 1.095 1.045 1.000 1.149 1.276 0.959 1.045 0.982 1.133 1.209 0.885 0.959 0.853 1.080 1.095
M4 0.953 0.910 0.870 1.000 1.110 0.834 0.910 0.855 0.986 1.052 0.770 0.834 0.742 0.940 0.953
M5 0.858 0.819 0.784 0.901 1.000 0.751 0.819 0.770 0.888 0.948 0.694 0.751 0.668 0.847 0.858
14 days
M1 1.142 1.090 1.043 1.199 1.331 1.000 1.090 1.024 1.182 1.261 0.923 1.000 0.889 1.127 1.142
M2 1.047 1.000 0.957 1.099 1.220 0.917 1.000 0.939 1.084 1.157 0.847 0.917 0.816 1.033 1.047
M3 1.115 1.065 1.019 1.170 1.299 0.976 1.065 1.000 1.154 1.231 0.902 0.976 0.868 1.100 1.115
M4 0.966 0.923 0.883 1.014 1.126 0.846 0.923 0.867 1.000 1.067 0.781 0.846 0.753 0.953 0.966
M5 0.905 0.865 0.827 0.950 1.055 0.793 0.865 0.812 0.937 1.000 0.732 0.793 0.705 0.893 0.905
28 days
M1 1.236 1.181 1.130 1.298 1.441 1.083 1.181 1.109 1.280 1.366 1.000 1.083 0.963 1.220 1.236
M2 1.142 1.090 1.043 1.199 1.331 1.000 1.090 1.024 1.182 1.261 0.923 1.000 0.889 1.127 1.142
M3 1.284 1.226 1.173 1.348 1.496 1.124 1.226 1.152 1.329 1.418 1.038 1.124 1.000 1.267 1.284
M4 1.014 0.968 0.926 1.064 1.181 0.888 0.968 0.909 1.049 1.119 0.820 0.888 0.789 1.000 1.014
M5 1.000 0.955 0.914 1.050 1.165 0.876 0.955 0.897 1.035 1.104 0.809 0.876 0.779 0.987 1.000
SUM 15.804 15.090 14.438 16.589 18.417 13.840 15.090 14.176 16.357 17.455 12.781 13.840 12.311 15.593 15.804

Step 3: Determine Weighted Decision Matrix
Weighted Decision Matrix for compressive strength
29
MIX
CS at 7 days CS at 14 days CS at 28 days
WEIGHTS
CS at 7
days
M1 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057
M2 0.058 0.058 0.058 0.058 0.058 0.058 0.058 0.058 0.058 0.058 0.058 0.058 0.058 0.058 0.058 0.058
M3 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060
M4 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055
M5 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040
CS at 14
days
M1 0.074 0.074 0.074 0.074 0.074 0.074 0.074 0.074 0.074 0.074 0.074 0.074 0.074 0.074 0.074 0.074
M2 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075
M3 0.076 0.076 0.076 0.076 0.076 0.076 0.076 0.076 0.076 0.076 0.076 0.076 0.076 0.076 0.076 0.076
M4 0.070 0.070 0.070 0.070 0.070 0.070 0.070 0.070 0.070 0.070 0.070 0.070 0.070 0.070 0.070 0.070
M5 0.051 0.051 0.051 0.051 0.051 0.051 0.051 0.051 0.051 0.051 0.051 0.051 0.051 0.051 0.051 0.051
CS at 28
days
M1 0.082 0.082 0.082 0.082 0.082 0.082 0.082 0.082 0.082 0.082 0.083 0.082 0.082 0.082 0.082 0.082
M2 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083
M3 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.086
M4 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077 0.077
M5 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055

Weighted Decision Matrix For Split Tensile Strength
30
MIX
TS at 7 days TS at 14 days TS at 28 days
WEIGHTS
TS at 7
days
M1 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063
M2 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066
M3 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069 0.069
M4 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060
M5 0.054 0.054 0.054 0.054 0.054 0.054 0.054 0.054 0.054 0.054 0.054 0.054 0.054 0.054 0.054 0.054
TS at 14
days
M1 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072
M2 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066
M3 0.071 0.071 0.071 0.071 0.071 0.071 0.071 0.071 0.071 0.071 0.071 0.071 0.071 0.071 0.071 0.071
M4 0.061 0.061 0.061 0.061 0.061 0.061 0.061 0.061 0.061 0.061 0.061 0.061 0.061 0.061 0.061 0.061
M5 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057 0.057
TS at 28
days
M1 0.078 0.078 0.078 0.078 0.078 0.078 0.078 0.078 0.078 0.078 0.078 0.078 0.078 0.078 0.078 0.078
M2 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072 0.072
M3 0.081 0.081 0.081 0.081 0.081 0.081 0.081 0.081 0.081 0.081 0.081 0.081 0.081 0.081 0.081 0.081
M4 0.064 0.064 0.064 0.064 0.064 0.064 0.064 0.064 0.064 0.064 0.064 0.064 0.064 0.064 0.064 0.064
M5 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063 0.063

Calculation Of The Sum Of The Weights & It’s Square Roots
31
MIX
WEIGHTS
OF CS
(X1)
WEIGHTS
OF TS
(X2) X1 + X2
SQUARES
OF X1
SQUARES
OF X2
M1 0.057 0.063 0.120 0.003 0.004
M2 0.058 0.066 0.124 0.003 0.004
M3 0.06 0.069 0.129 0.004 0.005
M4 0.055 0.060 0.115 0.003 0.004
M5 0.04 0.054 0.094 0.002 0.003
M1 0.074 0.072 0.146 0.005 0.005
M2 0.075 0.066 0.141 0.006 0.004
M3 0.076 0.071 0.147 0.006 0.005
M4 0.07 0.061 0.131 0.005 0.004
M5 0.051 0.057 0.108 0.003 0.003
M1 0.082 0.078 0.160 0.007 0.006
M2 0.083 0.072 0.155 0.007 0.005
M3 0.086 0.081 0.167 0.007 0.007
M4 0.077 0.064 0.141 0.006 0.004
M5 0.055 0.063 0.118 0.003 0.004
SUM 0.069 0.067
SQRT 0.263 0.259

STEP 4: Normalized priority vector for fifteen foam concrete with partial replacement of cement by GGBS and their
summation
Calculation of Eigen value for compressive strength
32
A
1 0.977 0.944 1.03 1.418 0.768 0.758 0.749 0.812 1.114 0.691 0.683 0.659 0.736 1.03
1.023 1 0.966 1.054 1.45 0.785 0.776 0.767 0.831 1.14 0.707 0.698 0.674 0.753 1.054
1.059 1.035 1 1.091 1.501 0.813 0.803 0.793 0.86 1.18 0.732 0.723 0.698 0.779 1.091
0.971 0.949 0.917 1 1.376 0.745 0.736 0.727 0.788 1.081 0.671 0.663 0.639 0.714 1
0.705 0.689 0.666 0.727 1 0.541 0.535 0.529 0.573 0.786 0.487 0.482 0.465 0.519 0.727
1.303 1.273 1.23 1.342 1.847 1 0.988 0.976 1.058 1.451 0.9 0.889 0.858 0.959 1.342
1.319 1.289 1.245 1.358 1.869 1.012 1 0.988 1.071 1.469 0.911 0.9 0.869 0.97 1.358
1.334 1.304 1.26 1.375 1.892 1.024 1.012 1 1.084 1.487 0.922 0.911 0.879 0.982 1.375
1.231 1.203 1.163 1.268 1.745 0.945 0.934 0.923 1 1.372 0.851 0.841 0.811 0.906 1.268
0.898 0.877 0.848 0.925 1.273 0.689 0.681 0.673 0.729 1 0.62 0.613 0.591 0.66 0.925
1.447 1.415 1.367 1.491 2.052 1.111 1.098 1.085 1.175 1.612 1 0.988 0.953 1.065 1.491
1.465 1.432 1.383 1.509 2.077 1.124 1.111 1.098 1.19 1.632 1.012 1 0.965 1.078 1.509
1.518 1.484 1.434 1.564 2.152 1.165 1.151 1.138 1.233 1.691 1.049 1.036 1 1.117 1.564
1.359 1.328 1.284 1.4 1.927 1.043 1.031 1.018 1.104 1.514 0.939 0.928 0.895 1 1.4
0.971 0.949 0.917 1 1.376 0.745 0.736 0.727 0.788 1.081 0.671 0.663 0.639 0.714 1
X1
0.057
0.058
0.06
0.055
0.04
0.074
0.075
0.076
0.07
0.051
0.082
0.083
0.086
0.077
0.055
AX1
0.851
0.871
0.902
0.826
0.601
1.109
1.122
1.136
1.048
0.764
1.232
1.247
1.292
1.157
0.826
EIGEN VALUE
14.935
15.016
15.025
15.024
15.013
14.986
14.966
14.948
14.974
14.984
15.026
15.025
15.027
15.026
15.024
15.000
= =

Calculation of Eigen value for split tensile strength
33
A
1 0.955 0.914 1.05 1.165 0.876 0.955 0.897 1.035 1.104 0.809 0.876 0.779 0.987 1
1.047 1 0.957 1.099 1.22 0.917 1 0.939 1.084 1.157 0.847 0.917 0.816 1.033 1.047
1.095 1.045 1 1.149 1.276 0.959 1.045 0.982 1.133 1.209 0.885 0.959 0.853 1.08 1.095
0.953 0.91 0.87 1 1.11 0.834 0.91 0.855 0.986 1.052 0.77 0.834 0.742 0.94 0.953
0.858 0.819 0.784 0.901 1 0.751 0.819 0.77 0.888 0.948 0.694 0.751 0.668 0.847 0.858
1.142 1.09 1.043 1.199 1.331 1 1.09 1.024 1.182 1.261 0.923 1 0.889 1.127 1.142
1.047 1 0.957 1.099 1.22 0.917 1 0.939 1.084 1.157 0.847 0.917 0.816 1.033 1.047
1.115 1.065 1.019 1.17 1.299 0.976 1.065 1 1.154 1.231 0.902 0.976 0.868 1.1 1.115
0.966 0.923 0.883 1.014 1.126 0.846 0.923 0.867 1 1.067 0.781 0.846 0.753 0.953 0.966
0.905 0.865 0.827 0.95 1.055 0.793 0.865 0.812 0.937 1 0.732 0.793 0.705 0.893 0.905
1.236 1.181 1.13 1.298 1.441 1.083 1.181 1.109 1.28 1.366 1 1.083 0.963 1.22 1.236
1.142 1.09 1.043 1.199 1.331 1 1.09 1.024 1.182 1.261 0.923 1 0.889 1.127 1.142
1.284 1.226 1.173 1.348 1.496 1.124 1.226 1.152 1.329 1.418 1.038 1.124 1 1.267 1.284
1.014 0.968 0.926 1.064 1.181 0.888 0.968 0.909 1.049 1.119 0.82 0.888 0.789 1 1.014
1 0.955 0.914 1.05 1.165 0.876 0.955 0.897 1.035 1.104 0.809 0.876 0.779 0.987 1
X2
0.063
0.066
0.069
0.060
0.054
0.072
0.066
0.071
0.061
0.057
0.078
0.072
0.081
0.064
0.063
AX2
0.946
0.991
1.036
0.901
0.812
1.080
0.991
1.055
0.914
0.857
1.170
1.080
1.215
0.976
0.946
EIGEN VALUE
15.021
15.013
15.012
15.023
15.034
15.005
15.013
14.858
14.987
15.028
15.000
15.005
14.998
15.252
15.021
15.018
= =

34
ALTERNATIVES
CRITERIA
CS TS SUM
EIGEN VALUE 15 15.018 -
7 DAYS
M1 0.057 0.063 0.12
M2 0.058 0.066 0.124
M3 0.06 0.069 0.129
M4 0.055 0.060 0.115
M5 0.04 0.054 0.094
14
DAYS
M1 0.074 0.072 0.146
M2 0.075 0.066 0.141
M3 0.076 0.071 0.147
M4 0.07 0.061 0.131
M5 0.051 0.057 0.108
28
DAYS
M1 0.082 0.078 0.16
M2 0.083 0.072 0.155
M3 0.086 0.081 0.167
M4 0.077 0.064 0.141
M5 0.055 0.063 0.118
Weights for fifteen foam concrete with partial replacement of cement by GGBS and their summation
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0
0.02
0.04
0.06
0.08
0.1
SUM
OF
PRIORITY
VECTOR
VALUES
PRIORITY
VECTOR
VALUES
CONCRETE MIXES
Priority vector values of all alternatives by AHP
CS TS SUM

Normalized priority vector for fifteen foam concrete with partial replacement of cement by GGBS
35
ALTERNATIVES
CRITERIA
CS TS
7 DAYS
M1 0.217 0.243
M2 0.221 0.255
M3 0.228 0.266
M4 0.209 0.232
M5 0.152 0.209
14
DAYS
M1 0.281 0.278
M2 0.285 0.255
M3 0.289 0.274
M4 0.266 0.236
M5 0.194 0.220
28
DAYS
M1 0.312 0.301
M2 0.316 0.278
M3 0.327 0.313
M4 0.293 0.247
M5 0.209 0.243
Vij = xij
(∑(xjk)2)1/2

Step 5: Identify positive & negative ideal solutions
• Positive ideal solutions (vj
+) = {0.327, 0.313} – maximum priority vector values
• Negative ideal solutions (vj
-) = {0.152, 0.209} – minimum priority vector values
Separation from positive ideal solutions:
H+ = [ ∑ (vj
+– vij)2]1/2
Separation from Negative ideal solutions:
H- = [ ∑ (vj
-– vij)2]1/2
36
0.130 0.073
0.121 0.083
0.109 0.096
0.143 0.062
0.204 0.000
0.057 0.147
H+ =
0.071
H- =
0.141
0.054 0.152
0.098 0.117
0.162 0.043
0.019 0.185
0.037 0.178
0.000 0.204
0.074 0.146
0.137 0.067

STEP 6: Relative Closeness Coefficient (RCC)
The relative closeness coefficient was calculated by using the below formula
37
Ci
* = H-
(H+ + H-)
0.360
0.405
0.467
0.301
0.000
0.719
0.664
Ci
* = 0.737
0.544
0.211
0.906
0.829
1.000
0.663
0.328
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
RELATIVE
CLOSENESS
COEFFICIENT
CONCRETE MIXES
RCC of all alternatives by TOPSIS

STEP 7: Ranking
From the obtained results of the relative closeness coefficient, the ranking is done based on the descending order of the
values.
Hence, the best concrete mix is M3 (10% GGBS) at 28 days & the worst concrete mix is M5 (20% GGBS) at 7 days.
38
AGE MIX RCC RANKING
7 DAYS
M1 0.360 11
M2 0.405 10
M3 0.467 9
M4 0.301 13
M5 0.000 15 WORST
14
DAYS
M1 0.719 5
M2 0.664 6
M3 0.737 4
M4 0.544 8
M5 0.211 14
28
DAYS
M1 0.906 2
M2 0.829 3
M3 1.000 1 BEST
M4 0.663 7
M5 0.328 12
0.000
0.200
0.400
0.600
0.800
1.000
1.200
1.400
PRIORITY
VECTOR
VALUES
CONCRETE MIXES
Summary of both technique
TOPSIS AHP

From the present study of two phase AHP-TOPSIS techniques, the following conclusions can be inferred.
1. With the help of ranking, the most suitable concrete mix for mechanical properties is M3 (10%
GGBS) at the age of 28 days and M5 (20% GGBS) is the worst alternative at the age of 7 days.
2. Both AHP and TOPSIS are different but the final results are most identical.
3. These tools help in distinguishing the best and worst concrete mix. Therefore, MCDM
techniques play vital role in decision making process and can now be widely used in civil
engineering.
4. This study will also provide economical as decision making is quite easy.
5. It can be validated by comparing the mechanical properties of the concrete mix results with thw
AHP-TOPSIS final results.
39
CONCLUSIONS

AHP in foam concrete

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