Evaluating the Elastic Constants of Concrete, Modified with Fly Ash and Marble Waste, and Their Effects on High-Rise Buildings Using ETABS Software

Abstract

This study involves partially replacing coarse aggregate with marble waste products, and partially replacing cement with fly ash, in order to obtain the best results. This study aims to determine how the use of these waste products affects the mechanical properties of the resulting concrete, which could have valuable implications for sustainable construction practices. Different samples were prepared by adding marble waste products, marble slurry powder, fly ash, and a combination of these in the concrete. The modulus of elasticity and Poisson’s ratio for the samples were calculated, and it was found that the samples with admixtures had lower moduli of elasticity and higher Poisson’s ratio values than did the conventional concrete mixture. Based on the values of elastic constants E and µ of the general and modified concrete mixtures, two structures are modelled for each concrete mixture and simulated using ETABS Ultimate software to evaluate and compare the practical applicability of the modified concrete mixtures. Both of the envisaged buildings are considered identical, having shear walls placed symmetrically. The response of the structure was analysed by applying earthquake load, wind load, and respective combinations according to IS codes. The storey displacement and storey stiffness under the lateral load and load combination were determined. The results showed that the modified concrete had comparable storey displacement and storey stiffness values to those of conventional concrete. The results indicate that the use of admixtures in concrete has several benefits, including improved workability, as well as adequate strength and durability, including resistance to deformation, as compared to conventional concrete.

1. Introduction

Concrete is a highly prevalent construction material on a global scale, owing to its exceptional mechanical properties, long-lasting nature, and adaptable characteristics. Nevertheless, the manufacturing process of concrete has a substantial ecological influence, due to the considerable energy consumption and the release of greenhouse gases linked to cement manufacturing [1,2]. Consequently, there is an increasing scholarly focus on the development of more environmentally friendly variants of concrete, obtained through the integration of byproducts derived from various industrial sectors.

The manufacturing process of cement, a crucial component in the creation of concrete, constitutes a significant contribution to carbon emissions. The production process entails subjecting limestone and other raw materials to elevated temperatures, resulting in the liberation of carbon dioxide (CO₂) as a secondary output [3,4]. According to the International Energy Agency, the cement sector is responsible for around 7% of worldwide carbon dioxide (CO₂) emissions [5].

In order to mitigate the environmental impacts of concrete, various strategies can be employed. These include utilising alternative materials during cement manufacturing, enhancing the efficiency of cement production processes, minimising the distances travelled during the transportation of raw materials and finished products, and embracing sustainable construction practices that prioritise energy conservation and waste reduction [6,7,8].

In essence, sustainable development in the context of concrete pertains to the use of ecologically sound and socially conscientious approaches in the manufacturing and utilisation of concrete. The objective encompasses the mitigation of environmental consequences associated with concrete manufacturing, the optimisation of natural resource utilisation, and the enhancement of social and economic advantages derived from concrete production. The aforementioned objectives can be attained by employing alternative materials, such as recycled aggregates and supplemental cementitious materials, optimising production methods to minimise waste and energy consumption, and designing concrete structures that enhance durability and resilience. The implementation of sustainable developmental practices in the concrete sector is of paramount importance for ensuring the long-term survival of the construction industry and for promoting environmental well-being. With the mounting worldwide call for infrastructure, the concrete sector’s role in leading green construction initiatives and safeguarding Earth’s health grows ever more pivotal.

In the quest to create sustainable concrete using marble waste powder (MWP), marble slurry powder (MSP), and fly ash, the challenges that occur include achieving consistent material properties across diverse samples, determining the optimal mixture for the best balance of strength and durability, and ensuring the modified concrete’s performance rivalled traditional concrete were paramount. The economic feasibility of such sustainable materials and understanding the long-term performance of the modified concrete also possess significant hurdles. To address these challenges, seventeen varied samples were used, each with different proportions of sustainable materials. Through rigorous testing, the elastic constants of each mixture were assessed, using the Compressometer cum Extensometer. The elastic constants serve as baselines for comparison between the modified concrete mixtures and the conventional concrete. Further evaluation was carried out for the structural response of the modified concrete under various loads, as defined by Indian Standard codes. The findings revealed that, despite the challenges, the modified concrete not only held its own against traditional concrete, but in some respects, even outperformed it, highlighting its immense potential for broader applications in sustainable construction.

2. Literature Review

2.1. Literature Review on Marble Waste

Khyaliya et al. [9] studied the substitution of river sand with marble waste in lean mortar. The experimental results demonstrated that the most favourable results were obtained when including marble debris at a range of 25–50%. This led to a decrease in water requirements and a notable enhancement in strength, with values increasing from 2.84 MPa to 7.04 MPa at a 50% replacement ratio. Additionally, the durability of the material was significantly improved. The marble waste mixture, comprising 25%, demonstrated favourable performance when subjected to sodium sulphate and sulfuric acid exposure. In accordance with the findings of Omer Farroq et al. [10], it is evident that marble waste can serve as a feasible alternative to river sand in lean mortar. It is advised that the replacement range for marble waste should fall within the range of 5–15%.

The study conducted by Valeria Corinaldesi et al. [11] investigated the utilisation of marble powder, a by-product generated during the process of cutting marble, as a potential mineral addition in self-compacting concrete. The powder demonstrated a narrow particle size distribution, with 90% of particles being smaller than 50 μm, 50% of which were smaller than 7 μm. The experiment involved the evaluation of cement pastes that included the addition of marble powder. These pastes were tested in different mortar combinations, specifically those with a sand–cement ratio of 3:1. The findings of the study revealed that replacing 10% of sand with marble powder resulted in the highest compressive strength, while also preserving the workability of the mixture. This level of substitution was shown to be comparable to the reference mixture after a curing period of 28 days. The use of marble powder resulted in enhanced cohesiveness in both mortar and concrete, even when combined with a superplasticising additive. The resulting specified minimal thixotropy values indicated the absence of energy loss during the installation of the concrete.

According to the findings of Bhaskar Prakash et al. [12], it was observed that the incorporation of additional cement additives, such as silica fume and fly ash, resulted in improved durability performance when mixed with WMP. A scanning electron microscopy (SEM) analysis demonstrated a high degree of compaction in cement composites with lower levels of cement replacement (10%) with waste mineral powder (WMP).

Singh et al. [13] extensively examined the use of wasted marble powder as a partial replacement for concrete sand and cement. This study explores substitution ratios with marble powder at 10–15%. This addition increases compressive and split tensile strengths by 15–20%. Marble powder can replace 35–50% of sand and improve strength and durability due to better compaction. The cost analysis shows that replacing 15% of cement with marble powder saves 9.077%. Replacing 25% of sand costs 3.27% more. Marble powder in concrete reduces carbon emissions, thus reducing carbon footprints. This approach also reduces energy consumption by 1.05%. Kore et al. [14] also stated that marble powder in concrete reduces the environmental impact of cement and sand extraction.

Silva et al. [15] investigated the effects of different ratios of waste marble fine aggregates on concrete. The researchers conducted an evaluation of the feasibility, compactness, robustness, and resistance to wear of several mixtures, including varying proportions (0%, 20%, 50%, and 100%) of alternative aggregates in place of the primary aggregates. The results indicated a decrease in workability, as well as a decrease in compressive and cracking tensile strengths across all concrete mixtures as the proportion of replacement material rose. Singh et al. [16], using regression analysis, concluded that WMP contributes approximately 8% to the total compressive strength of concrete.

Choudhary et al. [17] discovered that the porosity, interfacial transition zone (ITZ), and unit weight of the self-compacting concrete (SCC) mixtures had significant impacts on the ultrasonic pulse velocity (UPV) and dry material equivalent (DME) values. The utilisation of multiple replacement techniques, namely MSP, FA, and SF, at elevated levels resulted in reductions in both the ultimate pore volume (UPV) and dynamic mechanical energy (DME) values. However, when the combined mixture was analysed, it was found to have the highest UPV value, as well as a DME value that was comparable to the control mixture. The blended mixture exhibited enhanced microstructural properties. The examination conducted using field emission scanning electron microscopy (FESEM) revealed the presence of a reduced number of voids and an enhanced interfacial transition zone (ITZ).

Choudhary et al. [18] conducted a study with the objective of examining the durability performance of self-compacting high-strength concrete (SCHSC). This was achieved by including silica fume and fly ash as mineral admixtures, as well as waste marble slurry (WMS) as a potential substitute for cement. The durability values of the SCHSC mixtures were assessed using a series of tests, including water permeability, chloride penetration, carbonation, corrosion, and drying shrinkage. The microstructural development of SCHSC mixtures was analysed using X-ray diffraction (XRD) techniques. The findings of the study indicated that the inclusion of mineral additives and waste marble slurry (WMS) resulted in enhanced durability characteristics in the asphalt mixtures. The durability characteristics validate the superior performance of the SCHSC (self-compacting high-strength concrete) including 10% waste marble slurry (WMS), 15% fly ash, and 5% silica fume.

Vardhan et al. [19] investigated the behaviour of setting, the development of strength, and the microstructural characteristics of cement pastes with marble powder. The incorporation of cement replacement materials at a maximum of 10% preserves the desirable characteristics of the mixture, thus improving its workability while ensuring that its compressive strength remains uncompromised. The expansion and setting characteristics of cement are not affected by variations in the chemical composition between marble powder and cement. Sharma et al. [20] found that an excessive amount of replacement leads to delays in the process of hydration and results in the formation of a porous microstructure, which has a detrimental impact on the mechanical characteristics. The study recommends a maximum replacement of 5–10% of cement with marble powder in construction applications.

In the study conducted by Reddy et al. [21], the feasibility of substituting natural sand with waste marble dust (WMD) in concrete was investigated. The results of their study demonstrated that WMD can be utilised as a viable alternative to fine aggregate in concrete, with a substitution rate of up to 50%, while maintaining the concrete’s strength without any notable drop. It is worth mentioning that a substitution rate of 50% resulted in the attainment of the maximum compressive strength values of 23.91 MPa at the end of a 7-day period, and 35.54 MPa after 28 days, specifically for M25 grade concrete. Once the replacement percentage exceeded 50%, there was a noticeable decrease in compressive strength.

The study conducted by Gupta et al. [22] showed that the incorporation of a blend of marble cutting waste (MCW) and fly ash (FA) exhibits considerable potential in the development of environmentally sustainable concrete and in mitigating cement usage. In the context of high-strength concrete blends, it is possible to replace a portion of the overall cement content, specifically up to 10%, with a material known as MCW. This substitution has been seen to yield enhancements in the fresh, mechanical, and durability characteristics of the concrete. The inclusion of 15% fly ash as a replacement for cement did not exhibit any detrimental consequences. The utilisation of a combination of 15% fine aggregate and 10% medium-coarse aggregate demonstrated improved performance, resulting in the production of high-strength concrete that is both cost-effective and long-lasting.

Furthermore, the study conducted by Ahmadi et al. [23] revealed that the substitution of fine aggregate with marble waste resulted in a greater compressive strength compared to the control sample. The incorporation of steel fibres at a concentration of 0.5% resulted in enhancements to the microstructure of the cement paste, leading to an increase in compressive strength. The act of increasing the fibre count and substituting marble aggregate resulted in an elevation of the bending strength. The performance of mixtures incorporating both steel fibres and marble debris exhibited superior results compared to mixtures including only steel fibre. As the percentage of recycled aggregates and the dose of steel fibres increased, there was a corresponding drop in the rate of water absorption.

2.2. Literature Review on Fly Ash

Khankhaje et al. [24] reviewed several previous studies and observed that the incorporation of fly ash into Portland cement resulted in a decrease in void content and permeability. This phenomenon was attributed to the filler effect exhibited by fly ash. The study determined that the most effective level of cement substitution with FA ranged from 10% to 30%. Nevertheless, elevated replacement levels had an adverse effect on hydration, resulting in a decline in strength. The incorporation of fine aggregates into Portland cement resulted in improved resistance to abrasion and decreased drying shrinkage as compared to conventional Portland cement. In summary, the utilisation of fly ash as a partial substitute for cement presents an environmentally benign approach that contributes to the promotion of a more sustainable form of Portland cement.

Anish et al. [25] studied the utilisation of fly ash and silica fume in concrete. The strength increases in the concrete types were analysed over a curing period of up to 56 days, both with and without the presence of a superplasticiser. The research encompassed the substitution of 50% of cement with fly ash and 20% of fly ash with silica fume in M30 grade concrete. The results of the study provided empirical evidence supporting the efficacy of augmenting cement concrete with the incorporation of fly ash, silica fume, and superplasticiser. Mohana et al. [26] revealed that mortars containing 1% nano-fly ash demonstrated superior compressive strength compared to other compositions under various temperature settings. The mortars exhibited a remarkable capacity to maintain 67% of their initial strength following exposure to a peak temperature of 900 °C. This resulted in a notable decrease of 46% in greenhouse gas emissions, as well as a significant reduction of 18.3% in construction expenses pertaining to the implementation of the environmentally friendly mortar.

Singhal et al. [27] observed that the replacement of 35% of ordinary Portland cement with fly ash resulted in an elevation in the compaction factor and a decrease in the required dosage of admixture. However, the use of MSP as a replacement for fine aggregate resulted in a loss in workability. The integration of MSP and FA as substitutes for fine aggregate and OPC, respectively, has demonstrated enhanced permeability characteristics.

Shukla et al. [28] emphasised the importance of appropriate curing techniques for concrete under diverse environmental circumstances. The use of fly ash has been found to enhance strength by approximately 30% under typical loads and 20% under more challenging conditions. The material provides enhanced workability, reduced heat release, improved resistance to sulphates, and increased resilience to weather conditions. Fly ash is in accordance with the criteria set by sustainable construction standards and exhibits a wide range of applications. The research conducted in India’s building sector shows encouraging results. Significantly, the utilisation of fly ash contributes to environmental preservation through the mitigation of CO₂ emissions, the regulation of the greenhouse effect, and the mitigation of pollutants.

The examination of the function of high-rise structures in urban sustainability and energy consumption has been the subject of numerous studies. Saroglou et al. [29] emphasised the importance of constructing envelope designs in tall buildings, with a specific focus on the Mediterranean environment. They draw attention to the potential of double-skin façades (DSFs) in enhancing thermal efficiency. According to a comprehensive assessment conducted between 2005 and 2020 [30], it has been shown that high-rise structures, despite their space efficiency, tend to demonstrate increased energy consumption and carbon emissions. This conclusion was reiterated in further research [31], which examined the energy efficiency of tall office buildings, proposing DSFs as a viable method for achieving a balance between visibility and energy performance. Furthermore, a particular emphasis on the residential domain [32] has revealed the energy-conserving capabilities of fibre-reinforced lightweight aggregate concrete (LWAC), which presents significant energy efficiency advantages when compared to conventional building materials. In the context of urban construction dynamics, it is worth noting that a thermodynamic study [33] highlighted the significant increase in reinforced concrete high-rise buildings in Asian cities during the post-war period. This surge may be attributed mostly to economic incentives, rather than a focus on long-term structural durability. This development signifies a crucial turning point in the field of urban construction.

The carbon dioxide (CO₂) emissions resulting from the manufacture of concrete exhibit a direct correlation with the quantity of cement incorporated into the concrete mixture. For a more tangible perspective, consider that the production of 1 ton of cement results in approximately 0.9 tons of CO₂ emissions [34]. By replacing a portion of the cement with fly ash or marble powder, the need for cement is reduced, leading to potential decreases in CO₂ emissions and resulting in potential environmental benefits.

3. Research Methodology

3.1. Materials Used

In the present work, binding material ordinary Portland cement (OPC) 43 grade, conforming to BIS 269 [35], was obtained from M/s Ultratech Cement Limited, Bhopal, India. The fine aggregates used in this study consisted of sand granules sourced from the Narmada River, whereas the coarse aggregates of sizes 10 mm and 20 mm, derived from crushed basalt rock, were obtained from M/s Dhakad Traders, Bhopal, India. The fine aggregate, classified as Zone II, and the coarse aggregates have both been found in accordance to specifications outlined in BIS 383 [36].

Samples of wet MSP and MWP (Figure 1b) were collected from a local stone-cutting facility, M/s Taj Stone Company, Bhopal, India. The MSP obtained from the stone-cutting facility was first dried under the sun and then sieved through 75 µm, while the MWP was used as it was procured. Fly ash (FA) was obtained from the power generation plant of M/s Bharat Heavy Electricals Limited, Bhopal. Following the BIS 3812 [37], 82% of the procured FA, by weight, was passed through a 45µm sieve. The physical appearances of MSP, MWP, and FA can be observed in Figure 1. The specifications of the materials used are shown in

Table 1. Specifications of the materials used.

Specifications	Cement	Marble Waste Product	Marble Slurry	Fly Ash
Form	Powder	Coarse aggregate	Powder	Powder
Grain size	100% < 0.09 mm	100% < 10 mm	92% < 0.075 mm	82% < 0.045 mm
Colour	Dark Grey	White	Off-white	Light Grey
Specific Gravity	3.16	2.8	2.7	2.45

.

To determine various physical parameters of OPC and other materials, instruments manufactured by M/s Zeal International were used. Specific gravity was determined using a Le Chatelier flask; standard consistency, initial setting time, and final setting time were determined using a Vicat apparatus; soundness was determined using a Le Chatelier apparatus [38,39,40,41].

For the characterisation of materials—MSP, MWP, and FA—an X-ray Diffractometer with CuKα radiation (M/s Bruker AXS D2 Phaser) was used. The X-ray diffractograms for the OPC, MWP and FA are exhibited in Figure 2. A Slump Cone Apparatus (M/s Zeal International) was used to determine the workability of fresh concrete. A Compressometer cum Extensometer (LABTEST by M/s Zeal International) was employed for determining the lateral and longitudinal deformations in the cylindrical specimen by mounting it on a Compression Testing Machine (M/s Enkay Enterprises, New Delhi, India) with a capacity of 2000 kN. The software ETABS Ultimate [42], procured from M/s Computers & Structures Inc., USA, was used for the structural analysis and design of the structure.

The standard consistency, initial setting time, final setting time, and soundness of OPC were determined as 28%, 124 min, 236 min, and 1 mm, respectively. Other specifications of OPC, MWP, MSP, and FA are given in Table 1.

3.2. Modeling with ETABS

To evaluate and compare the practical applicability of the modified concrete mixtures, ETABS Ultimate software was used. ETABS software enhances structural modelling and architectural studies in 3D construction assessment and design. It integrates inspection and construction processes and works with building information modelling (BIM) to improve collaboration and efficiency. Users use it to generate complicated graphical diagrams, evaluate complex constructs, and visualise conceptual data. The program’s simple method comprises generating grid lines; arranging joints, frames, and shells; and assigning loads and structural attributes. Based on these assignments, analysis, design, and detailing provide graphically or tabularly displayed outputs suitable for printing or for incorporation into other software tools. Comprehensive functionality and user-friendliness empower building professionals with ETABS Ultimate.

A G + 20 storied RCC building is modelled in ETABS Ultimate software using the basic project information, such as units, building code, and design preferences, and a grid system for the building structure is created. This includes defining the number of columns in each direction, as well as the spacing between the two columns. In the present case, the metric system for units has been used and criteria from IS codes have been considered. The Z-axis has been taken as the vertical axis, while both the X- and Y-axes are in the horizontal plane. The specifications and design details of the G + 20 RCC building are shown in

Table 2. Specifications and design details of the G + 20 RCC building modelled in ETABS Ultimate.

Parameter	Description
Software	ETABS Ultimate
Number of Storeys	G + 20
Units	Metric System
Building Code	IS codes
Axis System	Z (Vertical), X & Y (Horizontal)
Total Height of the Structure	63 m
Height of Each Floor	3 m
Width in X-axis	25.725 m
Length in Y-axis	27.075 m
Column Spacing in X-direction	3.2 m
Column Spacing in Y-direction	3.4 m
Column Size	600 mm × 600 mm
Beam Size	300 mm × 400 mm
Slab Thickness	150 mm
Wall Thickness	200 mm
RCC Structure Specific Density	25 kN/m3
Material Nature (Columns, Beams, Slabs)	Isotropic
Loads Considered	Dead, Live, Wind, Seismic
Load Generation Tool	ETABS load generator

.

The height of the structure is 63 m, whereas the height of each floor is 3 m. The width of the structure in the X-axis is 25.725 m and the length in the Y-axis is 27.075 m. The grid system is made such that the spacing between two adjacent columns in the X-direction is 3.2 m, and that for the Y-direction is 3.4 m. The size of columns has been taken as 600 mm × 600 mm, while that of beams is taken as 300 mm × 400 mm. The thickness of each slab in the building is taken as 150 mm and that of each wall is taken as 200 mm. The RCC structure’s specific density is taken as 25 kN/m³.

It is also worth mentioning that the columns, beams, and slabs of the present structure are isotropic in nature. Shear walls, each with a width of 100 mm, have been placed diagonally opposite on the edges of the structure on each floor and around the elevator shaft. The loads, including dead loads, live loads, wind loads, and seismic loads, are applied to the structure using the ETABS load generator. The structure is analysed to determine the structural response of the building with respect to all of the above-mentioned loads, as illustrated in Figure 3.

3.3. Mix-Proportion Method

Standard concrete designated as specimen ‘A’ of minimum compressive strength (25 MPa) was prepared in accordance with the specifications outlined in BIS 456–2000 [43]. The preparation of mixture ‘A’ was carried out with OPC, water, coarse aggregate, and fine aggregate, as specified in

Table 3. Mix-proportioning quantities.

Mix Label		Items	OPC (kg/m3)	Water (L)	MSP (kg/m3)	FA (kg/m3)	Coarse Aggregates (kg/m3)	MWP (kg/m3)	Fine Aggregates (kg/m3)
	Mix
A	M25 Conventional Concrete		424	175	0	0	1247.54	0	583
B	5% MWP		424	175	0	0	1185.163	62.377	583
C	10%MWP		424	175	0	0	1122.786	124.754	583
D	15%MWP		424	175	0	0	1060.409	187.131	583
E	5% MSP		402.8	175	21.2	0	1274.54	0	583
F	10%MSP		381.6	175	42.4	0	1247.54	0	583
G	15%MSP		360.4	175	63.6	0	1247.54	0	583
H	5% FA		402.8	175	0	21.2	1247.54	0	583
I	10%FA		381.6	175	0	42.4	1247.54	0	583
J	15%FA		360.4	175	0	63.6	1247.54	0	583
K	5%FA + 5%WMP		402.8	175	0	21.2	1185.163	62.377	583
L	10%FA + 10%WMP		381.6	175	0	42.4	1122.786	124.754	583
M	5%FA + 5%MSP		381.6	175	21.2	21.2	1247.54	0	583
N	10%FA + 10%MSP		339.2	175	42.4	42.4	1247.54	0	583
O	5-5-5%		381.6	175	21.2	21.2	1183.38	55.61	583
P	10-10-10%		339.2	175	42.4	42.4	1121.1	111.22	583
Q	15-15-15%		296.8	175	63.6	63.6	1057.21	116.57	583

. In this study, 175 litres of water was consistently used across all mixtures, based on preliminary trials for optimal workability, with adjustments for admixture moisture content, ensuring comparability between mixtures, and in alignment with the relevant literature recommendations [17,18]. It is pertinent to note that a ratio of 60:40 for 20 and 10 mm coarse aggregates was used for the preparation ‘A’. In total, 16 more working samples of the modified concrete, labelled ‘B’ to ‘Q’, were also prepared by incorporating FA, MSP, and MWP into mixture ‘A’, and their respective amounts are given in Table 3. The mix-proportion method used has been illustrated in Figure 4.

Samples B, C, and D were prepared by partially replacing coarse aggregates with MWP in the ratios of 5, 10, and 15%, respectively. In samples E, F, and G, OPC is partially replaced with MSP in the ratios of 5, 10, and 15% respectively, while samples H, I, and J were prepared by replacing the OPC with FA in the ratios of 5, 10, and 15% respectively. To prepare mixture ‘K’, 5% each of OPC and coarse aggregates were replaced with FA and MWP, respectively, while in the case of mixture ‘L’, their replacement ratios were increased to 10%. Similarly, in samples M and N, only OPC was replaced with FA and MSP in ratios of 5 and 10% each, respectively. Lastly, In the samples O, P, and Q, OPC was replaced with FA and MSP, while coarse aggregates were replaced with MWP in the ratios of 5, 10, and 15% each, respectively.

3.4. Testing Procedure

3.4.1. Fresh Concrete Properties

The workability potentials of all 17 of the freshly prepared concrete mixtures (A to Q) were evaluated with a Slump Cone Test, using the following dimensions of the cone: top diameter, 10 cm; bottom diameter, 20 cm; height, 30 cm; the test was conducted as per the specifications of BIS 1199:1959 [44]. The concrete of each sample was filled in a slump cone in three layers of almost equal volumes. To avoid air entrapment, each layer was tamped around 25 times using the standard tamping rod.

3.4.2. Test for Elastic Constants of Hardened Concrete

Modulus of elasticity was tested for each sample according to the BIS 516:1959 [45]. The sample for the test must be a straight cylindrical specimen with a length-to-diameter ratio of at least 2:1. The cylindrical specimens used were 150 mm × 300 mm, as shown in Figure 5a. It is imperative to meticulously machine and refine a specimen in order to eliminate any abnormalities or roughness present on its surface.

The initial step of the testing protocol involves carefully placing the specimen within the compression testing apparatus as shown in Figure 5b. The specimen is subjected to an initial load of 5 kN, which is subsequently increased in a steady and controlled manner at a rate of 0.5 kN/s until the point of fracture of the specimen is attained. During this procedure, meticulous observation and documentation of both the load and deformation measurements are conducted. In order to provide precise and reliable outcomes, it is imperative to uphold the consistent application of axial load, hence mitigating any potential torsional or flexural effects on the specimen throughout the testing process. It is important to mention that the experiment is conducted within controlled environmental circumstances of standard room temperature and humidity, in order to ensure uniform testing parameters. The modulus of elasticity is calculated as the slope of the linear portion of the stress–strain curve obtained during the test. The stress is calculated as the load divided by the cross-sectional area of the specimen. The strain is calculated as the deformation divided by the original length of the specimen. The modulus of elasticity is expressed in units of force per unit area, megapascals (MPa).

3.4.3. Modelling of a G + 20 Structure Using ETABS

Due to growing urbanisation and sustainability objectives, high-rise buildings are now pivotal in contemporary cities. Therefore, a building model exemplifies this sustainable design approach. A new model is created in ETABS (an acronym for ‘Extended Three-Dimensional Analysis of Building System’) using the basic project information, such as units, building code, and design preferences. Then, the grid system is defined for the building. This includes defining the number of bays and columns in each direction, as well as the spacing between columns. The grid system creates the structural framing for the building. Now, the structural elements of the building, such as beams, columns, and slabs, are defined. The properties of the structural elements, such as material type, section properties, and load capacity, are assigned. The loads, including dead loads, live loads, wind loads, and seismic loads, are applied to the structure using the ETABS load generator. The structure is analysed to determine the structural response of the building to the applied loads. Figure 6 presents the plan (a) and elevation (b) of the modeled structure.

4. Results

4.1. Properties of Fresh Concrete

Figure 7 displays the Slump Cone Test results of all the 17 samples (A to Q) given in Section 3.1 and, on the basis of these results, the workability potentials of the freshly prepared concrete mixtures can be assessed. It is to be noted that mixture ‘A’ has no admixtures and possesses the lowest workability out of all the samples, and, on the other hand, sample ‘Q’, with the maximum amounts of MSP, MWP, and FA, exhibits the highest slump value and highest workability amongst all the mixtures.

It is also pertinent to note that, with the increase in amount of at least one admixture, i.e., MSP/MWP/FA, the workability of the prepared mixture increases. Due to the increase in the amount of only MWP in the concrete, the slump values, or workability of mixtures, follows the order B < C < D. An increase in the percentage of only MSP in the concrete mixture slump values increases in the order E < F < G, and similarly increasing with the amount of FA, the workability of mixtures increases in the order H < I < J.

Considering the above facts in view, attempts were made to add at least two admixtures. Between samples K and L, prepared by adding FA and MWP in cement and coarse aggregate, respectively, in ratios of 5 and 10% each, the slump value of sample L is found to be greater than that of sample K. Similarly, between the samples M and N, which were prepared by replacing cement with FA and MSP together in proportions of 5 and 10% each, respectively, the workability of sample N is better than that of sample M.

In the final attempt, samples O, P, and Q were prepared by incorporating all three admixtures, and the slump value follows the order O < P < Q, thereby indicating the best workability for concrete mixtures with the highest (15%) admixture addition.

4.2. Elastic Constants of Hardened Concrete

In the context of material testing, the modulus of elasticity (E) serves the purpose of quantifying a material’s resistance to elastic deformation under applied loads. It can be defined as the slope in the stress–strain curve within the elastic deformation range. The modulus of elasticity finds practical applications in estimating bending deflections and determining the deformation properties of concrete samples. Generally, stiffer materials exhibit higher elastic moduli.

Furthermore, the characteristics of aggregates play a crucial role in influencing the modulus of elasticity. The impact of aggregates depends on their volumetric ratio and their own elastic modulus when incorporated into concrete production. Therefore, when aggregates possess a higher modulus of elasticity than the cement paste, the overall concrete mixture will exhibit a greater modulus of elasticity. As the specific gravity of MWP is lower than those of crushed basalt rock aggregates, the unit weight of concrete containing MWP decreases.

Poisson’s ratio (µ) refers to the observed behaviour of a material to undergo perpendicular expansion with respect to compression direction. In contrast, when the material undergoes expansion rather than compression, it exhibits contraction in the transverse axes aligned with the expansion. From the present study, it can be ascertained that an increase in admixtures in concrete results in a decreased Poisson’s ratio in almost all cases. This is because the incorporation of admixtures results in a partial reduction in strength, resulting in moderately less ductile concrete mixtures. This results in higher values of deformations with respect to conventional concrete mixtures.

In the present study, Elastic constants E and µ were calculated for hardened concrete mixtures, and their values are presented in

Table 4. Evaluation of modulus of elasticity and Poisson’s ratio for concrete mixtures.

Mix Label	Failure Load (kN)	Deformation (mm)		Poisson’s Ratio (µ)	Failure Stress (σ) (MPa)	Longitudinal Strain (ε)	Elastic Modulus (E) (MPa)
		Longitudinal	Lateral
A	651	0.420	0.110	0.261904762	36.8390614	0.00140	26,313.61529
B	645	0.436	0.114	0.26146789	36.49953088	0.00145	25,114.35611
C	639	0.419	0.118	0.281622912	36.16000036	0.00140	25,890.21506
D	634	0.414	0.120	0.289855072	35.87705826	0.00138	25,997.86831
E	645	0.429	0.112	0.261072261	36.49953088	0.00143	25,524.14747
F	635	0.419	0.115	0.274463007	35.93364668	0.00140	25,728.14798
G	622	0.411	0.118	0.287104623	35.19799722	0.00137	25,691.96878
H	646	0.421	0.111	0.263657957	36.5561193	0.00140	26,049.49119
I	642	0.418	0.115	0.275119617	36.32976562	0.00139	26,073.99447
J	637	0.416	0.121	0.290865385	36.04682352	0.00139	25,995.30542
K	640	0.422	0.118	0.279620853	36.21658878	0.00141	25,746.39013
L	631	0.420	0.122	0.29047619	35.707293	0.00140	25,505.20929
M	642	0.428	0.115	0.268691589	36.32976562	0.00143	25,464.78899
N	634	0.426	0.124	0.291079812	35.87705826	0.00142	25,265.53399
O	646	0.419	0.122	0.291169451	36.5561193	0.00140	26,173.83244
P	636	0.414	0.116	0.280193237	35.9902351	0.00138	26,079.88051
Q	612	0.410	0.111	0.270731707	34.63211302	0.00137	25,340.57050

. A careful inspection of Table 4 reveals that incorporating admixtures into concrete mixtures decreases the value of E in cases B to Q. It is also important to note that, by increasing the amount of MSP, the value of E decreases. This may be due to the fact that MSP possesses lower specific gravity than cement, and its incorporation as an admixture decreases the unit weight of the concrete. A similar trend is observed when FA is used as a replacement for some of the cement contents. It is also interesting to note that the combined inclusion of MSP and FA, along with MWP, results in decreased values of E and, consequently, the compressive strength of the prepared concrete. It is worth mentioning that, with a decrease in compressive strength, the value of E decreases [43].

To evaluate values of Poisson’s ratio (µ) and the modulus of elasticity (E) of 17 cylindrical specimens of concrete samples A to Q, expressions (1) to (4) are used.

$$\mathrm{Poisson}’\mathrm{s}\mathrm{ratio}\left(\mathsf{\mu }\right)=\frac{\mathrm{Transverse}\mathrm{Contraction}\mathrm{or}\mathrm{Expansion}}{\mathrm{Longitudinal}\mathrm{Expansion}}$$

(1)

$$\mathrm{Failure}\mathrm{Stress}\left(\mathsf{\sigma }\right)=\frac{\mathrm{Fracture}\mathrm{Load}}{\mathrm{Cross}-\mathrm{sectional}\mathrm{area}}$$

(2)

$$\mathrm{Strain}\left(\mathsf{\epsilon }\right)=\frac{\mathrm{Change}\mathrm{in}\mathrm{Dimension}}{\mathrm{Original}\mathrm{Dimension}}$$

(3)

$$\mathrm{Modulus}\mathrm{of}\mathrm{Elasticity}\left(\mathrm{E}\right)=\frac{\mathrm{Failure}\mathrm{Stress}}{\mathrm{Strain}}$$

(4)

Captivatingly, out of all of the values of E (Figure 8), sample O (E = 26,173.83244) possesses a comparable value to mixture A (E = 26,313.61529), while all 15 of the other samples have values of E lower than that of sample O. This indicates that mixture O is a better-packed material than other concrete mixtures containing admixtures.

Table 4 also reveals that sample O has the highest value of µ (0.291169451) as compared to other mixtures, and its value is closest to that of sample A (µ = 0.261904762). It is also important to note that, out of all of the mixtures, the failure stress of sample O is at the maximum and close to that of A. Thus, it can be safely interpreted that sample O exhibits a higher value of deformation in comparison to A [17].

4.3. Modelling of G + 20 Structure Using ETABS

On the basis of the values of elastic constants E and µ of the samples A and O, two G + 20 structures are modelled for each concrete mixture and simulated in the ETABS Ultimate software, as shown in Figure 9. Both of the envisaged buildings are considered identical, having shear walls placed symmetrically. For both of the structures, the coefficient of thermal expansion is assumed to play a negligible role on the design values and structural responses to the materials and is hence treated as constant for both A and O. The responses of the structures are analysed by applying all of the loads according to IS 875 (part II and III) [46,47] and IS 1893 (part I) [48], i.e., earthquake load, wind load, and a respective combination, according to the BIS 456:2000.

4.3.1. Storey Displacement

Ground acceleration causes buildings to shake or vibrate during earthquakes. This movement can cause building levels to shift horizontally. Storey displacement is measured as the horizontal displacement at the top of one storey compared to the top of an adjacent storey. It is vital for analysing a building’s seismic performance and structural integrity.

In the present study, storey displacements of both the structures have been observed by evaluating the maximum storey displacement values in both the X- and Y-directions. In each case, a maximum load 1.5 times (dead load + superimposed load) was considered, and the response spectrum in the X-direction was used. The maximum storey displacement results under the applied load are detailed in

Table 5. Maximum storey displacement.

			Modified Concrete (Mix O)		Nominal Concrete (Mix A)
Storey	Elevation (m)	Location	X-Dir (mm)	Y-Dir (mm)	X-Dir (mm)	Y-Dir (mm)
Terrace Cabin	63	Top	143.9615	18.4161	144.7303	18.5144
Terrace	60	Top	157.7347	69.4071	158.5771	69.7777
19th Storey	57	Top	153.9730	67.1909	154.7953	67.5497
18th Storey	54	Top	149.7386	64.8124	150.5383	65.1586
17th Storey	51	Top	144.9025	62.2299	145.6763	62.5622
16th Storey	48	Top	139.4744	59.4519	140.2192	59.7694
15th Storey	45	Top	133.4882	56.5030	134.2011	56.8048
14th Storey	42	Top	126.9835	53.4005	127.6616	53.6857
13th Storey	39	Top	119.9940	50.1616	120.6348	50.4295
12th Storey	36	Top	112.5526	46.8024	113.1537	47.0524
11th Storey	33	Top	104.6922	43.3325	105.2513	43.5640
10th Storey	30	Top	96.4477	39.7660	96.9628	39.9784
9th Storey	27	Top	87.8553	36.1103	88.3245	36.3031
8th Storey	24	Top	78.9522	32.3761	79.3738	32.5490
7th Storey	21	Top	69.7711	28.5647	70.1437	28.7172
6th Storey	18	Top	60.3449	24.6790	60.6672	24.8108
5th Storey	15	Top	50.7076	20.7193	50.9784	20.8300
4th Storey	12	Top	40.9018	16.6940	41.1202	16.7832
3rd Storey	9	Top	31.0095	12.6312	31.1751	12.6986
2nd Storey	6	Top	21.2004	8.5984	21.3136	8.6443
1st Storey	3	Top	11.8289	4.7611	11.8921	4.7866
Plinth	0	Top	4.2234	1.8177	4.2460	1.8274
Base	−3	Top	0	0	0	0

and were found to be in close proximity between A and O.

From the table above, it can be asserted that mixture O, consisting of MWP, MSP, and FA at equal proportions of 5% each, does not have a substantial detrimental effect on structural stability in relation to storey displacement. From the observed similarities in displacements at different storeys for mixtures A and O, it is suggested that the structural responses of structures made from the two mixtures are nearly identical. The peak displacements observed around the terrace and terrace cabin regions indicate consistent structural behaviours for mixtures A and O, suggesting that the additives in mixture O do not introduce any unpredictable behaviours in terms of seismic response.

4.3.2. Storey Stiffness

Storey stiffness is another parameter which determines the resistance of the structure to external loads, like wind and other lateral forces. It also affects the deformation behaviour and reactivity of the structural system. It is well known that stiffer storeys deform less under lateral stresses, thereby reducing interstorey drift and displacement during an earthquake.

Table 6. Storey stiffness.

			Modified Concrete (Mix O)	Nominal Concrete (Mix A)
Storey	Elevation (m)	Location	X-Dir (kN/m)	X-Dir (kN/m)
Terrace Cabin	63	Top	75,737.7016	76,142.169
Terrace	60	Top	178,554.4426	179,507.989
19th Storey	57	Top	247,144.0866	248,463.927
18th Storey	54	Top	299,884.1652	301,485.657
17th Storey	51	Top	345,059.2864	346,902.03
16th Storey	48	Top	382,047.6818	384,087.957
15th Storey	45	Top	412,691.4547	414,895.379
14th Storey	42	Top	438,793.6226	441,136.942
13th Storey	39	Top	461,877.1789	464,343.773
12th Storey	36	Top	482,414.9526	484,991.226
11th Storey	33	Top	502,019.6463	504,700.616
10th Storey	30	Top	520,414.4175	523,193.622
9th Storey	27	Top	539,292.4578	542,172.478
8th Storey	24	Top	559,641.4586	562,630.15
7th Storey	21	Top	582,627.3814	585,738.826
6th Storey	18	Top	609,456.8083	612,711.532
5th Storey	15	Top	642,309.5954	645,739.765
4th Storey	12	Top	684,343.849	687,998.497
3rd Storey	9	Top	743,918.9361	747,891.737
2nd Storey	6	Top	840,013.4888	844,499.47
1st Storey	3	Top	1,015,974.9697	1,021,400.65
Plinth	0	Top	2,050,035.6949	2,060,983.64
Base	−3	Top	0	0

presents the maximum storey stiffness values for both of the buildings, considering a wind load acting in the X-direction, which were found to almost identical between the structures. This may be due to the fact that both A and O have almost equal values of E. The results are given in Table 6, as follows:

It can be seen that, for lower storeys, which bear more load, the stiffness values are inherently greater. This trend is consistent for both the mixtures. The close proximity in stiffness values for mixtures A and O, especially in the middle and upper storeys, emphasises the robustness of mixture O in withstanding lateral forces similar to conventional concrete. The results demonstrate that mixture O, consisting of waste materials, has the capacity for providing comparable structural performance to that of conventional concrete (mixture A) in key aspects, including storey displacement and stiffness.

5. Conclusions

This research examines the impact of several substitutions of sustainable materials on the mechanical and structural characteristics of concrete. A total of seventeen samples were generated by incorporating MWP (marble waste powder), MSP (marble slurry powder), fly ash, and various combinations thereof, into the concrete mixture. These materials were selected as filler materials with the intention of influencing not only the strength, but also other aspects, of the concrete. The elastic constants are crucial factors in assessing the mechanical reactions of modified concrete, since they provide insight into the material’s behaviour under loads.

The Compressometer cum Extensometer utilised for this study is specifically designed for measuring the longitudinal and lateral deflection values of 150 mm × 300 mm cylinders. The calculated value for the surface area of the loading face of the cylinder was determined to be 17,671.46 mm². The findings of the investigation demonstrated that the utilisation of the admixtures yielded affected the strength and various mechanical characteristics of the fresh and hardened concrete. The conclusions, limitations, and future scope of this research can be summarised as follows:

• The modulus of elasticity and Poisson’s ratio of the specimens were determined, revealing that the specimens with admixtures exhibit a decreased modulus of elasticity and an increased Poisson’s ratio compared to the conventional concrete mixture. This observation suggests that the incorporation of admixtures affects the rigidity and ability of concrete to withstand deformation.
• This study has meticulously compared the structural performance results of two concrete mixtures: the conventional mixture A and the modified mixture O (which incorporates marble waste product, marble slurry powder, and fly ash at 5% each). MWP was substituted for coarse aggregates, while MSP and FA were substituted for cement. Remarkably, mixture O exhibited comparable storey displacement and stiffness values across various building storeys, aligning closely with the performance of the conventional concrete.
• The utilisation of admixtures in concrete offers a range of advantages, encompassing enhanced workability, durability, and strength. The findings of this investigation provide confirmation that the incorporation of admixtures into concrete yields enhancements in its mechanical characteristics and capacity to withstand deformation.
• Moreover, the incorporation of admixtures into concrete results in a decrease in the quantity of cement used and a corresponding reduction in water demand. Consequently, this practice contributes to a decrease in the carbon emissions associated with the building sector. Given the growing apprehension around the ecological ramifications of construction materials, this factor has particular significance.
• In summary, the utilisation of a partial substitution of MWP, MSP, and FA in concrete offers several benefits, such as comparable strength, stiffness, and durability to that of conventional concrete, as well as a diminished ecological footprint that possesses particular significance for the construction sector and underscores the potential for additional investigation regarding the application of sustainable concrete.
• The seventeen samples give useful insights, but they may not fully reflect modified concrete property variations. Geographic, climatic, and Indian Standard code use may restrict its application. The long-term durability and economic feasibility of such concrete variations are also unknown. To better comprehend these concrete mixtures, future studies should increase the sample size, as well as the corresponding best mix proportion, include worldwide standards, and examine the long-term environmental and economic effects of using these mixtures. Using 3D printing and working with the industry might make the findings more applicable to real life.