Experimental Investigation of Mechanical Properties of Problematic Expansive Soil using Copper Slag and Its Statistical Validation

doi:10.21203/rs.3.rs-3337559/v1

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Research Article

Experimental Investigation of Mechanical Properties of Problematic Expansive Soil using Copper Slag and Its Statistical Validation

https://doi.org/10.21203/rs.3.rs-3337559/v1

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published 27 Dec, 2023

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This experimental research has been conducted to improve the mechanical properties of the problematic expansive soil using copper slag. The copper slag has been utilized to improve the Talab soil in Nainwa for the first time. These mechanical properties are consistency limits, compaction, and strength properties. The swelling properties show that the collected soil has a high degree of expansive nature and low specific gravity. Therefore, the copper slag has been added to the soil from 5–30% at a 5% variation by its oven-dry weight. The experimental results reveal that the free swell index of soil has decreased by 69.88% with the addition of 30% copper slag. It has also been observed that the liquid and plastic limits have been decreased. The plastic limit of soil decreases because copper slag takes place in voids. Due to this phenomenon, the maximum dry density of soil has been increased by 14.75% with the addition of 25% copper slag. The California bearing ratio (CBR) value of soil has been increased to 1.13% (soaked condition) and 3.8% (unsoaked condition) by adding 25% copper slag. This research introduces an empirical relationship between unsoaked and soaked CBR with a determination coefficient (R²) of 0.8254. Moreover, it has been observed that the unconfined compressive strength of soil has increased by 51.68% with the addition of 25% copper slag. Moreover, the value of R² for the experimental results obtained in this research is higher than the published experimental results, presenting the experimental study's accuracy and reliability. In addition, the analysis of variance (ANOVA) test accepts the research hypothesis for the present investigation.

Problematic expansive soil

Copper slag

Strength properties

Swelling behaviour

California bearing ratio

Expansive soil, also known as shrink-swell soil, is a type of soil that undergoes significant volume changes with changes in moisture content. These soils can expand when they absorb water and shrink when they dry out. This characteristic can lead to various problems and challenges, especially in construction and engineering projects. Foundation damage, structural instability, cracking and damage, infrastructure damage, utility disruption, landslides and erosion, construction delays and costs, and maintenance challenges are well-known issues associated with problematic expansive soils (PES). Several researchers and scientists introduced different techniques to mitigate these problems, i.e., soil testing, foundation design, draining system, soil stabilization, vegetation and landscaping, moisture barriers, and proper construction practices. Stabilization is the most popular and traditional process to improve the mechanical, chemical, and biological properties of PES. Chemical, bituminous, lime, cement, and mechanical are the conventional stabilization methods (Khatti and Grover, 2021). In recent decades, researchers have started using industrial waste or byproducts to improve the mechanical properties of PES.

Fakhrabadi et al. (2023) investigated the durability of clayey sandy soil under freezing-thawing (F-T) cycles. The researchers stabilized the soil with copper-slag-based geopolymer. The strength and stiffness of untreated soil increased until F-T cycle 3. The loss of strength was observed by mixing 11 M (Molarity) NaOH. The researchers reported that the high microcracks (microstructural analysis) developed due to soft-strain behavior in samples 8 M and 11 M. Tajaddini et al. (2023) studied the effect of copper slag (CS) and recycled glass powder (RGP) on the mechanical properties of low-plasticity clay soil. The authors found that CS improves the compaction and consistency parameters better than RGP. The UCS and CBR of 5% CS with an alkaline activator sample were found to be 3.11 and 1.68 times higher at 56 and 7 days of curing, respectively. Still, the UCS and CBR were found 4.03 and 1.90 times by adding 5% RGP. The authors concluded that the rich alumina and RGP silica increased the soil's CBR 10% higher than CS-stabilized soil. An excellent bond between soil particles and a well-structured alumina-silicate geopolymerized framework observed in EDX and SEM analysis confirms the effect of the additives. Hemanth and Sharma (2023) reported a significant effect of CS on the strength and compaction parameters of kaolin soil. Reddy et al. (2023) designed a retaining wall for the CS as an infill material compared with conventional infilled materials. The researchers found that CS has 41⁰ angle of shearing resistance at optimum moisture content and 38⁰ in saturated conditions. The researchers reported that CS is highly capable of bearing more pressure due to its relative unit weight. Stefanini et al. (2023) replaced blast furnace slag with CS and stainless steel slag (SSS) in the productivity of alkali-activated materials (AAMs). Wei et al. (2023) noted that copper slag enhances cohesive soil's mechanical properties. Debnath and Chouksey (2022) studied the effect of alkali-activated copper slag on soft soil's unconfined compressive strength (UCS). The UCS of soft soil was five times higher by adding 30% CS with a 10 M alkali-activated specimen. Soni et al. (2022) replaced fine-aggregate with copper slag in road construction work and introduced copper slag as a road material application. Ekinci et al. (2022) prepared different combinations of lime, copper slag, and cement materials to improve the UCS of marine clay. The authors noted that the UCS of marine clay was increased to 67.64kg/cm² (for 10% CS) and 63.52kg/cm² (for 20% CS) at 28 and 60 days of curing. Sharma and Kumar (2022) investigated the impact of combined CS and rice husk ash (RHA) on the geotechnical properties of soil. Forty-eight combinations were prepared using an alkali activator (AA), i.e., sodium hydroxide of 10 M (Molarity) and sodium silicate (SS). The investigators reported that OMC decreased with increased AA content, and MDD increased to 6%. The 5% RHA mixed with 3%, 6%, and 9% AA content and MDD was increased to 2.279g/cc, 2.385g/cc, and 2.313g/cc. The specific gravity was determined in the range of 1.57 to 3.41. In the condition of AA constant, the RHA content increased the UCS value up to 30%. The UCS was experimentally determined as 13.32 Mpa at 28 days curing period. The CBR value increased with decreasing the AA content, and the results of CBR were found according to the Ministry of Road Transport and Highways (MORT&H). Fakhrabadi et al. (2021) stabilized non-woven geotextile reinforcing clayey sand using CS. The authors mixed 10% and 15% CS with 2, 4, 8, 12, and 16 M NaOH. The alkaline activator solution was prepared with 30% NaOH and 70% Na₂SiO₃. The residual, peak strength, and failure axial strain results were acceptable. A negligible increase was noted for the angle of internal friction. Dinesh et al. (2021) studied the combined impact of CS and sawdust ash (SA) on the geotechnical properties of black cotton soil. The authors mixed 10–40% CS at 10% intervals and 2–6% at 2% intervals. The optimum results for UCS (i.e., 92 kN/m²) and CBR (i.e., 4.71% for 2.5mm) were determined for the specimen of 30% CS with 4% SA. Lavanya and Kumar (2021a) conducted an experimental study for CBR of expansive soil by mixing lime, cement, and copper slag. The researchers reported that soaked CBR increases with the ratio of cushion thickness to the expansive soil bed's thickness and the percentage of admixture. Sharma and Kumar (2021) noted that UCS, specific gravity, and MDD decreased with increased CS and increased RHA, lime, and cement. Ahirwar and Mandal (2021) improved the soft subgrade using bamboo grid-reinforced copper slag. The researchers reported that the footing settlement was reduced by up to 87%. Lavanya and Kumar (2021b) investigated the heave and swelling of the CS-cushioned clayey subgrade. 0.25, 0.5, 0.75, and 1.0 thickness ratios of the treated CS cushion and clayey subgrade bed. It was noted that soil heave decreases (i.e., 84.4%) with the increase in lime content and thickness of CS cushion. Muthukkumaran and Anusudha (2020) studied the characteristics of lime and CS-treated clay under dynamic and static loading. The investigators reported morphological changes in soil using an X-ray diffraction test. The optimum strength was determined by adding lime and CS in a 1:1 proportion. The investigators noted an increase in shear strength with a decrease in swelling. It was also noted (i) an increase in dynamic shear modulus, (ii) a decrease in damping ratio, and (iii) an increase in resilient modulus. Jagudi (2020) conducted an extensive study on improving the geotechnical properties of black cotton soil using CS and steel slag to complete doctoral research. Reddy and Reddy (2020) used as backfill materials for reinforced earth and conventional retaining walls. The authors reported combining CS and woven geotextile improves soil's mechanical properties. Kirithika and Stalin (2019) added 1%, 2%, and 3% nano CS to lime-stabilized soil to improve the mechanical properties of soil. The researchers reported that the UCS increased by adding 1% nano CS in lime-stabilized and virgin soil. It was also found that the plasticity index of virgin and lime-stabilized soil was increased due to nano CS. The UCS of lime stabilized soil was increased by 38% (immediate mix) and 106% (7 days curing) than virgin soil. Mahmoudi and Toufigh (2023) treated sandy soil using silica fume blend geopolymer and CS-based geopolymer. In addition, the researchers investigated the effect of the particle size of CS on the mechanical properties of soil. For that aim, researchers used coarse and fine-grained CS. The fine-grained CS with silica fume significantly increases the strength parameters. Moreover, the cracks developed in stabilized soil samples were analyzed by treating hydrated lime. Scanning Electron Microscopy (SEM) confirmed the high strength due to denser particles and uniform structure. Vasanthi et al. (2019) investigated the optimum CS and quarry dust dosage for improving strength using response surface methodology (RSM). Mathew et al. (2019) mixed terrazyme, CS, and lime to improve air-dried and marine clay's geotechnical characteristics. The authors found that terrazyme improved the strength parameters than CS and lime. Reshmi and Mandal (2019) compared the strength parameters, i.e., UCS and CBR, of cement kiln dust (CKD), CS, and fly ash (FA) stabilized soil. It was noted that pavement thickness decreases for CKD, CS, and FA materials. The geotechnical characteristics of combined CS and FA stabilized soil were better than those of FA and CS mixed soil. Conversely, the mechanical properties of combined CS and CKD-stabilized soil were better than those of CKD and CS-stabilized soil. Kumar et al. (2019) studied the characteristics of waste foundry sand (WFS) and blast furnace steel slag (BFSS) and found them better than conventional fill materials. Janalizadeh et al. (2019) used the ultrasonic pulse velocity method to study the effect of copper sludge on cemented clay. The copper sludge was added 0–35% at a 5% variation in soil and cured for 7, 28, and 60 days. It was observed that ultrasonic pulse velocity decreases with increasing copper sludge content for a seven and 28-day curing period. The optimum results were obtained by adding 15% copper sludge. Raj et al. (2018) mixed CS and FA to improve the MDD of soil. The researchers concluded that 6% and 9% CS and FA improve the properties of sub-based and based road pavement layers.

Literature Gap – The literature study reveals the capabilities of copper slag in improving the geotechnical properties of expansive soil. It can be noted that most researchers used copper slag with other waste materials and activators to improve the mechanical properties of problematic expansive soil (PES). The literature also shows that limited experimental studies have been conducted to improve the mechanical properties of expansive soil using copper slag, and most studies were published on low-plasticity expansive soils. It has also been observed that very few researchers analyzed the experimental results through statistical approaches to validate them.

Research Objectives – The following objectives for the present research can be mapped by considering the gap identified in the literature.

To improve the mechanical properties of problematic expansive soil collected from Nainwa, Bundi, using different percentages of copper slag for the first time.
To study the geotechnical characteristics of stabilized soil for understanding soil behaviour by consistency limits, compaction parameters, and strength parameters results.
To perform the statistical analysis for validating the experimental results.

Research Significance – Alemshet et al. (2023), Kabeta and Lemma (2023), Bharti et al. (2023), Panda et al. (2023), Wang et al. (2023), Balogun et al. (2023), Tanyıldızı et al. (2023), and Li et al. (2023) used different slag waste materials to improve the properties of soil and found positive experimental response. Therefore, the present research has been conducted to improve the mechanical properties of problematic expansive soil collected from the Nainwa, Bundi, using copper slag. This research will help to select the optimum dosage of copper slag to improve the mechanical properties of PES. This research will help civil engineers perform statistical analyses to validate the experimental results from published results.

The present research improves the mechanical properties of problematic expansive soil using copper slag. For this aim, the soil sample has been collected from the Talab, Naina, Bundi, as shown in Fig. 1. The copper slag has been collected from the Vishwakarma Industrial Area, Jaipur. From the literature study, it has been found that 0 to 30% copper slag has not been added to PES at 5% variations to improve the properties of soil. The improvement of mechanical properties of PES has been studied by performing consistency, compaction, and strength tests. The liquid limit (LL), plastic limit (PL), and plasticity index (PI) have been determined experimentally for each copper slag mixed soil sample. The maximum dry density and optimum moisture content have been determined by performing the standard proctor test. The California bearing ratio (CBR) for soaked (CBR_S) and unsoaked (CBR_U) conditions and unconfined compressive strength (UCS) tests have been performed to determine the strength parameters of soil. By analyzing the results obtained from experimental procedures, the optimum dosage of copper slag has been determined to achieve maximum improvement in the mechanical properties of soil. Furthermore, the test results have been validated by statistical analysis, i.e., coefficient of determination. In addition, an analysis of variance (ANOVA) test has been performed to find the hypothesis for the present research.

3.1 Materials

The present research investigates the mechanical properties of problematic expansive soil with copper slag. For this aim, the soil sample has been collected from the Talab, Naina, Bundi. The copper slag has been collected from the Vishwakarma Industrial Area, Jaipur. The grain size distribution tests (dry sieve, wet sieve, and hydrometer analyses) have been performed as per IS: 2720: 1985 (Part 4) for soil and copper slag samples. The consistency limits have been determined experimentally according to IS 2720: 1985 (Part 5). The specific gravity of soil samples and copper slag has been determined as per IS 2720: 1980 (Part 3). In addition, the free swell index test has been conducted according to IS 2720: 1977 (Part-40). The standard proctor test, the light compaction test, has been performed as per IS 2720: 1974 (Part 7). The California bearing ratio test has been performed using IS 2720: 1987 (Part 16). The strength test using unconfined compressive strength equipment has been carried out as per IS 2720: 1991 (Part 10). The summary of the physical properties of virgin soil and copper slag is mentioned in Table 1, and the chemical properties of copper slag are given in Table 2. The sieve analysis results for the virgin soil sample and copper slag are shown in Fig. 2.

Table 1

– Physical properties of virgin soil and copper slag
Particulars	Units	Soil Sample	Copper Slag
Gravel (4.75-2mm)	%	0.96	0
Sand (2-0.075mm)	%	2.84	1.5
Silt (0.075-0.002mm)	%	80.01	97.7
Clay (< 0.002mm)	%	6.85	0.8
Specific Gravity	-	2.56	3.55
Liquid Limit	%	45.25	-
Plastic Limit	%	21.97	-
Plasticity Index	%	23.28	-
Differential Free Swell	%	41.67	-
Optimum Moisture Content	%	19.4	-
Maximum Dry Density	g/cu.cm	1.65	-
Unconfined Compressive Strength	kg/sq.cm	2.8	-
Shear Strength	kg/sq.cm	1.4	-
California Bearing Ratio - Soaked	%	0.84	-
California Bearing Ratio - Unsoaked	%	2.04	-

Table 2

– Chemical properties of copper slag
Chemical composition	Value
SiO₂	7.55
Al₂O₃	13.05
Fe₂O₃	68.95
CaO	6.95
K₂O	0.69
MgO	0.99
Na₂O	0.09

3.2 Project Design

This is the first time copper slag has been used to improve the mechanical properties of problematic expansive soil located at Talab, Bundi. The copper slag has been added to PES from 0–30% at 5% variations. The strength, compaction, and consistency parameters for virgin soil, copper slag, and mixed soil samples have been experimentally determined, as mapped in Table 3.

Table 3

– Project design
Soil Samples	Sample ID	Sieve Analysis	Specific Gravity	Consistency Limits	Compaction Parameters	Soaked & Unsoaked CBR	Unconfined Compressive Strength
Copper slag	-	YES	YES	NO	NO	NO	NO
Virgin soil	PECS0	YES	YES	YES	YES	YES	YES
Soil + 5% CS	PECS1	YES	YES	YES	YES	YES	YES
Soil + 10% CS	PECS1	YES	YES	YES	YES	YES	YES
Soil + 15% CS	PECS1	YES	YES	YES	YES	YES	YES
Soil + 20% CS	PECS1	YES	YES	YES	YES	YES	YES
Soil + 25% CS	PECS1	YES	YES	YES	YES	YES	YES
Soil + 30% CS	PECS1	YES	YES	YES	YES	YES	YES

4.1 Swelling Index

The differential free swell index and swelling pressure are the swelling indexes of expansive soils. This experimental study has determined the differential free swell index (DFS) for soil and copper slag mixed soil. The DFS of virgin soil was determined experimentally as 41.67%, presenting a high degree of expansiveness. In addition, 5–30% copper slag at 5% variation has been mixed to control the swelling index of soil by its dry weight. Figure 3 shows the DFS value for the copper slag mixed soil and the percentage decrease in DFS value w.r.t the DFS value of virgin soil. Figure 3 depicts that the DFS of PES has started decreasing from 38.18–12.55%, with an increase in the copper slag from 5–30% in the soil. The maximum decrease in the DFS value of virgin soil has been determined experimentally as 69.88% by adding 30% copper slag.

4.2 Specific Gravity

The specific gravity of coarse and fine-grained soil is determined by a pycnometer and density bottle, respectively. The particle size distribution plot reveals that the PES and copper slag contain fine-grained particles. The specific gravity of PES and copper slag has been determined experimentally as 2.56 and 3.55, respectively. Furthermore, the specific gravity of copper slag mixed soil has been determined experimentally and graphically in Fig. 4.

Figure 4 illustrates that the specific gravity of PES has increased with increasing the copper slag content. The maximum increase in the specific gravity of soil has been obtained by adding 30% copper slag, i.e., 2.823. The scatter plot presents the specific gravity of the soil increases up to 10.27% with the addition of 30% copper slag.

4.3 Consistency Test Results

The consistency limits of cohesive soil are the liquid limit (LL), plastic limit (PL), and plasticity index (PI). The liquid limit of cohesive soil is determined by cone penetration and the Casagrande test apparatus. The plastic limit of the soil is determined by preparing a soil thread of 3mm. The number of threads is prepared, and the plastic limit is determined by oven dry method. The plasticity index is calculated by subtracting the plastic limit from the liquid limit. In this work, the consistency test has been performed for soil and copper slag mixed soil samples. The experimental results reveal that soil has an LL of 45.25%, PL of 21.97%, and PI of 23.3%. The consistency limits of copper slag mixed soil are presented in Fig. 5, and it shows that the liquid limit decreases with an increase in copper slag content. Also, the plastic limit decreases with an increase in copper slag. A maximum decrease in plasticity index has been calculated for soil sample PECS2, i.e., 10% copper slag mixed soil specimen. Further, the plasticity index has started increasing up to the addition of 30% copper slag.

Furthermore, the effect of copper slag content has been analyzed in terms of percentage variables. The percentage variation of consistency limits for copper slag mixed soil has been computed and shown in Fig. 6. It can be seen that the consistency limits of soil decrease with an increase in copper slag content. The liquid and plastic limit of soil has been decreased by 26.61% and 68.29%, respectively, by adding 30% copper slag. The percentage error bars show the accuracy (in other words, the least experimental error) of the experimental work.

4.4 Compaction Test Results

In this research, the standard proctor test (called the light compaction test) has been performed to find the optimum moisture content (OMC) and maximum dry density (MDD) of soil and copper slag mixed soil samples, as shown in Fig. 7.

Figure 7 illustrates that the soil sample has OMC and MDD of 19.4% and 1.654g/cc, respectively. The other plots present the OMC and MDD of copper slag mixed soil. A comparison of OMC and MDD of copper slag mixed soil w.r.t compaction parameters of virgin soil is presented in Fig. 8.

Figure 8 demonstrates that the OMC of soil has started decreasing with copper slag content up to 25%. Further increasing the copper slag content, the OMC starts increasing. It is well-known that the OMC and MDD of soil are inversely proportional to each other. This phenomenon has been observed for soil sample PECS5. The maximum dry density, i.e., 1.898g/cc, and optimum moisture content, i.e., 14.2%, have been determined for the PECS5 soil sample. Hence, the maximum density for problematic expansive soil can be achieved by adding 25% copper slag by dry weight of the soil. The 25% copper slag content has decreased the OMC by 26.80%, and MDD increased by 14.75% for the soil sample. Figure 9 shows the percentage variations in OMC and MDD of soil by adding copper slag.

Figure 9 illustrates that the soil's optimum moisture content has decreased with increased copper slag content. Conversely, the maximum dry density of soil has been increased with copper slag content. The maximum dry density of the soil has been increased by 14.75% by adding 25% copper slag, and the optimum moisture content of the soil has been decreased by 26.80% (a negative sign presents a decrease in OMC).

4.5 California Bearing Ratio Test Results

The soaked and unsoaked California bearing ratio (CBR) tests have been performed for virgin and copper slag mixed soil samples. The soaked CBR test has been carried out for a four-day curing period. The load has been measured for 2.5, 5.0, 7.5, 10.0, and 12.5mm deformations. The soaked and unsoaked CBR for the soil sample has been experimentally determined as 0.84% and 2.04%. The copper slag in the range of 5–30% at 5% variations has been mixed in soil to improve the mechanical properties of PES. The soaked and unsoaked CBR of copper slag mixed soil samples are presented in Fig. 10.

Figure 10 illustrates that PES soil's soaked and unsoaked CBR has increased to 1.13% and 3.8%, respectively. Moreover, an empirical relationship (Eq. 1) has been drawn between soaked and unsoaked CBR. The coefficient of determination (R² = 0.8254) of Eq. 1 reveals that soaked CBR has a very strong relationship with unsoaked CBR. Because of such R², the derived empirical equation may be used to predict the unsoaked CBR of copper slag-stabilized soil using soaked CBR.

$$Unsoaked CBR=4.9305*Soaked CBR-2.1934$$

Furthermore, the percentage variation for soaked and unsoaked CBR of copper slag mixed soil has been computed and presented in Fig. 11. The unsoaked CBR of soil increases more because of the absence of water. In soaked CBR, the voids between particles are filled by water instead of copper slag. Therefore, the soaked and unsoaked CBR of soil has been by 34.52% and 86.27% with the addition of 25% copper slag.

4.6 UCS Test Results

The unconfined compressive strength test has been performed according to Indian Standard 2720: 1991 (P-10) for virgin PES and copper mixed PES. Figure 12 illustrates the stress-strain behaviour of a cylindrical specimen (having an aspect ratio of 2) under loading conditions. Figure 12 reveals that stress in the soil increases with copper slag content.

Figure 12 shows that the PECS5 specimen, prepared by adding 25% CS, has attained a higher UCS value with axial strain. The peak value of UCS plots are summarized in Fig. 13. Figure 13 illustrates that virgin soil has a UCS of 2.8kg/cm², which has been increased to 4.247kg/cm² by adding 25% copper slag. Further increasing CS, the UCS of problematic expansive soil has started decreasing. Figure 13 also shows that the UCS of soil has been increased by 51.68% with the addition of 25% copper slag.

4.7 Analysis of Results

For the analysis of experimental results, a database has been constructed from the published research by Ashokbhai et al. (2018), Kavisri et al. (2018), Kumar et al. (2017), and Qureshi et al. (2015), and Tandel and Patel (2009). The database consists of consistency limits, compaction parameters, and soaked CBR results of copper slag mixed problematic expansive soils. Therefore, it has been decided to verify the present investigation using the compiled database. The statistics description for the compiled database is given in Table 4.

Table 4

– Statistical analysis of compiled database
Parameters	CS (%)	LL (%)	PL (%)	PI (%)	OMC (%)	MDD (g/cc)	CBRs (%)
Mean	0.23	48.27	26.73	21.77	19.50	1.97	5.42
Standard Error	0.02	2.82	1.04	1.86	1.27	0.07	0.65
Median	0.20	45.44	25.94	19.39	19.66	1.86	4.52
Standard Deviation	0.11	13.22	4.86	8.72	5.95	0.34	3.03
Sample Variance	0.01	174.75	23.58	76.00	35.37	0.11	9.20
Kurtosis	-1.15	0.75	-0.28	1.24	-1.30	-0.11	0.05
Skewness	0.11	1.19	0.64	1.43	0.19	0.86	0.95
Range	0.35	46.73	16.75	29.64	18.12	1.19	10.40
Minimum	0.05	33.50	20.47	13.37	11.00	1.54	1.80
Maximum	0.40	80.23	37.22	43.01	29.12	2.73	12.20
Sum	5.00	1061.97	588.09	478.84	428.93	43.44	119.21
Count	22.00	22.00	22.00	22.00	22.00	22.00	22.00
CL (95.0%)	0.05	5.86	2.15	3.87	2.64	0.15	1.34

For the analysis of results obtained in the present research, the following analysis statements have been made: (a) analysis of consistency limits concerning the copper slag content; (b) analysis of compaction parameters wrt the copper slag content; and (c) analysis of soaked CBR concerning the copper slag content. For that purpose, the reliability of the compiled database has been determined by determining the correlation matrix, as shown in Fig. 14.

Figure 14 shows that the LL (= -0.7437), PL (= -0.6430), and PI (= -0.7401) strongly (R = ± 0.61 to ± 0.80) correlate with the copper slag content. It has also been found that the LL very strongly (R = ± 0.81 to ± 1.00) correlates with PL (= 9277) and PI (= 9717). Regarding compaction parameters, the copper slag content moderately (R = ± 0.41 to ± 0.60) correlates with the copper slag content. The consistency parameters strongly correlate with optimum moisture content. Still, the maximum dry density moderately correlates with consistency parameters. The copper slag positive strongly correlates with the copper slag content. The positive correlation shows both values increase together, and the negative correlation shows both values are inversionally proportional. Hence, the compiled database is reliable for analyzing the present investigation. The linear and nonlinear equations have been derived for the compiled database and present research results, as summarized in Table 5.

Table 5

– Comparison of equations for databases
S.No.	Inputs	Linear Equations	R²	Nonlinear Equations	R²
Published Database Based
1	LL	LL’ = 68602–89.454*CS	0.5531	$L{L}^{{\prime }}=69.704{e}^{-1.757*CS}$	0.5726
2	PL	PL’ = 33.188–28.41*CS	0.4135	$P{L}^{{\prime }}=33.17{e}^{1.017*CS}$	0.4190
3	PI	PI’ = 35.109–58.711*CS	0.5478	$PI{\prime }=36.3{e}^{-2.531*CS}$	0.5810
4	OMC	OMC’ = 24.664–22.736*CS	0.1765	$OMC{\prime }=24.829{e}^{-1.267*CS}$	0.1811
5	MDD	MDD’ = 1.5912 + 1.6877*CS	0.3057	$MDD{\prime }=1.619{e}^{0.816*CS}$	0.3066
6	CBRs	CBRs’ = 0.5998 + 21.203*CS	0.5903	$CBRs{\prime }=1.844{e}^{4.1045*CS}$	0.5803
Present Research Database Based
7	LL	LL’ = 42.03–22.514*CS	0.9617	$L{L}^{{\prime }}=42.17{e}^{-0.589*CS}$	0.9660
8	PL	PL’ = 23.768–33.9*CS	0.9668	$P{L}^{{\prime }}=24.84{e}^{-1.973*CS}$	0.9393
9	PI	PI’ = 18.262 + 11.386*CS	0.6148	$PI{\prime }=18.365{e}^{0.5492*CS}$	0.6321
10	OMC	OMC’ = 15.507–7.657*CS	0.5812	$OMC{\prime }=16.503{e}^{-0.491*CS}$	0.5981
11	MDD	MDD’ = 1.7195 + 0.6469*CS	0.8768	$MDD{\prime }=1.721{e}^{0.3563*CS}$	0.8690
12	CBRs	CBRs’ = 0.894 + 0.8914*CS	0.8123	$CBRs{\prime }=0.8969{e}^{0.8806*CS}$	0.7888

Table 5 compares the coefficient of determination (R²) for linear and nonlinear equations derived using published and present research databases. From Table 5, it has been observed that nonlinear equations for both databases achieve higher R² than linear equations. The higher R² value reveals the high reliability of parameters. The present research results (in terms of equations) have achieved higher R² than the published database, presenting a good agreement of copper slag mixed PES properties. Hence, the copper slag as waste material improves the geotechnical properties of the problematic expansive soils.

4.8 Statistical Validation

For the statistical validation of results of the consistency, compaction, and strength parameters obtained from the experimental in this research, a statistical validation test called analysis of variance (ANOVA) has been performed. The ANOVA test is performed to find the hypothesis for the present investigation. The statements for the research hypothesis are as follows:

The specific gravity of the copper slag improves the geotechnical properties of the problematic expansive soils.
The density of problematic soil increased because the copper slag particles occur in void areas between the soil particles.

The ANOVA test has been performed using the Data Analysis tool of Microsoft Office 2019. The results of the ANOVA test have been summarized in Table 6. Table 6 reveals that each geotechnical property of copper slag mixed soil follows the statistical clauses of the research hypothesis. Also, the p-value has been calculated below the significance level, i.e., 95%. Therefore, the present investigation accepts the research hypothesis (H_R).

Table 6

– ANOVA test results
Source of Variation	SS	df	MS	F	P-value	F crit
ANOVA for LL
Between Groups	4312.64	1.00	4312.64	1866.64	0.00	4.96
Within Groups	23.10	10.00	2.31
ANOVA for PL
Between Groups	935.72	1.00	935.72	179.78	0.00	4.96
Within Groups	52.05	10.00	5.20
ANOVA for PI
Between Groups	1209.52	1.00	1209.52	1304.89	0.00	4.96
Within Groups	9.27	10.00	0.93
ANOVA for OMC
Between Groups	674.25	1.00	674.25	1512.76	0.00	4.96
Within Groups	4.46	10.00	0.45
ANOVA for MDD
Between Groups	8.24	1.00	8.24	1275.56	0.00	4.96
Within Groups	0.06	10.00	0.01
ANOVA for CBRs
Between Groups	2.30	1.00	2.30	265.38	0.00	4.96
Within Groups	0.09	10.00	0.01
ANOVA for CBRu
Between Groups	23.41	1.00	23.41	139.41	0.00	4.96
Within Groups	1.68	10.00	0.17
ANOVA for UCS
Between Groups	40.05	1.00	40.05	418.32	0.00	4.96
Within Groups	0.96	10.00	0.10

The present investigation has been conducted to improve the mechanical properties of problematic expansive soil near Talab, Nainwa. The copper slag waste material has been utilized for the first time to improve problematic expansive soil's consistency, compaction, and strength parameters. For this purpose, the copper slag has been mixed in the range of 5–30% at 5% variation. Based on the experimental outcomes, the following crisp conclusions are drawn:

The soil sample collected from near Talab, Nainwa, has a high degree of expansiveness. The differential free swell index has decreased by 12.55% because of the specific gravity of the copper slag, i.e., 3.55. The effect of the specific gravity of CS can be easily observed when the specific gravity of soil increases.
The liquid and plastic limit of the soil samples has been decreased by 26.61% and 68.29%, respectively. The particle size distribution showed that the copper slag sample consists of silt-size particles (ranging from 0.0075 to 0.0002mm). Because of these particles, the plastic limit of soil has decreased drastically.
The maximum dry density of soil has been increased by 14.75% with the addition of 25% copper slag. Conversely, the OMC of soil has decreased by 26.80% for the same specimen.
The maximum increase in CBR of soil has been decreased in unsoaked CBR conditions, i.e., 86.27%, because of the absence of water in the voids. The copper slag particles took place between the void in an unsoaked condition. On the other hand, the soaked CBR has been increased by 34.52% with the addition of 25% copper slag. Similarly, the UCS of soil has been increased to 4.247kg/cm² by adding 25% copper slag.
The analysis demonstrates that the experimental results obtained in this investigation have a very high correlation coefficient (R more than 0.8) than results available in the literature. Hence, it can be stated that copper slag can be used to improve the mechanical properties of Talab soil.
The ANOVA test also presents that the obtained results in this investigation follow the statistical clauses and accept the research hypothesis.

To conclude, this research introduces an application of copper slag for improving the mechanical properties of problematic expansive soils. The present research may be extended by determining the strength parameters of different curing periods and performing XRD tests. In addition, the marble dust may be added in a specific range to improve the properties of 25% copper slag mixed soil. A database may be compiled by performing several experiments to apply soft computing approaches for predicting the mechanical properties of copper slag mixed soil.

CONFLICT OF INTERESTS

The authors declare no conflict of interest.

DATA AVAILABILITY

All data, models, and code generated or used during the study appear in the submitted article.

CRediT Authorship Contribution Statement

Amit Kumar Jangid: Main author, literature review, manuscript preparation, statistical analysis, detailing, and overall analysis; Kamaldeep Singh Grover: Main author, conceptualization, detailing, overall analysis; comprehensive analysis, manuscript finalization, detailed review, and editing.

FUNDING

No funding was received in assisting the preparation of this manuscript.

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No competing interests reported.

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Experimental Investigation of Mechanical Properties of Problematic Expansive Soil using Copper Slag and Its Statistical Validation

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Abstract

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1. INTRODUCTION

2. RESEARCH METHODOLOGY

3. MATERIALS AND PROJECT DESIGN

3.1 Materials

3.2 Project Design

4. RESULTS AND DISCUSSION

4.1 Swelling Index

4.2 Specific Gravity

4.3 Consistency Test Results

4.4 Compaction Test Results

4.5 California Bearing Ratio Test Results

4.6 UCS Test Results

4.7 Analysis of Results

4.8 Statistical Validation

5. SUMMARY AND CONCLUSIONS

Declarations

References

Additional Declarations

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