Introduction

Expansive soil is known to contain a great amount of clay minerals that cause poor mechanical properties such as high compressibility, low shear strength, high shrinkage limits, and swelling pressures which pose a threat to geotechnics infrastructures. Broadly, expansive soils constitute extensive clay minerals capable of causing massive volumetric change and high compressibility upon moisture influx and load application due to their diffuse double layer and morphology. The poor mechanical properties of expansive soils are known to contribute to severe distress not only in building structures but also in pavement systems. Regrettably, the high compressibility of soil could trigger a complete collapse of pavement structure [1,2,3]. The ever-increasing demand for a sustainable supply of goods and services has forced pavement and geotechnical engineers to start enhancing the mechanical properties of substandard geomaterials for the construction of long-lasting pavement structures [4]. Road pavement constructed on expansive subgrade frequently requires routine maintenance. However, routine maintenance is known to come with indiscriminate cost obligations for road agencies which in most cases surmount the initial cost of constructed pavement when compared to the total cost of maintenance in the long run. Aside from the subgrade swelling activities that negatively influenced road pavement. The traffic loads, and climatic conditions, could, trigger structural distress in pavement structures [5,6,7]. However, the majority of pavement deformation is triggered by its weak subgrade.

Generally, several attempts have been made in the past by various scholars to address the issues of subgrade deformation caused by compressibility, and swelling activities without causing harm to the surrounding environments [8, 9]. In some cases, it has become a common practice to remove the problematic soil whenever they are encountered on-site. Thus, research has shown that mechanical, chemical, or biological techniques could be employed to improve the mechanical properties of any geomaterial to a desirable level suitable for long-term performance in pavement structures [5, 10]. Notably, the use of chemicals for ground improvement somewhat has notable setbacks. Because soil-chemical interaction depends on the soil type and the reactions between the clay minerals and chemical stabilizers used for the ground improvement [11, 12]. Realistically, proper checks and examinations are necessary to eliminate the risk of exacerbating toxic chemical compounds into the environment. Therefore, it is imperative to strike a balance between contamination of the groundwater table with toxic chemical stabilizers and the selection of suitable chemicals for ground improvement, to avoid complex environmental issues [13, 14]. Thus, several researchers have used environmentally friendly chemical stabilizers or mechanical techniques of ground improvement through the use of reinforcing geosynthetic fibres [15]. Additionally, Irem et al. [16] used three types of environmentally friendly chemical stabilizers i.e., polymers which are anionic polyacrylamide polymer, guar gum, and xanthan gum to enhance the strength characteristics of kaolinitic clay. The outcome revealed that the strength gain generated by synthetic and biological polymers was eight times more than that of pure clay. Boaventura et al. [17] proclaimed that longer curing times yielded improved soil shear parameters such as friction angle, shear stress, and cohesive intercept, through 5% of synthetic polymer exhibiting the highest values compared with untreated soil. They further indicated in their study that 2.5% gains in cohesiveness and cementation at the soil profile’s substrate level were facilitated by the addition of synthetic polymer to the soil.

Another method of ground improvement that is currently gaining much attention is the bio-mediated soil engineering technique. This method involves the use of microorganisms such as fungi, bacteria, and biopolymers which are utilized to address and resolve issues associated with problematic soils. Also, this method is potentially considered a sustainable alternative when compared to soil stabilization through chemicals [18]. According to Wang et al., [19] their study confirmed that soil comprises a plethora of microorganisms that are usually applied to assist as a natural host for much-needed metabolic activities. Hence, this bio-mediated soil improvement method offers incredible and appreciable soil mechanics for direct pavement applications. The soil improvement through bio-mediation, soil, and the enzymes secreted by the microorganisms are expected to undergo biochemical reactions to generate calcium carbonate (CaCO3) crystal-like compounds within the soil pore spaces Umar et al., [20]. The drawback to bio-mediated soil improvement is that the secretion of the enzymes by the microorganisms is not uniform with the soil matrix.

Therefore, the need to continue the search for environmentally sustainable stabilizing agents with a low carbon footprint on the environment is pivotal. The most notable studies have shown that the use of waste resources like fly ash, slag, silica fume, rice hush ash (RHA), and other non-traditional stabilizers for ground improvement is gaining widespread attention [21]. Despite the availability of different industrial wastes for soil improvement, fly ash remains the most commonly used waste subgrade stabilization. Meanwhile, the use of fly ash could be found in cement production, and cement replacement in concrete [22]. Also, fly ash plays a vital role in soil reclamation [23]. Other than the use of fly ash in soil stabilization, cement, and concrete production. Fly ashes are often used in the production of zeolite, oil stabilizer, clean fill, filler in asphalt, and mineral filler. Hence, in acid mine drainage, fly ash is employed for heavy metals adsorption, low-priced adsorbent for different gaseous and aqueous applications, and additive in anaerobic digestion and composting [24, 25].

The conceptual focus of chemical stabilization is associated with improving the strength and swelling properties of expansive soils. In most cases, the desired strength improvement is not achievable in the chemical stabilization process of soil. Consequently, even when the desired strength is achieved, the stabilized soil would fail to provide the required resistance against the dynamic resistance due to the brittleness of the stabilized soil particularly in pavement, rail tracks, etc. However, this is the gap this paper attempts to bridge through the application of activated desilicated fly ash, to improve the dynamic shear resistance expansive subgrade. Therefore, this study focuses on key factors associated with stabilizing expansive soils using an activated desilicated fly ash stabilizer. The DFA is an industrial byproduct generated through the chemical leaching of fly ash. Several approaches have been provided to recover Silica from fly ash. This process includes leaching with acid or alkali, proceeded by purification and separation procedures. Silwamba [26] reported an alkaline leaching procedure where Silica oxide is removed from fly ash using NaOH as a Na2SiO3 solution. The process is designed to extract silica and potassium silicate solution is also produced which could be used as a ceramic binder, high-temperature welding with carbon arc electrodes, paints, decorative coatings, and as adsorbents in acid mine drainage treatment.

Recently, the collapse of pavement structures in large numbers caused by improper design has been on the rise. Many design engineers often design pavement structures without considering the impact of the dynamic shear response of the subgrade. This continues to be a major challenge for the long-term performance of pavement structures. Therefore, is ideal to consider the dynamic shear modulus and damping ratio in pavement design and analysis even at a micro level. In the foregoing literature, many researchers have reported on the soil’s dynamic shear modulus and damping ratio [27,28,29] while the dynamic response of subgrade for pavement performance is still sketchy. On the other hand, the compressibility response of soil has a significant impact on pavement performance. Despite this overwhelming evidence, a limited number of studies have tried to treat compressible expansive subgrade soils using desilicated fly ash.

Therefore, this research study seeks to contextualize the possible potential of improving the hydromechanical behaviour of compressible expansive subgrade soil using nanomaterial composite. The effects of nano-desilicated fly ash on the compressible expansive subgrade were achieved using zero swelling tests (ZSTs), 1D consolidation tests, and dynamic triaxial (DT)) tests as the evaluation indices. In this study, 10%, 20%, and 30% of nano-disilicate fly ash (NDFA) activated with 5% nano-slag were used to improve the compressibility and dynamics performance of the expansive subgrade. The repeated response of the subgrade was ascertained by executing a series of dynamic resilient modulus tests under a range of confining pressures (20 kPa, 50 kPa, and 100 kPa). Furthermore, the study deliberates the abilities, opportunities, and challenges of using the proposed activated nano-desilicated fly ash to address the challenges of soil swelling, compressibility, cyclic stress resistance, and porosity. Therefore, expanding the knowledge of multiple stabilization influences and bridging the gaps of severe environmental issues of dumping fly ash in landfills.

Materials and Experimental Program

Materials

Expansive Soil

The soil sample was acquired from a testing site in Pietermaritzburg at a depth of 1.2 m having 1.6 m length and 1.3 m width using manual method of sample collection. An analysis of the particle size distribution was carried out following the ASTM D1140 [30] protocol. Figure 1 demonstrates the test result of particle size analysis. Subsequently, the soils that cleared the 0.075 mm sieve size were tested using a hydrometer, to further quantify the exact percentages of silt and clay particles representatives in the soil fines.

Fig. 1
figure 1

Soil gradation curve

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The investigated subgrade soil was observed to be predominantly a fat clay (CH) which is high in plasticity according to the (USCS) Unified Soil Classification System. The average effective particle diameter of D60 is greater than 0.019 mm. To assess the soil's potential for swelling, the expansive soil was subjected to the free swell index (FSI) test in accordance with Indian standard IS 2720 Part-40 [31]. The index properties of the examined expansive soil are summarised in (Table 1). The soil exhibits a significant capacity for water adsorption, as evidenced by its high liquid limit and plasticity index, which span a range of 82 to 95 degrees of saturation.

Table 1 Properties of soils
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Slag (GGBS)

The steel slag utilized in this investigation was acquired from Fry’s Metals in South Africa and it is a byproduct of the basic-oxygen-furnace (BOF) process. The material constitutes SiO2 + Al2O3 + FeO3 + CaO, of a total oxide of above 80% and 0.075 mm of particle size.

Disilicate Fly Ash (DFA)

The fly ash utilized in this study was acquired as coal fly ash from the Lethabo power station in South Africa. One crucial sign of the quality of the material for subgrade stabilization is the chemical makeup of FA. According to ASTM C6 [32] (2018), the FA used herein is quantified as class “F” because it has a compound proportion of SiO2 + Al2O3 + Fe2O3 content that is higher than 70%. Based on the XRF test result. The received fly ash was leached for silica using Potassium hydroxide (KOH) of 3 M concertation with the aid of a temperature-controlled hot plate Magnetic Stirrer mounted with a PT1000 probe to accurately measure the medium’s temperature. The desiliconization process lasted within a time frame of 6 h satisfying the conditions of 500 rpm agitation speed, 25 liquid–solid (L/S) ratio, and corresponding temperature of 100 °C following Anil et al. [33] procedures. The KOH solution was allowed to cool until the room was reached, and the insoluble residue and leached solution were separated using Whatman filter paper number 44. By employing ICP-AES analysis, the silica and alumina contents of the leached solution were ascertained, while EDX analysis was utilized to ascertain the residue.

Nanosized Materials

It was challenging obtaining FA and GGBS at the nano level, therefore the received FA and GGBS materials were synthesized through a top-to-bottom process to a nanoscale. The nanoscale of the FA and GGBS started by drying the individual materials in an outdoor environment for 7 days. Subsequently, the materials were further ground in a mechanical ball-milling for 6 h with 45-min pauses at a spin rate of 500 rpm. At each interval, Anionic and Toluene surface-active chemicals were included to cool the internal chamber of the mill to remove any formation of particle agglomerations. For each run of FA and GGBS, these conditions were repeated till the surface area of the nanomaterials increased from 0.08 m2/gm to 19.40 m2/gm and 0.02 m2/gm 23.15 m2/gm for GGBS and NDFA respectively. The initial test results presented in (Table 2) were used to quantify the percentages of chemical compositions of the compressible expansive subgrade soil, GGBS, FA, and NDFA.

Table 2 Chemical constituents of the used materials
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Sample Preparations

The sample preparation followed a standard procedure to achieve consistency with the fabricated specimens. The needed dry quantities of expansive soil with the corresponding percentages of NDFA and GGBS were mixed under dry conditions. The specimens were fabricated using optimum amounts of moisture content as attained from Proctor compaction tests. However, various moisture contents were applied to assess the effects of moisture contents on soil geotechnical properties. As shown in (Fig. 2), this test is designed to identify the different moisture contents of the composite and their associated dry densities. For easy specimen identification, the prepared specimens were encoded to have the following identities for example untreated expansive soil was designated as T0 whereas 10%NDFA + 5% nanoslag, 20%NDFA + 5% nanoslag, and 30%NDFA + 5% nanoslag were all encoded as T1, T2, and T3 respectively.

Fig. 2
figure 2

Soil compaction curve

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The expansive soil was firstly mixed with 10%, 20%, and 30% of nano-disilicate fly ash (NDFA) whereas 5% of nano-slag was used to activate the NDFA to trigger pozzolanic reaction in the presence of moisture. The dry mixing lasted for 20 min for uniform blending of the soil, NDFA, and nanoslag. Subsequently, the calculated quantities of moisture were added and automated mixing continued for another 10 min. The composite mixtures were covered with a waterproof bag and 2 h mellowing time was allowed for moisture distribution. Immediately after the mellowing of the composite materials, specimens’ fabrication commenced for different laboratory soil testing. Also, trial specimens were prepared for equipment calibration following 3 sets of fabricated specimens at different moisture levels for each laboratory soil testing to eliminate any form of test results discrepancies.

Experimental Work

The civil engineering standard tests regularly used to quantify the soil’s geotechnical properties for pavement construction purposes were conducted on the fabricated specimens. These tests were executed to examine the degree of durability and mechanical performance of the expansive subgrade treated with nano-desilicated FA.

Zero swelling Test (ZST)

The swelling pressure of the investigated subgrade was measured using the IS 2720 (Part 41) [34] protocol. The soil samples that had passed through an ASTM sieve aperture of 0.075 mm (#200) were utilized to perform the ZST. The specimens were fabricated using the initially obtained moisture contents from the compaction test results as previously stated in Sect. “Sample Preparations” above. Firstly, the composite material was compacted into an oedometer ring with a diameter and height of 75 mm and 18 mm respectively. As the specimens were loaded, after, distilled water was used inside the ring to soak it on a high-pressure oedometer frame under a vertical stress of 0.1 MPa. The mounted strain gauge started recording some vertical increase in the specimen volume as the fabricated specimen in the oedometer frame began to absorb water. The increase in specimen volume is known as swelling, and a vertical surcharge load was added to the oedometer ring beam to counter the vertical swelling and bring the strain gauge to a zero reading. Further swelling and vertical strain were allowed and vertical surcharge load to keep the strain gauge to a zero reading. The process continued until no further vertical strain (swelling) was recorded. At this stage, the total applied surcharged loads that were used to counter-react the swelling was summed and computed using Eq. 1. As proposed by Al-Mhaidib and Al-Shamrani [35].

$${P}_{s}\left(\text{kPa}\right)=\left({\sum }_{i}^{n}=1Mi\times g\times {b}_{r}/\pi \left({\varphi }^{2}\right)/4\right)/1000$$
(1)

where, Ps is the swelling stress in kPa, \(({\sum }_{i}^{n}=1{M}_{i})\) is the sum of surcharges, g is the acceleration due to gravity 9.81 m/s2, \({\text{b}}_{\text{r}}\) is equivalent to the beam ratio of the oedometer arm, \(\uppi \left({\varphi }^{2}\right)/4\) is the inner area of the ring.

One-Dimensional Compression Test

The one-dimensional compression test was performed on the fabricated specimens following the ASTM D2435/D2435M [36] protocol. The specimens bear the shape of the oedometer ring which corresponds to a diameter and height of 75 mm and 18 mm respectively. The following parameters dry mass of the sample, the height of the sample at the beginning of the test, the area of the sample, and specific gravity were measured and logged into the computer. Subsequently, the sample is positioned inside a metal ring with two porous disks located on both the top and bottom of the sample. After fabrication, the specimens were allowed to cure for 7 days before being it up on the oedometer frame to commence testing. The experimental setup is structured in a manner that a micrometer dial gauge is mounted load frame, and the specimen is saturated as the oedometer equipment is configured and connected to the data logger. Each load is kept for 24 h on a time and loading sequence of 0, 1/4, 1/2, 1, 2, 4, 8, 15, 30, 60 min, and 2, 4, 8, 24 h(s) and 12.5 kPa, 25 kPa, 50 kPa, 100 kPa, 200 kPa, 300 kPa, 400 kPa, and 800 kPa respectively. At the end of the test, the mathematical expression in Eqs. 2–4 was used to calculate the void ratio and pressure.

$${H}_{s}=\frac{{w}_{s}}{A{G}_{s}{\gamma }_{w}}=\frac{{M}_{s}}{A{G}_{s}{\rho }_{w}}$$
(2)

where \({w}_{s}\) is the weight of a solid, \({\text{M}}_{\text{s}}\) is the mass of the solid, \(A\) is the sample area, \({G}_{s}\) is the specific gravity, \({\gamma }_{w} and {\rho }_{w}\) are equivalents to the unit weight of water and density of water respectively.

$${H}_{v}=H-{H}_{s}$$
(3)

where \(H\) is the initial height of the specimen.

$${e}_{0}=\frac{{V}_{v}}{{V}_{s}}=\frac{{H}_{v}}{{H}_{s}}$$
(4)

where \({e}_{0}\) is the specimen’s initial void ratio.

Based on the void ratio-log pressure curve plotted using the one-dimensional oedometer test, the values of Compression Index (\({C}_{c}\)) and Coefficient of Compressibility (\({a}_{v}\)) were also determined using the mathematical expression in Eqs. 5 and 6. The Compression Index (\({C}_{c}\)) values were calculated using the slope of the normal compression line whereas the Coefficient of Compressibility (\({a}_{v}\)) values were determined using the slope of the void ratio and effective stress graph at a particular pressure. However, this is the reduction in void ratio per unit increase in stress.

$$c_{c} = \frac{\Delta e}{{\log_{10} \left( {\frac{{\sigma_{f}^{\prime } }}{{\sigma_{I}^{\prime } }}} \right)}}$$
(5)
$${a}_{v}=\frac{e-{e}_{0}}{{\sigma }^{\prime}-{\sigma }_{0}^{\prime}}=-\frac{\Delta e}{\Delta {\sigma }^{\prime}}=-\frac{de}{d{\sigma }^{\prime}}$$
(6)

where \(e-{e}_{0}=\Delta e=de\), \({\sigma }^{\prime}-{\sigma }_{0}^{\prime}=\Delta {\sigma }^{\prime}=d{\sigma }^{\prime}\) represent the variation in void ratio and effective applied stress respective for the specimens.

Dynamic Triaxial Test

The dynamic triaxial tests were performed following the ASTM 3999 [37] protocol, to evaluate the dynamic behavior of untreated and treated expansive subgrade at an applied 100 number of cycles. This testing procedure is designed to determine the modulus and damping properties of soils using the cyclic triaxial testing equipment. The fabricated specimens bearing a shape of 300 mm height and 150 mm diameter maintaining an aspect ratio of 2:1 were used for the specimens testing. A fully functioning Dynatrax cyclic triaxial set was used as a series of strain-controlled cyclic triaxial tests were executed. A 10-bar air compressor was used to provide the pneumatic loading device system, as the changes in volume, deformation, and vertical load were calculated by an electronic transducer. The (CDC) Compact Dynamic Controller unit was used to monitor and control variation during the testing time frame. The CDC system conveyed the transducer data back to the computer with the help of high-speed connectivity. The water back pressure of 97% was used to saturate and consolidate the specimens, this is considered sufficient water saturation for the undrained testing.

The test was performed using confined pressures of 50 kPa, 100 kPa, and 200 kPa at a cyclic loading rate of 0.1 constant strain and 1 Hz frequency. An applied cyclic loading in 100 cycles as the test data such as shear modulus and damping ratio which were required for this investigation were processed using an acquisition data logger system. The permanent strain values were computed as the average strain of the first cycle as stipulated by Vucetic and Mortezaie [38]. Upon the completion of the test, the damping ratio and dynamic shear modulus of the tested specimens were used as indicators to evaluate the degree of cyclic resistance for the treated and untreated specimens. The fabricated specimens and the dynamic triaxial testing setup are presented in (Fig. 3).

Fig. 3
figure 3

Fabricated specimens and dynamic triaxial tests setup

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Results and Discussion

Evaluation of Nano-Desilicated FA on Subgrade Swelling Pressure

The effect of activated NDFA on the reduction of swell pressure is presented in (Fig. 4). The examined subgrade soil recorded a swelling pressure of 780 kPa, this implies that the subgrade soil is highly expansive and has been indicated by the FSI swell index result. The treated subgrade soil recorded a paradigm decrease in swelling pressure, this was observed upon the introduction of NDFA activated with nano-slag. The expansive subgrade decreased in swelling pressure from 780 to 510 kPa upon the addition of 10% NDFA. A further decrease in swelling pressure was recorded as the percentage of activated NDFA increased. For instance, the swelling dropped from 510 to 210 kPa upon the inclusion of 20% NDFA and eventually decreased further to 95 kPa upon the inclusion of 30% NDFA. The reduction in swelling pressure of the expansive subgrade was expected due to the nanoscale effects of the stabilizer. The NDFA with a large surface area altered the double-diffused microstructure of the subgrade causing the subgrade to respond in a brittle manner with high stiffness. The addition of activated NDFA which has a larger surface area triggers a complete pozzolanic reaction in the presence of moisture. This reaction involves the transportation of calcium hydroxide in the presence of moulding water content of the sample within the soil. The calcium hydroxide from the nano-slag combines with the aluminate and silicate clay minerals as the Ca2+ ions within the soil and nano-slag dissolve. This compound then reacts with any dissolved SiO2 and Al2O3 located on clay particles to produce hydrated gels of C–S–H and C–A–H, which binds soil particles therefore reducing the swelling pressure significantly. This result obtained herein is in line with the study published by Rivera et al. [39] which concluded that alumina, silica, calcium oxide, and ferrite are the mixtures in an aqueous medium that activate a pozzolanic. The process of this reaction binds the spread particles of clayey soil by increasing van der Waal’s interparticle forces to form a strongly knitted soil matrix.

Fig. 4
figure 4

Variation of swelling pressure with NDFA

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Evaluation of Nano-Desilicated FA on Subgrade Compressibility

The compressibility behavior of soil treated with 10%, 20%, and 30% (T10, T20, and T30) of NDFA was evaluated using pressure-void ratio curves at three different moisture contents i.e., dry, opt, and wet sides to improve the soil compressibility. The variation of NDFA content with the soil compressibility is illustrated in (Fig. 5a–c). It was observed that the initial void ratios of the fabricated specimens treated with varying percentages of NDFA were significantly low compared to the untreated fabricated specimens. The untreated soil specimens recorded the highest void ratio value of 2.11 and this indicates that the soil is highly compressible due to the larger void ratio. However, upon the inclusion of NDFA, the soil’s initial void ratio gradually decreased. Hence, a significant reduction in the soil's initial void ratio was recorded when 30% of NDFA was used to stabilize the investigated soil. Therefore, this caused the initial void ratio to decrease from 2.64 to 0.81 at the optimum moisture level. Notably, it is observed that moisture contents have significant effects on the soil compressibility behavior in the sense that the void ratio increases as the moisture increases. However, this trend is more significant in untreated soil compared to treated soil specimens. This is because the amounts of C–S–H and C–A–H gels bind and precipitate the soil particles during the curing period. Similarly, during consolidation, the treated specimen absorbed more moisture to enhance the pozzolanic reaction. The reaction contributes to strength development as the C-S–H and C-A-H gels fill up the void space of the soil matrix causing the specimens to be stiffer to sustain the applied pressure during consolidation.

Fig. 5
figure 5

a, b Effects of NDFA on e-log \({\sigma }{\prime}\) curve @ dry and opt moisture contents. c Effects of NDFA on e-log \({\sigma }{\prime}\) curve @ wet-side of the optimum

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However, the applied pressure had significant effects on the untreated specimens due to their initial void ratio. Notably, the applied pressure increases, with the corresponding increase in the void ratio. Thus, the void ratio attained gradually decreases as moisture dissipates from the specimens. This implies that the untreated specimen has a larger porosity compared to the NDFA-treated specimens. It was also noted that the void ratios of the expansive soil cured with different percentages of NDFA decrease with the increase of the consolidation pressure at different rates. However, the expansive soil has experienced compression deformation under different consolidation pressures. At 600 kPa and 1200 kPa the consolidation pressure of the untreated specimens recorded void ratio values of 1.71 and 1.31 respectively. Whereas at the same consolidation pressure, the 20% NDFA (T20) treated specimens recorded 0.68 and 0.6. This showed that a significant decrease in void ratios of 40% and 46% was recorded upon the 20% addition of NDFA. As deliberated earlier for the swelling pressure, the NDFA has nanosized particles that fill the soil’s voids resulting in the interlocking of the soil particles through pozzolanic reactions hence translates to a significant decrease in the void ratio [40, 41].

Variation of Nano-Desilicated FA with Compression Index (\({{\varvec{C}}}_{{\varvec{c}}}\))

The variation of the compression index of the specimens fabricated with NDFA at different moisture content is presented in (Fig. 6). The Compression Index of both the treated and untreated soil was obtained from the slope of the log pressure versus void ratio graphs presented in Fig. 5a–c. The compression index value of the specimen fabricated with the optimum moisture content recorded a 0.65 value, this indicates that the soil is highly compressible, and this could be correlated with the soil plasticity index result as presented in Table 1. The high plasticity index of the investigated soil mobilized a high compressibility index in the fabricated specimens due to the void spaces within the soil matrix as supported by Akbarimehr and Aflaki [42]. However, the results of the test showed that the compression index of the expansive soil began to decrease as the NDFA increased. For example, the compression index value decreased from 0.65 to 0.47 upon a 10% addition of NDFA. Similarly, the compression index decreased further from 0.47 to 0.38 and 0.29 respectively for 20% and 30% NDFA addition. The decrease in compression index was accounted for by the addition of the NDFA waste to expansive soil. As matched to a similar test executed using lime and Fly ash it was detected that the multiple stabilizers performed better than a single stabilizer to achieve a desired decrease in soil compression index due to multiple stages of pozzolanic reaction. The reaction generates long-term strength through the creation of calcium aluminate hydrates (C–A–H) and calcium silicate hydrates (C–S–H) by reacting with the soil. The addition of nanoscale GGBS reacts with the formed aluminates and silicates and is solubilized by the clayey soil particles in the presence of moisture. Similarly, the increase in moisture content triggered in compressibility index value for the untreated soil. The addition of NDFA to the soil mobilized significant absorption of moisture. This enhanced the pozzolanic reaction for the complete development of compounds responsible for strength development therefore reducing the void within the soil matrix and fostering a decrease in the compressibility of the soil as also supported by Shriful et al. [43], Raj et al. [44].

Fig. 6
figure 6

Variation of the compression index with NDFA at different moisture contents

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Variation of Nano-Desilicated FA with Coefficient of Compressibility (\({{\varvec{a}}}_{{\varvec{v}}}\))

The results obtained for the variations of the Coefficient of Compressibility (\({a}_{v}\)) against nano-desilicated FA is presented in (Fig. 7a–c). The specimens fabricated using the optimum moisture content were used to measure the resistance against the Coefficient of Compressibility of the studied expansive soil. An investigation was conducted to analyze the values of the compressibility coefficient (\({a}_{v}\)) and effective stress for the specimens treated with NDFA, across various consolidation pressures. The expansive soil recorded coefficient of compressibility values which range from \(11.23 \times {10}^{-4}{m}^{2}/kN\) to \(6.1 \times {10}^{-4}{m}^{2}/kN\) as the pressure increases from 50 to 200 kPa. The trend indicates that the soil compressibility decreases with a given increased effective stress. It was noted that with the inclusion of NDFA, the coefficient of compressibility values varied from \(9.2 \times {10}^{-4}{m}^{2}/kN\) to \(0.42 \times {10}^{-4}{m}^{2}/kN\) over the range of applied effective stresses. The coefficient of compressibility decreased further upon the addition of the NDFA coupled with the synergy effect of applied effective stress. Generally, a great proportionality was observed between the NDFA content and the coefficient of compressibility. This implies that the addition of NDFA to the expansive soil significantly improved the soil's mechanical properties by reducing the coefficient of compressibility values to an average value of 23.2% compared to the soil's initial coefficient of compressibility values. This change could be attributed to the positively charged Ca2+ ions from the nano-slag which led to the development of a flocculated structure in the clay during the pozzolanic reaction. The flocculation leads to a reduction in the compressibility coefficient of treated soil as supported by Li et al. [45].

Fig. 7
figure 7

Variation of NDFA stabilizer on the compressibility coefficient of expansive soil

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Variation of Nano-Desilicated FA with Dynamic Shear Modulus

The variation of nano-desilicated FA with dynamic shear modulus at numerous confining pressures is illustrated in (Fig. 8). The specimens were fabricated using the optimum moisture content were used to assess the dynamic shear resistance of the studied expansive soil. Shear modulus is observed to rise with increasing NDFA content. However, it is evident that the increase in confining pressure also contributed to the increase in shear modulus. For the untreated soil samples, the shear modulus is improved by 84% at a confining pressure of 200 kPa compared to the samples tested at 50 kPa of confining pressure which recorded a lower shear modulus. The specimens treated with 20% nano-desilicated fly ash content show a strength enhancement of 63% at a confining stress of 200 kPa compared to specimens tested at 50 kPa which portrayed an average strength increase of 23% referenced to the same percentage of nano-desilicated fly ash content. The results simply indicate that both NDFA and confining pressure improved the stiffness of the soil however, beyond 20% NDFA content, the stiffness was significantly improved. The nano-desilicated fly ash relatively formed a stiffer soil matrix through a pozzolanic reaction the reaction between the soil and nano-desilicated fly ash endowed the composite of the soil with some stiffness that was shown by composites with 20% and 30% NDFA contents. The nano-desilicated fly ash additions reduced the average unit weight of the composite of the soil since nano-desilicated fly ash possesses a low unit weight of \(0.8g/{cm}^{3}\) [46, 47]. Essentially, the increase in the volume of non-dispersible fine aggregates (NDFA) resulted in variations in the volume of empty spaces within the soil composite. Given that the samples utilized in this study were produced through compaction, the inclusion of NDFA resulted in the dense packing of soil particles and the removal of voids from the soil matrix.

Fig. 8
figure 8

Variation of Dynamic shear modulus with nano-desilicated FA content

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This phenomenon was more noticeable at high NDFA content (30%) and thus improved the stiffness of the treated soils. As a result, a flocculated NDFA-soil interface was created when confinement increased and soil particle and NDFA cohesion increased. The improved NDFA-soil cohesion improved the soil composite’s mechanical properties by providing appreciable resistance against dynamic shear failure.

Furthermore, the deformation of 30% nano-desilicated FA treated and untreated soil specimens was evaluated through the variations of shear modulus with strain deformation at numerous confining pressures shown in (Fig. 9a, b) respectively. The results demonstrated that the untreated specimens portrayed a higher rate of shear modulus degradation than the specimens treated with nano-desilicated FA. The variation in shear modulus for the untreated soil specimens is slightly benefited by the confining pressure. Whereas the phenomenon significantly affects the rate of shear modulus degradation for the treated soil specimens. This might be attributed to the lack of strength development for the untreated soil due to lack of stabilizer which metamorphosed to weak stiffness of soil matrix as the cyclic loading progresses from low strain to higher strain energy. However, it was noted that the density and compressibility index of untreated specimens improved in the initial cycle due to the initial applied compression load and void spaces within the specimens. However, this resulted in an increased rate of shear modulus degradation for untreated soil samples. Furthermore, to illustrate the rate of shear modulus degradation with shear strain regarding normalized shear modulus \(\left(G/{G}_{max}\right)\) the modulus reduction curves are used [48]. Where \({G}_{max}\) is equivalent to the soil’s shear modulus and it is simply identified at a very low shear strain i.e., \((\varepsilon \le 5\times {10}^{-6})\) based on the study published elsewhere by Kumar et al. [49]. Due to the difficulty of obtaining the experimental data at a very small strain, an empirical correlation developed by Hardin and Drnevich [50] shown in Eq. 7, was used herein to compute \({G}_{max}\).

$${G}_{max}=\frac{{102132.65*\left(2.973-e\right)}^{2}*{\left(OCR\right)}^{k}{\left({\sigma }_{c}\right)}^{0.5}}{1+e}$$
(7)

where \(e\) and \(OCR\) are equal to the void ratio and over-consolidation ratio of the specimens was obtained from the e-log pressure curve as previously presented in (Fig. 4a–c). The correlation coefficient is \(k\) which is considered and taken as 1 to simplify the mathematical expression in Eq. 7, \({\sigma }_{c}\) is the confining pressure. The normalized shear moduli for treated and untreated soil specimens are depicted in (Fig. 9c, d) respectively. The result obtained from this investigation followed a similar trend to what has been reported by Seed and Idriss [51]; Kokusho [52]; Vucetic and Dobry [53] which supported that the cyclic degradation rate for treated soil is affected by confining pressure but slightly on the untreated soil due to weak inter-particulate bonding within the soil matrix. Generally nano-desilicated FA inclusion causes resistance against the rate of modulus degradation. This may be the result of the formation of tertiary compounds through pozzolanic reactions. The strength-developing compounds formed a stiffer matrix with strong creep of flocculated particles and hence formed a strong resistance against shear modulus degradation at a low strain level of less than 1.6% compared to the untreated soil which recorded a strain deformation at 2.5%. The anticipated outcome of the chemical reactions would be a macro structural modification of the soil, which would reinforce the confinement’s effects.

Fig. 9
figure 9

Variation of shear modulus with shear strain a untreated soil b treated soil 30% NDFA. Variation of G/Gmax with shear strain c untreated soil d treated soil 30% NDFA

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Variation of Nano-Desilicated FA with Damping Ratio

The damping ratio is used to demonstrate energy dissipation in a vibrating body mobilized through dynamic or cyclic loading. The dynamic response of geotechnical infrastructures is relatively proportional to soil stiffness and compressibility resistance supporting these infrastructures. On this basis, the damping ratio variation with nano-desilicated FA is presented in (Fig. 10). It is shown that increasing nano-desilicated FA contents triggered an increase in the damping ratio. Upon the inclusion of 30% NDFA, damping ratio improvements of 32.4%, 65.5%, and 82% for 50 kPa, 100 kPa, and 200 kPa, confining pressures respectively, are recorded. The recorded response of the NDFA-treated soil agrees with the findings published by Xin et al. [54]. It was found in each of these studies that the damping ratio and confining pressure exhibit a direct proportionality. Further, the result obtained herein is supported by Bo et al. [55] which indicated that the increase in confining pressure on the stiffness of treated soil ultimately enhanced damping properties. Conversely, the application of confining pressure increased the bonding between soil particles and enhanced the ability of the stabilized soil to resist shear forces, primarily due to the occurrence of a pozzolanic reaction. The enhanced shear resistance of the treated soil resulted in an overall improvement in its damping properties. Furthermore, the enhanced shear resistance of the treated soil is a direct indication of an improved soil mechanical property capable of withstanding critical damping due to vibration.

Fig. 10
figure 10

Variation of damping ratio with nano-desilicated FA

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The summary of swelling pressure, compressibility index, and dynamic shear modulus of the examined soil are presented in (Table 3). This study evaluates the influence of nano-desilicated fly ash activated with 5% nano-slag on the dynamic shear modulus and compressibility properties of expansive soil. By weight, the air-dried activated nano-desilicated fly ash was added to the expansive soil in several mix ratios i.e., T0 T1 T2, and T3 to fabricate the tested specimens. Thereafter, geotechnical properties such as swelling pressure, micro‑void compression index, compressibility coefficient, dynamic shear and modulus, and damping ratio of the expansive soil were assessed after a 28-day curing period. The results obtained in this study suggest that great proportionality exists between compressibility and normalized dynamic shear modulus. This observation is also confirmed by Hardin and Drnevich [50] in their study which supported and claimed that micro-voids and over-consolidated ratio are all functions of dynamic shear modulus depending on the soil type and confining pressure.

Table 3 Summary of swelling dynamic modulus and micro-void behaviour of the expansive soil
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Conclusions

In light of the test findings and the subsequent analysis performed in this study, the following conclusions are inferred:

  1. 1.

    The swelling pressure of the expansive soil was reduced to an average percentage of 34.6%, 4.36%, and 87.8% upon 10%, 20%, and 30% upon the inclusion of nano-desilicated fly ash. This indicates a progressive decrease in swelling pressure with corresponding synergy effects of the day curing period and increased dosages of nano-desilicated fly ash. The decreased swelling pressures owing to the completion of the pozzolanic reactions of activated nano-desilicated fly ash with the soil minerals in the presence of water content forming hydrated gel at a micro level to suppress the diffused double layer of the soil.

  2. 2.

    The e-log pressure- curves reveal the micro‑void of the expansive soil, confirming that the soil is highly compressible. Further test results on compressibility analysis demonstrated that the soil stabilized with nano-desilicated fly ash has a considerable trend in compressibility coefficient (\({a}_{v}\)) with the variation of NDFA for a range of effective stress. An increase in compressibility coefficient (\({a}_{v}\)) and compression index (\({C}_{c}\)) illustrated the impact of nanomaterials in improving the compressibility of highly compressible soil by filling up the micro-voids within the soil matrix irrespective of moisture content effects.

  3. 3.

    The inclusion of nano-desilicated fly ash caused an increase in dynamic shear modulus whereas the non-stabilized soil specimens recorded a decreased variation under the same confining pressures. The decrease was caused by the reduction in rigidity of the non-stabilized soil as a result of a significant number of voids. Consequently, the shear modulus experienced a slight enhancement as the level of confining pressure was increased.

  4. 4.

    A great proportionality exists between the maximum dynamic shear modulus, normalized shear modulus of the studied expansive soil and the effective confining pressure can be observed, indicating that a change in confining pressure could relatively influence the dynamic response of causing strain deformation at micro strain level which more pronounced in non-stabilized soil.

  5. 5.

    Increasing the dosages of nano-desilicated fly ash triggered a significant increase in the damping ratio. This implies that the nano-desilicated fly ash enhanced the attenuation of cyclic stress causing an increase in damping ratio. For the non-stabilized soil, the dynamic shear modulus decreases, and the damping ratio decreases within a large range of shear strain, which is related to the compactness and lack of cohesion of the particles with the soil.