Optimizing micaceous soil stabilization using response surface method

J. Zhang, A. Deng, M. Jaksa

School of Civil, Environmental and Mining Engineering, University of Adelaide, Adelaide, SA 5000, Australia

Keywords: Fiber Polymer Central composite design Unconfined compression strength (UCS)Mica

ABSTRACT Micaceous soil is a problematic soil due to its low strength and poor ductility. In this context, the performances of micaceous soils were improved by applying a combination of granulated blast furnace slag,fiber and polymer additive.The dosages examined included 0%-30%mica,3%-15%slag and 0.25%-1.25%fiber by weight, and 0.1-0.5 g/L polymer additive. Most of the combinations were found to increase the material strength and ductility, yet to be optimized. To refine the dosage, response surface method was used to conduct experimental design and develop predictive models for material strength. The developed models formulate the material strength as a nonlinear function of dosages and,by interrogating it,can optimize additive contents in terms of target requirements. The models were verified through trials and can be used to determine dosages to upscale micaceous soils to field conditions.

1. Introduction

Mica minerals are widely distributed around the world and naturally occur in igneous, sedimentary and certain metamorphic rocks(Galán and Ferrell,2013).Due to weathering processes,mica minerals break down to finer particles and are presented at varied levels in natural soils which form micaceous soils. In the presence of mica, micaceous soils suffer from deformation issue and adversely influence serviceability of infrastructure systems that are founded on them (Frempong, 1995). One instant problem is an invalid,or at least less effective,soil compaction.Compactive effort is offset completely or partially by mica rebound nature in load-unload actions(Weinert,1980).The compressible underlying stratum undermines the stability and serviceability of infrastructure systems of concern. In addition, mica particles are platy and crushable at micro-scale and,during compression or shearing,tend to rotate and orient them in a somewhat parallel fashion, yielding low shear resistance(Harris et al.,1984;Seethalakshmi and Sachan,2018).As per Sachan et al.(2019),soils with more than 10%mica is generally not recommended for pavements. Due to these problematic natures, micaceous soils less likely meet construction quality requirements in general field applications, and are usually avoided or replaced (Frempong, 1995; Zhang et al., 2019a). If unavoidable in some instances, expensive alternative foundation solutions including piles are installed which sometimes are not financially or logistically viable. Instead, the unsatisfactory performance of micaceous soils can be ameliorated through soil stabilization.

Soil stabilization incorporates a volume of additives,e.g.cement,lime, fly ash and slag, in soils. In contact with water, the additives trigger a series of short-to long-term main pozzolanic reactions in soils and improve stiffness and strength of the soil. The improvement has been verified on a variety of problematic soils, e.g.expansive soil (Al-Rawas, 2002), residual soil (Basha et al., 2005),kaolinite(Ge et al.,2018),lithomargic clay(Amulya et al.,2020),and high-plasticity soil(Hossain and Mol,2011).Of the varieties of soils,consistently better performance on strength, compaction,compressibility and/or microstructure (i.e. fabrics) are obtained.The levels of enhancement are varied depending mainly on dosage used, soil types examined, curing time and tests conducted. For example, Prabakar and Sridhar (2002) examined the effects of fly ash added to three types of soils.They found that addition of fly ash increased the shear strength for all three soils. The value of cohesion can be increased by addition of fly ash, but at varied levels(0.39 kg/cm2for loamy soils and 0.66 kg/cm2for clayey soil).Similar strength variation was obtained on cemented kaolinite by Ge et al.(2018). In their study, it was suggested that the unconfined compressive strength (UCS) increased with the cement content when the water content and the weight of soil were fixed.

In addition to the conventional pozzolanic additives, choices of additive have expanded to non-pozzolanic,low-cost,low-emission green materials. The materials are sourced from either natural or synthetic polymeric agents,resin or organic matters,or industry or municipal by-products that are disposed of from the factories or facilities. The examples include rice husk ash (Basha et al., 2005),fly ash, bottom ash, blast furnace slag, phosphogymsum and red mud(Al-Rawas,2002),kiln dust and volcanic ash(Al-Rawas,2002;Hossain and Mol, 2011; Bahadori et al., 2019), calcium carbide residue (Latifi et al., 2018), bacteria-induced calcite precipitation(Saffari et al., 2017; Latifi et al., 2018), and polymer and resin(Soltani et al., 2019a, b). These emerging additives can trigger pozzolanic or non-pozzolanic reactions, or a combination, if blended with soils, and develop soil strength. Usually, the obtained strength is comparable to those obtained from the pozzolanic additives depending on the dosage used and is equally qualified for suitable field applications. In applications, nonpozzolanic additives can use standard or readily modified equipment as for pozzolanic additives, thus offering an approachable solution.

Aside from the chemical stabilization,physically reinforced soils with natural or synthetic fibers provide alternative solutions to soil stabilization. The collection of fiber usually is distributed in a random and discrete fashion,which offers an excellent coverage of soils and inhibits development of potential slips or planes in the soils (Wang et al., 2017). Fibers have been successfully used to reinforce a range of problematic soils.The fibers are varied mainly in four factors: material, length, aspect ratio and dosage. As per a number of studies (e.g. Sarbaz et al., 2014; Danso et al., 2015;Sharma et al.,2015),the four factors of fiber collectively govern the strength development and ductility of stabilized soils. To this end,these factors can be optimized to stabilize the soil. For example,Danso et al. (2015) recommended fiber content of 0.5% by weight for high-plasticity soil,Prabakar and Sridhar(2002)recommended 0.75% for construction soils, and Kumar et al. (2006) attempted a combination of 2%of 3 mm plain fibers or 0.5%of 6 mm plain fibers to attain the optimal improvement. Although the recommended dosages are varied, many studies agree on the following fiberinduced outcomes: (i) reduced maximum dry unit weight, (ii)improved ductility,and(iii)moderate strength gain.The reduction of dry unit weight does not necessarily mean loose packing of materials, but occurrence of well-compacted lightweight fabrics.The lightweight nature arises from fiber offering much lower density than soils do.One concern is that the strength and ductility of fiber-reinforced soils are likely to turn down if the fiber contents are excessive or exceed the optimized dosage. This concern, however, can be overcome by applying a combined stabilization solution.

The combinations of fibers and pozzolanic additives are able to enhance both the strength and ductility.Recent studies(Estabragh et al.,2017;Shahbazi et al.,2017;Yadav and Tiwari,2017)indicated that if used in combination,the additives and the fiber complement each other and therefore optimize the stabilization. Tang et al.(2007) used the scanning electron microscopy to examine complementary interactions between pozzolanic additives and fibers.They found that the bond strength and friction at the interface govern the reinforcement results.The results depend on the additives used, normal stress acted on fibers, effective contact area of the interface,fiber strength and its surface roughness.On the factor affecting the fiber strength, Wei et al. (2018) examined lime stabilization mixed with different fibers and found that polypropylene fibers outperform jute, rick straw and wheat straw in improving soil strength.

Stabilization has been attempted on micaceous soils.Frempong(1995) examined lime and sand additions to micaceous soils. The additions enhanced a range of material performances including consistency, compaction, strength, and volume stability against wetting. He suggested the dosage of 6%-8% lime and 30% sand,depending on the soil conditions and target applications.As earlier studies, Frempong (1995) suggested a range of optimal dosages which, however, are subjected to variation depending on the ingredients used and the soils to be stabilized. Sobhani and Wong(2015) used mica power as a partial replacement of cement to stabilize clays. In their study, mica was found to reduce the optimum water content and increase the maximum dry density.Meanwhile,many of the previous studies adopted the matrix-based sample design and, based on the design test, developed performance-based optimal dosage. This is suitable for sample design involving a couple of ingredients or variables.If the number increases, the test pool grows dramatically and challenges the feasibility. Reducing the variable number is sometimes unacceptable as the insufficient test results may underrepresent material performance and therefore bias the optimal dosages.

Given the research outcomes and limitations that are identified from the past studies, this study examines the stabilization of micaceous soils using pozzolanic, non-pozzolanic and fiber inclusions,alone and in combination.The chosen additives were slag,polymer and polyether fibers. We used an advanced experimental design toolbox and a predictive modeling approach to scope dosages of individual ingredients,and to identify their contributions to performances of soils. The goal is to optimize the dosage and enhance the soil performance.

2. Materials and methods

The materials include artificial soils comprised of kaolinite and bentonite, and stabilizers which are ground mica, groundgranulated blast-furnace slag (GBFS), polypropylene fiber and polymetric agent. Each of the materials is outlined as follows.

2.1. Soils

The soil used in the experimental program was a mixture of two commercially available clays: kaolinite and sodium-activated bentonite. They were blended at 85% and 15% by weight, respectively.The physico-mechanical properties of the soil,as well as the test methods,are summarized in Fig.1 and Table 1.The liquid limit and plasticity index were respectively measured as 44% and 22%,from which the soil was characterized as clay of low plasticity(CL),in accordance with the Unified Soil Classification System (USCS).Furthermore, the standard Proctor compaction test, carried out as per ASTM D698-12 (2012), suggested that the optimal water content was 25.2%, corresponding to a maximum dry unit weight of 14.6 kN/m3.

Fig.1. Particle size distribution of the soil used.

Table 1 Physico-mechanical properties of the soil samples.

2.2. Ground mica

Commercially available ground mica, sourced from a local supplier, was used to artificially prepare the micaceous clay soils. The physical properties and chemical composition of the ground mica,as provided by the supplier,are summarized in Table 2.The product appeared as white powder with the particle size being silt-to-clay(<75 μm). The specific gravity of the ground mica, GMs，was found to be 2.8. The chemical composition of the ground mica, provided by the supplier,was found to be dominated by silicon dioxide(SiO2)and aluminum trioxide (Al2O3) with mass fractions of 49.5% and 29.2%, respectively. In terms of acidity, the pH value of the ground mica slurry was 7.8 which is alkalescent.

2.3. GBFS

The GBFS was sourced from a local manufacturer and was used as the cementitious additive.The physical properties and chemical composition,provided by the manufacturer,are provided in Table 3.The GBFS particles consist of fines of 96% by weight. The specific gravity and pH value of GBFS were 2.87 and 9.6, respectively. The chemical compositions are mainly dominated by CaO and SiO2with the contents of 44.7% and 27.1%, respectively.

2.4. Fiber

Polypropylene fiber was used to reinforce the soils.This type of fiber has been widely used in previous studies(e.g.Yetimoglu et al.,2005; Olgun, 2013; Estabragh et al., 2017). The diameter of the fibers was in the range of 20-30 μm, and fibers were cut into segments of approximately 10 mm in length, as shown in Fig. 2.Polypropylene fiber offers advantages,such as hydrophobicity,and resistance to alkalis, chemicals and chlorides. The physical and engineering properties, provided by the manufacturer, are provided in Table 4.

2.5. Polymer agent

A commercially manufactured polymer agent was used as the chemical binder in this study. This type of polymer is referred to as a polyacrylamide (PAM) (CH2CHCONH2), which is a watersoluble, anionic synthetic polymer formed from acrylamide subunits, as shown in Fig. 3. The polymer has been successfully implemented in several Australian roadway construction projects with a variety of soils (Georgees et al., 2015). The polymer presents in a granular form and, as per the manufacturer’s specification, is suggested to dilute at 200 g to 1 kg water ratio. Other properties include a specific gravity (at 25°C) of 0.8 and a pH value (at 25°C) of 6.9.

Table 2 The physical properties and chemical composition of ground mica.

2.6. Modeling method

Response surface methodology(RSM)is an empirical statistical and mathematical tool used to explore the response models (i.e.relationships) between several explanatory variables (e.g. ingredient dosages) and one or more response variables (e.g. material strength) (Myers et al., 2016). The relationships are provided in a list of descending order of desirability which represents the closeness of a response to its ideal value. The desirability is dimensionless and lies between 0 and 1.The greater a desirability value is, the more a response falls within the ideal intervals. In science field, modeling with desirability of more than 0.7 is acceptable. RSM uses a sequence of designed experiments to determine an optimal set of variables in order to obtain the desired response. The effect of an individual variable can be assessed while the other variables are varied (Singh et al., 2011),which takes advantage over the usual observatory comparison analysis. The RSM has been widely applied in chemical engineering and more recently in civil engineering (Shahbazi et al.,2017).

RSM usually uses two approaches to explore the response models.They are central composite design(CCD)and Box-Behnken design(BBD).CCD provides relatively better modeling results in the aspects of nonlinear modeling, provision of high-order modeling coefficients and processing of experimental data (Myers et al.,2016), and was used in the present study. In addition, CCD uses an optimal number of experiments to derive the relationships between the variables(Sahu et al., 2009).

Generally, a CCD design consists of 2nfactorial runs, 2n axial runs,and nccenter runs,where n is the number of variables in the experiment and can range between 3 and 10 (Myers et al., 2016).Center runs replicate a center point experiment and can be set between 2 and 6. The CCD processes the experiment results and yields a response model in the form as

where Y is the response of the experiment,Xiis the variable,and e is the experimental error.The function f is unknown and it may be complex, based on the relationship between the variables and the response.Therefore,RSM aims at identifying a suitable polynomial relationship between the variables and the response surface (i.e.the best-of-fit surface)(Gunaraj and Murugan,1999).In some cases,a higher-order polynomial, such as a quadratic model, may be applied and Eq. (1) can be expressed as

where β0is a constant, βiis the linear coefficient, βiiis the quadratic coefficient, and βijis the interaction coefficient. From the obtained mathematical form, we can scope variables (i.e.combinations of ingredients) where optimal stabilization is obtained.

Table 3 The physical properties and chemical composition of GBFS.

Fig. 2. Samples of polypropylene fibers.

Fig. 3. Samples of polymer agent.

2.7. Experimental design

We designed two combinations of additives: slag-fiber and slag-polymer, to stabilize micaceous soils. In each of the two combinations, we specified the value ranges for the ingredients that we had chosen.The ranges were 3%-15%of slag,0.25%-1.25%of fiber, and 0.1-0.5 g/L of polymer. The percentages are all by weight.Micaceous soils were formed by adding a volume of ground mica to soils.To explore the range of mica content,the contents that were examined are 15%and 30%.A control sample that contains no mica is used for comparison.The sets of ranges were determined in terms of the past studies and adjusted so that we can provide a suitable coverage for the ingredients,and comparison between the two combination scenarios. The ranges were used as the input values for the CCD processing, and the outputs in the form of sample dosages are provided in Tables 5 and 6. A total of 20 samples, including 6 center point runs (i.e. nc= 6), were designed for each sample stream. In each stream, the dosages were varied and arranged into a fashion by the CCD.Each ingredient was assigned a variable,A1,A2,B1,B2,C1and C2,to be used for the response surface modeling.

We prepared the samples using the optimum water content and maximum dry unit weight that are provided in Table 1. After the required volume of water was added to the samples, the samples were mixed manually and thoroughly for about 5 min to ensure that the mixtures were homogenous. The prepared samples were then cast into cylinder molds(φ50 mm×100 mm)and compacted to the maximum dry unit weight. The fresh samples were sealed using plastic membrane and placed into a fog room for curing. All samples were cured for 28 d before the test. UCS tests were conducted in accordance with ASTM D2166/D2166M-16 (2016). The samples were axially compressed at a rate of 1 mm/min(i.e.1%per minute), as adopted in Ang and Loehr (2003) and Soltani et al.(2019b). The load with respect to time was recorded continuously until the sample failed.The peak strength was recorded as the UCS for the samples tested.

Table 4 The physical and engineering properties of polypropylene fiber.

3. Results and discussion

3.1. UCS and CCD modeling

The UCS results obtained for the samples tested are presented in Tables 7 and 8. The strength values were varied depending on the dosages examined. The values varied from 80.54 kPa to 560.87 kPa for slag-fiber stabilized samples and from 76.35 kPa to 486.11 kPa for slag-polymer stabilized samples, which reflected usual strength results of natural and compacted soils. The ranges of strength values verified the capacity of CCD in experiment design.

The modeling approach was applied to the strength results,enabling prediction of UCS as a function of ingredient dosages:

where UCSSFand UCSSPare the UCSs of slag-fiber and slag-polymer stabilized soil samples, respectively. It is noteworthy that the intercepts and term coefficients are determined at varied levels of significance (i.e. p-value) depending on the data used to develop the model. This means that the predicted strength is indicative if a p-value is marginally significant or insignificant. As provided in Eq. (1), CCD modeling uses a quadratic polynomial function to model the strength results and,as shown in Eqs. (3) and (4), quadratic functions are developed for the tested samples.

We plotted the model and test results on the same graph, as presented in Fig. 4. Excellent agreement between the two sets of results is obtained.We also conducted a reliability test-analysis of variance(ANOVA)which tests the fitness and significance of the model.The test provided R2=0.9966 for the slag-fiber stabilized samples and 0.9989 for the slag-polymer stabilized samples.The R2values are close to 1 and thus suggest the excellent agreement between the model and test results. Therefore, the quadratic fitting models are considered as the optimal model to formulate the strength in terms of the dosages for the two stabilization scenarios.

In addition to the R2-value check, we further verified the obtained dosage models by conducting checkup tests.Two samples A and B that used dosages different from those in Tables 5 and 6 were prepared. The dosages, as provided in Table 9, were randomly designed in order to warrant their validity.The same dosages were applied to the obtained models to predict the UCS. The predicted and tested UCS results are provided in Table 9.Excellent agreement between the two sets of strength results was obtained, with an acceptable deviation of 4.1%for the slag-fiber sample and 6.03%for the slag-polymer sample.

Table 5 Experimental design of the slag-fiber stabilized micaceous soils.

Table 6 Experimental design of the slag-polymer stabilized micaceous soils.

Table 7 The UCS results of the slag-fiber stabilized micaceous soil samples.

Table 8 The UCS results of the slag-polymer stabilized micaceous soil samples.

Fig. 4. Predicted UCSs versus actual measurements for (a) slag-fiber and (b)slag-polymer stabilized micaceous soil samples.

Table 9 Two samples used to validate the dosage models.

3.2. Effects of mica, slag and fiber on UCS

The effects of ingredients on the UCS were analyzed by plotting three-dimensional (3D) response surface graphs. In the plots, the response(i.e.the UCS)is presented into a continuous curvy surface,in 3D space as a function of the ingredients of interest. Two ingredients are included in the plot, while the dosage of the third ingredient remains unchanged. The plots visualize the response and the interactions between the two chosen ingredients. As an example,the response plots are presented in Fig.5.The ingredient that we kept unchanged was 0.75%fiber(Fig.5a),9%slag(Fig.5b),and 15% mica (Fig.5c), respectively.

In Fig.5a,the UCS is inversely proportional to the mica content,while the slag and fiber contents remain unchanged.The higher the mica content is,the lower the UCS will be,as indicated by path OA.To the opposite, slag contributes to the strength development, as indicated by path OB.The strength is varied if both contents of mica and slag are increased.Assuming the contents of mica and slag are increased over path OC, the material still gains some strength, but at a moderate rate. The path-dependent strength model suggests that interaction is present between slag and mica, while the fiber content does not change.

Similar interactive effects arise from fiber and mica, as presented in Fig. 5b. It is shown that the fiber content improves the UCS,while the improvement rate is less significant when compared with that obtained by using the slag. The presence of mica again shows an adverse effect on the UCS of the soil. The UCS increases with the fiber content. The increase is marginal when 0.9% or higher fiber content is used as suggested by path ODE.

If the mica content remains unchanged,the UCS increases with both slag and fiber contents, at least within the tested ranges, as presented in Fig. 5c. It is seen that the slag is more effective (indicated by path OF) than the fiber (indicated by path OGH) in increasing the UCS.In addition,when the fiber content is 1.25%(i.e.the maximum dosage tested), the effectiveness of the slag on improving the UCS is most significant. It is noted that UCS-slag relationship (e.g. path OF) is pronounced, and hence it is worth to examine its full pathway.This,however,is less significant given the strength required to satisfy the backfill requirements has been obtained from the dosages examined.

The above UCS variations mainly arise from physical or chemical nature of ingredients.The reason for the slag effectively improving the strength is the initiation of chemical reactions in the soil-water medium. The chemical reactions consist of cation exchange and flocculation-agglomeration, and occur in the fine-grained soils,while the reactions are often negligible when paired with neutrally-charged soil particles, such as silts, gravels, and sands(Sharma and Sivapullaiah,2016).The reason is that the fine-grained soils, like clays, contain a notable amount of negative charges.During the short-term reactions, higher-valence cations substitute lower-valence ones, and cations of larger ionic radius replace smaller cations of the same valence. The order of substitution follows the Hofmeister series, i.e. Na+< K+< Mg2+< Ca2+. The slag contains additional calcium cations (Ca2+), which immediately substitute lower-valence ones (e.g. Na+), and/or the same valence cations of smaller ionic radius(e.g.Mg2+)in the vicinity of the clay particles(Zhang et al.,2019b).Due to the development of the strong van der Waals bonds between adjacent clay particles in the matrix,these cation exchanges lead to a decrease in the thickness of the diffused double layers,resulting in the aggregation and flocculation of the clay particles(Firoozi et al.,2017).Another reaction,referred to as pozzolanic activity, depends greatly on the time of curing.During pozzolanic reactions,ionized calcium(Ca2+)and hydroxide(OH-) units are released from the water-binder complex. These ions gradually react with silicate(SiO2)and aluminate(Al2O3)units in the soil, thereby forming strong cementation gels, namely calcium-silicate-hydrates (CSH), calcium-aluminate-hydrates(CAH) and calcium-aluminate-silicate-hydrates (CASH). These products promote further solidification and flocculation of the particles,which lead to the development of a dense uniform matrix,thus improving soil strength (Sharma and Sivapullaiah, 2016;Firoozi et al.,2017).On the other hand,fiber also promotes strength to some degree.The contribution originates from two phenomena:(i)the frictional resistance generated at the soil-fiber interface due to the roughness of the fiber surface, and (ii) the mechanical interlocking of the soil particles and fibers(Tang et al.,2007;Wang et al., 2017; Mirzababaei et al., 2018). The internal frictional resistance between the soil and the fibers is a function of the soil-fiber contact area. Therefore, a greater number of fibers in the soil will lead to the larger contact levels between the soil particles and the fibers,thus resulting in higher frictional resistance.The mechanical interlocking of soils and fibers is achieved during the sample preparation phase (e.g. soil compaction), and this process induces adhesion of the mixtures by immobilizing the soil particles undergoing loading. It should be noted that, in preparation of the fiber-soil mixture,care needs to be taken to prevent the formation of fiber clusters(Prabakar and Sridhar,2002;Estabragh et al.,2017;Yadav and Tiwari, 2017). The addition of fibers into slag-stabilized soils further enhances the strength of such soils. The presence of slag improves soil grading characteristics,reduces pores in the soils,and thus promotes particle contact.The improved contact benefits the interaction between the fibers and soil particles and thus contributes to strength development (Cai et al., 2006).

Fig. 5. 3D response surface plots of UCS for slag-fiber stabilized micaceous soil samples with constant ingredient of: (a) 0.75% fiber, (b) 9% slag, and (c) 15% mica.

3.3. Effects of mica, slag and polymer on UCS

Fig 6a shows the interactive effects of slag and mica on the UCS of micaceous soil samples at a polymer dosage of 0.3 g/L.Similarly,the slag additive contributes to the strength, while mica does oppositely. The improvement gained by the slag, however, is less noticeable than that obtained by the slag-fiber scenarios if the rest conditions remain the same. The plot for the polymer-mica combined effect at 9% slag content is presented in Fig. 6b. It is shown that the UCS increases with the polymer concentration of up to 0.3 g/L. Beyond this concentration, additional polymer exhibits a slightly adverse effect on strength.The combined effect of slag and polymer on micaceous clays is provided in Fig. 6c. Both slag and polymer have a positive effect on strength improvement. Considering 0.3 g/L of polymer to be a threshold for strength increase,the maximum UCS is obtained at 15% slag.

From the above results,polymer,as the chemical additive,has a positive effect on material strength.The improvement mechanism is varied depending on polymer additives used. Positively charged polymers are electrostatically attracted to the negatively charged soil particle surface, and non-ionic polymers achieve the adsorption through van der Waals forces and/or hydrogen bonding(Theng,1982;Wallace et al.,1986).Polymer is anionic which,in the presence of cations of double layers, enables polymer-soil adsorption. The degree of the adsorption is dependent on the amount and type of exchangeable cations, clay content, pH value and size of the polymer molecules (Theng,1982; Lu et al., 2002).The role of polymer in promoting strength can be attributed to its ability to form ionic bonds, thereby holding soil particles together through the cationic bridging mechanism. This will develop a flocculated soil structure, which further improves the strength.Moreover, polymer also acts as a bridging agent, which enhances the interlocking of the slag-soil flocculation, thus promoting a more significant improvement in the UCS of the micaceous soils.The strength promotion, however, is additive concentration dependent, as shown by the turn of strength at 0.3 g/L polymer level. One of the main reasons is related to polymer-soil interaction and its dependence on the contact surface area (Latifi et al.,2016). If the polymer-soil contacts have well evolved into steric stabilization, additional polymer supplies prevent soil particles from approaching each other or aggregating, and thus an adverse effect on strength.This explanation is subjected to characterization of particle contacts using microscale studies.

3.4. Dosage optimization

We further optimized the ingredient dosage in terms of UCS and material ductility intended.ASTM D4609-08(2008)specifies“if the UCS value reaches 345 kPa in any soil,the stabilization procedure has been effective”. Therefore, we chose the value of 345 kPa as the baseline for micaceous soils. Aside from the UCS, we also considered material ductility. In terms of the past studies (Olgun, 2013;Yadav and Tiwari, 2017), fiber inclusions contribute to material ductility and we set it “maximization” in this optimization. In contrast,the optimization aims to minimize slag content so that the pozzolanic reaction is sufficient simply to meet the strength requirement.Similar“minimization”setting is applied to polymer in a hope of cost reduction. We designed four example soils with varying mica contents,i.e.M=0%,10%,20%and 30%,by weight.The purpose is to replicate a range of micaceous soils. For each of the example soils, we applied the above intended conditions to the RSM model and then ran the model to obtain the optimal dosages.The dosages of the highest desirability obtained for each of the example soils are provided in Table 10. It is noteworthy that the fiber contents in slag-fiber samples remain at 1.25%. This agrees with the setting for fiber,i.e.“maximization”,to argument material ductility. Where the intended conditions are varied, the model allows for updating ingredient setting,and an optimal dosage can be obtained.

Fig. 6. 3D response surface plots of UCS for slag-polymer stabilized micaceous soil samples with constant ingredient of:(a)0.3 g/L polymer,(b)9%slag,and(c)15%mica.

Table 10Model-derived optimal dosage for micaceous soils to target UCS of 345 kPa.

4. Conclusions

RSM modeling was used to model UCS of micaceous soils as a function of the dosage of various additives.The additives included two combinations: (i) slag and fiber, and (ii) slag and polymer.Based on the findings and results, the following conclusions are drawn:

(1) The two combinations of additives were able to stabilize the micaceous soils.The additives exhibited varied effects on the stabilization. Slag exhibited a noticeable synergistic effect and,in the presence of fiber or polymer,greatly contributed to the stabilization of micaceous soils.

(2) RSM modeling, together with the CCD experimental design,provides a toolbox of modeling UCS of materials and enabling optimization of the additive dosage for soil stabilization.

(3) Models were developed as a tool to predict the UCS of the micaceous soils stabilized by the two combinations of additives.Excellent agreement was obtained between the model predictions and actual test results for the samples tested in this study. The performance of the model was verified by a separate set of tests.

(4) The RSM-based optimization was successful in determining the additive dosages in terms of the target UCS and,based on the developed models, identifying the most efficient dosage to meet the UCS requirements.

Declaration of competing interest

The authors wish to confirm that there are no known conflicts of interest associated with this publication, and there has been no significant financial support for this work that could have influenced its outcome.