The Simplest Possible Fully Correct Solution of the Clay Millennium Problem about P vs. NP. A Simple Proof That P ≠ NP = EXPTIME

In the current paper, I present probably the simplest possible abstract formal proof that P ≠ NP, and NP = EXPTIME, in the context of the standard mathematical set theory of computational complexity and deterministic Turing machines. My previous publications about the solution of the P vs. NP with the same result NP = EXPTIME, to be fully correct and understandable need the Lemma 4.1 and its proof of the current paper. The arguments of the current paper in order to prove NP = EXPTME are even simpler than in my previous publications. The strategy to solve the P vs. NP problem in the current paper (and in my previous publications) is by starting with an EXPTIME-complete language (problem) and proving that it has a re-formulation as an NP-class language, thus NP = EXPTIME. The main reason that the scientific community has missed so far such a simple proof, is because of two factors 1) It has been tried extensively but in vain to simplify the solutions of NP-complete problems from exponential time algorithms to polynomial time algorithms (which would be a good strategy only if P = NP) 2) It is believed that the complexity class NP is strictly a subclass to the complexity class EXPTIME (in spite the fact that any known solution to any of the NP-complete problems is not less than exponential). The simplicity of the current solution would have been missed if 2) was to be believed true. So far the majority of the relevant scientific community has considered this famous problem not yet solved. The present results definitely solve the 3rd Clay Millennium Problem about P versus NP in a simple, abstract and transparent way that the general scientific community, but also the experts of the area, can follow, understand and therefore become able to accept.

Predicting the friction angle of clays using a multi-layer perceptron neural network enhanced by yeo-johnson transformation and coral reefs optimization

The accurate prediction of the friction angle of clays is crucial for assessing slope stability in engineering applications.This study addresses the importance of estimating the friction angle and presents the development of four soft computing models:YJ-FPA-MLPnet,YJ-CRO-MLPnet,YJ-ACOC-MLPnet,and YJCSA-MLPnet.First of all,the Yeo-Johnson(YJ)transformation technique was used to stabilize the variance of data and make it more suitable for parametric statistical models that assume normality and equal variances.This technique is expected to improve the accuracy of friction angle prediction models.The friction angle prediction models then utilized multi-layer perceptron neural networks(MLPnet)and metaheuristic optimization algorithms to further enhance performance,including flower pollination algorithm(FPA),coral reefs optimization(CRO),ant colony optimization continuous(ACOC),and cuckoo search algorithm(CSA).The prediction models without the YJ technique,i.e.FPA-MLPnet,CRO-MLPnet,ACOC-MLPnet,and CSA-MLPnet,were then compared to those with the YJ technique,i.e.YJ-FPA-MLPnet,YJ-CRO-MLPnet,YJ-ACOC-MLPnet,and YJ-CSA-MLPnet.Among these,the YJ-CRO-MLPnet model demonstrated superior reliability,achieving an accuracy of up to 83%in predicting the friction angle of clay in practical engineering scenarios.This improvement is significant,as it represents an increase from 1.3%to approximately 20%compared to the models that did not utilize the YJ transformation technique.

Modelling of the elastoplastic behaviour of the bio-cemented soils using an extended Modified Cam Clay model

An elastoplastic constitutive model based on the Modified Cam Clay(MCC)model is developed to describe the mechanical behaviour of soils cemented via microbially induced calcite precipitation(MICP).It considers the increase of the elastic stiffness,the change of the yield surface due to MICP cementation and the degradation of calcium carbonate bonds during shearing.Specifically,to capture the typical contraction-dilation transition in MICP soils,the original volumetric hardening rule in the MCC model is modified to a combined deviatoric and volumetric hardening rule.The model could reproduce a series of drained triaxial tests on MICP-treated soils with different calcium carbonate contents.Further,we carry out a parametric study and observe numerical instability in some cases.In combination with an analytical analysis,our numerical modelling has identified the benefits and limitations of using MCCbased models in the simulation of MICP-cemented soils,leading to suggestions for further model development.

Numerical analysis of downward progressive landslides in long natural slopes with sensitive clay

Landslides occurring in sensitive clay often result in widespread destruction,posing a significant risk to human lives and property due to the substantial decrease in undrained shear strength during deformation.Assessing the consequences of these landslides is challenging and necessitates robust numerical methods to comprehensively investigate their failure mechanisms.While studies have extensively explored upward progressive landslides in sensitive clays,understanding downward progressive cases remains limited.In this study,we utilised the nodal integration-based particle finite element method(NPFEM)with a nonlinear strain-softening model to analyse downward progressive landslides in sensitive clay on elongated slopes,induced by surcharge loads near the crest.We focused on elucidating the underlying failure mechanisms and evaluating the effects of different soil parameters and strainsoftening characteristics.The simulation results revealed the typical pattern for downward landslides,which typically start with a localised failure in proximity to the surcharge loads,followed by a combination of different types of failure mechanisms,including single flow slides,translational progressive landslides,progressive flow slides,and spread failures.Additionally,inclined shear bands occur within spread failures,often adopting distinctive ploughing patterns characterised by triangular shapes.The sensitive clay thickness at the base,the clay strength gradient,the sensitivity,and the softening rate significantly influence the failure mechanisms and the extent of diffused displacement.Remarkably,some of these effects mirror those observed in upward progressive landslides,underscoring the interconnectedness of these phenomena.This study contributes valuable insights into the complex dynamics of sensitive clay landslides,shedding light on the intricate interplay of factors governing their behaviour and progression.

Molecular insights into oil detachment from hydrophobic quartz surfaces in clay-hosted nanopores during steam-surfactant co-injection

Thermal recovery techniques for producing oil sands have substantial environmental impacts.Surfactants can efficiently improve thermal bitumen recovery and reduce the required amount of steam.Such a technique requires solid knowledge about the interaction mechanism between surfactants,bitumen,water,and rock at the nanoscale level.In particular,oil sands ores have extremely complex mineralogy as they contain many clay minerals(montmorillonite,illite,kaolinite).In this study,molecular dynamics simulation is carried out to elucidate the unclear mechanisms of clay minerals contributing to the bitumen recovery under a steam-anionic surfactant co-injection process.We found that the clay content significantly influenced an oil detachment process from hydrophobic quartz surfaces.Results reveal that the presence of montmorillonite,illite,and the siloxane surface of kaolinite in nanopores can enhance the oil detachment process from the hydrophobic surfaces because surfactant molecules have a stronger tendency to interact with bitumen and quartz.Conversely,the gibbsite surfaces of kaolinite curb the oil detachment process.Through interaction energy analysis,the siloxane surfaces of kaolinite result in the most straightforward oil detachment process.In addition,we found that the clay type presented in nanopores affected the wettability of the quartz surfaces.The quartz surfaces associated with the gibbsite surfaces of kaolinite show the strongest hydrophilicity.By comparing previous experimental findings with the results of molecular dynamics(MD)simulations,we observed consistent wetting characteristics.This alignment serves to validate the reliability of the simulation outcomes.The outcome of this paper makes up for the lack of knowledge of a surfactant-assisted bitumen recovery process and provides insights for further in-situ bitumen production engineering designs.

Experimental investigation into effects of the natural polymer and nanoclay particles on the EOR performance of chemical flooding in carbonate reservoirs

This paper aims to investigate the tragacanth gum potential as a natural polymer combined with natural clay mineral(montmorillonite,kaolinite,and illite)nanoparticles(NPs)to form NP-polymer suspension for enhanced oil recovery(EOR)in carbonate reservoirs.Thermal gravimetric analysis(TGA)tests were conducted initially in order to evaluate the properties of tragacanth gum.Subsequently,scanning electron microscopy(SEM)and energy-dispersive X-ray(EDX)tests were used to detect the structure of clay particles.In various scenarios,the effects of natural NPs and polymer on the wettability alteration,interfacial tension(IFT)reduction,viscosity improvement,and oil recovery were investigated through contact angle system,ring method,Anton Paar viscometer,and core flooding tests,respectively.The entire experiment was conducted at 25,50,and 75℃,respectively.According to the experimental results,the clay minerals alone did not have a significant effect on viscosity,but the addition of minerals to the polymer solution leads to the viscosity enhancement remarkably,resulting mobility ratio improvement.Among clay NPs,the combination of natural polymer and kaolinite results in increased viscosity at all temperatures.Considerable wettability alteration was also observed in the case of natural polymer and illite NPs.Illite in combination with natural polymer showed an ability in reducing IFT.Finally,the results of displacement experiments revealed that the combination of natural polymer and kaolinite could be the best option for EOR due to its substantial ability to improve the recovery factor.

Discussion on“Dispersion characteristics of clayey soils containing waste rubber particles”[J Rock Mech Geotech Eng 15(2023)3050-3058]

We read with great interest the recent article by Erenson(2023)entitled“Dispersion characteristics of clayey soils containing waste rubber particles”.The author has studied the dispersion characteristics of clayey soils containing different percentages of waste rubber particles(WRPs)by performing several tests(viz.consistency limit,linear shrinkage limit,double hydrometer,crumb test and pinhole test)and scanning electron microscopy(SEM)analysis on five clayey(viz.Na-activated bentonite,refined ball clay,Ukrainian kaolin,Avanos kaolin and Afyon clay)samples containing 0%,5%,10%and 15%WRPs.It should be noted that Erenson(2023)has presented some interesting observations,but there are some serious issues that we want to share through this discussion and request the author of the original paper to address them to avoid their persistence in the scientific literature.

Performance of composite foundations with different load transfer platforms and substratum stiffness over silty clay

The semi-rigid pile-supported composite foundation is widely used in highway projects due to its effectiveness in increasing the bearing capacity and stability of foundations.It is crucial to understand the stress distribution across the embankment width and the behaviour of unreinforced foundations.Thus,five centrifuge tests were conducted to examine the bearing and deformation behaviours of NPRS(Non-Connected Piled Raft Systems)and GRPS(GeosyntheticReinforced Pile-Supported systems)with varying substratum stiffness,then a comparative analysis was conducted on embankment settlement,pressures underneath the embankments,and axial forces along the piles.The results indicated that greater substratum stiffness correlates with reduced settlement and deformation at various depths.Deformation occurring 5 meters from the embankment toe includes settlement in NPRS and upward movement in GRPS.The potential sliding surface is primarily located within the embankment in NPRS,whereas it may extend through both the embankment and foundation in GRPS.The pile-soil stress ratio and efficiency in NPRS are higher than in GRPS across the embankment.The axial force borne by end-bearing piles is significantly greater than that by floating piles.As the buried depth increases,the axial force in GRPS initially rises then declines,whereas in NPRS,it remains relatively constant within a certain range before decreasing.This study aids in assessing the applicability of composite foundations in complex railway environments and provides a reference for procedural measures under similar conditions.

Evolution model and failure mechanisms of rainfall-induced cracked red clay slopes:insights from Xinshao County,China

Red clay landslides are widely distributed worldwide,resulting in severe loss of life and property.Although rainfall-induced red clay slopes have received extensive attention,the role of cracks in the evolutionary process of red clay slopes and their connection to failure mechanisms is still poorly understood.A comprehensive approach integrating field investigation,laboratory tests,and numerical simulations was conducted to study the 168 red clay landslides in Xinshao County,China.The results show that red clay is prone to forming cracks at high moisture content due to its low swelling and high shrinkage properties.The failure mode of red clay slopes can be summarized in three stages:crack generation,slope excavation,and slope failure.Furthermore,the retrospective analysis and numerical simulations of the typical landslide in Guanchong indicated that intense rainfall primarily impacts the shallow layer of soil within approximately 0.5 m on the intact slope.However,cracks change the pattern of rainfall infiltration in the slope.Rainwater infiltrates rapidly through the preferential channels induced by the cracks rather than uniformly and slowly from the slope surface.This results in a significant increase in both the depth of infiltration and the saturated zone area of the cracked slope,reaching 3.8 m and 36.2 m^(2),respectively.Consequently,the factor of safety of the slope decreases by 13.4%compared to the intact slope,ultimately triggering landslides.This study can provide valuable insights into understanding the failure mechanisms of red clay slopes in China and other regions with similar geological settings.

Evaluation of red soil-bentonite mixtures for compacted clay liners

Compacted clay liners are an integral part of the waste landfills,which are provided to contain the leachate within the landfills and protect the surrounding environment.Generally,locally available natural soils are used for the construction of compacted clay liners if they satisfy the design criteria.However,not all soils in their natural state satisfy all the design criteria for the liner materials.Thus,there is a definite need to modify the locally available natural soils by blending with bentonite to meet the required design criteria for the liners.In view of this,the present study evaluates the suitability of an Indian red soil enhanced with bentonite as a liner material.To achieve this,a series of experiments were carried out using locally available red soil and bentonite.First,the suitability of the red soil was evaluated as a liner material.The experimental results showed that the red soil met all the selection criteria stipulated by the Environmental Protection Agencies(EPAs)for the liners except the hydraulic conductivity criterion.Therefore,the red soil was mixed with bentonite contents of 10%,20%and 30%,and the red soil-bentonite mixtures were evaluated for their suitability for liners in their compacted state.Further,as the liners in the arid and semi-arid regions are subjected to moisture variations due to seasonal moisture fluctuations and other factors,the red soil-bentonite mixtures were subjected to wetdry cycles,and their suitability was evaluated after wet-dry cycles.The experimental results revealed that all the red soil-bentonite mixtures met the stipulated EPA criteria for the liners in the as-compacted state.However,the red soil-bentonite mixtures with 20%and 30%bentonite contents only satisfied the hydraulic conductivity requirement even after wet-dry cycles.The experimental findings were supplemented with the microstructural insights captured through digital camera images,scanning electron microscopy(SEM),and mercury intrusion porosimetry(MIP)studies.

An improved creep model for unsaturated reticulated red clay

Establishment of a creep model is an important method to analyze the relationship between soil creep deformation and time,and the element model is widely used for studying soil creep.However,the element creep model is employed for fitting saturated soil,and the mechanical element model is generally linear,which cannot well fit the nonlinear deformation of the soil with time in practice.The creep process of the soil is not only time-dependent,but also related to the deviatoric stress level.Therefore,the fractional calculus theory and a parameter n reflecting the effect of deviatoric stress level on the creep properties of the soil were introduced into the element model,and the fractional qBurgers creep model was established by using the fractional Koeller dashpot and Caputo fractional calculus.The proposed model was used to fit the triaxial test data of reticulated red clay under different net confining pressures and matric suctions by unsaturated triaxial apparatus.The proposed model can well describe the nonlinearity of unsaturated reticulated red clay,has memory and global correlation to the creep development process of unsaturated reticulated red clay,and has clear physical meaning.The functional relationships of the model parameters with the matric suction,net confining pressure and deviatoric stress level were deduced,so that the creep curves of unsaturated reticulated red clay can be obtained for any conditions,which is of great value for the study of unsaturated soils.

Experimental study on seismic reinforcement of bridge foundation on silty clay landslide with inclined interlayer

A shaking table test for a bridge foundation reinforced by anti-slide piles on a silty clay landslide model with an inclined interlayer was performed.The deformation characteristics of the bridge foundation piles and anti-slide piles were analyzed in different loading conditions.The dynamic response law of a silty clay landslide with an inclined interlayer was summarized.The spacing between the rear anti-slide piles and bridge foundation should be reasonably controlled according to the seismic fortification requirements,to avoid the two peaks in the forced deformation of the bridge foundation piles.The“blocking effect”of the bridge foundation piles reduced the deformation of the forward anti-slide piles.The stress-strain response of silty clay was intensified as the vibration wave field appeared on the slope.Since the vibration intensified,the thrust distribution of the landslide underwent a process of shifting from triangle to inverted trapezoid,the difference in the acceleration response between the bearing platform and silty clay landslide tended to decrease,and the spectrum amplitude near the natural vibration frequency increased.The rear anti-slide piles were able to slow down the shear deformation of the soil in front of the piles and avoid excessive acceleration response of the bridge foundation piles.

Friction Characteristics Between Marine Clay and Construction Materials

Structure-soil interface friction characteristics is of importance to investigate the interaction between engineering structures and soils,especially for offshore structures.The interface friction behavior between marine clay and structural materials with different roughness was studied in this paper by using 3D optical scanning tests,a modified direct shear device and numerical simulation.Relationships between the surface roughness of structures,water content and interface friction angle were presented by model tests.The increase of water contents decreased the interface friction angles.For interfaces with different roughness,the interface friction angles will be smaller than that of the soil when the water content exceeds a certain value.The roughness of the interface and the water content of the soil are mutually coupled to influence the coefficient of friction(COF).This paper proposed a Finite Element Method(FEM)to simulate the interface direct shear tests of structures with different roughness.The surface models with different roughness are established based on the structure data obtained by 3D scanning.The Coupled Eulerian-Lagrangian(CEL)approach was employed to analyse soils sheared by irregular surfaces.The interface behavior for interfaces with different roughness under cyclic shear stresses was analyzed by FEM.

Effect of movability of water on the low-velocity pre-Darcy flow in clay soil

Water seepage in soil is a fundamental problem involving various scientific and engineering fields.According to the literature,low-velocity water seepage in low-permeability porous media,such as clay,does not follow Darcy's law,also known as pre-Darcy flow.The formation of immovable water due to water adsorption on the pore wall is believed to be responsible for the formation of pre-Darcy flow.However,this view lacks direct solid evidence.To investigate the pre-Darcy water flow in clay,head permeability experiments are conducted on six clay samples with different densities.The results indicate that water seepage in clay at low hydraulic gradients does not follow Darcy's law.A clear nonlinear relationship between flow velocity and hydraulic gradient is observed.Water flow in clay can be divided into the pre-Darcy flow and Darcy flow regions by the critical hydraulic gradient,which is 10-12 for the Albic soil with dry density between 1.3 g/cm^(3)and 1.8 g/cm^(3).According to the disjoining pressure theory,immovable water due to water adsorption on the pore wall is the primary reason for water flow deviating from Darcy's law in clay.The results indicate that the percentage of movable water ranges from 39.7%to 59.3%for the six samples at a hydraulic gradient of 1.As the hydraulic gradient increases,the percentage of moveable water also increases.Additionally,there is a strong correlation between the percentage of movable water and the variation in hydraulic conductivity with the hydraulic gradient.Furthermore,a quantitative relationship between the percentage of movable water and the hydraulic conductivity has been established.The results of this study suggest that water adsorption on the pore wall not only affects the water movability,but is also closely related to the pre-Darcy flow phenomenon in clay.

Compression properties of cost-efficient porous expanded clay reinforced AA7075 syntactic foams fabricated by industrial-oriented die casting technology

In today’s manufacturing industries,hard competition between rival firms makes it compulsory for researchers to design lighter and cheaper machine components due to the megatrends of cost-effectiveness and anti-pollution.At this point,aluminum syntactic foams(ASFs)are new-generation engineering composites and come into the upfront as a problem-solver.Owing to their features like low density,sufficient elongation,and perfect energy absorption ability,these advanced foams have been considerably seductive for many industrial sectors nowadays.In this study,an industrial-oriented automatic die casting technology was used for the first time to manufacture the combination of AA7075/porous expanded clay(PEC).Micro evaluations(optical and FESEM)reveal that there is a homogenous particle distribution in the foam samples,and inspections are compatible with the other ASF studies.Additionally,T6 aging heat treatment was operated on one half of the produced foams to explore the probable impact of aging on the compressive responses.Attained results show that PEC particles can be an alternative to expensive hollow spheres used in the previous works.Besides,a favorable relationship is ascertained between the aging treatment and mechanical properties such as compression strength and plateau strength.

Soil disturbance evaluation of soft clay based on stress-normalized smallstrain stiffness

Soil disturbance includes the change of stress state and the damage of soil structure.The field testing indices reflect the combined effect of both changes and it is difficult to identify the soil structure disturbance directly from these indices.In the present study,the small-strain shear modulus is used to characterize soil structure disturbance by normalizing the effective stress and void ratio based on Hardin equation.The procedure for evaluating soil sampling disturbance in the field and the further disturbance during the subsequent consolidation process in laboratory test is proposed,and then validated by a case study of soft clay ground.Downhole seismic testing in the field,portable piezoelectric bender elements for the drilled sample and bender elements in triaxial apparatus for the consolidated sample were used to monitor the shear wave velocity of the soil from intact to disturbed and even remolded states.It is found that soil sampling disturbance degree by conventional thin-wall sampler is about 30%according to the proposed procedure,which is slightly higher than that from the modified volume compression method proposed by Hong and Onitsuka(1998).And the additional soil disturbance induced by consolidation in laboratory could reach about 50%when the consolidation pressure is far beyond the structural yield stress,and it follows the plastic volumetric strain quite well.

Inflow and outflow permeability tests in a very soft clay under low stresses

In situ inflow and outflow permeability tests with the BAT probe at SarapuíII soft clay test site are presented.A description of the BAT permeability test is provided,discussing its advantages and shortcomings,especially in the case of very soft clays under low stresses.Pore pressures were monitored during probe installation and were found to be slightly lower than piezocone u2 pore pressures,consistent with the position of the filter.The role of filter tip saturation was investigated after the usual saturation procedure provided an unsatisfactory pore pressure response during probe installation.Results show that the vacuum saturation procedure provides adequate response during installation and increases the reliability of the coefficient of permeability determination in early measurements.Both inflow and outflow tests yielded similar results,indicating that careful execution of the test can lead to good test repeatability regardless of the loading condition.Various sequences of alternated inflow and outflow tests have yielded similar results,indicating that soil reconsolidation and filter clogging were negligible in the tests performed.Data are presented concerning the relationship between index parameters and the in situ coefficient of permeability for SarapuíII clay,which plot outside the range of existing databases.

Physical Experiments and Mechanism Study on the Occurrence State of Hydrogen in Clay Minerals

In recent years,natural hydrogen has been discovered in various geological environments both domestically and internationally,which has sparked a global interest among geologists and led to a surge in the exploration of hydrogen gas(Klein et al.,2019;Prinzhofer et al.,2019;Moretti and Webber,2021;Scott,2021;Bezruchko,2022).However,there is a lack of research on the occurrence state of natural hydrogen gas,which hinders a deeper understanding of its behavior in underground storage and migration.

Feasibility of compacted attapulgite/diatomite amended clayey soils as gas barrier materials

Compacted clay liners are extensively used as barriers to control the upward diffusion of vapors of volatile or semi-volatile organic contaminants released from unsaturated contaminated soils at industrycontaminated sites.This study aimed to investigate the gas diffusion barrier performance of compacted clayey soils amended with three agents including attapulgite and diatomite individually,and attapulgite/diatomite mixture.The properties including water retention,volumetric shrinkage,gas diffusion,and unconfined compressive strength were evaluated through a series of laboratory tests of amended compacted clayey soils.The results demonstrate that the decrease in volume proportions of interaggregate pores leads to an increase in unconfined compressive strength(qu).Both hydrophilic groups and microstructures of attapulgite and diatomite result in an increase in water retention percent(Wt)of compacted clayey soil specimens after amendment regardless of the type of agent or initial water content(w0).Furthermore,the ratio of the gas diffusion coefficient(De)to the gas diffusion coefficient in the air(Da)was significantly reduced owing to a decrease in volume proportions of inter-aggregate pores,hydrophilic group,and microstructures of attapulgite and diatomite.Scanning electron microscope analyses revealed that rod-shaped attapulgite filled the inter-aggregate pores formed by clay particles,whereas the disc-shaped diatomite particles,characterized by micropores,failed to obstruct the interaggregate pores due to their larger particle size.Mercury intrusion porosimetry(MIP)analyses showed a reduction in pore volume in the inter-aggregate pores,leading to a reduction in the total pore volume for both the attapulgite and attapulgite/diatomite mixture amended clays,which is in accordance with the scanning electron microscope(SEM)results.The findings are pertinent to the practical application of compacted clay liners as gas barriers against the upward migration of volatile or semi-volatile organic contaminants at contaminated sites.

Biopolymer stabilization of clayey soil

This study investigates the efficacy of sodium alginate(SA),xanthan gum(XG),guar gum(GG)and chitosan(CS)d each applied at five different solid biopolymer-to-water mass ratios(or dosages)and cured for 7 d and 28 d d on the unconfined compressive strength(UCS)performance of a high plasticity clayey soil.Moreover,on identifying the optimum biopolymer-treatment scenarios,their performance was compared against conventional stabilization using hydrated lime.For a given curing time,the UCS for all biopolymers followed a riseefall trend with increasing biopolymer dosage,peaking at an optimum dosage and then subsequently decreasing,such that all biopolymer-stabilized samples mobilized higher UCS values compared to the unamended soil.The optimum dosage was found to be 1.5%for SA,XG and CS,while a notably lower dosage of 0.5%was deemed optimum for GG.Similarly,for a given biopolymer type and dosage,increasing the curing time from 7 d to 28 d further enhanced the UCS,with the achieved improvements being generally more pronounced for XG-and CS-treated cases.None of the investigated biopolymers was able to produce UCS improvements equivalent to those obtained by the 28-d soilelime samples;however,the optimum XG,GG and CS dosages,particularly after 28 d of curing,were easily able to replicate 7-d lime stabilization outcomes achieved with as high as twice the soil’s lime demand.Finally,the fundamental principles of clay chemistry,in conjunction with the soil mechanics framework,were employed to identify and discuss the clayebiopolymer stabilization mechanisms.