International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 13 Issue: 05 | May 2026 www.irjet.net p-ISSN: 2395-0072
BEARING CAPACITY EVALUATION OF FOOTINGS ON PARTIALLY SATURATED SOILS USING MODIFIED CONSTITUTIVE APPROACHES
Vivek Kumar Gautam1 , Mr. Ushendra Kumar2
1Master of Technology, Civil Engineering, Lucknow Institute of Technology, Lucknow, India
2Head of Department, Department of Civil Engineering, Lucknow Institute of Technology, Lucknow, India
Abstract -The evaluation of bearing capacity of shallow foundations is a fundamental aspect of geotechnical engineering design. Conventional bearing capacity theories, such as those proposed by Terzaghi and Meyerhof, are primarily developed for dry or fully saturated soil conditions anddonotconsidertheeffectsofpartialsaturation.However, inrealfieldconditions,soilsoftenexistinapartiallysaturated state where matric suction significantly influences their mechanical behavior. This study investigates the bearing capacityofshallowfootingsrestingonpartiallysaturatedsoils using modified constitutive approaches that incorporate suction-dependent stress parameters. A combined analytical andnumerical frameworkisadopted,integratingunsaturated soil mechanics concepts with advanced constitutive models such as the Fredlund two-stress state variable approach and the Barcelona Basic Model. The modified effective stress concept is used to account for the contribution of matric suction to soil strength. A parametric study is conducted to evaluate the influence of degree of saturation, matric suction, footing size, and soil type on bearing capacity and load–settlementbehavior. Theresultsindicateasignificantincrease in bearing capacity with decreasing degree of saturation due to the enhancement in apparent cohesion. The modified approach provides more realistic and less conservative predictions compared to classical methods. The findings highlight the importance of incorporating unsaturated soil behavior for accurate and economical foundation design.
Key Words: Bearing capacity; Unsaturated soil; Matric suction; Constitutive modeling; Shallow foundations; Soil-water characteristic curve
1. INTRODUCTION
1.1 Background
1.1.1 Importance of Bearing Capacity in Foundation Design
Bearing capacity is a critical parameter in geotechnical engineering that determines the maximum load a soil can safelysupportwithoutundergoingshearfailureorexcessive settlement. It directly governs the design and stability of shallowfoundationssuchasisolatedfootings,stripfootings, andraftfoundations.Accurateestimationofbearingcapacity ensures structural safety and serviceability while also enablingeconomicaldesignbyavoidingover-conservative assumptions.Classicalbearingcapacitytheories,developed
basedonlimitequilibriumconcepts,considersoilstrength parameterssuchascohesion,internalfrictionangle,andunit weight.However,theseapproachesoftenrelyonsimplified assumptionsofsoilbehavior,whichmaynotfullyrepresent complexfieldconditions(Terzaghi,1943;Meyerhof,1963).
1.1.2 Real Field Condition: Partially Saturated Soils
In natural conditions, soils are rarely fully saturated or completely dry; instead, they exist predominantly in a partiallysaturatedstate,particularlyabovethegroundwater table.Insuchconditions,thepresenceofbothairandwater withinsoilporesleadstothedevelopmentofmatricsuction, which significantly influences soil strength and stiffness. Matricsuctioncontributestoapparentcohesion,enhancing the load-bearing capacity of soil under certain moisture conditions.However,thisbehaviorishighlydependenton environmental factors such as rainfall, evaporation, and seasonalchanges,makingsoilresponsemorecomplexand variable compared to saturated conditions (Fredlund and Rahardjo,1993).
1.2 Problem Statement
1.2.1
Limitations of Classical Theories
Classicalbearingcapacitytheories,includingthoseproposed byTerzaghiandMeyerhof,arewidelyusedinengineering practice due to their simplicity and practicality. These theoriesassumethatsoiliseitherfullysaturatedordryand do not account for intermediate states of saturation. Consequently,theyneglect theinfluenceof matricsuction and its contribution to shear strength. This limitation restricts their applicability in real-world scenarios where soils are partially saturated, leading to discrepancies between predicted and actual foundation performance (Hansen,1970).
1.2.2 Ignoring Matric Suction and Resulting Inaccuracies
The exclusion of matric suction in classical formulations results in inaccurate estimation of bearing capacity, often leadingtoconservativedesigns.Whileconservativedesigns may enhance safety, they can also increase construction costs unnecessarily. Conversely, under certain conditions, ignoringmoisturevariationsmayleadtounsafepredictions ifsuctiondecreasesduetowetting.Therefore,theinability oftraditionalmodelstocapturesuction-dependentbehavior
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highlightstheneedforimprovedanalyticalapproachesthat incorporateunsaturatedsoilmechanicsprinciples(Vanapalli etal.,1996).
1.3 Research Gap
1.3.1
Limited Integration of Constitutive Models in Design
Although significant advancements have been made in constitutivemodelingofunsaturatedsoils,theirintegration into routine geotechnical design practice remains limited. Advanced models such as the Barcelona Basic Model and Fredlund’stwo-stressvariableframeworkprovidea more realistic representation of soil behavior by incorporating suctioneffects.However,thesemodelsareoftenconfinedto research applications and are not widely adopted in standard design procedures due to their complexity and requirementforadditionalparameters(Alonsoetal.,1990).
1.3.2 Lack of Coupling Between SWCC and Bearing Capacity
The Soil-Water Characteristic Curve (SWCC) is a fundamentaltoolinunsaturatedsoilmechanicsthatdefines the relationship between matric suction and degree of saturation.Despiteitsimportance,thereisalackofunified frameworks that directly integrate SWCC into bearing capacity analysis. This disconnect limits the ability to accuratelypredicthowvariationsinmoisturecontentaffect soilstrengthandfoundationperformance.Bridgingthisgap isessentialfordevelopingcomprehensivemodelsthatcan simulaterealfieldconditionsmoreeffectively(LuandLikos, 2004).
1.4 Objectives
1.4.1
Evaluation Using Modified Constitutive Approaches
Theprimaryobjectiveofthisstudyistoevaluatethebearing capacity of shallow footings resting on partially saturated soils using modified constitutive approaches. These approachesincorporatesuction-dependentstressvariables andprovideamorerealisticrepresentationofsoilbehavior comparedtoclassicalmethods.
1.4.2 Comparison with Classical Methods
Another key objective is to compare the results obtained frommodifiedconstitutivemodelswiththosepredictedby classical bearing capacity theories. This comparison helps quantifytheinfluenceofmatricsuctionandhighlightsthe limitationsoftraditionaldesignapproaches.
1.4.3
Analysis of Saturation and Suction Effects
The study also aims to analyze the effect of degree of saturationandmatricsuctiononbearingcapacityandload–
settlementbehavior.Byconductingaparametricevaluation, theresearchseekstounderstandhowvariationsinmoisture conditions influence foundation performance, thereby contributing to more accurate and reliable geotechnical designpractices.
2. LITERATURE REVIEW
2.1 Unsaturated Soil Mechanics
2.1.1
Matric Suction and Effective Stress Concepts
Unsaturatedsoilmechanicsextendsclassicalsoilmechanics byconsideringthepresenceofbothairandwaterwithinsoil pores.Akeyparametergoverningthebehaviorofsuchsoils ismatricsuction,definedasthedifferencebetweenpore-air pressure and pore-water pressure. This suction induces negativepore-waterpressure,whichenhancesinter-particle bonding and contributes to the apparent cohesion of soil. Consequently,partiallysaturatedsoilsoftenexhibithigher shearstrengthandstiffnesscomparedtofullysaturatedsoils under similar stress conditions. The concept of effective stress in unsaturated soils has been modified to include suctioneffects,enablingamorerealisticrepresentationof stress distribution within the soil matrix. These developmentsformthetheoreticalfoundationforanalyzing themechanicalbehaviorofsoilsinnaturalfieldconditions (FredlundandRahardjo,1993).
2.2 Classical Bearing Capacity Theories
2.2.1
Terzaghi, Meyerhof, and Hansen Approaches
Classicalbearingcapacitytheorieshavelongbeenusedas thebasisforfoundationdesign.Terzaghi’stheoryintroduced theconceptofultimatebearingcapacitybasedonsoilshear strength parameters and assumed a simplified failure mechanism beneath shallow foundations. Meyerhof extendedthisformulationbyincorporatingfactorssuchas footingshape,depth,andloadinclination,therebyimproving its applicability to practical problems. Hansen further refined the approach by introducing additional correction factors to account for real field conditions. These models collectivelyprovideasystematicframeworkforestimating bearing capacity and remain widely used in engineering practice due to their simplicity and reliability under conventionalconditions(Terzaghi,1943;Meyerhof,1963).
2.2.2
Limitations under Unsaturated Conditions
Despite their widespread use, classical bearing capacity theoriesarelimitedintheirabilitytorepresentunsaturated soilbehavior.Thesemethodsassumethatsoiliseitherfully saturatedorcompletelydry,therebyneglectingtheinfluence of matric suction. As a result, they fail to capture the additional strength contribution arising from partial saturation. This limitation leads to discrepancies between predictedandactualbearingcapacity,particularlyinregions where soil moisture conditions vary significantly.
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
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Consequently, the application of these theories to unsaturatedsoilsoftenresultsinconservativeorinaccurate designoutcomes(Hansen,1970).
2.3 Constitutive Models for Unsaturated Soils
2
.3.1 Bishop’s Effective Stress Approach
Bishopproposedanextensiontotheclassicaleffectivestress conceptbyintroducingasuction-dependentparameterthat accounts for the degree of saturation. This formulation modifies the effective stress by incorporating the contribution of matric suction, thereby enabling the prediction of shear strength in partially saturated soils. Although this approach provides a useful framework, it involves simplifications regarding the variation of the suctionparameterwithsaturation(Bishop,1959).
2.3.2 Fredlund Two-Variable Approach
A more advanced representation of unsaturated soil behavior was developed through the two stress state variableapproach,whichconsidersbothnetnormalstress and matric suction as independent variables. This frameworkallowsforamorecomprehensivedescriptionof soilbehavior,includingstrength,deformation,andvolume changecharacteristicsundervaryingmoistureconditions.It has become one of the most widely accepted theoretical models in unsaturated soil mechanics due to its flexibility andaccuracy(FredlundandMorgenstern,1977).
2.3.3
Barcelona Basic Model (BBM)
The Barcelona Basic Model (BBM) is a widely recognized constitutive model that incorporates suction as a key variableinfluencingtheyieldsurfaceofsoil.Itisbasedonan elastoplastic framework and accounts for hardening and softening behavior under loading and wetting conditions. BBMeffectivelycapturesthecouplingbetweenmechanical and hydraulic responses of soil, making it suitable for advancednumerical simulationsofgeotechnical problems involvingunsaturatedsoils(Alonsoetal.,1990).
2.4 Bearing Capacity in Unsaturated Soils
2.4.1 Experimental and Analytical Findings
Research on the bearing capacity of unsaturated soils has demonstratedthatsoilstrengthissignificantlyinfluencedby moistureconditions.Experimentalstudieshaveshownthat as the degree of saturation decreases, matric suction increases, leading to higher shear strength and improved load-carrying capacity. Analytical models incorporating suction effects have also been developed to predict this behavior,oftenshowinggoodagreementwithexperimental observations. These findings highlight the importance of consideringunsaturatedsoilmechanicsinfoundationdesign (Vanapallietal.,1996).
2.4.2 Influence of Suction on Soil Strength
Matric suction plays a crucial role in enhancing the shear strengthofpartiallysaturatedsoilsbyincreasingapparent cohesion.Thiseffectisparticularlysignificantinsandyand silty soils, where suction can develop rapidly due to high permeability.However,thecontributionofsuctionishighly sensitive to changes in moisture content, which may vary due to environmental factors such as rainfall and evaporation.Asaresult,thebearingcapacityofsoilsunder unsaturated conditions is not constant but varies with saturationlevels,makingitessentialtoincorporatesuctiondependent models for accurate prediction of foundation performance(LuandLikos,2004).
3. METHODOLOGY
3.1
Research Framework
3.1.1 Analytical and Numerical Approach
The present study adopts a combined analytical and numerical framework to evaluate the bearing capacity of shallowfootingsonpartiallysaturatedsoils.Theanalytical approachisbasedonmodifiedbearingcapacityformulations that incorporate suction-dependent stress parameters, enabling a theoretical understanding of soil behavior. In parallel, numerical modeling is employed to simulate the complexstress–strainresponseofsoilunderfootingloads, capturing nonlinearity and spatial variation in soil properties.Thisintegratedmethodologyensuresthatboth simplified theoretical predictions and detailed simulation resultsareobtained,enhancingtheoverallreliabilityofthe study.
3.1.2
Comparison with IS Code
To validate the effectiveness of the modified approach, resultsobtainedfromanalyticalandnumericalmodelsare compared with classical predictions based on IS 6403 provisions. The IS code assumes saturated or dry soil conditionsanddoesnotconsidermatricsuction.Therefore, itservesasabaselinereferencetoquantifytheimprovement achievedthroughsuction-basedmodeling.Thiscomparison helps in identifying the limitations of conventional design practices and demonstrates the need for incorporating unsaturatedsoilbehaviorinfoundationanalysis.
3.2 Soil Properties and Parameters
3.2.1
Soil Types Considered
The study considers representative soil types commonly encounteredinfoundationengineering,includingsandysoil, silty sand, and clayey sand. These soils are selected to capturearangeofpermeabilityandsuctioncharacteristics, as the influence of partial saturation varies significantly across different soil classifications. Sandy soils typically
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exhibit rapid suction changes, while clayey soils show gradualvariationduetolowerpermeability.
3.2.2
Geotechnical Parameters
Key geotechnical parameters used in the analysis include unitweight(γ),cohesion(c),angleofinternalfriction(φ), elasticmodulus(E),andPoisson’sratio(ν).Inaddition,SoilWater Characteristic Curve (SWCC) parameters are incorporatedtodefinetherelationshipbetweensuctionand degreeofsaturation.Theseparameterscollectivelygovern the strength, stiffness, and hydraulic behavior of the soil underpartiallysaturatedconditions.
3.3 Constitutive Model
3.3.1
Model Selection
Thestudyutilizesadvancedconstitutivemodelssuchasthe Barcelona Basic Model (BBM) or the Fredlund two-stress variable approach to represent unsaturated soil behavior. These models incorporate suction as an independent variable influencing soil strength and deformation characteristics.
3.3.2 Justification of Selection
The selected models are capable of capturing suctiondependent stress–strain relationships and are widely validated in unsaturated soil mechanics research. Their ability to simulate both elastic and plastic behavior under varying moisture conditions makes them suitable for analyzingfootingperformanceinpartiallysaturatedsoils.
3.4 Incorporation of Matric Suction
3.4.1 Modified Effective Stress Concept
Matric suction is incorporated into the analysis using a modified effective stress framework. In this approach, effective stress is expressed as a function of net normal stressandsuction, witha parameterthataccountsforthe degreeofsaturation.Thisformulationenablestheinclusion of suction-induced strength in the analysis, thereby providing a more realistic representation of soil behavior comparedtoclassicaleffectivestressconcepts.
3.5 SWCC Integration
3.5.1 Relationship between Suction and Saturation
The Soil-Water Characteristic Curve (SWCC) is integrated intothemodelingframework toestablish therelationship betweenmatricsuctionanddegreeofsaturation.TheSWCC servesasacriticallinkbetweenhydraulicandmechanical behavior,allowingthevariationofsoilstrengthparameters with moisture content to be captured. This integration enhancestheaccuracyofconstitutivemodelingandbearing capacityprediction.
3.6 Bearing Capacity Formulation
3.6.1 Classical Equation
(Baseline)
Theclassicalbearingcapacityequationisusedasabaseline forcomparison.Itconsiderssoilcohesion,unitweight,and frictionangle,alongwithbearingcapacityfactors,underthe assumptionofsaturatedordryconditions.Thisformulation provides a reference point for evaluating the influence of suction.
3.6.2
Modified Equation with Suction
A modified bearing capacity formulation is developed by incorporating suction-dependent cohesion and effective stress. In this approach, matric suction contributes to apparentcohesion,resultinginincreasedshearstrengthand higherbearingcapacity.Themodifiedequationthusreflects the influence of partial saturation on soil behavior and providesmorerealisticpredictions.
4. RESULTS AND DISCUSSION
4.1
Validation of Model
4.1.1
Comparison with IS 6403 / Classical Results
Thevalidityoftheproposedmodifiedconstitutiveapproach is assessed by comparing the predicted bearing capacity with values obtained from classical methods based on IS 6403 and traditional theories. The classical approach assumes saturated or dry soil conditions and therefore provides relatively lower and constant bearing capacity values.Incontrast,themodifiedmodelincorporatessuction effects and shows higher bearing capacity under partially saturatedconditions.Thecomparisondemonstratesthatthe proposed approach aligns with classical results under saturated conditions, thereby confirming its consistency, while also extending the prediction capability to more realisticfieldscenarios.
4.2 Effect of Matric Suction
4.2.1
Increase in Bearing Capacity
The analysis clearly indicates that matric suction plays a significantroleinenhancingthebearingcapacityofsoil.As suction increases, the apparent cohesion of soil also increases, leading to improved shear strength. This additional strength allows the soil to sustain higher loads beforefailure.Theresultsshowthatevenmoderatelevelsof suction can produce noticeable improvement in bearing capacitycomparedtoclassicalpredictions.
4.2.2
Nonlinear Trend
The relationship between matric suction and bearing capacityisobservedtobenonlinear.Atlowersuctionlevels, the increase in bearing capacity is gradual; however, as
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
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suctionincreasesfurther,therateofimprovementbecomes morepronounced.Thisnonlinearbehaviorisattributedto thecomplexinteractionbetweensoilparticles,porewater, and air within the soil matrix. The results highlight that suctioneffectsaremoredominantwithinaspecificrangeof partialsaturation.
4.3 Effect of Degree of Saturation
4.3.1
Influence on Bearing Capacity
Thedegreeofsaturationisfoundtobea governingfactor influencing bearing capacity. As the degree of saturation decreases, the amount of air in the soil pores increases, leadingtohighermatricsuction.Thisresultsinanincrease insoilstrengthand,consequently,higherbearingcapacity. Thestudyshowsthatsoilsatlowersaturationlevelsexhibit significantlygreaterload-carryingcapacitycomparedtofully saturatedconditions.
4.4 Load–Settlement Behaviour
4.4.1
Higher Stiffness in Unsaturated Soils
The load–settlement response indicates that partially saturated soils exhibit higher stiffness compared to saturatedsoils.Thisisreflectedintheinitialportionofthe load–settlement curve, where smaller settlements are observedforthesameappliedload.Theincreasedstiffness isprimarilyduetothecontributionofmatricsuction,which enhances inter-particle bonding and resistance to deformation.
4.4.2 Delayed Failure Response
Another important observation is the delayed failure behaviorinunsaturatedsoils.Thefootingisabletosustain higher loads before reaching ultimate failure, and the progression of settlement is more gradual. This indicates improved performance and stability of foundations under partially saturated conditions when compared to classical saturatedassumptions.
4.5 Comparison: Classical vs Modified Models
4.5.1 Quantitative Improvement (%)
Aquantitativecomparisonbetweenclassicalandmodified approaches reveals a significant improvement in bearing capacity when suction effects are considered. The percentage increase varies depending on soil type and degree of saturation but generally shows a substantial enhancement under partially saturated conditions. The classical model consistently underestimates bearing capacity, whereas the modified model provides more realistic predictions, highlighting the importance of incorporatingunsaturatedsoilbehaviorindesign.
4.6 Effect of Soil Type
4.6.1
Sandy Soils – Highest Improvement
The results indicate that sandy soils exhibit the highest improvementinbearingcapacityduetosuctioneffects.This is because sandy soils have higher permeability, allowing rapid development of matric suction. As a result, the contribution of suction to apparent cohesion is more pronounced, leading to significant enhancement in loadcarryingcapacity.
4.6.2 Clayey Soils – Moderate Response
Incontrast,clayeysoilsshowamoremoderateresponseto suction.Duetotheirlowpermeability,thedevelopmentand variation of suction occur more slowly. While suction still contributestostrengthimprovement,theoverallincreasein bearingcapacityislesssignificantcomparedtosandysoils. This behavior reflects the influence of soil type on unsaturatedsoilmechanics.
4.7 Effect of Footing Geometry
4.7.1
Influence of Footing Width
Footingwidthisfoundtoinfluencethedistributionofstress within the soil mass. Smaller footings tend to concentrate stressoveralimitedarea,makingtheeffectofmatricsuction morepronounced.Incontrast,largerfootingsdistributethe loadoverawiderarea,reducingtherelativecontributionof suctionperunitstress.Thus,thepercentageimprovementin bearingcapacityduetosuctionishigherforsmallerfooting sizes.
4.7.2 Shape Factor (Square vs Strip Footing)
Theshapeofthefootingalsoaffectsbearingcapacity.Square footingsexhibitslightlyhigherbearingcapacitycomparedto stripfootingsduetomoreuniformstressdistributionintwo directions.Thisallowsbettermobilizationofsoilstrength, includingsuctioneffects.Stripfootings,ontheotherhand, showrelativelylowercapacityduetoone-dimensionalload distribution.Theseobservationsareconsistentwithclassical shape factor concepts, with additional influence from unsaturatedsoilbehavior.
5. CONCLUSION
This study presents a comprehensive evaluation of the bearing capacity of shallow footings resting on partially saturatedsoilsusingmodifiedconstitutiveapproaches.The findingsclearlydemonstratethatclassicalbearingcapacity theories,whichassumefullysaturatedordrysoilconditions, areinadequateforrepresentingrealfieldscenarioswhere soils are predominantly partially saturated. The incorporationofmatricsuctionintotheanalysissignificantly enhances the prediction of soil strength and bearing capacity. Results indicate that bearing capacity increases
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withdecreasingdegreeofsaturationduetothedevelopment ofsuction-inducedapparentcohesion,leadingtoimproved load-carryingcapacityandstiffnessofthesoil.
Theload–settlementanalysisfurtherrevealsthatpartially saturated soils exhibit higher initial stiffness and delayed failurecomparedtoclassicalpredictions,highlightingtheir improved performance under foundation loading. The comparisonbetweenclassicalandmodifiedmodelsshows thatconventionalapproachestendtounderestimatebearing capacity,resultinginconservativedesigns.Additionally,the influence of soil type and footing geometry is found to be significant,withsandysoilsshowinggreaterimprovement duetorapidsuctiondevelopment,whileclayeysoilsexhibit moderateenhancement.Smallerfootingwidthsandsquare geometries demonstrate a more pronounced effect of suction.
Overall,thestudyconfirmsthatincorporatingunsaturated soilmechanicsthroughmodifiedconstitutivemodelsleads tomorerealistic,reliable,andeconomicalfoundationdesign, particularlyinregionswithvariablemoistureconditions.
6.
FUTURE SCOPE
Future research should focus on field-scale validation of suction-based bearing capacity models through instrumented footing tests under controlled and natural moistureconditions.Long-termmonitoringoffoundations subjected to seasonal wetting and drying cycles would provide valuable insights into the temporal variation of matricsuctionanditsimpactonsoilperformance.Further studiesarerequiredtodevelopsimplifieddesignprocedures thatintegratesuctioneffectsintostandardcodessuchasIS 6403forpracticalapplication.Advancednumericalmodeling usingcoupledhydro-mechanical analysiscanimprovethe understanding of transient moisture flow and stress interaction.Additionally,extendingtheresearchtodifferent foundationsystems,includingraftandpilefoundations,and exploring machine learning-based predictive models can enhancetheapplicabilityandefficiencyofunsaturatedsoil analysisingeotechnicalengineering.
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