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
SETTLEMENT BEHAVIOR OF SHALLOW FOUNDATIONS ON STRATIFIED SOILS CONSIDERING NONLINEAR SOIL PROPERTIES
Ashutosh Kumar Yadav1 , 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 -Accurate prediction of settlement is a critical aspectinthedesignofshallowfoundations,particularlywhen dealing with stratified soil conditions and nonlinear soil behavior. Conventional approaches based on linear elastic assumptions often fail to capture the actual response of soil, leading to either unsafe or overly conservative designs. This study investigates the settlement behavior of shallow foundations resting on stratified soils by incorporating nonlinear soil properties through advanced constitutive modeling.Acombinationofanalyticalmethodsandnumerical modeling techniques is employed to evaluate the influence of soil layering, stress-dependent stiffness, and load intensity on settlement response. The analysis considers both two-layer and multi-layer soil systems representative of typical field conditions. Comparative evaluation is performed between linear elastic, Mohr–Coulomb, and Hardening Soil models to assess their effectiveness in predicting settlement. The results indicate that nonlinear models provide more realistic predictions, particularly at higher load levels, where stiffness degradation and plastic deformation become significant. Additionally,soilstratificationplaysacrucialrole,withweakover-strong configurations resulting in higher settlements compared to strong-over-weak arrangements. Parametric studies further highlight the influence of layer thickness, stiffness ratio, and foundation depth on settlement behavior. Thefindingsemphasizethenecessityofintegratingnonlinear soil behavior and stratification effects for reliable and economical foundation design.
Key Words: Shallow foundations, Settlement analysis, Stratified soils, Nonlinear soil behavior , Hardening Soil Model, Finite element analysis, Soil–structure interaction
1. INTRODUCTION
1.1 Background
1.1.1 Importance of Shallow Foundations
Shallowfoundationsarewidelyusedincivilengineeringdue to their simplicity, cost-effectiveness, and ease of construction. They are commonly adopted for low- to medium-rise structures, bridges, and industrial facilities wherecompetentsoilstrataareavailableneartheground surface.Thesefoundationstransferstructuralloadstothe supporting soil within a relatively shallow depth, making their performance highly dependent on the mechanical
behaviorofnear-surfacesoils.Theirwidespreadapplication inpracticemakesitessentialtounderstandtheirinteraction withsoilunderdifferentloadingandgroundconditionsto ensuresafetyandserviceability(Das,2015;Bowles,1996).
1.1.2 Settlement as a Governing Design Criterion
In geotechnical engineering, settlement is often a more criticaldesigncriterionthanultimatebearingcapacity.Even whenthesoilcansafelysupportappliedloadswithoutshear failure,excessivesettlementcanleadtostructuraldistress such as cracking, tilting, and misalignment. Differential settlement is particularly problematic, as it induces additional stresses within structural elements. Therefore, accurate prediction of settlement is essential to ensure serviceability and long-term performance of structures. Engineersmustevaluatenotonlytotalsettlementbutalso its distribution to avoid functional and aesthetic issues (Terzaghi,PeckandMesri,1996).
1.1.3 Issues with Conventional Linear Approaches
Traditionalsettlementanalysismethodsarelargelybasedon linearelastictheory,whichassumesconstantsoilstiffness andproportionalstress–strainbehavior.However,realsoils exhibit nonlinear and stress-dependent characteristics, especiallyunderincreasingloadlevels.Linearmodelsoften oversimplify soil response and fail to capture plastic deformationandstiffnessdegradation.Asaresult,theymay produce inaccurate predictions, either underestimating settlementinsoftsoilsoroverestimatingitinstiffsoils.This limitation becomes more significant in complex soil conditionssuchaslayereddeposits.
1.2 Problem Statement
1.2.1 Inaccuracy Due to Soil Stratification
Naturalsoildepositsarerarelyhomogeneousandtypically consist of multiple layers with varying stiffness, strength, and compressibility. Soil stratification significantly affects stressdistributionbeneathfoundations,leadingtocomplex settlement behavior. For example, the presence of a soft compressible layer beneath a stiff layer can result in excessive settlement that is not predicted by simplified models.Ignoringstratificationmaythereforeleadtounsafe oruneconomicaldesigns.
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
1.2.2 Inaccuracy Due to Nonlinear Soil Behavior
Soil exhibits nonlinear stress–strain behavior, where stiffness decreases with increasing stress and strain. This behavior is particularly important under higher load intensities,whereplasticdeformationbecomessignificant. Conventional linear approaches do not account for this variability,resultingininaccurateestimationofsettlement. The inability to capture stress-dependent stiffness and yieldingbehaviorlimitsthereliabilityoftraditionalmethods inrealisticgeotechnicalconditions.
1.3 Research Gap
1.3.1
Lack of Integrated Studieson Stratified Soilsand Nonlinearity
Althoughnumerousstudieshaveinvestigatedsettlementin stratifiedsoilsandnonlinearsoilbehaviorseparately,there is a lack of comprehensive research that integrates both aspectsintoaunifiedframework.Mostclassicalapproaches assume either homogeneous soil conditions or linear material behavior, which does not reflect actual field scenarios.Advancednumericalmethodshavebeenusedin recent studies, but systematic integration of layered soil profiles with nonlinear constitutive modeling remains limited. This gap highlights the need for research that simultaneously considers stratification and nonlinear soil responseforimprovedsettlementprediction(Brinkgreve, KumarswamyandSwolfs,2018).
1.4 Objectives of the Study
1.4.1
Analysis of Settlement in Stratified Soils
The primary objective of this study is to analyze the settlement behavior of shallow foundations resting on stratifiedsoilsystems.Byconsideringdifferentsoillayering configurations,thestudyaimstounderstandhowvariations in soil properties with depth influence settlement characteristics.
1.4.2 Comparison of Linear and Nonlinear Behavior
Anotherkeyobjectiveistocomparesettlementpredictions obtainedfromlinearelasticmodelswiththosederivedfrom nonlinear constitutive models. This comparison helps in quantifying the limitations of traditional approaches and highlights the importance of incorporating nonlinear soil behaviorinanalysis.
1.4.3 Evaluation of Key Influencing Parameters
Thestudyalsoaimstoevaluatetheinfluenceofimportant parameters such as soil stiffness, layer thickness, load intensity, and foundation depthonsettlement behavior. A parametricapproachisadoptedtoidentifythesensitivityof
settlementtothesevariablesandtoestablishtrendsthatcan assistinpracticaldesign.
1.5 Scope and Limitations
1.5.1
Static Loading Conditions
Theanalysisinthisstudyislimitedtostaticverticalloading conditions, which are representative of typical structural loads.Dynamiceffectssuchasseismicorcyclicloadingare not considered, although they may significantly influence settlementincertaincases.
1.5.2 Idealized Soil Layers
Thesoilprofileismodeledasaseriesofidealizedlayerswith uniform properties within each layer. While this simplification is necessary for analysis, actual field conditionsmayexhibitvariabilityandheterogeneitythatare notfullycapturedinthemodel.
1.5.3 Limited Field Validation
The study primarily relies on analytical and numerical modelingtechniques,withlimitedvalidationusingfielddata. Although comparisons with established theories and standards are performed, the absence of extensive field validationmayrestrictthegeneralizationofresultstoallsite conditions.
2. LITERATURE REVIEW
2.1
Settlement of Shallow Foundations
2.1.1
Types of Settlement
Settlementofshallowfoundationsisafundamentalaspectof geotechnicaldesignandistypicallyclassifiedintothreemain components: immediate, consolidation, and secondary settlement. Immediate settlement occurs instantaneously upon loading and is primarily associated with elastic deformationofsoilparticles,particularlyingranularsoils. Consolidationsettlementistime-dependentandtakesplace insaturatedcohesivesoilsduetothedissipationofexcess pore water pressure under sustained loading. Secondary settlement, also known as creep, occurs after primary consolidation and is attributed to long-term plastic adjustmentofsoilstructureunderconstantstress.Thetotal settlementisthecumulativeeffectofthesecomponents,and accurate estimation of each is essential for ensuring serviceabilityofstructures(Terzaghi,PeckandMesri,1996).
2.2 Settlement in Stratified Soils
2.2.1 Two-Layer and Multi-Layer Soil Systems
Natural soil deposits are generally stratified, consisting of multiplelayerswithvaryingmechanicalpropertiessuchas
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
stiffness,strength,andcompressibility.Two-layersystems are commonly used in research to simplify analysis and understand the fundamental interaction between layers, while multi-layer systems provide a more realistic representationoffieldconditions.Thepresenceofdifferent soil layers leads to non-uniform stress distribution and varying deformation responses within the soil mass. As a result, settlement behavior becomes more complex comparedtohomogeneoussoilconditions,requiringmore advanced analytical or numerical approaches for accurate prediction(Das,2015).
2.2.2
Strong-over-Weak vs Weak-over-Strong Configurations
The arrangement of soil layers plays a critical role in determining settlement characteristics. In a strong-overweak configuration, a stiff layer overlies a softer, more compressiblelayer,causingtheappliedloadtotransferto deeperstrataandoftenresultinginsignificantsettlementat depth. Conversely, in a weak-over-strong configuration, a soft layer is present near the surface, leading to higher immediate settlement due to its low stiffness. These configurations influence both the magnitude and distribution of settlement, highlighting the importance of consideringlayersequenceinfoundationanalysis(Bowles, 1996).
2.3 Nonlinear Soil Behavior
2.3.1 Stress-Dependent
Stiffness
Soilexhibitsinherentlynonlinearbehavior,wherestiffness isnotconstantbutvarieswithstressandstrainlevels.Atlow stress levels, soil tends to behave relatively stiff, while increasingstressleadstogradualreductioninstiffnessdue to particle rearrangement and plastic deformation. This stress-dependent stiffness is a key characteristic that influencessettlementbehavior,especiallyunderhigherload intensities.Ignoringthisnonlinearitycanresultininaccurate predictions,assoilresponsebecomesprogressivelysofter withincreasingload(DuncanandChang,1970).
2.3.2
Limitations of Linear Elastic Models
Linear elastic models assume a constant modulus of elasticityandaproportionalrelationshipbetweenstressand strain. While these assumptions simplify analysis, they do notaccuratelyrepresentrealsoilbehavior.Suchmodelsfail to capture important phenomena such as stiffness degradationandplasticyielding,whichbecomesignificantat higher stress levels. Consequently, linear approaches may underestimatesettlementinsoftsoilsoroverestimateitin stiffsoils,limitingtheirreliabilityincomplexgeotechnical problemsinvolvingstratificationandhighloads.
2.4 Constitutive Models
2.4.1
Linear Elastic Model
Thelinearelasticmodelisoneofthesimplestapproaches usedinsettlementanalysis.Itassumesthatsoilbehavesasa perfectly elastic material with constant stiffness and no permanent deformation. Although widely used in preliminarydesignduetoitssimplicity,thismodeldoesnot account for nonlinear or plastic behavior, making it unsuitable for accurate prediction under realistic loading conditions.
2.4.2 Mohr–Coulomb Model
The Mohr–Coulomb model is an elastic–perfectly plastic constitutivemodelthatdefinessoilbehaviorbasedonayield criterion involving cohesion and internal friction angle. It allowsforplasticdeformationbeyondtheelasticlimitbut assumes constant stiffness prior to yielding. While this modelprovidesabetterrepresentationthanlinearelasticity, it does not capture gradual stiffness degradation and is thereforelimitedinsimulatingstress-dependentbehavior.
2.4.3 Hardening Soil Model
The Hardening Soil Model is an advanced nonlinear constitutive model that incorporates stress-dependent stiffnessanddistinguishesbetweenloading,unloading,and reloading conditions. It accounts for both shear and compressionhardening,enablingmorerealisticsimulation of soil response under varying stress paths. This model is particularly effective in settlement analysis, as it captures theprogressivereductioninstiffnesswithincreasingload and provides more accurate predictions compared to simpler models (Brinkgreve, Kumarswamy and Swolfs, 2018).
3. METHODOLOGY
3.1 Research Framework
3.1.1
Overall Research Approach
The present study adopts a systematic and structured researchframeworktoinvestigatethesettlementbehavior of shallow foundations on stratified soils considering nonlinear soil properties. The methodology follows a sequential flow beginning with an extensive review of existingliterature,followedbythedevelopmentofanalytical and numerical models, detailed analysis of settlement behavior,andfinallyvalidationofresults.Thisstep-by-step approach ensures logical progression and coherence in addressingtheresearchobjectives.
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3.1.2 Flow: Literature → Modeling → Analysis → Validation
Initially,acomprehensiveliteraturereviewisconductedto understand existing theories, methods, and research gaps related to settlement and soil behavior. Based on this understanding,appropriatesoilandfoundationmodelsare developed, incorporating stratification and nonlinear characteristics. The next stage involves performing analytical and numerical analyses to evaluate settlement underdifferentconditions.Finally,theresultsarevalidated through comparison with established analytical solutions andcodalprovisionstoensureaccuracyandreliability.
3.2 Soil Profile Modeling
3.2.1
Two-Layer and Multi-Layer Soil Systems
Torepresentrealisticgroundconditions,thesoilprofileis modeledasastratifiedsystemconsistingofbothtwo-layer andmulti-layerconfigurations.Thetwo-layersystemisused tostudyfundamentalinteractionsbetweenastiffandasoft layer, providing clarity on the influence of layer arrangement. The multi-layer system, on the other hand, offers a more realistic simulation of natural soil deposits, wheremultiplestratawithvaryingpropertiescoexist.This approach allows for a comprehensive assessment of settlementbehaviorunderdifferentstratificationscenarios.
3.2.2 Typical Indian Soil Conditions
Thesoilprofilesconsideredinthisstudyarerepresentative oftypicalIndiansubsoilconditions,particularlythosefound inalluvial regionssuchastheIndo-Gangeticplains. These regionsarecharacterizedbyalternatinglayersofsand,silt, and clay with varying stiffness and compressibility. By incorporating such realistic soil conditions, the study ensures that the results are applicable to practical engineeringproblemscommonlyencounteredinIndia.
3.3 Foundation Model
3.3.1
Type of Foundation: Isolated and Strip Footing
The study focuses on shallow foundation systems, specifically isolated footings and strip footings, which are widelyusedincivil engineeringpractice.Isolatedfootings aretypicallyusedtosupportindividualcolumns,whilestrip footings are used for load-bearing walls. For detailed analysis,onetypeoffooting(generallyanisolatedfooting)is selectedastheprimarymodelduetoitssimplicityandease ofnumericalimplementation.
3.3.2 Geometry of Foundation (B, L, Df)
Thegeometryofthefoundationisdefinedbykeyparameters suchaswidth(B),length(L),anddepthofembedment(Df). These parameters influence stress distribution and the
extent of the soil affected by loading. The dimensions are selected based on typical engineering practices and are variedwithinreasonablerangesduringparametricanalysis tostudytheireffectonsettlementbehavior.
3.3.3
Loading Conditions: Uniform Static Load
Thefoundationissubjectedtoauniformlydistributedstatic vertical load, representing typical structural loading conditions. This assumption simplifies the analysis while capturing the essential behavior of the soil–foundation system.Themagnitudeofloadisvariedtostudyitsinfluence on settlement and to capture nonlinear soil response at differentstresslevels.
3.4 Constitutive Models
3.4.1 Linear Elastic Model (Baseline)
Thelinearelasticmodelisusedasareferenceorbaselinefor comparison. It assumes that soil behaves as a perfectly elasticmaterialwithconstantstiffnessandalinearstress–strainrelationship.Althoughthismodelsimplifiesanalysis,it doesnotrepresentactualsoilbehaviorundervaryingstress conditionsandisthereforeusedprimarilyforcomparative purposes.
3.4.2
Mohr–Coulomb Model
The Mohr–Coulomb model is an elastic–perfectly plastic model that accounts for yielding of soil beyond a defined stress limit. It is characterized by parameters such as cohesion,angleofinternalfriction,modulusofelasticity,and Poisson’s ratio. While it improves upon the linear elastic model by incorporating plastic behavior, it still assumes constant stiffness prior to yielding and does not capture gradualstiffnessdegradation.
3.4.3 Hardening Soil Model (Primary Model)
The Hardening Soil Model is employed as the primary constitutivemodelinthisstudyduetoitsabilitytosimulate nonlinear soil behavior more accurately. It incorporates stress-dependent stiffness and distinguishes between loading, unloading, and reloading conditions. This model accounts for both shear and compression hardening, enabling realistic prediction of settlement under varying loadlevelsandstratifiedsoilconditions.
3.5 Numerical Modeling
3.5.1
Software and Modeling Tool
Numericalanalysisiscarriedoutusingfiniteelement-based software, such as PLAXIS or a similar FEM tool, which is widelyusedingeotechnicalengineeringforsimulatingsoil–structure interaction problems. The software allows for
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
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detailed modeling of soil behavior, including stratification andnonlinearconstitutiverelationships.
3.5.2
Mesh Generation and Boundary Conditions
Thesoildomainisdiscretizedintofiniteelementsusingan appropriatemesh.Afinermeshisusednearthefoundation where stress gradients are high, while a coarser mesh is adoptedfartherawaytooptimizecomputationalefficiency. Boundaryconditionsarecarefullydefinedtoavoidboundary effects; the base is fixed in both directions, and lateral boundaries are restrained horizontally while allowing vertical movement. These conditions ensure realistic simulationofsoilbehaviorunderloading.
3.6 Parameters Considered
3.6.1
Soil Stiffness (E)
The modulus of elasticity (E) is a key parameter representingsoilstiffnessanddirectlyinfluencessettlement. Different values are assigned to various soil layers to simulate realistic conditions and to study the effect of stiffnessvariationonsettlementbehavior.
3.6.2
Layer Thickness
Thethicknessofindividualsoillayersisvariedtoassessits impactonsettlement.Thickercompressiblelayersgenerally result in higher settlement, as a larger volume of soil undergoesdeformationunderappliedloads.
3.6.3 Stiffness Ratio (E₁/E₂)
Theratioofstiffnessbetweenadjacentlayersisanimportant parameterinstratifiedsoilsystems.Variationsinstiffness ratio help in analyzing different configurations such as strong-over-weakandweak-over-strong,whichsignificantly influencesettlementcharacteristics.
3.6.4
Load Intensity
Loadintensityisvariedwithinaspecifiedrangetoevaluate itseffectonsettlementbehavior.Increasingloadlevelslead to higher stress in the soil, resulting in nonlinear deformationandstiffnessdegradation,whicharecapturedin theanalysis.
3.7 Validation Approach
3.7.1
Validation Using Analytical Solutions
Thenumericalresultsobtainedfromfiniteelementanalysis arevalidatedbycomparingthemwithanalyticalsolutions based on elastic theory. These solutions provide approximatesettlementvaluesandserveasabenchmarkfor evaluatingtheaccuracyofthenumericalmodel.
3.7.2 Codal Comparison (IS 8009)
Furthervalidationisperformedbycomparingthecomputed settlement values with those obtained using codal provisions, specifically IS 8009 (Part 1), which provides guidelinesforsettlementestimation.Thiscomparisonhelps ensure that the results are consistent with standard engineering practices and fall within acceptable limits, therebyenhancingthereliabilityofthestudy.
4. RESULTS
4.1 Model Validation
4.1.1
Mesh Convergence
The reliability of the numerical model is first established through a mesh convergence study. In finite element analysis,theaccuracyofresultsdependssignificantlyonthe discretization of the soil domain. A series of meshes with increasing refinement is analyzed to ensure that the computedsettlementvaluesdonotchangesignificantlywith further mesh refinement. It is observed that as the mesh becomes finer, the variation in settlement reduces and eventuallystabilizes,indicatingconvergenceofthesolution. Arelativelyfinemeshisadoptednearthefoundationwhere stress gradients are high, while a coarser mesh is used in regionsfartherawaytomaintaincomputationalefficiency. This approach ensures both accuracy and stability of the numericalresults.
4.1.2 Comparison with Analytical and IS Code Results
To further validate the numerical model, the computed settlement values are compared with analytical solutions based on elastic theory and with codal recommendations providedinIS8009(Part1).Thecomparisonshowsgood agreementatlowerloadlevels,wheresoilbehaviorremains approximately linear. However, slight deviations are observed at higher loads due to the incorporation of nonlinearsoilbehaviorinnumericalanalysis,whichisnot captured in analytical or codal methods. The deviations remainwithinacceptableengineeringlimits,confirmingthe reliabilityandapplicabilityofthedevelopedmodel.
4.2 Settlement in Homogeneous Soil
4.2.1
Linear vs Nonlinear Comparison
Settlement behavior in homogeneous soil is analyzed as a baseline case to understand the influence of soil nonlinearity. The results obtained from the linear elastic model show a proportional increase in settlement with increasingload,reflectingconstantsoilstiffness.Incontrast, the nonlinear model predicts a gradual increase in settlementatlowloadsfollowedbyamorerapidincreaseat higher loads. This difference arises due to stiffness degradationandtheonsetofplasticdeformationinthesoil.
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Thecomparisonclearlyindicatesthatlinearmodelstendto underestimate settlement at higher stress levels, while nonlinearmodelsprovideamorerealisticrepresentationof soilbehavior.
4.3 Settlement in Stratified Soil
4.3.1
Two-Layer Soil System
The analysis of two-layer soil systems highlights the significant influence of layer arrangement on settlement behavior. In the weak-over-strong configuration, higher settlementisobservedduetothepresenceofacompressible layer near the surface, which undergoes substantial deformationunderappliedload.Conversely,inthestrongover-weakconfiguration,thestiffupperlayerdistributesthe load more effectively, resulting in reduced surface settlement but increased stress transfer to deeper layers. The results demonstrate that both stiffness contrast and layerthicknessplayacrucialroleindeterminingsettlement magnitude.
4.3.2
Multi-Layer Soil System
For multi-layer soil systems, the settlement behavior becomes more complex due to the interaction between multiplelayerswithvaryingproperties.Theanalysisshows thatthepresenceofadditionalcompressiblelayersleadsto anincreaseintotalsettlement.However,thecontributionof each layer depends on its position relative to the stress influencezone.Layerslocated withinthiszonecontribute moresignificantlytosettlement,whiledeeperlayershavea relatively smaller effect. The results emphasize the importanceofconsideringtheentiresoilprofileratherthan simplifyingitintoasingleequivalentlayer.
4.4 Effect of Nonlinear Soil Behavior
4.4.1
Load–Settlement Curves
The load–settlement relationship obtained from different constitutive models provides valuable insight into soil behavior.Thelinearelasticmodelproducesastraight-line relationship, indicating constant stiffness. The nonlinear models, particularly the Hardening Soil Model, generate curved load–settlement responses, reflecting gradual stiffnessreductionwithincreasingload.Atlowerloadlevels, thecurvesfrombothmodelsaresimilar;however,athigher loads, the nonlinear model predicts significantly larger settlement. This demonstrates the importance of incorporating nonlinear behavior for accurate prediction underrealisticloadingconditions.
4.4.2
Stiffness Degradation
A key feature of nonlinear soil behavior observed in the resultsisstiffnessdegradation.Astheappliedloadincreases, the soil stiffness decreases due to particle rearrangement
andplasticdeformation.Thisreductioninstiffnessleadsto increasedsettlementathigherstresslevels.TheHardening Soil Model effectively captures this behavior, showing a progressive decline in apparent stiffness with increasing load.Thisphenomenonisnotrepresentedinlinearmodels, highlightingtheirlimitationinsimulatingrealsoilresponse.
4.5 Parametric Study
4.5.1 Effect of Layer Thickness
Thethicknessofsoillayers,particularlysoftcompressible layers, has a significant impact on settlement. The results indicatethatincreasingthethicknessofthesoftlayerleads toasubstantialincreaseinsettlement,asalargervolumeof soil undergoes compression. This effect is especially pronounced when the soft layer lies within the stress influencezonebeneaththefoundation.
4.5.2 Effect of Soil Stiffness
Soilstiffness,representedbythemodulusofelasticity,isa critical parameter governing settlement behavior. Higher stiffnessvaluesresultinlowersettlementduetoincreased resistance to deformation, while lower stiffness leads to greater settlement. The analysis shows a clear inverse relationship between soil stiffness and settlement magnitude.
4.5.3 Effect of Foundation Depth
Thedepthoffoundationembedmentinfluencessettlement byalteringstressdistributionandconfinementofthesoil.As thefoundationdepthincreases,thesoilexperienceshigher confiningpressure,whichenhancesitsstiffnessandreduces settlement.Additionally,deeperfoundationstransferloads to relatively stiffer soil layers, further contributing to reduceddeformation.
4.5.4 Effect of Load Intensity
Load intensity has a direct and significant effect on settlement. At lower loads, settlement increases gradually and may follow an approximately linear trend. However, beyond a certain load level, nonlinear effects become dominant, leading to a rapid increase in settlement. This behavior is attributed to stiffness degradation and plastic deformationinthesoil.Theresultshighlighttheimportance of considering nonlinear soil behavior, particularly for heavilyloadedfoundations.
5. CONCLUSION
Thisstudyinvestigatedthesettlementbehaviorofshallow foundations on stratified soils by incorporating nonlinear soilpropertiesthroughanalyticalandnumericalapproaches. The results clearly demonstrate that conventional linear elastic methods are inadequate for accurately predicting
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settlement, particularly at higher load intensities. Linear modelsassumeconstantstiffnessandfailtocapturestressdependent behavior, leading to underestimation of settlementwhensoilexperiencessignificantdeformation.In contrast, nonlinear constitutive models, especially the Hardening Soil Model, provide a more realistic representationbyaccountingforstiffnessdegradationand plasticdeformation.
The influence of soil stratification was found to be highly significant.Two-layerandmulti-layeranalysesrevealedthat layerarrangement,stiffnesscontrast,andthicknessgreatly affect settlement magnitude. Weak-over-strong configurations produced higher surface settlement due to the presence of compressible soil near the foundation, whereasstrong-over-weakarrangementsresultedinlower surface settlement but deeper stress transfer. Parametric studiesfurtherconfirmedthatincreasingsoftlayerthickness and load intensity leads to higher settlement, while increasing soil stiffness and foundation depth reduces settlement.
Model validation through analytical solutions and codal provisionsshowedgoodagreementwithinacceptablelimits, confirming the reliability of the adopted methodology. Overall, the study highlights that accurate settlement prediction requires simultaneous consideration of soil stratification and nonlinear behavior. The findings contributetosaferandmoreeconomicalfoundationdesign by providing improved understanding of soil–foundation interactionunderrealisticconditions.
6. FUTURE SCOPE
Futureresearchcanfocusonextendingthepresentstudyto include dynamic and cyclic loading conditions, such as seismic effects and machine-induced vibrations, which significantlyinfluencesettlementbehavior.Incorporationof advanced constitutive models, such as HSsmall or hypoplasticmodels,canfurtherimprovetheaccuracyofsoil response prediction, especially at small strain levels. Experimental validation through field tests or large-scale laboratorymodelsisessentialtoenhancethereliabilityof numericalresults.Additionally,theeffectsofgroundwater fluctuations and unsaturated soil conditions, including matric suction, should be considered for more realistic analysis.Theapplicationofmachinelearningtechniquesfor rapid settlement prediction based on parametric datasets alsopresentsapromisingdirectionforfuturegeotechnical research.
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